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Register a new userThe HI-to-H2 Transition in a Turbulent Medium
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We study the effect of density fluctuations induced by turbulence on the HI/H$_2$ structure in photodissociation regions (PDRs) both analytically and numerically. We perform magnetohydrodynamic numerical simulations for both subsonic and supersonic turbulent gas, and chemical HI/H$_2$ balance calculations. We derive atomic-to-molecular density profiles and the HI column density probability density function (PDF) assuming chemical equilibrium. We find that while the HI/H$_2$ density profiles are strongly perturbed in turbulent gas, the mean HI column density is well approximated by the uniform-density analytic formula of Sternberg et al. (2014). The PDF width depends on (a) the radiation intensity to mean density ratio, (b) the sonic Mach number and (c) the turbulence decorrelation scale, or driving scale. We derive an analytic model for the HI PDF and demonstrate how our model, combined with 21 cm observations, can be used to constrain the Mach number and driving scale of turbulent gas. As an example, we apply our model to observations of HI in the Perseus molecular cloud. We show that a narrow observed HI PDF may imply small scale decorrelation, pointing to the potential importance of subcloud-scale turbulence driving.
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We present a simple analytic procedure for generating atomic-to-molecular (HI-to-H$_2$) density profiles for optically thick clouds illuminated by far-ultraviolet radiation. Our procedure is based on the analytic theory for the structure of one-dimensional HI/H$_2$ photon-dominated regions, presented by Sternberg et al. (2014). Depth-dependent HI and H$_2$ density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity dependent H$_2$ formation rate coefficient, and dust absorption cross section. We use our procedure to generate a set of HI-to-H$_2$ transition profiles for a wide range of conditions, from the weak- to strong-field limits, and from super-solar down to low metallicities. We show that if presented as functions of dust optical depth the HI and H$_2$ density profiles depend primarily on the Sternberg $alpha G$ parameter (dimensionless) that determines the dust optical depth associated with the total photodissociated HI column. We derive a universal analytic formula for the HI-to-H$_2$ transition points as a function of just $alpha G$. Our formula will be useful for interpreting emission-line observations of HI/H$_2$ interfaces, for estimating star-formation thresholds, and for sub-grid components in hydrodynamics simulations.
The process of atomic-to-molecular (HI-to-H$_2$) gas conversion is fundamental for molecular-cloud formation and star formation. 21 cm observations of the star-forming region W43 revealed extremely high HI column densities, of 120-180 M$_{odot}$ pc$^{-2}$, a factor of 10-20 larger than predicted by HI-to-H$_2$ transition theories. We analyze the observed HI with an HI-to-H$_2$ transition theoretical model, and show that the theory-observation discrepancy cannot be explained by the intense radiation in W43, nor by variations of the assumed volume density or H$_2$ formation-rate coefficient. We show that the large observed HI columns are naturally explained by several ($9-22$) HI-to-H$_2$ transition layers, superimposed along the sightlines of W43. We discuss other possible interpretations such as a non-steady-state scenario, and inefficient dust absorption. The case of W43 suggests that HI thresholds reported in extra-galactic observations are probably not associated with a single HI-to-H$_2$ transition, but are rather a result of several transition layers (clouds) along the sightlines, beam-diluted with diffuse inter-cloud gas.
We apply the Sternberg et al. (2014) theoretical model to analyze HI and H2 observations in the Perseus molecular cloud. We constrain the physical properties of the HI shielding envelopes and the nature of the HI-to-H2 transitions. Our analysis (Bialy et al. 2015) implies that in addition to cold neutral gas (CNM), less dense thermally-unstable gas (UNM) significantly contributes to the shielding of the H2 cores in Perseus.
We study the H2 molecular content in high redshift damped Lyman-alpha systems (DLAs) as a function of the HI column density. We find a significant increase of the H2 molecular content around log N(HI) (cm^-2)~21.5-22, a regime unprobed until now in intervening DLAs, beyond which the majority of systems have log N(H2) > 17. This is in contrast with lines of sight towards nearby stars, where such H2 column densities are always detected as soon as log N(HI)>20.7. This can qualitatively be explained by the lower average metallicity and possibly higher surrounding UV radiation in DLAs. However, unlike in the Milky Way, the overall molecular fractions remain modest, showing that even at a large N(HI) only a small fraction of overall HI is actually associated with the self-shielded H2 gas. Damped Lyman-alpha systems with very high-N(HI) probably arise along quasar lines of sight passing closer to the centre of the host galaxy where the gas pressure is higher. We show that the colour changes induced on the background quasar by continuum (dust) and line absorption (HI Lyman and H2 Lyman & Werner bands) in DLAs with log N(HI)~22 and metallicity ~1/10 solar is significant, but not responsible for the long-discussed lack of such systems in optically selected samples. Instead, these systems are likely to be found towards intrinsically fainter quasars that dominate the quasar luminosity function. Colour biasing should in turn be severe at higher metallicities.
C$^+$ is a critical constituent of many regions of the interstellar medium, as it can be a major reservoir of carbon and, under a wide range of conditions, the dominant gas coolant. Emission from its 158$mu$m fine structure line is used to trace the structure of photon dominated regions in the Milky Way and is often employed as a measure of the star formation rate in external galaxies. Under most conditions, the emission from the single [CII] line is proportional to the collisional excitation rate coefficient. We here used improved calculations of the deexcitation rate of [CII] by collisions with H$_2$ to calculate more accurate expressions for interstellar C$^+$ fine structure emission, its critical density, and its cooling rate. The collision rates in the new quantum calculation are $sim$ 25% larger than those previously available, and narrow the difference between rates for excitation by atomic and molecular hydrogen. This results in [CII] excitation being quasi-independent of the molecular fraction and thus dependent only on the total hydrogen particle density. A convenient expression for the cooling rate at temperatures between 20 K and 400 K, assuming an LTE H$_2$ ortho to para ration is $Lambda ({rm LTE~OPR}) = left(11.5 + 4.0,e^{-100,mathrm K/T^{rm kin}}right);e^{-91.25,mathrm K/T^{rm kin}},n ({rm C}^{+}),n({rm H}_2)times 10^{-24};{rm ergs}~{rm cm}^{-3}~{rm s}^{-1}$. The present work should allow more accurate and convenient analysis of the [CII] line emission and its cooling.
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