Lifetimes of tidally limited star clusters with different radii

Gieles, M. and Baumgardt, H. (2008) Lifetimes of tidally limited star clusters with different radii. Monthly Notices of the Royal Astronomical Society, 389 1: L28-L32. doi:10.1111/j.1745-3933.2008.00515.x


Author Gieles, M.
Baumgardt, H.
Title Lifetimes of tidally limited star clusters with different radii
Journal name Monthly Notices of the Royal Astronomical Society   Check publisher's open access policy
ISSN 0035-8711
1365-2966
Publication date 2008-09-01
Year available 2008
Sub-type Article (original research)
DOI 10.1111/j.1745-3933.2008.00515.x
Open Access Status DOI
Volume 389
Issue 1
Start page L28
End page L32
Total pages 5
Place of publication Oxford, United Kingdom
Publisher Oxford University Press
Language eng
Abstract We study the escape rate of stars, (N)over dot, from clusters with different radii on circular orbits in a tidal field using analytical predictions and direct N-body simulations. We find that (N)over dot depends on the ratio R equivalent to r(h)/r(J), where r(h) is the half-mass radius and r(J) the radius of the zero-velocity surface around the cluster. For R greater than or similar to 0.05, the 'tidal regime', there is almost no dependence of (N)over dot on R. To first order this is because the fraction of escapers per half-mass relaxation time, t(rh), scales approximately as R(3/2), which cancels out the r(h)(3/2) term in t(rh). For R less than or similar to 0.05, the 'isolated regime', (N)over dot scales as R(-3/2). The dissolution time-scale, t(dis), falls in three regimes. Clusters that start with their initial R, R(i), in the tidal regime dissolve completely in this regime and their t(dis) is, therefore, insensitive to the initial r(h). Our model predicts that R(i) has to be 10(-20)-10(-10) for clusters to dissolve completely in the isolated regime. This means that realistic clusters that start with R(i) less than or similar to 0.05 always expand to the tidal regime before final dissolution. Their t(dis) has a shallower dependence on Ri than what would be expected when t(dis) is a constant times t(rh). For realistic values of R(i), the lifetime varies by less than a factor of 1.5 due to changes in R(i). This implies that the 'survival' or 'vital' diagram for globular clusters should allow for more small clusters to survive. We note that with our result it is impossible to explain the universal peaked mass function of globular cluster systems by dynamical evolution from a power-law initial mass function, since the peak will be at lower masses in the outer parts of galaxies. Our results finally show that in the tidal regime t(dis) scales as N(0.65)/omega, with omega the angular frequency of the cluster in the host galaxy.
Formatted abstract
We study the escape rate of stars,  , from clusters with different radii on circular orbits in a tidal field using analytical predictions and direct N-body simulations. We find that depends on the ratio ℜ ≡ rh/rJ, where rh is the half-mass radius and rJ the radius of the zero-velocity surface around the cluster. For ℜ ≳ 0.05, the ‘tidal regime’, there is almost no dependence of Ṅ  on ℜ. To first order this is because the fraction of escapers per half-mass relaxation time, trh, scales approximately as ℜ3/2, which cancels out the r3/2h term in trh. For 0.05, the ‘isolated regime’,   scales as ℜ−3/2. The dissolution time-scale, tdis, falls in three regimes. Clusters that start with their initial ℜ, ℜi, in the tidal regime dissolve completely in this regime and their tdis is, therefore, insensitive to the initial rh. Our model predicts that ℜi has to be 10−20–10−10 for clusters to dissolve completely in the isolated regime. This means that realistic clusters that start with ℜi ≲ 0.05 always expand to the tidal regime before final dissolution. Their tdis has a shallower dependence on ℜi than what would be expected when tdis is a constant times trh. For realistic values of ℜi, the lifetime varies by less than a factor of 1.5 due to changes in ℜi. This implies that the ‘survival’ or ‘vital’ diagram for globular clusters should allow for more small clusters to survive. We note that with our result it is impossible to explain the universal peaked mass function of globular cluster systems by dynamical evolution from a power-law initial mass function, since the peak will be at lower masses in the outer parts of galaxies. Our results finally show that in the tidal regime tdis scales as N0.65/ω, with ω the angular frequency of the cluster in the host galaxy.
Keyword Stellar dynamics
Methods : N-body simulations
Globular clusters : general
Galaxies : star clusters
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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