Testing lowered isothermal models with direct N-body simulations of globular clusters - II: Multimass models

Lowered isothermal models, such as the multimass Michie-King models, have been successful in describing observational data of globular clusters. In this study we assess whether such models are able to describe the phase space properties of evolutionary $N$-body models. We compare the multimass models as implemented in (Gieles \& Zocchi) to $N$-body models of star clusters with different retention fractions for the black holes and neutron stars evolving in a tidal field. We find that multimass models successfully reproduce the density and velocity dispersion profiles of the different mass components in all evolutionary phases and for different remnants retention. We further use these results to study the evolution of global model parameters. We find that over the lifetime of clusters, radial anisotropy gradually evolves from the low-mass to the high-mass components and we identify features in the properties of observable stars that are indicative of the presence of stellar-mass black holes. We find that the model velocity scale depends on mass as $m^{-\delta}$, with $\delta\simeq0.5$ for almost all models, but the dependence of central velocity dispersion on $m$ can be shallower, depending on the dark remnant content, and agrees well with that of the $N$-body models. The reported model parameters, and correlations amongst them, can be used as theoretical priors when fitting these types of mass models to observational data.Comment: 28 pages, 22 figures, published in MNRA

A stellar-mass black hole population in the globular cluster NGC 6101?

Dalessandro et al. observed a similar distribution for blue straggler stars and main-sequence turn-off stars in the Galactic globular cluster NGC 6101, and interpreted this feature as an indication that this cluster is not mass-segregated. Using direct N-body simulations, we find that a significant amount of mass segregation is expected for a cluster with the mass, radius and age of NGC 6101. Therefore, the absence of mass segregation cannot be explained by the argument that the cluster is not yet dynamically evolved. By varying the retention fraction of stellar-mass black holes, we show that segregation is not observable in clusters with a high black hole retention fraction (>50% after supernova kicks and >50% after dynamical evolution). Yet all model clusters have the same amount of mass segregation in terms of the decline of the mean mass of stars and remnants with distance to the centre. We also discuss how kinematics can be used to further constrain the presence of a stellar-mass black hole population and distinguish it from the effect of an intermediate-mass black hole. Our results imply that the kick velocities of black holes are lower than those of neutron stars. The large retention fraction during its dynamical evolution can be explained if NGC 6101 formed with a large initial radius in a Milky Way satellite.Comment: 10 pages, 7 figure

Mass models of NGC 6624 without an intermediate-mass black hole

An intermediate-mass black hole (IMBH) was recently reported to reside in the centre of the Galactic globular cluster (GC) NGC 6624, based on timing observations of a millisecond pulsar (MSP) located near the cluster centre in projection. We present dynamical models with multiple mass components of NGC 6624 - without an IMBH - which successfully describe the surface brightness profile and proper motion kinematics from the Hubble Space Telescope (HST) and the stellar mass function at different distances from the cluster centre. The maximum line-of-sight acceleration at the position of the MSP accommodates the inferred acceleration of the MSP, as derived from its first period derivative. With discrete realizations of the models we show that the higher-order period derivatives - which were previously used to derive the IMBH mass - are due to passing stars and stellar remnants, as previously shown analytically in literature. We conclude that there is no need for an IMBH to explain the timing observations of this MSP.Comment: 8 pages, 7 figures, MNRAS. Updated to match final journal styl

Unveiling stellar-mass black holes in globular clusters with dynamical models.

The recent discovery of a gravitational wave produced by two merging stellar-mass black holes started a search for environments where two stellar mass black holes can become a binary and merge. One favourable environment could be globular clusters, but the evolution of black holes in them is still widely debated. In this thesis, I present a method, based on isotropic lowered isothermal multimass models with which stellar mass black hole populations in globular clusters can be dynamically inferred and the main properties of the cluster can be estimated. In the models, I am using an improved stellar evolution code from Balbinot and Gieles (2018) to which I added black hole evolution. Before applying the multimass models to data, I made a detailed comparison between the properties of multimass models and collisional N-body simulations. I find that all dynamical stages are well described by the models and that a stellar mass black hole population reduces mass segregation. For the Milky Way globular cluster NGC 6101, I run three N-body simulations to show that the observed lack of observable mass segregation could be explained by a stellar mass black hole population. To differentiate this explanation from others, I create different multimass models and find that measuring the cluster's velocity dispersion could help to prove the black hole population. In the final chapter I follow-up on this prediction, and present new line-of-sight velocities of NGC 6101's velocities with the ESO MUSE instrument, I find, applying my method, that the cluster has 86+30-23 black holes, which could explain its currently observed lack of mass segregation. This thesis is concluded by a discussion on how to improve dynamical detections of BH populations with future observations and models.</p

Testing lowered isothermal models with direct N-body simulations of globular clusters - II. Multimass models

Lowered isothermal models, such as the multimass Michie–King models, have been successful in describing observational data of globular clusters. In this study, we assess whether such models are able to describe the phase space properties of evolutionary N-body models. We compare the multimass models as implemented in LIMEPY (Gieles & Zocchi) to N-body models of star clusters with different retention fractions for the black holes and neutron stars evolving in a tidal field. We find that multimass models successfully reproduce the density and velocity dispersion profiles of the different mass components in all evolutionary phases and for different remnants retention. We further use these results to study the evolution of global model parameters. We find that over the lifetime of clusters, radial anisotropy gradually evolves from the low- to the high-mass components and we identify features in the properties of observable stars that are indicative of the presence of stellar-mass black holes. We find that the model velocity scale depends on mass as m−δ, with δ ≃ 0.5 for almost all models, but the dependence of central velocity dispersion on m can be shallower, depending on the dark remnant content, and agrees well with that of the N-body models. The reported model parameters, and correlations amongst them, can be used as theoretical priors when fitting these types of mass models to observational data

Testing lowered isothermal models with direct N-body simulations of globular clusters - II. Multimass models

Lowered isothermal models, such as the multimass Michie–King models, have been successful in describing observational data of globular clusters. In this study, we assess whether such models are able to describe the phase space properties of evolutionary N-body models. We compare the multimass models as implemented in LIMEPY (Gieles & Zocchi) to N-body models of star clusters with different retention fractions for the black holes and neutron stars evolving in a tidal field. We find that multimass models successfully reproduce the density and velocity dispersion profiles of the different mass components in all evolutionary phases and for different remnants retention. We further use these results to study the evolution of global model parameters. We find that over the lifetime of clusters, radial anisotropy gradually evolves from the low- to the high-mass components and we identify features in the properties of observable stars that are indicative of the presence of stellar-mass black holes. We find that the model velocity scale depends on mass as m−δ, with δ ≃ 0.5 for almost all models, but the dependence of central velocity dispersion on m can be shallower, depending on the dark remnant content, and agrees well with that of the N-body models. The reported model parameters, and correlations amongst them, can be used as theoretical priors when fitting these types of mass models to observational data

A stellar-mass black hole population in the globular cluster NGC 6101?

Dalessandro et al. observed a similar distribution for blue straggler stars and main-sequence turn-off stars in the Galactic globular cluster NGC 6101, and interpreted this feature as an indication that this cluster is not mass-segregated. Using direct N-body simulations, we find that a significant amount of mass segregation is expected for a cluster with the mass, radius and age of NGC 6101. Therefore, the absence of mass segregation cannot be explained by the argument that the cluster is not yet dynamically evolved. By varying the retention fraction of stellar-mass black holes, we show that segregation is not observable in clusters with a high black hole retention fraction (>50 per cent after supernova kicks and >50 per cent after dynamical evolution). Yet all model clusters have the same amount of mass segregation in terms of the decline of the mean mass of stars and remnants with distance to the centre. We also discuss how kinematics can be used to further constrain the presence of a stellar-mass black hole population and distinguish it from the effect of an intermediate-mass black hole. Our results imply that the kick velocities of black holes are lower than those of neutron stars. The large retention fraction during its dynamical evolution can be explained if NGC 6101 formed with a large initial radius in a Milky Way satellite