Kinematics of Stellar Streams from Globular Clusters Depend on Black Hole Retention and Star Mass: A Selection Effect for Dark Matter Inference

TL;DR

This paper shows that the velocity dispersion $σ$ in stellar streams from globular clusters depends on stellar mass $m$ due to internal GC dynamics, especially after core collapse when mass segregation and BH depletion enhance high-velocity ejecta. Using a suite of Monte Carlo N-body GC simulations with BH retention under static Galactic tides and subsequent streaming modeled in Gala, the authors quantify how $σ$ grows with $m$ and how strong encounters generate exponential tails in the velocity distribution. They find that the $m$–$σ$ correlation is enhanced in core-collapsed, BH-depleted GCs and persists under observational velocity cuts, implying that stream kinematics could bias DM inferences toward warmer DM scenarios if not properly accounted for. The work highlights the need to consider GC-origin physics and selection effects when using GC streams to probe dark matter substructure, and suggests extending analyses to eccentric orbits and evolving potentials, as well as searching for $m$–$σ$ signals in observed streams.

Abstract

Velocity dispersion ($σ$) in stellar streams from globular clusters (GCs) is sensitive to heating by Galactic substructure, including dark matter (DM) subhalos. Recent studies have compared $σ$ in observed and modeled streams to probe DM properties, but have relied on stream models that neglect strong encounters, black holes (BHs), and mass segregation in GCs. Such phenomena may inflate stream $σ$ or introduce selection effects -- e.g., a $σ$ that depends on star mass ($m$). We investigate this prospect using Monte Carlo $N$-body simulations of GCs under static Galactic tides to generate mock streams with realistic mass and velocity distributions. We find $σ$ correlates with $m$, especially after core collapse (the GC's observable increase in central density upon ejecting its BHs), rising from $1.2$--$2.2\,{\rm km\,s}^{-1}$ between $m=0.3$--$0.8\,M_\odot$, with typical kinematic cuts on stream membership. Similar in magnitude to heating by Galactic substructure, this enhancement occurs because the GC's loss of BHs allows its most-massive stars to occupy its dense center, raising their likelihood of strong ejection via binary interactions and adding broad, exponential wings to the stream's velocity distribution. Streams' kinematics thus probe properties (density, BH retention) of their progenitor GCs. Our results also imply observations of streams from some GCs, especially those not subject to highly episodic mass loss, may select for higher $σ$ than predicted by models neglecting $σ$'s $m$-dependence. This would cause observed $σ$ in streams -- already on the low side of expectations for cold DM -- to further favor alternatives such as warm or ultralight DM.

Figures (16)

• Figure 1: Rolling average time evolution of GC properties in our simulations. Line style (dashed, solid) distinguishes simulations with different initial $r_v=(0.5,2)\,{\rm pc}$ and coloration (red, blue) indicates the initial high-mass binary fraction $f_{b,h}=(5\%,50\%)$, with specific shading distinguishing independent statistical realizations of the same $(r_v,f_{b,h})$ combination. Top left: number of particles (single stars plus binaries) relative to their initial number. Top right: number of BHs and BH--BH binaries (BBHs). Bottom left: density-weighted core radius $r_c$CasertanoHut1985. Bottom right: half-mass radius $r_h$. The BHs kinematically heat the GC via strong binary interactions and repeated segregation to the GC's center, inflating $r_h$ and supporting $r_c$ against collapse. The permanent drop in $r_c$ starting at $t\approx5\,{\rm Gyr}$ for GCs born with $r_v=0.5\,{\rm pc}$ (dashed curves) reflects the transition to an observably core-collapsed state that occurs once the GC has ejected the vast majority of its BHs.
• Figure 2: Mass segregation in our GCs, measured by stars' median radial positions $r$ versus $m$, excluding compact objects and binaries. Median $r$ is measured in nonoverlapping mass bins (width $0.1\,M_\odot$) centered on each data point and is normalized by the GC's global half-mass radius $r_h$. For simplicity, we combine data from all six simulations for each choice of $r_v$: $0.5\,{\rm pc}$ (dashed curves) and $2\,{\rm pc}$ (solid). Shading distinguishes profiles averaged over distinct GC age ranges (see legend), with darker shades indicating older GCs.
• Figure 3: Map of the surface number density $\Sigma$ of unbound stars (including those still on their way out of the GC) from one of our GCs born with $r_v=0.5\,{\rm pc}$, $f_{b,h}=50\%$. $\Sigma$ is averaged over ages $9$--$13\,{\rm Gyr}$ by stacking $401$ snapshots (one every $10\,{\rm Myr}$), finely binning by location, and dividing each bin count by $401$ and the bin area in ${\rm pc}^2$. We use Galactocentric cylindrical coordinates $(R,\phi,Z)$, with the radial coordinate expressed as $X=R-R_g$ so that $(X,\phi,Z)=(0,0,0)$ is the GC's center. The top panel is thus a view face-on to the GC's circular orbit after mapping it to the line segment $(X,Z)=0$, $\phi\in[-180^\circ,180^\circ]$. The bottom panel is a panoramic view edge-on to the GC's orbit from the perspective of the Galactic center. Unless noted otherwise, we select as stream members stars outside the GC's tidal radius $r_t\sim 0.01R_g$ with $\lvert X/R_g \rvert\leq0.05$, $\lvert Z/R_g\rvert\leq0.02$, and $\vert\phi\rvert\leq30^\circ$. Panel aspect ratios are scaled to avoid stretching the stream; i.e., each pixel has equal side lengths in parsecs.
• Figure 4: Distribution of our stream stars' velocities relative to the GC's orbital velocity, $v=\lvert\vec{v_\star}-\vec{v_c}\rvert$, for several GC age ranges: $1$--$5\,{\rm Gyr}$ (top row), $5$--$9\,{\rm Gyr}$ (middle), and $9$--$13\,{\rm Gyr}$ (bottom). We only count stars with $\lvert\phi\rvert\leq30^\circ$ and combine data from all six simulations for each choice of $r_v$---$0.5\,{\rm pc}$ (dashed curves) and $2\,{\rm pc}$ (solid). The left panels show the time-averaged number of stream stars with velocities ${>}v$ for several escape mechanisms: two-body relaxation (2BR; yellow), binary--single and binary--binary strong encounters (BS/BB; blue), and three-body binary formation (3BBF; red). The lighter set of curves includes stars regardless of mass, while the darker set counts only stars with $m\geq 0.6\,M_\odot$. The right panels show one minus the overall cumulative density function of $v$, including all escape mechanisms. Line shading again indicates distinct mass cuts, from including all $m$ (lightest) to just stars with $m\geq 0.8\,M_\odot$ (darkest). The prominence of the high-$v$ tail increases with $m$ during and after the GC's core collapse (dashed curves in the lowermost two right panels), precipitated by the loss of most BHs. Thin black curve fits, parameterized in Table \ref{['table:curve_fits_rel']}, are plotted atop all curves in the figure, based on stars with $v<100\,{\rm km\,s}^{-1}$ in the left column (except 2BR; $v<40\,{\rm km\,s}^{-1}$) and $v<40\,{\rm km\,s}^{-1}$ in the right column. Equivalent figures for $v$'s component velocities $(v_R,v_\phi,v_Z)$ are in the Appendix.
• Figure 5: The fraction $f_{\rm str}$ of stream members ejected by BS/BB encounters (top row) and three-dimensional velocity dispersion $\sigma_v$ (lower rows) in our stellar streams versus star mass $m$. As in Figure \ref{['fig:mass_segregation']}, we use non-overlapping mass bins of width $0.1\,M_\odot$ and combine the data from all six independent simulations for each choice of $r_v$---$0.5\,{\rm pc}$ (dashed curves) and $2\,{\rm pc}$ (solid curves). Shading again indicates time averages across several different $4\,{\rm Gyr}$-wide intervals in GC age (see legend). The upper two rows of panels include stars for which each $v$ component $(v_R,v_\phi,v_Z)\leq100\,{\rm km\,s}^{-1}$---nearly all $v$ but filtering out several extreme outliers. The bottom row includes only stars with $(v_R,v_\phi,v_Z)\leq20\,{\rm km\,s}^{-1}$, similar to kinematic cuts imposed in observations to help identify stream members. Each column of panels imposes a different angular cut on stream membership: only including stars with $\lvert\phi\rvert\leq3^\circ$ (left), $\lvert\phi\rvert\leq10^\circ$ (center), and $\lvert\phi\rvert\leq30^\circ$ (right, most typical of observed stream lengths). The $m$--$f_{\rm str}$ correlation in the top row causes an $m$--$\sigma_v$ correlation in the lower panels, albeit reduced under the more stringent velocity cut. Equivalent figures for $v$'s component velocities $(v_R,v_\phi,v_Z)$ are in the Appendix.