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Title:
Relativistic Ionization Fronts
Authors:
Shapiro, Paul R.; Iliev, Ilian T.; Alvarez, Marcelo A.; Scannapieco, Evan
Affiliation:
AA(Department of Astronomy, University of Texas, Austin, TX 78712-1083 .), AB(Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada.), AC(Department of Astronomy, University of Texas, Austin, TX 78712-1083 .), AD(Kavli Institute for Theoretical Physics, Kohn Hall, UC Santa Barbara, Santa Barbara, CA 93106.)
Publication:
The Astrophysical Journal, Volume 648, Issue 2, pp. 922-935. (ApJ Homepage)
Publication Date:
09/2006
Origin:
UCP
ApJ Keywords:
Cosmology: Theory, Galaxies: Halos, Galaxies: High-Redshift, ISM: H II Regions, Galaxies: Intergalactic Medium, ISM: Bubbles
DOI:
10.1086/506242
Bibliographic Code:
2006ApJ...648..922S

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.
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