Order-Disorder Phase Transition in Black-Hole Star Clusters

Touma, Jihad; Tremaine, Scott; Kazandjian, M. V.

doi:10.1103/physrevlett.123.021103

Cited by 15 publications

(11 citation statements)

References 16 publications

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“…2 Indeed, in the 'stable' simulation of Figure 2 in which the instability is suppressed, there is no apsidal clustering. We hypothesize that the inclination instability puffs (i ↑) and cools (e ↓) the system allowing it to undergo a phase transition to a lopsided state similar to the transition reported in Touma et al (2019) for spherically symmetric systems.…”

Section: Long-term Evolution Of the Inclination Instabilitysupporting

confidence: 52%

“…A recent series of papers (Touma et al 2019;Tremaine 2020a,b) show that spherical near-Keplerian potentials tend toward an ordered, lopsided state when the system is cooled below a critical temperature (directly related to RMS eccentricity of the orbits). The ordered lopsided state results from a phase transition, rather than dynamical instability, driven by resonant relaxation (Rauch & Tremaine 1996).…”

Section: Long-term Evolution Of the Inclination Instabilitymentioning

confidence: 99%

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Apsidal Clustering following the Inclination Instability

Zderic,

Collier,

Tiongco

et al. 2020

Preprint

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Disks of low-mass bodies on high-eccentricity orbits in near-Keplerian potentials can be dynamically unstable to buckling out of the plane. In this letter, we present N-body simulations of the long-term behavior of such a system, finding apsidal clustering of the orbits in the disk plane. The timescale over which the clustering is maintained increases with number of particles, suggesting that lopsided configurations are stable at large N. This discovery may explain the observed apsidal ( ) clustering of extreme trans-Neptunian Objects in the outer solar system.

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Section: Long-term Evolution Of the Inclination Instabilitysupporting

confidence: 52%

Section: Long-term Evolution Of the Inclination Instabilitymentioning

confidence: 99%

Apsidal Clustering following the Inclination Instability

Zderic,

Collier,

Tiongco

et al. 2020

Preprint

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“…For simplicity we have specialized to the case of a single stellar mass, and to a mono-energetic system -by which we mean that all stars have the same semimajor axis -but many of our conclusions also hold for systems with a more realistic distribution of masses and semimajor axes (Touma, Tremaine & Kazandjian 2019;.…”

Section: Discussionmentioning

confidence: 99%

“…The Appendix contains calculations of the linear stability of spherical equilibria, both thermodynamic and dynamical. Some of the results of this paper have been summarized previously in Touma, Tremaine & Kazandjian (2019).…”

mentioning

confidence: 98%

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

Tremaine

2020

Monthly Notices of the Royal Astronomical Society

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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 maximumentropy 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 ∼ 10 2 in semimajor axis, mostly for black-hole masses 10 7.5 M .

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“…The outcome of resonant relaxation was studied in a series of papers Touma & Tremaine (2014), Touma et al (2019), Tremaine (2019), and Tremaine (2020) (TT). TT argued that secular dynamics allows equilibria states that can be described by a language of conventional statistical mechanics, with temperature T serving as a measure of self-gravitation energy of the cluster.…”

mentioning

confidence: 99%

The Thermodynamics of Rotating Black-Hole Star Clusters

Gruzinov,

Levin,

Zhu

2020

Preprint

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Rotating star clusters near supermassive black holes are studied using Touma-Tremaine thermodynamics of gravitationally interacting orbital ellipses. A simple numerical procedure for calculating thermodynamic equilibrium states for an arbitrary distribution of stars over masses and semimajor axes is described. Spontaneous symmetry breaking and breakdown of thermodynamics at low positive temperatures are rigorously proven for non-rotating clusters. Rotation is introduced through a second temperature-like parameter. Both axially symmetric and lopsided rotational equilibria are found; the lopsided equilibria precess with the angular velocity that is given by the ratio of the two temperatures. Eccentric stellar disc in the nucleus of Andromeda galaxy may be an example of a lopsided thermodynamic equilibrium of a rotating black hole star cluster. Stellar-mass black holes occupy highly eccentric orbits in broken-symmetry star clusters, and form flattened disc-like configurations in rotating star clusters. They are attracted to orbits that are stationary in the frame of reference rotating with the angular velocity of the cluster. In spherical clusters, stellar-mass black holes' orbits are significantly more eccentric than those of the lighter stars if the temperature is negative, and more circular if the temperature is positive. Finally we note that planets, comets, dark matter particles and other light bodies tend to form a spherically symmetric non-rotating sub-cluster with maximum-entropy eccentricity distribution P(e) = 2e, even if their host cluster is rotating and lopsided.

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Order-Disorder Phase Transition in Black-Hole Star Clusters

Cited by 15 publications

References 16 publications

Apsidal Clustering following the Inclination Instability

Apsidal Clustering following the Inclination Instability

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

The Thermodynamics of Rotating Black-Hole Star Clusters

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