Numerical solutions of the complete two-body system in QUMOND

Context . Due to the non-linearity of the QUMOND field equations, the current modelling of binaries replaces the two-body system with an effective one-body system, where the central particle contains the total mass of both binary components and is orbited by a massless test particle. Aims . In this work, we quantify the discrepancy between the effective one-body treatment and the complete two-body solution in QUMOND. Methods . Particles are treated as the limits of Dirac sequences. Thus, the QUMOND contribution to the total kinematical acceleration of a particle is expressed as a Green’s integral, which is calculated numerically. Results . In the non-linear transition regime, the kinematical acceleration of the effective one-body system with a total mass of 2 M ⊙ is up to a factor of 1.44 higher than the Newtonian acceleration; whereas the acceleration is only boosted by a factor of 1.2-1.3 in the two-body system when employing the simple transition function.