Constraining the Physics of AM Canum Venaticorum Systems with the Accretion Disk Instability Model

Recent work by Levitan et al has expanded the long-term photometric database for AM CVn stars. In particular, their outburst properties are well-correlated with orbital period, and allow constraints to be placed on the secular mass transfer rate between secondary and primary if one adopts the disk instability model for the outbursts. We use the observed range of outbursting behavior for AM CVn systems as a function of orbital period to place a constraint on mass transfer rate versus orbital period P. We infer a rate ~5 x 10^{-9} Msun/yr (P/1000 s)^{-5.2}. We show the functional form so obtained is consistent with the recurrence time-orbital period relation found by Levitan et al using a simple theory for the recurrence time. Also, we predict their steep dependence of outburst duration on orbital period will flatten considerably once the longer orbital period systems have more complete observations.