wiki:u/erica/radpredictionsink

Version 4 (modified by Erica Kaminski, 9 years ago) ( diff )

Predictions for a radiating 'first hydrostatic core' sink particle

Given the following parameters:

l = h = r (box radius) .0069 (pc) = 2.14e+16 (cm)
2.03*10-16 (g cm-3)
n 1.2e+8 (cm-3)
T 10 (K)
.3
.23 (cm2 g-1)
.4 (cm2 g-1)

We computed the various time-scales as:

24 days
?
33 kyr
4 ky
24 days

Here is the initial condition:

Prediction: By 24 days, expect the diffusion wave to hit the boundary. Depending on the energy injection rate compared to the diffusion rate, the shape of the curve might be different. For instance, if energy injection rate (Er) >> diffusion rate (Dr), might expect the gaussian to be increasing in height as well as width. If Er = Dr, might expect the profile to be flat, as it grows in width. If Er << Dr, expect a gaussian that grows in width over time, but not height.

Check: Make time curves of Erad(x), and check that the wave hits the boundary by t=24 days.

Prediction: The total thermal energy (and thus the total energy) should increase like t2. This is because,

, where

(L is luminosity of FHSC)

(density doesn't change given t_diff << t_sc)

This holds as long as 4 pi B << the energy injected each time step. That way we can effectively ignore changes to thermal energy induced by increasing B(T).

Check: Make curve of e_total(t), E_total(t).

Prediction: The total radiative energy should increase as:

Check: Make curve of Erad_total(t).

Prediction: The thermal energy, e, of a zone immediately adjacent to the kernel should increase linearly. This is because, the difference between the energy injected into the grid, E*, and 4piB, is some height X (where X = L*dt-B). So, right next to kernel, expect the coupling time to go like:

Or,

*This assumes the energy injection rate is << diffusion rate, so that we know the difference in height between Erad and B*.

Check: Make a time query of a cell near the kernel.

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