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F. F. S. van der Tak

Publications and source records attributed to F. F. S. van der Tak.

112 records · Page 7Linked to original sources

Numerical methods for non-LTE line radiative transfer: Performance and convergence characteristics

Comparison is made between a number of independent computer programs for radiative transfer in molecular rotational lines. The test models are spherically symmetric circumstellar envelopes with a given density and temperature profile. The first two test models have a simple power law density distribution, constant temperature and a fictive 2-level molecule, while the other two test models consist of an inside-out collapsing envelope observed in rotational transitions of HCO+. For the 2-level molecule test problems all codes agree well to within 0.2%, comparable to the accuracy of the individual codes, for low optical depth and up to 2% for high optical depths (tau=4800). The problem of the collapsing cloud in HCO+ has a larger spread in results, ranging up to 12% for the J=4 population. The spread is largest at the radius where the transition from collisional to radiative excitation occurs. The resulting line profiles for the HCO+ J=4-3 transition agree to within 10%, i.e., within the calibration accuracy of most current telescopes. The comparison project and the results described in this paper provide a benchmark for future code development, and give an indication of the typical accuracy of present day calculations of molecular line transfer.

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Chemistry as a probe of the structures and evolution of massive star forming regions

We present detailed thermal and gas-phase chemical models for the envelope of the massive star-forming region AFGL 2591. Time- and space-dependent chemistry are used to study the physical structure proposed by van der Tak et al. (1999; 2000), and the chemical evolution of this region. The model is compared with observations for 29 species covering a wide range of conditions within the source. Taking appropriate care when comparing models with both emission and absorption measurements, we find that the majority of the chemical structure can be well-explained. In particular, we find that the nitrogen and hydrocarbon chemistry can be significantly affected by temperature, with the possibility of high-temperature pathways to HCN. While we cannot determine the sulphur reservoir, the observations can be explained by models with the majority of the sulphur in CS in the cold gas, SO$_{2}$ in the warm gas, and atomic sulphur in the warmest gas. The observed abundances of ions such as HCO$^+$ and N$_2$H$^+$ and the cold gas-phase production of HCN constrain the cosmic-ray ionization rate to $\sim 5.6 \times 10^{-17}$ s$^{-1}$, to within a factor of three. Finally, we find that the model and observations can simultaneously agree at a reasonable level and often to within a factor of three for $7 \times 10^{3} \leq t(\mathrm{yrs}) \leq 5 \times 10^{4}$, with a strong preference for $t \sim 3 \times 10^{4}$ yrs since the collapse and formation of the central luminosity source.

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Triply deuterated ammonia in NGC 1333

The Caltech Submillimeter Observatory has detected triply deuterated ammonia, ND3, through its 10a-00s transition near 310 GHz. Emission is found in the NGC 1333 region, both towards IRAS 4A and a position to the South-East where DCO+ peaks. In both cases, the hyperfine ratio indicates that the emission is optically thin. Column densities of ND3 are 3--6 x 10^11 cm^-2 for T_ex=10 K and twice as high for T_ex=5 K. Using a Monte Carlo radiative transfer code and a model of the structure of the IRAS source with temperature and density gradients, the estimated ND3 abundance is 3.2 x 10^-12 if ND3/H2 is constant throughout the envelope. In the more likely case that ND3/H2D+ is constant, ND3/H2 peaks in the cold outer parts of the source at a value of 1.0 x 10^-11. To reproduce the observed NH3/ND3 abundance ratio of ~1000, grain surface chemistry requires an atomic D/H ratio of ~0.15 in the gas phase, >10 times higher than in recent chemical models. More likely, the deuteration of NH3 occurs by ion-molecule reactions in the gas phase, in which case the data indicate that deuteron transfer reactions are much faster than proton transfers.

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Highly abundant HCN in the inner hot envelope of GL 2591: probing the birth of a hot core?

We present observations of the v2=0 and vibrationally excited v2=1 J=9-8 rotational lines of HCN at 797 GHz toward the deeply embedded massive young stellar object GL 2591, which provide the missing link between the extended envelope traced by lower-J line emission and the small region of hot (T_ex >= 300 K), abundant HCN seen in 14 micron absorption with the Infrared Space Observatory (ISO). The line ratio yields T_ex=720^+135_-100 K and the line profiles reveal that the hot gas seen with ISO is at the velocity of the protostar, arguing against a location in the outflow or in shocks. Radiative transfer calculations using a depth-dependent density and temperature structure show that the data rule out a constant abundance throughout the envelope, but that a model with a jump of the abundance in the inner part by two orders of magnitude matches the observations. Such a jump is consistent with the sharp increase in HCN abundance at temperatures >~230 K predicted by recent chemical models in which atomic oxygen is driven into water at these temperatures. Together with the evidence for ice evaporation in this source, this result suggests that we may be witnessing the birth of a hot core. Thus, GL 2591 may represent a rare class of objects at an evolutionary stage just preceding the `hot core' stage of massive star formation.

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