Extracting the BAO scale from BOSS DR12 dataset

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Abstract

We present the first application to real data from the BOSS DR12 dataset of the Extractor procedure (Noda et al., 2017, Nishimichi et al., 2018) to determine the acoustic scale imprinted on Baryonic Acoustic Oscillations (BAO). We show that, being largely insensitive to the broadband shape of the Power Spectrum, this procedure requires a lower number of nuisance parameters than those used by the BOSS collaboration, For non-reconstructed data our analysis improves the accuracy on the acoustic scale by about 20%, while for reconstructed ones we get essentially the same level of accuracy as the BOSS analysis.

Introduction

Measuring the acoustic scale from BAO’s is one of the main goals of present and forthcoming galaxy surveys. A sub-percent level measurement will give powerful constraints on the nature of Dark Energy and on possible modifications of General Relativity.

In practical data analyses, the nonlinear effects, which include redshift space distortions (RSD) and bias, are modelled by adding a number of nuisance parameters. In particular, in the BOSS analysis that we will use as a benchmark in this paper, namely that based on the DR12 dataset presented in [1], 10 parameters where introduced, of which only one was related to the observable of interest, the BAO scale, while the role of most of the remaining ones is to model UV effects. However, it is well known [2] that the information on the BAO scale is, to a great extent, insensitive to short scale effects, and can be robustly extracted from data. In particular, in [3], [4] we introduced an “Extractor” procedure, which, given a Power Spectrum (PS), projects out the smooth component and gives only the oscillating one. The leading nonlinear effect on BAO wiggles is the well understood damping caused by random motions coherent on large (O(10100h1Mpc)) scales. Once this effect is taken into account, the ‘extracted’ PS can be accurately modelled by as few as one nuisance parameter, which combines RSD and scale-dependent bias. The Extractor procedure was tested in [4] using N-body simulations as data and different models, with and without the inclusion of UV effects.

In this paper we test the Extractor procedure on real data, namely on the already mentioned BOSS DR12 dataset [1]. Our main purpose is to assess the improvement induced by the strong reduction in the number of nuisance parameters allowed by our procedure. Therefore, we will stick to a very simple model for the PS, given in Eq. (9), which, from a computational point of view, requires no more that common 1-loop integrals in SPT. We will not consider more elaborate theoretical models for the PS, like the TRG+UV effects of [3] or the Effective Field Theory of [5], although they can be included in the analysis with no extra effort.

Finally, we stress that our analysis, at this stage, focuses on the extraction of an oscillatory feature of a PS, rather than on the more general question of how to estimate cosmological distances in a model independent way (for a recent discussion, see for instance [6]). Therefore, to be concrete, and to make a direct comparison with the results of [1] we concentrate on the α dilation parameter introduced in Section 5.

The paper is organized as follows. In Section 2 we recall the definition of the BAO Extractor procedure, in Section 3 we summarize the aspects of the DR12 dataset which are more relevant to the following, in Section 4 we introduce our model for the galaxy PS, in Section 5 we describe our analysis, in Section 6 we report the convolutions necessary to account for the BOSS observation window functions, in Section 7 we test our procedure on the catalogue of mock galaxies used by the BOSS collaboration, and in Section 8 we perform the analysis on the real data. Finally, in Section 9 we discuss our results and conclude.

Section snippets

BAO extractor: definition

In this Section we summarize the procedure to extract the oscillatory part of a given PS, P(k), that we use in this paper [3]. As this procedure was already summarized in [4], we only present a very short description here, referring the interested reader to that discussion for more details.

The PS of Large Scale Structure (LSS) can be seen as the sum of a dominant smooth (“no-wiggle”) part and of an oscillatory (“wiggly”) component due to BAO: P(k)=Pnw(k)+Pw(k),Pw(k)Pnw(k)A(k)sinkrbao,where the

The BOSS data and reconstruction

The Baryon Oscillation Spectroscopic Survey (BOSS) was part of the effort of the SDSS-III collaboration to map our near Universe. It measured the spectroscopic redshift of luminous galaxies in the 0.2<z<0.75 redshift range and two regions of the sky, denoted by North Galactic Cup (NGC) and South Galactic Cup (SGC), from which, respectively, about 865 000 and 330 000 galaxies were measured [7]. The measurements were made with a 2.5 metre-aperture telescope at the Apache Point Observatory, New

The model

In [4] we tested the performance of a simple model function to reproduce the extracted PS obtained from N-Body simulations and found good agreement, both for matter and for halos, in real and redshift space. This is particularly interesting since the model did not include any short-scale effects, which are otherwise essential to model the full PS, and both the scale dependence of RSD and halo bias are encoded in a single exponential prefactor containing just one extra parameter.

We will use a

Determining the BAO scale

Our aim is to determine the BAO scale contained in the data. To do this, following the BOSS analysis, we are going to define a parameter α that rescales isotropically the BAO length imprinted in the data with respect to our fiducial cosmological model. In [4] we considered a function χ2(α), χ2(α,)=i,j=nminnmaxδR[P](ki;α,)cij1δR[P](kj;α,),with δR[P](ki;α,)R[Pmodel](kiα,)R[Pdata](ki),where cij is the covariance matrix of Eq. (25) below, and dots indicate other possible parameters of the

Window function

To be compared to BOSS data, the model PS has to be convolved with the survey window function provided by the BOSS collaboration. The window-corrected PS is given by [1] Pˆl(k)=(i)l4πdrr2jl(kr)ξˆl(r),where the ξˆl(r)’s are the window-corrected correlation function multipoles (including only monopole and quadrupole) ξˆ0(r)=W02(r)ξ0(r)+15W22(r)ξ2(r),ξˆ2(r)=W22(r)ξ0(r)+W02(r)+27W22(r)ξ2(r), with W02(r) and W22(r) the monopole and quadrupole of the window function. Expressing the correlation

Test on mock galaxies

Before applying the procedure to the experimental data we tested it on the MultyDark Patchy mock catalogues of the BOSS collaboration [9], [10]. The fiducial cosmological model used to generate these mocks was a flat ΛCDM model with the parameters reported in the second column of Table 1. The corresponding PDF for the three parameters and for the various redshift bins obtained from our analysis are shown in Fig. 1.

Testing our analysis on the mock data has the main purpose of choosing the

Application to BOSS DR12 data

Having tested our procedure, and found the optimal setup, with mock galaxies, we apply it to the experimental data. We use the same pipeline as the one established in analysing Mock data presented in Section 7, namely, we use the data [1] up to kkmax=0.225hMpc1 (respectively, up to kkmax=0.235hMpc1) for the pre-reconstruction (respectively, post-reconstruction) data). This corresponds to 22 (respectively, 23) bins. This gives 44 (respectively, 46) data in each simultaneous NGC+SGC fit (for

Conclusions

The Extractor procedure represents a promising approach to the study of BAOs, both from a theoretical and data analysis point of view. Despite using a simple model, Eq. (9), the procedure was able to reach a subpercent precision for all redshift bins, for reconstructed data, using only two nuisance parameter besides α. Applying the Extractor procedure on unreconstructed data gives constraints tighter by about 20% than those obtained in the standard analysis. On the other hand, for reconstructed

CRediT authorship contribution statement

Eugenio Noda: Conceptualization, Methodology, Software, Formal analysis. Marco Peloso: Conceptualization, Methodology, Software, Formal analysis. Massimo Pietroni: Conceptualization, Methodology, Software, Formal analysis.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

It is a pleasure to thank Florian Beutler for providing us with the processed PS for the BOSS experimental data and mock galaxy catalogue, and for clarifying correspondence on the use of these data, and Takahiro Nishimichi for discussions and for collaborating at the early stages of the present analyses. We thank an anonymous referee for suggestions that have improved our analysis.

MP acknowledges support from the European Union Horizon 2020 research and innovation programme (Italy) under the

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