Deuterium fractionation on interstellar grains studied with the direct master equation approach

We have studied deuterium fractionation on interstellar grains with the use of an exact method known as the direct master equation approach. We consider conditions pertinent to dense clouds at late times when the hydrogen is mostly in molecular form and a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen, oxygen and deuterium atoms, as well as CO molecules, are allowed to accrete on to dust particles and react there to produce various stable molecules. The surface abundances, as well as the abundance ratios between deuterated and normal isotopomers, are compared with those calculated with the Monte Carlo approach. We find that the agreement between the Monte Carlo and the direct master equation methods can be made as close as desired. Compared with previous examples of the use of the direct master equation approach, our present method is much more efficient. It should now be possible to run large-scale gas-grain models in which the diffusive dust chemistry is handled `exactly'.Comment: 7 pages, 3 figure

From Prestellar to Protostellar Cores II. Time Dependence and Deuterium Fractionation

We investigate the molecular evolution and D/H abundance ratios that develop as star formation proceeds from a dense-cloud core to a protostellar core, by solving a gas-grain reaction network applied to a 1-D radiative hydrodynamic model with infalling fluid parcels. Spatial distributions of gas and ice-mantle species are calculated at the first-core stage, and at times after the birth of a protostar. Gas-phase methanol and methane are more abundant than CO at radii $r\lesssim 100$ AU in the first-core stage, but gradually decrease with time, while abundances of larger organic species increase. The warm-up phase, when complex organic molecules are efficiently formed, is longer-lived for those fluid parcels in-falling at later stages. The formation of unsaturated carbon chains (warm carbon-chain chemistry) is also more effective in later stages; C$^+$, which reacts with CH$_4$ to form carbon chains, increases in abundance as the envelope density decreases. The large organic molecules and carbon chains are strongly deuterated, mainly due to high D/H ratios in the parent molecules, determined in the cold phase. We also extend our model to simulate simply the chemistry in circumstellar disks, by suspending the 1-D infall of a fluid parcel at constant disk radii. The species CH$_3$OCH$_3$ and HCOOCH$_3$ increase in abundance in $10^4-10^5$ yr at the fixed warm temperature; both also have high D/H ratios.Comment: accepted to ApJ. 55 pages, 7 figures, 3 table

The Highly Dynamic Behavior of the Innermost Dust and Gas in the Transition Disk Variable LRLL 31

We describe extensive synoptic multi-wavelength observations of the transition disk LRLL 31 in the young cluster IC 348. We combined four epochs of IRS spectra, nine epochs of MIPS photometry, seven epochs of cold-mission IRAC photometry and 36 epochs of warm mission IRAC photometry along with multi-epoch near-infrared spectra, optical spectra and polarimetry to explore the nature of the rapid variability of this object. We find that the inner disk, as traced by the 2-5micron excess stays at the dust sublimation radius while the strength of the excess changes by a factor of 8 on weekly timescales, and the 3.6 and 4.5micron photometry shows a drop of 0.35 magnitudes in one week followed by a slow 0.5 magnitude increase over the next three weeks. The accretion rate, as measured by PaBeta and BrGamma emission lines, varies by a factor of five with evidence for a correlation between the accretion rate and the infrared excess. While the gas and dust in the inner disk are fluctuating the central star stays relatively static. Our observations allow us to put constraints on the physical mechanism responsible for the variability. The variabile accretion, and wind, are unlikely to be causes of the variability, but both are effects of the same physical process that disturbs the disk. The lack of periodicity in our infrared monitoring indicates that it is unlikely that there is a companion within ~0.4 AU that is perturbing the disk. The most likely explanation is either a companion beyond ~0.4 AU or a dynamic interface between the stellar magnetic field and the disk leading to a variable scale height and/or warping of the inner disk.Comment: Accepted to ApJ. 10 pages of text, plus 11 tables and 13 figures at the en

Electron-attachment rates for carbon-rich molecules in protoplanetary atmospheres: the role of chemical differences

The formation of anionic species in the interstellar medium from interaction of linear molecules containing carbon, nitrogen and hydrogen as atomic components (polyynes) with free electrons in the environment is modelled via a quantum treatment of the collision dynamics. The ensuing integral cross sections are employed to obtain the corresponding attachment rates over a broad range of temperatures for the electrons. The calculations unequivocally show that a parametrization form often employed for such rates yields a broad range of values that turn out to be specific for each molecular species considered, thus excluding using a unique set for the whole class of polyynes.Comment: accepted to be published on MNRA

On the Maximal Excess Charge of the Chandrasekhar-Coulomb Hamiltonian in Two Dimensions

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum dot -- the maximal number of electrons does not exceed twice the nuclear charge. It result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of |\bx| T(\bp) + T(\bp) |\bx| which -- in two dimensions -- is false for the non-relativistic case T(\bp) = \bp^2, but is proven in this paper for T(\bp) = |\bp|, i.e., the ultra-relativistic kinetic energy

On groups and counter automata

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller-Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognised by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata.Comment: 18 page