The Thermal State of the Accreting White Dwarf in AM Canum Venaticorum Binaries

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Abstract
We calculate the heating and cooling of the accreting white dwarf (WD) in the ultracompact AM Canum Venaticorum (AM CVn) binaries and show that the WD can contribute significantly to their optical and ultraviolet emission. We estimate the WD's effective temperature, Teff, using the optical continuum for a number of observed binaries, and we show that it agrees well with our theoretical calculations. Driven by gravitational radiation losses, the time-averaged accretion rate, , decreases monotonically with increasing Porb, covering 6 orders of magnitude. If the short-period (Porb < 10 minutes) systems accrete at a rate consistent with gravitational radiation via direct impact, we predict their unpulsed optical/UV light to be that of the Teff > 50,000 K accreting WD. At longer Porb we calculate the Teff and absolute visual magnitude, MV, that the accreting WD will have during low accretion states, and we find that the WD naturally crosses the pulsational instability strip. Discovery and study of pulsations could allow for the measurement of the accumulated helium mass on the accreting WD, as well as its rotation rate. Accretion heats the WD core, but for Porb > 40 minutes, the WD's Teff is set by its cooling as plummets. For the two long-period AM CVn binaries with measured parallaxes, GP Com and CE 315, we show that the optical broadband colors and intensity are those expected from a pure helium atmosphere WD. This confirms that the WD brightness sets the minimum light in wide AM CVn binaries, allowing for meaningful constraints on their population density from deep optical searches, both in the field and in globular clusters.