Testing cosmic anisotropy with cluster scaling relations

TL;DR

This study tests large-scale cosmic anisotropy using cluster LT and YT scaling relations as distance indicators within a Bayesian forward model that marginalises latent cluster distances and incorporates local peculiar-velocity reconstructions. By jointly fitting LT and YT and accounting for selection effects, Malmquist biases, and velocity fields from linear and nonlinear reconstructions, the authors break degeneracies between $\delta H_0/H_0$ and zero-point anisotropies and assess multiple anisotropy models. They find no compelling evidence for dipole, quadrupole, or pixelised anisotropies once peculiar velocities are modeled; the $H_0$ dipole is tightly constrained (e.g., $\delta H_0/H_0 < 3.2\%$ with Carrick 2015 and $<2.1\%$ with Manticore-Local), and bulk-flow limits are $<1300\ \mathrm{km\,s^{-1}}$, while a ZP dipole remains weak and not cosmological. Overall, the results argue that apparent anisotropies in distance indicators largely reflect local velocity structure, underscoring the need for self-consistent reconstructions in isotropy tests and paving the way for enhanced analyses with forthcoming all-sky cluster samples.

Abstract

We test claims of large-scale anisotropy in the local expansion rate using cluster scaling relations as distance indicators. Using a Bayesian forward model, we jointly fit the X-ray luminosity--temperature (LT) and thermal Sunyaev-Zel'dovich--temperature (YT) relations, marginalising over the latent cluster distances and modelling selection effects as well as peculiar velocities. The latter are modelled using reconstructions of the local peculiar velocity field where we self-consistently account for possible anisotropic redshift--distance relations via an approximate scheme. This treatment proves crucial to the inferred anisotropy and breaks the degeneracy between anisotropy in scaling relation normalisations and underlying cosmological anisotropy. We apply our method to 312 clusters at $z \lesssim 0.2$, testing dipolar, quadrupolar and general (pixelised) anisotropy models. Bayesian model selection finds no more than weak evidence for any anisotropic model. For dipole models, we obtain upper limits of $δH_0 / H_0 < 3.2\%$ and bulk flow magnitude $< 1300\,\mathrm{km\,s^{-1}}$. Our results contrast with previous claims of statistically significant anisotropy from the same data, which we attribute to our principled forward modelling of both redshifts and scaling relation observables through latent distances and our treatment of the impact of anisotropic redshift--distance relations when modelling the local peculiar velocity field. Our work highlights the importance of accurately modelling peculiar velocities when testing isotropy with distance indicators, and motivates the further development of reconstructions that self-consistently treat large-scale deviations from the Hubble flow.

Figures (10)

• Figure 1: Left: A histogram of cluster CMB-frame redshifts, with clusters coloured by $Y_{\mathrm{SZ}}$ availability. For reference, the upper axis shows comoving distance in $h^{-1}\,\mathrm{Mpc}$ assuming $z^{\rm obs} = z_{\rm cosmo}$ (i.e. neglecting peculiar velocities). Only a small number of nearby clusters lack $Y_{\mathrm{SZ}}$ measurements. Right: Sky distribution in Galactic coordinates, with the same colour scheme. The supergalactic plane is shown as the dashed teal line and the CMB dipole direction as the black cross.
• Figure 2: The two cluster scaling relations used in this work, assuming that the observed redshifts are purely cosmological (i.e. neglecting peculiar velocities), with $H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ and $\Omega_{\rm m}=0.3$. Left: X-ray luminosity--temperature ($LT$) relation. Right: thermal Sunyaev–Zel'dovich–temperature ($YT$) relation. Due to the SNR cut of migkasCosmologicalImplicationsAnisotropy2021, the $YT$ relation (right) contains preferentially hotter clusters.
• Figure 3: The top two panels show the line-of-sight overdensity and velocity profiles toward the Coma cluster from the carrickCosmologicalParametersComparison2015 (pink) and Manticore-Local (green) reconstructions, with the cluster position for an illustrative set of scaling relation parameters in a no-anisotropy model shown in black. $v_{\rm los}$ is the line of sight velocity at the cluster radius. The bottom two panels illustrate the effect of a 10% zeropoint anisotropy (scaling relation-inferred cluster position shifts but velocity profile unchanged) versus a 10% $H_0$ anisotropy (both cluster and velocity profile shift together, preserving the velocity at the cluster position). The dashed grey line shows the original cluster position for comparison.
• Figure 4: Constraints on the dipolar bulk flow (top), $H_0$ anisotropy (bottom left), and ZP dipole (bottom right) for different peculiar velocity field models.
• Figure 5: The posterior on $\log \sigma_v$ (its prior is flat in this space) for different reconstructions for the constant $\bm{V}_{\rm ext}$ and $H_0$ dipole models for $LT$, $YT$ and $LTYT$ relations. Both carrickCosmologicalParametersComparison2015 and Manticore-Local find $\sigma_v \sim 200$--$250\,\mathrm{km}\,\mathrm{s}^{-1}$ for $LT$ and $LTYT$, consistent with small-scale peculiar velocity dispersion. For $YT$, $\sigma_v$ is less constrained. The no velocity field models prefer high values ($\sigma_v \sim 1500$--$2500\,\mathrm{km}\,\mathrm{s}^{-1}$), showing they cannot accurately predict cluster redshifts without the velocity field information. The plot is made using reflection KDE with Scott's rule for smoothing width.