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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

 Posted: March 24 2010 Unfortunately, in the small space for a Letter we could not spend too many words on reviewing the literature on the NVSS correlation function in general. Here's some additional information that may be useful to understand the issue. The radio sources and in particular NVSS auto correlation function has been studied exahustively. References include: Cress et al 1996, Cress & Kamionkowski 1998, Magliocchetti et al 1998, Blake and Wall 2002a (Mon.Not.Roy.Astron.Soc. 329 (2002) L37- L41), Blake and Wall 2002b (Mon.Not.Roy.Astron.Soc. 337 (2002) 993), Negrello et al 2006(Mon.Not.Roy.Astron.Soc.377:1557−1568,2007) and (Mon.Not.Roy.Astron.Soc.368:935−942,2006) ) Both FIRST and NVSS surveys since the first analyses showed that their correlation function did not have the same shape as expected in a standard LCDM model; one would have to play with the sources redshift distribution and biasing to make them match (for a heat-to- head comparison of FIRST and NVSS see Blake and Wall 2002b). Blake and Wall 2002a present probably the first robust determination of the NVSS correlation function. There they show that the correlation function is well described by two power laws: at small scales (separations of less than 0.1 degrees) one sees the effect of the size distribution of the sources (these are not points at these frequences and these resolutions) and at larger scales one sees the sources clustering. In our paper we exclude the small scales as we are not interested on the sources sizes. The large scales, >0.1 deg <10 deg,(where "large" is still small compared to the survey size), where one should see the clustering properties, may be to some extent affected by systematic effects involving non-uniform source sampling. In Blake & Wall 2002a sec 2.3 it is discussed how the effect of varying source density may enhance the correlation function. There they quantify that the effect depends on the flux cut, it is very small for sources >10mJy but increases rapidly below that flux cut. We work at the high flux cut and anyway report what happens when we apply a possible correction (the 10−4 mentioned). This is a conservative choice, see sec 4.3 of Blake and Wall 2002b and 2.3 of Blake and Wall 2002a. The correlation function we measure is fully consistent with the Blake \& Wall one (see discussion at the end of page 4 where we swapped our data and errors with the Blake&Wall ones). The part of the correlation function least affected by possible density gradients (arising from the difficulty in calibrating and matching the different configurations of the array-see discussion in Blake & Wall) is at separation <10 deg. In order to zoom in on the interesting part of the correlation function we use and show only scales up to 8 degrees separation. We are throwing away data -and information- at larger separation, but scales <10 deg are most reliable. The survey's large sky coverage allows us to compute the correlation to much larger separations. In fact the mean of the survey is computed from the full survey but then only correlations at separations <9 deg are shown. To see an example of the correlation function to larger separations see for example fig 10 of Hernandez-Monteagudo 2009 (0909.4294), concentrating on the blue/green symbols. In addition to that it may still be that non-zero fnl includes extra fluctuations (see discussion in Wands and Slosar) on the survey size. We compute that this effect is fully sub-dominant compared to the un-uniform source density effect and anyway does not change the results (that is the meaning of the sentence "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".). Indeed the theoretical variance on the scale of the survey is 5e−5 × fNL/fNL(best fit), which is smaller than the effect due to density gradients for all fNL<100. So to summarize: the correlation function does go to zero on large (>10 deg) scales but , whatever we do, a) these are larger than the scales of interests here b) it does not do it as sharply and at the scales predicted by LCDM ( ~2 degrees) for a biasing model for the sources in agreement with that of their optical counterpart. There are several ways out, each of them involve some "non-standard" solution: a) a bias model which decreases with z, based on a redshift dependent hosting halo mass (but then radio loud and radio quiet sources are not the same beast) see papers by Massardi et al 2010 and refs there. b) primordial non-gaussianity (but then you will have do be willing to drop gaussianity) c) some other systematic error in the survey that we could not find or think of d) a combination of different effects (mis-estimate of off diagonal covariance terms +strange bias evolution + strange Mmin+ bigger correction due to source density gradients than quantified by Blake and Wall) , each of them making our error-bars slightly underestimated 'til the integrated effect of all gives an fnl consistent with zero. The literature so far had concentrated on option a), so we hope we have opened the discussion about b). It is surely early to draw any definitive conclusions, but still one can conclude -as we do- that "our work should be seen as a “proof of principle”, indicating that future surveys probing scales ~ 100 Mpc at substantial redshifts can put stringent constraints on primordial non-Gaussianity". I hope this answers your questions, but please ask if you need further clarifications.
Anze Slosar

Joined: 24 Sep 2004
Posts: 205
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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