On the mass function of star clusters

Clusters that form in total 10^3 < N < 10^5 stars (type II clusters) lose their gas within a dynamical time as a result of the photo-ionising flux from O stars. Sparser (type I) clusters get rid of their residual gas on a timescale longer or comparable to the nominal crossing time and thus evolve approximately adiabatically. This is also true for massive embedded clusters (type III) for which the velocity dispersion is larger than the sound speed of the ionised gas. On expelling their residual gas, type I and III clusters are therefore expected to lose a smaller fraction of their stellar component than type II clusters. We outline the effect this has on the transformation of the mass function of embedded clusters (ECMF), which is directly related to the mass function of star-cluster-forming molecular cloud cores, to the ``initial'' MF of bound gas-free star clusters (ICMF). The resulting ICMF has, for a featureless power-law ECMF, a turnover near 10^{4.5} Msun and a peak near 10^3 Msun. The peak lies around the initial masses of the Hyades, Praesepe and Pleiades clusters. We also find that the entire Galactic population II stellar spheroid can be generated if star formation proceeded via embedded clusters distributed like a power-law MF with exponent 0.9 < beta < 2.6.Comment: 10 pages, 4 figures, accepted by MNRAS, small adjustments for consistency with published versio

The impact of mass loss on star cluster formation. I. Analytic results

We study analytically the disruptive effect of instantaneous gas removal from a cluster containing O stars. We setup an iterative calculation based on the stellar velocity distribution function to compute the fraction of stars that remain bound once the cluster has ejected the gas and is out of equilibrium. We show that the stellar bound fraction is a function of the initial cluster distribution function as well as the star formation efficiency, $\epsilon$, taken constant throughout the cluster. The case of the Plummer sphere is dealt with in greater details. We find for this case that up to ~ 50% of the stars may remain bound when $\epsilon$ assumes values < 1/2, contrary to expectations derived from the virial theorem. The fraction of bound stars is expressed algebraically for polytropic distribution functions.Comment: to appear in M

Black Hole Motion as Catalyst of Orbital Resonances

The motion of a black hole about the centre of gravity of its host galaxy induces a strong response from the surrounding stellar population. We treat the case of a harmonic potential analytically and show that half of the stars on circular orbits in that potential shift to an orbit of lower energy, while the other half receive a positive boost and recede to a larger radius. The black hole itself remains on an orbit of fixed amplitude and merely acts as a catalyst for the evolution of the stellar energy distribution function f(E). We show that this effect is operative out to a radius of approx 3 to 4 times the hole's influence radius, R_bh. We use numerical integration to explore more fully the response of a stellar distribution to black hole motion. We consider orbits in a logarithmic potential and compare the response of stars on circular orbits, to the situation of a `warm' and `hot' (isotropic) stellar velocity field. While features seen in density maps are now wiped out, the kinematic signature of black hole motion still imprints the stellar line-of-sight mean velocity to a magnitude ~18% the local root mean-square velocity dispersion sigma.Comment: revised version, typos fixed, added references, 20 pages MN styl

The impact of mass loss on star cluster formation. II. Numerical N-body integration & further applications

We subject to an N-body numerical investigation our analysis of Paper I on the survival of stellar clusters undergoing rapid mass loss. We compare analytical tracks of bound mass-fraction {\it vs} star formation efficiency $\epsilon$ to those obtained with N-body integration. We use these to argue that stellar clusters must develop massive cores of high-binding energy if they are to remain bound despite a star formation efficiency as low as 30% or lower suggested by observations. The average local virial ratio $$ is introduced to classify bound clusters as function of their critical $\epsilon$ for dissolution. Clusters dissolving at lower $\epsilon$ achieve the lowest ratio. We applied this classification parameter successfully to Michie-King and Hernquist-type distribution functions. The Plummer sphere is exceptional in that it defies this and other classification parameters we tried. The reasons for the discrepancy include less effective energy redistribution during the expansion phase for this case.Comment: MN, in the pres

Hubble-Lema\^itre fragmentation and the path to equilibrium of merger-driven cluster formation

This paper discusses a new method to generate self-coherent initial conditions for young substructured stellar cluster. The expansion of a uniform system allows stellar sub-structures (clumps) to grow from fragmentation modes by adiabatic cooling. We treat the system mass elements as stars, chosen according to a Salpeter mass function, and the time-evolution is performed with a collisional N-body integrator. This procedure allows to create a fully-coherent relation between the clumps' spatial distribution and the underlying velocity field. The cooling is driven by the gravitational field, as in a cosmological Hubble-Lema\^itre flow. The fragmented configuration has a `fractal'-like geometry but with a self-grown velocity field and mass profile. We compare the characteristics of the stellar population in clumps with that obtained from hydrodynamical simulations and find a remarkable correspondence between the two in terms of the stellar content and the degree of spatial mass-segregation. In the fragmented configuration, the IMF power index is ~0.3 lower in clumps in comparison to the field stellar population, in agreement with observations in the Milky Way. We follow in time the dynamical evolution of fully fragmented and sub-virial configurations, and find a soft collapse, leading rapidly to equilibrium (timescale of 1 Myr for a ~ 10^4 Msun system). The low-concentration equilibrium implies that the dynamical evolution including massive stars is less likely to induce direct collisions and the formation of exotic objects. Low-mass stars already ejected from merging clumps are depleted in the end-result stellar clusters, which harbour a top-heavy stellar mass function.Comment: 22 pages, accepted for publication in MNRA

Star cluster survival and compressive tides in Antennae-like mergers

Gravitational tides are widely understood to strip and destroy galactic substructures. In the course of a galaxy merger, however, transient totally compressive tides may develop and prevent star forming regions from dissolving, after they condensed to form clusters of stars. We study the statistics of such compressive modes in an N-body model of the galaxy merger NGC 4038/39 (the Antennae) and show that ~15% of the disc material undergoes compressive tides at pericentre. The spatial distribution of observed young clusters in the overlap and nuclear regions of the Antennae matches surprisingly well the location of compressive tides obtained from simulation data. Furthermore, the statistics of time intervals spent by individual particles embedded in a compressive tide yields a log-normal distribution of characteristic time ~10 Myr, comparable to star cluster formation timescales. We argue that this generic process is operative in galaxy mergers at all redshifts and possibly enhances the formation of star clusters. We show with a model calculation that this process will prevent the dissolution of a star cluster during the formation phase, even for a star formation efficiency as low as ~10%. The transient nature of compressive tides implies that clusters may dissolve rapidly once the tidal field switches to the usual disruptive mode.Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letters. For higher resolution, see http://astro.u-strasbg.fr/~renaud/publi/mnras08.pd

Global and regional estimates of the contribution of herpes simplex virus Type 2 infection to HIV incidence: a population attributable fraction analysis using published epidemiological data

Background A 2017 systematic review and meta-analysis of 55 prospective studies found the adjusted risk of HIV acquisition to be at least tripled in individuals with herpes simplex virus type 2 (HSV-2) infection. We aimed to assess the potential contribution of HSV-2 infection to HIV incidence, given an effect of HSV-2 on HIV acquisition. Methods We used a classic epidemiological formula to estimate the global and regional (WHO regional) population attributable fraction (PAF) and number of incident HIV infections attributable to HSV-2 infection by age (15–24 years, 25–49 years, and 15–49 years), sex, and timing of HSV-2 infection (established vs recently acquired). Estimates were calculated by incorporating HSV-2 and HIV infection data with pooled relative risk (RR) estimates for the effect of HSV-2 infection on HIV acquisition from a systematic review and meta-analysis. Because HSV-2 and HIV have shared sexual and other risk factors, in addition to HSV-related biological factors that increase HIV risk, we only used RR estimates that were adjusted for potential confounders. Findings An estimated 420 000 (95% uncertainty interval 317 000–546 000; PAF 29·6% [22·9–37·1]) of 1·4 million sexually acquired incident HIV infections in individuals aged 15–49 years in 2016 were attributable to HSV-2 infection. The contribution of HSV-2 to HIV was largest for the WHO African region (PAF 37·1% [28·7–46·3]), women (34·8% [23·5–45·0]), individuals aged 25–49 years (32·4% [25·4–40·2]), and established HSV-2 infection (26·8% [19·7–34·5]). Interpretation A large burden of HIV is likely to be attributable to HSV-2 infection, even if the effect of HSV-2 infection on HIV had been imperfectly measured in studies providing adjusted RR estimates, potentially because of residual confounding. The contribution is likely to be greatest in areas where HSV-2 is highly prevalent, particularly Africa. New preventive interventions against HSV-2 infection could not only improve the quality of life of millions of people by reducing the prevalence of herpetic genital ulcer disease, but could also have an additional, indirect effect on HIV transmission