On column density thresholds and the star formation rate

We present the results of a numerical study designed to address the question of whether there is a column density threshold for star formation within molecular clouds. We have simulated a large number of different clouds, with volume and column densities spanning a wide range of different values, using a state-of-the-art model for the coupled chemical, thermal and dynamical evolution of the gas. We show that star formation is only possible in regions where the mean (area-averaged) column density exceeds $10^{21} \: {\rm cm^{-2}}$. Within the clouds, we also show that there is a good correlation between the mass of gas above a K-band extinction $A_{\rm K} = 0.8$ and the star formation rate (SFR), in agreement with recent observational work. Previously, this relationship has been explained in terms of a correlation between the SFR and the mass in dense gas. However, we find that this correlation is weaker and more time-dependent than that between the SFR and the column density. In support of previous studies, we argue that dust shielding is the key process: the true correlation is one between the SFR and the mass in cold, well-shielded gas, and the latter correlates better with the column density than the volume density.Comment: 21 pages and 12 figures. Accepted for publication in MNRA

Is atomic carbon a good tracer of molecular gas in metal-poor galaxies?

Carbon monoxide (CO) is widely used as a tracer of molecular hydrogen (H2) in metal-rich galaxies, but is known to become ineffective in low metallicity dwarf galaxies. Atomic carbon has been suggested as a superior tracer of H2 in these metal-poor systems, but its suitability remains unproven. To help us to assess how well atomic carbon traces H2 at low metallicity, we have performed a series of numerical simulations of turbulent molecular clouds that cover a wide range of different metallicities. Our simulations demonstrate that in star-forming clouds, the conversion factor between [CI] emission and H2 mass, $X_{\rm CI}$, scales approximately as $X_{\rm CI} \propto Z^{-1}$. We recover a similar scaling for the CO-to-H2 conversion factor, $X_{\rm CO}$, but find that at this point in the evolution of the clouds, $X_{\rm CO}$ is consistently smaller than $X_{\rm CI}$, by a factor of a few or more. We have also examined how $X_{\rm CI}$ and $X_{\rm CO}$ evolve with time. We find that $X_{\rm CI}$ does not vary strongly with time, demonstrating that atomic carbon remains a good tracer of H2 in metal-poor systems even at times significantly before the onset of star formation. On the other hand, $X_{\rm CO}$ varies very strongly with time in metal-poor clouds, showing that CO does not trace H2 well in starless clouds at low metallicity.Comment: 16 pages, 9 figures. Updated to match the version accepted by MNRAS. The main change from the previous version is a new sub-section (3.6) discussing the possible impact of freeze-out and other processes not included in our numerical simulation

Does the CO-to-H2 conversion factor depend on the star formation rate?

We present a series of numerical simulations that explore how the `X-factor', $X_{CO}$ -- the conversion factor between the observed integrated CO emission and the column density of molecular hydrogen -- varies with the environmental conditions in which a molecular cloud is placed. Our investigation is centred around two environmental conditions in particular: the cosmic ray ionisation rate (CRIR) and the strength of the interstellar radiation field (ISRF). Since both these properties of the interstellar medium have their origins in massive stars, we make the assumption in this paper that both the strength of the ISRF and the CRIR scale linearly with the local star formation rate (SFR). The cloud modelling in this study first involves running numerical simulations that capture the cloud dynamics, as well as the time-dependent chemistry, and ISM heating and cooling. These simulations are then post-processed with a line radiative transfer code to create synthetic 12CO (1-0) emission maps from which $X_{CO}$ can be calculated. We find that for 1e4 solar mass virialised clouds with mean density 100 cm$^{-3}$, $X_{CO}$ is only weakly dependent on the local SFR, varying by a factor of a few over two orders of magnitude in SFR. In contrast, we find that for similar clouds but with masses of 1e5 solar masses, the X-factor will vary by an order of magnitude over the same range in SFR, implying that extra-galactic star formation laws should be viewed with caution. However, for denser ($10^4$ cm$^{-3}$), super-virial clouds such as those found at the centre of the Milky Way, the X-factor is once again independent of the local SFR.Comment: 16 pages, 5 figures. Accepted by MNRA

The Abundance of Molecular Hydrogen and its Correlation with Midplane Pressure in Galaxies: Non-Equilibrium, Turbulent, Chemical Models

Observations of spiral galaxies show a strong linear correlation between the ratio of molecular to atomic hydrogen surface density R_mol and midplane pressure. To explain this, we simulate three-dimensional, magnetized turbulence, including simplified treatments of non-equilibrium chemistry and the propagation of dissociating radiation, to follow the formation of H_2 from cold atomic gas. The formation time scale for H_2 is sufficiently long that equilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds. The equilibrium balance between radiative dissociation and H_2 formation on dust grains fails to predict the time-dependent molecular fractions we find. A simple, time-dependent model of H_2 formation can reproduce the gross behavior, although turbulent density perturbations increase molecular fractions by a factor of few above it. In contradiction to equilibrium models, radiative dissociation of molecules plays little role in our model for diffuse radiation fields with strengths less than ten times that of the solar neighborhood, because of the effective self-shielding of H_2. The observed correlation of R_mol with pressure corresponds to a correlation with local gas density if the effective temperature in the cold neutral medium of galactic disks is roughly constant. We indeed find such a correlation of R_mol with density. If we examine the value of R_mol in our local models after a free-fall time at their average density, as expected for models of molecular cloud formation by large-scale gravitational instability, our models reproduce the observed correlation over more than an order of magnitude range in density.Comment: 24 pages, 4 figures, accepted for publication in Astrophys. J, changes include addition of models with higher radiation fields and substantial clarification of the narrativ

The First Stellar Cluster

We report results from numerical simulations of star formation in the early universe that focus on gas at very high densities and very low metallicities. We argue that the gas in the central regions of protogalactic halos will fragment as long as it carries sufficient angular momentum. Rotation leads to the build-up of massive disk-like structures which fragment to form protostars. At metallicities Z ~ 10^-5 Zsun, dust cooling becomes effective and leads to a sudden drop of temperature at densities above n = 10^12 cm^-3. This induces vigorous fragmentation, leading to a very densely-packed cluster of low-mass stars. This is the first stellar cluster. The mass function of stars peaks below 1 Msun, similar to what is found in the solar neighborhood, and comparable to the masses of the very-low metallicity subgiant stars recently discovered in the halo of our Milky Way. We find that even purely primordial gas can fragment at densities 10^14 cm^-3 < n < 10^16 cm^-3, although the resulting mass function contains only a few objects (at least a factor of ten less than the Z = 10^-5 Zsun mass function), and is biased towards higher masses. A similar result is found for gas with Z = 10^-6 Zsun. Gas with Z <= 10^-6 Zsun behaves roughly isothermally at these densities (with polytropic exponent gamma ~ 1.06) and the massive disk-like structures that form due to angular momentum conservation will be marginally unstable. As fragmentation is less efficient, we expect stars with Z <= 10^-6 Zsun to be massive, with masses in excess of several tens of solar masses, consistent with the results from previous studies.Comment: 9 pages, 6 figures. Accepted by ApJ for publicatio

Gravitational fragmentation in turbulent primordial gas and the initial mass function of Population III stars

We report results from numerical simulations of star formation in the early universe that focus on the dynamical behavior of metal-free gas under different initial and environmental conditions. In particular we investigate the role of turbulence, which is thought to ubiquitously accompany the collapse of high-redshift halos. We distinguish between two main cases: the birth of Population III.1 stars - those which form in the pristine halos unaffected by prior star formation - and the formation of Population III.2 stars - those forming in halos where the gas is still metal free but has an increased ionization fraction. This latter case can arise either from exposure to the intense UV radiation of stellar sources in neighboring halos, or from the high virial temperatures associated with the formation of massive halos, that is, those with masses greater than 1e8 solar masses. We find that turbulent primordial gas is highly susceptible to fragmentation in both cases, even for turbulence in the subsonic regime, i.e. for rms velocity dispersions as low as 20 % of the sound speed. Contrary to our original expectations, fragmentation is more vigorous and more widespread in pristine halos compared to pre-ionized ones. We therefore predict Pop III.1 stars to be on average of somewhat lower mass, and form in larger groups, than Pop III.2 stars. We find that fragment masses cover over two orders of magnitude, indicating that the resulting Population III initial mass function was significantly extended in mass as well. This prompts the need for a large, high-resolution study of the formation of dark matter minihalos that is capable of resolving the turbulent flows in the gas at the moment when the baryons become self-gravitating. This would help determine which, if any, of the initial conditions presented in our study are realized in nature.Comment: Accepted for publication in Ap

Constraining the primordial initial mass function with stellar archaeology

We present a new near-field cosmological probe of the initial mass function (IMF) of the first stars. Specifically, we constrain the lower-mass limit of the Population III (Pop III) IMF with the total number of stars in large, unbiased surveys of the Milky Way. We model the early star formation history in a Milky Way-like halo with a semi-analytic approach, based on Monte-Carlo sampling of dark matter merger trees, combined with a treatment of the most important feedback mechanisms. Assuming a logarithmically flat Pop III IMF and varying its low mass limit, we derive the number of expected survivors of these first stars, using them to estimate the probability to detect any such Pop III fossil in stellar archaeological surveys. Following our analysis, the most promising region to find possible Pop III survivors is the stellar halo of the Milky Way, which is the best target for future surveys. We find that if no genuine Pop III survivor is detected in a sample size of $4 \times 10^6$ ($2 \times 10^7$) halo stars with well-controlled selection effects, then we can exclude the hypothesis that the primordial IMF extended down below $0.8 M_\odot$ at a confidence level of 68% (99%). With the sample size of the Hamburg/ESO survey, we can tentatively exclude Pop III stars with masses below $0.65 M_\odot$ with a confidence level of 95%, although this is subject to significant uncertainties. To fully harness the potential of our approach, future large surveys are needed that employ uniform, unbiased selection strategies for high-resolution spectroscopic follow-up.Comment: 19 pages, 14 figures, published in MNRA