The tidal evolution of anisotropic subhaloes: A new pathway to creating isotropic and cored satellites

TL;DR

This paper demonstrates that the common assumption of isotropic velocity distributions for subhaloes is insufficient, showing that pre-infall velocity anisotropy, quantified by $\beta(r)$, governs tidal stripping, core formation, and disruption. Using nine phase-space truncated NFW subhaloes with identical density profiles but different anisotropy on analytic host potentials, the authors find radially biased systems lose mass more rapidly and can form tidal cores, whereas tangentially biased systems resist stripping. They also show that tidal tracks are not universal but depend on initial anisotropy, though systems with the same anisotropy follow distinctive tracks that are largely orbit-independent. A key implication is tidal isotropisation, which erases pre-infall anisotropy and can alleviate the mass–anisotropy degeneracy in MW satellites, with significant consequences for interpreting dwarf-galaxy density profiles in a CDM framework.

Abstract

It is common practice, both in dynamical modelling and in idealised numerical simulations, to assume that galaxies and/or dark matter haloes are spherical and have isotropic velocity distributions, such that their distribution functions are ergodic. However, there is no good reason to assume that this assumption is accurate. In this paper we use idealised $N$-body simulations to study the tidal evolution of subhaloes that are anisotropic at infall. We show that the detailed velocity anisotropy has a large impact on the subhalo's mass loss rate. In particular, subhaloes that are radially anisotropic experience much more mass loss than their tangentially anisotropic counterparts. In fact, in the former case, the stripping of highly radial orbits can cause a rapid cusp-to-core transformation, without having to resort to any baryonic feedback processes. Once the tidal radius becomes comparable to the radius of the core thus formed, the subhalo is tidally disrupted. Subhaloes that at infall are tangentially anisotropic are far more resilient to tidal stripping, and are never disrupted when simulated with sufficient resolution. We show that the preferential stripping of more radial orbits, combined with re-virialisation post stripping, causes an isotropisation of the subhalo's velocity distributions. This implies that subhaloes that have experienced significant mass loss are expected to be close to isotropic, which may alleviate the mass-anisotropy degeneracies that hamper the dynamical modelling of Milky Way satellites.

Figures (16)

• Figure 1: Initial density (top panel), velocity anisotropy (middle), and 3D velocity dispersion profiles (bottom) of all nine subhaloes discussed in the text (colour coded as indicated). The latter is normalised by $\sigma_0 \equiv \sqrt{G \msz/\rsz}$. All subhaloes have identical, phase-space-truncated density profiles, but differ in their velocity anisotropy profiles. Note how subhaloes that are more radially anisotropic have a higher velocity dispersion in their central regions, and how the Osipkov– Merritt (OM) model transitions from being isotropic in the centre to maximally radially anisotropic ($\beta=1.0$) near the halo's truncation radius.
• Figure 2: Tidal evolution of an isotropic subhalo resolved with $\Npar = 10^7$ particles on a circular orbit with $\bigRE = 0.25$. Different columns correspond to different epochs, as indicated. Top row: Face-on density projection of all subhalo particles, colour-coded by surface density. Grey and green, dashed circles indicate the virial radius of the host halo and the circular orbit of the subhalo, respectively. Middle and Bottom rows: Face-on and edge-on zoom-in projections of the density of instantaneous bound (colour-coded) and unbound (black) particles. The blue, solid circle indicates the initial virial radius of the subhalo, anchored on its instantaneous centre of mass (marked by a cross), and the green, dashed curve marks the subhalo orbit. The bound mass fraction, $\fbound$, at each epoch is indicated in the panels in the middle row.
• Figure 3: Same as fig:Isotropic_Combine but for the radially anisotropic subhalo with $\beta(r) = +0.25$. Note that this subhalo undergoes significantly more mass stripping than its isotropic counterpart.
• Figure 4: Evolution of the bound mass fraction of subhaloes along orbits with $\bigRE=0.25$ and eccentricities $e = 0$ (top) and $0.9$ (bottom), colour-coded by the initial anisotropy as indicated. The orbital time and Hubble time are indicated by vertical lines. Subhaloes that are more radially anisotropic experience more rapid mass loss, which in the most extreme cases can lead to complete physical disruption in under a Hubble time.
• Figure 5: The ratio $\fbound/f_\text{bound,iso}$ of the bound mass fraction of an anisotropic subhalo to that of its isotropic counterpart, colour-coded as in fig:Analytical_IC. Results are plotted as a function of the orbital energy, characterised by $\bigRE$, for three different orbital eccentricities (different columns, as indicated), and evaluated at two different epochs— after one orbital period, $\torb$ (top panels) and after a Hubble time, $\tH$ (bottom panels). Star symbols indicate the cases where the subhalo is completely disrupted. Irrespective of the orbital parameters, more radially (tangentially) biased subhaloes are more susceptible to (resilient against) tidal stripping.