Populating the Black Hole Mass Gaps in Stellar Clusters: General Relations and Upper Limits

Theory and observations suggest that single-star evolution is not able to produce black holes with masses in the range 3–5M ⊙ and above ∼45M ⊙, referred to as the lower mass gap and the upper mass gap, respectively. However, it is possible to form black holes in these gaps through mergers of compact objects in, e.g., dense clusters. This implies that if binary mergers are observed in gravitational waves with at least one mass-gap object, then either clusters are effective in assembling binary mergers, or our single-star models have to be revised. Understanding how effective clusters are at populating both mass gaps have therefore major implications for both stellar and gravitational wave astrophysics. In this paper we present a systematic study of how efficient stellar clusters are at populating both mass gaps through in-cluster mergers. For this, we derive a set of closed form relations for describing the evolution of compact object binaries undergoing dynamical interactions and mergers inside their cluster. By considering both static and time-evolving populations, we find in particular that globular clusters are clearly inefficient at populating the lower mass gap in contrast to the upper mass gap. We further describe how these results relate to the characteristic mass, time, and length scales associated with the problem.

Isochrone fitting of ACS survey globular clusters using the PAdova and TRieste Stellar Evolution Code (PARSEC)

We present new isochrone fits to color magnitude diagrams (CMDs) of five globular clusters (GCs) including NGC 1261, NGC 1851, NGC 2298, NGC 3201, and NGC 4590. We used archival data obtained from the Advanced Camera for Survey (ACS) on board the Hubble Space Telescope (HST). The data of these five GCs were collected in F606W (V) and F814W (I) filters. In this study, the isochrone fitting to GC CMDs was analyzed using the PAdova and TRieste Stellar Evolution Code (PARSEC), which is the fundamental tool for age and distance estimation and modelling the evolution of stellar clusters and other galaxies. The main purpose is to estimate the fundamental physical properties of the GC samples using the PARSEC code and compare with results from published articles. The fundamental physical parameters determined in the study are age, metallicity, reddening, and distance modulus. The theoretical isochrone fits properly with the shape of CMD at the turn-off point that can be used to estimate the age and metallicity of clusters. We found that the age of these five GCs; NGC 1261, NGC 1851, NGC 2298, NGC 3201, and NGC 4590 are 12.6±1.0 Gyr, 12.0±1.0 Gyr, 12.7±1.0 Gyr, 12.0±1.0 Gyr, and 13.0±1.0 Gyr, respectively. Among the analyzed clusters, the results show that NGC 4590 is the oldest GC and has lowest metallicity value compare with other cluster samples. Studies of the properties and distribution of GCs play an important role to understand formation and evolution of the Milky Way.

On the initial mass-radius relation of stellar clusters

Young stellar clusters across nearly five orders of magnitude in mass appear to follow a power-law mass-radius relationship (MRR), $R_{\star }\propto M_{\star }^{\alpha }$, with α ≈ 0.2 − 0.33. We develop a simple analytic model for the cluster mass-radius relation. We consider a galaxy disc in hydrostatic equilibrium, which hosts a population of molecular clouds that fragment into clumps undergoing cluster formation and feedback-driven expansion. The model predicts a mass-radius relation of $R_{\star }\propto M_{\star }^{1/2}$ and a dependence on the kpc-scale gas surface density $R_{\star }\propto \Sigma _{\rm g}^{-1/2}$, which results from the formation of more compact clouds (and cluster-forming clumps within) at higher gas surface densities. This environmental dependence implies that the high-pressure environments in which the most massive clusters can form also induce the formation of clusters with the smallest radii, thereby shallowing the observed MRR at high-masses towards the observed $R_{\star }\propto M_{\star }^{1/3}$. At low cluster masses, relaxation-driven expansion induces a similar shallowing of the MRR. We combine our predicted MRR with a simple population synthesis model and apply it to a variety of star-forming environments, finding good agreement. Our model predicts that the high-pressure formation environments of globular clusters at high redshift naturally led to the formation of clusters that are considerably more compact than those in the local Universe, thereby increasing their resilience to tidal shock-driven disruption and contributing to their survival until the present day.

Predicting Images for the Dynamics Of stellar Clusters (π-DOC): a deep learning framework to predict mass, distance and age of globular clusters.

Dynamical mass estimates of simple systems such globular clusters (GCs) still suffer from up to a factor of 2 uncertainty. This is primarily due to the oversimplifications of standard dynamical models that often neglect the effects of the long-term evolution of GCs. Here, we introduce a new approach to measure the dynamical properties of GCs, based on the combination of a deep-learning framework and the large amount of data from direct N-body simulations. Our algorithm, π-DOC (Predicting Images for the Dynamics Of stellar Clusters) is composed of two convolutional networks, trained to learn the non-trivial transformation between an observed GC luminosity map and its associated mass distribution, age, and distance. The training set is made of V-band luminosity and mass maps constructed as mock observations from N-body simulations. The tests on π-DOC demonstrate that we can predict the mass distribution with a mean error per pixel of 27%, and the age and distance with an accuracy of 1.5 Gyr and 6 kpc, respectively. In turn, we recover the shape of the mass-to-light profile and its global value with a mean error of 12%, which implies that we efficiently trace mass segregation. A preliminary comparison with observations indicates that our algorithm is able to predict the dynamical properties of GCs within the limits of the training set. These encouraging results demonstrate that our deep-learning framework and its forward modelling approach can offer a rapid and adaptable tool competitive with standard dynamical models.

The properties of clusters, and the orientation of magnetic fields relative to filaments, in magnetohydrodynamic simulations of colliding clouds

ABSTRACT We have performed Smoothed Particle Magneto-Hydrodynamics (SPMHD) calculations of colliding clouds to investigate the formation of massive stellar clusters, adopting a timestep criterion to prevent large divergence errors. We find that magnetic fields do not impede the formation of young massive clusters (YMCs), and the development of high star formation rates, although we do see a strong dependence of our results on the direction of the magnetic field. If the field is initially perpendicular to the collision, and sufficiently strong, we find that star formation is delayed, and the morphology of the resulting clusters is significantly altered. We relate this to the large amplification of the field with this initial orientation. We also see that filaments formed with this configuration are less dense. When the field is parallel to the collision, there is much less amplification of the field, dense filaments form, and the formation of clusters is similar to the purely hydrodynamical case. Our simulations reproduce the observed tendency for magnetic fields to be aligned perpendicularly to dense filaments, and parallel to low density filaments. Overall our results are in broad agreement with past work in this area using grid codes.

Formation of supermassive black holes in galactic nuclei – I. Delivering seed intermediate-mass black holes in massive stellar clusters

ABSTRACT Supermassive black holes (SMBHs) are found in most galactic nuclei. A significant fraction of these nuclei also contains a nuclear stellar cluster (NSC) surrounding the SMBH. In this paper, we consider the idea that the NSC forms first, from the merger of several stellar clusters that may contain intermediate-mass black holes (IMBHs). These IMBHs can subsequently grow in the NSC and form an SMBH. We carry out N-body simulations of the simultaneous merger of three stellar clusters to form an NSC, and investigate the outcome of simulated runs containing zero, one, two, and three IMBHs. We find that IMBHs can efficiently sink to the centre of the merged cluster. If multiple merging clusters contain an IMBH, we find that an IMBH binary is likely to form and subsequently merge by gravitational wave emission. We show that these mergers are catalyzed by dynamical interactions with surrounding stars, which systematically harden the binary and increase its orbital eccentricity. The seed SMBH will be ejected from the NSC by the recoil kick produced when two IMBHs merge, if their mass ratio q ≳ 0.15. If the seed is ejected then no SMBH will form in the NSC. This is a natural pathway to explain those galactic nuclei that contain an NSC but apparently lack an SMBH, such as M33. However, if an IMBH is retained then it can seed the growth of an SMBH through gas accretion and tidal disruption of stars.

On dark matter and dark energy

The dark matter hypothesis was created to explain the reason for the preservation of stellar clusters from dispersion. The weak point of this hypothesis is the great age of space, which is 13.8 billion years. Based on experimental data, it is shown that the age of space does not exceed 10 thousand years. In this case, the hypothesis of dark matter is not needed, since stellar clusters cannot scatter in such short cosmic time. The dark energy hypothesis was created to explain the reason for the accelerated expansion of space. The basis for this phenomenon is a large amount of spectral redshift of distant luminous space objects. It is shown that this value is mainly determined by the significant absorption of light energy of distant space objects by a huge amount of intergalactic gas, and not by the movement of these objects. In this case, the hypothesis of dark energy is not needed, and space should not rapidly expand and scatter in space.