Collision frequency between dark matter subhaloes within Milky Way-like galaxies

TL;DR

The study addresses the frequency of collisions between dark matter subhaloes (DMSHs) within Milky Way–like halos under CDM. It combines an analytic framework based on an NFW host potential and an Eddington-inverted distribution function to predict phase-space distributions and collision rates, with comprehensive orbital integrations of DMSHs in 27 MW-like halos from the Phi-4096 Uchuu simulations for validation. Violent DMSH encounters occur frequently, with an average rate of about $2.1\times10^2\ \mathrm{Gyr^{-1}}$ and a characteristic timescale of $\tau_{\mathrm{violent}} \approx 4.7$ Myr; the numerical results largely reproduce the analytic distributions, though self-gravity enhances high-velocity tails and tidal disruption reduces central densities. The work links collision statistics to halo structure, offers insight into the missing satellite problem, and suggests a substantial fraction of DMSHs in MW-like halos are dark satellites, with implications for observing faint interactions and the formation of dark-matter-deficient remnants.

Abstract

In the standard cold dark matter (CDM) model, sub-galactic structures hierarchically collide and merge to build up larger structures. Mergers and collisions between dwarf galaxies and dark matter subhaloes (DMSHs) play an important role in the evolution and formation of structures within a massive galaxy. We investigate the collision frequency between DMSHs associated with a massive host galaxy such as the Milky Way. We analytically estimate the density distribution of DMSH pairs for the relative distance and relative velocity ($r_\mathrm{rel}$-$v_\mathrm{rel}$) and the distance from the centre of the host halo and relative velocity ($r$-$v_\mathrm{rel}$) planes, based on the distribution function of the host halo in the phase space. Then, we evaluate the collision frequencies of DMSHs by integrating the orbital evolution of DMSHs in Milky-Way-like host haloes selected from cosmological $N$-body simulations. The frequency of violent encounters, in which the relative distance of DMSHs is shorter than the sum of scale radii, is averaged as $2.1\times 10^2\,\mathrm{Gyr}^{-1}$. Since the time scale of violent encounters, $4.7\,\mathrm{Myr}$, is shorter than the dynamical time of the host halo, collisions between DMSHs occur frequently within the host halo. Although interactions between DMSHs produce pairs with higher relative velocities, the density distributions of all and colliding pairs between DMSHs provided by numerical results are approximately similar to those of the analytical model neglecting the interactions of DMSHs on $r_\mathrm{rel}$-$v_\mathrm{rel}$ plane for all pairs and $r$-$v_\mathrm{rel}$ plane for colliding pairs. We compare our results with observed colliding dwarf galaxies and provide insight into the abundance of DMSHs.

Figures (9)

• Figure 1: Probability density $P_\mathrm{rel}(r_\mathrm{rel},v_\mathrm{ref})$ for the relative distance $r_\mathrm{rel}$ and relative velocity $v_\mathrm{rel}$ in the host halo with $c_\mathrm{host}=8.14$ calculated by equation \ref{['eq:Prel']}. The white dashed and dotted contours correspond to the regions that contain 39% ($1\sigma$) and 86% ($2\sigma$) of the total probability mass from the highest value probability density, respectively. The top sub-panel indicates the probability depending on the relative distance, which is integrated by the relative velocity. The right sub-panel indicates the probability depending on the relative velocity, which is integrated by the relative distance.
• Figure 2: Density distribution of collision frequency ${c_\mathrm{sub}^2\mathrm{d}k_\gamma}/({N_\mathrm{sub}^2\eta^2\mathrm{d} r\,\mathrm{d}v_\mathrm{rel}\,\mathrm{d}t})$ between DMSHs within a host galaxy for $\gamma = 1.5$ and $c_\mathrm{host}=8.14$. The top sub-panel indicates the dependence of the collision frequency on the radius of a host halo. The right sub-panel indicates the dependence of the collision frequency on the relative velocity.
• Figure 3: Density distribution of DMSHs encounters for relative distance $r_\mathrm{rel}$ and relative velocity $v_\mathrm{rel}$ between all DMSH pairs in each Milky Way-like host halo. The horizontal and vertical axes are normalised as the virial radius and the virial velocity of each host halo, respectively. Each panel is labelled with the number of the corresponding host halo. The bottom right panel shows the distribution stacked for all host haloes. The white dashed and dotted contours correspond to the regions that contain 39% ($1\sigma$) and 86% ($2\sigma$) of the total probability mass from the highest value probability density, respectively.
• Figure 4: Same as Fig. \ref{['fig: rrel_vrel_all']}, but the density distribution for colliding DMSH pairs satisfied with the violent, gentle, and grazing encounters.
• Figure 5: Density distribution of dark matter subhaloes encounters for the distance from the centre of each host halo $r$ and the relative velocity $v_\mathrm{rel}$ between colliding pairs of dark matter subhaloes in each Milky Way-like host halo. The horizontal and vertical axes are normalised as the virial radius and the virial velocity of each host halo, respectively. Each panel is labelled with the number of the corresponding host halo. The white dashed and dotted contours correspond to the regions that contain 39% ($1\sigma$) and 86% ($2\sigma$) of the total probability mass from the highest value probability density, respectively.