The Physics of Mass Transfer in Substellar and Low-Mass Binaries

Abstract

Several dozen binary ultracool and brown dwarf systems have been identified to date. These systems represent valuable probes of star and planet formation at the lowest mass scales. To date, the study of these ultracool binaries has been constrained to the non-interacting case. In this paper, we investigate the dynamics, stability, and evolution of mass transferring ultracool binaries using numerical simulations with accepted equations of state for brown dwarfs. We find that there exists a donor mass inversion, above which the donor dwarf is more massive than the accretor, but below which the accretor is more massive than the donor. Below the hydrogen burning limit, objects with mass ratios $q \sim 1$ are unstable, but slight deviations from this mass ratio are stable at the onset of mass transfer and remain stable throughout extended periods. We compute theoretical mass transfer rates using several angular momentum loss prescriptions and predict lifespans of $\sim 100$ Myrs. We predict that all mass transferring ultracool binaries are tidally locked and possess orbital periods ranging from just under $1$ hour to $3.5$ hours. We find that mass transfer proceeds via direct impact onto the accretor forming a UV or optically bright hotspot on the surface of the accretor.

Figures (4)

• Figure 1: The mass--radius and mass--density relations used in the analysis of aBDBs in this work. These relations are derived from 1 Gyr COND isochrones Baraffe_BD_Evolution.
• Figure 2: The orbital period at the onset of Roche lobe overflow. We note that as expected the minimum possible orbital separation at which accretion begins is greater than the contact separation for two BDs. Note the inversion in the accretor/donor mass ratio around the regime where the mass/density relation of one component reaches its maximum.
• Figure 3: The Roche lobe exponent, $\zeta_L$ as a function of component masses. In the $M_\mathrm{acc} > M_\mathrm{don}$ regime $\zeta_L$ is primarily negative and the donor physical radius exponent is $\zeta_s \approx -0.2$. Therefore these systems are stable where $\zeta_L \lesssim -0.2$. In the $M_\mathrm{don} > M_\mathrm{acc}$ regime, $\zeta_L > 0$, which promotes instability and rapid mergers, aside from the region at $q \approx 1$ where $\zeta_L$ is small, and $\zeta_s$ increases quickly due to the occurrence of hydrogen fusion above the $80 \, M_\mathrm{Jup}$ limit.
• Figure 4: The equilibrium mass transfer rate predicted by the AML equations for arbitrary mass combinations. We simulate the three prescriptions for external orbital torques from Subsection \ref{['subsec:AML']}. Gray hatched regions represent the regions of unstable mass transfer predicted by Equation \ref{['eq:stability']}. Black arrows show which direction systems in each regime evolve over time. If magnetic braking is extremely inefficient for BDs, GR sets a minimum limit to $\dot{M}$. Traditional saturated magnetic braking predicts that high mass binaries in $M_\mathrm{acc} > M_\mathrm{don}$ diverge from $q \approx 1$ quickly, but should live $t \sim 10^2-10^3$ Myrs. Disrupted prescriptions predict extremely high mass transfer rates with very short lifespans $t \sim 1$ Myr.