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We present a survey of the ortho-H2D+(1_{1,0}-1_{1,1}) line toward a sample of 10 starless cores and 6 protostellar cores, carried out at the Caltech Submillimeter Observatory. The high diagnostic power of this line is revealed for the study of the chemistry, and the evolutionary and dynamical status of low-mass dense cores. The line is detected in 7 starless cores and in 4 protostellar cores. N(ortho-H2D+) ranges between 2 and 40x10^{12} cm^{-2} in starless cores and between 2 and 9x10^{12} cm^{-2} in protostellar cores. The brightest lines are detected toward the densest and most centrally concentrated starless cores, where the CO depletion factor and the deuterium fractionation are also largest. The large scatter observed in plots of N(ortho-H2D+) vs. the observed deuterium fractionation and vs. the CO depletion factor is likely to be due to variations in the ortho-to-para (o/p) ratio of H2D+ from >0.5 for T_{kin} < 10 K gas in pre-stellar cores to ~0.03 (consistent with T_{kin} ~15 K for protostellar cores). The two Ophiuchus cores in our sample also require a relatively low o/p ratio (~0.3). Other parameters, including the cosmic-ray ionization rate, the CO depletion factor (or, more in general, the depletion factor of neutral species), the volume density, the fraction of dust grains and PAHs also largely affect the ortho-H2D+ abundance. The most deuterated and H2D+-rich objects (L429, L1544, L694-2 and L183) are reproduced by chemical models of centrally concentrated (central densties ~10^{6} cm^{-3}) cores with chemical ages between 10^4 and 10^6 yr. Upper limits of the para-H3O+ (1_1- -2_1+) and para-D2H+ (1_{1,0}-1_{0,1}) lines are also given. (Abridged)
In this note, we prove that a semigroup $S$ is left amenable if and only if every two nonzero elements of $ell^1_+(S)$ have a common nonzero right multiple, where $ell^1_+(S)$ is the positive part of the Banach algebra $ell^1(S)$, or equivalently the
We report new calculations of interstellar 15N fractionation. Previously, we have shown that large enhancements of 15N/14N can occur in cold, dense gas where CO is frozen out, but that the existence of an NH + N channel in the dissociative recombinat
The one-phase and two-phase Muskat problems with arbitrary viscosity contrast are studied in all dimensions. They are quasilinear parabolic equations for the graph free boundary. We prove that small data in the scaling invariant homogeneous Besov spa
We present a catalogue of dense cores in a $sim 4^circtimes2^circ$ field of the Taurus star-forming region, inclusive of the L1495 cloud, derived from Herschel SPIRE and PACS observations in the 70 $mu$m, 160 $mu$m, 250 $mu$m, 350 $mu$m, and 500 $mu$
Molecular clouds are a fundamental ingredient of galaxies: they are the channels that transform the diffuse gas into stars. The detailed process of how they do it is not completely understood. We review the current knowledge of molecular clouds and t