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Register a new userReduction of chemical networks. I. The case of molecular clouds
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D. Wiebe INASAN
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We present a new method to analyse and reduce chemical networks and apply this technique to the chemistry in molecular clouds. Using the technique, we investigated the possibility of reducing the number of chemical reactions and species in the UMIST 95 database simultaneously. In addition, we did the same reduction but with the ``objective technique in order to compare both methods. We found that it is possible to compute the abundance of carbon monoxide and fractional ionisation accurately with significantly reduced chemical networks in the case of pure gas-phase chemistry. For gas-grain chemistry involving surface reactions reduction is not worthwhile. Compared to the ``objective technique our reduction method is more effective but more time-consuming as well.
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We present three numerical simulations of randomly driven, isothermal, non-magnetic, self-gravitating turbulence with different rms Mach numbers Ms and physical sizes L, but approximately the same value of the virial parameter, alpha approx 1.2. We obtain the following results: a) We test the hypothesis that the collapsing centers originate from locally Jeans-unstable (super-Jeans), subsonic fragments; we find no such structures. b) We find that the fraction of small-scale super-Jeans structures is larger in the presence of self-gravity. c) The velocity divergence of subregions of the simulations exhibits a negative correlation with their mean density. d) The density probability density function (PDF) deviates from a lognormal in the presence of self-gravity. e) Turbulence alone in the large-scale simulation does not produce regions with the same size and mean density as those of the small-scale simulation. Items (b)-(e) suggest that self-gravity is not only involved in causing the collapse of Jeans-unstable density fluctuations produced by the turbulence, but also in their {it formation}. We also measure the star formation rate per free-fall time, as a function of Ms for the three runs, and compare with the predictions of recent semi-analytical models. We find marginal agreement to within the uncertainties of the measurements. However, the hypotheses of those models neglect the net negative divergence of dense regions we find in our simulations. We conclude that a) part of the observed velocity dispersion in clumps must arise from clump-scale inwards motions, and b) analytical models of clump and star formation need to take into account this dynamical connection with the external flow and the fact that, in the presence of self-gravity, the density PDF may deviate from a lognormal.
This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these properties should be preserved by model reduction procedures, although traditional projection based approaches struggle to do this. We propose a projection based model reduction algorithm which uses generalised block diagonal Gramians to preserve structure and positivity. Two algorithms are presented, one provides more accurate reduced order models, the second provides easier to simulate reduced order models. The results are illustrated through numerical examples.
Molecular clouds are essentially made up of atomic and molecular hydrogen, which in spite of being the simplest molecule in the ISM plays a key role in the chemical evolution of molecular clouds. Since its formation time is very long, the H2 molecules can be transported by the turbulent motions within the cloud toward low density and warm regions, where its enhanced abundance can boost the abundances of molecules with high endothermicities. We present high resolution simulations where we include the evolution of the molecular gas under the effect of the dynamics, and we analyze its impact on the abundance of CH+.
Edge Cloud 2 (EC2) is a molecular cloud, about 35 pc in size, with one of the largest galactocentric distances known to exist in the Milky Way. We present observations of a peak CO emission region in the cloud and use these to determine its physical characteristics. We calculate a gas temperature of 20 K and a density of n(H2) ~ 10^4 cm^-3. Based on our CO maps, we estimate the mass of EC2 at around 10^4 M_sun and continuum observations suggest a dust-to-gas mass ratio as low as 0.001. Chemical models have been developed to reproduce the abundances in EC2 and they indicate that: heavy element abundances may be reduced by a factor of five relative to the solar neighbourhood (similar to dwarf irregular galaxies and damped Lyman alpha systems); very low extinction (Av < 4 mag) due to a very low dust-to-gas ratio; an enhanced cosmic ray ionisation rate; and a higher UV field compared to local interstellar values. The reduced abundances may be attributed to the low level of star formation in this region and are probably also related to the continuing infall of primordial (or low metallicity) halo gas since the Milky Way formed. Finally, we note that shocks from the old supernova remnant GSH 138-01-94 may have determined the morphology and dynamics of EC2.
We have extensively mapped a sample of dense molecular clouds (L1512, TMC-1C, L1262, Per 7, L1389, L1251E) in lines of HC3N, CH3OH, SO and C^{18}O. We demonstrate that a high degree of chemical differentiation is present in all of the observed clouds. We analyse the molecular maps for each cloud, demonstrating a systematic chemical differentiation across the sample, which we relate to the evolutionary state of the cloud. We relate our observations to the cloud physical, kinematical and evolutionary properties, and also compare them to the predictions of simple chemical models. The implications of this work for understanding the origin of the clumpy structures and chemical differentiation observed in dense clouds are discussed.
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