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
Hi everyone, I think this is once again an example where I am slow or uneager to follow Gary's advice, but it turns out to that his idea is brilliant...
Apart from the question of using the Hoyle et al P(k), which is more a test of self-consistency between two different, but roughly equivalent, methods of analysing the same data set, and which seems to be OK in the smoothed plot of Gary's second message, I think that the first plot, based on the BBKS 1984 CDM-like P(k) is definitely very exciting: I think it makes it clear that for standard acoustic wave theory, we should *expect* to have peaks at these sorts of length scales in the correlation function, and that the correlation function can be *expected* to function as a better standard ruler than the power spectrum. :) :) :)
So the question gets back to: what is the best way of calculating the correlation function from the data to best constrain the local cosmological parameters...
I'll try to get the next version of DE out soon...
Best wishes to Gary for your talk tomorrow if I don't write anything sooner - and Micha� F, hope you learn a lot and meet a lot of people during this week. Maybe you could give us an informal talk about it mid-July (e.g. 15-19 July), since a few people may be here in Piwnice (e.g. Marcin, me).
On Sun, 30 Jun 2002, Gary Mamon wrote:
I finally computed the correlation function extpected from Hoyle etal.'s P(k) obtained from their analysis of the 2QZ-10k quasar sample.
...
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).
Cze�� Boud
Best wishes to Gary for your talk tomorrow if I don't write anything sooner - and Michał F, hope you learn a lot and meet a lot of people during this week. Maybe you could give us an informal talk about it mid-July (e.g. 15-19 July), since a few people may be here in Piwnice (e.g. Marcin, me).
I will try to give a full report ;) regards - michal
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Boud Roukema -
Gary Mamon -
Michal Frackowiak