Reionization

Reionization returns some neutral cosmic gas to an ionized state after cosmological recombination. The resulting free electrons increase the cosmological optical depth through Thomson scattering and create a second contribution to the cosmological visibility function.

For full hydrogen ionization after instantaneous reionization, $n_{e0}=3{\Omega }_b{H}_0^2/(8\pi G{m}_p)$ and $H(z)=H_0(1+z)\sqrt{1+{\Omega }_{m}z}$. Integrating Thomson scattering givesFor ${\Omega }_m=1$, $\kappa ={\Omega }_b{C}_H[(1+z_{\mathrm{re}}{)}^{3/2}-1]$. At fixed baryon density and redshift, lowering the matter density reduces the expansion rate and increases the optical depth.

// Target: cosmology.bigb

If each collapsed baryon supplies $N_{\gamma }$ effective ionizing photons and $N_{\mathrm{req}}$ photons per cosmic baryon are required, the threshold collapsed fraction is $f_{\mathrm{coll}}=N_{\mathrm{req}}/N_{\gamma }$. The Press-Schechter formalism gives $\mathrm{erfc}[{\delta }_{\mathrm{sc}}/(\sqrt{2}\sigma (M_{\min },z))]=f_{\mathrm{coll}}$. Escape losses and recombinations must either be incorporated in the effective yield/requirement or counted separately, not twice.

Photoionization can heat a shallow halo's gas well above its virial temperature. If the heated sound speed exceeds the escape-speed scale, the previous hydrostatic equilibrium is lost and a pressure-driven outflow removes gas. A crossing time gives a useful estimate, but photon supply, the gas profile, shielding and recombinations can delay the process. This particularly affects haloes whose virial temperatures are below the usual atomic cooling threshold and reduces their subsequent star formation.

Ignoring velocities and evolving potentials, a thin reionization screen transmits the primary Cosmic microwave background anisotropy with amplitude $e^{-{\tau }_{\mathrm{re}}}$ and adds a direction-averaged source. A plane wave propagating a distance $\Delta \chi$ from recombination to the screen has monopole factor $j_0(k\Delta \chi )=\sin (k\Delta \chi )/(k\Delta \chi )$. This suppresses the rescattered source at $k\Delta \chi \gg 1$, while coherent large-scale modes are unchanged to leading order.

The primary small-scale Cosmic microwave background power spectrum measures the amplitude $A_s{e}^{-2{\tau }_{\mathrm{re}}}$, because reionization damps each temperature amplitude once. The unaffected large-scale temperature modes are few and limited by cosmic variance. Polarization and gravitational lensing provide additional information that partly breaks this degeneracy.