Simulation (Reionisation)
From Eric's Wiki
A note about the sizes of simulated volumes used to study re-ionisation. As is always the case in cosmological simulations, there are competing factors in determining the size of the simulation volume: mass resolution versus truncation of the primordial power spectrum at large scales. High mass resolution is crucial for reionisation simulations because most of the reionisation volume is in low-density regions, so to properly model it, you need low-mass particles. Small-scale power is modelled by low-mass particles. It is important to know whether the diffuse medium collapses into small high-density regions or stays diffuse. Small halos would remove gas from the ambient, lowering the mean opacity, but also create dense regions where recombination would be more effective, increasing the mean opacity. Truncation of the power spectrum at large scales affects the amount of matter collapsed into large halos. Power at large scales acts like a vacuum cleaner, thinning the low-density regions. Clearly an intrinsically thinner medium would have a different opacity. BR04 detail the required scale for reproducing the correct mass fraction in halos. The criterion: The scale Lbox is large enough for mass M if the fraction F of mass in halos of mass M from the simulation with size Lbox is comparable to the fraction expected FPS from P-S formalism when the full spectrum is taken into account. "Comparable" is defined by the fraction (1-ε) such that Fsim = (1 − ε)FPS. The paper examines M = M * and 10M * , galaxy to group sizes. An increase by a foctor of 10 for M and the required scale doubles. With ε=0.1 and M = M * , the scale required for z > 2 is 50h-1Mpc. MW04 find a minimum box size of 25h − 1Mpc is required to achieve convergence of the flux power-spectrum for z > 3.
If you have a model of the distribution of gas, from, say, a simulation, and an estimate for the gas temperatures, from, say, a polytrope model, and you assume almost complete ionisation, then the mean metagalactic emissivity, ε, is all that is needed to self-consistently compute nHI. It must be done iteratively, since nHI → τ → Γ → nHI. MW03 does this computation in an average sense to draw some interesting conclusions:
- attenuation is sensitive on ε
- QSO's are sufficient to produce the UV background at z > 4, indeed
- Lyman-break galaxies decrease significantly with redshift to not over-produce UV photons.
For z > 5, fluctuations in the sources (i.e. discrete sources versus a uniform radiation field) increase the optical depth. MW04 continued the work determining the sensitivity to field fluctuations. Background fluctuations increase the large-scale power and suppress power at intermediate scales. The increase in power can be understood by the creating of large voids. The suppression of power can be understood by the correlation between source and gas location: since the sources are preferentially near density peaks, the sources tend to erase the signature of the peaks preferentially.
Codes: WN05 describe photoionisation in the hydrodynamical code, Zeus.
KB00 have implemented RT in an SPH code, using essentially a photon-counting method.
Radiation hydrodynamics (RHD) is the set of equations that govern a radiation field coupled to matter. Approximations of LTE and intregrating of opacities and emission over frequency to get mean opacities and emission allows RHD to be solved as diffusion equations. This is the diffusion approximation. The diffusion approximation works best when the gas is optically thick. If the gas is optically thin, then infinite fluxes are predicted. Forcing the flux to be limited by F < c E, where E is the photon energy density, gives the flux-limited diffusion approximation. WBM05 give an efficient implementation of the flux-limited diffusion approximation in SPH.
WWD05 added non-LTE calculations into a simulation of ionisation.
Theuns98 discusses simulations of the Lyα forest using Hydra.
To get the geometry of ionisation right, Iliev05 found you need a volume at least 30 Mpc in size (presumably comoving).
C2-Ray is a fast, photon-conserving algorithm for photoionisation (MIAS05). Doesn't do the temperatures, however.
--Etittley 11:34, 25 June 2007 (BST)
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