Dear all,
I finally computed the correlation function extpected from Hoyle etal.'s P(k) obtained from their analysis of the 2QZ-10k quasar sample.
I used the final part of eq. (21.40) of Peebles (1993) book to convert P(k) to xi(r). I now understand that last equation as resulting from the integral over angles of the previsou integral (which is in fact triple: dk dtheta dphi).
I extended the P(k) beyond the values of Hoyle et al in two ways:
1) I used the theoretical BBKS (Bardeen et al. 84, appendix) P(k) (black & white plot). Notice that Hoyle's points are about a factor of 10000 too high so the P(k) is highly discontinuous.
2) I moved up the BBKS P(k) on each side of the Hoyle range so as to make the whole P(k) continuous.
3) Same as 2) with a step in log k decreased from 0.075 (Hoyle et al.'s step) to 0.01. (see 4th attached file).
The three xi(r) plots are attached. The calculation were done with Omega = 0.3, h = 0.7, Omegab = 0.04.
Even though Hoyle's peak is at 2 pi h / 89 Mpc, the 1st plot shows xi(r) with peaks at 67, 127 and 255 h-1 Mpc, close to what we (Boud really) gave in RMB02. This gives us some confidence that Boud's calculations are not completely wrong :-) and that there is no simple relation such as peak in xi at 2 pi / k_peak, where k_peak is the peak in P(k).
However, in the 2nd plot, the peaks are very narrow and marginally significant at 90.6, 107.6, 109.3, 127.8, 180.6 and 255.0 h-1 Mpc.
Finally, in the 3rd plot, it is hard to distinguish anything! However, with some imagination, one can guess excess broad power around 140 h-1 Mpc and a finer excess around 255 h-1 Mpc...
Let me know what you think.
all the best
Gary