Abstract

We analyze proper motions from the Hubble Space Telescope (HST) and the second Gaia data release along with line-of-sight velocities from the MUSE spectrograph to detect imprints of an intermediate-mass black hole (IMBH) in the center of the nearby, core-collapsed, globular cluster NGC 6397. For this, we use the new MAMPOSST-PM Bayesian mass-modeling code, along with updated estimates of the surface density profile of NGC 6397. We consider different priors on velocity anisotropy and on the size of the central mass, and we also separate the stars into components of different mean mass to allow for mass segregation. The velocity ellipsoid is very isotropic throughout the cluster, as expected in post-core collapsed clusters subject to as strong a Galactic tidal field as NGC 6397. There is strong evidence for a central dark component of 0.8 to 2% of the total mass of the cluster. However, we find robust evidence disfavoring a central IMBH in NGC 6397, preferring instead a diffuse dark inner subcluster of unresolved objects with a total mass of 1000 to 2000 M⊙, half of which is concentrated within 6 arcsec (2% of the stellar effective radius). These results require the combination of HST and Gaia data: HST for the inner diagnostics and Gaia for the outer surface density and velocity anisotropy profiles. The small effective radius of the diffuse dark component suggests that it is composed of compact stars (white dwarfs and neutron stars) and stellar-mass black holes, whose inner locations are caused by dynamical friction given their high progenitor masses. We show that stellar-mass black holes should dominate the mass of this diffuse dark component, unless more than 25% escape from the cluster. Their mergers in the cores of core-collapsed globular clusters could be an important source of the gravitational wave events detected by LIGO.

Highlights

  • When the Laser Interferometer Gravitational-Wave Observatory (LIGO) first detected gravitational waves coming from a stellar-mass black hole merger (Abbott et al 2016) and the Event Horizon Telescope (EHT) released the first image of the supermassive black hole (SMBH) in M 87 (Event Horizon Telescope Collaboration 2019), astronomers obtained the most compelling evidence about the existence of those intriguing and particular objects

  • We used 6 Markov chain Monte Carlo (MCMC) chains run in parallel and stopped the exploration of parameter space after one of the chains reached a number of steps Nsteps = 10 000 Nfree, where Nfree is the number of free parameters of the model

  • Among models 1 to 6, the most likely one and very strongly favored by AICc yields an intermediate-mass black hole (IMBH) mass of 511+−125087 M, while model 1, which is weakly favored by BIC over model 6, yields an IMBH mass of 658+−73038 M

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Summary

Introduction

When the Laser Interferometer Gravitational-Wave Observatory (LIGO) first detected gravitational waves coming from a stellar-mass black hole merger (Abbott et al 2016) and the Event Horizon Telescope (EHT) released the first image of the supermassive black hole (SMBH) in M 87 (Event Horizon Telescope Collaboration 2019), astronomers obtained the most compelling evidence about the existence of those intriguing and particular objects. Giersz et al (2015) proposed that hard binaries containing stellar-mass BHs merge with other stars and binaries, which can be a fast or slow process These models present, drawbacks: The short relaxation time needed in the Portegies Zwart & McMillan (2002) scenario usually requires primordial mass segregation in order not to eliminate too many GCs candidates, while the assumption by Miller & Hamilton (2002) of BH seeds above ≈50 M is not expected as the massive progenitors are fully exploded in pairinstability supernovae (e.g., Woosley 2017). Many of the mass modeling studies performed with this cluster assumed or constrained its surface density parameters to values estimated long ago (e.g., Trager et al 1995), that may suffer from problems such as radial incompleteness, which is better addressed by missions such as HST and Gaia This lack of accuracy on the surface density can strongly impact the dynamical analysis of NGC 6397. We provide new fits to the surface density parameters of this cluster by jointly modeling HST and Gaia data

MAMPOSSt-PM
Dark component
Velocity anisotropy profile
Center
Distance
Method
HST data
HST absolute positions
HST absolute proper motions
Gaia data
Data cleaning
Positional accuracy
Proper motions
HST proper motion filtering
HST color-magnitude filtering
Removal of X-ray binaries
HST final numbers
Quality flags
Gaia proper motion filtering and the bulk proper motion of NGC 6397
Maximum projected radius
Gaia color-magnitude filtering
Gaia final numbers and comparison to HST
MUSE data cleaning
Merging of the different datasets
Rotation
Practical considerations
Basic approach
Choice of model and main parameters
Stitching HST and Gaia
Surface density results
Multiple populations
Multiple chemical populations
Mass segregation
MAMPOSSt-PM assumptions and priors
Marginal distributions and covariances
Bayesian information
MAMPOSSt-PM runs
Velocity anisotropy
Intermediate mass black hole
CUO density profile
Presence of an IMBH in addition to the CUO
Two-mass populations
10.1. Main results
10.2. Robustness
10.3. Effects of the dataset
10.4. Velocity anisotropy
10.5. Intermediate mass black hole
10.6. Cluster of unresolved objects
10.7. Final thoughts
New coefficients for VM20 approximation extending to very low radii
Choice of deprojection approximation
Proper motion distribution function
Findings
Convolution of field stars distribution

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