arXiv subjects

Sambaran Banerjee

Publications and source records attributed to Sambaran Banerjee.

40 records · Page 3Linked to original sources

arXiv2011

Stellar mass black holes in star clusters: gravitational wave emission and detection rates

We investigate the dynamics of stellar-mass black holes (BH) in star clusters focusing on the dynamical formation of BH-BH binaries, which are very important sources of gravitational waves (GW). We examine the properties of these BH-BH binaries through direct N-body computations of Plummer clusters, having initially N(0) <= 10^5 low mass stars and a population of stellar mass BHs, using the state-of-the-art N-body integrator "NBODY6". We find that the stellar mass BHs segregate rapidly into the cluster core to form a central dense sub-cluster of BHs in which BH-BH binaries form via 3-body encounters. While most of the BH binaries finally escape from the cluster by recoils due to super-elastic encounters with the single BHs, we find that for clusters with N(0) >= 5 X 10^4, typically a few of them dynamically harden to the extent that they can merge via GW emission within the cluster. Also, for each of such clusters, there are a few escaped BH binaries that merge within a Hubble time, most of the mergers happening within a few Gyr of cluster evolution. These results imply that the intermediate-aged massive clusters constitute the most important class of star clusters that can produce dynamical BH-BH mergers at the present epoch. The BH-BH merger rates obtained from our computations imply a significant detection rate (~ 30/yr) for the "Advanced LIGO" GW detector that will become operative in the near future. Finally, we briefly discuss our ongoing development on this work incorporating the formation of BHs in star clusters from stellar evolution. In particular, we highlight the effect of stellar metallicity on the BH sub-cluster driven expansion of a star cluster's core.

astro-ph.GA↗

arXiv2009

Stellar-mass black holes in star clusters: implications for gravitational wave radiation

We study the dynamics of stellar-mass black holes (BH) in star clusters with particular attention to the formation of BH-BH binaries, which are interesting as sources of gravitational waves (GW). We examine the properties of these BH-BH binaries through direct N-body simulations of star clusters using the GPU-enabled NBODY6 code. We perform simulations of N <= 10^5 Plummer clusters of low-mass stars with an initial population of BHs. Additionally, we do several calculations of star clusters confined within a reflective boundary mimicking only the core of a massive cluster. We find that stellar-mass BHs with masses ~ 10 solar mass segregate rapidly into the cluster core and form a sub-cluster of BHs within typically 0.2 - 0.5 pc radius, which is dense enough to form BH-BH binaries through 3-body encounters. While most BH binaries are ejected from the cluster by recoils received during super-elastic encounters with the single BHs, few of them harden sufficiently so that they can merge via GW emission within the cluster. We find that for clusters with $N \ga 5\times 10^4$, typically 1 - 2 BH-BH mergers occur within them during the first ~ 4 Gyr of evolution. Also for each of these clusters, there are a few escaping BH binaries that can merge within a Hubble time, most of the merger times being within a few Gyr. These results indicate that intermediate-age massive clusters constitute the most important class of candidates for producing dynamical BH-BH mergers. Old globular clusters cannot contribute significantly to the present-day BH-BH merger rate since most of the mergers from them would have occurred earlier. In contrast, young massive clusters are too young to produce significant number of BH-BH mergers. Our results imply significant BH-BH merger detection rates for the proposed "Advanced LIGO" GW detector. (Abridged)

astro-ph.SR↗

arXiv2008

Evolution of Compact-Binary Populations in Globular Clusters: A Boltzmann Study II. Introducing Stochasticity

We continue exploration of the Boltzmann scheme started in Banerjee and Ghosh (2007, henceforth Paper I) for studying the evolution of compact-binary populations of globular clusters, introducing in this paper our method of handling the stochasticity inherent in dynamical processes of binary formation, destruction and hardening in globular clusters. We describe these stochastic processes as "Wiener processes", whereupon the Boltzmann equation becomes a stochastic partial differential equation, the solution of which requires the use of "Ito calculus" (this use being the first, to our knowledge, in this subject), in addition to ordinary calculus. We focus on the evolution of (a) the number of X-ray binaries $N_{XB}$ in globular clusters, and (b) the orbital-period distribution of these binaries. We show that, although the details of the fluctuations in the above quantities differ from one "realization" to another of the stochastic processes, the general trends follow those found in the continuous-limit study of Paper I, and the average result over many such realizations is close to the continuous-limit result. We investigate the dependence of $N_{XB}$ found by these calculations on two essential globular-cluster parameters, namely, the star-star and star-binary encounter-rate parameters $Γ$ and $γ$, for which we had coined the name Verbunt parameters in Paper I. We compare our computed results with those from CHANDRA observations of Galactic globular clusters, showing that the expected scalings of $N_{XB}$ with the Verbunt parameters are in good agreement with the observed ones. We indicate what additional features can be incorporated into the scheme in future, and how more elaborate problems can be tackled.

astro-ph↗

arXiv2007

Evolution of Compact-Binary Populations in Globular Clusters: A Boltzmann Study. I. The Continuous Limit

We explore a Boltzmann scheme for studying the evolution of compact binary populations of globular clusters. We include processes of compact-binary formation by tidal capture and exchange encounters, binary destruction by dissociation and other mechanisms, and binary hardening by encounters, gravitational radiation and magnetic braking, as also the orbital evolution during mass transfer, following Roche lobe contact. For the encounter processes which are stochastic in nature, we study the probabilistic, continuous limit in this introductory work, deferring the specific handling of the stochastic terms to the next step. We focus on the evolution of (a) the number of X-ray sources N_{XB} in globular clusters, and (b) the orbital-period distribution of the X-ray binaries, as a result of the above processes. We investigate the dependence of N_{XB} on two essential cluster properties, namely, the star-star and star-binary encounter-rate parameters 'Gamma' and 'gamma', which we call Verbunt parameters. We compare our model results with observation, showing that the model values of N_{XB} and their expected scaling with the Verbunt parameters are in good agreement with results from recent X-ray observations of Galactic globular clusters, encouraging us to build more detailed models.

astro-ph↗