Modeling Globular Cluster Stellar Streams with a Basis-Expansion N-body Code

Abstract

Globular cluster stellar streams probe galaxy-formation processes and can potentially reveal the distribution of dark matter in galaxies. In many theoretical studies, streams are modeled with particle-spray or direct N-body codes. But particle-spray methods abstract away the internal dynamics of the progenitor by making strong assumptions about the escape physics, while direct N-body is prohibitively expensive for realistic (N>10^5) systems. In this paper, we present the stream-modeling capabilities of KRIOS, a new basis-expansion N-body code for collisional stellar dynamics, that bridges this runtime vs. accuracy gap. We show that KRIOS reproduces NBODY6++GPU cluster models, and their associated streams, more accurately than particle spray in a fraction of the NBODY6++GPU wall-clock time. We then compare KRIOS to various particle-spray methods on 10 orbits similar to known Milky Way streams. The morphology and kinematics of these streams most disagree when the progenitor is tightly bound to the host, as these systems are often subject to stronger tidal forces. Finally, we discuss which elements of the progenitor physics are most important for modeling stellar streams and how these might be incorporated into particle-spray methods.

Figures (16)

• Figure 1: A model produced by the KRIOS hybrid $N$-body code (Orbit 3, Table \ref{['tab:orbit_info']}), where we see both stream-like and shell-like features at ${t\!=\!5\,{\rm Gyr}}$. The unbound particles are color coded by their energy with respect to the host $E$, which is mostly conserved for escapers modulo small perturbations from the cluster potential. The bound particles (Section \ref{['subsec:non_rf_subsec']}) are shown in black. Top panel: The stream shown in the MW's reference frame, with a bulge and disk added for illustrative purposes. Bottom panel: The stream shown in the great-circle reference frame for an observer stationed at the Galactic center. The angle $\phi_{1}$ subtends an element of the stream track and $\phi_{2}$ subtends the angle out of the progenitor's instantaneous orbital plane (see Figure \ref{['fig:reference_frames']} for the axis definitions). The stream progenitor (i.e., the cluster) is at ${\phi_{1}\!=\!\phi_{2}\!=\!0^{\circ}}$. Both the leading (blue) and trailing (red) tails contain epicyclic density fluctuations kupper2010 and energy feathering amorisco2015, both well-known features of streams in axisymmetric potentials bonaca2025. The density fluctuations are most clear near the progenitor; see Figure \ref{['fig:krios_ps_comp_3']} for a direct comparison.
• Figure 2: The time-dependent SCF reference frame (black, unprimed) with respect to the fixed host reference frame (black, primed). Integration along the orbit (green) is broken up into substeps (purple) that adapt to the host potential's tidal tensor (Equation \ref{['eq:tidal_tensor']}). The unit vectors that define the great-circle reference frame (bottom panel of Figure \ref{['fig:example_krios_snapshot']}, red axes) are ${\hat{\phi}_{1}'\!\parallel\!(\boldsymbol{\Omega}_{\rm cluster}'\times\boldsymbol{r}_{\rm cluster}')}$ and $\hat{\phi}_{2}'\!\parallel\!\boldsymbol{\Omega}_{\rm cluster}'$, where ${\boldsymbol{\Omega}_{\rm cluster}'\!\parallel\!\boldsymbol{r}_{\rm cluster}'\times\boldsymbol{v}_{\rm cluster}'}$.
• Figure 3: Top panel: The integrals of motion for the second set of Table \ref{['tab:orbit_info']} orbits compared to the known population of MW GCs harris2010vasiliev2021chen2025b and stellar streams malhan2022. chen2025c classifies MWGCs based on extinction $A_{V}$ and background density $N_{\rm bg}$. Bottom panel: The sampled orbits compared to the MWGCs and streams in the meridional plane, showing that our sample is biased toward orbits in the MW halo. Orbits 3 (closer to ${z'\!=\!0}$) and 5 are boldened for illustrative purposes, as they are the stream models shown explicitly in Sections \ref{['sec:results']} and \ref{['sec:discussion']}.
• Figure 4: Top panel: The cluster's Lagrange radii (i.e., the smallest radii that enclose ${\{1\%, 10\%, 30\%, 50\%, 70\%, 80\%, 90\%, 99\%\}}$ of the cluster mass) as a function of time for the eccentric validation orbit. The solid line is the KRIOS result and the shaded region represents the ensemble of NBODY6++GPU runs (10 for each orbit). Bottom panel: The number of particles outside the bound radius (defined in Section \ref{['subsec:non_rf_subsec']}) as a function of time, color coded by orbit.
• Figure 5: Integrals-of-motion and stream-track information for each of the validation models. First row: a scatter plot of the stream particles' integrals of motion; contours encase $1\sigma$, $2\sigma$, and $3\sigma$ of the particles for the ${e\!\neq\!0}$ test. Second row: Particle counts along the stream track. The solid lines represent the KRIOS result in each panel, while in the top-right panel the translucent contours represent the entire NBODY6++GPU ensemble. In the bottom row, each of the ensemble models are displayed separately. There are small discrepancies in the circular orbit tests consistent with the mass-loss rates shown in Figure \ref{['fig:cluster_validation']}, whereas there is good agreement for the eccentric orbit validation test.