extra covariance in cross-correlation along the line-of-sight

[londumas]

Looking at the stack of the 10 cross-correlations, we observe extra covariance along the line-of-sight than compared to the data and expected by direct computation (Wick).
The plots give the variance times the number of pairs:

• as a function of bin index for data
• the same for mocks
• in 2d for data
• the same for mocks

These plots give a indication that something is different between data and mocks along the line-of-sight, however they don't mean that anything is wrong, neither in LyaCoLoRe nor in picca, but is asks for investigations.
It was a tackled in part there, but apparently not deep enough in PR igmhub/picca#437

[londumas]

I put this ticket there, because I have no idea if it is a picca or a LyaCoLoRe ticket, and that it is not observed in data.
My plan is to both look at:

• the same variance but when using the random catalog of quasars
• the same variance but on a finer grid across the line-of-sight.

[londumas]

In the Lya absorption in the Lyb region, it is not observed for some reasons.

[londumas]

This is also observed in the cross-correlation of the raw field:

[londumas]

@jfarr03 and @andreufont, and also @jmarclegoff and @TEtourneau , I have a guess on what it is:
If I understand correctly how the mocks are done, you have:

• a box of resolution ~2Mpc/h -> delta_large_scale
• to add smaller scales, you add uncorrelated small scales with the proper power spectrum -> delta_small_scale
• This gives you delta = delta_large_scale+delta_small_scale
• I seem to remember that the quasars are drown from the delta_large_scale, but then there should be an exclusion radius of ~2Mpc/h around each quasar. Thing that I don't observe. See plots bellow.
  Thus if two quasars are drown from the same simulation pixel, basically they are the same quasar with a bit different RA and DEC. Let's call them quasar A and quasar B.
• Thus if I correlate the forest of quasar A with quasar B and the forest of quasar B with quasar A, I am actually computing the 1d cross-correlation QSOxpixels, since the pixels are from the same line-of-sight. This has way more covariance than the 3d cross-correlation, and thus it explains the behavior of this ticket.
• I thus predict that if I remove all quasars within ~4Mpc/h of the host quasar of a forest, in the computation of the cross-correlation, then the extra variance should disappear. I will try to find some spots on the queue to compute that.

The following plots give for the data, the London and the Saclay mocks the number of pairs divided by r_transverse for the auto-correlation of quasars. We can see that there are a lot of pairs near a quasar in both mocks, compared to data.

[TEtourneau]

In our mocks, we cannot have 2 QSO in the same cell.
The only thing that can happen is that 2 QSO are drawn in 2 adjacent cells, and then the random placement inside each cell makes the QSO to be very close to each other. But even if they are very close, they are in a different cell.
@jfarr03 @andreufont Is that the same for you ?

Maybe we can check this in our mock, to see if the feature is also here.

[londumas]

Here is the status of this ticket as of v8.0:

1. first two plots: variance*nb_pairs for auto and cross on the raw
2. last two plots: variance*nb_pairs for autoLyb and crossLyb on the raw

The difference between these two cross and crossLyb really show that the issue comes from quasars very near the pixels.
@jfarr03, no need to worry about that, I just wanted to update the status.