Old Globular Clusters (GCs) in the Milky Way have ages of about 13 Gyr, placing their formation time in the reionization epoch. We propose a novel scenario for the formation of these systems based on the merger of two or more atomic cooling halos at
high-redshift (z>6). First generation stars are formed as an intense burst in the center of a minihalo that grows above the threshold for hydrogen cooling (halo mass M_h~10^8 Msun) by undergoing a major merger within its cooling timescale (~150 Myr). Subsequent minor mergers and sustained gas infall bring new supply of pristine gas at the halo center, creating conditions that can trigger new episodes of star formation. The dark-matter halo around the GC is then stripped during assembly of the host galaxy halo. Minihalo merging is efficient only in a short redshift window, set by the LCDM parameters, allowing us to make a strong prediction on the age distribution for old GCs. From cosmological simulations we derive an average merging redshift <z>=9 and narrow distribution Dz=2, implying average GC age <t_age>=13.0+/-0.2 Gyr including ~0.2 Gyr of star formation delay. Qualitatively, our scenario reproduces other general old GC properties (characteristic masses and number of objects, metallicity versus galactocentric radius anticorrelation, radial distribution), but unlike age, these generally depend on details of baryonic physics. In addition to improved age measurements, direct validation of the model at z~10 may be within reach of ultradeep gravitationally lensed observations with the James Webb Space Telescope.
We show that supersonic MHD turbulence yields a star formation rate (SFR) as low as observed in molecular clouds (MCs), for characteristic values of the free-fall time divided by the dynamical time, $t_{rm ff}/t_{rm dyn}$, the alfv{e}nic Mach number,
${cal M}_{rm a}$, and the sonic Mach number, ${cal M}_{rm s}$. Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, $epsilon_{rm ff}$, on the above parameters. Our main results are: i) $epsilon_{rm ff}$ decreases exponentially with increasing $t_{rm ff}/t_{rm dyn}$, but is insensitive to changes in ${cal M}_{rm s}$, for constant values of $t_{rm ff}/t_{rm dyn}$ and ${cal M}_{rm a}$. ii) Decreasing values of ${cal M}_{rm a}$ (stronger magnetic fields) reduce $epsilon_{rm ff}$, but only to a point, beyond which $epsilon_{rm ff}$ increases with a further decrease of ${cal M}_{rm a}$. iii) For values of ${cal M}_{rm a}$ characteristic of star-forming regions, $epsilon_{rm ff}$ varies with ${cal M}_{rm a}$ by less than a factor of two. We propose a simple star-formation law, based on the empirical fit to the minimum $epsilon_{rm ff}$, and depending only on $t_{rm ff}/t_{rm dyn}$: $epsilon_{rm ff} approx epsilon_{rm wind} exp(-1.6 ,t_{rm ff}/t_{rm dyn})$. Because it only depends on the mean gas density and rms velocity, this law is straightforward to implement in simulations and analytical models of galaxy formation and evolution.
The observed similarities between the mass function of prestellar cores (CMF) and the stellar initial mass function (IMF) have led to the suggestion that the IMF is already largely determined in the gas phase. However, theoretical arguments show that
the CMF may differ significantly from the IMF. In this Letter, we study the relation between the CMF and the IMF, as predicted by the IMF model of Padoan and Nordlund. We show that 1) the observed mass of prestellar cores is on average a few times smaller than that of the stellar systems they generate; 2) the CMF rises monotonically with decreasing mass, with a noticeable change in slope at approximately 3-5 solar masses, depending on mean density; 3) the selection of cores with masses larger than half their Bonnor-Ebert mass yields a CMF approximately consistent with the system IMF, rescaled in mass by the same factor as our model IMF, and therefore suitable to estimate the local efficiency of star formation, and to study the dependence of the IMF peak on cloud properties; 4) only one in five pre-brown-dwarf core candidates is a true progenitor to a brown dwarf.
(abridged) We develop a model which describes the coevolution of the mass function of dense cores and of the IMF in a protocluster clump. In the model, cores injected in the clump evolve under the effect of gas accretion. Accretion onto the cores fol
lows a time-dependent accretion rate that describes accretion in a turbulent medium. Once the accretion timescales of cores exceed their contraction timescales, they are turned into stars. We include the effect of feedback by the newly formed massive stars through their stellar winds. A fraction of the winds energy is assumed to counter gravity and disperse the gas from the protocluster and as a consequence, quench further star formation. The latter effect sets the final IMF of the cluster. We apply our model to a clump that is expected to resemble the progenitor clump of the Orion Nebula Cluster (ONC). Our model is able to reproduce both the shape and normalization of the ONCs IMF and the mass function of dense cores in Orion. The complex features of the ONCs IMF,i.e., a shallow slope in the mass range ~0.3-2.5 Msol,a steeper slope in the mass range ~2.5-12 Msol, and a nearly flat tail at the high mass end are reproduced. The model predicts a rapid star formation process with an age spread for the stars of 2.3 10^5 yr which is consistent with the fact that 80% of the ONCs stars have ages of <=0.3 Myr. The model predicts a primordial mass segregation with the most massive stars being born in the region between 2-4 times the core radius of the cluster. In parallel, the model also reproduces, simultaneously, the mass function of dense cores in Orion. We study the effects of varying the model parameters on the resulting IMF and show that the IMF of stellar clusters is expected to show significant variations, provided variations in the clumps and cores properties exist.
