Watching Beta Lyrae Evolve

ABSTRACT

From October 1992 to October 1995, 480 photometric brightness measurements of the well-known eclipsing binary Beta Lyrae were made using a solid-state photometer along with U, B, V, R, and I filters. Five times of minimum were graphically determined from the photometric data. Analysis of the light curves showed that Beta Lyrae was significantly redder during the primary eclipses. The calculated rate of mass transfer between the stars was 2.7 x 10²⁵ kg/year.

I. INTRODUCTION

Beta Lyrae is an eclipsing binary star that is apparently evolving. New observations are always needed to help us better understand this dynamical system. Beta Lyrae's brightness and relatively short period make it a good target for student observers and beginning photometrists. In this paper we will show the results of three years of observations by students at the Texas A&M Observatory.

Beta Lyrae is one of the most familiar, yet oddest variable stars in the sky. The primary star of this close binary is classified from its spectrum as a giant of type B7 and probably has about twice the mass of the Sun. The secondary star seems to be largely invisible even though it appears to be far more massive with about 12 times the Sun's mass. The secondary is probably concealed at least partially by a thick, opaque torus of matter orbiting and spiraling into it. Figure 1 shows a model of the Beta Lyrae based roughly on modeling by Wilson (1973; 1981).

Figure 1: Model of Beta Lyrae made using Mathematica.

Even the Voyager spacecraft and telescopes onboard the space shuttle have observed this eclipsing binary star (Kondo 1994; Nordsieck 1995). Observations from last spring's space shuttle-based Astro-2 mission have revealed some interesting information about the material around the secondary star. Data from the polarimeter onboard Astro-2 showed an abrupt shift in the polarization angle between Beta Lyrae's ultraviolet and visible-light emissions which seems to imply that there is outlying matter at right angles to the system's accretion disk. These observations not only give information about the structure of the material around the secondary but also give the orientation of the accretion disk rotation axis with respect to celestial north (about 15 degrees measured from celestial north, clockwise looking out from Earth). Measuring this orbital parameter is extraordinary since this parameter cannot be determined by modeling eclipsing binary star light curves.

The orbital period of Beta Lyrae has increased from 12.89 days when it was first observed by John Goodricke in 1784 to a current cycle of 12.94 days (Gilman 1978). The orbital slowdown must be caused by the lighter primary losing gas to the secondary - thereby creating the accretion torus. The changes in the torus and masses of the stars effect the light curves noticeably over time. Monitoring the subtle changes in the light curve will allow us to understand the evolution of this and other eclipsing binary stars.

II. PHOTOMETRY

A 14-inch Schmidt-Cassegrain (f/11) telescope was used along with two SSP-3 Optec solid state photometers and filters closely matching the Johnson U, B, V R and I filter system to measure the brightness of Beta Lyrae. All measurements were made at the Texas A&M University Observatory located just west of College Station, Texas (30.6deg.N, 96.3deg.W). The comparison star used for all measurements was Gamma Lyrae. The aperture of the photometer was small enough to exclude the light from the visual companion Beta² Lyrae which is only 46 arc seconds away. From 1992 to 1995, 480 photometric brightness measurements were made. An Optec SSPCARD (IBM PC Interface Card) was added to the teaching observatory in 1995 and have made data collection process much more efficient.

III. RESULTS

Figures 2 through 6 show the U, B, V, R and I light curves (differential magnitude versus orbital phase). The data were corrected for atmospheric extinction and the error of each measurement was computed using the method described by Iacovone (1995) with the average of these error values being +/- 0.016 magnitudes. During primary minimum (phase=0.0) Beta Lyrae became on average 1.2 magnitudes dimmer in the U filter, 1.1 magnitudes dimmer in the B filter, 1.0 magnitudes dimmer in the V and R filters and 0.8 magnitudes dimmer in the I filter. These results show that the Beta Lyrae system becomes redder during primary minimum. No such color change, however, was observed for the secondary minimum. Also based on Figures 2 through 6 it appears that there is some orbit-to-orbit variations in the brightness of Beta Lyrae. This kind of variation appears to have been seen by others as well (Aslan, 1987; Landis 1973).

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Figure 2: Ultraviolet Filter Light Curve.

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Figure 3: Blue Filter Light Curve.

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Figure 4: Visual Filter Light Curve.

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Figure 5: Red Filter Light Curve.

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Figure 6: Infrared Filter Light Curve.

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Figure 7: Primary Minimum on June 15, 1995 with a Parabolic Fit.

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which is based on 100 years of observations. This equation gives the heliocentric Julian date, T, of primary minima on epoch E. Photometry from Wilson (1974) and Landis (1973) seems to show that at least sometimes the primary minimum occurs to the right of zero phase. On July 16, 1995 we had the opportunity to observe Beta Lyrae near zero phase as shown in Figure 7. Note that strictly speaking the primary minimum occurred at around 0.025 phase on this day. In other words, the light curve appears not to be symmetric about zero phase. We believe that features like this and the orbit-to-orbit variations are due to irregularities in the accretion torus, but the proof will require more study and observations.

Based on our other photometric observations we were also able to graphically determine five heliocentric Julian date (HJD) times of primary and secondary minimum: 2448919.65, 2449184.75, 2449197.75, 2449883.50, 2449889.75. Figure 8 shows the observed minus computed (O-C) diagram for these times of minima along with observations from the British Astronomical Association (Isles, 1994). The O-C values were calculated from the old 1993 ephemeris published by Cracow Observatory, Poland:

We also observed Beta Lyrae with the naked eye and with the eye through binoculars using Gamma Lyrae and Zeta Lyrae as comparison stars. Figure 9 shows 159 visual magnitude estimates with the phase again calculated using Equation 1. The visual data show that the primary minimum is about 0.8 magnitudes deep which is similar to what the photometric data show in the V filter. These eye observations were part of a campaign organized by Isles (1993; 1994).

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Figure 8: O-C deviations for primary () and secondary () minima. The solid symbols are from values in the text, the open symbols are from BAA observers and the curve is from Equation 1.

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Figure 9: Human Eye Magnitude Estimates in 1993 and 1995.

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IV. MASS TRANSFER

The rate of mass transfer from the primary to the secondary can be approximated using the orbital period increase given in Equation 1 and some elementary physics. The angular momentum of the system about its center of mass is

where I is the moment of inertia and is the angular velocity about the center of mass. For a period, , semimajor axis length, a, and masses m₁ and m₂,

for a circular orbit. Using Kepler's Third Law

and Equations 3 and 4 we get

where G is the universal gravitational constant. For the case of conservation of angular momentum (dL/dt = 0) and conservation of mass (dm1/dt = -dm2/dt), the time derivative of Equation 6 gives

From Equation 1, we see that for Beta Lyrae the current instantaneous values for the period and its derivative are = dT/dE ~ 12.94 days and d/dt ~ 2.2 x 10^-4 days/year = 19 seconds/year. If we use the accepted values for the masses of each star (m₁=2 M_Sun and m₂=12 M_Sun), then we find that dm₁/dt ~ -2.7 x 10²⁵ kg/year. This corresponds to a mass transfer of about 4.5 Earth masses per year!

V. CONCLUSIONS

An extensive photometric study of Beta Lyrae has been carried out in the Johnson U, B, V, R and I filters. During primary minimum we found that Beta Lyrae became a little redder. Primary minima were found to occur on HJD 2449184.75, 2449197.75, 2449883.50, and secondary minima were found to occur on HJD 2448919.65 and 2449889.75. The measured slowdown in the orbital period of Beta Lyrae over the last 100 years has been used to calculate a mass transfer rate of 2.7 x 10²⁵ kg/year from the primary to the secondary star.

VI. ACKNOWLEDGMENTS

We would like to thank to Phil McJunkins, John Harper and Dan Carona for their assistance with data collection and analysis. The authors would also like to thank the Department of Physics for their support of the Texas A&M Observatory and student projects like this. We are grateful to the Centre de Données Astronomiques de Strasbourg for access to the SIMBAD database (http://cdsweb.u-strasbg.fr/).

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