Chemistry and cooling in metal-free and metal-poor gas

I summarize four of the most important areas of uncertainty in the study of the chemistry and cooling of gas with zero or very low metallicity. These are: i) the importance and effects of HD cooling in primordial gas; ii) the importance of metal-line and dust cooling in low metallicity gas; iii) the impact of the large uncertainties that exist in the rate coefficients of several key reactions involved in the formation of H2; and iv) the effectiveness of grain surface chemistry at high redshifts.Comment: 5 pages, 2 figures. To appear in "First Stars III", eds. B. O'Shea, A. Heger & T. Abel. This revised version fixes a minor error brought to my attention by K. Omuka

Molecular cooling in the diffuse interstellar medium

We use a simple one-zone model of the thermal and chemical evolution of interstellar gas to study whether molecular hydrogen (H2) is ever an important coolant of the warm, diffuse interstellar medium (ISM). We demonstrate that at solar metallicity, H2 cooling is unimportant and the thermal evolution of the ISM is dominated by metal line cooling. At metallicities below 0.1 Z_solar, however, metal line cooling of low density gas quickly becomes unimportant and H2 can become the dominant coolant, even though its abundance in the gas remains small. We investigate the conditions required in order for H2 to dominate, and show that it provides significant cooling only when the ratio of the interstellar radiation field strength to the gas density is small. Finally, we demonstrate that our results are insensitive to changes in the initial fractional ionization of the gas or to uncertainties in the nature of the dust present in the low-metallicity ISM.Comment: 13 pages, 6 figures. Minor changes to match version accepted by MNRA

Approximations for modelling CO chemistry in GMCs: a comparison of approaches

We examine several different simplified approaches for modelling the chemistry of CO in three-dimensional numerical simulations of turbulent molecular clouds. We compare the different models both by looking at the behaviour of integrated quantities such as the mean CO fraction or the cloud-averaged CO-to-H2 conversion factor, and also by studying the detailed distribution of CO as a function of gas density and visual extinction. In addition, we examine the extent to which the density and temperature distributions depend on our choice of chemical model. We find that all of the models predict the same density PDF and also agree very well on the form of the temperature PDF for temperatures T > 30 K, although at lower temperatures, some differences become apparent. All of the models also predict the same CO-to-H2 conversion factor, to within a factor of a few. However, when we look more closely at the details of the CO distribution, we find larger differences. The more complex models tend to produce less CO and more atomic carbon than the simpler models, suggesting that the C/CO ratio may be a useful observational tool for determining which model best fits the observational data. Nevertheless, the fact that these chemical differences do not appear to have a strong effect on the density or temperature distributions of the gas suggests that the dynamical behaviour of the molecular clouds on large scales is not particularly sensitive to how accurately the small-scale chemistry is modelled.Comment: 18 pages, 10 figures. Minor revisions, including the addition of a comparison of simulated and observed C/CO ratios. Accepted by MNRA

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