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

Magnetic field-induced vertigo in the MRI environment

This review discusses the theory behind, and the experimental evidence for, the perception of vertigo in a high magnetic field found in a magnetic resonance imaging (MRI) environment. Recent experiments have shown that there is an eye nystagmus response that is proportional to magnetic field exposure and not purely one of rate of change of magnetic field. The mechanism of transduction can be attributed to the Lorentz forces on the endolymph in the ear canals, producing a static pressure due to the vector product of the magnetic field and current density. The adaption and response of the measurable effect reveals time constants which support such a mechanism and explain why the balance system responds in the way we observe and feel. The position and movement of the head relative to the direction of field is of fundamental importance to the sensation of vertigo, as are ambient conditions such as lighting levels. Recent surveys of subjects undergoing seven tesla or higher MRI scans report that although there is a high perception of vertigo-like effects, these are not intolerable and are not generally the cause of subject withdrawal. This review argues that the International Commission on Non-Ionizing Radiation guidelines on low-frequency fields still need to acknowledge the role of a high magnetic field in producing vertigo sensations rather than rate of change of field alone

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

Star formation in metal-poor gas clouds

Observations of molecular clouds in metal-poor environments typically find that they have much higher star formation rates than one would expect based on their observed CO luminosities and the molecular gas masses that are inferred from them. This finding can be understood if one assumes that the conversion factor between CO luminosity and H2 mass is much larger in these low metallicity systems than in nearby molecular clouds. However, it is unclear whether this is the only factor at work, or whether the star formation rate of the clouds is directly sensitive to the metallicity of the gas. To investigate this, we have performed numerical simulations of the coupled dynamical, chemical and thermal evolution of model clouds with metallicities ranging from 0.01 Z_solar to Z_solar. We find that the star formation rate in our model clouds has little sensitivity to the metallicity. Reducing the metallicity of the gas by two orders of magnitude delays the onset of star formation in the clouds by no more than a cloud free-fall time and reduces the time-averaged star formation rate by at most a factor of two. On the other hand, the chemical state of the clouds is highly sensitive to the metallicity, and at the lowest metallicities, the clouds are completely dominated by atomic gas. Our results confirm that the CO-to-H2 conversion factor in these systems depends strongly on the metallicity, but also show that the precise value is highly time-dependent, as the integrated CO luminosity of the most metal-poor clouds is dominated by emission from short-lived gravitationally collapsing regions. Finally, we find evidence that the star formation rate per unit H2 mass increases with decreasing metallicity, owing to the much smaller H2 fractions present in our low metallicity clouds.Comment: 14 pages, 6 figures. Updated to match version accepted by MNRA

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

A novel receive-only liquid nitrogen (LN2)-cooled RF coil for high-resolution in vivo imaging on a 3-Tesla whole-body scanner

The design and operation of a receive-only liquid nitrogen (LN2)-cooled coil and cryostat suitable for medical imaging on a 3-T whole-body magnetic resonance scanner is presented. The coil size, optimized for murine imaging, was determined by using electromagnetic (EM) simulations. This process is therefore easier and more cost effective than building a range of coils. A nonmagnetic cryostat suitable for small-animal imaging was developed having good vacuum and cryogenic temperature performance. The LN2-cooled probe had an active detuning circuit allowing the use with the scanner's built-in body coil. External tuning and matching was adopted to allow for changes to the coil due to temperature and loading. The performance of the probe was evaluated by comparison of signal-to-noise ratio (SNR) with the same radio-frequency RF) coil operating at room temperature (RT). The performance of the RF coil at RT was also benchmarked against a commercial surface coil with a similar dimension to ensure a fair SNR comparison. The cryogenic coil achieved a 1.6- to twofold SNR gain for several different medical imaging applications: For mouse-brain imaging, a 100-mu m resolution was achieved in an imaging time of 3.5 min with an SNR of 25-40, revealing fine anatomical details unseen at lower resolutions for the same time. For heavier loading conditions, such as imaging of the hind legs and liver, the SNR enhancement was slightly reduced to 1.6-fold. The observed SNR was in good agreement with the expected SNR gain correlated with the loaded-quality factor of RF coils from the EM simulations. With the aid of this end-user-friendly and economically attractive cryogenic RF coil, the enhanced SNR available can be used to improve resolution or reduce the duration of individual scans in a number of biomedical applications