21 cm Signals from Early Ionizing Sources

We investigate the 21 cm signals from the UV ionizing sources in thereionization epoch. The formation and evolution of 21 cm emission andabsorption regions depend essentially on the kinetics of photons in thephysical and frequency spaces. To solve the radiative transfer equation, we usethe WENO algorithm, which is effective to capture the sharp ionization profileand the cut-off at the front of light $(r=ct)$ and to handle the small fractionof neutral hydrogen and helium in the ionized sphere. We show that a sphericalshell of 21 cm emission and absorption will develop around a point source oncethe speed of the ionization front (I-front) is significantly lower than thespeed of light. The 21 cm shell extends from the I-front to the front of light;its inner part is the emission region and its outer part is the absorptionregion. The 21 cm emission region depends strongly on the intensity,frequency-spectrum and life-time of the UV ionizing source. For a source ofshort life-time, no 21 cm emission region can be formed if the source dies outbefore the I-front speed is significantly lower than the speed of light. Yet, a21 cm absorption region can form and develop even after the emission of thesource ceases.Comment: 25 pages, 9 figures, accepted by Ap