COMMISSION 27 OF THE I. A. U.
         INFORMATION BULLETIN ON VARIABLE STARS
                      Number 1944

                                   Konkoly Observatory
                                   Budapest
                                   1981 March 31

                                   HU ISSN 0374-0676



THE SHOCK RADIATION EFFECT ON THE PULSATING VARIABLE STARS, LIGHT
                    AND COLOUR CURVES


   As is known several lines of spectroscopic evidence point to the
existence of shock fronts in the atmospheres of pulsating variable 
stars. The correlation between the maximum width of the
loop L_U-B in the U-B, B-V plane and strength of the hydrogen 
emission lines, which we revealed (Batyushkova and Erleksova,
1980), may be one more argument for the explanation of these
peculiarities using the shock model. The calculation of shock 
radiation is essential for the radius determination by Wesselink's
method. The task of removing of the excess radiation from the
light and colour curves must be solved before the Wesselink's
method may be used (Klimishin, 1972).
  We have calculated the excess radiation from the shock in
U,B,V-bands and the changes in colour indices Delta(U-B) and Delta(B-V)
because of this shock. The propagation of the shock has been 
regarded in the atmosphere of W Vir type star with a velocity
D=80km/sec, which is in accordance with the observable velocities 
on the level where tau= 0.1 and rho= 2.5 x 10^9g/cm^3. We have
supposed that the atmosphere consists of pure hydrogen and the
radiation is due to the free-bound and free-free transitions.
The necessary values of electron concentration and temperature
have been obtained from shock structure calculations by Whitney
and Skalafuris' (1963.) method. The numerical results indicate
that the shock wave has no effect on the colour index B-V within 
0.01m and the relation between the amount of the V-band radiation 
and Delta(U-B) colour excess may be represented as
               DeltaV = 0.66Delta(U-B)        (1)                     
that is different from Abt's result for RR Lyr (Abt, 1959).
  Our results were applied to BL Her (P=1.31d). The normal light
curve was obtained by combination of Abt and Hardie's (1960) and
also Gavrilova and Kiselyov's (1979) observations. Then DeltaV was
calculated and the light curve was corrected on the radiation
from the shock (Fig.1) by using of the U-B, B-V diagram (Fig.2)
and supposing that the relation (1) is performed on all phases
of ascending branch of the light curve.

                       [FIGURE 1]

 Figure 1. The normal V, B-V, U-B light and colour curves
 of BL Her. The minimum value of the colour index U-B exactly
 corresponds to the phase of the hump on the ascending branch of
 the light curve. The dashed line represents the light curve
 corrected on the shock radiation effect.

                       [FIGURE 2]

 Figure 2.  The observed colours of BL Her as a function of
 phase. The letters M and m indicate the phases of maximum and
 minimum light, respectively. The maximum width of the loop corresponds
 to the phase of a hump on the ascending branch. The arrow
 points the trend in which the loop is described.


Further on the radius was calculated by Wesselink's method. The
radial velocity curve, which was presented by Abt and Hardie
(1960), was used. Taking into account the phase lag between the
light and radial velocity curves by Frolov's (1966) method, we
have received R= (4.99+-0.18)X10^6km for 14 phase pairs instead of
R=(6.7+-1.3)X10^6km with uncorrected light curve.
  As is seen the removing of the shock radiation effect from
the light and colour curves led us not only to a smaller mean radius,
but it decreased significantly the mean relative error of its
determination. We obtained the absolute magnitude of BL Her
M_V=-0.21m according to our value of radius, and this is in full
accord with the existing period-luminosity relations.
  It is proposed to publish the results of the work in the
Tajik Bulletin in more details.
  The author would like to thank Professor I.A. Klimishin for
continued encouragement and helpful discussion of the results
obtained.


                        B.N. BATYUSHKOVA
                  Astrophysical Institute of Tajik
                 Academy of Sciences, Dushanbe, USSR


References:

Abt, H., 1959, Ap.J., 130, 824. [BIBCODE 1959ApJ...130..824A ]
Abt, H., and Hardie, R., 1960, Ap.J., 131, 155. [BIBCODE 1960ApJ...131..155A ]
Batyushkova, B.N., and Erleksova, G.E., 1980. I.B.V.S., 1809.
Frolov, M.S., 1966, A.C., 274.
Gavrilova, I.I., and Kiselyov, N.N., 1979, Taj.Bull., 68, 42.
Klimishin, I.A., 1972, in "The shock waves in nonuniform media"
  University of Lvov Press.
Whitney, C., and Skalafuris, A., 1963, Ap.J., 138, 200. [BIBCODE 1963ApJ...138..200W ]