Evolution of the kinematic properties of rotating multiple-population globular clusters

TL;DR

This study probes how rotating multiple-population globular clusters evolve under two-body relaxation and galactic tides using NBODY6++GPU simulations. Four initial misalignment configurations between a cluster's internal rotation and its orbital angular momentum are tested, with FG and SG populations initialized as spatially distinct Rotating components. The results show rapid erosion of FG/SG spatial differences within a few $t_{\rm rh,i}$, while rotational differences and velocity anisotropy—especially in the SG—persist longer, with low-mass stars displaying the strongest signatures. The galactic tidal field gradually aligns the cluster's internal angular momentum with its orbital angular momentum, more quickly in the outer regions and for low-mass stars, implying that present-day kinematics may understate primordial differences. These findings help interpret observed kinematic disparities in globular clusters and support formation scenarios in which SG stars start more centrally concentrated and rapidly rotating.

Abstract

Globular clusters (GCs) host multiple stellar populations differing in their chemical and dynamical properties. A number of models for the formation of multiple populations predict that the subsystem of second generation (SG) stars is characterized by a more centrally concentrated spatial distribution and a more rapid rotation than the system of first generation (FG) stars. We present the results of N-body simulations exploring the long-term dynamical evolution of rotating multiple-population GCs. We study the evolution of systems starting with four different orientations of the GC's total internal angular momentum vector relative to the orbital angular momentum. We explore the evolution driven by two-body relaxation and the effects of the GC's interaction with the galactic tidal field. We focus on the kinematic differences between the two generations and we quantify them by exploring the FG and SG rotation velocity and angular momenta. We find that kinematic differences between the generations persist for most of the GCs' lifetimes, although the strength of these differences decreases after a few relaxation times. The differences can be seen most clearly in the lowest-mass stars. We find that the GCs' internal angular momentum gradually aligns with the orbital angular momentum, although there is little difference in this alignment between the FG and SG systems. We also find that stars in the GC's outer regions align with the orbital angular momentum vector more rapidly than those in the inner regions leading to a variation of the orientation of the internal angular momentum with the clustercentric distance. The alignment between internal angular momentum and orbital angular momentum occurs more rapidly for low-mass stars. We study the evolution of the anisotropy in the velocity distribution and find the SG to be characterized by a stronger radial anisotropy than the FG.(abridged)

Figures (19)

• Figure 1: Surface mass density profiles as a function of the projected distance from the cluster's centre normalised by the projected half-mass radius (R${\rm_h}$) of the total cluster (see Methods for a complete definition). The profiles are shown at a few representative times in the Delta0 model. All densities are normalised by the central bin of the total surface mass density (FG + SG). Time is normalised by the initial half-mass relaxation time of the cluster, $t_{\rm rh,i}$. The difference between the profiles of the two generations is gradually erased as the system evolves.
• Figure 2: Radial profiles of the rotation velocity are shown at representative times for the Delta0 model. The rotation velocity is normalised by the central velocity dispersion (inner 1$\%$ of stars) of all stars (FG + SG). The radius is normalised by the projected half-mass radius (R$_{\rm h}$) of all stars (FG +SG). Time is normalised by the initial half-mass relaxation time of the cluster, $t_{\rm rh,i}$.
• Figure 3: Radial profiles of the velocity anisotropy are shown at representative times in the Delta0 model. We define anisotropy to be the ratio of tangential velocity dispersion over the radial velocity dispersion, $\sigma_{\rm T} / \sigma_{\rm R}$, with a completely isotropic system having a value of $\sigma_{\rm T} / \sigma_{\rm R}$ = 1. Time and radius normalisations are the same as described in Fig. \ref{['fig:rot_prof']}.
• Figure 4: Radial profiles of the rotation velocity are shown at representative times for the Delta0 model for different mass groups. The line-of-sight is the same as described in Fig. \ref{['fig:rot_prof']}. The rotation velocity is normalised by the central velocity dispersion (inner 1$\%$ of stars) of all stars (FG + SG). Time and radius normalisations are the same as described in Fig. \ref{['fig:rot_prof']}. Mass groups are split into low (0.1 - 0.3 $M_\odot$), intermediate (0.3 - 0.7 $M_\odot$), and high (0.7 - 1 $M_\odot$) mass bins.
• Figure 5: The time evolution of the differences between the maximum rotation velocities of the FG and SG stars is shown for different mass groups. Velocities are normalised by the peak rotation velocity for all stars (FG + SG), computed at each time. Dots correspond to the peak velocity values taken directly from the rotation profiles. Lines represent the peak velocity values taken from best-fit rotation curves to the rotation profiles (as described in Eq. \ref{['eq:rot']}). The time has been limited to when simulations have approximately 10$\%$ of the initial stars remaining.