A semi-analytic dynamical friction model that reproduces core stalling

Abstract

We present a new semi-analytic model for dynamical friction based on Chandrasekhar's formalism. The key novelty is the introduction of physically motivated, radially varying, maximum and minimum impact parameters. With these, our model gives an excellent match to full N-body simulations for isotropic background density distributions, both cuspy and shallow, without any fine-tuning of the model parameters. In particular, we are able to reproduce the dramatic core-stalling effect that occurs in shallow/constant density cores, for the first time. This gives us new physical insight into the core-stalling phenomenon. We show that core stalling occurs in the limit in which the product of the Coulomb logarithm and the local fraction of stars with velocity lower than the infalling body tends to zero. For cuspy backgrounds, this occurs when the infalling mass approaches the enclosed background mass. For cored backgrounds, it occurs at larger distances from the centre, due to a combination of a rapidly increasing minimum impact parameter and a lack of slow moving stars in the core. This demonstrates that the physics of core-stalling is likely the same for both massive infalling objects and low-mass objects moving in shallow density backgrounds. We implement our prescription for dynamical friction in the direct summation code NBODY6 as an analytic correction for stars that remain within the Roche volume of the infalling object. This approach is computationally efficient, since only stars in the inspiralling system need to be evolved with direct summation. Our method can be applied to study a variety of astrophysical systems, including young star clusters orbiting near the Galactic Centre; globular clusters moving within the Galaxy; and dwarf galaxies orbiting within dark matter halos.

A semi-analytic dynamical friction model for cored galaxies

“…Fig. 9 shows the cuspy case γ = 1, which was already described well by the Maxwellian model in Petts et al (2015), as f (v * ) more closely resembles Maxwellian form in cuspy models. Interestingly, the model only considering the slow stars slightly over-predicts the force, and the model with all the stars reproduces the inspiral excellently.…”

“…Thus, from equation 11c, vtyp = vs as assumed in Petts et al (2015). This calculation only holds for isotropic backgrounds, for stars moving slower than the infalling satellite and when one ignores the velocity dependence in log(Λ).…”

“…In Table 1 we briefly summarise the differences in our updated models as compared to our model presented in Petts et al (2015). The new models use bmax and bmin as described in P15, with the exception of the P16f model which includes the relative velocity dependence of interactions in log(Λ).…”

“…), the formula has been very successful at reproducing the orbital evolution. Although the formula has remained largely unchanged, its application has seen many improvements in recent years (Hashimoto et al 2003;Just & Peñarrubia 2005;Just et al 2011;Petts et al 2015). Typically, log(Λ) is poorly defined, with bmax being of the order of the size of the system and bmin the impact parameter for a 90 degree deflection (Binney & Tremaine 2008).…”

“…Hashimoto et al 2003). The variations of log(Λ) are also especially important when bmax/bmin approaches unity (Petts et al 2015), which for most systems occurs at approximately M s ∼ M enc where the satellite is assumed to form a quasi two-body system with the galactic centre and dynamical friction becomes inefficient (e.g. Binney & Tremaine 2008;Gualandris & Merritt 2008).…”