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Abstract

Galaxy recession velocities are commonly used to measure the Hubble constant, $H_0$, with peculiar velocities treated as random noise. Around massive clusters, however, these motions can be predicted by the gravitational potential of the central halo, allowing them to be modeled rather than averaged over. Past analyses relied on analytic approximations for the distance-infall-velocity relation, whose accuracy has not been tested using realistic cosmological simulations. We use halos from the IllustrisTNG simulation to quantify the bias and precision of several commonly used Hubble-flow models. We find that widely used fitting functions systematically underestimate $H_0$, whereas the full analytical solution reduces but does not eliminate these biases. We develop a simulation-based method to infer $H_0$ and apply it to TRGB distance samples around the Virgo Cluster. We find $H_0=74.4\pm 2.9$ and $73.4\pm 3.9$ km s$^{-1}$ Mpc$^{-1}$ (stat) for the minor and the major infall models, respectively. Correcting for the bias calibrated on TNG halos, these measurements raise the value of $H_0$ to $81.6 \pm 7.8$ and $87.3 \pm 8.8$ km s$^{-1}$ Mpc$^{-1}$ (stat+sys), where the minor infall model has the smallest bias from the Virgo mocks. We show that statistical errors are dominated by the residual velocity scatter around the infall model, while systematic errors are dominated by the transformation to the structure's comoving frame and halo population variance. These results establish a framework for interpreting cluster infall measurements and explain trends in previous $H_0$ inferences.

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