Abstract
Recently, Vitral & Mamon detected a central concentration of dark objects in the core-collapsed globular cluster NGC 6397, which could be interpreted as a subcluster of stellar-mass black holes. However, it is well established theoretically that any significant number of black holes in the cluster would provide strong dynamical heating and is fundamentally inconsistent with this cluster's core-collapsed profile. Claims of intermediate-mass black holes in core-collapsed clusters should similarly be treated with suspicion, for reasons that have been understood theoretically for many decades. Instead, the central dark population in NGC 6397 is exactly accounted for by a compact subsystem of white dwarfs (WDs), as we demonstrate here by inspection of a previously published model that provides a good fit to this cluster. These central WD subclusters are in fact a generic feature of core-collapsed clusters, while central black hole subclusters are present in all non-collapsed clusters.
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Globular clusters (GCs) are highly dynamic systems hosting a variety of stellar phenomena, particularly involving compact objects. Recently, analyzing a heightened central velocity dispersion in NGC 6397, Vitral & Mamon (2021) detected a central dark population speculated to be a subcluster of stellar-mass black holes (BHs) of total mass 103 M⊙ within the central 6'' (0.07 pc). However, this hypothesis would contradict longstanding consensus from GC modeling that any substantial BH population would dynamically heat a cluster enough to prevent core collapse and sustain a large, easily resolvable core (Merritt et al. 2004; Mackey et al. 2007; Wang et al. 2016; Kremer et al. 2019a). For lists of Galactic GCs that are expected to currently retain large BH populations, see Askar et al. (2018), Weatherford et al. (2020), and Shishkovsky et al. (2020).
1. No Stellar-mass BH Population in NGC 6397
Massive star evolution produces hundreds to thousands of BHs in typical GCs, most of which are initially retained (e.g., Kroupa 2001). These BHs quickly mass-segregate to the cluster core, assembling a dense central BH subsystem (e.g., Spitzer 1969; Kulkarni et al. 1993). Three-body encounters within this BH-dominated core produce many dynamically hard BH binaries (e.g., Morscher et al. 2015), which then provide energy to passing stars through scattering interactions. This further hardens the binaries while heating the rest of the cluster (Breen & Heggie 2013). Scattered BH binaries receive significant recoil kicks, displacing them from the core (and sometimes ejecting them altogether); they further heat the cluster through dynamical friction while sinking back to the core. Overall, BH dynamics acts as a strong energy source in a process called "BH burning" (for a review, see Kremer et al. 2019b). This process is well-understood and well-supported by a wide scientific consensus (Merritt et al. 2004; Mackey et al. 2007; Peuten et al. 2016; Wang et al. 2016; Chatterjee et al. 2017; Arca Sedda et al. 2018; Kremer et al. 2019a; Antonini & Gieles 2020).
The energy generated by BH burning inflates the cluster and supports it against gravothermal contraction. Hence, clusters that retain sizable BH populations today exhibit large core radii, flat central surface brightness profiles (well fit by King models), and reduced mass segregation in their luminous stellar populations (e.g., Chatterjee et al. 2017; Kremer et al. 2020; Weatherford et al. 2020). Via this mechanism, GCs exceeding a critical mass fraction in BHs may even evolve toward 100% BH clusters, after ejecting all of their stars (Gieles et al. 2021; Weatherford et al. 2021). Importantly, GCs only evolve toward traditional "core-collapsed" surface brightness profiles after almost all BHs have been ejected. Since NGC 6397 is core-collapsed, it should therefore be expected to have retained very few, if any, BHs at present.
While direct probes of the BH population are sparse (binary counts from X-ray/radio/radial-velocity measurements are instructive but typically small; e.g., Strader et al. 2012; Giesers et al. 2018), indirect probes such as the degree of mass segregation are powerful when combined with careful modeling. Along these lines, Weatherford et al. (2020) leverage a known anti-correlation between clusters' observable mass segregation and BH retention to place an upper-bound, at 95% (67%) confidence, on the BH content presently retained in NGC 6397: <16 (<8) BHs with total mass <420 M⊙ (<200 M⊙). This eliminates BHs as a plausible explanation for NGC 6397's central dark population.
2. No IMBHs in Core-collapsed Clusters
For similar reasons, claims of intermediate-mass BHs (IMBHs) at the centers of core-collapsed GCs (e.g., Gerssen et al. 2002; Kamann et al. 2016; Perera et al. 2017) have not withstood follow-up studies (e.g., McNamara et al. 2003; Murphy et al. 2011; Kirsten & Vlemmings 2012; Gieles et al. 2018; Tremou et al. 2018). Like stellar-mass BHs, IMBHs are dynamical heat sources that inflate the cluster core significantly (Shapiro 1977; Marchant & Shapiro 1980; Heggie et al. 2007). Clusters with IMBHs should resemble standard King models except within the IMBH's small radius of influence (Baumgardt et al. 2005). Searches for IMBHs in core-collapsed clusters in pursuit of the theorized cusp in the surface density are therefore misguided. Instead, such searches should target clusters which have not undergone core collapse, where stronger cases for IMBHs might be made.
3. The Alternative: A Massive Subsystem of White Dwarfs
In Figure 1, we illustrate a GC model that closely fits NGC 6397's surface brightness and velocity dispersion profiles. The initial cluster contained N = 4 × 105 stars and was relatively compact (virial radius rv = 1 pc). The present-day model agrees well with many observations, including numbers of cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries (Rui et al. 2021). This model belongs to a large, recently released model grid, the CMC Cluster Catalog, designed to broadly probe the space of realistic Galactic GCs without any directed attempt to fit any particular cluster (Kremer et al. 2020).
Figure 1. The enclosed mass of WDs and neutron stars vs. projected radius for our best-fitting NGC 6397 model. The shading indicates projection uncertainties. In contrast to BHs, WDs are a natural and obvious "dark" population contributing 103 M⊙ (black dashed line) within 6'' of the cluster center, in concordance with observed properties of NGC 6397's dark population. Not shown here are BHs, as this model for NGC 6397 contains only a single remaining BH, of mass 17.4 M⊙.
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This best-fitting model for NGC 6397 possesses only a single BH. However, it contains close to 103 M⊙ in white dwarfs (WDs) within the central 6'' (see Figure 1), completely accounting for the dark population detected by Vitral & Mamon (2021). In our model, the WD population is dominated by heavy WDs with a mean mass ≈1 M⊙; most of these are carbon–oxygen WDs (86%), with a sizable minority of oxygen-neon WDs (14%). Crucially, both the lack of stellar-mass BHs and the presence of a centrally concentrated WD population are generic, robust features expected in all core-collapsed GCs, rather than esoteric predictions expected to apply only to NGC 6397 (see, e.g., Kremer et al. 2020, where this result was demonstrated generally). We will further explore the implications of these WD subsystems in core-collapsed clusters in a forthcoming work (K. Kremer et al. 2021, in preparation).