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Register a new userNEI Modelling of the ISM - Turbulent Dissipation & Hausdorff Dimension
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High-resolution non-ideal magnetohydrodynamical simulations of the turbulent magnetized ISM, powered by supernovae types Ia and II at Galactic rate, including self-gravity and non-equilibriuim ionization (NEI), taking into account the time evolution of the ionization structure of H, He, C, N, O, Ne, Mg, Si, S and Fe, were carried out. These runs cover a wide range (from kpc to sub-parsec) of scales, providing resolution independent information on the injection scale, extended self-similarity and the fractal dmension of the most dissipative structures.
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We present a study of a star formation prescription in which star formation efficiency depends on local gas density and turbulent velocity dispersion, as suggested by direct simulations of SF in turbulent giant molecular clouds (GMCs). We test the model using a simulation of an isolated Milky Way-sized galaxy with a self-consistent treatment of turbulence on unresolved scales. We show that this prescription predicts a wide variation of local star formation efficiency per free-fall time, $epsilon_{rm ff} sim 0.1 - 10%$, and gas depletion time, $t_{rm dep} sim 0.1 - 10$ Gyr. In addition, it predicts an effective density threshold for star formation due to suppression of $epsilon_{rm ff}$ in warm diffuse gas stabilized by thermal pressure. We show that the model predicts star formation rates in agreement with observations from the scales of individual star-forming regions to the kiloparsec scales. This agreement is non-trivial, as the model was not tuned in any way and the predicted star formation rates on all scales are determined by the distribution of the GMC-scale densities and turbulent velocities $sigma$ in the cold gas within the galaxy, which is shaped by galactic dynamics. The broad agreement of the star formation prescription calibrated in the GMC-scale simulations with observations, both gives credence to such simulations and promises to put star formation modeling in galaxy formation simulations on a much firmer theoretical footing.
Supersonic turbulence is a large reservoir of suprathermal energy in the interstellar medium. Its dissipation, because it is intermittent in space and time, can deeply modify the chemistry of the gas. We further explore a hybrid method to compute the chemical and thermal evolution of a magnetized dissipative structure, under the energetic constraints provided by the observed properties of turbulence in the cold neutral medium. For the first time, we model a random line of sight by taking into account the relative duration of the bursts with respect to the thermal and chemical relaxation timescales of the gas. The key parameter is the turbulent rate of strain a due to the ambient turbulence. With the gas density, it controls the size of the dissipative structures, therefore the strength of the burst. For a large range of rates of strain and densities, the models of turbulent dissipation regions (TDR) reproduce the CH+ column densities observed in the diffuse medium and their correlation with highly excited H2. They do so without producing an excess of CH. As a natural consequence, they reproduce the abundance ratios of HCO+/OH and HCO+/H2O, and their dynamic range of about one order of magnitude observed in diffuse gas. Large C2H and CO abundances, also related to those of HCO+, are another outcome of the TDR models that compare well with observed values. The abundances and column densities computed for CN, HCN and HNC are one order of magnitude above PDR model predictions, although still significantly smaller than observed values.
In this paper we prove the Hausdorff dimension of the set of (nondegenerate) singular two-dimensional vectors with uniform exponent $mu$ $in$ (1/2, 1) is 2(1 -- $mu$) when $mu$ $ge$ $sqrt$ 2/2, whereas for $mu$ textless{} $sqrt$ 2/2 it is greater than 2(1 -- $mu$) and at most (3 -- 2$mu$)(1 -- $mu$)/(1 + $mu$ + $mu$ 2). We also establish that this dimension tends to 4/3 (which is the dimension of the set of singular two-dimensional vectors) when $mu$ tends to 1/2. These results improve upon previous estimates of R. Baker, joint work of the first author with M. Laurent, and unpublished work of M. Laurent. We also prove a lower bound on the packing dimension that is strictly greater than the Hausdorff dimension for $mu$ $ge$ 0.565. .. .
We compute the Hausdorff dimension of limit sets generated by 3-dimensional self-affine mappings with diagonal matrices of the form A_{ijk}=Diag(a_{ijk}, b_{ij}, c_{i}), where 0<a_{ijk}le b_{ij}le c_i<1. By doing so we show that the variational principle for the dimension holds for this class.
The latest observations of molecular gas and the atomic hydrogen content of local and high-redshift galaxies, coupled with how these correlate with star formation activity, have revolutionized our ideas about how to model star formation in a galactic context. A successful theory of galaxy formation has to explain some key facts: (i) high-redshift galaxies have higher molecular gas fractions and star formation rates than local galaxies, (ii) scaling relations show that the atomic-to-stellar mass ratio decreases with stellar mass in the local Universe, and (iii) the global abundance of atomic hydrogen evolves very weakly with time. We review how modern cosmological simulations of galaxy formation attempt to put these pieces together and highlight how approaches simultaneously solving dark matter and gas physics, and approaches first solving the dark matter N-body problem and then dealing with gas physics using semi-analytic models, differ and complement each other. We review the observable predictions, what we think we have learned so far and what still needs to be done in the simulations to allow robust testing by the new observations expected from telescopes such as ALMA, PdBI, LMT, JVLA, ASKAP, MeerKAT, SKA.
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