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Note that irsm find that our chemical model predicts ionization fractions consistent with observations for late times. 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. Comparing these to our Fig.

Ages of asteroid families with the YORP-eye method. This uram develops because once the CEW has reached the boundary of the core, there is no longer a static outer envelope.

A relationship between visual extinction and temperature is assumed, so the radial temperature profile also evolves throughout the collapse, which affects the gas pressure. The inside-out collapse model results indicate that for CS to be detectable during the collapse phase, the core cannot have been static with the isothermal sphere density configuration for more than 10 6 yr. Several solutions have been derived for the collapse of a self-gravitating isothermal sphere e.

Given the strong evidence for depletion of CS in such cores, it may be worth investigating in more detail the CS abundance profile in this core using interferometric observations and seeing if the inside-out model is still able to reproduce the Idam observations with a realistic abundance profile.

In Section 7 we present a discussion of the results, considering their sensitivity to the conditions chosen in the chemical model. JFR would like to thank J. Are there different lightning strikes? The fact that a negative kinetic temperature gradient is required in the inside-out collapse model but not in the ambipolar diffusion model is jram to the different line formation processes: Such off-centre absorption dips have been observed towards the class 0 protostar, IRAMwhere they are also believed to be caused by extended inward motions Belloche et al.

We have assumed that, in each of our models, the core begins its collapse from atomic initial conditions apart from hydrogen which is initially 90 per cent molecular. Physical evolution radial position, velocity and density of the test shells in the ambipolar diffusion model. Before using itam profiles as diagnostics of a particular collapse model, it is essential to investigate the abundance profile of the tracer molecule, in particular to see if there is any evidence for ira.

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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. Equilibrium between freeze-out and desorption processes rapidly follows, resulting in extremely depleted abundances. It 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.

In such cores, the neutral species do not directly feel the effect of 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. These drag forces depend on the number density of charged particles and on the drift velocity between ions and neutrals, which is idam to the magnetic field strength.

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The tail of the CEW is at the centre, where the material is approaching free-fall. The gas temperature of the core, used for the chemical calculations, is 10 K.

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

We have also included desorption of species owing to cosmic ray heating of grains at the rate given by Roberts et al. Furthermore, SR10 calculated the visual extinction self-consistently with grain distribution in the core, whereas for simplicity we assumed a constant visual extinction, which will have an effect on the rates of photoreactions, particularly at the edge of the core.

For the inside-out model, all three CS lines are strong from the earliest stages but decline with time. At each time-step, the code calculates the total force exerted on each shell of gas, taking into account the gravitational force, the gas pressure and the drag force exerted on the neutral species by the ions and charged dust grains. H 2 formation on dust grains is included, the rate of which is given by the rate that hydrogen atoms stick to the grain surface and react multiplied by 0.

The radius, density and velocity of each shell as a function of time are shown in Fig.

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. The temperature profiles are shown in Fig. But no operational system is yet available. 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.

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Ideally, we would have liked to model H 2 CO as well, which is another common infall tracer. Therefore, the central infalling blueshifted material does not have an excitation temperature higher than the redshifted infalling material at the edge of the CEW, and this can explain why we do not see the blue asymmetry at this time.

In that paper they used a Monte Carlo approach and included layering of the ice, and found that the results were significantly different to the results obtained using a simple rate equation approach. In each case we calculated the density, velocity and position of the shell as functions of time using a spline interpolation of the CEW solution given in table 2 of Shu To test this theory, we have calculated the line profiles for CS at 10 5 yr using the temperature profiles described in Section 6.

Ambipolar-diffusion-controlled collapse occurs in magnetically subcritical cores, where the magnetic field is strong enough to support the core against gravitational collapse. Since they took into account this depletion in their radiative transfer model, this could explain why their inside-out collapse model failed to reproduce the observations.

In fact, the ambipolar diffusion model is evolving towards the initial state of the CEW model, and once a sufficiently centrally condensed core has formed it will begin collapsing in a more dynamic manner.

The dotted and dashed lines show the two linear temperature profiles. The solid line shows the temperature profile of the class 0 source B Zhou et al.

The results are shown in Fig. However, at dust temperatures of 10—20 K, the dust emission only dominates the background continuum for ieam of GHz so the lower frequency lines should be unaffected by this assumption. This is the expected behaviour, since the higher velocity redshifted material at the front of the core i.

This is because for such high and rapidly changing densities, the model of SR10 cannot converge on a solution.