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A Search for Annihilating Dark Matter in 47 Tucanae and Omega Centauri

A plausible formation scenario for the Galactic globular clusters 47 Tuc and Omega Cen is that they are tidally stripped remnants of dwarf galaxies, in which case they are likely to have retained a fraction of their dark matter cores. In this study, we have used the ultra-wide band receiver on the Parkes telescope (Murriyang) to place upper limits on the annihilation rate of exotic Light Dark Matter particles (X) via the XX/$e^+e^-$ channel using measurements of the recombination rate of positronium (Ps). This is an extension of a technique previously used to search for Ps in the Galactic Centre. However, by stacking of spectral data at multiple line frequencies, we have been able to improve sensitivity. Our measurements have resulted in 3-sigma flux density (recombination rate) upper limits of 1.7 mJy (1.4x10$^{43}$ s$^{-1}$) and 0.8 mJy (1.1x10$^{43}$ s$^{-1}$) for 47 Tuc and Omega Cen, respectively. Within the Parkes beam at the cluster distances, which varies from 10 to 23 pc depending on the frequency of the recombination line, we calculate upper limits to the dark matter mass and rms dark matter density of <1.2-1.3x10$^5$ fn$^{-0.5}$ (mX/MeV c$^{-2}$) solar masses and <48-54 fn$^{-0.5}$ (mX/MeV c$^{-2}$) solar masses pc$^{-3}$ for the clusters, where fn=Rn/Rp is the ratio of Ps recombination transitions to annihilations, estimated to be 0.01. The radio limits for Omega Cen suggest that, for a fiducial dark/luminous mass ratio of 0.05, any contribution from Light Dark Matter is small unless the cross section <7.9x10$^{-28}$ (mX/MeV c$^{-2}$)$^2$ cm$^3$ s$^{-1}$. Owing to the compactness and proximity of the clusters, archival 511-keV measurements suggest even tighter limits than permitted by CMB anisotropies, <8.6x10$^{-31}$ (mX/MeV c$^{-2}$)$^2$ cm$^3$ s$^{-1}$. Our recombination rate limits substantially improve on previous radio limits for the Milky Way.