Constraints on the dark mass distribution surrounding Sgr A*: simple ${\chi }^2$ analysis for the redshift of photons from orbiting stars

Abstract

Sagittarius A* (Sgr A*) is the central supermassive black hole with the mass $\sim 4\times 10^6{M}_{\odot }$ in the Milky Way and stars are orbiting around it. In May 2018, one of the nearest stars to Sgr A* named S0-2/S2 experienced the pericenter passage. The redshift of photons from S0-2 had varied from $4000\mathrm{km}{\mathrm{s}}^{-1}$ to $-2000\mathrm{km}{\mathrm{s}}^{-1}$ during the pericenter passage, which is within $0.5\mathrm{yr}$. In this paper, we show that this steep variation of the redshift gives a strong constraint on a dark mass distribution inside the orbit of S0-2. By applying a simple ${\chi }^2$ analysis to the observed redshift, we can easily distinguish between the two models, the point mass model and the point mass plus an extended mass model without the best-fitting parameter search. Our redshift data during the pericenter passage in 2018 with Subaru/IRCS bound the amount of the extended mass inside the orbit of S0-2 less than $0.5\%$ ($\sim 2\times 10^4{M}_{\odot }$) of the mass of Sgr A*. This constraint obtained by our simple analysis is comparable to previous works with the best-fitting parameter search to the motion of S0-2 including the effect of the extended mass. We consider both the power-law and the Plummer models for the dark mass distribution model, but the significant difference between these results is not found.

10 pages, 9 figures, 2 tables