Multi-frequency test of dark matter annihilation into long-lived particles in Sirius

New long-lived particles produced at the colliders may escape from conventional particle detectors. Using satellites or ground telescopes, we can detect the photons generated from the annihilation of the star-captured dark matter into a pair of long-lived particles. When the propagation length of these long-lived particles surpasses the interplanetary distance between the Sun and Jupiter, it becomes unfeasible to detect such dark matter signals originating from the Sun or Jupiter on Earth. Our analysis of the dark matter-induced photons produced by prompt radiation, inverse Compton scattering, and synchrotron radiation mechanisms reveals that a decay length of about $10^{-3}$ pc for long-lived particles is required for maximum detectability. We investigate the parameters that allow the long-lived particle's lifetime to be consistent with Big Bang nucleosynthesis while also allowing it to escape the confines of our solar system. The Sirius system is proposed as a promising target for the indirect detection of such long-lived particles. Utilizing the prompt, inverse Compton scattering, and synchrotron radiation, upper limits on the dark matter-proton spin-independent and spin-dependent cross section are estimated with the Fermi-LAT null-signal observation and the capabilities of the upcoming Square Kilometre Array radio telescope.