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At each radial point in the core, smmol calculates the level populations, the line source functions and the emergent line profile. In this respect the model of SR10 appears iarm perform slightly better, despite the fact that the mass-to-flux ratios are similar in both models [approximately two and approximately three times the critical value in the models of Pavlyuchenkov et al. The temperature is assumed to remain at 10 K throughout the collapse, and the density as a function of time for 2246 shell is calculated by the dynamical models described in Sections 2.

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The core contracts with time see the evolution of the outer shell, plotted with the black solid line in Fig. For the inside-out model, all three CS lines are strong from the earliest stages but decline with time.

Latest Most Read Most Cited Relaxation by thermal conduction of a irzm confined mountain on an accreting neutron star. The chemical abundances are not significantly affected by this simplification; running the chemical model at temperatures of 6.

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We have taken preliminary results from the dynamical model from SR10 to couple with our chemical model. This is lightning and is characterized by its bright flash and the deafening sound of thunder. Since a factor of 4 difference in the ionization fraction might be significant, as it means that the gas in our model would be less strongly coupled to the magnetic field compared to the gas in the SR10 model and may therefore have a higher infall velocity, in Section 7.

Here we concentrate on the commonly used solution derived by Shuwhich was solved by finding similarity solutions to the continuity mass-conservation equation and force equation for an ideal isothermal flow. However, the main formation route of H 2 CO is believed to be via the hydrogenation of CO on grain surfaces and subsequent desorption into the gas phase Fuchs et al.

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Related articles in Web of Science Google Scholar. Why are there thunderstorms? So far, we have assumed a constant temperature of 10 K across the core, but now we look at how the line profile shapes are affected by other temperature profiles to test the sensitivity and possible degeneracies of the results to the free parameters. At this point, we stop the collapse and set the velocity to zero. It is difficult to compare the abundances predicted by our chemical model to previously published chemical models of infalling cores, because of the varied range of parameters used e.

Physical evolution radial position, velocity and density of the test shells in the ambipolar diffusion model. We have therefore investigated the effect on the line profiles for both models of keeping the core static for a period of time, t statranging from 10 3 to 10 8 yr, allowing the chemistry to reach a more evolved state before the collapse is initiated.

These drag forces depend on the number density of charged particles and on the drift velocity between ions and neutrals, which is related to the magnetic field strength.

The differences in infall velocities could be due to differences in boundary conditions and the fact that Pavlyuchenkov et al. These results support the interpretation of Zhou et al.

We have used the results for a core of a mass of 6. For the inside-out collapse model to exhibit the blue asymmetry it is necessary to suppress freeze-out and impose a negative temperature gradient on the core, whereas the ambipolar diffusion model exhibits the blue asymmetry even when there is significant freeze-out, and for all the kinetic temperature profiles tested.

The core is embedded in a cylindrical magnetic field, which evolves throughout the collapse, although its geometry always remains cylindrical. Due to the large differences in core sizes and therefore molecular column densities, we cannot make a quantitative comparison to their results, but nevertheless, their resulting line profiles show notable qualitative similarities to those we have derived. The temperatures in the core range from 6.

This paper is organized as follows. The thin lines show T ex using a constant CS abundance of 2. The first temperature profile we consider is that deduced from dust continuum observations of the class 0 source B Zhou et al. This sort of behaviour has been noted in previous studies e.

This is something that we can address in future work, and we therefore leave modelling the H 2 CO line profiles until we have a suitable model. If a negative kinetic temperature gradient is imposed, then this can change the excitation temperature gradient in the core and could give rise to the blue asymmetry. To test the importance of these effects, we have re-run our chemical model for the shells at the outer edges of the envelopes ieam both collapse models.

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This is particularly likely in cases where the parent molecular cloud has been dispersed [e. Obviously, for outer shells, this increase in abundance occurs at later times. Once a shell gets close to the core centre, the density and velocity rapidly tend towards infinity and the solution is no longer valid. The systemic infall therefore begins to dominate the line-broadening, and at 10 6 yr the core centre and the core edge are radiatively decoupled because of the relatively LVG.

In Section 2 we describe dynamical collapse models studied, and in Section 3 we describe the chemical model, the results of which are given in Section 4.

Could we store lightning current as a renewable energy? We have used a fractional abundance for CS of 2. At this time, one of the main differences between these two models is that the inside-out collapse model has a static envelope, whereas in the ambipolar diffusion model there are extended low-velocity inward motions. Episodic excursions of low-mass protostars on the Hertzsprung—Russell diagram.

The line profiles for CS show double-peaked profiles that are approximately symmetric until the final time, 2. These abundance profiles are then used as an input to a radiative transfer model, along with the density and velocity profiles appropriate for each collapse model. His works will lead to the design and manufacture of radioactive lightning rods, using radioactive sources around the tip of the rod to maintain a permanent ionization.

Unlike the inside-out collapse, where the envelope material is static, this redshift in the absorption is the main cause of the blue-skewed asymmetry in the line profiles. For radii of 1. Instead, it is more likely that it is contracting from lower densities, and therefore the chemical time-scales could be longer than those presented here. In progress issue alert. We have used a constant turbulent velocity of 0.