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Register a new userCentral energy equipartition in multi-mass models of globular clusters
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In the construction of multi-mass King-Michie models of globular clusters, an approximated central energy equipartition between stars of different masses is usually imposed by scaling the velocity parameter of each mass class inversely with the stellar mass, as if the distribution function were isothermal. In this paper, this isothermal approximation (IA) has been checked and its consequences on the model parameters studied by a comparison with models including central energy equipartition correctly. It is found that, under the IA, the temperatures of a pair of components can differ to a non-negligible amount for low concentration distributions. It is also found that, in general, this approximation leads to a significantly reduced mass segregation in comparison with that given under the exact energy equipartition at the centre. As a representative example, an isotropic 3-component model fitting a given projected surface brightness and line-of-sight velocity dispersion profiles is discussed. In this example, the IA gives a cluster envelope much more concentrated (central dimensionless potential W=3.3) than under the true equipartition (W=0.059), as well as a higher logarithmic mass function slope. As a consequence, the inferred total mass (and then the global mass-to-light ratio) results a factor 1.4 times lower than the correct value and the amount of mass in heavy dark remnants is 3.3 times smaller. Under energy equipartition, the fate of stars having a mass below a certain limit is to escape from the system. This limit is derived as a function of the mass and W of the giants and turn-off stars component.
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It is widely believed that globular clusters evolve over many two-body relaxation times toward a state of energy equipartition, so that velocity dispersion scales with stellar mass as sigma ~ m^{-eta} with eta = 0.5. We show that this is incorrect, using direct N-body simulations with a variety of realistic IMFs and initial conditions. No simulated system ever reaches a state close to equipartition. Near the center, the luminous main-sequence stars reach a maximum eta_{max} ~ 0.15 pm 0.03. At large times, all radial bins convergence on an asymptotic value eta_{infty} ~ 0.08 pm 0.02. The development of this partial equipartition is strikingly similar across our simulations, despite the range of initial conditions employed. Compact remnants tend to have higher eta than main-sequence stars (but still eta < 0.5), due to their steeper (evolved) mass function. The presence of an intermediate-mass black hole (IMBH) decreases eta, consistent with our previous findings of a quenching of mass segregation under these conditions. All these results can be understood as a consequence of the Spitzer instability for two-component systems, extended by Vishniac to a continuous mass spectrum. Mass segregation (the tendency of heavier stars to sink toward the core) has often been studied observationally, but energy equipartition has not. Due to the advent of high-quality proper motion datasets from the Hubble Space Telescope, it is now possible to measure eta. Detailed data-model comparisons open up a new observational window on globular cluster dynamics and evolution. Comparison of our simulations to Omega Cen observations yields good agreement, confirming that globular clusters are not generally in energy equipartition. Modeling techniques that assume equipartition by construction (e.g., multi-mass Michie-King models) are approximate at best.
The energy densities in magnetic fields and cosmic rays (CRs) in galaxies are often assumed to be in equipartition, allowing for an indirect estimate of the magnetic field strength from the observed radio synchrotron spectrum. However, both primary and secondary CRs contribute to the synchrotron spectrum, and the CR electrons also loose energy via bremsstrahlung and inverse Compton. While classical equipartition formulae avoid these intricacies, there have been recent revisions that account for the extreme conditions in starbursts. Yet, the application of the equipartition formula to starburst environments also presupposes that timescales are long enough to reach equilibrium. Here, we test equipartition in the central molecular zones (CMZs) of nearby starburst galaxies by modeling the observed gamma-ray spectra, which provide a direct measure of the CR energy density, and the radio spectra, which provide a probe of the magnetic field strength. We find that in starbursts, the magnetic field energy density is significantly larger than the CR energy density, demonstrating that the equipartition argument is frequently invalid for CMZs.
We explain dark energy with equipartition theorem in string landscape.
For a sample of nine Galactic globular clusters we measured the inner kinematic profiles with integral-field spectroscopy that we combined with existing outer kinematic measurements and HST luminosity profiles. With this information we are able to detect the crucial rise in the velocity-dispersion profile which indicates the presence of a central black hole. In addition, N-body simulations compared to our data will give us a deeper insight in the properties of clusters with black holes and stronger selection criteria for further studies. For the first time, we obtain a homogeneous sample of globular cluster integral- field spectroscopy which allows a direct comparison between clusters with and without an intermediate-mass black hole.
Globular clusters should be born with significant numbers of stellar-mass black holes (BHs). It has been thought for two decades that very few of these BHs could be retained through the cluster lifetime. With masses ~10 MSun, BHs are ~20 times more massive than an average cluster star. They segregate into the cluster core, where they may eventually decouple from the remainder of the cluster. The small-N core then evaporates on a short timescale. This is the so-called Spitzer instability. Here we present the results of a full dynamical simulation of a globular cluster containing many stellar-mass BHs with a realistic mass spectrum. Our Monte Carlo simulation code includes detailed treatments of all relevant stellar evolution and dynamical processes. Our main finding is that old globular clusters could still contain many BHs at present. In our simulation, we find no evidence for the Spitzer instability. Instead, most of the BHs remain well-mixed with the rest of the cluster, with only the innermost few tens of BHs segregating significantly. Over the 12 Gyr evolution, fewer than half of the BHs are dynamically ejected through strong binary interactions in the cluster core. The presence of BHs leads to long-term heating of the cluster, ultimately producing a core radius on the high end of the distribution for Milky Way globular clusters (and those of other galaxies). A crude extrapolation from our model suggests that the BH--BH merger rate from globular clusters could be comparable to the rate in the field.
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