tokens: is to get the power spectrum. The power spectrum obtained for the fiducial model is depicted in Figure 4 . To get the power spectrum, the 21 cm brightness temperature distribution, , is Fourier transformed and then the dimensionless power spectrum is obtained using the following prescription: The spherically averaged power spectrum is obtained by averaging Δ 2 ( k ) over all possible angles:where is the cosine of the angle that wavevector k makes with the line-of-sight direction. Figure 4. Power spectrum of 21 cm brightness temperature distribution for three redshifts. The power spectrum obtained is of expected magnitude (see, e.g., Mesinger et al. 2011 ) and also seems to show the expected trend with respect to the redshift. 2.5. Salient Features of the Method This method of generating 21 cm maps has the following features: 1. A simple and intuitive method where excursion set formalism is used only for getting the collapse fraction. 2. An explicitly photon conserving method where one can compute the mean neutral hydrogen fraction once one knows, the mean collapse fraction () and the other two reionization parameters ( n ion and n rec ). 3. The expression for mean neutral hydrogen fraction is: . 4. Method is fairly fast. It takes about 3–4 minutes to propagate 10 million photon rays and generate a temperature cube (64 × 64 × 64) on an ordinary intel core i5 machine with 8 GB memory. 5. It is precise even with a small number of photon rays as it automatically assigns more rays to more overdense regions or more luminous objects. 2.6. Stability Analysis To check if the reionization procedure is giving a convergent answer, two tests were performed. In the first test, the step size was halved, twice, from the value chosen earlier, that is, it was made to be 0.025 and 0.0125 of the grid cell size. And, in the second test, the number of photon rays was doubled, again twice, to 20 million and 40 million. The effect of these two procedures on temperature maps and power spectrum is summarized in Tables 1 and 2 respectively. In the case of temperature maps the quantity listed is , where is the absolute value of the difference in brightness temperature measured with respect to the fiducial case, that is, with respect to step size of .05 and ray count of 10 million case. In this case, indicates the average over all the grid cells. Table 1 Percentage Change in Temperature Maps with Respect to the Fiducial Case Table 2 Percentage Change in Power Spectrum with Respect to Fiducial Case As seen from Table 1 , the change in δT b averaged over the whole grid cell is small (≲5%). Also the increment in going from the double to the four times case is smaller than going from the fiducial to the double case. In the case of changing step size, the percentage change is nearly the same. In the case of the power spectrum, in Table 2 , the quantity listed is , that is a fractional change in 21 cm power spectrum averaged over all k values. The smallness of values in the
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