COMMUNICATIONS                  MITTEILUNGEN
FROM THE                        DER
KONKOLY OBSERVATORY             STERNWARTE
OF THE                          DER UNGARISCHEN AKADEMIE
HUNGARIAN ACADEMY OF SCIENCES   DER WISSENSCHAFTEN

                  BUDAPEST - SZABADSAGHEGY



                        No. 94.
                    (Vol. 11, Part 1)





                    PERIOD CHANGES
             OF BRIGHT SOUTHERN CEPHEIDS

                     L. SZABADOS





                    BUDAPEST. 1989

ISBN 963 8361 30 1
HU ISSN 0238 - 2091







       PERIOD CHANGES OF BRIGHT SOUTHERN CEPHEIDS




                    ABSTRACT



  O-C diagrams have been constructed for 44 bright southern Cepheids, mainly 
for studying the effects of duplicity on the pulsation period. Because 
the light-time effect in the O-C diagrams of binary Cepheids has to be 
accompanied with properly phased variations in the gamma-velocity, the 
radial velocities of the programme stars have been studied, as well. 
Light-time effect is found or suspected in eleven cases (V496 Aql, AX 
Cir, AG Cru, BG Cru, BF Oph, AP Pup, AT Pup, Y Sgr, AP Sgr, R TrA, and V 
Vel), and a preliminary value of the orbital period is suggested for 14 Cepheid
binaries (V496 Aql, AX Cir, AG Cru, Y Oph, BF Oph, AP Pup, AT Pup, U 
Sgr,  Y Sgr, AP Sgr, BB Sgr, RV Sco, R TrA, and V Vel). The phenomenon 
of the phase jump (i.e. the return of the pulsation period to an earlier 
value) is present in the O-C diagram of eight Cepheid binaries (U Aql, 
YZ Car, KN Cen, S Mus, S Nor, Y Oph, U Sgr, and V350 Sgr).





                  INTRODUCTION





Period changes of more than a hundred northern Cepheids were
studied in a series of papers (Szabados, 1977, 1980, 1981, 1983, and 1984).
The large number of the programme stars and the homogeneous method of the
analysis enabled the determination of the period changes as a function of
the pulsation period. A general agreement of the observed period changes
with the theoretically calculated values was found. In addition to the
frequently occurring parabolic O-C diagrams corresponding to the continuous
period change as a result of the stellar evolution, two special kinds of
period variations were also revealed in several cases, both of them being
characteristic of binary Cepheids:
1. light-time effect due to the orbital motion,
2. stepwise O-C graph, i.e. rejump (return) of the pulsation period to an
earlier value. In what follows, the term "phase jump" will be used for this
phenomenon.
   This paper is dealing with a similar study: period changes of 44
(mostly bright) southern Cepheids are discussed here. Because the southern
Cepheid variable stars were observed on rare occasions before the
photoelectric era, secular period variations have remained undiscovered
in most cases. The time interval of less than fifty years covered with
photoelectric observations is not long enough to reveal the evolutionary
period changes unambiguously (there are, however, some exceptions). At the
same time, due to their accuracy, these photoelectric observations can be
used successfully for searching for both light-time effect and phase jump
in the O-C diagrams.
For this reason the sample of stars studied here is arbitrarily chosen:
it contains the bright southern Cepheids for which presence of a companion
has been suspected or discovered. In addition, some other bright Cepheids
without any evidence for duplicity have also been included, considering
that any evolutionary period changes are likely to be expected in these
very bright Cepheids with the longest available coverage of photometric
observations.
  The current ephemerides (the moment of the light maximum, and the value
of the pulsation period) are also determined, and these pieces of
information may be useful for planning future observations in any
wavelength interval, or for determining their phases.
  Due to the inhomogeneous (and arbitrary) selection of the programme
stars, the statistical study of the period changes has not been attempted.
Instead, duplicity effects are placed in the centre of interest. Because
the most straightforward way to discover the presence of a companion is to
detect variations in the mean radial velocity (so called gamma-velocity), the
radial velocity data are also analysed and intercompared with the relevant
parts of the O-C diagrams.



                   O-C DIAGRAMS


   In order to study the period changes, all the available photometric
observations have been analysed. At the final step, however, the results
based on visual observations were omitted because of their very low
accuracy. Nevertheless, there are one or two cases where the very early
visual data have been used but after J.D.2420000 only the photographic and
photoelectric observations were taken into account.
   Homogeneity of the O-C diagrams has been achieved by re-analysing all
observations without accepting the originally published moments of normal
maxima. The new moments of normal maxima were determined by fitting the
master light curve to the light curve to be analysed. The master light
curve has been the most reliable seasonal light curve available in the
literature for the given star (mostly but not necessarily from the paper by
Moffett and Barnes, 1984). Whenever it was possible, the longer
observational series were grouped into seasonal light curves.
   Depending on the number and quality of the observations and the
distribution of the data points, a weight has been assigned to each light
curve. This weight is 3 for the master curves and other best quality light
curves, and 2 or 1 is assigned to the light curves of poorer coverage
and/or showing wide scatter. Note that these weights were determined before
performing the curve fitting procedure, i.e. without knowing how much the
corresponding O-C residual will deviate from the final O-C curve.
   The weight was never larger than 1 in the case of the photographic
observations, and there are numerous O-C residuals in the tables of this
paper where no weight has been assigned (these are based on visual or
photographic observations without exception). These latter O-C residuals
are still useful but have not been taken into account when determining the
shape of the O-C curve.
   The exact calculation of the error for each O-C residual would have
been extremely time-consuming. Instead, based on the large body of the
previous O-C diagrams (Szabados, 1977, 1980, 1981) the following average
uncertainties could be deduced: for w=3, 2, and 1 the standard deviation is
about 0.002, 0.004 and 0.008 part of the pulsation period.
   Throughout this study the blue (or closest to Johnson's B band) light
curves were analysed. There are quite a few series of photometric
observations obtained in red and/or infrared bands. Although these
observations are very important in some respects, they were omitted from
this study because the shape of the light curve at long wavelength differs
from the blue light curve, and the necessary corrections to be applied for
removing the systematic differences between the moments of maxima in
different spectral regions have not been determined yet.
The O-C residuals are given in tabular form and shown plotted in
figures. The successive columns in the tables of the O-C residuals contain
the following data:

1. Moment of normal maximum;
2. The corresponding epoch;
3. O-C residual (in days);
4. Type of observation and the weight assigned to the residual (pe for
   photoelectric, pg for photographic, and vis for visual observations);
5. Source of the observational data.

   The O-C diagram (usually the upper panel of the figure) shows the O-C
residuals listed in the corresponding table, and the curve thought to be
the best interpretation of the O-C plot is also drawn. These curves were
obtained by the weighted least squares method applied to the data points.
The weights are visualized in the figure as circles of increasing diameter.
Photoelectric observations are denoted with filled circles, while open
circles refer to the O-C residuals based on photographic observations. If
no weight has been assigned to an O-C residual, it is shown plotted as a
small dot.





                  RADIAL VELOCITIES



   Because one of the main aims of this study is to search for light-time
effect in the O-C diagrams, it was appropriate to carry out a simultaneous
investigation of the radial velocity measurements in order to check the
results on duplicity obtained from the O-C diagrams.
   The radial velocity data have been collected from the literature, and
they were analysed after the trend of the period variation had been
determined from the O-C diagram. This step is crucial because any fitting
error due to the use of an inaccurate pulsation period can be eliminated,
and only the observational (and in some cases a systematic zero-point)
error of the radial velocity measurements remains as a possible source of
error.
   It is almost impossible to get rid of the systematic errors because
most of the early papers containing radial velocity data do not give enough
information for converting the data into a common system. Nevertheless,
thanks to the existence of the IAU standard radial velocity system, these
systematic errors have become much smaller in the last decades, e.g.
according to Welch et al. (1987) the zero-point correction applied to the
radial velocity measurement series of U Aql is less than 1 km/s for eight
instruments, and the correction slightly exceeds 1 km/s in only one case.
In view of this, no corrections have been applied to the observational data
analysed here, and, of course, this can be an additional source of error.
The only exception is Paddock's (1917) radial velocity measurement series,
for which Lloyd Evans (1982) introduced +4 km/s correction, and this value
is so large that it was also applied here.
   The individual radial velocity series were used for constructing the
seasonal radial velocity curves using the accurate value of the pulsation
period. The centre-of-mass velocity of the Cepheid (i.e. the gamma-velocity)
was then determined in two steps. At first, the gamma-velocity of the best
radial velocity curve was determined graphically for each variable, then
these radial velocity normal curves were fitted to the properly phased
other radial velocity curves. If the gamma-velocity seemed to be constant, the
radial velocity measurement series were not always divided into seasonal
curves.
    As to variability of the gamma-velocity, there is a reasonable lower limit
(4-5 km/s), and if the fluctuation of the gamma-velocity exceeds this value,
the presence of a companion to the Cepheid is suspected. It is hoped that
the above limit overestimates the real threshold of detection because much
smaller variations in the gamma-velocity can be revealed by using the recent
radial velocity measurement techniques. Unfortunately most of the available
radial velocity data have been obtained at a higher level of uncertainty.
    Because the relative errors of the radial velocity measurements are
larger than those of the photometric measurements, the standard deviations
have been calculated for the individual radial velocity measurement series.
The standard deviation of the date of observation is formal, and it only
indicates the length of the observational interval. The standard deviation
of the gamma-velocity does not contain the contribution of the possible
zero-point error.
   The successive columns in the tables of the gamma-velocities give the
following data:

1-2. Mean date of the observations and its standard deviation;
3-4. gamma-velocity and its standard deviation;
5. Number of radial velocity observations used;
6. Source of the observational data.

   The gamma-velocity data of the individual Cepheids are plotted in most
cases in the lower panel of the figures. The plot is missing in those cases
where no obvious change in the gamma-velocity is seen. Error bars (according
to the standard deviations listed in the tables) are only shown, if the bar
exceeds the size of the circle.



          REMARKS ON THE INDIVIDUAL VARIABLES



   The list of the programme stars can be found in Table 1. The ordinal
number following the name of the Cepheid gives the page number where the
discussion on the given star begins. The Cepheids involved in this study
are arranged in alphabetical order of constellations, and within one
constellation, according to the IAU nomenclature of variable stars.


               Table 1. Programme stars

Cepheid     Page   Cepheid   Page   Cepheid     Page
U Aql       9      GH Lup    31     WZ Sgr      57
V496 Aql    10     R Mus     33     AP Sgr      58
V Car       12     S Mus     34     BB Sgr      60
YZ Car      14     S Nor     35     V350 Sgr    62
l Car       15     RS Nor    37     RV Sco      63
                   SY Nor    38     RY Sco      65
V Cen       17     Y Oph     39     V500 Sco    66
XX Cen      18     BF Oph    43     V636 Sco    67
AZ Cen      20                      Y Sct       68
KN Cen      21     AP Pup    46     R TrA       69
AX Cir      23     AT Pup    47
                                    S TrA       71
S Cru       24     MY Pup    49     T Vel       72
T Cru       25     U Sgr     50     V Vel       73
AG Cru      27     W Sgr     52     AH Vel      75
BG Cru      28     X Sgr     54
beta Dor    30     Y Sgr     55


   It was not my intention to give a comprehensive history on each
variable. I do hope, however, that neither photoelectric or photographic,
nor radial velocity observation published in the literature escaped my
attention. The additional remarks on the individual Cepheids mostly concern
the previous studies on both the changes in the gamma-velocity and the period
variations. The available other evidence regarding the duplicity of these
stars is also discussed briefly. A systematic application of the known
duplicity tests is beyond the scope of this paper but such a study is
planned for the near future. The compilation on the binary Cepheids will be
published in due time.
   Although the phase difference between the gamma-velocity variations and
the sinusoidal wave in the O-C diagram is a good indicator whether this
phenomenon can be interpreted as a light-time effect, there is an
additional criterion that makes use of the amplitude of these oscillations.
Assuming a circular orbit, the radial velocity and O-C variations have to
obey the following relationship in a binary system:

    2K = a*sini*Porb^-1*3.77*10^-6                 (1)

where 2K is conventionally the total amplitude of the gamma-velocity variation
(in km/s), a*sini is the projected radius of the orbit, and at the same
time this quantity is the half amplitude of the wave in the O-C diagram (in
days), and Porb is the orbital period (in days). This test is frequently
used during this study as a very strong criterion when deciding whether
light-time effect is expected or not (if the orbital period has been known
from radial velocity measurements), and to judge reality of interpreting
the O-C wave in terms of duplicity.



U Aquilae


   U Aql is one of the spectroscopic binary Cepheids with known orbit
(Welch et al., 1987). According to various estimates, the companion is a
main-sequence B8-A1 star (Leonard and Turner, 1986). The radial velocity
observations have not been re-analysed here, the orbital period of 1856.4
days (Welch et al., 1987) is accepted, although the more recently published
radial velocity data (Wilson et al., 1989) may slightly alter this value.
   The O-C residuals are listed in Table 2, and are shown plotted in
Figure 1. The O-C diagram of U Aql can be well approximated by two lines
showing a phase jump (i.e. rejump of the period). The O-C residuals have
been calculated with the formula:

      C = 2434922.400 + 7.023958d*E                   (2)
               +-.031  +-.000029




             
             Figure 1. O-C diagram of U Aql


               Table 2. O-C residuals for U Aql

Norm.max.                        Type,
JD2400000+   E            O-C    weight   Reference

32765.994    -307        -0.051d pe 2     Eggen (1951)
33110.132    -258        -0.087  pe 3     Eggen (1951)
34950.444    + 4         -0.052  pe 1     Walraven et al. (1958)
35294.581    + 53        -0.089  pe 1     Irwin (1961)
36109.319    +169        -0.130  pe 1     Svolopoulos (1960)
37233.200    +329        -0.082  pe 2     Mitchell et al. (1964)
38673.155    +534        -0.039  pe 1     Wisniewski and Johnson (1968)
39059.541    +589        +0.030  pe 1     Wisniewski and Johnson (1968)
40253.609    +759        +0.025  pe 2     Feltz and McNamara (1980)
40801.469    +837        +0.016  pe 2     Feltz and McNamara (1980)
40822.484    +840        -0.041  pe 3     Pel (1976)
41194.809    +893        +0.015  pe 2     Feltz and McNamara (1980)
42922.639    +1139       -0.049  pe 2     Dean (1977)
43365.210    +1202       +0.012  pe 3     Moffett and Barnes (1984)
43674.270    +1246       +0.018  pe 3     Moffett and Barnes (1984)
44039.528    +1298       +0.031  pe 2     Moffett and Barnes (1984)
44467.988    +1359       +0.029  pe 2     Eggen (1985)
45563.595    +1515       -0.101  pe 1     Eggen (1985)


   This period is valid after J.D.2438600, while between J.D.2432700 and
J.D.2437300 the pulsation period was 7.023920 +- 3.0*10^-5 days. The phase
jump occurred at about J.D.2438000, and it amounts to 0.1 day.
There are no early photographic observations available in the
literature, therefore the longer time-scale behaviour of the O-C diagram of
U Aql cannot be studied. According to the phase relations of the radial
velocity curves, the O-C residuals might be even more negative at about
J.D.2421840. A single straight line fitted to the photoelectric O-C
residuals is almost as good as the phase jump approximation. In view of the
values of the orbital period and the orbital radial velocity amplitude, the
expected light-time effect has such a low amplitude (see equation (1)) that
the effect cannot be detected.



V496 Aquilae


   Its spectroscopic binary nature was revealed by Gieren (1982) but there
is no agreement on the type of the companion (Leonard and Turner, 1986).
The variable gamma-velocity of V496 Aql is well illustrated in Figure 2 (lower
panel), and in Table 3. There is a number of periods that fits the data
points reasonably well: 1200, 1780, 2700, 3600, 5350, and 10750 days. It is
impossible to choose the true value of the orbital period from the
available radial velocity measurements alone.


              Table 3. gamma-velocities of V496 Aql

JD         sigma  v gamma  sigma    n   Reference
2400000+    [d]   [km/s]   [km/s]

33918       31    6.8       0.8    15   Stibbs (1955)
34202       28    0.6       1.5     5   Stibbs (1955)
40448       27    6.8       0.4     4   Lloyd Evans (1980)
44053       10   18.0       4.0     2   Barnes et al. (1988)
44423        4    7.7       0.4    25   Gieren (1981a)
44486       46   14.5       1.6     7   Barnes et al. (1988)
44822       47    4.6       2.3     4   Barnes et al. (1988)


  The O-C diagram (see Table 4 and the upper panel of Figure 2) can be
approximated by a straight line with the light-time effect superimposed on
it. The sine-wave was fitted by using the method of weighted least squares,
and the 1500 - 13000 day interval was analysed. The best fit was achieved
assuming an orbital period of 1882 +- 23 days. The moments of the light
maxima can be predicted as follows:

   C = 2436017.084 + 6.807055d*E - 0.023*cos(2pi(0.00362*E - 0.006)) (3)
            +-.004  +-.000008     +-.008        +-.00004    +-.031




    
    Figure 2. Upper panel: O-C diagram of V496 Aql
              Lower panel: gamma-velocities for the same Cepheid


                 Table 4. O-C residuals for V496 Aql

Norm.max        E       O-C     Type,    Reference
JD2400000+                      weight

34567.181    -213       0.000d  pe 2     Eggen et al. (1957)
35608.663    - 60      +0.002   pe 2     Walraven et al. (1958)
37187.908    +172      +0.011   pe 2     Mitchell et al. (1964)
40366.791    +639      -0.001   pe 2     Stobie (1970)
40809.275    +704      +0.024   pe 3     Pel (1976)
41122.357    +750      -0.018   pe 2     Pel (1976)
41149.613    +754      +0.010   pe 2     Feltz and McNamara (1980)
44410.200   +1233      +0.017   pe 3     Moffett and Barnes (1984)
44410.214   +1233      +0.031   pe 3     Gieren (1981b)
44621.218   +1264      +0.016   pe 2     Eggen (1985)
44907.121   +1306      +0.023   pe 1     Moffett and Barnes (1984)


   This value of the orbital period is in reasonable agreement with the 1780
day period, one of the values suggested by the radial velocity data. The
amplitude of the wave is, however, twice larger than the value expected
from equation (1). This suggests that the orbital period may be longer.
More spectroscopic and photometric data are necessary to determine the
value of the orbital period unambiguously.
   The O-C residuals have been calculated with the elements:

       C = 2436017.084 + 6.807055d*E                      (4)
                +-.004  +-.000008

If no sinusoidal term is assumed in the O-C diagram, then the least squares
fit results in the following formula:

       C = 2436017.085 + 6.807070d*E                      (5)
                +-.004  +-.000005

which is practically identical with the linear part of the sinusoidal fit
(i.e. with equation (4)).



V Carinae


   V Car was reported to be a suspected binary (Lloyd Evans, 1968) but
later on Lloyd Evans (1982) explained the scatter in the radial velocity
data as due to the variability of the bump on the velocity curve. Here the
scatter in the radial velocity data is attributed to the variation in the
gamma-velocity (see Table 5 and the lower panel of Figure 3).


             Table 5. gamma-velocities of V Car

JD        sigma  v gamma       sigma   n   Reference
2400000+   [d]   [km/s]       [km/s]

34009      20    15.2           0.8   14   Stibbs (1955)
34095      20    14.0           1.2    7   Stibbs (1955)
39252      64     8.7           1.1    4   Lloyd Evans (1968)
39611      41     8.3           1.1    4   Lloyd Evans (1968)
39932      48    12.2           0.6    2   Lloyd Evans (1980)
40338      16    12.5           0.3    5   Lloyd Evans (1980)
40666      51    13.2           0.3    6   Lloyd Evans (1980)



    
    Figure 3. Upper panel: O-C diagram of V Car
              Lower panel: gamma-velocities for the same Cepheid



             Table 6. O-C residuals for V Car

Norm.max.       E        O-C    Type,   Reference
JD2400000+                      weight

35230.691    -332       +0.034d pe 1    Irwin (1961)
35351.218    -314       +0.021  pe 1    Walraven et al. (1958)
39630.343    +325       -0.027  pe 2    Cousins and Lagerweij (1968)
39958.494    +374       -0.013  pe 3    Cousins and Lagerweij (1968)
40742.012    +491       -0.006  pe 3    Pel (1976)
42858.163    +807       -0.003  pe 1    Dean (1977)
44425.219   +1041       +0.031  pe 2    Eggen (1985)


   The O-C diagram (Table 6 and the upper panel of Figure 3) contains
very few points, and for the sake of simplicity it is approximated by a
straight line:

         C = 2437453.952 + 6.696672d*E           (6)
                  +-.009  +-.000016

Further observations are  to be obtained in order to decide whether a
parabola fits better, and even the light-time effect cannot be excluded.



YZ Carinae


   According to Coulson (1983) YZ Car belongs to a binary system with an
orbital period of about 850 days. Coulson also derived tentative orbital
parameters, and concluded that the companion is probably a main-sequence A0
star. The radial velocity measurements of YZ Car have not been analysed
again here.

                Table 7. O-C residuals for  YZ Car

Norm.max.     E        O-C    Type,    Reference
JD2400000+                    weight

34725.613  - 10       +0.197d pe 2     Walraven et al. (1958)
35216.089  + 17       +0.202  pe 3     Irwin (1961)
37831.903  +161       +0.173  pe 3     Walraven et al. (1964)
41737.333  +376       +0.006  pe 3     Madore (1975)
43989.866  +500       +0.008  pe 2     Coulson and Caldwell (1985)
44280.475  +516       -0.033  pe 2     Coulson and Caldwell (1985)
44280.593  +516       +0.085  p 1     EEggen (1983b)
44680.082  +538       -0.068  pe 2     Coulson and Caldwell (1985)
44771.006  +543       +0.028  pe 2     Eggen (1983b)
45007.127  +556       -0.004  pe 3     Coulson and Caldwell (1985)
45715.615  +595       +0.027  pe 2     Coulson and Caldwell (1985)




                  
                  Figure 4. O-C diagram of YZ Car


   The O-C diagram has been constructed on the basis of the available
observations listed in Table 7. The plot of the O-C residuals (see Figure
4) can be well approximated by two sections of straight lines showing the
phenomenon of the phase jump seen in numerous binary Cepheids.
   The O-C residuals have been calculated with the elements:

       C = 2434907.072 + 18.165573d*E             (7)
                +-.071   +-.000137

The previous value of the pulsation period (between J.D.2434700 and
2437900) was 18.165412 + 2.0*10^-5 days, therefore it can be stated that the
star returned to the same pulsation period after an 0.16 day phase jump,
occurred at about J.D.2440000.
   Another fact worth mentioning is that the pulsation period differs
considerably from the value given in the GCVS (Kholopov et al., 1985-1987).
Coulson (1983) used an almost correct value of the pulsation period but did
not call the attention explicitly to the correction to be applied to the
period in the catalogue.



l Carinae


                  
                  Figure 5. O-C diagram of l Car


   The gamma-velocity of this long period Cepheid can be considered as being
constant (see Table 8), therefore the individual values of the gamma-velocity
are not plotted in a diagram.
   The O-C diagram (see Table 9 and Figure 5) is based on only the
photoelectric normal maxima. The previous values of the pulsation period
can be followed in Parenago's (1956) paper. The O-C residuals have been
calculated with the formula:

      C = 2440736.230 + 35.551341d*E                 (8)
               +-.015   +-.000397


                Table 8. gamma-velocities of l Car

JD        sigma   v gamma   sigma   n   Reference
2400000+   [d]     [km/s]   [km/s]

17441      402     2.2      0.8    17   Jacobsen (1934)
21655       25     2.0      0.8    15   Jacobsen (1934)
22435       19     1.8      0.6    28   Jacobsen (1934)
34086       61     1.0      0.7    21   Stibbs (1955)
35641       19     0.7      1.0     5   Lloyd Evans (1968)
37722       52     4.4      0.7    21   Dawe (1969)
39238       33     0.9      1.1     4   Lloyd Evans (1968)
39901       38     2.0      0.3     5   Lloyd Evans (1980)
40307       61     3.2      0.2    12   Lloyd Evans (1980)
40663       44     0.0      0.3     6   Lloyd Evans (1980)



                 Table 9. O-C residuals for l Car

Norm.max.      E        O-C    Type,  Reference
JD2400000+                     weight

33807.235   -195       +3.516d pe 2   Eggen et al. (1957)
34766.489   -168       +2.884  pe 2   Eggen et al. (1957)
35228.242   -155       +2.470  pe 2   Irwin (1961)
35263.849   -154       +2.526  pe 1   Walraven et al. (1958)
37751.037   - 84       +1.120  pe 2   Lake (1962)
38141.594   - 73       +0.612  pe 1   Feinstein and Muzzio (1969)
38461.577   - 64       +0.633  pe 1   Feinstein and Muzzio (1969)
38852.400   - 53       +0.391  pe 1   Feinstein and Muzzio (1969)
39563.259   - 33       +0.223  pe 3   Feinstein and Muzzio (1969)
39563.437   - 33       +0.401  pe 3   Landolt (1971)
40629.547    - 3       -0.029  pe 2   Eggen (1971)
40736.226      0       -0.004  pe 3   Pel (1976)
41127.387   + 11       +0.092  pe 2   Pel (1976)
41731.656   + 28       -0.012  pe 3   Madore (1975)
41838.299   + 31       -0.023  pe 3   Dean et al. (1977)
42549.300   + 51       -0.048  pe 2   Dean et al. (1977)
43189.300   + 69       +0.027  pe 3   Dean (1981)


   Two values of the pulsation period are apparent in Figure 5: before
J.D.2440000 the period was 35.531758 +- 6.21*10^-4 days, while after this epoch
the value of the period has been 35.551341 +- 3.97*10^-4 days. Although Figure
5 suggests a continuous period increase, a parabolic fit was not attempted
because the early part of the O-C diagram (Parenago, 1956) would contradict
to this interpretation.



V Centauri


   Although Gieren (1982) found no evidence for the variable gamma-velocity,
according to the present study variability in the gamma-velocity cannot be
ruled out (see Table 10 and the lower panel of Figure 6). Especially
Stibbs' (1955) seasonal curves suggest a short period (several hundred
days) variation.

                Table 10. gamma-velocities of V Cen

JD        sigma    v gamma   sigma        n   Reference
2400000+   [d]      [km/s]   [km/s]

33848       22      -25.1    1.1          9   Stibbs (1955)
34165       54      -19.5    1.1          8   Stibbs (1955)
39268       37      -23.9    1.0          5   Lloyd Evans (1968)
40371       28      -23.2    0.3          4   Lloyd Evans (1980)
40759       15      -20.8    0.3          3   Lloyd Evans (1980)
44422        4      -23.9    0.4         26   Gieren (1981a)




     
     Figure 6. Upper panel: O-C diagram of V Cen
               Lover panel: gamma-velocities for the same Cepheid


                Table 11. O-C residuals for V Cen

Norm.max.        E        O-C    Type,    Reference
JD2400000+                       weight

16162.649    -4395       -0.364d pg 1     Shapley (1930)
17953.707    -4069       -0.305  pg 1     Shapley (1930)
20272.216    -3647       -0.205  pg 1     Shapley (1930)
21794.004    -3370       -0.216  pg 1     Shapley (1930)
23986.101    -2971       -0.170  pg 1     Shapley (1930)
24260.903    -2921       -0.061  pg 1     Voute (1927b)
24656.476    -2849       -0.046  pg 1     Voute (1927b)
25035.485    -2780       -0.113  pg 1     Voute (1927b)
25793.717    -2642       -0.034  pg 1     Dartayet et al. (1949)
26139.928    -2579       +0.064  pg 1     Dartayet et al. (1949)
34869.621    - 990       +0.011  pe 3     Walraven et al. (1958)
35193.758    - 931       +0.011  pe 3     Irwin (1961)
40335.980    + 5         -0.021  pe 3     Stobie (1970)
40748.007    + 80        -0.034  pe 3     Pel (1976)
42852.197    + 463       +0.007  pe 2     Dean (1977)
44417.952    + 748       +0.012  pe 3     Gieren (1981b)
44494.877    + 762       +0.023  pe 2     Eggen (1985)


  The O-C diagram (Table 11 and the upper panel of Figure 6) shows one
period change. The O-C residuals have been computed using the ephemeris:

    C = 2440308.532 + 5.493861d*E             (9)
             +-.005  +-.000007

The period change occurred at about J.D.2427000, and before that epoch the
pulsation period was 5.494058 +- 2.6*10^-5 days.



XX Centauri


   Spectroscopic binary nature of XX Cen was discovered by Coulson et
al. (1985). The value of the orbital period was determined recently
(Szabados, 1989), its value is 909.4 +- 29.0 days.
   According to equation (1), no detectable light-time effect is expected
in the O-C diagram, therefore the phase shift mentioned by Coulson et al.
(1985) is not caused by the orbital motion but, instead, it reflects the
strong period change determined here.

   The O-C residuals have been calculated with the formula:

       C = 2440366.125 + 10.954027d*E            (10)
                +-.010   +-.000027

As is seen in the O-C diagram (see Table 12 and Figure 7), the period of
XX Cen is continuously decreasing as follows:

    P = 10.954027d - 15.5d*10^-7*E              (11)
        +-.000027    +-.6

where the E epoch number is the same as in equation (10).


               Table 12. O-C residuals for XX Cen

Norm.max        E        O-C    Type,  Reference
JD2400000+                      weight

26398.368   -1275       -1.373d pg 1   van Gent and Oosterhoff (1948)
27691.409   -1157       -0.907  pg 1   van Gent snd Oosterhoff (1948)
34812.261   - 507       -0.172  pe 1   Walraven et al. (1958)
35206.584   - 471       -0.194  pe 3   Irwin (1961)
35469.522   - 447       -0.153  pe 1   Walraven et al. (1958)
37846.692   - 230       -0.007  pe 3   Walraven et al. (1964)
40377.080   + 1         +0.001  pe 3   Stobie (1970)
41110.923   + 68        -0.076  pe 2   Grayzeck (1978)
41592.936   + 112       -0.040  pe 1   Grayzeck (1978)
41768.228   + 128       -0.012  pe 2   Madore (1975)
42874.573   + 229       -0.024  pe 3   Dean (1977)
44068.488   + 338       -0.098  pe 3   Coulson et al. (1985)
44659.979   + 392       -0.125  pe 3   Coulson et al. (1985)
45010.518   + 424       -0.114  pe 3   Coulson et al. (1985)



               
               Figure 7. O-C diagram of XX Cen



AZ Centauri



   AZ Cen may be a spectroscopic binary because Balona found a strongly
discordant gamma-velocity in comparison with other radial velocity
measurements (Gieren, 1982). Unfortunately Balona's observations have
remained unpublished, and the available radial velocity data show a
constant gamma-velocity (see Table 13).
   The O-C residuals have been computed with the formula:

       C = 2435223.389 + 3.212279d*E                      (12)
                +-.011  +-.000004

It should be emphasized that this pulsation period  strongly differs  from
that given in the GCVS (Kholopov et al., 1985-1987). The O-C diagram is
parabolic (see Table 14, and Figure 8) showing a continuous decrease in the
period. The instantaneous value of the pulsation period can be obtained
from the formula:

     P = 3.212279d - 9.79d*10^-8*E                        (13)
        +-.000004   +-.35

where the E epoch number is the same as in equation (12).

                 Table 13. gamma-velocities of AZ Cen

JD         sigma  v gamma     sigma   n   Reference
2400000+    [d]   [km/s]      [km/s]

34138       33    -12.1        0.9   11   Stibbs (1955)
43178        4    -11.5        0.4    7   Stobie and Balona (1979)
43311       37    -13.1        0.3   10   Stobie and Balona (1979)
43531        4    -12.5        0.6    4   Stobie and Balona (1979)
44423        4    -12.7        0.4   22   Gieren (1981a)




               
               Figure 8. O-C diagram of AZ Cen


                 Table 14. O-C residuals for AZ Cen

Norm.max.        E        O-C    Type,    Reference
JD2400000+                       weight

23253.740    -3726       -0.697d pg 1     de Jager (1947)
34709.464    - 160       +0.040  pe 1     Walraven et al. (1958)
35220.172    - 1         -0.005  pe 3     Irwin (1961)
35451.504    + 71        +0.043  pe 2     Walraven et al. (1958)
40738.672    +1717       -0.200  pe 3     Pel (1976)
41795.508    +2046       -0.204  pe 3     Dean et al. (1977)
42540.691    +2278       -0.270  pe 3     Dean et al. (1977)
43179.904    +2477       -0.300  pe 3     Stobie and Balona (1979)
44316.936    +2831       -0.415  pe 1     Eggen (1985)
44400.508    +2857       -0.362  pe 3     Gieren (1981b)
44634.956    +2930       -0.410  pe 1     Eggen (1985)
45055.732    +3061       -0.443  pe 1     Eggen (1985)



KN Centauri


   The presence of a companion to the Cepheid KN Cen has been suspected on
various grounds: large UV excess (Walraven et al., 1964), peculiar loop in
the two-colour diagram (Stobie, 1970; Madore, 1977; and Pel, 1978), the
shape of the Ca II K line (Lloyd Evans, 1968), and finally the companion
was revealed with the help of an IUE spectrum (Bhm Vitense and Proffitt,
1985). The available radial velocity observations also give evidence for
the binary nature (see Table 15 and the lower panel of Figure 9). This
variation has not been reported before.

                Table 15. gamma-velocities of KN Cen

JD        sigma   v gamma        sigma   n   Reference
2400000+   [d]     [km/s]        [km/s]

41539      194     -48.8          4.5    6   Grayzeck (1978)
43975        5     -40.8          0.4    6   Coulson and Caldwell (1985)
44400       56     -40.0          0.4    9   Coulson and Caldwell (1985)
44703       35     -39.5          0.3   16   Coulson and Caldwell (1985)
45092        2     -38.0          0.5    3   Coulson and Caldwell (1985)


   The O-C residuals (see Table 16 and upper panel of Figure 9) have been
calculated with the elements:

    C = 2436242.009 + 34.029641d*E            (14)
             +-.195   +-.000787

                    Table 16. O-C residuals for KN Cen

Norm.max.       E        O-C    Type,    Reference
JD2400000+                      weight

34638.470    - 47       -4.146d pe 2     Walraven et al. (1958)
35216.974    - 30       -4.146  pe 3     Irwin (1961)
35250.816    - 29       -4.333  pe 1     Walraven et al. (1958)
37871.756    + 48       -3.676  pe 1     Walraven et al. (1964)
40356.990    +121       -2.606  pe 2     Stobie (1970)
41106.302    +143       -1.946  pe 3     Pel (1976)
41582.839    +157       -1.824  pe 2     Grayzeck (1978)
44034.776    +229       -0.021  pe 2     Coulson and Caldwell (1985)
44647.361    +247       +0.031  pe 3     Coulson and Caldwell (1985)
45123.728    +261       -0.017  pe 3     Coulson and Caldwell (1985)



     
     Figure 9. Upper panel: O-C diagram of KN Cen
               Lower panel: gamma-velocities for the same Cepheid


Three values of the pulsation period could be determined:
before J.D.2437000                    P = 34.026583d +- .003999d
between J.D.2437000 and J.D.2444000   P = 34.047490d +- .001315d
after J.D.2444000                     P = 34.029641d +- .000787d .
The first and the third value is nearly the same, i.e. a phase jump
occurred, although not very suddenly.
   Additional photometric and radial velocity measurements on this binary
Cepheid are urgently needed both for confirming the rejump in the pulsation
period, and in order to determine the orbital period.



AX Circinis


   Its composite spectrum was discovered by Jaschek and Jaschek (1960).
Lloyd Evans (1971) revealed the spectroscopic binary nature of AX Cir,
while Bhm Vitense and Proffitt (1985) were able to detect the companion
using IUE spectra.
   The variable gamma-velocity is shown in the lower panel of Figure 10 (see
also Table 17). The observed extrema of the gamma-velocity correspond to the
full amplitude of the gamma-velocity variation, as is seen in the O-C wave to
be discussed below (see Figure 10).

                 Table 17. gamma-velocities of AX Cir

JD         sigma  v gamma     sigma   n   Reference
2400000+    [d]    [km/s]     [km/s]

38570        6    -17.7        0.9    6   Evans (1965)
39618       50    -26.0        1.1    4   Lloyd Evans (1968)
39900       33    -26.4        0.2    7   Lloyd Evans (1980)
40258       11    -26.8        0.6    2   Lloyd Evans (1980)
40387       46    -30.9        0.2   14   Lloyd Evans (1980)
40745       71    -33.3        0.2   15   Lloyd Evans (1980)

                 Table 18. O-C residuals for AX Cir

Norm.max.    E            O-C    Type,    Reference
JD2400000+                       weight

38220.425    + 4         -0.006d pe 3     Cousins and Evans (1967)
39533.527    +253        +0.043  pe 3     Cousins and Evans (1967)
39617.878    +269        +0.021  pe 3     Mauder and Schffel (1968)
42855.659    +883        -0.008  pe 3     Dean (1977)
42971.687    +905        +0.007  pe 3     Dean (1977)
44474.595    +1190       +0.023  pe 2     Eggen (1985)
45381.576    +1362       -0.005  pe 2     Eggen (1985)


  The O-C residuals listed in Table 18 have been computed with the
formula:

     C = 2438199.338 + 5.273306d*E             (15)
              +-.002  +-.000008

A sinusoidal term is superimposed on the straight line in the O-C graph. A
weighted least squares fit applied to the O-C residuals resulted in the




        
        Figure 10. Upper panel: O-C diagram of AX Cir
                   Lower panel: gamma-velocities for the same Cepheid


value of 4600 +- 83 days for the orbital period. The moments of the normal
maxima can be predicted as follows:

   C = 2438199.338 + 5.273306d*E - 0.032cos(2pi(0.00115*E + 0.222))   (16)
            +-.002  +-.000008     +-.002       +-.00002    +-.018

Although each parameter (amplitude, phase, period) of this wave are in
agreement with the pattern of the gamma-velocity changes, further observations
are desirable to confirm or refine the above value of the orbital period.



S Crucis


   The gamma-velocity of S Cru seems to be constant (see Table 19).

                    Table 19. gamma-velocities of S Cru

JD        sigma    v gamma   sigma   n  Reference
2400000+   [d]     [km/s]    [km/s]

33832        9      -6.0      1.3    6   Stibbs (1955)
34167       46      -6.9      1.1    8   Stibbs (1955)
40383       46      -5.0      0.2    7   Lloyd Evans (1980)
44423        4      -7.8      0.4   25   Gieren (1981a)




             
             Figure 11. O-C diagram of S Cru


             Table 20. O-C residuals for S Cru

Norm.max.     E       O-C       Type,   Reference
JD2400000+                      weight

25785.558    -1959   -0.286d    pg 1     Dartayet et al. (1949)
26109.086    -1890   -0.366     pg 1     Dartayet et al. (1949)
34921.939    - 11    +0.034     pe 1     Walraven et al. (1958)
35208.046    + 50    +0.053     pe 2     Irwin (1961)
40310.536    +1138   -0.145     pe 3     Stobie (1970)
40774.862    +1237   -0.126     pe 3     Pel (1976)
42852.392    +1680   -0.253     pe 1     Dean (1977)
44414.058    +2013   -0.347     pe 3     Gieren (1981b)
45126.915    +2165   -0.365     pe 2     Eggen (1985)

   The O-C residuals (listed in Table 20) have been computed with the
elements:

       C = 2434973.495 + 4.689970d*E            (17)
                +-.015  +-.000007

As is seen in Figure 11, the pulsation period is continuously decreasing.
The instantaneous value of the period is:

       P = 4.689970d - 1.747d*10^-7*E            (18)
          +-.000007   +-.109

where the E epoch number is the same as in equation (17).



T Crucis


  On the basis of the available radial velocity measurements, variability
in the gamma-velocity can be suspected (see Table 21 and the lower panel of
Figure 12). Jaschek and Jaschek (1956) found strong Ca II emission which
may be partly caused by the presence of the companion.


                 Table 21. gamma-velocities of T Cru

JD        sigma    v gamma       sigma  n   Reference
2400000+   [d]      [km/s]       [km/s]

33831        9      -5.5          1.1   8   Stibbs (1955)
34106       19      -7.8          1.1   9   Stibbs (1955)
40363       34     -12.8          0.3   6   Lloyd Evans (1980)

                 Table 22. O-C residuals for T Cru

Norm.max     E            O-C    Type,    Reference
JD2400000+                       weight

25794.799    -1299       -0.022d pg 1     Dartayet et al. (1949)
26117.971    -1251       -0.044  pg 1     Dartayet et al. (1949)
33814.110    - 108       +0.052  pe 2     Eggen et al. (1957)
34871.193    + 49        +0.023  pe 3     Eggen et al. (1957)
34958.726    + 62        +0.025  pe 1     Walraven et al. (1958)
35214.551    + 100       -0.012  pe 2     Irwin (1961)
40318.333    + 858       +0.008  pe 1     Stobie (1970)
40742.458    + 921       -0.059  pe 3     Pel (1976)
41819.814    +1081       -0.014  pe 3     Dean et al. (1977)
42102.620    +1123       -0.002  pe 3     Dean et al. (1977)
42587.418    +1195       +0.006  pe 2     Dean et al. (1977)
43260.823    +1295       +0.091  pe 1     Dean (1981)




          
          Figure 12. Upper panel: O-C diagram of T Cru
                     Lower panel: gamma-velocities for the same Cepheid



   The O-C diagram contains very few data points (see Table 22). The
residuals have been calculated with the elements:

       C = 2434541.243 + 6.733196d*E             (19)
                +-.010  +-.000011

The photographic observations have also been taken into account in the
fitting procedure. If the deviations from the straight line (see Figure 12,
upper panel) are caused by a light-time effect, the gamma-velocity variations
may well exceed the range observed so far. In any case, more photometric
and spectroscopic observations are needed.



AG Crucis


   Gieren (1982) already noted that AG Cru might belong to a spectroscopic
binary. The present study based on the same radial velocity data (see Table
23 and the lower panel of Figure 13) confirm his conclusion. The presence
of a blue companion is also suspected in Pel's (1978) photometry.

                Table 23. gamma-velocities of AG Cru

JD        sigma   v gamma       sigma   n   Reference
2400000+   [d]    [km/s]        [km/s]

34154       41     -4.4          0.8   17   Stibbs (1955)
40577      199     -6.5          0.3    5   Lloyd Evans (1980)
44423        4     -8.5          0.4   23   Gieren (1981a)

                Table 24. O-C residuals for AG Cru

Norm.max.    E            O-C    Type,    Reference
JD2400000+                       weight

27439.121    -1947       +1.523d pg       O'Herne (1937)
34778.239    - 34        -0.026  pe 2     Walraven et al. (1958)
35219.538    + 81        -0.012  pe 3     Irwin (1961)
39559.471    +1212       -0.013  pe 3     Landolt (1971)
40760.517    +1525       -0.027  pe 3     Pel (1976)
41098.205    +1613       -0.018  pe 2     Pel (1976)
42894.075    +2081       +0.017  pe 2     Dean (1977)
44421.305    +2479       +0.020  pe 3     Gieren (1981b)

Although the O-C diagram contains very few data points (see Table 24
and the upper panel of Figure 13), a sine wave can be reliably fitted to
the O-C residuals. Moreover, the parameters of the light-time effect wave
are in agreement with the changes in the gamma-velocity. The O-C residuals
have been computed with the elements:

       C = 2434908.732 + 3.837254d*E             (20)
                +-.001  +-.000001

and the moments of the light maxima can be predicted as follows:

    C = 2434908.732 + 3.837254*E - 0.026d*cos(2pi(0.000604*E + 0.110))  (21)
             +-.001  +-.000001    +-.001         +-.000008    +-.012



          
          Figure 13. Upper panel: O-C diagram of AG Cru
                     Lower panel: gamma-velocities for the same Cepheid


   The orbital period is 6350 +- 90 days. According to the phase relations no
radial velocity observation of AG Cru was performed during the epochs when
the Cepheid was strongly moving away on its orbit. Therefore the expected
amplitude of the gamma-velocity variations may reach 10 km/s (see equation 1).
   If the first O-C residual is correct, a period change might have
occurred before J.D.2435000, but O'Herne's (1937) photographic normal maximum
seems to be of very low quality (this O-C residual has not been plotted in
Figure 13).



BG Crucis

   
   According to the available radial velocity observations, BG Cru is a
new spectroscopic binary. Its duplicity can also be suspected on the basis
of the extremely low amplitude light variations in the ultraviolet band
(Dean, 1981). In addition to the data points listed in Table 25 (shown
plotted in the lower panel of Figure 14), there is one more series of
radial velocity observations (Lunt, 1921). These latter data, however,
cannot be used because the moments of these three observations have not
been published. The average value of these radial velocity measurements is
-14.9 km/s, being more positive than any other gamma-velocity determined for
BG Cru.


        
        Figure 14. Upper panel: O-C diagram of BG Cru
                   Lower panel: gamma-velocities for the same Cepheid

               Table 25. gamma-velocities of BG Cru

JD        sigma  v gamma      sigma   n   Reference
2400000+   [d]   [km/s]       [km/s]

19902        1   -17.4         2.0    2   Campbell and Moore (1928)
21449      175   -26.2         1.2    4   Campbell and Moore (1928)
40449        9   -19.9         0.4    3   Lloyd Evans (1980)
40728       62   -24.4         0.2   16   Lloyd Evans (1980)
43178        4   -20.9         0.4    9   Stobie and Balona (1979)
43319       29   -20.0         0.3   10   Stobie and Balona (1979)
43533        4   -19.6         0.3   10   Stobie and Balona (1979)

               Table 26. O-C residuals for BG Cru

Norm.max.    E        O-C     Type,    Reference
JD2400000+                    weight

39327.323    -319    -0.009d  pe 1     Stobie and Alexander (1970)
40393.683    0       +0.023   pe 3     Stobie and Alexander (1970)
40771.369    +113    -0.018   pe 1     Cousins and Lagerwey (1971)
41112.338    +215    -0.007   pe 3     Cousins and Lagerwey (1971)
43181.468    +834    -0.021   pe 3     Stobie and Balona (1979)
43562.551    +948    -0.008   pe 2     Dean (1981)
43636.112    +970    +0.014   pe 2     Eggen (1985)
43997.102    +1078   -0.010   pe 3     Arellano Ferro (1981)
44622.258    +1265   +0.057   pe 1     Eggen (1985)


   More than ten values could be determined as possible orbital periods
using a least squares sinus fit but after comparing these values with the
O-C diagram to be discussed below, three values remained as the most
probable ones: 4050, 4950, and 6650 days.
   The O-C residuals have been computed with the formula:

       C = 2440393.660 + 3.342720d*E            (22)
                +-.008  +-.000010

Although the light-time effect is apparent (see Table 26 and the upper
panel of Figure 14), an exact determination of the orbital period cannot be
carried out because of the limited time interval covered with photometric
observations. The pattern of the O-C graph is in agreement with a nearly
5000 day long orbital period. Both much shorter and much longer values can
be excluded.



beta Doradus



  The gamma-velocity of this Cepheid variable is constant (see Table 27).
Lloyd Evans (1968) could not find any variation larger than 3 km/s in the
gamma-velocity of beta Dor either. Moreover, this star has not been suspected as
having a companion by any other method.


               Table 27. gamma-velocities of beta Dor

JD      sigma v gamma sigma  n   Reference
2400000+ [d]  [km/s]  [km/s]

16619   191   5.1     1.3    6   Lunt (1924)
17297   798   7.9     0.7   12   Applegate (1927)
19129   921   6.1     1.7    4   Lunt (1924)
21712   564   8.0     0.3   54   Applegate (1927)
22815   136   6.9     0.5   35   Lunt (1924)
34024    29   8.8     0.6   23   Stibbs (1955)
40281   514   7.9     0.5   13   Lloyd Evans (1968,1980)


              Table 28. O-C residuals for beta Dor

Norm.max.   E           O-C    Type,  Reference
JD2400000+                     weight

25639.776  -1551       +0.108d pg     Dartayet et al. (1949)
25993.962  -1515       -0.033  pg     Dartayet et al. (1949)
26397:617  -1474       +0.082  pg     Dartayet et al. (1949)
34438.765  - 657       -0.031  pe 1   Eggen et al. (1957)
34812.843  - 619       +0.035  pe 2   Eggen et al. (1957)
35216.360  - 578       +0.013  pe 2   Irwin (1961)
35570.654  - 542       -0.021  pe 1   Walraven et al. (1958)
40511.600  - 40        +0.028  pe 2   Hutchinson et al. (1975)
40796.967  - 11        -0.035  pe 3   Hutchinson et al. (1975)
40924.940  + 2         -0.014  pe 3   Pel (1976)
41732.014  + 84        -0.019  pe 3   Dean et al. (1977)
43198.610  + 233       +0.056  pe 1   Dean (1981)
43493.849  + 263       +0.022  pe 2   Eggen (1985)
43887.415  + 303       -0.109  pe 1   Schmidt and Parsons (1982)
44665.128  + 382       +0.053  pe 2   Eggen (1985)



                  
                  Figure 15. O-C diagram of beta Dor


   The early part of the O-C diagram of beta Dor was published by Iroshnikov
(1958). In the present study the O-C residuals have been calculated with
the elements:

       C = 2440905.269 + 9.842425d*E              (23)
                +-.008  +-.000024

The photoelectric part of the O-C diagram (see Table 28 and Figure 15) can
be well approximated by a straight line, assuming a constant period during
the last decades. A parabolic fit to these O-C residuals (including the
photographic points at about J.D.2426000) would contradict to the O-C
pattern determined by Iroshnikov (1958).



GH Lupi


   The variation in the gamma-velocity of GH Lupi has not been reported yet.
Although the effect is not very large, it can be readily detected
especially in the radial velocity observational series obtained by Coulson
and Caldwell (1985) (see Table 29 and the lower panel of Figure 16). This
variation might have been hidden till now because the pulsation period was
not known accurately enough. The unusually low amplitude light variation

                  Table 29. gamma-velocities of GH Lup

JD         sigma  v gamma  sigma        n   Reference
2400000+    [d]   [km/s]   [km/s]

41602      214    -21.5    4.5          6   Grayzeck (1978)
43974        5    -15.0    0.4          7   Coulson and Caldwell (1985)
44408       52    -16.0    0.3         10   Coulson and Caldwell (1985)
44721       32    -16.9    0.3         17   Coulson and Caldwell (1985)
45092        2    -18.9    0.6          4   Coulson and Caldwell (1985)


               Table 30. O-C residuals for GH Lup

Norm.max.    E          O-C    Type,  Reference
JD2400000+                     weight

38202.145   -315       -0.474d pg     Strohmeier (1967)
41088.014   - 4        -0.047  pe 3   Pel (1976)
41413.010   + 31       +0.221  pe 1   Grayzeck (1978)
44029.154   +313       -0.017  pe 3   Coulson and Caldwell (1985)
44455.880   +359       -0.076  pe 3   Coulson and Caldwell (1985)
44651.017   +380       +0.224  pe 1   Eggen (1985)
44734.257   +389       -0.038  pe 3   Coulson and Caldwell (1985)
45142.455   +433       -0.069  pe 2   Coulson and Caldwell (1985)
45569.543   +479       +0.233  pe 1   Eggen (1985)



      
      Figure 16. Upper panel: O-C diagram of GH Lup
                 Lower panel: gamma-velocities for the same Cepheid


may be also due to the presence of a companion. Pel's (1978) photometry
gives evidence for a red companion.
   The O-C residuals listed in Table 30 and plotted in Figure 16 (upper
panel) have been computed by the formula:

       C = 2441125.173 + 9.277948d*E            (24)
                +-.056  +-.000167

This value of the pulsation period, assumed to be constant between
J.D.2441000 and 2445600, considerably differs from the value given in the
GCVS (Kholopov et al., 1985-1987). A change in the period might have
occurred before J.D.2441000, if the photographic O-C residual obtained
from Strohmeier's (1967) data is real.



R Muscae


   The Cepheid R Muscae is probably a spectroscopic binary (Lloyd Evans,
1982). This earlier conclusion is confirmed here (see Table 31 and the
lower panel of Figure 17). There is, however, no sign of any companion in
the study made by Eichendorf et al. (1982) covering an exceptionally wide
wavelength range.
   The O-C residuals listed in Table 32 have been calculated with the
elements:

       C = 2426496.033 + 7.510159d*E                (25)
                +-.020  +-.000028

As is readily seen in Figure 17, R Mus has a continuously increasing
period:

       P = 7.510159d + 1.25d*10^-7*E                (26)
          +-.000028   +-.10

where the E epoch number is the same as in equation (25). The photographic
O-C residuals were also taken into account during the fitting procedure. A
sine-wave superimposed on the parabola was also searched for but without
any physically acceptable result.

                 Table 31. gamma-velocities of R Mus

JD        sigma  v gamma  sigma    n   Reference
2400000+   [d]   [km/s]   [km/s]

33832        9   +4.2     1.2      7   Stibbs (1955)
34125       31   +2.4     1.2      7   Stibbs (1955)
40389       43   -2.0     0.2     14   Lloyd Evans (1980)
40727       67   +1.3     0.2     18   Lloyd Evans (1980)

                 Table 32. O-C residuals for R Mus

Norm.max     E            O-C    Type,    Reference
JD2400000+                       weight

19346.327    - 952       -0.035d pg       Hertzsprung (1928)
26105.508    - 52        +0.003  pg 1     Dartayet et al. (1949)
26473.501    - 3         -0.002  pg 1     Dartayet et al. (1949)
34141.479    +1018       +0.104  pe 1     Eggen et al. (1957)
34839.906    +1111       +0.086  pe 3     Walraven et al. (1958)
34907.506    +1120       +0.094  pe 3     Eggen et al. (1957)
35207.854    +1160       +0.037  pe 3     Irwin (1961)
37836.518    +1510       +0.145  pe 3     Walraven et al. (1964)
42853.512    +2178       +0.359  pe 2     Dean (1977)
43596.970    +2277       +0.305  pe 3     Eggen (1985)
44648.445    +2417       +0.358  pe 3     Eggen (1985)




              
              Figure 17. Upper panel: O-C diagram of R Mus



S Muscae


   This Cepheid has long been known as a spectroscopic binary. Its orbital
period is 506 days (Lloyd Evans, 1971). The presence of a blue companion is
predicted by the two-colour diagrams (Stobie, 1970; Dean, 1977; Pel, 1978).
Bhm-Vitense and Proffitt (1985) detected the effect of the companion in
the IUE spectrum of S Mus. The radial velocity observations of S Muscae are
not re-discussed here.



                   
                   Figure 18. O-C diagram of S Mus


                  Table 33. O-C residuals for S Mus

Norm.max.    E            O-C    Type,    Reference
JD2400000+                       weight

26128.045    -1467       -0.081d pg 1     Dartayet et al. (1949)
26466.032    -1432       -0.190  pg 1     Dartayet et al. (1949)
33807.521    - 672       -0.206  pe 1     Eggen et al. (1957)
34541.889    - 596       +0.012  pe 1     Eggen et al. (1957)
34628.743    - 587       -0.073  pe 2     Walraven et al. (1958)
34918.458    - 557       -0.155  pe 3     Eggen et al. (1957)
35227.609    - 525       -0.120  pe 3     Irwin (1961)
37845.449    - 254       -0.106  pe 3     Walraven et al. (1964)
40308.825    + 1         +0.002  pe 3     Stobie (1970)
42859.006    + 265       -0.024  pe 2     Dean (1977)
43602.870    + 342       +0.030  pe 2     Eggen (1985)
44694.391    + 455       -0.015  pe 2     Eggen (1985)
45148.433    + 502       +0.013  pe 1     Eggen (1985)


The light curve of this Cepheid is double-peaked. The moment of the
first maximum was used when constructing the O-C diagram. The O-C residuals
listed in Table 33 have been calculated with the elements:

       C = 2440299.163 + 9.659875d*E                (27)
                +-.012  +-.000036

The O-C diagram in Figure 18 can be best approximated by two almost
parallel lines. The phase jump occurred at about J.D.2439000, before that
epoch the pulsation period was 9.659899 +- 4.0*10^-5 days (taking into
account the photographic O-C residuals, as well). The value of the phase
jump was about 0.1 day, and after the phase jump the elements given in
equation (27) have been valid. The parabolic fit would be somewhat worse.
The amplitude of the light-time effect expected according to equation (1)
is about 0.01 day, therefore this effect can hardly be pointed out in the
O-C diagram of S Muscae.



S Normae


   S Nor is one of the most important stars among the Cepheid variables
because of its membership in the open cluster NGC 6087. This calibrating
Cepheid may belong to a spectroscopic binary system (Breger, 1970). Its
duplicity is also suspected on the basis of photometric evidence (Madore,
1977). The gamma-velocities listed in Table 34, including more recent than
Breger's data suggest a variation with a period of either 3300 or 6350 days
(see the lower panel of Figure 19). Even longer periods can be excluded
because the corresponding light-time effect is not seen in the O-C diagram
(see below).

                  Table 34. gamma-velocities of S Nor

JD         sigma v gamma      sigma    n   Reference
2400000+   [d]   [km/s]       [km/s]

18418       11   -5.8           1.0    5   Campbell and Moore (1928)
33905       22   +3.8           0.9   12   Stibbs (1955)
34213       22   +3.5           1.2    7   Stibbs (1955)
38514       44   +5.6           0.3   12   Feast (1967)
38619        7   +9.4           0.5    5   Feast (1967)
38953       17   +7.1           0.1   20   Breger (1970)
39288      121   +8.0           1.9    2   Lloyd Evans (1968)
40377       29   +3.4           0.2    8   Lloyd Evans (1980)
40814       12   +3.1           0.3    3   Lloyd Evans (1980)
41412        4   +2.6           7.1    3   Grayzeck (1978)
41793        4   -2.4           5.8    4   Grayzeck (1978)
45772      198   +5.9           0.2   10   Mermilliod et al. (1987)
46286       53   +5.8           0.1   13   Mermilliod et al. (1987)


                 Table 35. O-C residuals for S Nor

Norm.max.    E            O-C    Type,    Reference
JD2400000+                       weight

16580.963    -2813       +0.767d pg       Shapley (1930)
18199.911    -2647       +0.511  pg       Shapley (1930)
20248.050    -2437       +0.259  pg       Shapley (1930)
21350.020    -2324       -0.001  pg       Shapley (1930)
23203.204    -2134       -0.123  pg       Shapley (1930)
24276.419    -2024       +0.125  pg 1     ten Bruggencate (1927a)
24676.279    -1983       +0.061  pg 1     ten Bruggencate (1927a)
25037.357    -1946       +0.232  pg 1     ten Bruggencate (1927a)
34576.828    - 968       +0.052  pe 3     Walraven et al. (1958)
35230.372    - 901       +0.062  pe 3     Irwin (1961)
36830.115    - 737       +0.109  pe 2     Fernie (1961)
37844.464    - 633       +0.016  pe 3     Walraven et al. (1964)
38888.164    - 526       +0.012  pe 3     Breger (1970)
39268.525    - 487       -0.042  pe 3     Breger (1970)
39678.266    - 445       +0.021  pe 2     Schmidt (1971)
41424.213    - 266       -0.042  pe 1     Grayzeck (1978)
41882.705    - 219        0.000  pe 3     Dean et al. (1977)
42545.994    - 151       +0.001  pe 3     Dean et al. (1977)
43492.182    - 54        +0.027  pe 3     Dean (1981)
43784.761    - 24        -0.021  pe 2     Eggen (1980)


   The O-C residuals have been computed with the ephemeris:

    C = 2444018.884 + 9.754244d*E             (28)
           +-.009    +-.000024



      
      Figure 19. Upper panel: O-C diagram of S Nor
                 Lower panel: gamma-velocities for the same Cepheid


   The O-C diagram is approximated by two sections of almost parallel lines
(see Table 35 and the upper panel of Figure 19). Before the phase jump the
most reliable photographic observations have been taken into account in the
fitting procedure which resulted in the period P = 9.754190 + 3.0*10^-5 days.
The phase jump might have occurred at about J.D.2437500, and it amounted to
0.06 day. The observed changes in the gamma-velocity are too small to cause any
noticeable light-time effect, assuming an orbital period of several
thousand days.



RS Normae


   RS Nor has been completely neglected spectroscopically: there is not a
single radial velocity measurement published in the literature. The
situation is not much better as far as photometric observations are
concerned, because the O-C diagram (see Table 36 and Figure 20) contains a
few scattered points. Madore (1977) gives evidence for a B8 dwarf
photometric companion.
   The O-C residuals have been computed with the elements:
 
         C = 2435308.175 + 6.198136d*E            (29)
                  +-.009  +-.000012


                Table 36. O-C residuals for RS Nor

Norm.max.    E            O-C    Type,    Reference
JD2400000+                       weight

25583.330    -1569       +0.030d pg 1     Kruytbosch (1930b)
34737.872    - 92        -0.074  pe 1     Walraven et al. (1958)
35227.600    - 13        +0.001  pe 3     Irwin (1961)
35332.962    + 4         -0.006  pe 1     Walraven et al. (1958)
40768.737    + 881       +0.004  pe 3     Pel (1976)
41103.449    + 935       +0.017  pe 2     Pel (1976)



             
             Figure 20. O-C diagram of RS Nor



The early photographic observations were also used when determining the
average pulsation period.



SY Normae


   An early type photometric companion to this Cepheid was suspected by
Madore (1977). A companion was later found using IUE measurements
(Bhm-Vitense and Proffitt,1985) but it cannot be ruled out that these two
stars form only an optical pair. Radial velocity measurements would be very
important in order to find the physical relation between the two stars, if
it really exists. The only available radial velocity data published by
Grayzeck (1978) are not suitable for drawing any conclusion.
   The O-C residuals listed in Table 37 and plotted in Figure 21 have been
calculated with the elements:

       C = 2440731.750 + 12.645687d*E                  (30)
                +-.004  +-.000016

The pulsation period has been stable since J.D.2434700. It is worth
mentioning that the moment of the normal maximum given in equation (30)
strongly differs from the value given in the GCVS (Kholopov et al.,


                Table 37. O-C residuals for SY Nor

Norm.max.    E        O-C  Type,     Reference
JD2400000+                 weight

25600.646   -1197    +5.783d  pg     Kruytbosch (1930a)
34750.337   - 473    -0.003   pe 3   Walraven et al. (1958)
35218.235   - 436    +0.005   pe 3   Irwin (1961)
40390.261   -   27   -0.055   pe 1   Stobie (1970)
40769.693   +    3   +0.006   pe 3   Pel (1976)
41111.126   +   30   +0.005   pe 3   Pel (1976)
41591.643   +   68   -0.014   pe 2   Grayzeck (1978)
41920.457   +   94   +0.012   pe 3   Madore (1975)



            
            Figure 21. O-C diagram of SY Nor


1985-1987). This deviation is probably caused by Kruytbosch's (1930a)
ephemeris. Unfortunately the original photographic observations have not
been published, therefore it cannot be decided whether there was a real
period change, or Kruytbosch published an erroneous ephemeris.



Y Ophiuchi


   Y Oph belongs to a spectroscopic binary system. Its orbital period was
determined by Abt and Levy (1978) as being 2612 days. Evans and Lyons
(1986) questioned this value of the orbital period, and even doubted the
variability in the gamma-velocity. The presence of a blue photometric
companion is suspected by Pel (1978) but such a blue star is not seen in an
IUE spectrum (Evans and Lyons, 1986). All the available radial velocity
data were subjected to a period analysis which resulted in the value of
1222.5 +- 10 days for the orbital period. The gamma-velocities are listed in
Table 38, and the orbital radial velocity curve folded with the recently
determined period is shown in Figure 22. In this figure open circles denote


                Table 38. gamma-velocities of Y Oph

JD        sigma  v gamma  sigma     n   Reference
2400000+   [d]    [km/s]  [km/s]

17066       27    -4.9    0.3      42   Albrecht (1907)
17440        6    -9.4    2.0       2   Albrecht (1907)
25356       13    -4.8    1.0       5   Sanford (1935)
26549       32    -1.0    0.6      14   Sanford (1935)
26911       35    -8.3    0.8       7   Sanford (1935)
27226       45   -11.8    0.6      11   Sanford (1935)
34482       29    -7.0    0.6      12   Abt (1954)
34599       32    -7.9    1.1       4   Abt (1954)
40365       36    -5.8    0.2       9   Lloyd Evans (1980)
40718       25    -7.8    0.5       4   Abt and Levy (1978)
40762       50    -6.4    0.2       7   Lloyd Evans (1980)
40792       28    -7.3    0.4       4   Evans and Lyons (1986)
41110       23    -6.3    0.5       3   Evans and Lyons (1986)
41116       36    -7.2    0.6       4   Abt and Levy (1978)
41534       79    -6.1    0.3       6   Abt and Levy (1978)
42228       86    -6.5    0.2       3   Abt and Levy (1978)
42565       35    -7.3    0.3       2   Abt and Levy (1978)
42900       27   -10.1    0.5       6   Abt and Levy (1978)
43281       26    -8.2    0.5       4   Abt and Levy (1978)
43350       46    -9.4    1.1      13   Wilson et al. (1989)
43639       46    -5.1    1.0      17   Barnes et al. (1987)
43976        5    -5.8    0.5       5   Coulson and Caldwell (1985)
44013       58   -10.1    1.1      12   Barnes et al. (1987)
44049        4    -9.0    0.5       3   Evans and Lyons (1986)
44181        3   -10.0    1.0       2   Coulson and Caldwell (1985)
44415       47    -6.4    0.4       9   Coulson and Caldwell (1985)
44446       23    -7.9    0.5       3   Evans and Lyons (1986)
44449        1   -12.5    1.3       1   Beavers and Eitter (1986)
44759       36    -8.8    0.6       4   Coulson and Caldwell (1985)
44819       25    -6.2    0.7       2   Evans and Lyons (1986)
45092        2    -7.2    0.7       3   Coulson and Caldwell (1985)
45388        1    -9.5    2.7       3   Barnes et al. (1987)
45501       21    -8.6    0.3       6   Evans and Lyons (1986)
45875        I    -9.9    0.7       1   Evans and Lyons (1986)


those low weight gamma-velocities that are based on one or two radial velocity
measurements. The semi-amplitude of the orbital radial velocity variations
is 1.60 + 0.47 km/s. In spite of its low amplitude, the orbital effect
seems to be real because its consequences also appear in the O-C diagram
(see below).
   The early part of the O-C diagram was constructed by Detre (1970). In
the present paper all the photoelectric and photographic series of
observations are discussed. The O-C residuals listed in Table 39 have been
calculated with the elements:

    C = 2439853.173 + 17.126908d*E            (31)
             +-.033   +-.000139


             Table 39. O-C residuals for Y Oph

Norm.max     E          O-C    Type,  Reference
JD2400000+                     weight

25077.192   -863       +4.541d pg     ten Bruggencate (1927b)
32781.493   -413       +1.733  pe 2   Eggen (1951)
33106.646   -394       +1.475  pe 3   Eggen (1951)
34322.185   -323       +1.003  pe 3   Abt (1954)
34733.130   -299       +0.902  pe 2   Walraven et al. (1958)
35281.188   -267       +0.899  pe 3   Irwin (1958)
35691.858   -243       +0.524  pe 2   Prokof'yeva (1961)
37079.101   -162       +0.487  pe 2   Mitchell et al. (1964)
37472.819   -139       +0.286  pe 1   Mitchell et al. (1964)
37815.507   -119       +0.436  pe 1   Williams (1966)
38603.166   - 73       +0.257  pe 1   Wisniewski and Johnson (1968)
39014.145   - 49       +0.190  pe 3   Wisniewski and Johnson (1968)
39682.123   - 10       +0.219  pe 3   Schmidt (1971)
40401.559   + 32       +0.325  pe 1   Feltz and McNamara (1980)
40778.016   + 54       -0.010  pe 3   Pel (1976)
40812.402   + 56       +0.122  pe 1   Feltz and McNamara (1980)
40829.354   + 57       -0.053  pe 2   Evans (1976)
41188.978   + 78       -0.093  pe 2   Feltz and McNamara (1980)
42953.217   +181       +0.074  pe 3   Dean (1977)
43038.950   +186       +0.172  pe 2   Dean (1981)
43312.747   +202       -0.061  pe 3   Moffett and Barnes (1984)
43672.337   +223       -0.136  pe 2   Moffett and Barnes (1984)
44015.145   +243       +0.133  pe 3   Moffett and Barnes (1984)
44032.132   +244       -0.007  pe 2   Coulson and Caldwell (1985)
44443.162   +268       -0.022  pe 3   Coulson and Caldwell (1985)
44460.261   +269       -0.050  pe 3   Eggen (1983b)
44871.342   +293       -0.015  pe 3   Coulson and Caldwell (1985)
46292.876   +376       -0.014  pe 3   Berdnikov (1987)
46601.179   +394       +0.004  pe 1   Lloyd et al. (1987)



           Table 40. Changes in the pulsation period of Y Oph

J.D. interval         P

2432781 - 2433106    17.113288d
                     +-.000010
  34733 -   35281    17.126813d
                     +-.000007
  35281 -   35691    17.111255d
                     +-.000001
  39014 -   39682    17.127643d
                     +-.000001
  40778 -   46601    17.126908d
                      +.000139



           
           Figure 22. Orbital velocity curve of Y Oph

          
           Figure 23. O-C diagram of Y Oph



  The O-C diagram (see Figure 23) is of complex structure. It is approximated
with sections of straight lines, representing two characteristic periods:
either 17.112 or 17.127 days. Table 40 summarizes the individual periods
and the time intervals in which the given period was valid.
   The alternating periods can be considered as a special case of the
phase jump: there is an interval of finite length when the star pulsates
with another period before returning to the "original" pulsation period. As
in the previous cases, the phase jump is a characteristic feature of binary
Cepheids. Moreover, the final part of the O-C diagram (after J.D.2440000)
shows unusually wide scatter, if approximated by a single period. The
dashed lines, however, suggest that this part also consists of several
phase jumps, and the predominant period is the shorter one (17.112 days).
The cyclic occurrence of this pulsation period can also be suspected, the
cycle length being about 2400 days in the first case, and about 1200 days
in the second case (N.B. the orbital period determined above is just over
1200 days). This phenomenon cannot be interpreted as a light-time effect
because of the large amplitude but it gives a further support to the
reality of the 1222.5 day spectroscopic orbital period, and calls the
attention that the binary companion is able to control the changes in the
pulsation period.



BF Ophiuchi


   According to Mianes (1963) and Balona (1977), BF Oph has a red
photometric companion, while Gieren (1982) already suspected the
spectroscopic binary nature of this Cepheid. The analysis of the available
radial velocity data (see Table 41) suggests an orbital period of 4420 +- 80
days. The orbital velocity curve is shown in Figure 24. Although the plot
of the data is not too convincing, this period is also supported by the
features in the O-C diagram (see below).


                Table 41. gamma-velocities of BF Oph

JD       sigma v gamma sigma n   Reference
2400000+ [d]   [km/s]  [km/s]

25597   219   -32.5   2.6    4   Joy (1937)
26152    45   -33.2   2.2    5   Joy (1937)
33905    21   -30.0   1.1    9   Stibbs (1955)
34199    14   -31.8   1.5    5   Stibbs (1955)
40559   210   -29.4   0.2   13   Lloyd Evans (1980)
44233   207   -28.3   1.1   13   Barnes et al. (1988)
44423     4   -29.2   0.4   22   Gieren (1981a)
44945   295   -28.2   2.3    4   Barnes et al. (1988)



           
           Figure 24. Orbital velocity curve of BF Oph



           
           Figure 25. Upper panel: O-C diagram of BF Oph
                      Lower panel: gamma-velocities for the same Cepheid

The O-C residuals listed in Table 42 have been calculated with the
elements:

       C = 2444435.105 + 4.067698d*E                      (32)
                +-.005  +-.000001

The O-C diagram (Figure 25) can be best represented by a sine-wave
superimposed on a parabola. The moments of the normal maxima can be
predicted as follows:

C = 2444435.105 + 4.067698d*E - 4.87d*10^-9*E^2 - 0.017d*cos(2n(0.000904*E+0.046)) (33)
         +-.005  +-.000001     +-.89             +-.005        +-.000073  +-.081


                Table 42. O-C residuals for BF Oph

Norm.max.    E           O-C    Type,  Reference
JD2400000+                      weight

15618.712   -7084       -0.820d pg     Shapley (1930)
16558.440   -6853       -0.731  pg     Shapley (1930)
17180.773   -6700       -0.755  pg     Shapley (1930)
18030.957   -6491       -0.720  pg     Shapley (1930)
18572.053   -6358       -0.628  pg     Shapley (1930)
19479.214   -6135       -0.564  pg     Shapley (1930)
20069.022   -5990       -0.572  pg     Shapley (1930)
20870.376   -5793       -0.554  pg     Shapley (1930)
21541.624   -5628       -0.477  pg     Shapley (1930)
22440.589   -5407       -0.473  pg     Shapley (1930)
23351.842   -5183       -0.384  pg     Shapley (1930)
24149.199   -4987       -0.296  pg     Shapley (1930)
25320.776   -4699       -0.216  pg     Shapley (1930)
26781.021   -4340       -0.275  pg     O'Connell (1937)
27269.159   -4220       -0.260  pg     O'Connell (1937)
34790.528   -2371       -0.065  pe 1   Walraven et al. (1958)
35229.827   -2263       -0.077  pe 3   Irwin (1961)
37113.244   -1800       -0.005  pe 1   Mitchell et al. (1964)
37471.204   -1712       -0.002  pe 2   Mitchell et al. (1964)
39549.798   -1201       -0.002  pe 2   Takase (1969)
40338.898   -1007       -0.035  pe 3   Stobie (1970)
40761.959   - 903       -0.015  pe 3   Pel (1976)
42856.824   - 388       -0.014  pe 2   Dean (1977)
44361.869   - 18        -0.017  pe 3   Moffett and Barnes (1984)
44414.749   - 5         -0.018  pe 3   Gieren (1981b)
44809.332   + 92        -0.001  pe 3   Eggen (1985)


Here only the photoelectric O-C residuals have been taken into account.
According to the cosine term, the orbital period is 4500 +- 360 days, being
in a very good agreement with the spectroscopic value. The amplitude and
the phase of the wave is also adequate to the spectroscopic binary
interpretation of the gamma-velocity changes. It is worth mentioning that,
according to this value of the orbital period, BF Oph has not been observed
spectroscopically during the orbital phases when the Cepheid is strongly
moving away from us, i.e. the amplitude of the gamma-velocity variations is
larger than observed so far.
   A simple parabolic fit applied to the whole set of O-C residuals
resulted in the pulsation period as a function of time:

   C = 4.067665d - 4.12d*10^-8*E                (34)
      +-.000008   +-.22

where the E epoch number is the same as in equations (32) and (33).



AP Puppis



   This Cepheid is likely to be a spectroscopic binary with one of the
largest orbital velocity amplitude (see Table 43 and the lower panel of
Figure 26). The extremely large shift between Joy's (1937) and the more
recent radial velocity data was already noted by Lloyd Evans (1982) but no
subsequent radial velocity observations followed this discovery.
   The O-C residuals have been calculated with the elements:

    C = 2440689.133 + 5.084274d*E             (35)
             +-.019  +-.000027


                 Table 43. gamma-velocities of AP Pup

JD        sigma  v gamma  sigma        n   Reference
2400000+   [d]    [km/s]  [km/s]

28620       27   46.1     2.3          5   Joy (1937)
33980       26   17.0     0.7         21   Stibbs (1955)
34138       36   18.5     3.0          2   Stibbs (1955)
40335       17   13.7     0.3          4   Lloyd Evans (1980)
40629        8   13.0     0.4          3   Lloyd Evans (1980)



     
     Figure 26. Upper panel: O-C diagram of AP Pup
                Lower panel: gamma-velocities for the same Cepheid


                 Table 44. O-C residuals for AP Pup

Norm.max.    E            O-C    Type,    Reference
JD2400000+                       weight

35182.832    -1083       -0.032d pe 1     Irwin (1961)
35299.806    -1060       +0.003  pe 2     Walraven et al. (1958)
40740.008    + 10        +0.032  pe 3     Pel (1976)
42854.964    + 426       -0.070  pe 1     Dean (1977)

The small number of the photometric observational series (see Table 44  and
the upper panel of Figure 26) does not allow a reliable search for the
light-time effect expected in this binary system. The plot of the O-C
residuals can be approximated by a free-hand sinusoidal term (taking into
account the phases prescribed by the gamma-velocity variations) suggesting a
long (about 9000 - 10000 days) orbital period, and a slightly shorter
pulsation period than used in equation (35). Any further photometric and/or
spectroscopic observations may play a decisive role in determining the
orbital period of this neglected star.



AT Puppis


   The changing gamma-velocity of AT Pup was first reported by Gieren (1985).
His conclusion is confirmed here (see Table 45 and the lower panel of
Figure 27).



      
      Figure 27. Upper panel: O-C diagram of AT Pup
                 Lower panel: gamma-velocities for the same Cepheid


                     Table 45. gamma-velocities of AT Pup

JD         sigma   v gamma  sigma     n   Reference
2400000+    [d]     [km/s]  [km/s]

28614       25       24.2    2.6      4   Joy (1937)
34019       42       29.1    0.8     16   Stibbs (1955)
34163       20       28.2    1.5      5   Stibbs (1955)
45042        2       20.6    0.5     20   Gieren (1985)


                   Table 46. O-C residuals for AT Pup

Norm.max.    E           O-C    Type, Reference
JD2400000+                      weight

30750.437   -1499       -0.015d pg     Erleksova (1961)
34142.642   - 990       -0.234  pg     Erleksova (1961)
35215.887   - 829       -0.034  pe 1   Irwin (1961)
35589.121   - 773       -0.034  pe 3   Walraven et al. (1958)
37648.645   - 464       +0.043  pe 2   Mitchell et al. (1964)
40741.152       0       +0.046  pe 3   Pel (1976)
42893.867   + 323       +0.005  pe 1   Dean (1977)
44513.455   + 566       +0.027  pe 1   Eggen (1985)
45046.576   + 646       -0.042  pe 3   Gieren (1985)



The O-C residuals have been calculated with the ephemeris:

       C = 2440741.106 + 6.664879d*E                  (36)
                +-.011  +-.000020

Gieren's (1985) observations made in 1981 were omitted because there can be
a systematic error of unknown origin in the published moments of the
observations in the case of each of the three stars (AT Pup, T Vel, V Vel)
studied here from his sample. Such an error is not present in Gieren's 1982
observations, both the O-C residual, and the light curve is the most
reliable among the observations on AT Pup. This latter statement is also
true for the 1982 observations on T Vel and V Vel.
   The wave-like pattern of the photoelectric O-C residuals (see Table 46
and the upper panel of Figure 27), together with the variation in the
gamma-velocity, is in accord with a very long (about 20000 days) orbital
period. From the radial velocity observations alone the orbital period can
be much shorter but in that case the light-time effect interpretation of
the O-C diagram fails.




MY Puppis


   No variability in the gamma-velocity of MY Pup is seen in the available
data (see Table 47).
   The O-C residuals have been computed with the elements:

       C = 2441043.597 + 5.694998d*E                 (37)
                +-.013  +-.000031

The plot of the O-C residuals (see Table 48 and Figure 28) can be well
approximated by a parabola. This is the only star in this sample where


                   Table 47. gamma-velocities of MY Pup

JD        sigma  v gamma      sigma     n   Reference
2400000+   [d]    [km/s]      [km/s]

24422      301   11.4           1.0     5   Neubauer (1929)
43172       56   13.4           0.2    23   Stobie and Balona (1979)
43533        4   12.8           0.4     9   Stobie and Balona (1979)


                   Table 48. O-C residuals for MY Pup

Norm.max.    E           O-C      Type,     Reference
JD2400000+                        weight

24421.80     -2919      +1.90d    vr 1      Neubauer (1929)
39107.348    - 340      +0.050    pe 1      Stobie (1972)
41043.599    0          +0.002    pe 3      Stobie (1972)
43184.919    + 376      +0.003    pe 3      Stobie and Balona (1979)
44284.122    + 569      +0.071    pe 1      Eggen (1985)
44568.948    + 619      +0.147    pe 1      Eggen (1985)



              
              Figure 28. O-C diagram of MY Pup


radial velocity measurements were also used when determining the shape of
the O-C graph. The period change has been so strong since the twenties that
it could not be avoided making exceptions lacking suitable photometric
observations. The continuously increasing period can be calculated as
follows:

       P = 5.694998 + 4.47d*10^-7*E                  (38)
          +-.000031  +-.12

where E corresponds to the epoch number used in equation (37).



U Sagittarii


   U Sgr is the other "classical" cluster-member Cepheid, it belongs to
the open cluster M25. Duplicity of U Sgr has long been debated, the various
pieces of evidence are summarized by Leonard and Turner (1986). Gieren
(1982) suspected the variation in the gamma-velocity, preferring a long
orbital period, similarly to an earlier study performed by Wallerstein
(1960). Table 49 summarizes the gamma-velocities of U Sgr. Joy's (1937) and
Hayford's (1932) data have been omitted because of much lower quality of
those early observations. The 800 - 8000 day interval was studied when
searching for the possible orbital period. The best curve was obtained at
Porb = 4550 +- 230 days. The gamma-velocities folded with this period are shown


                Table 49. gamma-velocities of U Sgr

JD       sigma v gamma sigma  n   Reference
2400000+ [d]   [km/s]  [km/s]

33916     33    3.5     0.8  14   Stibbs (1955)
34202     27    5.1     2.1   3   Stibbs (1955)
37223    151    3.8     0.6  11   Jacobsen (1970)
38200     28    3.7     2.0   2   Jacobsen (1970)
38955     19    6.8     0.5  14   Breger (1967)
39314      1    5.0     2.0   1   Jacobsen (1970)
39377      5    3.5     1.9   2   Lloyd Evans (1968)
40392     49    3.0     0.2   7   Lloyd Evans (1980)
40816     12    1.4     0.4   3   Lloyd Evans (1980)
43361     42    3.4     1.2  12   Wilson et al. (1989)
43668     31    7.1     1.2  11   Barnes et al. (1987)
44015     61    2.7     1.4   8   Barnes et al. (1987)
44112    146    2.9     0.2   6   Mermilliod et al. (1987)
44423      4    0.1     0.4  26   Gieren (1981a)
45182     18    2.0     0.5   2   Mermilliod et al. (1987)
45880      3    2.0     0.3   4   Mermilliod et al. (1987)
46275     10    2.6     0.1  30   Mermilliod et al. (1987)



         
         Figure 29. Orbital velocity curve of U Sgr



         Table 50. O-C residuals for U Sgr

Norm.max     E           O-C    Type,  Reference
JD2400000+                      weight

14496.341   -2316       +0.336d vis    Pickering (1904)
15946.443   -2101       +0.214  pg     Shapley (1930)
17329.147   -1896       +0.146  pg     Shapley (1930)
18475.855   -1726       +0.165  pg     Shapley (1930)
19609.067   -1558       +0.179  pg     Shapley (1930)
20459.006   -1432       +0.219  pg     Shapley (1930)
21308.978   -1306       +0.292  pg     Shapley (1930)
23244.642   -1019       +0.075  pg     Shapley (1930)
24674.684   - 807       +0.129  pg     Voute and ten Bruggencate (1927)
24694.765   - 804       -0.026  pg     Shapley (1930)
25059.149   - 750       +0.116  pg     Voute and ten Bruggencate (1927)
33133.030   + 447       -0.042  pe 2   Eggen (1951)
34758.595   + 688       -0.078  pe 2   Walraven et al. (1958)
35284.729   + 766       -0.071  pe 3   Irwin (1961)
35952.493   + 865       -0.085  pe 2   Johnson (1960)
36782.149   + 988       -0.092  pe 3   Sandage (1960)
37099.195   +1035       -0.072  pe 3   Wampler et al. (1961)
37119.444   +1038       -0.059  pe 2   Mitchell et al. (1961)
37180.138   +1047       -0.072  pe 2   Mitchell et al. (1964)
37800.793   +1139       +0.022  pe 1   Williams (1966)
38920.467   +1305       -0.012  pe 2   Wisniewski and Johnson (1968)
39675.918   +1417       -0.026  pe 2   Schmidt (1971)
40788.948   +1582       +0.041  pe 3   Pel (1976)
40829.379   +1588        0.000  pe 1   Feltz and McNamara (1980)
42448.200   +1828       -0.034  pe 2   Dean et al. (1977)
43486.971   +1982       -0.028  pe 3   Dean (1981)
43608.399   +2000       -0.014  pe 3   Moffett and Barnes (1984)
44411.081   +2119       -0.014  pe 3   Gieren (1981b)
44458.345   +2126       +0.033  pe 3   Eggen (1985)
44721.388   +2165       +0.012  pe 3   Berdnikov (1986)




      
      Figure 30. Upper panel: O-C diagram or U Sgr
                 Lower panel: gamma-velocities for the same Cepheid


in Figure 29 (the zero phase is arbitrarily chosen at J.D.2400000). In this
figure open circles denote those gamma-velocities which are only based on two
velocity measurements. Assuming that this orbital period is correct, the
full amplitude of the orbital radial velocity variation is 2K = 3.6 +- 1.3
km/s.
   Although Figure 29 is not fully convincing, i.e. another value of the
orbital period cannot be excluded, the O-C diagram gives a further support
to binary nature of U Sgr. The O-C residuals have been computed with the
elements:

     C = 2430117.955 + 6.745229d*E             (39)
              +-.030  +-.000016

As is seen in Figure 30 (based on the data listed in Table 50), the O-C
diagram can be characterized by a phase jump occurred at about J.D.2437500.
Before the phase jump (of an amplitude of 0.07 day) the pulsation period
was 6.745192 +- 1.5d*10^-5 days. This pattern of the O-C diagram cannot be
explained with a light-time effect because its expected amplitude is less
than 0.01 day. According to numerous other cases, the rejumping period is a
typical feature of binary Cepheids, therefore duplicity of U Sgr can be
stated beyond doubt.



W Sagittarii


   This Cepheid belongs to a multiple star system: at present four
components are identified (Babel et al., 1989, and references therein). The
Cepheid itself is a member of a spectroscopic binary system in this
hierarchy. The orbital period is 1780 +- 5 days, and the orbital velocity
amplitude is the least among the well-studied spectroscopic binary
Cepheids (K = 2.35 +- 0.47 km/s, - Babel et al., 1989).
  The O-C residuals have been calculated with the elements:

      C = 2443374.622 + 7.594904d*E             (40)
               +-.006  +-.000008

The O-C diagram (see Table 51 and Figure 31) can be well described
assuming a constant period. Although Babel et al. (1989) approximate the


                Table 51. O-C residuals for W Sgr

Norm.max.    E            O-C    Type,    Reference
JD2400000+                       weight

14491.629    -3803       +0.427d vis      Pickering (1904)
15220.531    -3707       +0.218  pg       Shapley (1930)
16306.666    -3564       +0.282  pg       Shapley (1930)
17392.573    -3421       +0.118  pg       Shapley (1930)
18471.022    -3279       +0.090  pg       Shapley (1930)
19640.603    -3125       +0.056  pg       Shapley (1930)
20605.127    -2998       +0.027  pg       Shapley (1930)
21782.113    -2843       +0.197  pg       Shapley (1930)
23232.817    -2652       -0.120  pg       Shapley (1930)
24440.488    -2493       -0.038  pg       Shapley (1930)
24577.282    -2475       +0.047  pg       Voute (1927a)
25443.229    -2361       +0.175  pg       Shapley (1930)
34572.151    -1159       +0.023  pe 2     Walraven et al. (1958)
34868.304    -1120       -0.026  pe 3     Eggen et al. (1957)
35248.090    -1070       +0.015  pe 3     Irwin (1961)
37253.091    - 806       -0.039  pe 1     Mitchell et al. (1964)
37883.539    - 723       +0.033  pe 3     Walraven et al. (1964)
38650.553    - 622       -0.039  pe 2     Wisniewski and Johnson (1968)
40017.674    - 442        0.000  pe 3     Cousins and Lagerweij (1968)
42858.147    - 68        -0.022  pe 2     Dean (1977)
43617.650    + 32        -0.009  pe 3     Moffett and Barnes (1984)
43754.383    + 50        +0.016  pe 3     Babel et al. (1989)
45508.797    + 281       +0.007  pe 3     Babel et al. (1989)



              
              Figure 31. O-C diagram of W Sgr


O-C graph by a parabola (continuous period increase), the parabolic fit to
the data in Table 51 has been of much lower accuracy as compared with the
linear fit. No effect of duplicity is seen in the O-C diagram, since the
amplitude of the light-time effect is much smaller than the limit of
detection.



X Sagittarii


   X Sgr belongs to a spectroscopic binary system with an orbital period
of 507.25 days (Szabados, 1989). Because the effect of the orbital motion
on the radial velocity variations is rather small, the value of the orbital
period is tentative, and needs confirmation. Nevertheless, a blue
photometric companion to X Sgr has been suspected by Pel (1978).
   The O-C residuals listed in Table 52 have been calculated with the
elements:

       C = 2440741.492 + 7.012777d*E                           (41)
                +-.015  +-.000028


                Table 52. O-C residuals for X Sgr

Norm.max.    E           O-C    Type,  Reference
JD2400000+                      weight

15531.897   -3595       +1.338d pg 1   Shapley (1930)
16422.246   -3468       +1.065  pg 1   Shapley (1930)
17228.609   -3353       +0.958  pg 1   Shapley (1930)
17922.830   -3254       +0.914  pg 1   Shapley (1930)
18652.136   -3150       +0.892  pg 1   Shapley (1930)
19144.481   -3037       +0.793  pg 1   Shapley (1930)
20152.889   -2936       +0.910  pg 1   Shapley (1930)
20888.857   -2831       +0.537  pg 1   Shapley (1930)
21569.130   -2734       +0.570  pg 1   Shapley (1930)
22501.724   -2601       +0.465  pg 1   Shapley (1930)
23329.154   -2483       +0.387  pg 1   Shapley (1930)
24353.118   -2337       +0.486  pg 1   Shapley (1930)
24514.329   -2314       +0.403  pg 1   Voute (1927a)
25440.009   -2182       +0.396  pg 1   Shapley (1930)
34871.956   - 837       +0.158  pe 1   Eggen et al. (1957)
35222.549   - 787       +0.112  pe 3   Irwin (1961)
35250.607   - 783       +0.119  pe 2   Walraven et al. (1958)
37129.933   - 515       +0.021  pe 2   Mitchell et al. (1964)
39051.428   - 241       +0.015  pe 3   Wisniewski and Johnson (1968)
40762.530   + 3          0.000  pe 3   Pel (1976)
42852.333   + 301       -0.005  pe 3   Dean (1977)
43658.808   + 416        0.000  pe 3   Moffett and Barnes (1984)
44437.218   + 527       -0.007  pe 3   Eggen (1985)




                  
                  Figure 32. O-C diagram of X Sgr


   As is seen in Figure 32, the O-C diagram of X Sgr is parabolic. The
parabola fitted to the photographic and photoelectric O-C residuals has
resulted in the following temporal variation in the pulsation period:

       P = 7.012777d + 1.65*10^-7*E                      (42)
          +-.000028   +-.21

where the E epoch number is the same as in equation (41). It has to be
noted, however, that the period increase used to be even stronger during
the visual observations made by Schmidt (Hertzsprung, 1934) in the last
century.



Y Sagittarii



                   Table 53. gamma-velocities of Y Sgr

JD         sigma v gamma  sigma  n   Reference
2400000+   [d]   [km/s]   [km/s]

16615      173   +1.5      1.1   8   Duncan (1908)
18152       22   +2.7      0.6  27   Duncan (1908)
22691      368   -6.0      0.6  24   Duncan (1922)
23377      165   -6.0      0.4  22   ten Bruggencate (1930)
23550      363   -3.0      0.5  16   Campbell and Moore (1928)
24134      141   -4.9      0.6  14   ten Bruggencate (1930)
25089       90   -3.5      0.6  15   ten Bruggencate (1930)
25794       20   -4.0      0.5  16   ten Bruggencate (1930)
40380       47   -3.3      0.2   8   Lloyd Evans (1980)
40765       51   -1.8      0.2   7   Lloyd Evans (1980)
43354       45   -1.1      1.2  12   Wilson et al. (1989)
43649       41   -3.6      1.1  14   Barnes et al. (1987)
44014       62   -2.7      1.4   8   Barnes et al. (1987)
44796        1   -6.6      1.3   1   Beavers and Eitter (1986)


   The changing gamma-velocity of Y Sgr was first reported by ten Bruggencate
(1930). The recent determination of the gamma-velocities confirms this
conclusion (see Table 53 and the lower panel of Figure 33). The pattern of
the gamma-velocity changes suggests a very long (P > 10000 days) orbital
period.

              Table 54. O-C residuals for Y Sgr

Norm.max.     E           O-C    Type,    Reference
JD2400000+                       weight

14499.428    -4549       +0.205d vis      Pickering (1904)
18176.856    -3912       -0.010  vis      Nijland (1923)
18962.147    -3776       +0.101  vis      Nijland (1923)
24712.345    -2780       +0.012  pg       ten Bruggencate (1928)
25070.247    -2718       -0.035  pg       ten Bruggencate (1928)
25439.689    -2654       -0.089  pg       ten Bruggencate (1928)
29839.040    -1892       -0.054  pg       Filin (1950b)
30681.845    -1746       -0.163  pg       Filin (1950b)
31449.885    -1613       +0.018  pg       Filin (1950b)
32408.117    -1447       -0.131  pg       Filin (1950b)
33118.360    -1324       -0.014  pe 2     Eggen (1951)
33141.471    -1320       +0.004  pg       Filin (1950b)
34879.244    -1019       -0.011  pe 2     Walraven et al. (1958)
35271.837    - 951       -0.008  pe 3     Irwin (1961)
36097.317    - 808       -0.121  pe 1     Svolopoulos (1960)
37130.873    - 629        0.000  pe 2     Mitchell et al. (1964)
37800.726    - 513       +0.141  pe 1     Williams (1966)
38937.984    - 316       +0.043  pe 1     Wisniewski and Johnson (1968)
40779.682    + 3         +0.033  pe 3     Pel (1976)
40820.055    + 10        -0.008  pe 2     Feltz and McNamara (1980)
42881.153    + 367       -0.006  pe 2     Dean (1977)
43441.162    + 464       -0.015  pe 3     Moffett and Barnes (1984)
44041.585    + 568       -0.024  pe 3     Moffett and Barnes (1984)
44821.027    + 703       +0.012  pe 1     Eggen (1985)



        
        Figure 33. Upper panel: O-C diagram of Y Sgr
                   Lower panel: gamma-velocities for the same Cepheid



  The O-C residuals have been computed with the elements:

      C = 2440762.329 + 5.773380d*E             (43)
               +-.009  +-.000013

The light-time effect expected in such a long period spectroscopic binary
is present in the O-C diagram (see Table 54 and the upper panel of Figure
33) but the limited time-base of the photoelectric observations does not
allow the successful determination of the long orbital period. A cycle
length as long as 10000 - 12000 days is in accordance with the
photoelectric O-C residuals but a much longer period cannot be ruled out,
either.



WZ Sagittarii


   The available radial velocity measurements might indicate a variable
gamma-velocity (see Table 55 and the lower panel of Figure 34). Joy's (1937)
first two observations have not been taken into account here. Further good
quality radial velocity data are necessary.


                 Table 55. gamma-velocities of WZ Sgr

JD        sigma   v gammma  sigma   n   Reference
2400000+   [d]     [km/s]   [km/s]

25985      282     -10.6     1.8    8   Joy (1937)
44327      231     -12.5     2.8    3   Barnes et al. (1988)
44589      297     -18.3     0.2   21   Coulson and Caldwell (1985)



     
     Figure 34. Upper panel: O-C diagram of WZ Sgr
                Lower panel: gamma-velocities for the same Cepheid


                Table 56. O-C residuals for WZ Sgr

Norm.max.        E    O-C     Type,    Reference
JD2400000+                    weight

15929.289       -896 +0.025d  pg       Shapley (1930)
17022.168       -846 +0.414   pg       Shapley (1930)
18114.435       -796 +0.192   pg       Shapley (1930)
19250.773       -744 +0.341   pg       Shapley (1930)
21129.367       -658 -0.147   pg       Shapley (1930)
23183.108       -564 -0.286   pg       Shapley (1930)
24450.260       -506 -0.422   pg       Shapley (1930)
24865.634       -487 -0.194   pg       Voute (1930a)
25805.161       -444 -0.208   pg       Voute (1930a)
29956.518       -254 -0.311   pg       Filin (1950b)
30983.476       -207 -0.293   pg       Filin (1950b)
32010.500       -160 -0.209   pg       Filin (1950b)
32971.974       -116 -0.125   pg       Filin (1950b)
33124.977       -109 -0.071   pe 2     Eggen (1951)
34632.661       - 40 -0.022   pe 2     Walraven et al. (1958)
35244.562       - 12 +0.084   pe 2     Irwin (1961)
37232.733       + 79 -0.075   pe 2     Mitchell et al. (1964)
37910.227       +110 +0.075   pe 3     Walraven et al. (1964)
41908.570       +293 -0.093   pe 1     Madore (1975)
42870.045       +337 -0.009   pe 2     Dean (1977)
43372.555       +360 -0.044   pe 3     Dean (1981)
44399.590       +407 +0.051   pe 3     Coulson and Caldwell (1985)
44486.967       +411 +0.029   pe 3     Moffett and Barnes (1984)
44508.828       +412 +0.040   pe 1     Eggen (1983b)
44923.961       +431 +0.027   pe 3     Coulson and Caldwell (1985)
45776.012       +470 -0.064   pe 3     Berdnikov (1986)


   The O-C residuals have been computed with the elements:

       C = 2435506.675 + 21.849789d*E           (44)
                +-.017 +-.000053

The pulsation period has been constant since the early photoelectric
observations (see Table 56  and the upper panel of Figure 34), while before
J.D.2433000 some changes occurred in the period. However, those earlier
variations were not secular ones (such long period Cepheids usually show
much larger continuous period changes indicating stellar evolution
(Szabados, 1981)).



AP Sagittarii



   The present study confirms Gieren's (1982) statement concerning the
variable gamma-velocity of AP Sgr. The data in Table 57 (shown plotted in the
lower panel of Figure 35) were analysed for possible periodicity. A number
of periods (5625, 6725, 7200, and 7500 days) describe the variable
gamma-velocity reasonably well, the most probable value of the orbital period


                Table 57. gamma-velocities of AP Sgr

JD         sigma   v gamma  sigma     n   Reference
2400000+    [d]    [km/s]   [km/s]

21733         1     - 6.4    4.5      1   Joy (1937)
24694       700     -18.9    2.6      3   Joy (1937)
26313       157     -18.3    2.0      6   Joy (1937)
39279        19     -19.7    0.8      6   Lloyd Evans (1968)
40592       219     -18.6    0.2     10   Lloyd Evans (1980)
44062         2     - 8.3    2.3      4   Barnes et al. (1988)
44423         4     -14.7    0.4     22   Gieren (1981a)
44579       168     -13.5    1.4      9   Barnes et al. (1988)


                 Table 58. O-C residuals for AP Sgr

Norm.max      E           O-C    Type,    Reference
JD2400000+                       weight

16021.186    -3959       -0.053d pg       Shapley (1930)
17381.853    -3690       +0.035  pg       Shapley (1930)
18469.235    -3475       -0.035  pg       Shapley (1930)
19652.935    -3241       +0.113  pg       Shapley (1930)
20750.509    -3024       +0.119  pg       Shapley (1930)
21640.649    -2848       +0.066  pg       Shapley (1930)
23679.094    -2445       +0.171  pg       Shapley (1930)
25868.992    -2012       -0.009  pg 1     Voute (1930b)
29829.379    -1229       +0.030  pg       Filatov (1966)
31280.959    - 942       -0.012  pg       Filatov (1966)
32540.355    - 693       -0.037  pg       Filatov (1966)
33369.887    - 529       -0.003  pg       Filatov (1966)
34391.562    - 327       -0.027  pg       Filatov (1966)
34720.309    - 262       -0.045  pe 2     Walraven et al. (1958)
35276.695    - 152       -0.030  pe 2     Irwin (1961)
36010.163    - 7         +0.040  pg       Filatov (1966)
37208.869    + 230       +0.020  pe 1     Mitchell et al. (1964)
39282.603    + 640       +0.009  pe 1     Takase (1969)
40370.067    + 855       +0.021  pe 2     Stobie (1970)
40794.903    + 939       -0.008  pe 3     Pel (1976)
44077.489    +1588       -0.010  pe 3     Moffett and Barnes (1984)
44426.508    +1657       +0.013  pe 3     Gieren (1981b)
44492.235    +1670       -0.013  pe 3     Moffett and Barnes (1984)
44659.170    +1703       +0.011  pe 2     Eggen (1985)


being the longest one (see the discussion below).
   The O-C residuals listed in Table 58 have been calculated with the
elements:

       C = 2436045.528 + 5.057916d*E              (45)
                +-.004  +-.000003

The O-C diagram (see the upper panel of Figure 35) shows a wave-like
pattern, the weighted least squares fit to the data points results in the
following formula for predicting the moments of the normal maxima:

  C = 2436045.528 + 5.057916d*E - 0.035d*cos(2pi(0.000665*E + 0.151))  (46)
           +-.004  +-.000003     +-.006         +-.000017    +-.024

     

      
      Figure 35. Upper panel: O-C diagram of AP Sgr
                      Lower panel: gamma-velocities for the same Cepheid


indicating an orbital period of 7608 + 194 days. The combination of the
photometric and spectroscopic evidence (including the amplitude and phase
relations) suggests that the orbital period is near 7500 days.



BB Sagittarii


   The Cepheid BB Sgr may be a coronal member of the open cluster Cr394
(Turner and Pedreros, 1985). Its spectroscopic binary nature was first
suspected by Gieren (1982), and later on confirmed by Barnes et al. (1988).
Gieren assumes a red companion to BB Sgr. The study of the available
observational data confirms the changing gamma-velocity (see Table 59 and the
lower panel of Figure 36) but the orbital period cannot be determined yet.
   The O-C residuals have been calculated with the elements:

       C = 2436053.475 + 6.637005d*E             (47)
                +-.009  +-.000005


                   Table 59. gamma-velocities of BB Sgr

JD        sigma  v gamma  sigma        n   Reference
2400000+   [d]    [km/s]  [km/s]

25558      368   + 8.6    2.6          4   Joy (1937)
26314      158   - 1.5    2.3          5   Joy (1937)
39284       16   + 7.5    0.8          6   Lloyd Evans (1968)
40407       44   + 8.2    0.3          4   Lloyd Evans (1980)
40799       27   + 7.3    0.3          5   Lloyd Evans (1980)
44062        2   +15.1    4.0          2   Barnes et al. (1988)
44423        4   + 4.1    0.4         24   Gieren (1981a)
44486       45   +11.1    1.8          6   Barnes et al. (1988)
44821       44   + 8.3    2.3          4   Barnes et al. (1988)


                 Table 60. O-C residuals for BB Sgr

Norm.max.     E           O-C    Type,    Reference
JD2400000+                       weight

15644.972    -3075       +0.287d pg 1     Shapley (1930)
16680.382    -2919       +0.325  pg 1     Shapley (1930)
17788.766    -2752       +0.329  pg 1     Shapley (1930)
18837.317    -2594       +0.233  pg 1     Shapley (1930)
19958.922    -2425       +0.184  pg 1     Shapley (1930)
21067.273    -2258       +0.155  pg 1     Shapley (1930)
22096.026    -2103       +0.173  pg 1     Shapley (1930)
23337.157    -1916       +0.184  pg 1     Shapley (1930)
25819.325    -1542       +0.112  pg 1     Voute (1930d)
34938.469    - 168       +0.011  pe 1     Walraven et al. (1958)
35283.586    - 116       +0.004  pe 2     Irwin (1961)
36756.971    + 106       -0.027  pe 1     Weaver et al. (1961)
37141.943    + 164       -0.001  pe 1     Mitchell et al. (1964)
40374.151    + 651       -0.014  pe 1     Stobie (1970)
40447.184    + 662       +0.012  pe 1     Lloyd Evans and Stobie (1971)
40805.592    + 716       +0.021  pe 3     Pel (1976)
41157.395    + 769       +0.063  pe 1     Feltz and McNamara (1980)
42239.185    + 932       +0.021  pe 3     Dean et al. (1977)
42551.084    + 979       -0.019  pe 3     Dean et al. (1977)
43526.814    +1126       +0.071  pe 2     Dean (1981)
44409.527    +1259       +0.063  pe 3     Moffett and Barnes (1984)
44422.808    +1261       +0.070  pe 3     Gieren (1981b)
44721.439    +1306       +0.035  pe 2     Turner and Pedreros (1985)
44907.311    +1334       +0.071  pe 3     Moffett and Barnes (1984)
45040.034    +1354       +0.054  pe 3     Turner and Pedreros (1985)
45212.646    +1380       +0.104  pe 3     Eggen (1985)



      
      Figure 36. Upper panel: O-C diagram of BB Sgr
                 Lower panel: gamma-velocities for the same Cepheid


The pattern of the O-C diagram (see Table 60 and the upper panel of Figure
36) shows a continuously increasing period:

    P = 6.637005d + 7.2d*10^-8*E                 (48)
       +-.000005   +-.6

where the E epoch number has to be calculated from the zero-point indicated
in equation (47). A check on the presence of a possible light-time effect
was also performed, and there is weak evidence for an approximately 4550
day orbital period (using only the photoelectric O-C residuals). Although
this value is consistent with the tendency of the gamma-velocity changes, a
completely different orbital period cannot be ruled out.



V350 Sagittarii


   Its spectroscopic binary nature was suspected by Lloyd Evans (1971),
later on confirmed by Gieren (1982), and Lloyd Evans [1982). The orbital
period was determined recently (Szabados, 1989), and its value is 1129
days.
   The O-C residuals listed in Table 61 have been computed with the
ephemeris:

      C = 2435317.170 + 5.154178d*E            (49)
               +-.020  +-.000012

The O-C diagram in Figure 37 offers two obvious approximations: a phase
jump, or a parabolic O-C graph. Equation (49) has been obtained assuming
that the first approximation is correct. In this case the former value of
the pulsation period was 5.154139 +- 1.9*10^-5 days. The 0.06 day phase jump


                  Table 61. O-C residuals for V350 Sgr

Norm.max.     E          O-C    Type,  Reference
JD2400000+                      weight

25560.345   -1893       +0.034d pg     Voute (1930c)
26106.715   -1787       +0.061  pg     Voute (1930c)
33075.072   - 435       -0.031  pe 1   Eggen (1951)
34940.902   - 73        -0.013  pe 2   Walraven et al. (1958)
35306.827   - 2         -0.035  pe 2   Irwin (1961)
37244.780   + 374       -0.053  pe 2   Mitchell et al. (1964)
40373.404   + 981       -0.015  pe 1   Stobie (1970)
40435.281   + 993       +0.012  pe 1   Feltz and McNamara (1980)
41136.257   +1129       +0.020  pe 1   Feltz and McNamara (1980)
42883.488   +1468       -0.015  pe 1   Dean (1977)
44373.048   +1757       -0.013  pe 2   Moffett and Barnes (1984)
44414.287   +1765       -0.007  pe 3   Gieren (1981b)
44888.487   +1857       +0.008  pe 2   Moffett and Barnes (1984)
44919.423   +1863       +0.019  pe 2   Eggen (1985)



                 
                 Figure 37. O-C diagram of V350 Sgr



occurred between J.D.2437500 and 2440000. If, however, the continuous
period increase interpretation is accepted, the pulsation period can be
calculated as follows:

       P = 5.154168d + 3.04d*10^-8*E            (50)
          +-.000004   +-.58

where the E epoch number has to be calculated according to equation (49).
Additional observations are necessary to decide which of the above
interpretations is the correct one.



RV Scorpii


   Moffett and Barnes (1987) found almost 6 km/s discrepancy between their
own and the previous gamma-velocity determinations. The variable gamma-velocity
is also seen in the present study (see Table 62  and the lower panel of
Figure 38).
   The O-C residuals have been computed with the elements:

       C = 2434925.379 + 6.061352d*E              (51)
                +-.009  +-.000004

The whole data set (see Table 63) can be well approximated by a parabola,


                   Table 62. gamma-velocities of RV Sco

JD         sigma      v gamma  sigma     n   Reference
2400000+   [d]         [km/s]  [km/s]

18433       15         -23.0    1.2      7   Paddock (1917)
25104      238         -17.7    1.8      7   Joy (1937)
25983      338         -20.9    2.3      5   Joy (1937)
33942      145         -18.8    0.8     15   Stibbs (1955)
40530      213         -21.6    0.2      7   Lloyd Evans (1980)
44055        9         -13.0    1.6      7   Barnes et al. (1988)
44423        4         -18.9    0.4     24   Gieren (1981a)
44456       18         - 7.5    2.0      5   Barnes et al. (1988)
44798        1         -14.4    2.8      3   Barnes et al. (1988)


                 Table 63. O-C residuals for RV Sco

Norm.max.     E           O-C    Type,    Reference
JD2400000+                       weight

14474.195    -3374       -0.181d vis 1    Pickering (1904)
16274.495    -3077       -0.103  pg 1     Shapley (1930)
18141.361    -2769       -0.133  pg 1     Shapley (1930)
19638.618    -2522       -0.030  pg 1     Shapley (1930)
20753.897    -2338       -0.040  pg 1     Shapley (1930)
23196.583    -1935       -0.079  pg 1     Shapley (1930)
24342.277    -1746       +0.020  pg 1     Shapley (1930)
24711.873    -1685       -0.127  pg 1     Voute (1927c)
25075.607    -1625       -0.074  pg 1     Voute (1927c)
34901.138    - 4         +0.005  pe 1     Walraven et al. (1958)
35240.579    + 52        +0.011  pe 3     Irwin (1961)
37277.192    + 388       +0.009  pe 1     Mitchell et al. (1964)
40344.212    + 894       -0.015  pe 3     Stobie (1970)
40780.652    + 966       +0.008  pe 3     Pel (1976)
41574.662    +1097       -0.019  pe 3     Dean et al. (1977)
41950.453    +1159       -0.032  pe 3     Dean et al. (1977)
43538.527    +1421       -0.032  pe 3     Dean (1981)
44023.428    +1501       -0.039  pe 3     Gieren (1981b)
44247.691    +1538       -0.046  pe 3     Moffett and Barnes (1984)
44835.688    +1635        0.000  pe 2     Eggen (1985)



         
         Figure 38. Upper panel: O-C diagram of RV Sco
                    Lower panel: gamma-velocities for the same Cepheid


corresponding to a continuously decreasing period:

      P = 6.061352d - 2.75*10^-8*E               (52)
         +-.000004   +-.54

where the E epoch number is calculated according to equation (51). The O-C
residuals based on the photoelectric observations made after J.D.2440000
seem to form a part of a wave superimposed on the parabola, indicating a
possible light-time effect. Assuming an orbital period of about 8000 days,
this interpretation is in agreement with the trend of the gamma-velocity
variations (see Figure 38). Further observations are needed before carrying
out a more thorough analysis.



RY Scorpii


  RY Sco is a member of a visual triple star system (Proust et al.,
1981). The faint companions may or may not influence the photometric
behaviour of this Cepheid. A blue photometric companion was reported by
Madore (1977) and Pel (1978) but Bohm-Vitense and Proffitt (1985) failed to
find any evidence for a blue companion using IUE spectra. The available
spectroscopic data do not allow to draw any conclusion regarding the
variation in the gamma-velocity (see Table 64).


                 Table 64. gamma-velocities of RY Sco

JD      sigma v gamma sigma  n   Reference
2400000+ [d]   [km/s] [km/s]

22868     1   -17.7   4.5    1   Joy (1937)
25515   270   -17.2   1.8    7   Joy (1937)
27034   315   -17.2   4.5    2   Joy (1937)
33934    94   -19.3   1.0   10   Stibbs (1955)
40579   242   -20.5   0.3    4   Lloyd Evans (1980)
44123   158   -15.4   1.8    6   Barnes et al. (1988)
44250   198   -17.8   0.2   18   Coulson and Caldwell (1985)
44785   149   -17.6   0.3   17   Coulson and Caldwell (1985)


                Table 65. O-C residuals for RY Sco

Norm.max.     E         O-C    Type,  Reference
JD2400000+                     weight

16415.032   -583       +8.149d pg     Shapley (1930)
17938.584   -508       +7.690  pg     Shapley (1930)
19563.398   -428       +6.893  pg     Shapley (1930)
20762.244   -369       +6.850  pg     Shapley (1930)
23281.083   -245       +5.991  pg     Shapley (1930)
24439.079   -188       +5.739  pg     Shapley (1930)
25047.825   -158       +4.881  pg     Wallenquist (1928)
26673.167   - 78       +4.611  pg     Wallenquist (1928)
31019.120   +136       +2.053  pg     Filatov (1966)
33335.314   +250       +1.751  pg     Filatov (1966)
35244.432   +344       +0.775  pe 2   Irwin (1961)
35244.615   +344       +0.958  pg     Filatov (1966)
35487.784   +356       +0.286  pe 1   Mitchell et al. (1964)
38251.601   +492       +0.563  pg     Filatov (1966)
40343.964   +595       -0.049  pe 3   Stobie (1970)
41075.606   +631       +0.068  pe 3   Pel (1976)
41908.631   +672       -0.033  pe 1   Madore (1975)
44062.665   +778       +0.066  pe 1   Moffett and Barnes (1984)
44326.737   +791       -0.024  pe 3   Coulson and Caldwell (1985)
44529.910   +801       -0.052  pe 2   Moffett and Barnes (1984)
44875.432   +818       +0.027  pe 3   Coulson and Caldwell (1985)



            
            Figure 39. O-C diagram of RY Sco


   The O-C residuals listed in Table 65 have been calculated with the
elements:

       C = 2428253.527 + 20.320144d*E                    (53)
                +-.101   +-.000139

Figure 39 shows that the above elements are only valid after J.D.2440000.
Before that epoch the pulsation period cannot be characterized by a single
value.



V500 Scorpii


   The discrepancy  between the gamma-velocities reported by Moffett and
Barnes (1987) is confirmed here (see Table 66 and the lower panel of
Figure 40). Madore (1977) assumed a blue photometric companion. Such a
companion is not suspected on the basis of Pel's (1978) photometry, nor in


              Table 66. gamma-velocities of V500 Sco

JD           sigma  v gamma  sigma   n  Reference
2400000+      [d]    [km/s]  [km/s]

34182          37    -14.0    0.9   12  Stibbs (1955)
44359         343     -7.4    1.3   10  Barnes et al. (1988)


              Table 67. O-C residuals for V500 Sco

Norm.max      E           O-C    Type,    Reference
JD2400000+                       weight

34729.921    -1038       -0.038d pe 1     Walraven et al. (1958)
35251.730    - 982       +0.028  pe 3     Irwin (1961)
37282.750    - 764       -0.023  pe 2     Mitchell et al. (1964)
37869.731    - 701       -0.003  pe 3     Walraven et al. (1964)
44335.597    - 7         -0.023  pe 3     Moffett and Barnes (1984)
44782.853    + 41        +0.025  pe 3     Eggen (1985)


       
       Figure 40. Upper panel: O-C diagram of V500 Sco
                  Lower panel: gamma-velocities for the same Cepheid


the study of an IUE spectrum obtained by Bohm-Vitense and Proffitt (1985).
The O-C residuals listed in Table 67 have been computed with the
elements:

       C = 2444400.838 + 9.316839d*E               (54)
                +-.010  +-.000015

The O-C diagram (in the upper panel of Figure 40) simply shows a constant
period.



V636 Scorpii


  This Cepheid belongs to a spectroscopic binary system with an orbital
period of 1318 days (Lloyd Evans, 1971). The blue companion has been
discovered in an IUE study (Bohm-Vitense and Proffitt, 1985).


                  Table 68. O-C residuals for V636 Sco

Norm.max.      E          O-C    Type,    Reference
JD2400000+                       weight

34743.483     -827       +0.064d pe 2     Walraven et al. (1958)
35232.792     -755       -0.001  pe 3     Irwin (1961)
37849.532     -370       -0.051  pe 3     Walraven et al. (1964)
40350.817     - 2        -0.010  pe 2     Stobie (1970)
42852.033     +366       -0.038  pe 2     Dean (1977)
44456.179     +602       +0.049  pe 2     Eggen (1985)
45020.306     +685       +0.037  pe 1     Eggen (1985)
45706.740     +786       -0.012  pe 1     Eggen (1985)



              
              Figure 41. O-C diagram of V636 Sco


   The O-C residuals listed in Table 68 have been calculated with the
elements:

       C = 2440364.421 + 6.796859d*E                    (55)
                +-.011  +-.000018

The O-C diagram plotted in Figure 41 has been approximated by a straight
line. According to equation (1) no detectable light-time effect is
expected.



Y Scuti


  The variable gamma-velocity of Y Scuti was first noticed by Moffett and
Barnes (1987). Their conclusion is confirmed here (see Table 69 and the
lower panel of Figure 42). The orbital period can be as long as several
thousand days because the radial velocity data obtained by Barnes et al.
(1988) cover three consecutive years, and no obvious change in the
gamma-velocity is seen in their data.
  The O-C residuals have been calculated with the elements:

      C = 2434947.209 + 10.341483d*E           (56)
               +-.007   +-.000008

Photographic observations were also taken into account in the fitting
procedure. The O-C graph can be best represented by a straight line (see
Table 70 and the upper panel of Figure 42). The number of the O-C residuals


                       Table 69. gamma-velocities of Y Sct

JD         sigma   v gammma      sigma   n   Reference
2400000+    [d]     [km/s]       [km/s]

25362      371      12.0          2.6    4   Joy (1937)
28080      425       3.5          2.0    6   Joy (1937)
44521      339      18.5          1.3   11   Barnes et al. (1988)


                Table 70. O-C residuals for Y Sct

Norm.max.    E           O-C    Type,  Reference
JD2400000+                      weight

16342.813   -1799       -0.068d pg 1   Shapley (1930)
18028.602   -1636       +0.059  pg 1   Shapley (1930)
19631.411   -1481       -0.062  pg 1   Shapley (1930)
21337.791   -1316       -0.026  pg 1   Shapley (1930)
23220.027   -1134       +0.060  pg 1   Shapley (1930)
24347.261   -1025       +0.072  pg 1   Shapley (1930)
29869.583   - 491       +0.042  pg 1   Filin (1950a), Solov'yov (1956)
31317.362   - 351       +0.014  pg 1   Filin (1950a), Solov'yov (1956)
32610.015   - 226       -0.019  pg 1   Filin (1950a), Solov'yov (1956)
33106.422   - 178       -0.003  pg 1   Filin (1950a)
33178.761   - 171       -0.054  pg 1   Solov'yov (1956)
34833.443   - 11        -0.010  pe 1   Walraven et al. (1958)
36767.263   + 176       -0.047  pe 2   Weaver et al. (1961)
37491.251   + 246       +0.037  pe 2   Ponsen and Oosterhoff (1966)
40841.857   + 570       +0.003  pe 3   Pel (1976)
44285.578   + 903       +0.010  pe 3   Moffett and Barnes (1984)
44947.444   + 967       +0.021  pe 3   Moffett and Barnes (1984)
45495.492   +1020       -0.030  pe 1   Berdnikov (1986) '
45878.138   +1057       -0.019  pe 3   Berdnikov (1986)




          
          Figure 42. Upper panel: O-C diagram of Y Sct
                     Lower panel: gamma-velocities for the same Cepheid


obtained from photoelectric observations is not enough to reveal the
light-time effect expected in this case.




R Trianguli Australis


   Its spectroscopic binary nature was already suspected by Gieren (1982).
His conclusion is confirmed here (see Table 71 and the lower panel of
Figure 43). It has to be noted that the gamma-velocity obtained from Paddock's


                Table 71. gamma-velocities of R TrA

JD         sigma  v gamma     sigma   n   Reference
2400000+    [d]    [km/s]     [km/s]

18432       24    -16.4        0.9   13   Paddock (1917)
33849       23    - 7.5        1.1    8   Stibbs (1955)
34172       44    -10.2        1.2    7   Stibbs (1955)
39265       36    -14.9        0.8    6   Lloyd Evans (1968)
40364       28    -12.9        0.3    4   Lloyd Evans (1980)
40792       12    -14.1        0.3    4   Lloyd Evans (1980)
44423        4    -13.1        0.4   26   Gieren (1981a)


                Table 72. O-C residuals for R TrA

Norm.max.     E           O-C    Type,    Reference
JD2400000+                       weight

16259.101    -7252       +0.032d pg 1     Shapley (1930)
18119.820    -6703       +0.033  pg 1     Shapley (1930)
20278.701    -6066       -0.062  pg 1     Shapley (1930)
21648.047    -5662       +0.012  pg 1     Shapley (1930)
23810.290    -5024       -0.110  pg 1     Shapley (1930)
25728.752    -4458       +0.015  pg 1     Dartayet et al. (1949)
34920.515    -1746       +0.032  pe 1     Walraven et al. (1958)
35201.826    -1663       +0.032  pe 3     Irwin (1961)
40339.938    - 147       -0.015  pe 1     Stobie (1970)
40770.398    - 20        +0.006  pe 3     Pel (1976)
42410.823    + 464       +0.016  pe 3     Dean et al. (1977)
43234.389    + 707       -0.015  pe 3     Dean (1981)
44417.257    +1056       -0.008  pe 3     Dean (1981)
44681.614    +1134       -0.015  pe 3     Eggen (1985)



     
     Figure 43. Upper panel: O-C diagram of R TrA
                Lower panel: gamma-velocities for the same Cepheid


(1917) observations still has the most negative value, although a +4 km/s
correction has been applied to his data as discussed in the Introduction.
   The O-C residuals have been calculated with the ephemeris:

       C = 2440838.178 + 3.389287d*E                   (57)
                +-.007  +-.000002

The O-C residuals listed in Table 72 and shown plotted in the upper panel
of Figure 43 suggest an orbital period of about 3500 days, if the wave-like
pattern of the photoelectric O-C residuals is caused by a light-time
effect. This value is in accord with the gamma-velocity variations but further
photometric and spectroscopic observations are necessary to confirm that
the above hypothesis is correct.



S Trianguli Australis


   The variability of the gamma-velocity may or may not be real (see Table 73
and the lower panel of Figure 44). Gieren (1982) also noticed these changes
but the question on the spectroscopic binary nature of S TrA is still open.


                  Table 73. gamma-velocities of S TrA

JD        sigma  v gamma  sigma    n   Reference
2400000+   [d]    [km/s]  [km/s]

18416       12      2.0     0.8    7   Campbell and Moore (1928)
20680        2      3.5     2.0    2   Campbell and Moore (1928)
33855       23      8.1     1.1    8   Stibbs (1955)
34173       38      5.0     1.1    8   Stibbs (1955)
39265       36      2.2     1.0    S   Lloyd Evans (1968)
40554      202      3.6     0.4    3   Lloyd Evans (1980)
44423        4      4.3     0.4   23   Gieren (1981a)


                  Table 74. O-C residuals for S TrA

Norm.max.     E           O-C    Type,    Reference
JD2400000+                       weight

15895.762    -3928       -0.053d pg 1     Shapley (1930)
17995.176    -3596       -0.030  pg 1     Shapley (1930)
20277.932    -3235       -0.045  pg 1     Shapley (1930)
21745.045    -3003       +0.024  pg 1     Shapley (1930)
24027.839    -2642       +0.048  pg 1     Shapley (1930)
25482.306    -2412       +0.118  pg 1     Dartayet et al. (1949)
25798.453    -2362       +0.091  pg 1     Dartayet et al. (1949)
34575.331    - 974        0.000  pe 3     Walraven et al. (1958)
35207.668    - 874       -0.010  pe 3     Irwin (1961)
37092.091    - 576       +0.021  pe 1     Eggen (1961)
40342.320    - 62        -0.011  pe 3     Stobie (1970)
40753.357    + 3          0.000  pe 3     Pel (1976)
41518.515    + 124       +0.019  pe 2     Dean et al. (1977)
42176.137    + 228       +0.001  pe 3     Dean et al. (1977)
42555.556    + 288       +0.012  pe 3     Dean et al. (1977)
43605.266    + 454       +0.027  pe 1     Eggen (1985)
43681.122    + 466       +0.001  pe 1     Dean (1981)
44420.971    + 583       +0.005  pe 3     Gieren (1981b)
44642.260    + 618       -0.027  pe 3     Eggen (1985)



         
         Figure 44. Upper panel: O-C diagram of S TrA
                    Lower panel: gamma-velocities for the same Cepheid


The O-C residuals have been computed with the elements:

       C = 2440734.386 + 6.323465d*E                   (58)
                 +-.003 +-.000005

As one can see in the upper panel of Figure 44 (based on the data listed in
Table 74), a period change occurred between J.D.2426000 and 2434500. The
former value of the pulsation period was 6.323570 + 1.8*10^-5 days.



T Velorum


   Gieren (1985) suspects the presence of a red companion on the basis of
the amplitude of the light variation in different colours. The gamma-velocity
study performed here (see Table 75 and the lower panel of Figure 45) is
still inconclusive as far as variability in the gamma-velocity is concerned.


   The O-C residuals have been calculated with the elements:

       C = 2440713.286 + 4.639819d*E             (59)
                +-.004  +-.000004


                   Table 75. gamma-velocities of T Vel

JD        sigma  v gamma  sigma   n   Reference
2400000+   [d]    [km/s]  [km/s]

34063      53      8.6     0.7   20   Stibbs (1955)
40473     190      6.3     0.3    5   Lloyd Evans (1980)
45042       2      5.2     0.5   20   Gieren (1985)


                Table 76. O-C residuals for T Vel

Norm.max    E           O-C    Type,    Reference
JD2400000+                     weight

18201.069  -4852       +0.185d pg       Hertzsprung (1937)
26302.088  -3106       +0.080  pg       Hertzsprung (1937)
33786.067  -1493       +0.031  pe 1     Eggen et al. (1957)
34741.844  -1287       +0.005  pe 1     Walraven et al. (1958)
34843.895  -1265       -0.020  pe 2     Eggen et al. (1957)
35205.814  -1187       -0.007  pe 2     Irwin (1961)
40745.774  + 7         +0.009  pe 3     Pel (1976)
41803.658  + 235       +0.015  pe 3     Dean et al. (1977)
42555.282  + 397       -0.012  pe 3     Dean et al. (1977)
44299.894  + 773       +0.028  pe 3     Eggen (1985)
44800.940  + 881       -0.027  pe 2     Eggen (1985)
45052.229  + 933       -0.008  pe 3     Gieren (1985)


              
              Figure 45. Upper panel: O-C diagram of T Vel
                         Lower panel: gamma-velocities for the same Cepheid



   The O-C residuals listed in Table 76 and shown plotted in the upper panel
of Figure 45 show constancy of the period, at least in the photoelectric
era. Hertzsprung's (1937) observations suggest that the pulsation period of
T Vel is increasing. Further observations will decide whether a parabolic
fit is better. Similarly to AT Pup, Gieren's (1985) observations made in
1981 have not been taken into account (see the remarks on AT Pup).



V Velorum


  Pel (1978) suspects a blue photometric companion to this Cepheid.
Variability of the gamma-velocity is suspected here (see Table 77 and the
lower panel of Figure 46).


                      Table 77. gamma-velocities of V Vel

JD       sigma  v gamma   sigma   n   Reference
2400000+   [d]   [km/s]   [km/s]

34092      45   -29.0     0.8    17   Stibbs (1955)
39245      40   -30.7     1.1     4   Lloyd Evans (1968)
40381      23   -29.4     0.3     4   Lloyd Evans (1980)
40690      57   -27.5     0.3     6   Lloyd Evans (1980)
45042       2   -26.3     0.4    21   Gieren (1985)


                   Table 78. O-C residuals for V Vel

Norm.max.     E           O-C    Type,    Reference
JD2400000+                       weight

34809.091    -1356       +0.001d pe 2     Walraven et al. (1958)
35233.090    -1259       +0.009  pe 2     Irwin (1961)
40268.520    - 107       -0.002  pe 3     Stobie (1970)
40766.834    + 7         +0.013  pe 3     Pel (1976)
41789.624    + 241       -0.021  pe 3     Dean et al. (1977)
42585.158    + 423       -0.017  pe 3     Dean et al. (1977)
44412.289    + 841       +0.018  pe 3     Eggen (1985)
45037.336    + 984       +0.006  pe 3     Gieren (1985)




       
       Figure 46. Upper panel: O-C diagram of V Vel
                  Lower panel: gamma-velocities for the same Cepheid


    The O-C residuals have been calculated with the elements:

       C = 2440736.224 + 4.371043d*E             (60)
                +-.003  +-.000006

These elements have been obtained by a linear least squares fit to the O-C
residuals listed in Table 78. The upper panel of Figure 46, however, shows
that a light-time effect interpretation of these data is also possible.
Assuming an orbital period of about 7500 days, the gamma-velocity variations
are properly phased with respect to the O-C wave. Similarly to AT Pup and T
Vel, Gieren's (1985) photometric observations obtained in 1981 have not
been taken into account here (see the remark on AT Pup).



AH Velorum


   AH Vel belongs to a binary system based on both photometric (Gieren,
1980b) and spectroscopic (Lloyd Evans, 1968 and 1982, and Gieren, 1980a)
criteria. The orbital period cannot be determined yet. The individual
gamma-velocities are listed in Table 79 and shown plotted in the lower panel of
Figure 47.
   The O-C residuals have been calculated with the elements:

       C = 2442035.703 + 4.227231d*E                    (61)
                +-.007  +-.000007


                Table 79. gamma-velocities of AH Vel

JD       sigma  v gamma  sigma   n   Reference
2400000+  [d]    [km/s]  [km/s]

33979     22     25.8     0.7   18   Stibbs (1955)
34108     38     28.5     1.3    6   Stibbs (1955)
39230     44     22.5     0.8    6   Lloyd Evans (1968)
39643     72     21.3     0.8    7   Lloyd Evans (1968)
39899     30     23.0     0.2    8   Lloyd Evans (1980)
40300     54     23.2     0.2   12   Lloyd Evans (1980)
40653     49     21.0     0.2    9   Lloyd Evans (1980)
42036      7     24.5     0.3   37   Gieren (1977)


                Table 80. O-C residuals for AH Vel

Norm.max.     E           O-C    Type,  Reference
JD2400000+                       weight

33889.864    -1927       +0.035d pe 2   Eggen et al. (1957)
34824.060    -1706       +0.013  pe 1   Walraven et al. (1958)
35.187.584   -1620       -0.005  pe 3   Irwin (1961)
40256.017    - 421       -0.022  pe 3   Stobie (1970)
40725.254    - 310       -0.007  pe 3   Pel (1976)
41765.136     - 64       -0.024  pe 3   Dean et al. (1977)
42035.677        0       -0.026  pe 3   Gieren (1980a)
43895.726    + 440       +0.041  pe 1   Eggen (1980)
44681.992    + 626       +0.042  pe 3   Eggen (1983a)




          
          Figure 47. Upper panel: O-C diagram of AH Vel
                     Lower panel: gamma-velocities for the same Cepheid



Although a constant period is assumed here (see the upper panel of Figure
47 and Table 80), neither a parabolic O-C graph, nor a light-time effect
with a very long orbital period can be excluded. Further photometric and
radial velocity observations are needed as for most of the previously
discussed Cepheids.




                          GENERAL REMARKS



   Because the sample of Cepheids studied here is inhomogeneous and is not
large enough, any statistics concerning the period changes, including a
comparison with previous results, may lead to false conclusions. It is,
however, important to note that all kinds of period changes known from
earlier studies are observed here, too. Particularly important among them
are: the continuous period increase or decrease (due to stellar evolution),
the wave-like pattern of the O-C graph (due to the light-time effect in
binary systems), and the phase jump (return to an earlier value of the
pulsation period). This latter kind of period change also occurs in binary
Cepheids.
   Table 81 summarizes the results on the period changes and variability
of the gamma-velocity of the Cepheids studied here. Because the normal maxima
published in the GCVS (Kholopov et al., 1985-1987) were only modified in
the discussion on the individual variables instead of transferring them to
a more recent epoch, it is worthwhile to give the actual values of the
normal maximum and the pulsation period valid for e.g. J.D.2445000, taking
into account the period variations when necessary. The successive columns
of Table 81 give the following data:

1. Name of the Cepheid
2. Moment of the normal maximum just following J.D.2445000
3. Pulsation period at J.D.2445000
4. Characteristic features in the O-C diagram (~: light-time effect, -:
   decreasing period, +: increasing period)
5. Variability in the gamma-velocity
6. Value of the orbital period
7. Reference to the paper where the value cited in the previous column has
   been published.
   
   There are four stars in this sample for which the catalogued value of
the pulsation period needs a considerable correction: YZ Car, AZ Cen, KN
Cen, and GH Lup. In addition, the starting epoch needs a big correction in
the case of SY Nor.
   Light-time effect has been discovered in the O-C diagram of V496 Aql,
AX Cir, AG Cru, BG Cru (uncertain), BF Oph, AP Pup, AT Pup, Y Sgr, AP Sgr,
R TrA, and V Vel. A preliminary value of the orbital period has been
suggested on the basis of the light-time effect and/or the variations in
the gamma-velocity for the following Cepheids: V496 Aql, AX Cir, AG Cru, Y
Oph, BF Oph, AP Pup, AT Pup, U Sgr, Y Sgr, AP Sgr, BB Sgr, RV Sco, R TrA,
and V Vel. A phase jump is revealed in the O-C diagram of U Aql, YZ Car, KN
Cen, S Mus, S Nor, Y Oph, U Sgr, and V350 Sgr. If an O-C diagram can be
equally well represented by a phase jump or a constant period of another
value, the phase jump interpretation is preferred here. This more or less
provocative step may encourage others to observe these stars
photometrically. Similarly, some of the orbital periods, and even the
variation in the gamma-velocity assumed for a particular Cepheid variable can
be doubted. In any case, more regular photometric and radial velocity
observations would be desirable on each Cepheid studied here.
Even if some of the orbital periods suggested in Table 81 is not well
determined, the half of the programme stars belongs to spectroscopic binary
systems. Keeping in mind that the spectroscopic binaries can only be
revealed in favourable cases (depending on the value of the orbital
inclination), and that the binary nature can also be discovered on the


         Table 81. Summary on the periods, period changes, and duplicity

Cepheid     Norm.max.           P         O-C diagram                v gamma      Porb     Source
            JD2400000+                                                            [gay]

U Aql       45001.780           7.023958d linear with phase jump     variable     1856.4   Welch et al. (1987)
V496 Aql    45002.397           6.807055  linear ~                   variable     1780n   present paper
V Car       45001.101           6.696672  linear                     variable
YZ Car      45007.131          18.165573  linear with phase jump     variable   ~ 850      Coulson (1983)
l Car       45002.391          35.551341  two linear sections        constant
V Cen       45000.289           5.493861  two linear sections        variable ?
XX Cen      45010.493          10.953370  parabolic ( - )            variable     909.4    Szabados (1989)
AZ Cen      45001.112           3.211981  parabolic ( - )            variable ?
KN Cen      45021.656          34.029641  linear with phase jump     variable
AX Cir      45001.903           5.273306  linear ~                   variable   ~ 4600     present paper
S Cru       45000.251           4.689596  parabolic ( - )            constant
T Cru       45004.630           6.733196  linear                     variable
AG Cru      45000.710           3.837254  linear ~                   variable   ~ 6350     present paper
BG Cru      45003.271           3.342720  linear ~:                  variable
Beta Dor    45009.560           9.842425  linear                     constant
GH Lup      45003.355           9.277948  linear :                   variable
R Mus       45001.446           7.510467  parabolic ( + )            variable
S Mus       45003.522           9.659875  linear with phase jump     variable     506      Lloyd Evans (1971)
S Nor       45004.063           9.754244  linear with phase jump     variable
RS Nor      45002.060           6.198136  linear                     not observed!
SY Nor      45005.992          12.645687  linear                     one series only
Y Oph       45008.372          17.126908  linear with phase jumps    variable     1222.5   present paper


                                     Table 81. (cont.)

Cepheid     Norm.max.           P         O-C diagram                v gamma      Porb     Source
            JD2400000+                                                            [day]

BF Oph      45000.515           4.067510d parabolic ~ ( - )          variable   ~ 4500     present paper
AP Pup      45000.597           5.084274  linear ~                   variable   ~ 10000    present paper
AT Pup      45006.629           6.664879  linear ~                   variable   ~ 20000    present paper
MY Pup      45001.729           5.695309  parabolic ( + )            constant
U Sgr       45004.675           6.745229  linear with phase jump     variable     4550     present paper
W Sgr       45007.526           7.594904  linear                     variable     1780     Babel et al. (1989)
X Sgr       45005.293           7.012877  parabolic ( + )            variable     507.25   Szabados (1989)
Y Sgr       45005.763           5.773380  linear ~                   variable  >= 10000:   present paper
WZ Sgr      45011.333          21.849789  linear + earlier changes   variable ?
AP Sgr      45003.097           5.057916  linear ~                   variable   ~ 7500     present paper
BB Sgr      45000.224           6.637102  parabolic ( + )            variable   ~ 4550 ?   present paper
V350 Sgr    45002.267           5.154178  linear with phase jump     variable     1129     Szabados (1989)
RV Sco      45005.369           6.061306  parabolic ( - )            variable   ~ 8000 ?   present paper
RY Sco      45017.646          20.320144  linear with period change  variable ?
V500 Sco    45006.433           9.316839  linear                     variable
V636 Sco    45006.676           6.796859  linear                     variable     1318     Lloyd Evans (1971)
Y Sct       45009.472          10.341483  linear                     variable
R TrA       45000.222           3.389287  linear ~                   variable   ~ 3500     present paper
S TrA       45002.725           6.323465  linear with period change  variable ?
T Vel       45000.479           4.639819  linear                     constant
V Vel       45002.362           4.371043  linear ~                   variable   ~ 7500     present paper
AH Vel      45003.219           4.227231  linear                     variable


basis of a number of photometric methods not discussed here, the following
conclusion may not be an exaggeration: the frequency of Cepheid binaries is
higher than thought ever since these variables have been known as pulsating
stars.

  The author is grateful to Drs. M. Kun and B. Szeidl for their comments,
advice and encouragement during the various stages of this project. Thanks
are also due to Mr. A. Holl and Dr. K. Olah for computer-related advice,
and Mrs. I. Nemeth for preparing the figures.




Budapest - Szabadsaghegy, June 26, 1989.



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