COMMISSION 27 OF THE I. A. U.
        INFORMATION BULLETIN ON VARIABLE STARS
                      NUMBER 820

	                            Konkoly Observatory
        	                    Budapest
                	            1973 August 23



        AN IMPROVED EPHEMERIS FOR BETA LYRAE




   As Beta Lyrae is presently under intense study using both
ground based equipment and space facilities, there is a need for
more reliable phases in the binary orbit. It is the aim of this
note to warn observers that the currently accepted cubic ephemeris 
formula by Wood and Forbes (1) is already more than 9 hours
off and to supply an improved (quadratic) ephemeris giving 
reasonable representation of the minimum epochs observed during the
last 25-30 years.
   In the table we assembled all available photoelectrically 
determined times of primary minimum since 1944. In the column of O-C
values, the heading (Herczeg) stays for the proposed formula:

   Min.I = JD2439108.12 + 12.93266dE + 0.458 x 10^-5 E^2.

                      [FIGURE 1]

Fig. 1 shows these observations, plotted against a linear formula 
and supplemented, in order to fill the rather serious gaps,
by a few visual minima determined by Gaposchkin (11), by the 
Berliner Arbeitsgemeinschaft (12), further a number of photographically 
derived epochs also published by Gaposchkin. Plates of
photographic patrol seem to be ill-suited for the photometry of
such a bright variable but careful visual epoch determinations
compare surprisingly well with photoelectric results.
The following comments may be of interest.
   1. It was impossible to derive a minimum epoch from Belton
and Woolf's six-color photometry in 1961 (13). Moreover, a plot
of the individual observations reveals how strongly asymmetric
the light curve was at the time of observations (more precisely,
on JD2437491): the actual minimum of light has not been reached
before phase 0.03. This is a quite characteristic, recurrent 
disturbance, a drop of brightness immediately following zero phase,
resulting in a "wedge-shaped" bottom of the light curve; see for
instance Fig. 1 in Larsson-Leander's report of the 1959 campaign
(4).
   2. Minimum epochs of the same campaign all show markedly 
positive residuals. Our Fig. 1 indicates, however, that these O-C
values are either due to a short-term period change or, possibly,
to the above mentioned distortions of the light curve. It is worth
mentioning that a comparison between Stebbins' observations in 1915
and those of Guthnick in 1916 discloses almost exactly the same 
temporary phase shift.
   3. Under these circumstances the scatter in Fig. 1 and 2 may
not entirely be due to errors of observation or reduction. Times
of minimum light referred to under (7) through (10) are not given
in the original publications: they are normal epochs derived by the
present author, using simple graphical construction. Since some of
these series of measurements show difficult, asymmetric light curves,
the 3-decimal accuracy of the timing is probably not granted.
   As to the basic period variation exhibited in Fig. 1, it deserves
some further comment.

                           [FIGURE 2]

   Recent failures of the Wood-Forbes ephemeris formula correspond
almost entirely to an unexpected and unusual increase of the binary
period. In Fig. 2, the residuals of photoelectrically determined
epochs are shown against Wood and Forbes (dots) together with a few
visual timings by Pannekoek, Menze, Danjon, Parenago and McLaughlin,
based mainly on longer series of observations (circles). The O-C
values are systematically negative but, apart from the scatter, nearly 
constant indicating a correct representation of the period changes
between about 1890 and 1960. In this case, as in the case of Prager's
earlier formula (14) too, this is equivalent to an approximately linear 
increase of the period, for several decades, since the cubic term
has a small coefficient. Thus the contribution to the O-C values of
the E^3 term in the Wood-Forbes formula remains less than 0.01d from its
zero epoch in 1950 up to 1969. The sudden increase of the residuals
after 1960 can only be explained by a substantial change in the rate
of the lengthening of the period: for the time interval 1950-1966, Wood
and Forbes predicted an increase of the period of 0.0315d while the
actual increase turned out to be close to 0.004d.
  This is a novel feature in the period changes exhibited by Beta
Lyrae, for earlier evidence strongly suggests that dP/dE > 0, yet
d^2P/dE^2 =< 0 throughout. It is an obvious challenge to the "asymptotic"
representation, using exponential terms, as put forward recently (15).
Further observations may indicate whether this abrupt change in the
pattern of period variations could be related to reports of an 
increased spectroscopic "activity" in the system.
  A more complete discussion of the period of Beta Lyrae is in 
progress. I am much obliged to Dr. Douglas Hall (Dyer Obs., Nashville)
for sending lists of unpublished observations and to Dr. Kwan-Yu Chen
(U. of Florida, Gainesville) for supplying information from the files
of the Card Catalogue of Eclipsing Variables.



         	          TABLE
        Beta Lyrae, photoelectric minima 1944-72

Min. I (hel.)   		O-C                        Obs.          Ref.
	                (Wood-Forbes)   (Herczeg)
JD2431337.30    	-0.05           +0.05(5)   	Guthnick         (2)
    36379.472       	-0.049           0.00     	Wood, Walker     (3)
      793.47      	+0.12           +0.15      	IAU campaign,    (4)
      806.405     	+0.124          +0.15      	1959             (4)
      819.36      	+0.15           +0.18                   	 (4)
    37478.72        	+0.05           +0.04      	Engelkeimer      (5)
    39677.24:       	+0.24:          +0.07:     	Herczeg          (6)
    40142.713       	+0.157          -0.05     	Lovell, Hall     (7)
      479.04          	+0.24(5)        +0.01      	Herczeg          (6)
      724.751		+0.239          -0.02      	Lovell, Hall     (8)
    41086.860       	+0.235          -0.06      	Landis et al.    (9)
JD2441539.661   	+0.388          +0.04      	Landis et al.    (10)


References:
(1) D.B. Wood and J.E. Forbes (1963) A.J. 68, 257. [BIBCODE 1963AJ.....68..257W ]
(2) P.Guthnick, Abhandl.Deutscher Akademie Berlin, Jahrg. 1945/46,
     Math. Kl. Nr.1.
(3) D.B. Wood and M.F. Walker (1960) Ap.J. 131, 363. [BIBCODE 1960ApJ...131..363W ]
(4) G. Larsson-Leander (1970) Vistas in Astronomy (ed.A. Beer)
     Vol. 12, 183-197. [BIBCODE 1970VA.....12..183L ]
(5) D. Engelkeimer, Amateur Astron., Jan. 1962.
(6) T. Herczeg (1973) IBVS No. 805.
(7) L.P. Lovell and D.S. Hall (1970) P.A.S.P. 82, 345. [BIBCODE 1970PASP...82..345L ]
(8) L.P. Lovell and D.S. Hall (1971) P.A.S.P. 83, 357. [BIBCODE 1971PASP...83..357L ]
(9) H.E. Landis, L.P. Lovell, D.S. Hall (1973) P.A.S.P. 85, 133. [BIBCODE 1973PASP...85..133L ]
(10) H.E. Landis, L.P. Lovell, T.H. Frazier, D.S. Hall: private comm.
(11) S. Gaposchkin (1956) A.J. 61, 397. [BIBCODE 1956AJ.....61..397G ]
(12) W. Braune and J. Hubscher (1967) A.N. 290, 105. [BIBCODE 1967AN....290..105B ]
(13) M.J.S. Belton and N.J. Woolf (1965) Ap.J. 141, 145. [BIBCODE 1965ApJ...141..145B ]
(14) R. Prager (1933) Kleinere Veroff. Berlin-Babelsberg, Nr. 11.
(15) T. Herczeg, reported on the Struve Memorial Symposium
     (Parkesville, B.C., 1972).

                           T. J. HERCZEG
                           Department of Physics
                           and Astronomy
                           University of Oklahoma
                           Norman, Oklahoma