Bulk Flow Motion Detection in the Local Universe with Pantheon$+$ Type Ia Supernovae

The {\em bulk flow} in the Local Universe is a collective phenomenon due to the peculiar motions of matter structures, which, instead of moving in random directions, appears to follow an approximate dipole velocity flow. We apply a directional analysis to investigate, through the Hubble-Lemaître diagram, the angular dependence of the Hubble constant $H_0$ of a sample of Type Ia Supernovae from the Pantheon+ catalog in the Local Universe ($0.015\le z\le 0.06$). We perform a directional analysis that reveals a statistically significant dipole variation of $H_0$, at more than $99.9\mathrm{\%}$ confidence level, showing that matter structures follow a dipole bulk flow motion towards $(l,b)=(326{\mathrm{.}}^{\circ }1\pm 11{\mathrm{.}}^{\circ }2,27{\mathrm{.}}^{\circ }8\pm 11{\mathrm{.}}^{\circ }2)$, close to the Shapley supercluster $(l_{\text{scalebox}0.6Shapley},b_{\text{scalebox}0.6Shapley})=(311{\mathrm{.}}^{\circ }5,32{\mathrm{.}}^{\circ }3)$, with velocity $132.14\pm 109.3$ km s${}^{-1}$ at the effective distance $102.83\pm 10.2$~Mpc. Interestingly, the antipodal direction of this dipole points close to the Dipole Repeller structure. Our analyses confirm that the gravitational dipole system Shapley-Dipole Repeller explains well the observed bulk flow velocity field in the Local Universe. Furthermore, we performed robustness tests that support our results. Additionally, our approach provides a measurement of the Hubble constant $H_0=70.39\pm 1.4$~$\text{km s}{}^{-1}\text{ Mpc}{}^{-1}$, at the effective distance $102.8$~Mpc, $z\simeq 0.025$. Note that this value was obtained using the first order approximation of the Hubble law because our methodology is model-independent. If one assumes, for instance, cosmography at second order with the $\mathrm{\Lambda }$CDM value $q_0=-0.55$, which is a model-dependent hypothesis, then $H_0=72.6\pm 1.5$ km s${}^{-1}$ Mpc${}^{-1}$, but our results: bulk flow velocity, dipole direction and its statistical significance remain the same.