Stellar Mass Segregation in Dark Matter Halos

TL;DR

This study shows that collisional relaxation can drive stellar mass segregation even when stars are embedded in a smooth, dark matter-dominated halo, particularly for systems with $\Upsilon_\mathrm{dyn}$ up to about 50. Using collisional N-body simulations of two-component stellar populations in cuspy Hernquist halos for UMa3/U1, Delve 1, and Eridanus 3, the authors demonstrate that low-mass stars expand their half-light radii while high-mass stars contract, with observable segregation after ~10 Gyr. The work also reveals dynamical binary formation among high-mass stars and highlights that tides do not erase the segregation signature, though they modulate the stellar population through adiabatic expansion. These findings imply caution when using mass segregation to classify faint stellar systems and suggest mass segregation could enhance massive binaries in the centers of dark matter-dominated dwarfs, with implications for gravitational wave source populations and interpretations of ambiguous star clusters versus dwarf galaxies.

Abstract

We study the effect of stellar mass segregation driven by collisional relaxation within the potential well of a smooth dark matter halo. This effect is of particular relevance for old stellar systems with short crossing times, where small collisional perturbations accumulate over many dynamical timescales. We run collisional $N$-body simulations tailored to the ambiguous stellar systems Ursa Major 3/Unions 1, Delve 1 and Eridanus 3, modelling their stellar populations as two-component systems of high- and low-mass stars, respectively. For Ursa Major 3/Unions 1 (Delve 1), assuming a dynamical-to-stellar mass ratio of 10, we find that after 10 Gyr of evolution, the radial extent of its low-mass stars will be twice as large as (40 per cent larger than) that of its high-mass stars. We show that weak tides do not alter this relative separation of half-light radii, whereas for the case of strong tidal fields, mass segregation facilitates the tidal stripping of low-mass stars. We further find that as the population of high-mass stars contracts and cools, the number of dynamically formed binaries within that population increases. Our results call for caution when using stellar mass segregation as a criterion to separate star clusters from dwarf galaxies, and suggest that mass segregation increases the abundance of massive binaries in the central regions of dark matter-dominated dwarf galaxies.

Figures (8)

• Figure 1: Several Milky Way satellites have relaxation times $T_\mathrm{rel}$ shorter than $10\,\mathrm{Gyr}$ even in the presence of substantial amounts of dark matter. Those objects may exhibit stellar mass segregation driven by collisional relaxation. Shown are stellar masses $M_\star$ and (3D) half-light radii $r_\mathrm{h}$ of dwarf galaxies (open circles), ambiguous stellar clusters (triangles), as well as the "micro galaxy" candidates UMa3/U1, Del1 and Eri3 (red filled circle, diamond and square, respectively). See footnote \ref{['Footnote:References']} for references. Curves of constant relaxation time $T_\mathrm{rel} = 1\,\mathrm{Gyr}$ and $10\,\mathrm{Gyr}$ are computed assuming a dynamical-to-stellar mass ratio of $\Upsilon_\mathrm{dyn} = 10$ within the half-light radius, with stellar masses sampled from a Chabrier2003 present-day mass function (see text for details).
• Figure 2: Stellar mass segregation in $N$-body realizations of the example systems UMa3/U1 (top), Del1 (center) and Eri1 (bottom). Each system is embedded in a cuspy dark matter halo, with an initial dynamical-to-stellar mass ratio of $\Upsilon_\mathrm{dyn} = 10$. Shown are $\{x,y\}$ projections of snapshots at $t/\mathrm{Gyr}=0$, $2.5$, $5$, $7.5$ and $10$. The axes are expressed in units of the initial half-light radius $r_\mathrm{h0}$. Individual high-mass stars are shown as dark grey points, while low-mass stars are shown in blue. The median half-light radii of high-mass and low-mass stars (computed over a sample of $N$-body realizations, see text) are shown as black and blue circles, respectively. Over a period of $10\,\mathrm{Gyr}$, the half-light radius of the population of low-mass stars expands, while the half-light radius of the high-mass population contracts. Consistent with the relaxation time estimates of Fig. \ref{['fig:Trelax']}, the effect is largest for the UMa3/U1 model, and smallest for the Eri3 model. Dynamically formed binaries consisting of two high-mass stars are highlighted in red (see Sec. \ref{['sec:Binaries']}). A video supplementing this figure is available in Appendix \ref{['Appendix:Animations']}.
• Figure 3: As stellar mass segregation progresses, the half-light radius of the low-mass stars expands as the population heats up, whereas the population of high-mass stars contracts and cools down. The same systems are shown as in Fig. \ref{['fig:Snapshots']}, with an initial dynamical-to-stellar mass ratio of $\Upsilon_\mathrm{dyn} = 10$. Thick blue (black) lines show the median time evolution of the low-mass (high-mass) stellar population computed from all $N$-body realizations (see text), whereas light blue (grey) lines show individual runs. Poisson noise widens the distribution of half-light radii and velocity dispersions, most notably for the case of UMa3/U1 (left) with $N_\star=50$ stars.
• Figure 4: As the population of high-mass stars contracts and cools, the number of dynamically formed binaries consisting of two massive stars increases. At the same time, as the population of low-mass stars expands and heats up, the number of dynamically formed binaries consisting of a massive and a low-mass star decreases. Shown is the fraction $f_\mathrm{bin}$ of high-mass stars that are in binary systems relative to the total number of high-mass stars. Simulation results are shown as shaded bands, computed from a sample of $2000$$N$-body realizations of the UMa3/U1 model. Dashed curves show the model predictions of Eq. \ref{['Eq:BinaryFraction']}.
• Figure 5: Stellar mass segregation plays a substantial role in the dynamical evolution of systems akin to UMa3/U1 if their dynamical-to-stellar mass ratios $\Upsilon_\mathrm{dyn}$ are smaller than ${\sim}50$. Shown is the median ratio of half-light radii between the populations of low-mass and high-mass stars after $10\,\mathrm{Gyr}$ of evolution for different (initial) dynamical-to-stellar mass ratios $\Upsilon_\mathrm{dyn}$, computed over all $N$-body realizations (see text). Error bars span the $16^\mathrm{th}$ to $84^\mathrm{th}$ percentiles of the underlying distribution.