Clustering at large scales disagree with linear model

[cramirezpe]

In the process of validating 2LPT velocities, we found something strange in the clustering of our sources in the snapshot boxes. We tried to check that velocities behave as expected in the linear regime so we took a look at the ratio between the quadrupole and the monopole, in the case where b=0 (unclustered):
$P_{\ell =0} (k) = \left( 1 + \frac{2}{3}\beta + \frac{1}{5}\beta^2\right) b^2 P(k)$
$P_{\ell = 2} (k) = \left( \frac{4}{3} \beta + \frac{4}{7} \beta^2 \right) b^2 P(k) $
$P_{\ell = 2}/P_{\ell = 0} (k, b=0) = 20/7 $

And we get:

We are surprised by the lack of agreement on the data points for the expected power. ¿Do you have any idea why this could be happening?

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To give a little bit of context, we took a look also at normally clustered mocks (positive bias), where the disagreement is not as large:

And also at the monopole/quadrupole separately for the unclustered (b=0) mocks:

where it seems that most of the issues come from the large scales of the quadrupole.

[cramirezpe]

Continuing with this, I have taken a look at the power spectrum of the field:
$1 + \frac{1}{h} \frac{\partial v_r}{\partial r} $

And I noticed similar effects as in the galaxies. I generated 6 different types of realisations:

$\eta$ field realizations:
v1: 1 Gpc/h, 1024 grid
v2: 2 Gpc/h, 1024 grid
v3: 1 Gpc/h, 512 grid

Unclustered mocks realizations (with RSD):
v8: 1 Gpc/h, 1024 grid
v9: 2 Gpc/h, 1024 grid
v10: 1 Gpc/h, 512 grid

And I compared both sets, giving similar results:

So it seems that whatever it is in the velocities is already in the eta field.

[andreufont]

There seem to be two things going on here:

• At low-k there seem to be a bias where the power of the eta field is too low, by something like 10%. The orange data points (40 boxes of 2 Gpc/h) have tiny errorbars and confirm this. I don't think this can be explained by numerical artefacts in our measurement (maybe we are too close to the box size?), since the problem is clear even at k=0.03 h/Mpc, ten times the fundamental mode (0.003 h/Mpc).

• At high-k the power goes up, no idea why. It looks like shot-noise, but there is no shot-noise in the eta field... what could be causing this? It doesn't seem to be something related to cell size, I think, since the problem is clear at k=0.15 h/Mpc and this is 10 times larger scales than the Nyquist frecuency (1.5 h/Mpc).

[damonge]

OK, at least we seem to find the root cause of some of this. It is indeed intriguing, since here I'm literally just taking the Gaussian density field (which presumably does recover the right power spectrum) and operating on it in Fourier space before putting it in the grid, so not too many things can go wrong...

I'll try to look into it, but it may not be before next week. If you want to check the modifications I made to the code in the last commit, let me know if you see anything strange.

[andreufont]

@cramirezpe - could you redo the test but using this time the Gaussian density field in the box? It might be useful to fully debug the code you are using... Is this already printed to disk with the same format that the new eta field?

[damonge]

It should be, yes

[cramirezpe]

Going back to these issues again, I computed the clustering for the gaussian field in a small box (1000 Mpc/h, N-grid: 512).

For the same box, I included a source following the lognormal density field. In this case I included a lognormal model with smoothing (similarly to what we did for the paper). In this case I have problems measuring the quadrupole:

So I have issues in the sources clustering even without added velocities.