Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field toy model

Understand

The computational cost of inspiral and merger simulations for black-hole binaries increases in inverse proportion to the square of the mass ratio $q:=m_2/m_1\leq 1$.

• One factor of $q$ comes from the number of orbital cycles, which is proportional to $1/q$, and another is associated with the required number of time steps per orbit, constrained (via the Courant-Friedrich-Lewy condition) by the need to resolve the two disparate length scales.
• This problematic scaling makes simulations progressively less tractable at smaller $q$.
• Here we propose and explore a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4} \lesssim q\lesssim 10^{-2}$), where purely perturbative methods may not be adequate.