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\IBVShead{4161}{15 February 1995}


\centerline{\ft POSSIBLE LOW AMPLITUDE LIGHT VARIATIONS OF DI Her}
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The eccentric eclipsing binary DI~Herculis (B4\,V and B5\,V; P = 10\fd 55; 
e = 0.49) is an important test case of general relativity for stars 
composed of non-degenerate matter because it is expected to have a 
large relativistic contribution to its apsidal motion (Rudjk\o bing, 
1959; Guinan and Maloney, 1985).  DI~Her has well determined orbital 
and physical properties and an accurately measured apsidal motion rate 
of $\dot{\omega}_{obs} = 1\fdg 04/100$yr $\pm 0\fdg 15/100$yr 
determined from the recent analysis of numerous times of primary and 
secondary eclipses (Guinan et al., 1994).  The most 
remarkable feature of DI~Her is that its observed apsidal motion rate is 
significantly smaller than that predicted by general relativity and 
classical effects.  The total predicted rate of apsidal motion is 
$\dot{\omega}_{gr+cl} = 4\fdg 27/100$yr $\pm 0\fdg 30/100$yr where the 
general relativistic term is the major contribution.

We are currently carrying out an intensive study of DI~Her to search
for the reason(s) for the large discrepancy between the observed and
predicted apsidal motion rates.  In a previous paper, we have
refined the value of the apsidal motion rate and have also searched
for evidence of variations in the O$-$C's of the photoelectric
eclipse timings, obtained over the last 30 years, that could arise
from the light time effects of a possible third body (Guinan et al.,
1994).  No evidence of the presence of a third body
was uncovered from this analysis.

Another possible solution for the smaller than expected apsidal motion
rate is tidal dissipation of the system's angular momentum arising from
induced pulsations in the stars as they move in their eccentric orbit
(see Papaloizou and Pringle, 1980; Savoniji and Papaloizou, 1983).
In this case the discrepancy in apparent apsidal motion is produced by
a decrease in the orbital eccentricity as the orbit circularizes.
However, as discussed by Guinan and Maloney (1985) the rate of change of
the eccentricity needed to explain the observed discrepancy is
large ($\dot{e} \simeq -0\fdg 01/100$yr) and the induced pulsations in
the stars, if present, must be significant and should be observable.
With this in mind, we carried out intensive UBV photoelectric photometry 
of DI~Her using the Fairborn-Villanova 0.8m Automatic Photoelectric 
Telescope (APT) on Mt. Hopkins, Arizona.

Many eclipse timings have been obtained for DI~Her, but there have
been few attempts to observe the system for a significant amount of time 
outside of eclipses.  During the springs of 1993 and 1994, DI~Her
was observed continuously (with comparison and check stars) for up to 
4 -- 5 hours on several nights outside of eclipses.  A description of the
equipment, filters, comparison and check stars, and reduction technique
is found in Guinan et al. (1994).  In Figure 1 we present the
U and V light curves obtained during 1993/94.  From this figure it is
apparent that there are small light variations outside the eclipses on
time scales significantly shorter than the 10.55 day orbital period.
The variations are largest in the U bandpass and barely noticeable in the
V bandpass.
In Figure 2 we plot two long runs on an expanded magnitude and time
scale to show examples of the light variations in the U bandpass.  To 
search for possible periodicities, all of the data were 
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Figure 1.  The U and V band light curves of DI~Her obtained in 1993/94 
are plotted.  The magnitudes are differential measured relative to a 
nearby comparison star HD\,174932.  Note the small light variations in 
the U observations outside the eclipses.  
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Figure 2.  The delta U mags of DI~Her for the nights of 21 and 22 June 1993 
are shown.  Small systematic variations are noticeable on time scales of 
several hours.
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Figure 3.  The results of period searches of the U observations outside 
of eclpises using the Lomb--Scargle method are shown.  The two most prominent 
periods found are 0.4885 days and 0.9558 days and are indicated along with 
several other possible periods.
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\noindent analyzed using the 
Lomb--Scargle algorithm (Press and Teukolsky, 1988).

\noindent  We narrowed down the 
possible range of periods to 0.4 to 2.0 days by trial and error and then 
analyzed the data in this restricted period range.  The results are 
difficult to interpret because there is no single highly prominent peak in 
the periodogram.  This is in most part caused by the low 
amplitude nature of the light variations (0.01 -- 0.02 mag) and gaps in 
the data set.  Our analysis reveals two prominent periods of 0.4885 day 
and 0.9558 day having relative powers of 201.0 and 197.6 on the periodogram.  
However, there are other possible periods including 1.2165 days with a lower 
relative power of 155; it is possible that the 0.4885 day and 0.9558 day 
periods are aliases of each other.  It may also be possible, however, to 
have multiple periods.  In Figure 3, we plot the U light curves computed 
with the 0.4885 day and 0.9558 day periods, respectively.  As shown in the 
figure, both periods result in a low amplitude sinusoidal light curve.  It 
is difficult to discern which one of the two periods is better.  The 
amplitudes of the U, B, V light variations are 0.020 mag, 0.013 mag, and 
0.010 mag, respectively.  

We are confident that the light variations discussed above are real.  
However, there is an uncertainty in the source of the variability 
because all measurements were made with respect to a nearby comparison 
star (HD\,174932; B9; V=+8.9) which itself could be the source of the 
observed light variations.  Although this is unlikely, we cannot be 
certain that the comparison is constant in light because the check star 
(HD\,343238; A2; V=+9.7) observations show considerable scatter.  The 
scatter in the check star data is probably due to centering problems 
with the APT acquiring this faint star (the limiting magnitude for 
acquisition is +9.6 -- +9.7 mag); it is also possible that the check 
star may be intrinsically variable.  We plan further observations 
next season to resolve this dilemma using additional comparison stars.

The characteristics of the light variations reported here (whether 
from DI~Her or the comparison star HD~174932) are very similar to 
those found by Waelkens and Rufener 
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\noindent (1985) and Waelkens (1987, 1991) 
for a proposed new class of stars called slowly pulsating B stars (SPB 
stars).  These stars generally have spectral types ranging from B3 to 
B8 (with luminosity classes of IV -- V) and have light amplitudes of a 
few thousandths or hundredths of a magnitude that increase with decreasing 
wavelength; multiple periods are typically seen in the range of about 
1.0 -- 3.0 days.  All the SPB stars seem to show the same dependence 
of the amplitude on wavelength, with amplitudes in the U bands about 
twice as large as in the V bands.  Furthermore, North and Paltani (1994) 
have found that the ratio of the amplitude in the (U$-$B) index and V 
magnitude is very well correlated with the effective temperatures of 
the SPB stars.  Waelkens (1991) explains the light variations from 
the SPB stars as arising from non-radial oscillations in the g modes 
with large radial wave numbers {\em k} and low orders {\em l}.  The 
ratio of the amplitude of the (U$-$B) to the amplitude in V for our 
differential magnitude measures of DI~Her is $A_{(U-B)}/A_{V}$ = 0.70.  
This ratio is similar to that found for SPB stars with spectral types of 
B4 -- B6 which is close the spectral type of the components of DI~Her.  
On the other hand, the comparison star has a spectral type of B9 which 
is near the observed upper limit for SPB stars.  Furthermore, B8 -- B9 
SPB stars have an amplitude ratio of $A_{(U-B)}/A_{V}$ = 0.9 -- 1.1 which 
is not consistent with our observed value.  This evidence lends some 
support to the hypothesis that the light variations are coming from one 
or both of DI~Her's components and not the comparison star.  Observations 
planned for the future should resolve this issue.

If future photometry confirms that the light variations
arise from DI~Her rather than the comparison star, these low 
amplitude non-radial pulsations would not be sufficient to explain the 
discrepancy in DI~Her's apsidal motion rate from tidal dissipation.  It 
would appear more likely that the light variations may be quite common 
for stars of their spectral class and is not related to them being members 
of an eccentric binary system.  It is possible that many more B-type stars 
will show low amplitude light variations and have not yet been discovered 
because they have not been adequately sampled.

This research was in part supported from NSF grants AST-9315365 and 
AST-8616362 which we gratefully acknowledge.
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\beginauthors
James J. MARSHALL
Edward F. GUINAN
George P. McCOOK
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\authorsrightcol
Department of Astronomy 
and Astrophysics
Villanova University
Villanova, PA  19085 
\endauthors

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\references

Guinan, E.F., Marshall, J.J., Maloney, F.P., 1994,  {\it I.B.V.S.}, No.\,4101

Guinan, E.F. and Maloney, F.P., 1985, {\it Astrophys. J.}, {\bf 90}, 1519

North, P. and Paltani, S., 1994, {\it Ast. and Astrophys.}, {\bf 288}, 155

Papaloizou, J. and Pringle, J.E., 1980, {\it M.N.R.A.S.}, {\bf 193}, 603

Press, W.H. and Teukolsky, S.A., 1988, {\it Comput. Phys.}, {\bf 2}, No. 6, 77

Rudkj\o bing, M., 1959, {\it Ann. Astrophys.}, {\bf 22}, 111

Savoniji, G.J. and Papaloizou, J.C.B., 1983, {\it M.N.R.A.S.}, {\bf 203}, 581

Waelkens, C., 1987, in:  {\em Stellar Pulsations.  A Memorial to J.P. 
Cox}, A.N. Cox, W.M. Sparks and S.G. Starrfield (eds.), Lecture Notes in 
Physics, Springer, p. 75.

Waelkens, C., 1991, {\it Ast. and Astrophys.}, {\bf 246}, 453

Waelkens, C. and Rufener, F., 1985, {\it Ast. and Astrophys.}, {\bf 152}, 6

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