Spiral Shocks in Young Circumbinary Disks

Abstract

Numerical simulations of binary star formation suffer from serious mismatch with observations. Equal mass binaries are abundant in numerical simulations while also unequal mass binaries are commonly observed. The discrepancy should be due to errors in the numerical simulations. In this paper we discuss the evaluation of the Coriolis force as a source of errors in the numerical simulations. Simulations of an accreting young binary is often performed in the frame co-rotating with the binary. We demonstrate that the specific angular momentum changes spuriously at a shock front, if it is evaluated either solely with the density and velocity at the cell center. We show that the spurious change is erased out if a half of it is evaluated from the numerical flux on the cell surface. We name this method of evaluating the Coriolis force HH type since a half is evaluated from the numerical mass flux and the other half is from the momentum density in the cell. We prove that simulations conserve the momentum measured in the rest frame only when HH type Coriolis force is adopted. The numerical error is serious around shock waves since the difference between the numerical mass flux and momentum density is large there. The shock waves drive gas accretion through angular momentum transfer and should be simulated accurately.