Mon. Not. R. Astron. Soc. 369, 909–920 (2006) doi:10.1111/j.1365-2966.2006.10341.x Non-Gaussianity in the Very Small Array cosmic microwave background maps with smooth goodness-of-fit tests Jos´e Alberto Rubi˜no-Mart´ın,1 Antonio M. Aliaga,2 R. B. Barreiro,2 Richard A. Downloaded from https://academic.oup.com/mnras/article-abstract/369/2/909/3101589 by California Institute of Technology user on 19 May 2020 Battye,3 Pedro Carreira,3 Kieran Cleary,3† RodD.Davies,3 Richard J. Davis,3 Clive Dickinson,3‡ Ricardo G´enova-Santos,1 Keith Grainge,4 Carlos M. Guti´errez,1 Yaser A. Hafez,3 Michael P. Hobson,4 Michael E. Jones,4§ R¨udiger Kneissl,4 Katy Lancaster,4 Anthony Lasenby,4 J. P. Leahy,3 Klaus Maisinger,4 Enrique Mart´ınez-Gonz´alez,2 Guy G. Pooley,4 Nutan Rajguru,4 Rafael Rebolo,1,5 Jos´e Luis Sanz,2 Richard D. E. Saunders,4 Richard S. Savage,4¶ Anna Scaife,4 Paul Scott,4 Anˇze Slosar,4|| Angela C. Taylor,4 David Titterington,4 Elizabeth Waldram4 and Robert A. Watson3†† 1Instituto de Astrof´ısica de Canarias, 38200 La Laguna, Tenerife, Spain 2IFCA, CSIC-Univ. de Cantabria, Avda. los Castros, s/n, E-39005 Santander, Spain 3Jodrell Bank Observatory, School of Physics and Astronomy, University of Manchester, Macclesfield, Cheshire SK11 9DL 4Astrophysics Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE 5Consejo Superior de Investigaciones Cient´ıficas, Spain Accepted 2006 March 17. Received 2006 February 9; in original form 2005 November 4 ABSTRACT We have used the Rayner and Best smooth tests of goodness-of-fit to study the Gaussianity of the Very Small Array (VSA) data. These tests are designed to be sensitive to the presence of ‘smooth’ deviations from a given distribution, and are applied to the data transformed into normalized signal-to-noise eigenmodes. In a previous work, they have been already adapted and applied to simulated observations of interferometric experiments. In this paper, we extend the practical implementation of the method to deal with mosaiced observations, by introducing the Arnoldi algorithm. This method permits us to solve large eigenvalue problems with low computational cost. Out of the 41 published VSA individual pointings dedicated to cosmological [cosmic mi- crowave background (CMB)] observations, 37 are found to be consistent with Gaussianity, whereas four pointings show deviations from Gaussianity. In two of them, these deviations can be explained as residual systematic effects of a few visibility points which, when corrected, have a negligible impact on the angular power spectrum. The non-Gaussianity found in the other two (adjacent) pointings seems to be associated to a local deviation of the power spec- trum of these fields with respect to the common power spectrum of the complete data set, at angular scales of the third acoustic peak ( = 700–900). No evidence of residual systematics is found in this case, and unsubtracted point sources are not a plausible explanation either. If E-mail: [email protected] †Present address: Jet Propulsion Laboratory, 4800 Oak Grove Drive, MS 264-767, Pasadena, CA 91109, USA. ‡Present address: California Institute of Technology, Department of Astronomy, MS 105-24, 1200 E. California Blvd., Pasadena, CA 91125, USA. §Present address: Astrophysics Group, Denys Wilkinson Building, University of Oxford. ¶Present address: Astronomy Centre, University of Sussex. ||Present address: Faculty of Mathematics & Physics, University of Ljubljana, 1000 Ljubljana, Slovenia. Present address: Astrophysics Group, Denys Wilkinson Building, University of Oxford. ††Present address: Instituto de Astrof´ısica de Canarias, 38200 La Laguna, Tenerife, Spain. C 2006 The Authors. Journal compilation C 2006 RAS 910 J. A. Rubino-Mart˜ ´ın et al. those visibilities are removed, the differences of the new power spectrum with respect to the published one only affect three bins. A cosmological analysis based on this new VSA power spectrum alone shows no differences in the parameter constraints with respect to our published results, except for the physical baryon density, which decreases by 10 per cent. Finally, the method has been also used to analyse the VSA observations in the Corona Borealis supercluster region. Our method finds a clear deviation (99.82 per cent) with respect Downloaded from https://academic.oup.com/mnras/article-abstract/369/2/909/3101589 by California Institute of Technology user on 19 May 2020 to Gaussianity in the second-order moment of the distribution, and which cannot be explained as systematic effects. A detailed study shows that the non-Gaussianity is produced in scales of ≈ 500, and that this deviation is intrinsic to the data (in the sense that cannot be explained in terms of a Gaussian field with a different power spectrum). This result is consistent with the Gaussianity studies in the Corona Borealis data presented in G´enova-Santos et al. which show a strong decrement that cannot be explained as primordial CMB. Key words: methods: data analysis – methods: statistical – cosmic microwave background – cosmology: observations. In this paper, we present the results of a Gaussianity analysis 1 INTRODUCTION of the complete set of observations of the Very Small Array (VSA) The study of the Gaussianity of the primordial density fluctuations is dedicated to measure the CMB power spectrum (see Dickinson et al. a very important tool in constraining theories of structure formation. 2004, and references therein), as well as an analysis of the data from Inside the inflationary paradigm, there is a huge number of theories the Corona Borealis supercluster survey presented in G´enova-Santos (see Bartolo et al. 2004 for a recent review on the subject), each one et al. (2005). Here, we will complement the previous Gaussianity predicting different non-Gaussian signatures. Thus, any detection studies of the VSA data by considering a different family of methods, of non-Gaussianity would help to discriminate among these sce- called the smooth tests of goodness-of-fit (STGOF). narios for the generation of cosmological perturbations. Because In Section 2, we give a brief overview of the VSA experiment. In of this reason, the study of the Gaussianity of cosmic microwave Section 3, we review the STGOF methods, and how these methods background (CMB) maps is becoming of major importance in mod- can be adapted to the study of the Gaussianity of interferometric ern cosmology. In particular, since the publication of the first year experiments. Section 4 describes how these methods can be fur- Wilkinson Microwave Anisotropy Probe (WMAP) results (Bennett ther adapted to deal with large data sets or mosaiced observations. et al. 2003), several groups have tested the non-Gaussian nature Section 5 presents the calibration of the method using Gaussian sim- of those maps using a wide set of techniques (Chiang et al. 2003; ulations of mosaiced observations with the VSA. Section 6 presents Komatsu et al. 2003; Eriksen et al. 2004a,b; Park 2004; Vielva et al. the results of our analysis, and finally conclusions are presented in 2004; Cruz et al. 2005). Section 7. Furthermore, there are other reasons showing the importance of the study of the Gaussianity of the CMB. The majority of the in- 2 THE VERY SMALL ARRAY flationary models predict the primordial non-Gaussian signal to be smaller than the contribution from secondary effects such as gravita- The VSA is a 14-element heterodyne interferometer sited at the tional lensing, reionization, Sunyaev–Zel’dovich (SZ) effect, or the Teide Observatory (Tenerife). The instrument is designed to im- contribution of local foregrounds or unresolved point sources in the age the CMB on scales going from 2◦ to 10 arcmin, and operates maps. Thus, tools to test Gaussianity could be used to trace the pres- at frequencies between 26 and 36 GHz with a 1.5-GHz bandwidth ence of these foregrounds. For example, the analysis of the WMAP and a system temperature of ∼30 K. The VSA has observed in two data using the bispectrum allowed Komatsu et al. (2003) to perform configurations of antennas. The first one is the so-called ‘compact estimates of the source number counts of unresolved sources in the configuration’, which covers the multipole range ∼ 150–900 with 41-GHz channel (see also Gonz´alez-Nuevo, Toffolatti & Arg¨ueso a primary beam of 4◦.6 FWHM (full width at half-maximum) at 2005). 34.1 GHz. This configuration was used during the first observing In addition, systematic effects may produce spurious detections of season (2000 September–2001 September). The results of this cam- non-Gaussianities, so non-Gaussian methods could help in charac- paign are presented in Scott et al. (2003); Tayloret al. (2003); Watson terizing the properties of a given experiment (e.g. Banday, Zaroubi et al. (2003) and Rubi˜no-Mart´ın et al. (2003). &G´orski 2000). The second one, the ‘extended configuration’, provided obser- The Gaussianity of the VSA data was already examined using vations up to = 1500 with a primary beam of 2◦.10 FWHM (at several methods in two separate papers (Savage et al. 2004; Smith 33 GHz) and an angular resolution of 11 arcmin during two sepa- et al. 2004), which were based on the data presented in Taylor et al. rate campaigns. Those results were presented in two separate sets of (2003) and Grainge et al. (2003). In Savage et al. (2004), a selection papers: Grainge et al. (2003), Slosar et al. (2003) for the second sea- of non-Gaussianity tests are applied to the data. Most of these tests son of observations (2001 September–2002 April); and Dickinson are based on real-space statistics and are applied to the maximum- et al. (2004), Rebolo et al. (2004) for the third one (2002 April–2003 entropy reconstruction of the regions observed by the instrument.