No evidence for local $H_0$ anisotropy from Tully--Fisher or supernova distances

Claims of local ($z \lesssim 0.05$) anisotropy in the Hubble constant have been made based on direct distance tracers such as Tully-Fisher galaxies and Type Ia supernovae. We revisit these using the CosmicFlows-4 Tully-Fisher W1 subsample, 2MTF and SFI++ Tully-Fisher catalogues, and the Pantheon+ supernova compilation (all restricted to $z < 0.05$), including a dipole in either the Tully-Fisher zero-point or the standardised supernova absolute magnitude. Our forward-modelling framework jointly calibrates the distance relation, marginalises over distances, and accounts for peculiar velocities using a linear-theory reconstruction. We compare the anisotropic and isotropic model using the Bayesian evidence. In the CosmicFlows-4 sample, we infer a zero-point dipole of amplitude $0.087 \pm 0.019$ mag, or $4.1\pm0.9$ per cent when expressed as a dipole in the Hubble parameter. This is consistent with previous estimates but at higher significance: model comparison yields odds of $877:1$ in favour of including the zero-point dipole. In Pantheon+ we infer zero-point dipole amplitude of $0.049 \pm 0.013$ mag, or $2.3\pm 0.6$ per cent when expressed as a dipole in the Hubble parameter. However, by allowing for a radially varying velocity dipole, we show that the anisotropic zero-point model captures local flow features (or possibly systematics) in the data rather than an actual linearly growing effective bulk flow caused by anisotropy in the zero-point or expansion rate. Crucially, inferring a more general bulk flow curve we find results fully consistent with expectations from the standard cosmological model.