MNRAS 000, 000{000 (0000) Preprint 20 March 2019 Compiled using MNRAS LATEX style file v3.0 An estimation of the local growth rate from Cosmicflows-3 peculiar velocities Alexandra Dupuy1 ?, Helene M. Courtois1, Bogna Kubik1 1University of Lyon, UCB Lyon 1, CNRS/IN2P3, IPN Lyon, 69622 Villeurbanne, France 20 March 2019 ABSTRACT This article explores three usual estimators, noted as v12 of the pairwise velocity, 1 and 2 of the observed two-point galaxy peculiar velocity correlation functions. These estimators are tested on mock samples of Cosmicflows-3 dataset (Tully et al. 2016) , derived from a numerical cosmological simulation, and also on a number of constrained realizations of this dataset. Observational measurements errors and cosmic variance are taken into consideration in the study. The result is a local measurement of f σ8 = 0:43 ¹±0:03ºobs ¹±0:11ºcosmic out to z = 0:05, in support of a ΛCDM cosmology. 1 INTRODUCTION in order to constrain the growth rate of large scale struc- tures and related parameters. On the one hand, Hudson Since the late 70's, several publications discussed the theory 0:55 & Turnbull(2012) measured f σ8 ≡ Ωm σ8 = 0:40 ± 0:07 of galaxy pairwise peculiar velocity statistics, such as the by comparing the observed peculiar velocities of 245 su- 2-point peculiar velocity correlation function ( 1 and 2) or pernovae (extracted from a compilation dubbed the First the mean pairwise velocity (v12; Monin & Yaglom 1975; Amendment, A1) to the galaxy density field predicted by Davis & Peebles 1977; Peebles 1980, 1987; Gorski 1988). It the Point Source Catalogue Redshift Survey (PSCz, Saun- has been shown that such statistics can be measured di- ders et al. 2000). This method has been later applied by rectly from only the radial part of peculiar velocities. Since Carrick et al.(2015) on galaxies from the 2M++ redshift these statistics are related to the growth factor of large scale compilation (Lavaux & Hudson 2011), finding a much more structures f = Ωγ , where γ is the growth index (Lahav et al. m accurate estimate of the growth factor f σ8 = 0:401 ± 0:024. 1991), observed peculiar velocities can be used as cosmolog- On the other hand, Johnson et al.(2014) analyzed the two- ical probes to estimate the matter density parameter Ωm point statistics of the peculiar velocity field and obtained (Ferreira et al. 1999; Juszkiewicz et al. 1999). However, f f σ8 = 0:418 ± 0:065 from a sample gathering peculiar veloc- and σ8, the amplitude of the density fluctuations on 8 Mpc ities of ∼ 9,200 galaxies from the Six Degree Field Galaxy −1 h scales (where h = H0/100 and H0 is the Hubble con- Survey peculiar velocity catalog (6dFGS, Jones et al. 2004, stant), are degenerate and cannot be constrained separately 2006, 2009) and various supernovae distance measurements. when using only galaxy peculiar velocity data. Alternatively, using again the same two-point statistic (v12) The first attempts of constraining cosmological param- as Juszkiewicz et al.(2000) and Feldman et al.(2003), ap- eters such as the density parameter have been made by plied on the Cosmicflows-2 catalog containing ∼8,000 galaxy Peebles(1976), Kaiser(1990) and Hudson(1994). Later, distances (CF2, Tully et al. 2013), Ma et al.(2015) found Juszkiewicz et al.(2000) gave Ωm = 0:35 ± 0:15 with mea- Ω0:6 +0:384 +0:73 surprising results: m h = 0:102−0:044 and σ8 = 0:39−0:1 . surements of the mean pairwise velocity on the Mark III Moreover, by measuring the covariance of radial peculiar catalog of radial peculiar velocities of roughly 3,000 spi- velocities in two catalogs, a sample of 208 low redshift su- ral and elliptical galaxies (Willick et al. 1995, 1996, 1997). pernovae (named SuperCal) and a set of roughly 9,000 pe- arXiv:1901.03530v2 [astro-ph.CO] 19 Mar 2019 Then, Feldman et al.(2003) obtained a very similar value of culiar velocities from 6dFGS, Huterer et al.(2016) evalu- +0:17 +0:22 Ωm = 0:30 and also measured σ8 = 1:13 . This was ated +0:048 at . Finally, Adams & Blake −0:07 −0:23 f σ8 = 0:428−0:045 z = 0:02 done by using the same estimator of Juszkiewicz et al.(2000) (2017) measured +0:067 by modelling the cross- f σ8 = 0:424−0:064 , but on a much larger dataset combining peculiar velocities covariance of the galaxy overdensity and peculiar velocity of approximately 6,400 galaxies extracted from several cat- fields and applying their analysis to the observed peculiar alogs: Mark III, Spiral Field I-Band (Giovanelli et al. 1994, velocities from the 6dFGS data. 1997a,b; Haynes et al. 1999a,b), Nearby Early-type Galaxies Survey (da Costa et al. 2000) and the Revised Flat Galaxy Despite the increase in number of measurements and in Catalog (Karachentsev et al. 2000). redshift coverage, peculiar velocity catalogs are still not large A decade later, datasets improved and methods of an- enough and remain noticeably sparse at large distances. alyzing peculiar velocity to constrain cosmology evolved. Hence, growth rate estimations are affected by uncertainties Some authors proposed new statistical methodologies using introduced by cosmic variance as they are obtained from lo- observed peculiar velocities, which differs from v12 and 1;2, cal observations. Hellwing et al.(2016) discussed the effect © 0000 The Authors 2 Dupuy et al. of the observer location in the universe on the derivation in Gaussian distributed errors on peculiar velocities: of two-point peculiar velocity statistics (v , and ) by 12 1 2 cz considering two sets of randomly chosen observers and Lo- u = cz ln : (1) cal Group -like observers. The authors showed that the local H0d environment, especially the Virgo cluster, systematically in- Equation1 will be used throughout this paper to derive troduces deviations from predictions. radial peculiar velocities from observed distances. More recently, Nusser(2017) measured f σ8 = 0:40±0:08 This article will only focus on the CF3 distances cata- by measuring velocity - density correlations on the largest log. Two radial peculiar velocity samples will be considered: and most recent catalog of ∼ 18,000 accurate galaxy dis- the ungrouped sample and the grouped sample, containing tances, Cosmicflows-3 (CF3, Tully et al. 2016). And, last galaxies and groups of galaxies respectively. Groups are fre- but not least, Wang et al.(2018) analyzed the peculiar ve- quently used by authorsp because they allow to reduce un- locity correlation functions through the estimators 1 and certainties with an N improvement on observed distances, 2 applied to the Cosmicflows catalogs (CF2 and CF3) to and thus on radial peculiar velocities. These uncertainties constrain cosmological parameters: Ω +0:205 and m = 0:315−0:135 are due to the virial motions of group members. However, +0:440. σ8 = 0:92−0:295 the methodology presented in this article is valid for pairs On the grounds of the previous literature works intro- of galaxies, and not for pairs of groups of galaxies. The CF3 duced above, this article studies two classical two-point pe- grouped catalog is tested in this article since recent studies culiar velocity statistics, using radial peculiar velocities pro- (Ma et al. 2015; Nusser 2017, both introduced above in Sec- vided by the Cosmicflows-3 catalog, to constrain the local tion1) made use of the grouped versions of the Cosmicflows value of the growth rate factor f σ8. Its structure is orga- catalogs to derive f σ8. However, it will be seen in the discus- nized as follows. Section 2 provides details on the peculiar sion that using grouped data to constrain the growth rate velocity data used for the analysis. The methodology of two- leads to incoherent results. point correlation functions of peculiar velocities is described Tully et al.(2016) shows that the most consistent value in Section 3 and is tested and validated on mocks in Sec- of the Hubble constant with CF3 distances when computing −1 −1 tion 4. Section 5 shows the velocity statistics measured on radial peculiar velocities is H0 = 75 ± 2 km s Mpc . This observed peculiar velocities. The main result of this article, value is preferred as it minimizes the monopole term with the estimate of the growth rate from Cosmicflows radial pe- CF3 distances and results in a tiny global radial infall and culiar velocities, is discussed in Section 6. outflow in the peculiar velocity field. A larger value of H0 would give a large overall radial infall towards the position of the observer, while choosing a smaller H0 would yield a large radial outflow (cf. Figure 21 in Tully et al. 2016). For these reasons, in this article the value H0 = 75 km 2 DATA s−1 Mpc−1 is used to compute radial peculiar velocities of 2.1 Observed peculiar velocities: Cosmicflows-3 CF3 galaxies and groups. We note that this high value of H0 is consistent with other values of the Hubble constant The latest CF3 catalog (Tully et al. 2016) provides dis- measured in the local universe. tances for 17,648 galaxies which can be redistributed within 11,936 groups, up to 150 Mpc h−1. It is an expansion of the previous CF2 catalog (Tully et al. 2013). It contains 2.2 Cosmicflows mock catalogs 8,188 galaxy distances with a homogeneous volume cover- age up to 80 Mpc h−1, mostly derived with the Tully-Fisher A three-dimensional peculiar velocity field computed with (TF) relation (Tully & Fisher 1977), linking the luminosity the Constrained Realization (CR) methodology (Hoffman & to the HI line width for spiral galaxies, and the Fundamen- Ribak 1991) is considered to construct mock catalogs.