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Register a new userNon-Gaussianity in the WMAP data using the peak-peak correlation function
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We present a search for non-Gaussianity in the WMAP first-year data using the two-point correlation function of maxima and minima in the temperature map. We find evidence for non-Gaussianity on large scales, whose origin appears to be associated with unsubstracted foregrounds, but which is not entirely clear. The signal appears to be associated most strongly with cold spots, and is more pronounced in the Southern galactic hemisphere. Removal of the region of sky near the galactic plane, or filtering out large-scale modes removes the signal. Analysis of individual frequency maps shows strongest signal in the 41GHz Q band. A study of difference maps tests the hypothesis that the non-Gaussianity is due to residual foregrounds and noise, but shows no significant detection. We suggest that the detection is due to large-scale residual foregrounds affecting more than one frequency band, but a primordial contribution from the Cosmic Microwave Background cannot be excluded.
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We derive the peak luminosity - peak energy (L_iso - E_peak) correlation using 22 long Gamma-Ray Bursts (GRBs) with firm redshift measurements. We find that its slope is similar to the correlation between the time integrated isotropic emitted energy E_iso and E_peak (Amati et al. 2002). For the 15 GRBs in our sample with estimated jet opening angle we compute the collimation corrected peak luminosity L_gamma, and find that it correlates with E_peak. This has, however, a scatter larger than the correlation between E_peak and E_gamma (the time integrated emitted energy, corrected for collimation; Ghirlanda et al. 2004), which we ascribe to the fact that the opening angle is estimated through the global energetics. We have then selected a large sample of 442 GRBs with pseudo--redshifts, derived through the lag-luminosity relation, to test the existence of the L_iso-E_peak correlation. With this sample we also explore the possibility of a correlation between time resolved quantities, namely L_iso,p and the peak energy at the peak of emission E_peak,p.
We discuss the effect of local type non-Gaussianity on the abundance of primordial black holes (PBH) based on the peak theory. We provide the PBH formation criterion based on the so-called compaction function and use the peak theory statistics associated with the curvature perturbation with the local type non-Gaussianity. Providing a method to estimate the PBH abundance, we demonstrate the effects of non-Gaussianity. It is explicitly shown that the value of non-linear parameter $|f_{rm NL}| sim 1$ induces a similar effect to a few factors of difference in the amplitude of the power spectrum.
The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity, and elongation of the signals local features. In the present work, the non-Gaussianity of the WMAP temperature data of the cosmic microwave background (CMB) is analyzed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcminutes and 30 degrees on the celestial sphere. While no detection is made neither in the orientation analysis nor in the elongation analysis, a strong detection is made in the excess kurtosis of the signed-intensity of the WMAP data. The non-Gaussianity is observed with a significance level below 0.5% at a wavelet scale corresponding to an angular size around 10 degrees, and confirmed at neighbour scales. This supports a previous detection of an excess of kurtosis in the wavelet coefficient of the WMAP data with the axisymmetric Mexican hat wavelet (Vielva et al. 2004). Instrumental noise and foreground emissions are not likely to be at the origin of the excess of kurtosis. Large-scale modulations of the CMB related to some unknown systematics are rejected as possible origins of the detection. The observed non-Gaussianity may therefore probably be imputed to the CMB itself, thereby questioning the basic inflationary scenario upon which the present concordance cosmological model relies. Taking the CMB temperature angular power spectrum of the concordance cosmological model at face value, further analysis also suggests that this non-Gaussianity is not confined to the directions on the celestial sphere with an anomalous signed-intensity.
From a sample of 32 GRBs with known redshift (Guidorzi et al. 2005) and then a sample of 551 BATSE GRBs with derived pseudo-redshift (Guidorzi 2005), the time variability/peak luminosity correlation (V vs. L) found by Reichart et al. (2001) was tested. For both samples the correlation is still found but less relevant due to a much higher spread of the data. Assuming a straight line in the logL-logV plane (logL = m logV + b), as done by Reichart et al., the slope was found lower than that derived by Reichart et al.: m = 1.3_{-0.4}^{+0.8} (Guidorzi et al. 2005), m = 0.85 +- 0.02 (Guidorzi 2005), to be compared with m = 3.3^{+1.1}_{-0.9} (Reichart et al. 2001). Reichart & Nysewander (2005) attribute the different slope to the fact we do not take into account in the fit the variance of the sample, and demonstrate that, using the method by Reichart (2001), the data set of Guidorzi et al. (2005) in logL-logV plane is still well described with slope m = 3.4^{+0.9}_{-0.6}. Here we compare the results of two methods accounting for the variance of the sample, that implemented by Reichart (2001) and that by DAgostini (2005). We demonstrate that the method by Reichart (2001) provides an inconsistent estimate of the slope when the sample variance is comparable with the interval of values covered by the variability. We also show that, using the DAgostini method, the slope is consistent with that derived by us earlier and inconsistent with that derived by Reichart & Nysewander (2005). Finally we discuss the implications on the interpretations and show that our results are in agreement with the peak energy/variability correlation found by Lloyd-Ronning & Ramirez-Ruiz (2002) and the peak energy/peak luminosity correlation (Yonetoku et al. 2004; Ghirlanda et al. 2005) [abridged].
Higher Criticism is a recently developed statistic for non-Gaussian detection, proposed in Donoho & Jin 2004. We find that Higher Criticism is useful for two purposes. First, Higher Criticism has competitive detection power, and non-Gaussianity is detected at the level 99% in the first year WMAP data. We find that the Higher Criticism value of WMAP is outside the 99% confidence region at a wavelet scale of 5 degrees (99.46% of Higher Criticism values based on simulated maps are below the values for WMAP). Second, Higher Criticism offers a way to locate a small portion of data that accounts for the non-Gaussianity. Using Higher Criticism, we have successfully identified a ring of pixels centered at (lapprox 209 deg, bapprox -57 deg), which seems to account for the observed detection of non-Gaussianity at the wavelet scale of 5 degrees. Note that the detection is achieved in wavelet space first. Second, it is always possible that a fraction of pixels within the ring might deviate from Gaussianity even if they do not appear to be above the 99% confidence level in wavelet space. The location of the ring coincides with the cold spot detected in Vielva et al. 2004 and Cruz et al. 2005.
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