PREPRINT

Constraining the Hubble constant and its lower limit from the proper motion of extragalactic radio jets

Tiger Yu-Yang Hsiao, Tomotsugu Goto, Tetsuya Hashimoto, Daryl Joe D. Santos, Yi Hang Valerie Wong, Seong Jin Kim, Bjorn Jasper R. Raquel, Simon C. -C. Ho, Bo-Han Chen, Ece Kilerci, Ting-Yi Lu, Alvina Y. L. On, Yu-Wei Lin, Cossas K. -W. Wu

Submitted on 11 September 2022

Abstract

The Hubble constant (${H}_{0}$) is a measurement to describe the expansion rate of the Universe in the current era. However, there is a $4.4\sigma$ discrepancy between the measurements from the early Universe and the late Universe. In this research, we propose a model-free and distance-free method to constrain ${H}_{0}$. Combining Friedman-Lema\^itre-Robertson-Walker cosmology with geometrical relation of the proper motion of extragalactic jets, the lower limit (${H}_{0,\mathrm{m}\mathrm{i}\mathrm{n}}$) of ${H}_{0}$ can be determined using only three cosmology-free observables: the redshifts of the host galaxies, as well as the approaching and receding angular velocities of radio jets. Using these, we propose to use the Kolmogorov-Smirnov test (K-S test) between cumulative distribution functions of ${H}_{0,\mathrm{m}\mathrm{i}\mathrm{n}}$ to differentiate cosmology. We simulate 100, 200, and 500 extragalactic jets with 3 levels of accuracy of the proper motion (${\mu }_{a}$ and ${\mu }_{r}$), at $10\mathrm{%}$, $5\mathrm{%}$, and $1\mathrm{%}$, corresponding to the accuracies of the current and future radio interferometers. We perform K-S tests between the simulated samples as theoretical distributions with different ${H}_{0}$ and power-law index of velocity distribution of jets and mock observational data. Our result suggests increasing sample sizes leads to tighter constraints on both power-law index and the Hubble constant at moderate accuracy (i.e., $10\mathrm{%}$ and $5\mathrm{%}$) while at $1\mathrm{%}$ accuracy, increasing sample sizes leads to tighter constraints on power-law index more. Improving accuracy results in better constraints in the Hubble constant compared with the power-law index in all cases but it alleviates the degeneracy.

Preprint

Comment: 13 pages, 14 figures, accepted for publication in MNRAS

Subjects: Astrophysics - Cosmology and Nongalactic Astrophysics; Astrophysics - Astrophysics of Galaxies