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(Abriged) At present, there are two scenarios for the formation of massive stars: 1) The accretion scenario and 2) The coalescence scenario, which implies the merging of intermediate mass stars. We examine here some properties of the first one. We calculate three different sets of birthlines, i.e. tracks followed by a continuously accreting star. First, three models with a constant accretion rate ($dot{M}_{rm{accr}}$ = $10^{-6}$, $10^{-5}$, $10^{-4}$ M$_{odot}$ yr$^{-1}$). Then several birthlines following the accretion models of Bernasconi and Maeder (cite{BM96}), which have $dot{M}_{rm{accr}}$ increasing only slightly with mass. Finally we calculate several birthlines for which $dot{M}_{accr} = dot{M}_{mathrm{ref}} ({frac{M}{M_{odot}}}) ^{phi}$, with values of $phi$ equal to 0.5, 1.0 and 1.5 and also for different values of $dot{M}_{mathrm{ref}}$. The best fit to the observations of PMS stars in the HR diagram is achieved for $phi$ between 1.0 or 1.5 and for $dot{M}_{mathrm{ref}} simeq 10^{-5}$ M$_{odot}$ yr$^{-1}$. Considerations on the lifetimes favour values of $phi$ equal to 1.5. These accretion rates do well correspond to those derived from radio and IR observations of mass outflows. We emphasize the importance of the accretion scenario for shaping the IMF, and in particular for determining the upper mass limit of stars. In the accretion scenario, this upper mass limit will be given by the mass for which the accretion rate is such that the accretion induced shock luminosity is of the order of the Eddington luminosity.
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We consider the conditions required for a cluster core to shrink, by adiabatic accretion of gas from the surrounding cluster, to densities such that stellar collisions are a likely outcome. We show that the maximum densities attained, and hence the viability of collisions, depends on a competition between core shrinkage (driven by accretion) and core puffing up (driven by relaxation effects). The expected number of collisions scales as $N_{core}^{5/3} tilde v^2$ where $N_{core}$ is the number of stars in the cluster core and $tilde v$ is the free fall velocity of the parent cluster (gas reservoir). Thus whereas collisions are very unlikely in a relatively low mass, low internal velocity system such as the Orion Nebula Cluster, they become considerably more important at the mass and velocity scale characteristic of globular clusters. Thus stellar collisions in response to accretion induced core shrinkage remains a viable prospect in more massive clusters, and may contribute to the production of intermediate mass black holes in these systems.
We study feedback during massive star formation using semi-analytic methods, considering the effects of disk winds, radiation pressure, photoevaporation and stellar winds, while following protostellar evolution in collapsing massive gas cores. We find that disk winds are the dominant feedback mechanism setting star formation efficiencies (SFEs) from initial cores of ~0.3-0.5. However, radiation pressure is also significant to widen the outflow cavity causing reductions of SFE compared to the disk-wind only case, especially for >100Msun star formation at clump mass surface densities Sigma<0.3g/cm2. Photoevaporation is of relatively minor importance due to dust attenuation of ionizing photons. Stellar winds have even smaller effects during the accretion stage. For core masses Mc~10-1000Msun and Sigma~0.1-3g/cm2, we find the overall SFE to be 0.31(Rc/0.1pc)^{-0.39}, potentially a useful sub-grid star-formation model in simulations that can resolve pre-stellar core radii, Rc=0.057(Mc/60Msun)^{1/2}(Sigma/g/cm2)^{-1/2}pc. The decline of SFE with Mc is gradual with no evidence for a maximum stellar-mass set by feedback processes up to stellar masses of ~300Msun. We thus conclude that the observed truncation of the high-mass end of the IMF is shaped mostly by the pre-stellar core mass function or internal stellar processes. To form massive stars with the observed maximum masses of ~150-300Msun, initial core masses need to be >500-1000Msun. We also apply our feedback model to zero-metallicity primordial star formation, showing that, in the absence of dust, photoevaporation staunches accretion at ~50Msun. Our model implies radiative feedback is most significant at metallicities ~10^{-2}Zsun, since both radiation pressure and photoevaporation are effective in this regime.
There is currently no accepted theoretical framework for the formation of the most massive stars, and the manner in which protostars continue to accrete and grow in mass beyond sim10Msun is still a controversial topic. In this study we use several prescriptions of stellar accretion and a description of the Galactic gas distribution to simulate the luminosities and spatial distribution of massive protostellar population of the Galaxy. We then compare the observables of each simulation to the results of the Red MSX Source (RMS) survey, a recently compiled database of massive young stellar objects. We find that the observations are best matched by accretion rates which increase as the protostar grows in mass, such as those predicted by the turbulent core and competitive accretion (i.e. Bondi-Hoyle) models. These accelerating accretion models provide very good qualitative and quantitative fits to the data, though we are unable to distinguish between these two models on our simulations alone. We rule out models with accretion rates which are constant with time, and those which are initially very high and which fall away with time, as these produce results which are quantitatively and/or qualitatively incompatible with the observations. To simultaneously match the low- and high-luminosity YSO distribution we require the inclusion of a swollen-star pre-main-sequence phase, the length of which is well-described by the Kelvin-Helmholz timescale. Our results suggest that the lifetime of the YSO phase is sim 10^5yrs, whereas the compact Hii-region phase lasts between sim 2 - 4 times 10^5yrs depending on the final mass of the star. Finally, the absolute numbers of YSOs are best matched by a globally averaged star-formation rate for the Galaxy of 1.5-2Msun/yr.
Supermassive stars (SMS; ~ 10^5 M_sun) formed from metal-free gas in the early Universe attract attention as progenitors of supermassive black holes observed at high redshifts. To form SMSs by accretion, central protostars must accrete at as high rates as ~ 0.1-1 M_sun/yr. Such protostars have very extended structures with bloated envelopes, like super-giant stars, and are called super-giant protostars (SGPSs). Under the assumption of hydrostatic equilibrium, SGPSs have density inverted layers, where the luminosity becomes locally super-Eddington, near the surface. If the envelope matter is allowed to flow out, however, a stellar wind could be launched and hinder the accretion growth of SGPSs before reaching the supermassive regime. We examine whether radiation-driven winds are launched from SGPSs by constructing steady and spherically symmetric wind solutions. We find that the wind velocity does not reach the escape velocity in any case considered. This is because once the temperature falls below ~ 10^4 K, the opacity plummet drastically owing to the recombination of hydrogen and the acceleration ceases suddenly. This indicates that, in realistic non-steady cases, even if outflows are launched from the surface of SGPSs, they would fall back again. Such a wind does not result in net mass loss and does not prevent the growth of SGPSs. In conclusion, SGPSs will grow to SMSs and eventually collapse to massive BHs of ~ 10^5 M_sun, as long as the rapid accretion is maintained.
Accretion-driven luminosity outbursts are a vivid manifestation of variable mass accretion onto protostars. They are known as the so-called FU Orionis phenomenon in the context of low-mass protostars. More recently, this process has been found in models of primordial star formation. Using numerical radiation hydrodynamics simulations, we stress that present-day forming massive stars also experience variable accretion and show that this process is accompanied by luminous outbursts induced by the episodic accretion of gaseous clumps falling from the circumstellar disk onto the protostar. Consequently, the process of accretion-induced luminous flares is also conceivable in the high-mass regime of star formation and we propose to regard this phenomenon as a general mechanism that can affect protostars regardless of their mass and/or the chemical properties of the parent environment in which they form. In addition to the commonness of accretion-driven outbursts in the star formation machinery, we conjecture that luminous flares from regions hosting forming high-mass star may be an observational implication of the fragmentation of their accretion disks.
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