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

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. 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

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

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

Analytic Review of Modeling Studies of ARV Based PrEP Interventions Reveals Strong Influence of Drug-Resistance Assumptions on the Population-Level Effectiveness

Background Four clinical trials have shown that oral and topical pre-exposure prophylaxis (PrEP) based on tenofovir may be effective in preventing HIV transmission. The expected reduction in HIV transmission and the projected prevalence of drug resistance due to PrEP use vary significantly across modeling studies as a result of the broad spectrum of assumptions employed. Our goal is to quantify the influence of drug resistance assumptions on the predicted population-level impact of PrEP. Methods All modeling studies which evaluate the impact of oral or topical PrEP are reviewed and key assumptions regarding mechanisms of generation and spread of drug-resistant HIV are identified. A dynamic model of the HIV epidemic is developed to assess and compare the impact of oral PrEP using resistance assumptions extracted from published studies. The benefits and risks associated with ten years of PrEP use are evaluated under identical epidemic, behavioral and intervention conditions in terms of cumulative fractions of new HIV infections prevented, resistance prevalence among those infected with HIV, and fractions of infections in which resistance is transmitted. Results Published models demonstrate enormous variability in resistance-generating assumptions and uncertainty in parameter values. Depending on which resistance parameterization is used, a resistance prevalence between 2% and 44% may be expected if 50% efficacious oral PrEP is used consistently by 50% of the population over ten years. We estimated that resistance may be responsible for up to a 10% reduction or up to a 30% contribution to the fraction of prevented infections predicted in different studies. Conclusions Resistance assumptions used in published studies have a strong influence on the projected impact of PrEP. Modelers and virologists should collaborate toward clarifying the set of resistance assumptions biologically relevant to the PrEP products which are already in use or soon to be added to the arsenal against HIV

A Bayesian approach to estimate changes in condom use from limited human immunodeficiency virus prevalence data.

Evaluation of large-scale intervention programmes against human immunodeficiency virus (HIV) is becoming increasingly important, but impact estimates frequently hinge on knowledge of changes in behaviour such as the frequency of condom use over time, or other self-reported behaviour changes, for which we generally have limited or potentially biased data. We employ a Bayesian inference methodology that incorporates an HIV transmission dynamics model to estimate condom use time trends from HIV prevalence data. Estimation is implemented via particle Markov chain Monte Carlo methods, applied for the first time in this context. The preliminary choice of the formulation for the time varying parameter reflecting the proportion of condom use is critical in the context studied, because of the very limited amount of condom use and HIV data available. We consider various novel formulations to explore the trajectory of condom use over time, based on diffusion-driven trajectories and smooth sigmoid curves. Numerical simulations indicate that informative results can be obtained regarding the amplitude of the increase in condom use during an intervention, with good levels of sensitivity and specificity performance in effectively detecting changes. The application of this method to a real life problem demonstrates how it can help in evaluating HIV interventions based on a small number of prevalence estimates, and it opens the way to similar applications in different contexts