Non-Periodic Phenomena in Variable Stars
IAU Colloquium, Budapest, 1968
SOME REMARKS ON THE SPECTRAL AND LIGHT VARIABILITY
OF P CYGNI
L. LUUD
Estonian Academy of Sciences, Tartu
The unusual profiles of the spectral lines and its peculiar variability
make P Cygni one of the most interesting stars in the sky. This interest is
enhanced by the fact that each observational study adds as many problems
as it resolves.
P Cygni was observed spectroscopically at the Tartu Observatory during
the years 1961 to 1963. 44 spectrograms secured with a one-prism spectrograph
giving dispersion 160 A/mm at H_gamma were used to determine spectrophotometric
gradients in the Greenwich system. The gradients show according to the sequential
test no variations exceeding the accuracy of measurement. In Table 1 the mean
absolute gradients for different years are given. It must be mentioned that
Dolidze (1958) found variations of the spectrophotometric gradient, but
the spectral range used by her was smaller.
Table 1
Observations, year Greenwich 1961 1962 1963
Catalogue
Gradient 1.03 +-0.02 1.02+-0.04 1.00+-0.04 1.03+-0.07
For spectral line investigations 32 spectrograms with dispersions from
1.5 A/mm to 36 A/mm were taken at the Crimean Astrophysical Observatory
in 1964-1966, every year during some weeks. On the spectrograms obtained
in the same year the differences in spectral line contours do not exceed the
accuracy of measurement. The mean contours determined by spectrograms taken
in different years differed systematically (Fig. 1). The detailed review
of spectral line contours is given in the Publications of Tartu Observatory
(Luud et al. 1968).
The Balmer decrements observed are in good agreement with the calculations
by A. Boyarchuk (1966), if we assume that T_e = 10000 deg, T* = 20000 deg
and W = 10^-2. The probabilities for the exit of L_alpha-quanta (beta_12)
are given in Table 2.
Supposing that in a rough approximation the P Cygni-type contours can be
divided into components as shown in Fig. 2, we should be able to carry
out the coarse analysis of the P Cyg atmosphere. From the curve-of-growth
analysis we get the data given in Table 2.
Table 2
Year log n_e log N_2H tau_H_beta beta_12 V_T T_i
1964 12.36 15.98 30 2.5*10^-4 23 19400 deg
1965 12.26 15.68 21 5*10^-4 40 21800 deg
1966 12.80: 15.37 12 1*10^-3 24 21400 deg
Fig. 1
Fig. 2
From more extended data published in our (Luud 1967a, b) papers we
concluded that spectral variations are due mainly to variable amount of atoms
in the volume in which the spectrum is formed. The variations of physical
conditions seem to have less effect.
If we assume that the luminosity of P Cyg is M_v= -8 and T* = 29000 deg
(Luud 1967 b, c) then we get for the photosphere R* = 62 R_sun. From the
formula
Delta M = 4piR^2rho(R)V(R)dt
we obtain, assuming rho(R*) = n_e m_H, n_e = 10^12 cm^-3 and V (R*)~~150 km/sec,
that the mass loss of P Cygni is 9*10^-5 M_sun/year. The result Delta M = 2*10^-6
M_sun/year for giant B stars (Jenkins and Morton, 1967) suggests that this
may be a real value.
The mass of the atmosphere can be checked by the formula
M_atm = N_+ H*4piR^2_atm*m_H
where N_+H are available from N_2H using the Boltzman and Saha equations.
From W = 10^-2 we get R_atm = 5 R*, and finally M_atm = 6*10^-6 M_sun.
These figures show that as a result of mass-loss atoms of the atmosphere
replace rapidly - during some tens of days. Therefore the spectral line
variations are probably due to the nonstationary outflow of matter.
It should be mentioned, that the variability of P Cygni spectral line
contours is described by a number of observers (Herman 1968; Lacroute,
1938; Wilson, 1936) No periodicity has been found.
The light variability of P Cygni was at first discovered in 1600. Here we
shall only provide some remarks about contemporary photoelectric observations
and will not touch earlier history of light variations.
The most extensive data are published by Magalashvili and Kharadze
(1956). By these and unpublished data they have found that P Cygni was
variable with a W UMa-type light curve and with a period of 0.500656d.
The observations published after the paper of the Georgian scientists do not
seem to confirm regular variability (Alexander and Wallerstein, 1967). Here
we shall briefly discuss these results.
According to the mass-luminosity relation by Paranego and Masjevic
(1951) the luminosity of P Cyg, M_v = -8^m, corresponds to 100 M_sun. If we
could detect the W UMa type eclipse, the secondary component would have
a brightness of M_v~~ -7^m and the minimum mass of 30 M_sun, if it is of the
spectral class A0. If we now assume that M_1 + M_2 = 100 M_sun, we get from
the orbital period a_1 + a_2 = 12 R_sun. Consequently the radii of the stars
turn out to be greater than their separation and the assumption of eclipsing
type variability must be dropped.
If P Cygni has very peculiar components and they are actually main sequence
stars with M_1 + M_2 = 30M_sun and M_1:M_2 = 2, the orbital velocity of the
primary should be 600 km/sec. If the light varies with Delta m = 0.1m, we
should have i >~ 45 deg and an observable radial velocity of 420 km/sec. Line
displacements of 14 A, that correspond to this velocity, had never been observed.
For example in Table 3 we give H_10 displacements from the spectra taken
in July 24/25 with a dispersion of 15 A/mm. If we had observed in the most
unfavourable time, the displacement would have a value of ~ 60 km/sec.
It follows that orbital movements are excluded.
Table 3
Time (UT) V_e V_a1 V_a2
20^h39^m -36 -142 -218
21^h00^m -36 -142 -224
21^h42^m -38 -141 -227
On Fig. 3 we plotted the published Abastumani observations with the
period 0.500656d. We see no serious arguments why this periodicity is not
valid. Near the phases 0.8-1.2 there is a very great scatter that seems to
suggest that P Cygni had at that time irregular light outbursts.
Fig. 3
There is a serious suggestion that the observations of the Georgian
scientists may be interpreted in another way. Schwarzschild and Harm (1959)
have shown that very massive stars must be pulsationally non-stable and must
have little light variations with periods of approximately half a day and
amplitudes near to 0.05m. Taking into account the possible differences of the
main structural parameters of P Cygni from those used in this stellar structure
calculations the agreement seems to be quite reasonable.
We may guess that in the case of P Cygni we have two kinds of irregular
variations generated respectively by non-stationary mass loss and by pulsational
instability.
To close our brief discussion, we must say that in spite of the quite
favourable brightness of P Cygni we have no systematic simultaneous photoelectric
and spectral observations of it, but this seems to be the only way for receiving
new important data on the subject treated above.
REFERENCES
Alexander, T., Wallerstein, G., 1967, Publ. astr. Soc. Pacific 79, 500.
Boyarchuk, A. A., 1966, Izv. Krym. astrofiz. Obs. 35, 45.
Dolidze, M. V., 1958, Abastumanski astrofiz. Obs. Gora Kanobili Bjull. No. 23. 69.
Herman, R., 1964, Ann. Astrophys. 27, 507.
Jenkins, E. B., Morton, D. C., 1967, Report on XIII IAU Gen. Assembly.
Lacroute, P., 1938, C. R. hebd. Seanc. Acad. Sci. Paris 206, 1091.
Luud, L., 1967a, Astron. Zu. 44, 267.
Luud, L., 1967b, Astrophysics, 3, 379.
Luud, L., 1967c, Publ. Estonian Acad. Sci. Phys. Math. 16, 319.
Luud, L., Poldmets, A., Leesmae, H., 1968, Tartu Publ. 36, in press.
Magalashvili, N. L., Kharadze, E. K., 1956, Abastumanski astrofiz. Obs. Gora Kanobili
Bjull. No. 20, 3.
Magalashvili, N. L., Kharadze, E. K., 1967, Astr. Cirk. Izdov bjuro astr. Soobsc. Kazan
No. 467; Inf. Bull. Var. Stars, No. 210.(IBVS N°.210)
Paranego, P. P., Masjevic, A. H., 1951, Publ. Sternberg astr. Inst. No. 20.
Schwarzschild, M., Harm, R., 1959, Astrophys. J., 129, 637.