Does the Mass Accretion Rate Depend On the Radius of the Accreting Star?

In some circumstances, the mass accretion rate M^dot onto a compact star may depend not only on external boundary conditions, but also on the radius R of the star. Writing the dependence as a power-law in which M^dot is proportional to R^p, we estimate the power-law index, p, for transient binary systems in a quiescent state. We use the observed luminosities $L$ of accreting neutron stars (R=10^6 cm) in soft X-ray transients and white dwarfs (R=10^9 cm) in similar cataclysmic variables, and estimate M^dot in each system through the relation L=(GM/R)*M^dot, where M is the mass of the star. From the available data we infer that p~0.9+-0.5. This radial dependence is consistent with radiatively inefficient accretion flows that either are convective or lose mass via a wind.