Abstract
We derive the equations for the propagation of relativistic ionization fronts (I-fronts) in both static and moving gases, including the cosmologically expanding intergalactic medium (IGM). For the supersonic R-type phase that occurs right after a source turns on, relativistic corrections can be significant up until the light crossing time of the equilibrium Strömgren sphere. When q, the ratio of this light-crossing time to the recombination time, exceeds unity, the time for the expanding I-front to reach the Strömgren radius is delayed by a factor of q. For a static medium, we obtain exact analytical solutions and apply them to the illustrative problems of an O star in a molecular cloud and a starburst in a high-redshift cosmological halo. Relativistic corrections can be important both at early times when the H II regions are small and at later times if a density gradient causes the I-front to accelerate. An analytical solution is also derived for a steady source in a cosmologically expanding IGM. Here relativistic corrections are significant for short-lived, highly luminous sources such as QSOs at the end of reionization (z ≃ 6) but negligible for weaker or higher redshift sources. Finally, we numerically solve the equations for relativistic, cosmological I-fronts in the presence of evolving small-scale structure, for a large-galaxy starburst and a luminous QSO. For such strong and short-lived sources at z ∼ 7, relativistic corrections are quite significant, and small-scale structure can decrease the size of the H II region by up to an additional ∼25%. However, most of the IGM was ionized by smaller, higher redshift sources. Thus, the effect of relativistic corrections on global reionization is small and can usually be neglected.
Original language | English (US) |
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Pages (from-to) | 922-935 |
Number of pages | 14 |
Journal | Astrophysical Journal |
Volume | 648 |
Issue number | 2 I |
DOIs | |
State | Published - Sep 10 2006 |
Externally published | Yes |
Keywords
- Cosmology: Theory
- Galaxies: Halos
- Galaxies: High-redshift
- H II regions
- ISM: Bubbles
- Intergalactic medium
ASJC Scopus subject areas
- Astronomy and Astrophysics
- Space and Planetary Science