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\indent By studying cool, low-mass companions to white dwarf stars (Zuckerman \& Becklin, ApJ, 386, 260, 1992), we have been attempting to determine the initial mass function (IMF) for star formation at the very bottom of the main sequence. Some of the white dwarf - red dwarf (WD-RD) binaries measured, however, may have shared a common envelope in the past. If the pair were once sufficiently close to share such an envelope, mass transfer could have altered the mass of the secondary, meaning that the mass measured for the red dwarf is not the initial mass and it should therefore be removed from the IMF sample.
\indent We have observed 16 WD-RD binaries (so far) with the Hamilton echelle spectrograph on the 3-meter telescope at Lick Observatory. Primarily, our goal is to measure changes in radial velocity due to orbital motion, to infer which binaries have closely-separated components (so that mass transfer has occurred in the past). Eleven of the 16 binaries exhibited H$\alpha$ emission from the red dwarf, and thus radial velocities and equivalent widths were measurable. Of these eleven, PG 0308+096, GD 245, LTT 2980, and PG 1026+002 display large and rapid changes in H$\alpha$ radial velocity and are clearly close binaries. GD 123, PG 1643+143, Rosat 1631+78, PG 1210+464, and GD 984 have shown very small or negligible changes in radial velocity and are unlikely to be close binaries. The data suggest a correlation between the amount of H$\alpha$ variability (as measured by the equivalent width) and the inferred closeness of the binary components.
This research is supported by NSF grant no. AST-9115053 to UCLA.
