scholarly journals Order–disorder phase transition in black hole star clusters – III. A mono-energetic cluster

2020 ◽  
Vol 493 (2) ◽  
pp. 2632-2651 ◽  
Author(s):  
Scott Tremaine
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Maximum Entropy ◽  
Semimajor Axis ◽  
Star Clusters ◽  
Gravitational Energy ◽  
Stellar Orbits ◽  
Disorder Phase Transition ◽  
Wide Range ◽  
Temperature Equilibrium

ABSTRACT Supermassive black holes at the centres of galaxies are often surrounded by dense star clusters. For a wide range of cluster properties and orbital radii the resonant relaxation times in these clusters are much shorter than the Hubble time. Since resonant relaxation conserves semimajor axes, these clusters should be in the maximum-entropy state consistent with the given semimajor axis distribution. We determine these maximum-entropy equilibria in a simplified model in which all of the stars have the same semimajor axes. We find that the cluster exhibits a phase transition from a disordered, spherical, high-temperature equilibrium to an ordered low-temperature equilibrium in which the stellar orbits have a preferred orientation or line of apsides. Here ‘temperature’ is a measure of the non-Keplerian or self-gravitational energy of the cluster; in the spherical state, temperature is a function of the rms eccentricity of the stars. We explore a simple two-parameter model of black hole star clusters – the two parameters are semimajor axis and black hole mass – and find that clusters are susceptible to the lopsided phase transition over a range of ∼102 in semimajor axis, mostly for black hole masses $\lesssim 10^{7.5}\, \mathrm{M}_{\odot }$.

scholarly journals Order-disorder phase transition in black-hole star clusters. II. A scale-free cluster

2019 ◽  
Author(s):  
Scott Tremaine
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Relaxation Time ◽  
Critical Temperature ◽  
Semimajor Axis ◽  
Star Clusters ◽  
Relativistic Effects ◽  
Scale Free ◽  
Disorder Phase Transition ◽  
Wide Range

Abstract The supermassive black holes found at the centres of galaxies are often surrounded by dense star clusters. The ages of these clusters are generally longer than the resonant-relaxation time and shorter than the two-body relaxation time over a wide range of radii. We explore the thermodynamic equilibria of such clusters using a simple self-similar model. We find that the cluster exhibits a phase transition between a high-temperature spherical equilibrium and a low-temperature equilibrium in which the stars are on high-eccentricity orbits with nearly the same orientation. In the absence of relativistic precession, the spherical equilibrium is metastable below the critical temperature and the phase transition is first-order. When relativistic effects are important, the spherical equilibrium is linearly unstable below the critical temperature and the phase transition is continuous. A similar phase transition has recently been found in a model cluster composed of stars with a single semimajor axis. The presence of the same phenomenon in two quite different cluster models suggests that lopsided equilibria may form naturally in a wide variety of black-hole star clusters.

scholarly journals Order-Disorder Phase Transition in Black-Hole Star Clusters

2019 ◽  
Vol 123 (2) ◽  
Author(s):  
Jihad Touma ◽  
Scott Tremaine ◽  
Mher Kazandjian
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Star Clusters ◽  
Disorder Phase Transition

scholarly journals Population synthesis of black hole binary mergers from star clusters

2020 ◽  
Vol 492 (2) ◽  
pp. 2936-2954 ◽  
Author(s):  
Fabio Antonini ◽  
Mark Gieles
Keyword(s):  
Black Hole ◽  
Globular Clusters ◽  
Initial Conditions ◽  
Star Clusters ◽  
Population Synthesis ◽  
Wide Range ◽  
Binary Mergers ◽  
Cluster Properties ◽  
Black Hole Binary ◽  
Merger Rate

ABSTRACT Black hole (BH) binary mergers formed through dynamical interactions in dense star clusters are believed to be one of the main sources of gravitational waves (GWs) for Advanced LIGO and Virgo. Here, we present a fast numerical method for simulating the evolution of star clusters with BHs, including a model for the dynamical formation and merger of BH binaries. Our method is based on Hénon’s principle of balanced evolution, according to which the flow of energy within a cluster must be balanced by the energy production inside its core. Because the heat production in the core is powered by the BHs, one can then link the evolution of the cluster to the evolution of its BH population. This allows us to construct evolutionary tracks of the cluster properties including its BH population and its effect on the cluster and, at the same time, determine the merger rate of BH binaries as well as their eccentricity distributions. The model is publicly available and includes the effects of a BH mass spectrum, mass-loss due to stellar evolution, the ejection of BHs due to natal and dynamical kicks, and relativistic corrections during binary–single encounters. We validate our method using direct N-body simulations, and find it to be in excellent agreement with results from recent Monte Carlo models of globular clusters. This establishes our new method as a robust tool for the study of BH dynamics in star clusters and the modelling of GW sources produced in these systems. Finally, we compute the rate and eccentricity distributions of merging BH binaries for a wide range of cluster initial conditions, spanning more than two orders of magnitude in mass and radius.

Electrochemical Properties of Ag5Te2Cl0.8Br0.2, a Representative of the Solid Solutions Ag5Te2Cl1–xBrx

2008 ◽  
Vol 63 (9) ◽  
pp. 1083-1086 ◽  
Author(s):  
Melanie Bawohl ◽  
Tom Nilges
Keyword(s):  
Phase Transition ◽  
Transition Temperature ◽  
Phase Space ◽  
Ionic Conductivity ◽  
Phase Transition Temperature ◽  
Solid Solutions ◽  
Electronic Conductivity ◽  
Space Group ◽  
Disorder Phase Transition ◽  
Wide Range

Impedance spectroscopic investigations of Ag5Te2Cl0.8Br0.2, a selected representative of the solid solutions Ag5Te2Cl1−xBrx with x = 0 - 1, proved the mixed-conducting property of this class of materials. Two polymorphs are realized in the temperature range of 309 to 410 K, the monoclinic β - phase (space group P21/n) and the tetragonal α-phase (space group I4/mcm) with an order-disorder phase transition temperature of 336 K (DSC). A sharp increase of the total and ionic conductivity can be observed at 337 K, in good accordance with the phase transition temperature. The electronic conductivity exceeds the ionic conductivity by approximately one order of magnitude over a wide range of temperature. Conductivities are σion = 6.9×10−5 (309 K) and σtot = 4.80×10−4 Ω−1 cm−1 (310 K) for β -Ag5Te2Cl0.8Br0.2 and σion = 1.6×10−2 (395 K) and σtot = 1.73×10−1 Ω−1 cm−1 (394 K) for α-Ag5Te2Cl0.8Br0.2.

ORDER-DISORDER PHASE TRANSITION OF Au(110)-(1x2) RECONSTRUCTION

1988 ◽  
Vol 49 (C6) ◽  
pp. C6-269-C6-273 ◽  
Author(s):  
H. Q. NGUYEN ◽  
Y. KUK ◽  
P. J. SILVERMAN
Keyword(s):  
Phase Transition ◽  
Disorder Phase Transition

scholarly journals MONITORING STELLAR ORBITS AROUND THE MASSIVE BLACK HOLE IN THE GALACTIC CENTER

2009 ◽  
Vol 692 (2) ◽  
pp. 1075-1109 ◽  
Author(s):  
S. Gillessen ◽  
F. Eisenhauer ◽  
S. Trippe ◽  
T. Alexander ◽  
R. Genzel ◽  
...  
Keyword(s):  
Black Hole ◽  
Galactic Center ◽  
Massive Black Hole ◽  
Stellar Orbits

scholarly journals Null geodesics and thermodynamic phase transition of four-dimensional Gauss–Bonnet AdS black hole

2021 ◽  
pp. 168461
Author(s):  
Kartheek Hegde ◽  
Naveena Kumara A. ◽  
Ahmed Rizwan C.L. ◽  
Md Sabir Ali ◽  
Ajith K.M.
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Null Geodesics ◽  
Thermodynamic Phase

scholarly journals The Merger Rate of Black Holes in a Primordial Black Hole Cluster

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 372-378
Author(s):  
Viktor D. Stasenko ◽  
Alexander A. Kirillov
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Mass Spectrum ◽  
Star Clusters ◽  
Primordial Black Hole ◽  
Primordial Black Holes ◽  
Central Black Hole ◽  
Solar Mass ◽  
Merger Rate

In this paper, the merger rate of black holes in a cluster of primordial black holes (PBHs) is investigated. The clusters have characteristics close to those of typical globular star clusters. A cluster that has a wide mass spectrum ranging from 10−2 to 10M⊙ (Solar mass) and contains a massive central black hole of the mass M•=103M⊙ is considered. It is shown that in the process of the evolution of cluster, the merger rate changed significantly, and by now, the PBH clusters have passed the stage of active merging of the black holes inside them.

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