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-Lema\^{\i}tre 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 $99.9\%$ confidence level, showing that matter structures follow a dipole bulk flow motion towards $(l,b) = (326.^\circ1 \pm 11.^\circ2,27.^\circ8 \pm 11.^\circ2)$, close to the Shapley supercluster $(l_{\scalebox{0.6}{Shapley}},b_{\scalebox{0.6}{Shapley}}) = (311.^\circ5, 32.^\circ3)$, 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$^{-1}$ 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 $\Lambda$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.