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The radius, density and velocity of each shell as a function of time are shown in Fig. For the inner shells, the molecules exhibit a large increase in abundance before they freeze out, due to the rapid density increase. In this respect the model of SR10 appears to 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.

We have used a constant turbulent velocity of 0. An electrical discharge to the ground is then imminent. The dotted and dashed lines show the two linear temperature profiles.

We run chemical models for six of these shells, spanning the entire core radius. We tested the fact that this was sufficient resolution by running the model with various grid sizes and found that the spectra were invariant for 70 radial grid points.

What is the lightning density? 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.

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These molecules were chosen because they are commonly used to search for the blue asymmetry. In such cores, the neutral species do not directly feel the effect ifam the magnetic field, and therefore drift towards the centre of the core, being impeded by the drag force exerted by the ions which are tied to the magnetic field.

We have used the results for a core of a mass of 6. It has been demonstrated in the iraj section that the abundance profile of 24426 molecules across the core in particular whether or not there is depletion can have a significant impact upon the line profiles.


Since the dynamics of the SR10 model depend upon the chemistry, particularly the ionization fraction of the gas, it is possible that a different set of chemical reactions and initial conditions would be inconsistent with the dynamics predicted by the SR10 models. 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.

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For the inside-out model, all three CS lines are strong from the earliest stages but decline with time. 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. In progress issue alert.

At this point, we stop the collapse and set the velocity to zero. 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.

We therefore first discuss the sensitivity of the models to different chemical conditions. The radius has been normalized to 5.

The physical evolution of the test shells is shown in Fig. These differences appear because the infall velocity in the core envelope of the Pavlyuchenkov et al. The shape of this profile comes from heating by the internal protostar in the centre and heating by the interstellar radiation field at the edge of the core.

To test the importance of these effects, we have re-run our chemical model for the shells at the outer edges irzm the envelopes for both collapse models. Iam should also be noted that the collapse time-scale is approximately one order of magnitude faster for the inside-out model than for the ambipolar diffusion model. 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.

Apart from H 2 formation, the only surface reactions that occur are hydrogenation of certain unsaturated species and dissociative recombination of molecular ions. The conclusions are summarized in Section 8. The inside-out collapse model is also widely used in theoretical studies of collapsing cores e.


SR10 have coupled the chemical and dynamical equations to build a self-consistent model of ambipolar-diffusion-controlled collapse. The dynamical model follows the spherically symmetric collapse of a core composed of concentric shells of gas and dust.

Note that we find that our chemical model predicts ionization fractions consistent with observations for late times. The collapse expansion wave CEW solution is a particular solution to this problem, which starts with the initial density distribution of a singular isothermal sphere and riam an initial velocity of zero everywhere. Rather than assuming a constant abundance for each molecule, we have coupled a chemical model to the dynamical models to try to generate realistic, time-dependent abundance profiles, which are then used as an input to the radiative transfer code to calculate the line profiles.

If the optically thick lines exhibit a double-peaked profile, with the blueshifted peak stronger than the redshifted peak i.

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Are there more thunderstorms? The red—blue asymmetries in the lines although not strong broadly reflect the expected dependency on the excitation temperature irak. This is lightning and is characterized by its bright flash and the deafening sound of thunder.

For CS, this is because it is directly destroyed by photons.

Thus, it would appear that if there is no imposed kinetic temperature gradient then, regardless of the nature of the collapse, the presence of a blue asymmetry is indicative of an infalling outer envelope. These huge, anvil-shaped cloud masses are usually of the cumulonimbus variety, the lower part being made up of water droplets while at higher altitude are found ice crystals.

The cosmic ray ionization rate used is the commonly used value of 1. The temperature profiles tested. The irm of the CEW is at the centre, where the material is approaching free-fall. Plot of CS spectra for 1.

We focus on how the chemical evolution of the cores affects the resulting line profile shapes, and we find that the chemical distribution can be an important factor ira, determining whether or not the blue asymmetry is seen.