Poetry in (Proper) Motion: Internal Kinematics of Globular Clusters with HST

M. Libralato (libra[at]stsci.edu) and A. Bellini (bellini[at]stsci.edu)

Globular clusters (GCs) have revealed themselves to be far more complex than we originally thought: GCs rotate, present kinematic anisotropies, host multiple stellar populations (mPOPs), slowly interact with the surrounding Galaxy and break apart forming tidal tails. Most of the new findings in the field of GCs of the two last decades have been made possible thanks to exquisite photometry and spectroscopy, but now the contribution (and impact) of high-precision astrometry is exponentially growing.

The internal kinematics of GCs is one of the research fields that is benefiting the most from the new "Renaissance of astrometry" in the Gaia era. Nevertheless, stars in the very core of GCs and at the faint end of the color-magnitude diagrams (CMDs) are and will be out of Gaia's reach, leaving Hubble Space Telescope (HST) as the only tool to obtain high-precision astrometric measurements for these stars.

In this newsletter we describe the results obtained for the GC NGC 362 (Libralato et al. 2018). The results of this paper are part of a broader project focused on producing high-precision proper motion (PM) catalogs for over 60 GCs for the "Hubble Space Telescope UV Legacy Survey of Galactic GCs" (GO-13297) and ancillary programs, and are obtained within the HSTPROMO collaboration. NGC 362 is a post core-collapsed cluster, and as such its centermost regions are extremely crowded. This cluster therefore represents an ideal benchmark to test our reduction tools, which are optimized for crowding environments. We were able to measure internal PMs with a precision of a few tens of μas year-1 even for faint main-sequence stars in the cluster's core. For brighter Hubble stars at the faint limit of Gaia, our PM precision is >80 times better than Gaia's end-of-mission predictions.


Internal Proper Motions of Multiple Stellar Populations

In the recent years, the paradigm of GCs made up of simple stellar populations, i.e., stars born at the same time from the same proto-cluster cloud and with the same chemical composition, has been demolished. It is a fact now that formally all GCs host mPOPs characterized by stars with different chemical composition and age, forming well-distinct sequences on a CMD. So far, most of the theoretical effort has been focused on developing formation scenarios able to account for all the photometric and spectroscopic observational pieces of information, but all the proposed theories failed to account for all the available evidence (see the review of Renzini et al. 2015), and many questions are still unanswered.

Dynamical models (e.g., Vesperini et al. 2013) predict that second-generation (2G) stars, born at a later stage from the material processed by first-generation (1G) stars, formed initially more centrally concentrated than 1G stars, and then slowly diffused outward preferentially along radial orbits, due to two-body interactions. After many local two-body relaxation times, any difference in spatial distribution and kinematics of 1G and 2G stars is expected to be erased. This happens first in the cluster's core, where the local two-body relaxation time is short, and later also in the cluster's outskirts, where the local two-body relaxation is much longer, reaching a few Gyrs in some clusters. Massive clusters have longer relaxation times at any radial distance, so they are more likely to still retain some fossil signature of the initial spatial segregation between 1G and 2G stars. Since GC stars migrate outward preferentially along radial orbits, if this fossil signature is still present we would expect 2G stars to be more radially anisotropic (σrad > σtan) than 1G stars at least in the cluster outskirts. High-precision PMs represent one of the most-effective ways to measure these effects and constrain the formation and dynamical evolution of these ancient stellar systems (see the discussion in, e.g., Hénault-Brunet et al. 2015).

The internal kinematics of mPOPs in GCs might seem a niche research field at a first glance, but GCs are among the oldest objects in the Universe and understanding how their mPOPs formed and have evolved will shed light on the chain of events that occurred at the dawn of GCs, and hence of the Milky Way. To date, there exists only a handful of observational works on the internal kinematics of mPOPs.

For instance, Anderson & van der Marel (2010) investigated the core of the GC NGC 5139 (ω Cen), and found no significant kinematic differences between 1G and 2G stars. Similarly, Libralato et al. (2019) found no difference in the kinematics of the mPOPs in the core of NGC 6352. These results work in favor of theoretical predictions, since the relaxation time in the core of these GCs is too short and any initial difference between the kinematic properties of 1G and 2G stars have long been erased. It is in the clusters' outskirts where our attention should be focused. Richer et al. (2013; but also Milone et al. 2018 with Gaia) showed that 2G stars in the outskirt of 47 Tuc are more radially-anisotropic than 1G stars. Similar results have been found for stars in the outskirts of NGC 2808 (Bellini et al. 2015) and ω Cen (Bellini et al. 2018).

NGC 362 hosts at least four distinct stellar populations (one 1G and three subsequent 2Gs), which we isolated by means of the distinct location of theirs stars on CMDs and pseudo-two-color diagrams (e.g., see the top panels of Fig. 1 for red-giant-branch stars). We computed tangential and radial velocity-dispersion profiles for each population, and found no significant difference between the kinematics of the mPOPs. We did find a marginal (~2.2-σ level) signature of 2G stars with a smaller velocity dispersion than 1G stars (see bottom panels of Fig. 1). In addition, we found no evidence of radial anisotropy for both 1G and 2G stars.

Analysis of the internal kinematics of the mPOPs in NGC 362
Figure 1: (Figure 5 of Libralato et al. 2018) in panels (a), we show the mF814W versus CF275W,F336W,F438W (left), mF814W versus (mF275W-mF814W) (middle) and pseudo-two-color diagram (right) used to tag 1G (population A in yellow) and 2G (populations B, C and D in azure, green and red, respectively) stars. In panels (b), (c) and (d), we present the combined, radial and tangential velocity-dispersion profiles of 1G and 2G stars, respectively. In the rightmost panels (2–4), we show the comparison between the kinematics of 1G and 2G stars. (See Libralato et al. (2018) for the complete description of the Figure.)


Kinematics of GCs as a Whole

The exquisite PMs of Hubble allowed us to analyze the kinematics of NGC 362 as a whole. NGC 362 is a dynamically old GC that experienced a collapse of its core. To verify this, we measured the level of systemic rotation of the cluster in the plane of the sky, and found it consistent with being a non-rotating cluster. As GCs age, they loose angular momentum (e.g., Tiongco et al. 2017), and NGC 362 has likely lost most of its initial angular momentum, thus confirming its advanced dynamical state. We further confirmed this through the measurement of the cluster's state of energy equipartition.

GCs are expected to evolve over time toward a state of full energy equipartition. When this happens, the velocity dispersion of their stars, σμ, should scale with the stellar mass m as m where η, the level of energy equipartition, is equal to 0.5 (Spitzer 1969, 1987). Recent N-body simulations have instead shown that full energy equipartition is actually never reached, and GCs only achieve at best partial energy equipartition (e.g., Trenti & van der Marel 2013; Bianchini et al. 2016; Webb & Vesperini 2017). Furthermore, η is not constant over the entire cluster, but is expected to decrease as the distance from the cluster's center increases (the two-body relaxation time in the outskirts of GCs is longer than in the centermost regions).

Measuring how the velocity dispersion varies as a function of the stellar mass in GCs is a challenging task because it requires to measure very precise PMs for stars several magnitudes fainter than the main-sequence turn-off. Over the years, many efforts (and reduction tools) have been developed in exploiting very crowded environments with Hubble data, so that we can use Hubble PMs to study the actual state of energy equipartition in GCs for the first time.

We computed the velocity dispersion of stars in NGC 362 down to stellar masses of about ~0.45 (i.e., five magnitudes below the main-sequence turn-off) and estimated the global and the local (i.e., at different radial distances) values of the level of energy equipartition η (Fig. 2). We find that η decreases from ~0.4 at the center to ~0.1 at 2 half-light radii: a result also supported by numerical simulations. Bianchini et al. (2018) also proposed that the collapse of the core in a GC should leave peculiar kinematic signatures in the global and local levels of energy equipartition. Following Bianchini et al. prescriptions, we compared the local and global level of energy equipartition and were able, for the first time, to infer that NGC 362 is in a post-core-collapsed state using kinematic arguments.

Level of energy equipartition in NGC 362
Figure 2: (Figure 11 of Libralato et al. 2018) measurement of the level of energy equipartition in the GC NGC 362. First, we divided the main sequence of NGC 362 in 10 magnitude (i.e., mass) bins (panel a) and we computed the average value of the velocity dispersion σμ for each bin. The obtained velocity dispersion as a function of stellar mass was then fitted in a log-log plane with a weighted least-squares straight line. The slope of the straight line gives us the level of energy equipartition η (panel b). The same procedure was repeated at different radial distances. The variation of η as a function of distance from the cluster's center (panel c) is in agreement with the theoretical predictions: the further from the center, the lower is the level of energy equipartition. (See Libralato et al. (2018) for the complete description of the Figure.)

The aforementioned examples are only a few proofs of the key role of high-precision astrometry in stellar astrophysics. Hubble has now paved the path. The upcoming James Webb Space Telescope (JWST) and Wide-Field InfraRed Space Telescope (WFIRST) will help us to explore fainter and further regions, and build a complete kinematic picture of GCs.



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