Arbitrarily Degenerate Helium White Dwarfs as Donors in AM CVn Binaries

We apply the Deloye & Bildsten (2003) isentropic models for donors in ultracompact low-mass X-ray binaries to the AM CVn population of ultracompact, interacting binaries. The mass-radius relations of these systems’ donors in the mass range of interest ($M_2<0.1\text{msun}$) are not single-valued, but parameterized by the donor’s specific entropy. This produces a range in the relationships between system observables, such as orbital period, $\text{Porb}$, and mass transfer rate, $\text{Mdot}$. For a reasonable range in donor specific entropy, $\text{Mdot}$ can range over several orders of magnitude at fixed $\text{Porb}$. We determine the unique relation between $\text{Mdot}$ and $M_2$ in the AM CVn systems with known donor to accretor mass ratios, $q=M_2\mathrm{/}{M}_1$. We use structural arguments, as well as each system’s photometric behavior, to place limits on $\text{Mdot}$ and $M_2$ in each. Most systems allow a factor of about 3 variation in $\text{Mdot}$, although V803 Cen, if the current estimates of its $q$ are accurate, is an exception and must have $M_2\approx 0.02\text{msun}$ and $\Mdot \approx 10^{-10} \msun$yr$^{-1}$. Our donor models also constrain each donor’s core temperature, $T_c$, range and correlate $T_c$ with $M_2$. We examine how variations in donor specific entropy across the white dwarf family \citep{nele01a} of AM CVn systems affects this population’s current galactic distribution. Allowing for donors that are not fully degenerate produces a shift in systems towards longer $\text{Porb}$ and higher $\text{Mdot}$ increasing the parameter space in which these systems can be found. This shift increases the fraction of systems whose $\text{Porb}$ is long enough that their gravity wave (GW) signal is obscured by the background of detached double white dwarf binaries that dominate the GW spectrum below a frequency $\approx 2$ mHz.