Competitive Accretion and the IMF

Competitive accretion occurs when stars in a cluster accrete from a shared reservoir of gas. The competition arises due to the relative attraction of stars as a function of their mass and location in the cluster. The low relative motions of the stars and gas in young, gas dominated clusters results in a tidal limit to the accretion whereas in the stellar dominated cluster cores, the high relative velocities results in Bondi-Hoyle accretion. The combination of these two accretion processes produces a two power-law IMF with $\gamma \approx -1.5$, for low-mass stars which accrue their mass in the gas dominated regime, and a steeper, $\gamma\approx -2.5$, IMF for higher-mass stars that form in the core of a cluster. Simulations of the fragmentation and formation of a stellar cluster show that the final stellar masses, and IMF, are due to competitive accretion. Competitive accretion also naturally results in a mass segregated cluster and in a direct correlation between the richness of a cluster and the mass of the most massive star therein. The {\sl knee} where the IMF slope changes occurs near the Jeans mass of the system.Comment: 6 pages, 5 figures to appear in the IMF@50, eds E. Corbelli, F. Palla, and H. Zinnecke

Core dissolution and the dynamics of massive stars in young stellar clusters

We investigate the dynamical effects of rapid gas expulsion from the core of a young stellar cluster. The aims of this study are to determine 1) whether a mass-segregated core survives the gas expulsion and 2) the probable location of any massive stars that have escaped from the core. Feedback from massive stars is expected to remove the gas from the core of the cluster first, as that is where most massive stars are located. We find that gas expulsion has little effect on the core for a core star formation efficiency, of greater than 50%. For lower values of star formation efficiency down to 20%, a reduced core survives containing the majority of the massive stars while some of them are dispersed into the rest of the cluster. In fact we find that ejected stars migrate from radial to tangential orbits due to stellar encounters once they leave the core. Thus, the location of massive stars outside of the core does not exclude their forming in the dense cluster core. Few massive stars are expected to remain in the core for a star formation efficiency lower than 20%.Comment: 8 pages, 7 figures, accepted for publication in MNRA

Clumpy and fractal shocks, and the generation of a velocity dispersion in molecular clouds

We present an alternative explanation for the nature of turbulence in molecular clouds. Often associated with classical models of turbulence, we instead interpret the observed gas dynamics as random motions, induced when clumpy gas is subject to a shock. From simulations of shocks, we show that a supersonic velocity dispersion occurs in the shocked gas provided the initial distribution of gas is sufficiently non-uniform. We investigate the velocity size-scale relation $\sigma \propto r^{\alpha}$ for simulations of clumpy and fractal gas, and show that clumpy shocks can produce realistic velocity size-scale relations with mean $\alpha \thicksim 0.5$. For a fractal distribution, with a fractal dimension of 2.2 similar to what is observed in the ISM, we find $\sigma \propto r^{0.4}$. The form of the velocity size-scale relation can be understood as due to mass loading, i.e. the post-shock velocity of the gas is determined by the amount of mass encountered as the gas enters the shock. We support this hypothesis with analytical calculations of the velocity dispersion relation for different initial distributions. A prediction of this model is that the line-of sight velocity dispersion should depend on the angle at which the shocked gas is viewed.Comment: 11 pages, 17 figures, accepted for publication in MNRA

Ionizing feedback from massive stars in massive clusters III: Disruption of partially unbound clouds

We extend our previous SPH parameter study of the effects of photoionization from O-stars on star-forming clouds to include initially unbound clouds. We generate a set of model clouds in the mass range $10^{4}-10^{6}$M$_{\odot}$ with initial virial ratios $E_{\rm kin}/E_{\rm pot}$=2.3, allow them to form stars, and study the impact of the photoionizing radiation produced by the massive stars. We find that, on the 3Myr timescale before supernovae are expected to begin detonating, the fractions of mass expelled by ionizing feedback is a very strong function of the cloud escape velocities. High-mass clouds are largely unaffected dynamically, while lower-mass clouds have large fractions of their gas reserves expelled on this timescale. However, the fractions of stellar mass unbound are modest and significant portions of the unbound stars are so only because the clouds themselves are initially partially unbound. We find that ionization is much more able to create well-cleared bubbles in the unbound clouds, owing to their intrinsic expansion, but that the presence of such bubbles does not necessarily indicate that a given cloud has been strongly influenced by feedback. We also find, in common with the bound clouds from our earlier work, that many of the systems simulated here are highly porous to photons and supernova ejecta, and that most of them will likely survive their first supernova explosions.Comment: 14 pages, 13 figures (some degraded and greyscaled), accepted by MNRA

Star Formation Around Super-Massive Black Holes

The presence of young massive stars orbiting on eccentric rings within a few tenths of a parsec of the supermassive black hole in the Galactic centre is challenging for theories of star formation. The high tidal shear from the black hole should tear apart the molecular clouds that form stars elsewhere in the Galaxy, while transporting the stars to the Galactic centre also appears unlikely during their stellar lifetimes. We present numerical simulations of the infall of a giant molecular cloud that interacts with the black hole. The transfer of energy during closest approach allows part of the cloud to become bound to the black hole, forming an eccentric disc that quickly fragments to form stars. Compressional heating due to the black hole raises the temperature of the gas to 100-1000K, ensuring that the fragmentation produces relatively high stellar masses. These stars retain the eccentricity of the disc and, for a sufficiently massive initial cloud, produce an extremely top-heavy distribution of stellar masses. This potentially repetitive process can therefore explain the presence of multiple eccentric rings of young stars in the presence of a supermassive black hole.Comment: 20 pages includingh 7 figures. "This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science, 321, (22 August 2008), doi:10.1126/science.1160653". Reprints and animations can be found at http://star-www.st-and.ac.uk/~iab1

Ionization--induced star formation V: Triggering in partially unbound clusters

We present the fourth in a series of papers detailing our SPH study of the effects of ionizing feedback from O--type stars on turbulent star forming clouds. Here, we study the effects of photoionization on a series of initially partially unbound clouds with masses ranging from $10^{4}$--$10^{6}$M$_{\odot}$ and initial sizes from 2.5-45pc. We find that ionizing feedback profoundly affects the structure of the gas in most of our model clouds, creating large and often well-cleared bubble structures and pillars. However, changes in the structures of the embedded clusters produced are much weaker and not well correlated to the evolution of the gas. We find that in all cases, star formation efficiencies and rates are reduced by feedback and numbers of objects increased, relative to control simulations. We find that local triggered star formation does occur and that there is a good correlation between triggered objects and pillars or bubble walls, but that triggered objects are often spatially-mixed with those formed spontaneously. Some triggered objects acquire large enough masses to become ionizing sources themselves, lending support to the concept of propagating star formation. We find scant evidence for spatial age gradients in most simulations, and where we do see them, they are not a good indicator of triggering, as they apply equally to spontaneously-formed objects as triggered ones. Overall, we conclude that inferring the global or local effects of feedback on stellar populations from observing a system at a single epoch is very problematic.Comment: 17 pages, 11 figures (mostly degraded to get under the submission size limit), accepted by MNRA

T Tauri variability in the context of the beat-frequency model

We examine the implications of a beat frequency modulated model of T Tauri accretion. In particular we show that measurements of the variability of accretion generated lines can be used in conjunction with existing photometry to obtain a measurement of the underlying photospheric and disc flux. This provides an independent way of checking spectral energy distribution modelling. In addition, we show how spectroscopy of T Tauri stars can reveal the inclination angle between the magnetic axis and the plane of the disc.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

Ionisation-induced star formation II: External irradiation of a turbulent molecular cloud

In this paper, we examine numerically the difference between triggered and revealed star formation. We present Smoothed Particle Hydrodynamics (SPH) simulations of the impact on a turbulent 10^4 solar-mass molecular cloud of irradiation by an external source of ionising photons. In particular, using a control model, we investigate the triggering of star formation within the cloud. We find that, although feedback has a dramatic effect on the morphology of our model cloud, its impact on star formation is relatively minor. We show that external irradiation has both positive and negative effects, accelerating the formation of some objects, delaying the formation of others, and inducing the formation of some that would not otherwise have formed. Overall, the calculation in which feedback is included forms nearly twice as many objects over a period of \sim0.5 freefall times (\sim2.4 Myr), resulting in a star--formation efficiency approximately one third higher (\sim4% as opposed to \sim3% at this epoch) as in the control run in which feedback is absent. Unfortunately, there appear to be no observable characteristics which could be used to differentiate objects whose formation was triggered from those which were forming anyway and which were simply revealed by the effects of radiation, although this could be an effect of poor statistics.Comment: 12 pages, 9 figures, accepted by MNRA

The relation between accretion rates and the initial mass function in hydrodynamical simulations of star formation

We analyse a hydrodynamical simulation of star formation. Sink particles in the simulations which represent stars show episodic growth, which is presumably accretion from a core that can be regularly replenished in response to the fluctuating conditions in the local environment. The accretion rates follow $\dot{m} \propto m^{2/3}$, as expected from accretion in a gas-dominated potential, but with substantial variations over-laid on this. The growth times follow an exponential distribution which is tapered at long times due to the finite length of the simulation. The initial collapse masses have an approximately lognormal distribution with already an onset of a power-law at large masses. The sink particle mass function can be reproduced with a non-linear stochastic process, with fluctuating accretion rates $\propto m^{2/3}$, a distribution of seed masses and a distribution of growth times. All three factors contribute equally to the form of the final sink mass function. We find that the upper power law tail of the IMF is unrelated to Bondi-Hoyle accretion.Comment: 13 pages, 13 figures, MNRAS accepte