Constraining annihilating dark matter using the multi-frequency radio flux profiles of the M33 galaxy

Radio data can give stringent constraints for annihilating dark matter. In general, radio observations can detect very accurate radio flux density with high resolution and different frequencies for nearby galaxies. We are able to obtain the radio flux density as a function of distance from the galactic center and frequencies $S(r,\nu)$. In this article, we demonstrate a comprehensive radio analysis of the M33 galaxy, combining the radio flux density profile $S(r)$ and the frequency spectrum $S(\nu)$ to get the constraints of dark matter annihilation parameters. By analyzing the archival radio data obtained from the Effelsberg telescope, we show that the dark matter annihilation contributing to the radio flux density might be insignificant in the disk region of the M33 galaxy. Moreover, by including the baryonic radio contribution, we constrain the $2\sigma$ conservative upper limits of the annihilation cross section, which can be complementary to the existing constraints based on neutrino, cosmic-ray, and gamma-ray observations. Our results indicate that analyzing the galactic multi-frequency radio flux profiles can give useful and authentic constraints on dark matter for the leptophilic annihilation channels.