COMMISSION 27 OF THE I. A. U.
                  INFORMATION BULLETIN ON VARIABLE STARS
                               Number 2471

                                                      Konkoly Observatory
                                                      Budapest
                                                      7 February 1984

                                                      HU ISSN 0374-0676



      POSSIBLE DISCOVERY OF REPEATING OSCILLATIONS IN THE BRIGHTNESS OF
                 BY DRACONIS ON TIMESCALES OF 1-3 HOURS


  Considerable attention is now paid in the physics of solar-late type stars
to study minutes-to-hours oscillations as probes of the internal structure
of stars. Notable in this respect are variations on such timescales of the
brightness (Rojzman, 1984) or the flux in emission lines (Baliunas et al.
1981, Linsky et al. 1982) which were observed in several red dwarf stars. Of
course, such variations may be connected with flares and may not be a manifestation
of oscillations. The task to select variations originating from stellar
oscillations is difficult especially because of scarcity of existing 
observational data of high accuracy. No attempts have been made to discover 
periodicities of the order of minutes or hours in red dwarf stars, except in
Baliunas et al. (1981).
  A program to search for and investigate small amplitude brightness variations
in the red dwarf flare star BY Dra has been carried out at the Crimean
Observatory. Observations were obtained with the 5-channel photoelectric
photometer installed on the 125-cm reflector. The photometer was constructed
and built at the Helsinki Observatory by V. Piirola. Spectral bands are close
to UBVRI. Following relations were obtained


            deltaV = deltav - 0.131 delta(b-v)
            deltaB = deltab + 0.062 delta(b-v)
            deltaU = deltau + 0.063 delta(u-b)
            deltaR = deltar
            deltaI = deltai - 0.236 delta(r-i)

where u,b,v,r,i, are instrumental extra-atmospheric magnitudes. All 5 magnitudes
are recorded simultaneously. The time interval between successive records
is 24 sec in our observations.
  Continuous observations of BY Dra were interrupted every 20-30 minutes in
order to observe the comparison star BD +51d2408. The magnitude differences
deltam between BY Dra and BD +51d2408 and air masses F(z) were computed for each



observation. Corrections for the differential extinction alpha delta F(z) were 
computed and added to deltam supposing that the extinction coefficient alpha does not
vary during the night. Values of alpha were obtained from observations of the
comparison star. Further uncertainties connected with variations of alpha will
be estimated.
  BY Dra and BD +51d2408 were observed for 5 nights. For one night we 
observed BD +51d2408 instead of BY Dra and BD +51d2410 as the comparison star.
In this last night continuous observations of BD +51d2408 were interrupted
every 20-30 minutes to observe BD +51d2410. The journal of observations is
given in Table I.

                                 Table I

Date, 1983      Observed      Comparison    Time of         Number of
                star          star          obs. U.T.       obs.

24-25 Febr.     BY Dra        BD +51d2408   23h45m-03h24m   476x5
14 March        BY Dra        BD +51d2408   0025-0246       300x5
19-20 Apr.      BY Dra        BD +51d2408   2045-0121       604x5
22-23 Apr.      BY Dra        BD +51d2408   1945-0131       691x5
23-24 Apr.      BY Dra        BD +51d2408   2000-01 30      616x5
17-18 Jun.      BD +5102408   BD +51d2410   1925-00 29      556x5

Obtained time series deltam for each night were analyzed by the method of
power spectra Fourier transforms. We used explicit formulae for the case of
unevenly spaced data (Ferraz Mello, 1977) (a description of such method is
also given in Deeming (1975)). It is supposed that the time series

                     f(t_1),f(t_2)...f(t_n)

                     f(t_j) =Delta m(t_j) - Delta m

                     summa f(t_j)=0
is such that

f(t) = y_1(t) + y_2(t) + ... + y_n(t) + x(t)

y(t) are periodical functions

y_1(t) = C_1 sin(2pi omega_1t + phi_1)

y_n (t) = C_n sin(2pi omega_nt + phi_n)

x(t) is a chance variable with a gaussian distribution, and omega is the frequency
related with the period P as omega = 1/P.

 The first step of computations is the determination of the coefficient of




spectral correlation


           S (omega) =I(omega)/summa f^2(t_j)

where I(omega) is the power. S(omega) is computed for a number of values of omega. Also
the semiamplitude C_1, the phase phi_1 and the frequency omega_1 are found of the
function y_1(t) which corresponds to the maximum of S(omega). For a given sample
and a given result S(omega) it is possible to conclude whether the periodicity is
significant or not.
  After one periodicity is found the filtered time series can be obtained
and the next step can be made i.e. computation of S'(omega) and values of C_2,
phi_2, omega_2 of the function y_2(t) corresponding to the maximum of S'(omega). This
process is going on until periodicities found become insignificant.
  Examples of power spectra corresponding to the first step are shown on
Figures 1,2. They are obtained from the U-band time series of BY Dra (23-24
Apr.) - Figure 1, and BD +51d2408 (17-18 Jun.) - Figure 2. The spectrum for
BY Dra displays rather high maxima in the interval 0<omega<2*10^-2 min^-1 . Much
lower maxima are seen in the spectrum for the comparison star, approximately
in the same frequency interval. However, maxima in Figure 2 are higher than
the statistical limit determined by non-periodic variations with a gaussian
distribution. Probably the maxima of power spectra come from real brightness
variations of the star itself in the case of BY Dra and from variations of


                                [FIGURE 1]


                                [FIGURE 2]


the extinction coefficient alpha in the case of the comparison star. Corresponding
semiamplitudes of variations for the comparison star are from 0.001m for the
I-band to 0.003m for the U-band. It should be noted that the differential
extinction is approximately the same for pairs BY Dra, BD +51d2408, and
BD +51d2408, BD +51d2410. Therefore, values from 0.001m (I) to 0.003m (U) can
be taken as estimates of amplitude limits to which the detection of brightness 
oscillations of BY Dra is restricted by the (not taken into account)
influence of extinction variations. It is also possible to estimate the
errors of one measurement of deltam. These are +-0.014m for U and +-0.006m for B,V,
R,I bands.
  We also note that higher maxima in the spectrum of BD +51d2408 are concentrated
in the interval of 2.10^-2 10^-1min-1 which includes the frequency of
observing of the comparison star. The spectrum of BY Dra in this interval is
approximately the same as the spectrum of BD +51d2408. Thus, the study of
light variations of BY Dra with periods of 10-50 min in our case seems to be
prevented by extinction variations. No maxima are seen in the spectra in the
frequency interval of 0.2 -:- 1 min-1. So we confine the further study by
frequencies not higher than 2.10^-2 min^-1.
  For each band and each night of observations of BY Dra parameters of 
functions


y_1,y_2... were obtained as it was described. The number of filtrations
was 3 because further ones were found to be unexpedient. Thus 91 maxima were
selected in the spectra. For each of them the parameter Delta omega was found which is
the difference of frequencies corresponding to S(omega)_max and 0.5 S(omega)max     When
these maxima are taken together they overlap so that it is impossible to select
any dominating oscillation. Therefore, this part of the analysis is useful
only to estimate amplitudes of oscillations and the accuracy of the determination
of the frequency of some oscillation. Corresponding values are plotted
in Figures 3,4. Semiamplitudes C are expressed in stellar magnitudes. In
Figure 4 values of delta omega for the night of 14 March are 
distinguished by open
circles to show that the accuracy of the frequency determination on that
night was much lower due to the short duration of observations.


                              [FIGURE 3]
                              Figs. 3-4.

  This result prompted us to examine averaged spectra to search for frequencies
of dominating oscillations. The following procedure was applied. Each
spectrum was normalized assuming its maximum value of S(omega) as a unity. Then
spectra of 5 bands were averaged for each night and the mean spectrum for
5 nights was also obtained. These spectra are shown in the left side of
Figure 5. One can see here that the only oscillation with the frequency of


                               [FIGURE 5]


about 1.38*10^-2min^-1 repeats on all 5 nights. On 3 of the 5 spectra low
frequency oscillations are strong.
  It is quite possible that low frequency oscillations affect the other ones
and, for this reason, spectra differ from one another. In order to exclude
this effect we filtered oscillations with the frequency of 3.14^-4 min from
each of the spectra. Owing to the finite resolution all oscillations with
frequencies up to 3.10^-3 min^-1 were also filtered snore or less. Resulting
spectra are shown in the right side of Figure 5, for exception of the
spectrum of 14 March which is not included because of its low frequency 
resolution. The oscillation repeating on spectra in the left side of Figure 5
is again repeating in the right hand. The frequency is about 1.32*10^-2 min^-1
i.e. a little less. Also repeating in all spectra in the right side is the
oscillation with the frequency of about 5.7*10^-3 min^-1 . Moreover, it seems


that in the filtered spectra the third repeating oscillation exists with the
frequency of about 9.10^-3 min^-1 . It is clearly seen in the spectra of 19-20
Apr., 23-24 Apr. and probably it is present in the spectra of 24-25 Febr.,
22-23 Apr. as an unresolved part of the low frequency maximum on the former
and as a step on the later.
  We conclude that our observations reveal the probable oscillation with the
frequency of 1.35.10^-2 +-4.10^-4 min^-1  (P = 74+-2 min) and possible oscillations
with frequencies of 5.7*10^-3 +-9.10^-4min^-1 (P = 175+-28 min) and 9*10^-3 +-6*10^-4
min^-1 (P = 111+-8 min). Errors of frequencies are obtained from differences
between their values corresponding to separate nights. The oscillation with
the frequency of 5.7*10^-3min^-1 is considered only as possible because 
of the
uncertainty introduced by low frequency oscillations. We note that the
frequency of the corresponding maximum differs considerably on unfiltered and
filtered spectra (3*10^-3min^-1 and 5.7*10^-3min^-1, respectively). The accuracy
of the frequency determination for this oscillation may be less than that
given by us. For the other two frequencies (9*10^-3min^-1 and 
1.35*10^-2min^-1) the accuracy given seems quite appropriate.
  What can be said about the origin of brightness variations? As the 
observations of BY Dra show there are several oscillations with frequencies 
repeating from night to night. Semiamplitudes are usually equal to several 
thousandths of magnitude, possibly increasing with decreasing frequency, seldom
reaching 0.03m in the U-band (see Figure 3). These oscillations could be
hardly connected with the flare activity as there are no indications of flares
during the intervals of our observations. If only the periods are considered
it seems likely that the observed oscillations are similar to long period
solar oscillations. The range of the later is 30-300 minutes, their amplitudes
increase with decreasing frequency (Grec et al., 1980). The mass and the
radius of the main component of BY Dra are 0.7M_Sun or 0.5M_Sun and >= 0.9R_Sun
respectively (Vogt, Fekel, 1979), the gravity acceleration being <= 0.86g_sun=
2.4*10^4 cm/sec^2. If the oscillations of BY Dra and the Sun are identified
with g-modes the assumption can be made that the ranges of periods overlap
because of the closeness of gravity accelerations. Just the same is observed.
The resemblance of oscillations may be a consequence of the resemblance of
internal structures which depend on the mass and the radius. However, it
should be noted that the 5-minute oscillations are not found in this study
of BY Dra.
  These results are encouraging for further investigations of minutes-to-
hours light variations of BY Dra and other dwarf stars.



  The author thanks A.B. Severny and V.A. Kotov for useful discussions,
N.I. Bondar, J.S. Efimov, I.V. Iljin, M.N. Lovkaya, N.I. Merkulova,
N.N. Petrova, N.M. Shakhovskoy for the help in observations, S.A. Bondarenko
for making computations.





                  P.F. CHUGAINOV

            Crimean Astrophysical Observatory
            P.O., Nauchnyj, Crimea
            U.S.S.R. 334413





References:

Baliunas, S.L., Hartmann, L., Vaughan, A.H., Liller, W., Dupree, A.K., 1981,
  Ap.J., 246, 473 [BIBCODE 1981ApJ...246..473B ]
Deeming, T.J., 1975, Astrophys. Space Sci., 36, 137 [BIBCODE 1975Ap&SS..36..137D ]
Ferraz-Mello, S., 1977, Colloq. on Binary Stars, Sao Paulo, [BIBCODE 1978sbc..conf..146F ]
Grec, G., Fossat, E., Pomerantz, M., 1980, Nature 288, 541 [BIBCODE 1980Natur.288..541G ]
Linsky, J.L., Bornmann, P.L., Carpenter, K.G., Wing, R.F., Giampapa, M.S.,
  Worden, S.P., Hege, E.K., 1982, Ap.J., 260, 670 [BIBCODE 1982ApJ...260..670L ]
Rojzman, G.S., 1984, Astr.J. U.S.S.R. (in press)
Vogt, S.S., Fekel, F., 1979, Ap.J., 234, 958 [BIBCODE 1979ApJ...234..958V ]