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

                       Number 1005

                                   Konkoly Observatory
                                   Budapest
                                   1975 June 9



   ON THE PERIOD-LUMINOSITY RELATION OF THE DELTA SCUTI STARS


    Taking into consideration 28 delta Scuti stars with known 
trigonometric or dynamic (or group) parallax the period-luminosity
relation is discussed in this paper. This relation was obtained
by Frolov (1969) on the basis of 6 delta Scuti stars with known 
trigonometric parallaxes for the first time.
    A list of selected 28 delta Scuti stars is given in the Table
which contains the name of the star, HD number, spectrum, mean <V>
magnitude, logarithm of period P, trigonometric or dynamic (or
group) parallax, observed absolute magnitude M_V with its mean 
error epsilon, weight estimated from the error epsilon of the observed 
absolute magnitude, absolute magnitude calculated from E_q. (1) and (2),
subdivision and remark. The list was made using information 
included in papers given by Seeds and Yanchak (1972), Baglin et al.
(1973), Kukarkin et al. (1969, 1971, 1974), Broglia (1973), 
Jenkins (1952, 1963), Russell and Moore (1940). Only for two stars
of this list, namely Y Cam and AB Cas, "photometric" parallaxes
were determined using the new method which had been elaborated
for the eclipsing binaries by one of us (Dworak 1974).
    We discuss only such a sample of delta Scuti stars for which
absolute magnitudes are known from geometric methods. We did not
use absolute magnitudes obtained by Stromgren intermediate-band
colours, Crawford's photoelectric H_beta indices etc., because the
absolute magnitudes determined in this way can be seriously 
erroneous for some delta Scuti stars with peculiar spectrum.



                                Table
                     Data for 28 selected delta Scuti Stars
---------------------------------------------------------------------------------------------------------------
Name          HD     Spectrum       <V>     log P     parallax          M_V obs.  weight M_V cal, subdiv.  Rem.
---------------------------------------------------------------------------------------------------------------
V1208 Aql   181333   F2 III         5.55m -0.803    0.002"+-.007"     -2.9m+-(7.6m)  0   -0.23m   bright
                     (F0)
UV Ari       17093   A7 IV          5.18  -1.432    0.024   .006       2.08   0.55   2   2.07     faint
KW Aur       33959   A9 V           5.02  -1.058    0.007      d      -0.75          1   0.13     bright   SB
gamma Boo   127762   A7 III         3.05  -0.538    0.016   .005      -0.93   0.70   2  -0.60     bright
Kappa^2 Boo 124675   A7 IV          4.56  -1.161    0.014   .006       0.29   0.95   2   0.28     bright   DS
                     (A8 IV)
Y Cam                A7 Vm         10.45  -1.2000      #               0.70   0.60   2   0.33     bright   EB
AO CVn      115604   F0 II          4.74  -0.914    0.014   .005       0.47   0.80   2  -0.07     bright
                     (F0 IIIp)
AB Cas               A3            10.2   -1.237       #               2.10   0.30   3   1.91     faint    EB
beta Cas       432   F2 IV          2.28  -0.982    0.072   .007       1.57   0.25   3   1.69     faint
epsilon Cep 211336   F0 IV          4.19  -1.376    0.037   .005       2.03   0.30   3   2.02     faint
FM Com      107131   A7 V           6.44  -1.260    0.012      g       1.84          1   1.92     faint
gamma CrB   149436   AO IV          3.86  -1.523    0.026   .005       0.94   0.45   3   0.79     bright   SB
                     (A1 V )
tau Cyg     202444   F0 IV          3.70  -0.854    0.046   .004       2.01   0.20   3   1.58     faint    SB
                     (F5 IV)
delta Del   197461   A7 IIIp        4.45  -0.8655   0.008   .006      -1.03   1.65   1  -0.14     bright   SB
                     (F0 IV)
CL Dra      143466   F0 IV          4.97  -1.161    0.019   .006       1.36   0.70   2   1.84     faint
S Eri        32045   F0 IV          4.79    -       0.015   .011       0.67   1.60   1   -        -
o^1 Eri      26574   F2 II-III      4.05  -1.097    0.028   .007       1.30   0.55   2   1.79     faint
                     (F2)
HR 8666     215664  dA8            5.76m  -1.284   0.018"+-.007"     2.04m+-0.85   2    1.95m    faint    Lac
V571 Mon   55057    A8n           5.46   -0.960   0.020   .005      1.96   0.55   2    1.67    faint
tau  Peg   220061   A5 IV        4.62   -1.252   0.031   .007      2.08   0.50   3    1.92   faint
                    (A5 V)
rho  Pup    67523   F6 IIp      2.75   -0.851   0.031 .007      0.21   0.50   3   -0.16   bright   DS
                    (F5 II)
delta Sct  172748   F3 III-IV   4.72   -0.713   0.020 .005    1.22   0.55   2    1.46   faint    DS
                    (F3)
delta Ser  138918   F0 IV       4.27   -0.866   0.015 .005    0.15   0.75   2   -0.14   bright   DS
                    (dF0)
   o Ser   160613   A2 V        4.26   -1.276   0.003 .006   -3.35  (4.3)   0    0.44   bright   SB
                    (A2 IV)
V480 Tau    30780   dA5         5.11   -1.377   0.009 .006   -0.12   1.45   1    0.58   bright
  nu UMa    84999   F2 IV       3.76   -0.877   0.036 .005    1.54   0.30   3    1.60   faint    DS
                    (F0 IV)
  FZ Vel    77140   F0 III      5.18   -1.183   0.007 .009   -0.6    2.8    1    0.31   bright   DS
  FG Vir   106384   dF3         6.55   -1.155   0.010 .011    1.56   2.4    1    1.83   faint
--------------------------------------------------------------------------------------------------------------


Remarks:  d - dynamic parallax,    g - group parallax, # - photometric parallax, DS - double star,
       EB - eclipsing binary, SB - spectroscopic binary, Lac - in Lacerta.




    Looking carefully on the data gathered in the Table it is
easy to notice that all the stars can be divided into two distinct
groups as regards their absolute magnitudes. Both groups
are being delimited by the 1M line. Stars more luminous than
1M, called "bright delta Scuti" or "rho Puppis stars", are more 
scattered in the log P - M_V diagram than the "faint delta Scuti stars"
with M_V > 1M. The mean values of the absolute magnitudes for
both groups together with the standard deviations are as follows:
Bright delta Scuti stars: <M_V> = +0.12m + 0.64m (we reject two stars,
namely V1208 Aql and o Ser, with the greatest errors in M_V).
Faint delta Scuti stars: <M_V> = +1.79m + 0.32m.
    Taking this into consideration we tried to find the period-
-luminosity relation separately for both groups, especially that
one of bright delta Scuti stars, rho Puppis, does not confirm the 
Frolov's (1969, 1970) period-luminosity relation.
    Using the method of least squares we calculated for the
stars presented in the Table the coefficients of regression lines
expressing the array means of M_V as a function of log P. These
calculations were carried out taking the weights of the absolute
magnitudes into consideration. The weight for each star was 
defined according to the arbitrary rules:

w =   0   if   the error in M_V epsilon > 3M,
w =   1   if   1M < epsilon < 3M
w =   2   if   0.5M < epsilon <= 1M
w =   3   if   epsilon <= 0.5M.

Together with the parameters of the best regression lines we 
computed the areas of confidence overlapping the true regression line
M_V = a log P + b   with frequency 0.98 (see Fig. 1,).
As a result of our calculations we obtained the following
regression lines:

Bright delta Scuti stars:  M_V = -1.41M log P - 1.36M
                                 +-.39         +-.43
Faint delta Scuti stars:   M_V = -0.84M log P + 0.86M
                                 +-.22         +-.25


    The scantiness of data did not allow us to explain, what
was the reason for the division into bright and faint delta Scuti
stars. However, on the basis of the available information we can
make conjectures that the bright or rho Puppis stars are rather
unusual variables. For the majority of them the spectra belong
to the II, III and V class of luminosity and very often emission 
lines are appearing. On the other hand, the lack of overtones 
is very probable for these stars as well as the gaps in
variability. Some of the bright delta Scuti stars, namely rho Pup,
gamma Boo, gamma CrB, Y Cam, were already called untypical or unusual
variables.
    On the contrary, the faint delta Scuti variables seem to be
typical subgiant stars and may be called normal delta Scuti stars.
    Our suggestion that the delta Scuti stars may be divided into
two distinct groups is confirmed by Elliott (1974).


                           T.Z. DWORAK
                           S. ZIEBA
                       Astronomical Observatory
                    of the Jagiellonian University
                             Cracow

References:

Baglin et al, 1973, Astron. a. Astrophys., 23, 227. [BIBCODE 1973A&A....23..221B ]
Broglia, P., 1973, IBVS, No. 823.
Dworak, T.Z., 1974, Acta Cosmologica, Z.2., 13. [BIBCODE 1974AcC.....2...13D ]
Elliott, H., 1974, A.J., 79, 1082. [BIBCODE 1974AJ.....79.1082E ]
Frolov, M.S., 1969, A.C., No. 505. [BIBCODE 1969ATsir.505....1F ]
          1970 Pulsirujushchije zvezdy, Moskva: Izd. "Nauka",
             Chapter 6.
Jenkins, L.F., 1952, GC of Stellar Parallaxes, Yale.
          1963, Ibid. Suppl.
Kukarkin et al., 1969, GCVS, Third Ed., Moskva: Izd. AN SSSR.
            1971, Ibid. First Suppl.
            1974, Ibid. Second Suppl.
Russell, H.N. and Moore, C., 1940, The Masses of the Stars,
                   Chicago.
Seeds, M.A. and Yanchak, G.A., 1972, The Delta Scuti Stars.
            An Annotated Catalogue and Bibliography,
            Pennsylvania: Bartol Research Foundation
            of the Franklin Institute.


                       [FIGURE 1]

 Fig. 1. The best regression lines together with their areas of confidence
 which are to overlap the true regression lines with the frequency 98%
 calculated for the delta Scuti stars.