Redshifted 21 Centimeter Signatures around the Highest Redshift Quasars

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Abstract
The Lyα absorption spectrum of the highest redshift quasars indicates that they are surrounded by giant H II regions, a few megaparsecs in size. The neutral gas around these H II regions should emit 21 cm radiation in excess of the cosmic microwave background and enable future radio telescopes to measure the transverse extent of these H II regions. At early times, the H II regions expand with a relativistic speed. Consequently, their measured sizes along the line of sight (via Lyα absorption) and transverse to it (via 21 cm emission) should have different observed values due to relativistic time delay. We show that the combined measurement of these sizes would directly constrain the neutral fraction of the surrounding intergalactic medium (IGM) as well as the quasar lifetime. Based on current number counts of luminous quasars at z 6, an instrument like LOFAR should detect 2 redshifted 21 cm shells per field (with a radius of 11°) around active quasars as bright as those already discovered by Sloan Digital Sky Survey, and 200 relic shells of inactive quasars per field. We show that Lyα photons from the quasar are unable to heat the IGM or to couple the spin and kinetic temperatures of atomic hydrogen beyond the edge of the H II region. The detection of the IGM in 21 cm emission around high-redshift quasars would therefore gauge the presence of a cosmic Lyα background during the reionization epoch.
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