Black Hole Retention Fractions Research Articles

Stellar-mass Black Holes in Globular Clusters: Dynamical consequences and observational signatures

AbstractSizeable number of stellar-mass black holes (BHs) in globular clusters (GCs) can strongly influence the dynamical evolution and observational properties of their host cluster. Using results from a large set of numerical simulations, we identify the key ingredients needed to sustain a sizeable population of BHs in GCs up to a Hubble time. We find that while BH natal kick prescriptions are essential in determining the initial retention fraction of BHs in GCs, the long-term survival of BHs is determined by the size, initial central density and half-mass relaxation time of the GC. Simulated GC models that contain many BHs are characterized by relatively low central surface brightness, large half-light and core radii values. We also discuss novel ways to compare simulated results with available observational data to identify GCs that are most likely to contain many BHs.

Blue Straggler Stars beyond the Milky Way. IV. Radial Distributions and Dynamical Implications

Blue straggler stars have been proposeed as powerful indicators to measure the dynamical state of Galactic globular clusters. Here we examine for the first time if this framework of blue straggler stars as dynamical clocks, which was specifically developed for Galactic globular clusters, may also hold for younger globular clusters in the Large Magellanic Cloud. Using Hubble Space Telescope observations, we study seven Large Magellanic Cloud star clusters with ages between ~700 Myr and 7 Gyr. We confirm that our sample clusters are consistent with the empirical correlation previously derived for Galactic globular clusters, within a modest tolerance. We suggest that to further examine if blue straggler stars can measure the dynamical state of their host clusters over an extended range of dynamical ages, more studies of dynamically older Magellanic Cloud clusters are required. We discuss the physical implications of our results in terms of their central, dimensionless King potential, as well as the initial retention fraction of black holes.

The black hole retention fraction in star clusters

Context. Recent research has been constraining the retention fraction of black holes (BHs) in globular clusters by comparing the degree of mass segregation with N-body simulations. They are consistent with an upper limit of the retention fraction being 50% or less. Aims. In this work, we focus on direct simulations of the dynamics of BHs in star clusters. We aim to constrain the effective distribution of natal kicks that BHs receive during supernova (SN) explosions and to estimate the BH retention fraction.Methods. We used the collisional N-body code nbody6 to measure the retention fraction of BHs for a given set of parameters, which are: the initial mass of a star cluster, the initial half-mass radius, and σBH, which sets the effective Maxwellian BH velocity kick distribution. We compare these direct N-body models with our analytic estimates and newest observational constraints. Results. The numerical simulations show that for the one-dimensional velocity kick dispersion σBH < 50 km s−1, clusters with radii of 2 pc and that are initially more massive than 5 × 103 M⊙ retain more than 20% of BHs within their half-mass radii. Our simple analytic model yields a number of retained BHs that is in good agreement with the N-body models. Furthermore, the analytic estimates show that ultra-compact dwarf galaxies should have retained more than 80% of their BHs for σBH ≤ 190 km s−1. Although our models do not contain primordial binaries, in the most compact clusters with 103 stars, we have found evidence of delayed SN explosions producing a surplus of BHs compared to the IMF due to dynamically formed binary stars. These cases do not occur in the more populous or expanded clusters.

The global mass functions of 35 Galactic globular clusters – II. Clues on the initial mass function and black hole retention fraction

In this paper we compare the mass function slopes of Galactic globular clusters recently determined by Sollima & Baumgardt (2017) with a set of dedicated N-body simulations of star clusters containing between 65,000 to 200,000 stars. We study clusters starting with a range of initial mass functions (IMFs), black hole retention fractions and orbital parameters in the parent galaxy. We find that the present-day mass functions of globular clusters agree well with those expected for star clusters starting with Kroupa or Chabrier IMFs, and are incompatible with clusters starting with single power-law mass functions for the low-mass stars. The amount of mass segregation seen in the globular clusters studied by Sollima & Baumgardt (2017) can be fully explained by two-body relaxation driven mass segregation from initially unsegregated star clusters. Based on the present-day global mass functions, we expect that a typical globular cluster in our sample has lost about 75% of its mass since formation, while the most evolved clusters have already lost more than 90% of their initial mass and should dissolve within the next 1 to 2 Gyr. Most clusters studied by Sollima & Baumgardt also show a large difference between their central and global MF slopes, implying that the majority of Galactic globular clusters is either near or already past core collapse. The strong mass segregation seen in most clusters also implies that only a small fraction of all black holes formed in globular clusters still reside in them.

On the link between energy equipartition and radial variation in the stellar mass function of star clusters

We make use of $N$-body simulations to determine the relationship between two observable parameters that are used to quantify mass segregation and energy equipartition in star clusters. Mass segregation can be quantified by measuring how the slope of a cluster's stellar mass function $\alpha$ changes with clustercentric distance r, and then calculating $\delta_\alpha = \frac{d \alpha(r)}{d ln(r/r_m)}$ where $r_m$ is the cluster's half-mass radius. The degree of energy equipartition in a cluster is quantified by $\eta$, which is a measure of how stellar velocity dispersion $\sigma$ depends on stellar mass m via $\sigma(m) \propto m^{-\eta}$. Through a suite of $N$-body star cluster simulations with a range of initial sizes, binary fractions, orbits, black hole retention fractions, and initial mass functions, we present the co-evolution of $\delta_\alpha$ and $\eta$. We find that measurements of the global $\eta$ are strongly affected by the radial dependence of $\sigma$ and mean stellar mass and the relationship between $\eta$ and $\delta_\alpha$ depends mainly on the cluster's initial conditions and the tidal field. Within $r_m$, where these effects are minimized, we find that $\eta$ and $\delta_\alpha$ initially share a linear relationship. However, once the degree of mass segregation increases such that the radial dependence of $\sigma$ and mean stellar mass become a factor within $r_m$, or the cluster undergoes core collapse, the relationship breaks down. We propose a method for determining $\eta$ within $r_m$ from an observational measurement of $\delta_\alpha$. In cases where $\eta$ and $\delta_\alpha$ can be measured independently, this new method offers a way of measuring the cluster's dynamical state.

High-velocity stars in the cores of globular clusters: the illustrative case of NGC 2808

We report the detection of five high-velocity stars in the core of the globular cluster NGC 2808. The stars lie on the the red giant branch and show total velocities between 40 and 45 km/s. For a core velocity dispersion sigma_c = 13.4 km/s, this corresponds to up to 3.4 sigma_c. These velocities are close to the estimated escape velocity (~ 50 km/s) and suggest an ejection from the core. Two of these stars have been confirmed in our recent integral field spectroscopy data and we will discuss them in more detail here. These two red giants are located at a projected distance of ~ 0.3 pc from the center. According to their positions on the color magnitude diagram, both stars are cluster members. We investigate several possible origins for the high velocities of the stars and conceivable ejection mechanisms. Since the velocities are close to the escape velocity, it is not obvious whether the stars are bound or unbound to the cluster. We therefore consider both cases in our analysis. We perform numerical simulations of three-body dynamical encounters between binaries and single stars and compare the resulting velocity distributions of escapers with the velocities of our stars. We compare the predictions for a single dynamical encounter with a compact object with those of a sequence of two-body encounters due to relaxation. If the stars are unbound, the encounter must have taken place recently, when the stars were already in the giant phase. After including binary fractions and black-hole retention fractions, projection effects, and detection probabilities from Monte-Carlo simulations, we estimate the expected numbers of detections for all the different scenarios. Based on these numbers, we conclude that the most likely scenario is that the stars are bound and were accelerated by a single encounter between a binary of main-sequence stars and a ~ 10 M_sun black hole.