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 [1003.3451] Primordial Non-Gaussianity and the NRAO VLA Sky Survey
 Authors: Jun-Qing Xia, Matteo Viel, Carlo Baccigalupi, Gianfranco De Zotti, Sabino Matarrese, Licia Verde Abstract: The NRAO VLA Sky Survey (NVSS) is the only dataset that allows an accurate determination of the auto-correlation function (ACF) on angular scales of several degrees for Active Galactic Nuclei (AGNs) at typical redshifts $z \simeq 1$. Surprisingly, the ACF is found to be positive on such large scales while, in the framework of the standard hierarchical clustering scenario with Gaussian primordial perturbations it should be negative for a redshift-independent effective halo mass of order of that found for optically-selected quasars. We show that a small primordial non-Gaussianity can add sufficient power on very large scales to account for the observed NVSS ACF. The best-fit value of the parameter $f_{\rm NL}$, quantifying the amplitude of primordial non-Gaussianity of local type is $f_{\rm NL}=62 \pm 27$ ($1\,\sigma$ error bar) and \$25

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Patrick McDonald

Joined: 06 Nov 2004
Posts: 17
Affiliation: CITA

 Posted: March 19 2010 This paper claims to find ~3 sigma evidence for local-form non-Gaussianity based on a measurement that the NVSS correlation function does not go to zero by separations ~8 degrees, when it should have been consistent with zero by ~2−3 degrees for standard Gaussian LCDM (given their error bars). My first question when seeing any correlation function that "does not go to zero" is "doesn't any measured correlation function *need* to become consistent with zero as you go to large separations, and why haven't the authors shown me that theirs does??" In other words: you may or may not have built in an integral constraint that forces your points to go negative somewhere, but in any case you should have a term in the covariance matrix corresponding to adding a constant to the correlation function, which guarantees that any fit results will not be sensitive to a shift in the mean of the survey (or scales much larger than the ones you think you can control). It looks to me like the authors' measurement is essentially completely based on this kind of constant term in the correlation function, i.e., if I am allowed to add a constant to the Gaussian case, it doesn't look like it can be distinguished from the non-Gaussian case. If the authors have some reason to believe this is not a problem, it should be clarified in the paper. That is a general observational consideration (you can't measure fluctuations in the mean of your survey), but there is a related theoretical issue: Naively, the constant contribution to the correlation function is infinite in this model for non-Gaussianity (although they may be leaving out the part of the calculation that gives that), so it is not clear what their predictions that look like they are going flat at large separations mean. There is an easy solution to both problems: marginalize over a free constant added to the correlation function prediction. It seems pretty clear though that they will find nothing of any significance when doing this. This is really a general problem with the correlation function. Looking at it at a given separation does not really correspond to what one is intuitively thinking when thinking about a certain "scale", e.g., the value at a relatively small separation is affected by fluctuations in something as large-scaled as the mean of the survey. Usually this doesn't matter, however, because one has measurements showing that the correlation goes to zero on scales larger than the ones of interest (to better precision than the changes of interest on your scale), which implicitly constrain the kind of constant term you should generally marginalize over.
Carlos E Cunha

Joined: 19 Mar 2010
Posts: 1
Affiliation: U. of Michigan

 Posted: March 19 2010 The authors do claim to take into account the integral constraint. At the end of Sec. 4 they state that "the correction proposed by Wands & Slozar (2009) to account for the infrared divergence of the non-Gaussian halo correlation function is fully negligible for our best-fit fnl value". The Wands & Slozar correction is just the sample variance at the scale of the survey. But, considering how large their best-fit fnl is and the volume of the survey. it is surprising that they find that the correction is negligible.
Patrick McDonald

Joined: 06 Nov 2004
Posts: 17
Affiliation: CITA

 Posted: March 19 2010 The basic problem doesn't really have anything to do with fNL, and isn't really accessible to a calculation of corrections. It is basically just: if your correlation function is positive at every separation you say you trust, you necessarily have sensitivity to constant shifts coming from larger scale structure, whether it is real large-scale structure or just systematic errors in the measurement.
Jun-Qing Xia

Joined: 02 Jan 2005
Posts: 22
Affiliation: SISSA, Italy

Anze Slosar

Joined: 24 Sep 2004
Posts: 204
Affiliation: Brookhaven National Laboratory

 Posted: March 24 2010 I am still confused about some of the issues here. The correlation function must do more than just go to zero at large scales, it must integrate to zero, which means it must necessarily go below zero at large separations. At what distance does your correlation function actually go through zero? Could we se xi(theta)theta2 plotted for some large values of theta? I also disagree with Pat on the importance of this effect. What one is doing is essentially forcing integral constraint by setting mean n to the mean n of the survey, which is different from the mean n of the universe. This essentially ignores modes larger than survey. But it doesn't matter for large surveys because cosmic mean n is going to be pretty close to measured mean n. But true, it is still the safest to marginalise over it. Also, in Wands and Slosar (for definition of Slozar (note z) , see http://www.urbandictionary.com/define.php?term=slozar ) we worked out, how to calculate xi to be compared with observations, because xi, when calculated from P(k) is formally divergent for any r. So in that sense it is not a correction, because it takes you from infinity to a finite value. But I agree that this is not the only possible way to calculate theory to be compared with your observations and I tend to trust Matarrese and Verde....
Patrick McDonald

Joined: 06 Nov 2004
Posts: 17
Affiliation: CITA

 Posted: March 25 2010 If you don't trust scales >R, it seems like the most often correct thing to do would be to high-pass filter both the theory and observations to remove the power on scales >R. This would remove a constant from the correlation function at separations <
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