# The dipole anisotropy of WISE × SuperCOSMOS number counts

The dipole anisotropy of WISE × SuperCOSMOS number counts Abstract We probe the isotropy of the Universe with the largest all-sky photometric redshift data set currently available, namely WISE × SuperCOSMOS. We search for dipole anisotropy of galaxy number counts in multiple redshift shells within the 0.10 < z < 0.35 range, for two subsamples drawn from the same parent catalogue. Our results show that the dipole directions are in good agreement with most of the previous analyses in the literature, and in most redshift bins the dipole amplitudes are well consistent with Lambda cold dark matter-based mocks in the cleanest sample of this catalogue. In the z < 0.15 range, however, we obtain a persistently large anisotropy in both subsamples of our data set. Overall, we report no significant evidence against the isotropy assumption in this catalogue except for the lowest redshift ranges. The origin of the latter discrepancy is unclear, and improved data may be needed to explain it. large-scale structure of Universe, cosmology: observations, cosmology: theory 1 INTRODUCTION The current standard model of cosmology, called Lambda cold dark matter (ΛCDM), assumes Friedmann–Lemaître-Robertson–Walker as its background metric, and that the Universe is approximately homogeneous and isotropic on large scales, a feature of the so-called ‘cosmological principle’ (CP). Despite the good agreement between ΛCDM and a plethora of cosmological observations (e.g. Planck Collaboration XIII 2016; SDSS Collaboration 2017), direct tests of the CP need to be performed in order to assess whether it is a valid cosmological assumption or just mathematical simplification. Persistent lack of isotropy or homogeneity on large scales would require a complete reformulation of the current cosmological scenario, and thus of our understanding of the Universe. It is well accepted that the spatial distribution of cosmic objects becomes statistically homogeneous on scales around 100–150 Mpc h−1 (Hogg et al. 2005; Scrimgeour et al. 2012; Laurent et al. 2016; Pandey & Sarkar 2016; Gonçalves et al. 2018; Ntelis et al. 2017). The only major dipole anisotropy, observed in the cosmic microwave background, is in the standard framework interpreted as an imprint of our own peculiar motion, rather than actual cosmological signal (Kogut et al. 1993; Planck Collaboration XXVII 2014). We will refer to it as the kinematic dipole hereafter (Maartens et al. 2018). However, probing this quantity is not our goal here, and we look instead for a number count dipole in the intrinsic galaxy distribution.1 The observed galaxy count dipole is not expected to be aligned with the kinematic one since the intrinsic galaxy density fluctuations dominate over this signal on the scales of z < 1 (Gibelyou & Huterer 2012; Yoon & Huterer 2015). However, the presence of a larger dipole than predicted by these intrinsic fluctuations in the standard model would thus indicate deviations from isotropy or homogeneity. Therefore, all-sky infrared and optical catalogues are ideal probes for this test. This was previously performed by Itoh et al. (2010), Gibelyou & Huterer (2012), Appleby & Shafieloo (2014), Yoon et al. (2014), Alonso et al. (2015), Bengaly et al. (2017), and none of these papers reported compelling signal against the CP. In this work, we reassess the isotropy of the Universe on the z < 0.5 scales using the WISE × SuperCOSMOS catalogue (Bilicki et al. 2016, hereafter WI×SC),2 which is currently the largest and deepest all-sky photometric redshift (photo-z) data set available. We check for concordance between the number count dipole in WI×SC and in synthetic data sets assuming real data specifications, in addition to the power spectrum of the ΛCDM model. We therefore extend the analysis of Bengaly et al. (2017) where another WISE-based catalogue was used, namely WISE-2MASS (W2M, Kovács & Szapudi 2015), which not only was shallower than WI×SC, but also did not include redshift information, and it comprised 10 times fewer sources. If found, strong discrepancies between the observational data and their respective mocks would hint at potential evidence against the cosmic isotropy assumption, unless we are restricted by persisting systematics. 2 DATA SELECTION The WI×SC photo-z catalogue (Bilicki et al. 2016) is based on a cross-match of two photometric all-sky samples, WISE (Wright et al. 2010) and SuperCOSMOS (Peacock et al. 2016). This data set is flux-limited to B < 21, R < 19.5, and 13.8 < W1 < 17 (3.4 μm, Vega) and provides photo-zs for all the included sources, ranging from 0 < z < 0.4 (mean 〈z〉 ≃ 0.2) with typical photo-z error σδz = 0.033 (1 + z). The data come with a fiducial mask which removes low Galactic latitudes (|b| ≤ 10° up to |b| ≤ 17° by the Bulge), areas of high Galactic extinction [E(B − V) > 0.25], as well as other contaminated regions. Here we however apply more strict cuts to avoid selection effects due to extinction, namely E(B − V) > 0.10, and require 0.10 < zphot < 0.35 to remove low-redshift prominent structures as well as the high-redshift tail of WI×SC, where the data are very sparse. The original WI×SC data have had specific galaxy selection applied to remove stellar and quasar contamination (the latter being minimal). As purity is more important for our purposes than completeness, we applied a more aggressive colour cut than originally in Bilicki et al. (2016), namely W1 − W2 > 0.2 over the entire sky, which should guarantee very efficient star removal (Jarrett et al. 2017). We will call this WI×SC sample with the additional cleanup ‘Fiducial’ from now on. In an alternative approach to galaxy identification in WI×SC, Krakowski et al. (2016) used the Support Vector Machines classification algorithm which separates sources in multicolour space using best-fitting hyperplanes, and obtained a purer galaxy sample than the main WI×SC one, yet less complete. This ‘SVM’ data set comes with probability estimates of sources belonging to a given class, and we applied a conservative lower cutoff of pgal > 2/3, so that our selected objects have at least 67 per cent of probability of being a galaxy rather than any other class (star or active galactic nucleus). This cut results in pgal, mean ≃ 0.90 in each redshift bin, besides >35 per cent of the SVM sources with pgal > 0.95. After applying the WI×SC mask as well as our additional cuts on E(B − V) and photo-z’s, we obtained samples of 9.5 and 8.3 million galaxies over fsky ≃ 0.545 for the Fiducial and SVM data sets, of median redshifts $$z\mathrm{^{Fid}_{med}} \simeq 0.22$$ and $$z\mathrm{^{SVM}_{med}} \simeq 0.20$$. Depending on the redshift range, these two WI×SC subsets typically have ∼50–75 per cent common sources. We show the redshift distribution of both data sets in Fig. 1; number count maps of these samples for the full redshift range (0.10 < z < 0.35) are featured in Fig. 2, and Fig. 3 exhibits objects in the 0.15 < z ≤ 0.20 bin only. All maps were produced using HEALPix (Górski et al. 2005) with resolution of Nside = 128 (pixel size of ∼0.5°). Figure 1. View largeDownload slide The redshift distribution of the WI×SC Fiducial (red dashed curve) and of the SVM sample (black solid curve), both given in counts per square arcminute per redshift bin. Figure 1. View largeDownload slide The redshift distribution of the WI×SC Fiducial (red dashed curve) and of the SVM sample (black solid curve), both given in counts per square arcminute per redshift bin. Figure 2. View largeDownload slide Left-hand panel: The density contrast of galaxy number counts (clipped at δmax = 2.0 to ease visualization) of the WI×SC Fiducial sample in the 0.10 < z < 0.35 range, i.e. the full sample analysed here. Right-hand panel: Same as the left-hand panel, but for the SVM sample. The grey area corresponds to the masked region as discussed in Section 2. Figure 2. View largeDownload slide Left-hand panel: The density contrast of galaxy number counts (clipped at δmax = 2.0 to ease visualization) of the WI×SC Fiducial sample in the 0.10 < z < 0.35 range, i.e. the full sample analysed here. Right-hand panel: Same as the left-hand panel, but for the SVM sample. The grey area corresponds to the masked region as discussed in Section 2. Figure 3. View largeDownload slide Same as Fig. 2, but for galaxies within 0.10 < z ≤ 0.15 only. Figure 3. View largeDownload slide Same as Fig. 2, but for galaxies within 0.10 < z ≤ 0.15 only. 3 METHODOLOGY The isotropy of galaxy number counts is estimated with the delta-map method first presented in Alonso et al. (2015) (see also Bengaly et al. 2017), in which the sky is decomposed into 768 large healpix pixels (Nside = 8), and hemispheres are constructed using the respective pixel centres as symmetry axes. The delta-map is then computed as   \begin{eqnarray} \Delta _i = 2 \times \left( \frac{n_i^{\rm U} - n_i^{\rm D}}{n_i^{\rm U} + n_i^{\rm D}} \right)\,, \end{eqnarray} (1)where $$n_i^j \equiv N^j_i/(4\pi f^j_{{\rm sky},i})$$ are counts in the i-th hemisphere, i ∈ 1, ..., 768, j represents the hemispheres indexes ‘up’ (U) and ‘down’ (D) defined according to this pixellization scheme, whereas $$N^j_i$$ and $$f^j_{{\rm sky},i}$$ are the total number of objects and the observed fraction of the sky encompassed in each of these hemispheres, respectively. The dipole of galaxy number counts is obtained by expanding the delta-map from (1) into spherical harmonics. From the {aℓm}, coefficients we select the ℓ = 1 terms, i.e. the {a1m}, to reconstruct only the dipole component of the delta-map, Δdip = ∑a1mY1m. Therefore, we quote the maximum value of the Δdip map as our dipole amplitude A, in addition to the direction where it points to. In this work, the WI×SC catalogue is additionally decomposed into redshift shells before the delta-map calculation: cumulative ones, i.e. 0.10 < z ≤ 0.15; 0.10 < z ≤ 0.20; ...; 0.10 < z < 0.35, and disjoint ones, 0.10 < z ≤ 0.15; 0.15 < z ≤ 0.20; ...; etc. The statistical significance of the delta-map dipoles is calculated from WI×SC mock catalogues produced with the flask code3 (Xavier et al. 2016). These mocks are full-sky lognormal realizations of the density field in redshift shells based on the input angular power spectra $$C_{\ell }^{(z_i z_j)}$$ (zi and zj denoting different redshift shells) provided by camb sources (Challinor & Lewis 2011), which are Poisson-sampled according to the WI×SC selection function. The input $$C_{\ell }^{(z_i z_j)}$$ were computed for redshift distributions that are convolutions of the Δz = 0.05 shells with Gaussian scatter of σδz = 0.033 (1 + z) (representing WI×SC photo-z errors) using ΛCDM best-fitting parameters (Planck Collaboration XIII 2016), and they include linear redshift space distortions, gravitational lensing distortions of the volume elements, and non-linear contributions modelled by halofit (Smith et al. 2003; Takahashi et al. 2012). We applied a linear scaling factor to each $$C_{\ell }^{(z_i z_j)}$$ – playing a role similar to galaxy bias – which was used to match the variances of counts in pixels to the ones observed in the real data. We additionally compared the Fiducial data set source distribution to SDSS (York et al. 2000) in a 1°-wide strip centred on declination δ = 30° and estimated that it still contained a fraction fstar of stars that is well fitted by fstar = 0.71exp ( − 0.09|b|) + 0.013. Therefore, we Poisson-sampled stars according to this distribution and included them in our mocks. By adjusting the selection function normalization and the $$C_{\ell }^{(z_i z_j)}$$ scaling factors, we made our simulations match the Fiducial data set in terms of fstar, mean number of objects (galaxies + stars) and variance in the pixels.4 Following the prescriptions above, we produced 1000 full-sky mocks of both Fiducial and SVM data sets in each Δz = 0.05 photo-z bin, spanning the 0.10 < z < 0.35 range, using the same resolution as for the real data maps (Nside = 128). From these realizations, we computed how many of them featured a dipole amplitude at least as large as the real data for each z-bin analysed, hereafter quoted as p-values. Low p-values, such as p < 0.005 (Planck Collaboration XIII 2016), will be regarded as an indication that the model cannot fully describe the observations, and thus might be interpreted as challenging the concordance model. 4 RESULTS The dipoles resulting from the delta-map analyses of the two WI×SC samples are shown for the full redshift range in Fig. 4, while the dipole directions and amplitudes for each redshift bin are presented in Table 1 for both Fiducial and SVM data sets. The error bars of A and (l, b) were estimated from 1000 simulations with fixed underlying density fluctuations (and therefore fixed dipole direction and amplitude), but with different Poisson noise, for each z-bin. Then, σA corresponds to the average deviation from the fiducial dipole value, i.e. the quoted A, and σ(θ) denotes the average angular distance from the observed dipole direction, as given by this set of simulations. We readily verify that the dipole amplitude decreases when we probe the number counts at larger depths, as it goes from A ≃ 0.10 in the thinnest (0.10 < z ≤ 0.15) to A ≃ 0.03 in the thickest (0.10 < z < 0.35) cumulative shell, while the deepest shell (0.30 < z < 0.35) gives A = 0.01 − 0.04 depending on the sample. This behaviour was also noted by Yoon et al. (2014) when comparing their results with those in Gibelyou & Huterer (2012), which used shallower catalogues in some of their analyses. This amplitude decrease with increased redshift is due to the smoother rms density fluctuations in the large-scale structure in higher z, in addition to the increasing volume probed in these larger cumulative shells. Figure 4. View largeDownload slide Left-hand panel: The Delta-map dipole of the WI×SC Fiducial data set in the 0.10 < z < 0.35 range. Right-hand panel: Same as the left-hand panel, but for the WI×SC SVM galaxies. Both maps are represented in Galactic coordinates. Further details on the amplitudes and directions, as well as on the other redshift bins, are presented in Table 1. Figure 4. View largeDownload slide Left-hand panel: The Delta-map dipole of the WI×SC Fiducial data set in the 0.10 < z < 0.35 range. Right-hand panel: Same as the left-hand panel, but for the WI×SC SVM galaxies. Both maps are represented in Galactic coordinates. Further details on the amplitudes and directions, as well as on the other redshift bins, are presented in Table 1. Table 1. The amplitude (and its respective error bar down to two significant digits; col.2), direction (col.3), uncertainty on the direction (col.4), and statistical significance (given in p-values; col.5) of the WI×SC dipole obtained from the Fiducial (top) and SVM (bottom) samples. We highlight the cases where significant deviation from isotropy according to the p < 0.005 criterion was found. z-bin (Fiducial)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\it {\bf z}}} \le 0.15}$$  1.474 (18)  (56.5°, 69.8°)  0.6°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.20}$$  0.701 (11)  (20.8°, 70.2°)  0.7°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.25}$$  0.394 (09)  (346.1°, 69.8°)  1.0°  0.001  0.10 < z ≤ 0.30  0.250 (07)  (317.9°, 61.2°)  1.5°  0.084  0.10 < z < 0.35  0.225 (07)  (319.9°, 59.7°)  1.5°  0.129  0.15 < z ≤ 0.20  0.303 (13)  (325.2°, 43.8°)  2.5°  0.129  0.20 < z ≤ 0.25  0.200 (10)  (272.8°, −9.9°)  6.9°  0.332  0.25 < z ≤ 0.30  0.293 (13)  (262.6°, −42.2°)  3.2°  0.017  0.30 < z < 0.35  0.112 (22)  (27.7°, −59.3°)  9.7°  0.773  z-bin (SVM)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.15}$$  0.863 (14)  (29.3°, 65.7°)  1.0°  < 0.001  0.10 < z ≤ 0.20  0.417 (08)  (342.1°, 26.3°)  2.6°  0.019  0.10 < z ≤ 0.25  0.371 (06)  (332.6°, −3.2°)  2.8°  0.010  0.10 < z ≤ 0.30  0.320 (06)  (335.0°, −7.1°)  2.7°  0.010  0.10 < z < 0.35  0.316 (06)  (339.6°, −9.7°)  2.7°  0.007  $$\mathbf {0.15 < {\rm {\bf {\it z}}} \le 0.20}$$  0.674 (14)  (315.4°, −34.2°)  1.5°  < 0.001  $$\mathbf {0.20 < {\rm {\it {\bf z}}} \le 0.25}$$  0.682 (16)  (310.5°, −52.4°)  1.2°  < 0.001  0.25 < z ≤ 0.30  0.166 (17)  (13.3°, −48.5°)  5.1°  0.236  $$\mathbf {0.30 < {\rm {\bf {\it z}}} < 0.35}$$  0.370 (19)  (18.6°, −18.8°)  8.7°  < 0.001  z-bin (Fiducial)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\it {\bf z}}} \le 0.15}$$  1.474 (18)  (56.5°, 69.8°)  0.6°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.20}$$  0.701 (11)  (20.8°, 70.2°)  0.7°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.25}$$  0.394 (09)  (346.1°, 69.8°)  1.0°  0.001  0.10 < z ≤ 0.30  0.250 (07)  (317.9°, 61.2°)  1.5°  0.084  0.10 < z < 0.35  0.225 (07)  (319.9°, 59.7°)  1.5°  0.129  0.15 < z ≤ 0.20  0.303 (13)  (325.2°, 43.8°)  2.5°  0.129  0.20 < z ≤ 0.25  0.200 (10)  (272.8°, −9.9°)  6.9°  0.332  0.25 < z ≤ 0.30  0.293 (13)  (262.6°, −42.2°)  3.2°  0.017  0.30 < z < 0.35  0.112 (22)  (27.7°, −59.3°)  9.7°  0.773  z-bin (SVM)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.15}$$  0.863 (14)  (29.3°, 65.7°)  1.0°  < 0.001  0.10 < z ≤ 0.20  0.417 (08)  (342.1°, 26.3°)  2.6°  0.019  0.10 < z ≤ 0.25  0.371 (06)  (332.6°, −3.2°)  2.8°  0.010  0.10 < z ≤ 0.30  0.320 (06)  (335.0°, −7.1°)  2.7°  0.010  0.10 < z < 0.35  0.316 (06)  (339.6°, −9.7°)  2.7°  0.007  $$\mathbf {0.15 < {\rm {\bf {\it z}}} \le 0.20}$$  0.674 (14)  (315.4°, −34.2°)  1.5°  < 0.001  $$\mathbf {0.20 < {\rm {\it {\bf z}}} \le 0.25}$$  0.682 (16)  (310.5°, −52.4°)  1.2°  < 0.001  0.25 < z ≤ 0.30  0.166 (17)  (13.3°, −48.5°)  5.1°  0.236  $$\mathbf {0.30 < {\rm {\bf {\it z}}} < 0.35}$$  0.370 (19)  (18.6°, −18.8°)  8.7°  < 0.001  View Large The comparison between the dipole amplitude of the actual observations and lognormal WI×SC mocks, for the cumulative bins, shows only marginal agreement for the SVM sample in the two thickest bins, while the Fiducial sample performs slightly better, reaching p = 0.129 in the largest redshift shell. When analysing the tomographic bins, on the other hand, we find good consistency between the Fiducial data and its mocks, however the performance of the SVM sample was good only in the 0.25 < z ≤ 0.30 shell. Moreover, we find that both SVM and Fiducial data show a larger dipole amplitude than the mocks in the lowest redshift shell, 0.10 < z ≤ 0.15, which interestingly is the bin presenting the best mutual agreement between these two samples. However, we also note that the concordance between data and simulations improves when the cumulative redshift shells encompass more distant galaxies. This is more evident for the Fiducial sample, where p > 0.05 in the two thickest redshift shells, yet less than ∼ 2 per cent of the SVM realizations have A larger than the real data in the same ranges. In the tomographic z-bins, we found that the Fiducial data is in good concordance with its ΛCDM-based mocks except for the 0.25 < z ≤ 0.30 bin which, interestingly, is the redshift shell where the SVM dipole amplitude agrees best with simulations. From these results, we conclude that the Fiducial data set shows better concordance with its respective mocks than the SVM one, and that the WI×SC data agree with the isotropy hypothesis of the Universe apart from the lowest redshift ranges examined here. At present, we cannot unambiguously resolve the reason for the latter discrepancy, and better all-sky data covering these redshifts will be needed for that purpose. We also stress that the directions of the number count dipoles in cumulative redshift shells, especially in the range 0.10 < z < 0.35 of the SVM data set, are in good agreement with similar analyses in the literature. We calculate the probabilities Pθ that the alignments between the corresponding directions would occur at random such as   \begin{eqnarray} P_\theta = \frac{1}{4\pi }\int _0^\theta 2\pi \sin \theta ^{\prime }\,\mathrm{d}\theta ^{\prime } = \frac{1-\cos \theta }{2}, \end{eqnarray} (2)where cos θ = sin b1sin b2 + cos b1cos b2cos (l1 − l2). A quantitative assessment of the concordance between these dipole directions is provided in Table 2. For instance, Bengaly et al. (2017) obtained a dipole anisotropy with A = 0.0507 pointing towards (l, b) = (323°, −5°) in the W2M catalogue which peaks at z ∼ 0.14, which is consistent with the results from Yoon et al. (2014), i.e. (l, b) = (310°, −15°). Furthermore, Appleby & Shafieloo (2014) and Alonso et al. (2015) found, using different methods, preferred directions of respectively (l, b) = (320°, 6°) and (l, b) = (315°, 30°) in the 2MPZ (Bilicki et al. 2014) Table 2. The probability that randomly picked directions are closer to each other than the measured distance between the corresponding dipoles, where small values indicate strongly aligned directions. WI×SC Fid full and WI×SC SVM full correspond to the Fiducial and SVM samples analysed in the 0.10 < z < 0.35 range, respectively, while both WI×SC Lowz cases represent the 0.10 < z ≤ 0.15 bins. The remaining directions were obtained using the WISE-2MASS and 2MASS photo-z data sets (respectively W2M and 2MPZ), as reported by Bengaly et al. (2017), Alonso et al. (2015), Yoon et al. (2014), Appleby & Shafieloo (2014) for W2M-17, 2MPZ-15, W2M-14, and 2MPZ-14, respectively. Dipole  WI×SC Fid full  WI×SC SVM full  W2M-17  2MPZ-15  W2M-14  2MPZ-14  WI×SC Fid low-z  WI×SC SVM low-z  WI×SC Fid full  –  0.227  0.247  0.249  0.275  0.263  0.815  0.764  WI×SC SVM full  0.227  –  0.007  0.013  0.013  0.091  0.253  0.239  W2M-17  0.247  0.007  –  0.005  0.016  0.072  0.287  0.259  2MPZ-15  0.249  0.013  0.005  –  0.022  0.067  0.377  0.340  W2M-14  0.275  0.013  0.016  0.022  –  0.076  0.217  0.186  2MPZ-14  0.263  0.091  0.072  0.067  0.076  –  0.580  0.541  WI×SC Fid low-z  0.815  0.253  0.287  0.377  0.217  0.580  –  0.233  WI×SC SVM low-z  0.764  0.239  0.259  0.340  0.186  0.541  0.233  –  Dipole  WI×SC Fid full  WI×SC SVM full  W2M-17  2MPZ-15  W2M-14  2MPZ-14  WI×SC Fid low-z  WI×SC SVM low-z  WI×SC Fid full  –  0.227  0.247  0.249  0.275  0.263  0.815  0.764  WI×SC SVM full  0.227  –  0.007  0.013  0.013  0.091  0.253  0.239  W2M-17  0.247  0.007  –  0.005  0.016  0.072  0.287  0.259  2MPZ-15  0.249  0.013  0.005  –  0.022  0.067  0.377  0.340  W2M-14  0.275  0.013  0.016  0.022  –  0.076  0.217  0.186  2MPZ-14  0.263  0.091  0.072  0.067  0.076  –  0.580  0.541  WI×SC Fid low-z  0.815  0.253  0.287  0.377  0.217  0.580  –  0.233  WI×SC SVM low-z  0.764  0.239  0.259  0.340  0.186  0.541  0.233  –  View Large 5 CONCLUSIONS In this work, we probed the cosmological isotropy at the 0.10 < z < 0.35 interval through the directional dependence of the galaxy counts in the WISE × SuperCOSMOS catalogue. To do so, we adopted a hemispherical comparison method, and its dipole contribution provided our diagnostic of cosmological anisotropy. The observational samples consisted of two data sets, namely ‘Fiducial’ and ‘SVM’, which differ in how galaxies were identified in them: through colour cuts in the former, and by means of automatized classification in the latter. Thanks to the availability of redshift information, we were able to perform this test in tomographic z-bins, which enabled a natural extension of the analysis carried out in Bengaly et al. (2017) with the shallower W2M sample. We found overall good agreement between the WI×SC dipole directions obtained here and those from previous analyses in the literature. As far as the dipole amplitudes are concerned, their level of agreement with ΛCDM mocks is different for various redshift shells and sample selections. In both Fiducial and SVM cases, the lowest redshift bin 0.10 < z < 0.15 is discrepant from the mocks; at higher redshifts, the Fiducial sample exhibits good agreement with the simulations, which is generally not the case for the SVM one. Interestingly, the z < 0.15 range is the only case in which both samples agree with each other regarding the dipole direction. In all other cases, the dipole amplitudes and directions significantly differ between Fiducial and SVM selections in individual z-shells. Although there is some interception of roughly ∼50–75 per cent between the two WI×SC-based data sets, they rely upon different methods to separate galaxies from stars and quasars, resulting in distinct samples from the same catalogue, and perhaps selecting different galaxy types for each one of them. However, it is very unlikely that this difference would explain such effect, as no significant colour discrepancy was found between the two samples. Even if we credit the better agreement between the Fiducial sample and the lognormal realizations to a more rigorous criterion to eliminate stars, as described in Section 2, or to different galaxy types, this procedure still cannot explain the large A obtained for both pre-selections in the 0.10 < z ≤ 0.15 redshift shell. This result could be an indication of either related systematics in both data sets, or the presence of very large, local density fluctuations, which can increase the number counts dipole as pointed out by Rubart et al. (2014). A more thorough investigation of these hypotheses will be pursued in the future, but it may require better all-sky data sets, which at present are not available for the relevant redshift ranges. This work presents the first contribution of the WI×SC catalogue to cosmology in the form of an updated test of the large-scale isotropy of the Universe, in which we found no significant departure from this fundamental hypothesis for z > 0.15, yet we are still very limited by the completeness and systematics of the available data. None the less, the WI×SC data set can be considered a testbed for forthcoming surveys, especially LSST (LSST Science Collaboration 2009) and SKA (Schwarz et al. 2015), as they will reach much deeper scales on large sky areas and, therefore, will enable much more precise tests of the CP in the years to come (Itoh et al. 2010; Yoon & Huterer 2015). Acknowledgements CAPB acknowledges South African SKA Project, besides CAPES for financial support in the early stage of this work. CPN is supported by the DTI-PCI Programme of the Brazilian Ministry of Science, Technology, Innovation and Communications (MCTIC). HSX acknowledges FAPESP for financial support. MB is supported by the Netherlands Organization for Scientific Research, NWO, through grant number 614.001.451, and by the Polish National Science Center under contract #UMO-2012/07/D/ST9/02785. AB thanks the Capes PVE project 88881.064966/2014-01. JSA is supported by CNPq and FAPERJ. We thank the Wide Field Astronomy Unit at the Institute for Astronomy, Edinburgh, for archiving the WISE × SuperCOSMOS catalogue. We also acknowledge using the healpix package for the derivation of the results presented in this work. Footnotes 1 For simplicity, we look for the largest order anisotropic mode, which is a dipole in the number counts of galaxies. 2 http://ssa.roe.ac.uk/WISExSCOS 3 http://www.astro.iag.usp.br/∼flask 4 The simulation input files are available at: http://www.astro.iag.usp.br/flask/sims/wisc17.tar.gz REFERENCES Alonso D. et al.  , 2015, MNRAS , 449, 670 https://doi.org/10.1093/mnras/stv309 CrossRef Search ADS   Appleby. S., Shafieloo A., 2014, J. Cosmol. Astropart. 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# The dipole anisotropy of WISE × SuperCOSMOS number counts

, Volume 475 (1) – Mar 1, 2018
5 pages

/lp/ou_press/the-dipole-anisotropy-of-wise-supercosmos-number-counts-5Z4Lcg75KV
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journal_eissn:11745-3933
ISSN
1745-3925
eISSN
1745-3933
D.O.I.
10.1093/mnrasl/sly002
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### Abstract

Abstract We probe the isotropy of the Universe with the largest all-sky photometric redshift data set currently available, namely WISE × SuperCOSMOS. We search for dipole anisotropy of galaxy number counts in multiple redshift shells within the 0.10 < z < 0.35 range, for two subsamples drawn from the same parent catalogue. Our results show that the dipole directions are in good agreement with most of the previous analyses in the literature, and in most redshift bins the dipole amplitudes are well consistent with Lambda cold dark matter-based mocks in the cleanest sample of this catalogue. In the z < 0.15 range, however, we obtain a persistently large anisotropy in both subsamples of our data set. Overall, we report no significant evidence against the isotropy assumption in this catalogue except for the lowest redshift ranges. The origin of the latter discrepancy is unclear, and improved data may be needed to explain it. large-scale structure of Universe, cosmology: observations, cosmology: theory 1 INTRODUCTION The current standard model of cosmology, called Lambda cold dark matter (ΛCDM), assumes Friedmann–Lemaître-Robertson–Walker as its background metric, and that the Universe is approximately homogeneous and isotropic on large scales, a feature of the so-called ‘cosmological principle’ (CP). Despite the good agreement between ΛCDM and a plethora of cosmological observations (e.g. Planck Collaboration XIII 2016; SDSS Collaboration 2017), direct tests of the CP need to be performed in order to assess whether it is a valid cosmological assumption or just mathematical simplification. Persistent lack of isotropy or homogeneity on large scales would require a complete reformulation of the current cosmological scenario, and thus of our understanding of the Universe. It is well accepted that the spatial distribution of cosmic objects becomes statistically homogeneous on scales around 100–150 Mpc h−1 (Hogg et al. 2005; Scrimgeour et al. 2012; Laurent et al. 2016; Pandey & Sarkar 2016; Gonçalves et al. 2018; Ntelis et al. 2017). The only major dipole anisotropy, observed in the cosmic microwave background, is in the standard framework interpreted as an imprint of our own peculiar motion, rather than actual cosmological signal (Kogut et al. 1993; Planck Collaboration XXVII 2014). We will refer to it as the kinematic dipole hereafter (Maartens et al. 2018). However, probing this quantity is not our goal here, and we look instead for a number count dipole in the intrinsic galaxy distribution.1 The observed galaxy count dipole is not expected to be aligned with the kinematic one since the intrinsic galaxy density fluctuations dominate over this signal on the scales of z < 1 (Gibelyou & Huterer 2012; Yoon & Huterer 2015). However, the presence of a larger dipole than predicted by these intrinsic fluctuations in the standard model would thus indicate deviations from isotropy or homogeneity. Therefore, all-sky infrared and optical catalogues are ideal probes for this test. This was previously performed by Itoh et al. (2010), Gibelyou & Huterer (2012), Appleby & Shafieloo (2014), Yoon et al. (2014), Alonso et al. (2015), Bengaly et al. (2017), and none of these papers reported compelling signal against the CP. In this work, we reassess the isotropy of the Universe on the z < 0.5 scales using the WISE × SuperCOSMOS catalogue (Bilicki et al. 2016, hereafter WI×SC),2 which is currently the largest and deepest all-sky photometric redshift (photo-z) data set available. We check for concordance between the number count dipole in WI×SC and in synthetic data sets assuming real data specifications, in addition to the power spectrum of the ΛCDM model. We therefore extend the analysis of Bengaly et al. (2017) where another WISE-based catalogue was used, namely WISE-2MASS (W2M, Kovács & Szapudi 2015), which not only was shallower than WI×SC, but also did not include redshift information, and it comprised 10 times fewer sources. If found, strong discrepancies between the observational data and their respective mocks would hint at potential evidence against the cosmic isotropy assumption, unless we are restricted by persisting systematics. 2 DATA SELECTION The WI×SC photo-z catalogue (Bilicki et al. 2016) is based on a cross-match of two photometric all-sky samples, WISE (Wright et al. 2010) and SuperCOSMOS (Peacock et al. 2016). This data set is flux-limited to B < 21, R < 19.5, and 13.8 < W1 < 17 (3.4 μm, Vega) and provides photo-zs for all the included sources, ranging from 0 < z < 0.4 (mean 〈z〉 ≃ 0.2) with typical photo-z error σδz = 0.033 (1 + z). The data come with a fiducial mask which removes low Galactic latitudes (|b| ≤ 10° up to |b| ≤ 17° by the Bulge), areas of high Galactic extinction [E(B − V) > 0.25], as well as other contaminated regions. Here we however apply more strict cuts to avoid selection effects due to extinction, namely E(B − V) > 0.10, and require 0.10 < zphot < 0.35 to remove low-redshift prominent structures as well as the high-redshift tail of WI×SC, where the data are very sparse. The original WI×SC data have had specific galaxy selection applied to remove stellar and quasar contamination (the latter being minimal). As purity is more important for our purposes than completeness, we applied a more aggressive colour cut than originally in Bilicki et al. (2016), namely W1 − W2 > 0.2 over the entire sky, which should guarantee very efficient star removal (Jarrett et al. 2017). We will call this WI×SC sample with the additional cleanup ‘Fiducial’ from now on. In an alternative approach to galaxy identification in WI×SC, Krakowski et al. (2016) used the Support Vector Machines classification algorithm which separates sources in multicolour space using best-fitting hyperplanes, and obtained a purer galaxy sample than the main WI×SC one, yet less complete. This ‘SVM’ data set comes with probability estimates of sources belonging to a given class, and we applied a conservative lower cutoff of pgal > 2/3, so that our selected objects have at least 67 per cent of probability of being a galaxy rather than any other class (star or active galactic nucleus). This cut results in pgal, mean ≃ 0.90 in each redshift bin, besides >35 per cent of the SVM sources with pgal > 0.95. After applying the WI×SC mask as well as our additional cuts on E(B − V) and photo-z’s, we obtained samples of 9.5 and 8.3 million galaxies over fsky ≃ 0.545 for the Fiducial and SVM data sets, of median redshifts $$z\mathrm{^{Fid}_{med}} \simeq 0.22$$ and $$z\mathrm{^{SVM}_{med}} \simeq 0.20$$. Depending on the redshift range, these two WI×SC subsets typically have ∼50–75 per cent common sources. We show the redshift distribution of both data sets in Fig. 1; number count maps of these samples for the full redshift range (0.10 < z < 0.35) are featured in Fig. 2, and Fig. 3 exhibits objects in the 0.15 < z ≤ 0.20 bin only. All maps were produced using HEALPix (Górski et al. 2005) with resolution of Nside = 128 (pixel size of ∼0.5°). Figure 1. View largeDownload slide The redshift distribution of the WI×SC Fiducial (red dashed curve) and of the SVM sample (black solid curve), both given in counts per square arcminute per redshift bin. Figure 1. View largeDownload slide The redshift distribution of the WI×SC Fiducial (red dashed curve) and of the SVM sample (black solid curve), both given in counts per square arcminute per redshift bin. Figure 2. View largeDownload slide Left-hand panel: The density contrast of galaxy number counts (clipped at δmax = 2.0 to ease visualization) of the WI×SC Fiducial sample in the 0.10 < z < 0.35 range, i.e. the full sample analysed here. Right-hand panel: Same as the left-hand panel, but for the SVM sample. The grey area corresponds to the masked region as discussed in Section 2. Figure 2. View largeDownload slide Left-hand panel: The density contrast of galaxy number counts (clipped at δmax = 2.0 to ease visualization) of the WI×SC Fiducial sample in the 0.10 < z < 0.35 range, i.e. the full sample analysed here. Right-hand panel: Same as the left-hand panel, but for the SVM sample. The grey area corresponds to the masked region as discussed in Section 2. Figure 3. View largeDownload slide Same as Fig. 2, but for galaxies within 0.10 < z ≤ 0.15 only. Figure 3. View largeDownload slide Same as Fig. 2, but for galaxies within 0.10 < z ≤ 0.15 only. 3 METHODOLOGY The isotropy of galaxy number counts is estimated with the delta-map method first presented in Alonso et al. (2015) (see also Bengaly et al. 2017), in which the sky is decomposed into 768 large healpix pixels (Nside = 8), and hemispheres are constructed using the respective pixel centres as symmetry axes. The delta-map is then computed as   \begin{eqnarray} \Delta _i = 2 \times \left( \frac{n_i^{\rm U} - n_i^{\rm D}}{n_i^{\rm U} + n_i^{\rm D}} \right)\,, \end{eqnarray} (1)where $$n_i^j \equiv N^j_i/(4\pi f^j_{{\rm sky},i})$$ are counts in the i-th hemisphere, i ∈ 1, ..., 768, j represents the hemispheres indexes ‘up’ (U) and ‘down’ (D) defined according to this pixellization scheme, whereas $$N^j_i$$ and $$f^j_{{\rm sky},i}$$ are the total number of objects and the observed fraction of the sky encompassed in each of these hemispheres, respectively. The dipole of galaxy number counts is obtained by expanding the delta-map from (1) into spherical harmonics. From the {aℓm}, coefficients we select the ℓ = 1 terms, i.e. the {a1m}, to reconstruct only the dipole component of the delta-map, Δdip = ∑a1mY1m. Therefore, we quote the maximum value of the Δdip map as our dipole amplitude A, in addition to the direction where it points to. In this work, the WI×SC catalogue is additionally decomposed into redshift shells before the delta-map calculation: cumulative ones, i.e. 0.10 < z ≤ 0.15; 0.10 < z ≤ 0.20; ...; 0.10 < z < 0.35, and disjoint ones, 0.10 < z ≤ 0.15; 0.15 < z ≤ 0.20; ...; etc. The statistical significance of the delta-map dipoles is calculated from WI×SC mock catalogues produced with the flask code3 (Xavier et al. 2016). These mocks are full-sky lognormal realizations of the density field in redshift shells based on the input angular power spectra $$C_{\ell }^{(z_i z_j)}$$ (zi and zj denoting different redshift shells) provided by camb sources (Challinor & Lewis 2011), which are Poisson-sampled according to the WI×SC selection function. The input $$C_{\ell }^{(z_i z_j)}$$ were computed for redshift distributions that are convolutions of the Δz = 0.05 shells with Gaussian scatter of σδz = 0.033 (1 + z) (representing WI×SC photo-z errors) using ΛCDM best-fitting parameters (Planck Collaboration XIII 2016), and they include linear redshift space distortions, gravitational lensing distortions of the volume elements, and non-linear contributions modelled by halofit (Smith et al. 2003; Takahashi et al. 2012). We applied a linear scaling factor to each $$C_{\ell }^{(z_i z_j)}$$ – playing a role similar to galaxy bias – which was used to match the variances of counts in pixels to the ones observed in the real data. We additionally compared the Fiducial data set source distribution to SDSS (York et al. 2000) in a 1°-wide strip centred on declination δ = 30° and estimated that it still contained a fraction fstar of stars that is well fitted by fstar = 0.71exp ( − 0.09|b|) + 0.013. Therefore, we Poisson-sampled stars according to this distribution and included them in our mocks. By adjusting the selection function normalization and the $$C_{\ell }^{(z_i z_j)}$$ scaling factors, we made our simulations match the Fiducial data set in terms of fstar, mean number of objects (galaxies + stars) and variance in the pixels.4 Following the prescriptions above, we produced 1000 full-sky mocks of both Fiducial and SVM data sets in each Δz = 0.05 photo-z bin, spanning the 0.10 < z < 0.35 range, using the same resolution as for the real data maps (Nside = 128). From these realizations, we computed how many of them featured a dipole amplitude at least as large as the real data for each z-bin analysed, hereafter quoted as p-values. Low p-values, such as p < 0.005 (Planck Collaboration XIII 2016), will be regarded as an indication that the model cannot fully describe the observations, and thus might be interpreted as challenging the concordance model. 4 RESULTS The dipoles resulting from the delta-map analyses of the two WI×SC samples are shown for the full redshift range in Fig. 4, while the dipole directions and amplitudes for each redshift bin are presented in Table 1 for both Fiducial and SVM data sets. The error bars of A and (l, b) were estimated from 1000 simulations with fixed underlying density fluctuations (and therefore fixed dipole direction and amplitude), but with different Poisson noise, for each z-bin. Then, σA corresponds to the average deviation from the fiducial dipole value, i.e. the quoted A, and σ(θ) denotes the average angular distance from the observed dipole direction, as given by this set of simulations. We readily verify that the dipole amplitude decreases when we probe the number counts at larger depths, as it goes from A ≃ 0.10 in the thinnest (0.10 < z ≤ 0.15) to A ≃ 0.03 in the thickest (0.10 < z < 0.35) cumulative shell, while the deepest shell (0.30 < z < 0.35) gives A = 0.01 − 0.04 depending on the sample. This behaviour was also noted by Yoon et al. (2014) when comparing their results with those in Gibelyou & Huterer (2012), which used shallower catalogues in some of their analyses. This amplitude decrease with increased redshift is due to the smoother rms density fluctuations in the large-scale structure in higher z, in addition to the increasing volume probed in these larger cumulative shells. Figure 4. View largeDownload slide Left-hand panel: The Delta-map dipole of the WI×SC Fiducial data set in the 0.10 < z < 0.35 range. Right-hand panel: Same as the left-hand panel, but for the WI×SC SVM galaxies. Both maps are represented in Galactic coordinates. Further details on the amplitudes and directions, as well as on the other redshift bins, are presented in Table 1. Figure 4. View largeDownload slide Left-hand panel: The Delta-map dipole of the WI×SC Fiducial data set in the 0.10 < z < 0.35 range. Right-hand panel: Same as the left-hand panel, but for the WI×SC SVM galaxies. Both maps are represented in Galactic coordinates. Further details on the amplitudes and directions, as well as on the other redshift bins, are presented in Table 1. Table 1. The amplitude (and its respective error bar down to two significant digits; col.2), direction (col.3), uncertainty on the direction (col.4), and statistical significance (given in p-values; col.5) of the WI×SC dipole obtained from the Fiducial (top) and SVM (bottom) samples. We highlight the cases where significant deviation from isotropy according to the p < 0.005 criterion was found. z-bin (Fiducial)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\it {\bf z}}} \le 0.15}$$  1.474 (18)  (56.5°, 69.8°)  0.6°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.20}$$  0.701 (11)  (20.8°, 70.2°)  0.7°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.25}$$  0.394 (09)  (346.1°, 69.8°)  1.0°  0.001  0.10 < z ≤ 0.30  0.250 (07)  (317.9°, 61.2°)  1.5°  0.084  0.10 < z < 0.35  0.225 (07)  (319.9°, 59.7°)  1.5°  0.129  0.15 < z ≤ 0.20  0.303 (13)  (325.2°, 43.8°)  2.5°  0.129  0.20 < z ≤ 0.25  0.200 (10)  (272.8°, −9.9°)  6.9°  0.332  0.25 < z ≤ 0.30  0.293 (13)  (262.6°, −42.2°)  3.2°  0.017  0.30 < z < 0.35  0.112 (22)  (27.7°, −59.3°)  9.7°  0.773  z-bin (SVM)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.15}$$  0.863 (14)  (29.3°, 65.7°)  1.0°  < 0.001  0.10 < z ≤ 0.20  0.417 (08)  (342.1°, 26.3°)  2.6°  0.019  0.10 < z ≤ 0.25  0.371 (06)  (332.6°, −3.2°)  2.8°  0.010  0.10 < z ≤ 0.30  0.320 (06)  (335.0°, −7.1°)  2.7°  0.010  0.10 < z < 0.35  0.316 (06)  (339.6°, −9.7°)  2.7°  0.007  $$\mathbf {0.15 < {\rm {\bf {\it z}}} \le 0.20}$$  0.674 (14)  (315.4°, −34.2°)  1.5°  < 0.001  $$\mathbf {0.20 < {\rm {\it {\bf z}}} \le 0.25}$$  0.682 (16)  (310.5°, −52.4°)  1.2°  < 0.001  0.25 < z ≤ 0.30  0.166 (17)  (13.3°, −48.5°)  5.1°  0.236  $$\mathbf {0.30 < {\rm {\bf {\it z}}} < 0.35}$$  0.370 (19)  (18.6°, −18.8°)  8.7°  < 0.001  z-bin (Fiducial)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\it {\bf z}}} \le 0.15}$$  1.474 (18)  (56.5°, 69.8°)  0.6°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.20}$$  0.701 (11)  (20.8°, 70.2°)  0.7°  < 0.001  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.25}$$  0.394 (09)  (346.1°, 69.8°)  1.0°  0.001  0.10 < z ≤ 0.30  0.250 (07)  (317.9°, 61.2°)  1.5°  0.084  0.10 < z < 0.35  0.225 (07)  (319.9°, 59.7°)  1.5°  0.129  0.15 < z ≤ 0.20  0.303 (13)  (325.2°, 43.8°)  2.5°  0.129  0.20 < z ≤ 0.25  0.200 (10)  (272.8°, −9.9°)  6.9°  0.332  0.25 < z ≤ 0.30  0.293 (13)  (262.6°, −42.2°)  3.2°  0.017  0.30 < z < 0.35  0.112 (22)  (27.7°, −59.3°)  9.7°  0.773  z-bin (SVM)  A × 10−1  (l, b)  σ(θ)  p-value  $$\mathbf {0.10 < {\rm {\bf {\it z}}} \le 0.15}$$  0.863 (14)  (29.3°, 65.7°)  1.0°  < 0.001  0.10 < z ≤ 0.20  0.417 (08)  (342.1°, 26.3°)  2.6°  0.019  0.10 < z ≤ 0.25  0.371 (06)  (332.6°, −3.2°)  2.8°  0.010  0.10 < z ≤ 0.30  0.320 (06)  (335.0°, −7.1°)  2.7°  0.010  0.10 < z < 0.35  0.316 (06)  (339.6°, −9.7°)  2.7°  0.007  $$\mathbf {0.15 < {\rm {\bf {\it z}}} \le 0.20}$$  0.674 (14)  (315.4°, −34.2°)  1.5°  < 0.001  $$\mathbf {0.20 < {\rm {\it {\bf z}}} \le 0.25}$$  0.682 (16)  (310.5°, −52.4°)  1.2°  < 0.001  0.25 < z ≤ 0.30  0.166 (17)  (13.3°, −48.5°)  5.1°  0.236  $$\mathbf {0.30 < {\rm {\bf {\it z}}} < 0.35}$$  0.370 (19)  (18.6°, −18.8°)  8.7°  < 0.001  View Large The comparison between the dipole amplitude of the actual observations and lognormal WI×SC mocks, for the cumulative bins, shows only marginal agreement for the SVM sample in the two thickest bins, while the Fiducial sample performs slightly better, reaching p = 0.129 in the largest redshift shell. When analysing the tomographic bins, on the other hand, we find good consistency between the Fiducial data and its mocks, however the performance of the SVM sample was good only in the 0.25 < z ≤ 0.30 shell. Moreover, we find that both SVM and Fiducial data show a larger dipole amplitude than the mocks in the lowest redshift shell, 0.10 < z ≤ 0.15, which interestingly is the bin presenting the best mutual agreement between these two samples. However, we also note that the concordance between data and simulations improves when the cumulative redshift shells encompass more distant galaxies. This is more evident for the Fiducial sample, where p > 0.05 in the two thickest redshift shells, yet less than ∼ 2 per cent of the SVM realizations have A larger than the real data in the same ranges. In the tomographic z-bins, we found that the Fiducial data is in good concordance with its ΛCDM-based mocks except for the 0.25 < z ≤ 0.30 bin which, interestingly, is the redshift shell where the SVM dipole amplitude agrees best with simulations. From these results, we conclude that the Fiducial data set shows better concordance with its respective mocks than the SVM one, and that the WI×SC data agree with the isotropy hypothesis of the Universe apart from the lowest redshift ranges examined here. At present, we cannot unambiguously resolve the reason for the latter discrepancy, and better all-sky data covering these redshifts will be needed for that purpose. We also stress that the directions of the number count dipoles in cumulative redshift shells, especially in the range 0.10 < z < 0.35 of the SVM data set, are in good agreement with similar analyses in the literature. We calculate the probabilities Pθ that the alignments between the corresponding directions would occur at random such as   \begin{eqnarray} P_\theta = \frac{1}{4\pi }\int _0^\theta 2\pi \sin \theta ^{\prime }\,\mathrm{d}\theta ^{\prime } = \frac{1-\cos \theta }{2}, \end{eqnarray} (2)where cos θ = sin b1sin b2 + cos b1cos b2cos (l1 − l2). A quantitative assessment of the concordance between these dipole directions is provided in Table 2. For instance, Bengaly et al. (2017) obtained a dipole anisotropy with A = 0.0507 pointing towards (l, b) = (323°, −5°) in the W2M catalogue which peaks at z ∼ 0.14, which is consistent with the results from Yoon et al. (2014), i.e. (l, b) = (310°, −15°). Furthermore, Appleby & Shafieloo (2014) and Alonso et al. (2015) found, using different methods, preferred directions of respectively (l, b) = (320°, 6°) and (l, b) = (315°, 30°) in the 2MPZ (Bilicki et al. 2014) Table 2. The probability that randomly picked directions are closer to each other than the measured distance between the corresponding dipoles, where small values indicate strongly aligned directions. WI×SC Fid full and WI×SC SVM full correspond to the Fiducial and SVM samples analysed in the 0.10 < z < 0.35 range, respectively, while both WI×SC Lowz cases represent the 0.10 < z ≤ 0.15 bins. The remaining directions were obtained using the WISE-2MASS and 2MASS photo-z data sets (respectively W2M and 2MPZ), as reported by Bengaly et al. (2017), Alonso et al. (2015), Yoon et al. (2014), Appleby & Shafieloo (2014) for W2M-17, 2MPZ-15, W2M-14, and 2MPZ-14, respectively. Dipole  WI×SC Fid full  WI×SC SVM full  W2M-17  2MPZ-15  W2M-14  2MPZ-14  WI×SC Fid low-z  WI×SC SVM low-z  WI×SC Fid full  –  0.227  0.247  0.249  0.275  0.263  0.815  0.764  WI×SC SVM full  0.227  –  0.007  0.013  0.013  0.091  0.253  0.239  W2M-17  0.247  0.007  –  0.005  0.016  0.072  0.287  0.259  2MPZ-15  0.249  0.013  0.005  –  0.022  0.067  0.377  0.340  W2M-14  0.275  0.013  0.016  0.022  –  0.076  0.217  0.186  2MPZ-14  0.263  0.091  0.072  0.067  0.076  –  0.580  0.541  WI×SC Fid low-z  0.815  0.253  0.287  0.377  0.217  0.580  –  0.233  WI×SC SVM low-z  0.764  0.239  0.259  0.340  0.186  0.541  0.233  –  Dipole  WI×SC Fid full  WI×SC SVM full  W2M-17  2MPZ-15  W2M-14  2MPZ-14  WI×SC Fid low-z  WI×SC SVM low-z  WI×SC Fid full  –  0.227  0.247  0.249  0.275  0.263  0.815  0.764  WI×SC SVM full  0.227  –  0.007  0.013  0.013  0.091  0.253  0.239  W2M-17  0.247  0.007  –  0.005  0.016  0.072  0.287  0.259  2MPZ-15  0.249  0.013  0.005  –  0.022  0.067  0.377  0.340  W2M-14  0.275  0.013  0.016  0.022  –  0.076  0.217  0.186  2MPZ-14  0.263  0.091  0.072  0.067  0.076  –  0.580  0.541  WI×SC Fid low-z  0.815  0.253  0.287  0.377  0.217  0.580  –  0.233  WI×SC SVM low-z  0.764  0.239  0.259  0.340  0.186  0.541  0.233  –  View Large 5 CONCLUSIONS In this work, we probed the cosmological isotropy at the 0.10 < z < 0.35 interval through the directional dependence of the galaxy counts in the WISE × SuperCOSMOS catalogue. To do so, we adopted a hemispherical comparison method, and its dipole contribution provided our diagnostic of cosmological anisotropy. The observational samples consisted of two data sets, namely ‘Fiducial’ and ‘SVM’, which differ in how galaxies were identified in them: through colour cuts in the former, and by means of automatized classification in the latter. Thanks to the availability of redshift information, we were able to perform this test in tomographic z-bins, which enabled a natural extension of the analysis carried out in Bengaly et al. (2017) with the shallower W2M sample. We found overall good agreement between the WI×SC dipole directions obtained here and those from previous analyses in the literature. As far as the dipole amplitudes are concerned, their level of agreement with ΛCDM mocks is different for various redshift shells and sample selections. In both Fiducial and SVM cases, the lowest redshift bin 0.10 < z < 0.15 is discrepant from the mocks; at higher redshifts, the Fiducial sample exhibits good agreement with the simulations, which is generally not the case for the SVM one. Interestingly, the z < 0.15 range is the only case in which both samples agree with each other regarding the dipole direction. In all other cases, the dipole amplitudes and directions significantly differ between Fiducial and SVM selections in individual z-shells. Although there is some interception of roughly ∼50–75 per cent between the two WI×SC-based data sets, they rely upon different methods to separate galaxies from stars and quasars, resulting in distinct samples from the same catalogue, and perhaps selecting different galaxy types for each one of them. However, it is very unlikely that this difference would explain such effect, as no significant colour discrepancy was found between the two samples. Even if we credit the better agreement between the Fiducial sample and the lognormal realizations to a more rigorous criterion to eliminate stars, as described in Section 2, or to different galaxy types, this procedure still cannot explain the large A obtained for both pre-selections in the 0.10 < z ≤ 0.15 redshift shell. This result could be an indication of either related systematics in both data sets, or the presence of very large, local density fluctuations, which can increase the number counts dipole as pointed out by Rubart et al. (2014). A more thorough investigation of these hypotheses will be pursued in the future, but it may require better all-sky data sets, which at present are not available for the relevant redshift ranges. This work presents the first contribution of the WI×SC catalogue to cosmology in the form of an updated test of the large-scale isotropy of the Universe, in which we found no significant departure from this fundamental hypothesis for z > 0.15, yet we are still very limited by the completeness and systematics of the available data. None the less, the WI×SC data set can be considered a testbed for forthcoming surveys, especially LSST (LSST Science Collaboration 2009) and SKA (Schwarz et al. 2015), as they will reach much deeper scales on large sky areas and, therefore, will enable much more precise tests of the CP in the years to come (Itoh et al. 2010; Yoon & Huterer 2015). Acknowledgements CAPB acknowledges South African SKA Project, besides CAPES for financial support in the early stage of this work. CPN is supported by the DTI-PCI Programme of the Brazilian Ministry of Science, Technology, Innovation and Communications (MCTIC). HSX acknowledges FAPESP for financial support. MB is supported by the Netherlands Organization for Scientific Research, NWO, through grant number 614.001.451, and by the Polish National Science Center under contract #UMO-2012/07/D/ST9/02785. AB thanks the Capes PVE project 88881.064966/2014-01. JSA is supported by CNPq and FAPERJ. We thank the Wide Field Astronomy Unit at the Institute for Astronomy, Edinburgh, for archiving the WISE × SuperCOSMOS catalogue. We also acknowledge using the healpix package for the derivation of the results presented in this work. Footnotes 1 For simplicity, we look for the largest order anisotropic mode, which is a dipole in the number counts of galaxies. 2 http://ssa.roe.ac.uk/WISExSCOS 3 http://www.astro.iag.usp.br/∼flask 4 The simulation input files are available at: http://www.astro.iag.usp.br/flask/sims/wisc17.tar.gz REFERENCES Alonso D. et al.  , 2015, MNRAS , 449, 670 https://doi.org/10.1093/mnras/stv309 CrossRef Search ADS   Appleby. S., Shafieloo A., 2014, J. Cosmol. Astropart. 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Monthly Notices of the Royal Astronomical Society: LettersOxford University Press

Published: Mar 1, 2018

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