Gamma-ray flux limits from brown dwarfs: Implications for dark matter annihilating into long-lived mediators

Brown dwarfs (BDs) are celestial objects representing the link between the least massive main-sequence stars and giant gas planets. In the first part of this article, we perform a model-independent search of a gamma-ray signal from the direction of nine nearby BDs in 13 years of \Fermi-LAT data. We find no significant excess of gamma rays, and we, therefore, set 95\% confidence level upper limits on the gamma-ray flux with a binned-likelihood approach. In the second part of the paper, we interpret these bounds within an exotic mechanism proposed for gamma-ray production in BDs: If the dark matter (DM) of the universe is constituted of particles with non-negligible couplings to the standard model, BDs may efficiently accumulate them through scatterings. DM particles eventually thermalise, and can annihilate into light, long-lived, mediators which later decay into photons outside the BD. Within this framework, the current Fermi-LAT stacked upper limits on the gamma-ray flux of the selected BDs do not enable setting a bound on the DM-nucleon cross-section. An improvement of approximately a factor of 9 in the gamma-ray limits is required to obtain bounds on the scattering cross-section $\sigma_{\chi n}$ $\sim 10^{-36}$ cm$^{2}$ for DM masses below 10 GeV. This improvement would cover a larger portion of the parameter space in mediator decay length and DM mass. The code and data to reproduce the results of this study are available on GitLab at \github{https://gitlab.in2p3.fr/francesca.calore/brown-dwarfs-gamma}.