Gravothermal oscillations in two-component models of star clusters

Breen, Philip G.; Heggie, Douglas C.

doi:10.1111/j.1365-2966.2011.20036.x

Cited by 13 publications

(43 citation statements)

References 29 publications

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“…We can compare the dependence on m max in Table with the results of the two‐component models of Breen & Heggie () if we fix the stellar mass of the light component in that earlier paper. This is done in Appendix (see Table ).…”

Section: Critical Value Of Nmentioning

confidence: 96%

“…As decreasing total mass ratio for two‐component systems is the analogue of decreasing α, these systems have the same stability trends as the multicomponent systems in Table . Now we will attempt to extend the interpretation of Breen & Heggie () from two‐component to multicomponent models in a way which also accounts for the dependence on m max .…”

Section: Critical Value Of Nmentioning

confidence: 99%

“…Breen & Heggie () first argued that for the two‐component case, the dynamics of the system were dominated by the heavier component. The reasoning behind this emphasis on N 2 is that the heavier component concentrates within the central region where it behaves like a one‐component system deep in the potential well of the low‐mass stars, and it can exhibit gravothermal instability like the central part of a one‐component system .…”

Section: Critical Value Of Nmentioning

confidence: 99%

“…Their research supported the applicability of the Goodman stability parameter ε (see Goodman ) as a stability criterion. Breen & Heggie (), whose research focused on the more general Spitzer unstable two‐component case, indicated that the occurrence of gravothermal instability depends approximately on the number of stars in the heavier component. Breen & Heggie () also found that the critical value of ε depended on the parameters of the mass function (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…The main aim of this paper is to provide a theoretical understanding of the onset of gravothermal oscillations in multicomponent systems. As this paper follows on from the research of Breen & Heggie (), it is worthwhile attempting to extend the concepts developed in that paper to the multicomponent case. Although two‐component systems may be realistic approximations of multicomponent systems (Kim & Lee ), it is best to have a better understanding of gravothermal oscillations in multicomponent systems as real globular clusters contain a continuous mass spectrum.…”

Section: Introductionmentioning

confidence: 99%

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Gravothermal oscillations in multicomponent models of star clusters

Breen¹,

Heggie²

2012

Monthly Notices of the Royal Astronomical Society

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In this paper, gravothermal oscillations are investigated in multicomponent star clusters which have power‐law initial mass functions (IMFs). For the power‐law IMFs, the minimum masses (mmin) were fixed and three different maximum stellar masses (mmax) were used along with different power‐law exponents (α) ranging from 0 to −2.35 (Salpeter). The critical number of stars at which gravothermal oscillations first appear with increasing N was found using the multicomponent gas code spedi. The total mass (Mtot) is seen to give an approximate stability condition for power‐law IMFs with fixed values of mmax and mmin independent of α. The value Mtot/mmax ≃ 12 000 is shown to give an approximate stability condition which is also independent of mmax, though the critical value is somewhat higher for the steepest IMF that was studied. For appropriately chosen cases, direct N‐body runs were carried out in order to check the results obtained from spedi. Finally, evidence of the gravothermal nature of the oscillations found in the N‐body runs is presented.

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Section: Critical Value Of Nmentioning

confidence: 96%

Section: Critical Value Of Nmentioning

confidence: 99%

Section: Critical Value Of Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gravothermal oscillations in multicomponent models of star clusters

Breen¹,

Heggie²

2012

Monthly Notices of the Royal Astronomical Society

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Gravothermal catastrophe: The dynamical stability of a fluid model

Sormani

Bertin

2013

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A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for the onset of the gravothermal catastrophe, under different external conditions, coincide with those obtained from thermodynamical arguments. This suggests that the gravothermal catastrophe may reduce to Jeans instability, rediscovered in an inhomogeneous framework. We find normal modes and frequencies for the fluid system and show that instability develops on the dynamical time scale. We then discuss several related issues. In particular, (1) for perturbations at constant total energy and constant volume, we introduce a simple heuristic term in the energy budget to mimic the role of binaries. (2) We outline the analysis of the two-component case and show how linear perturbation analysis can also be carried out in this more complex context in a relatively straightforward way. (3) We compare the behavior of the fluid model with that of the collisionless sphere. In the collisionless case the instability seems to disappear, which is at variance with the linear Jeans stability analysis in the homogeneous case. We argue that a key ingredient for understanding the difference lies in the role of the detailed angular momentum in a collisionless system. A spherical stellar system is expected to undergo the gravothermal catastrophe only in the presence of some collisionality, which suggests that the instability is dissipative and not dynamical. Finally, we briefly comment on the meaning of the Boltzmann entropy and its applicability to the study of the dynamics of selfgravitating inhomogeneous gaseous systems.

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The hunt for self-similar core collapse

Pavlík

Šubr

2018

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Context. Core collapse is a prominent evolutionary stage of self-gravitating systems. In an idealised collisionless approximation, the region around the cluster core evolves in a self-similar way prior to the core collapse. Thus, its radial density profile outside the core can be described by a power law, ρ ∝ r −α . Aims. We aim to find the characteristics of core collapse in N-body models. In such systems, a complete collapse is prevented by transferring the binding energy of the cluster to binary stars. The contraction is, therefore, more difficult to identify. Methods. We developed a method that identifies the core collapse in N-body models of star clusters based on the assumption of their homologous evolution. Results. We analysed different models (equal-and multi-mass), most of which exhibit patterns of homologous evolution, yet with significantly different values of α : the equal-mass models have α ≈ 2.3, which agrees with theoretical expectations, the multi-mass models have α ≈ 1.5 (yet with larger uncertainty). Furthermore, most models usually show sequences of separated homologous collapses with similar properties. Finally, we investigated a correlation between the time of core collapse and the time of formation of the first hard binary star. The binding energy of such a binary usually depends on the depth of the collapse in which it forms, for example from 100 kT to 10 4 kT in the smallest equal-mass to the largest multi-mass model, respectively. However, not all major hardenings of binaries happened during the core collapse. In the multi-mass models, we see large transfers of binding energy of ∼ 10 4 kT to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses.

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Gravothermal oscillations in two-component models of star clusters

Cited by 13 publications

References 29 publications

Gravothermal oscillations in multicomponent models of star clusters

Gravothermal oscillations in multicomponent models of star clusters

Gravothermal catastrophe: The dynamical stability of a fluid model

The hunt for self-similar core collapse

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