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It is generally taken for granted that our Universe is free of antimatterobjects and domains. This certitude has recently been challenged by thepossible detection of anti-helium nuclei by AMS-02. Should the observation beconfirmed, the existence of nearby antistars would make a plausible hypothesisto explain the origin of the antinuclei. In this paper we use the 10-yearsFermi Large Area Telescope (LAT) gamma-ray source catalog to set constraints onthe abundance of antistars around the Sun. We identify in the catalog 14antistar candidates not associated with any objects belonging to establishedgamma-ray source classes and with a spectrum compatible with baryon-antibaryonannihilation. We use them along with an estimate of the LAT sensitivity toantistars to set upper limits on the local antistar fraction $f_{\bar{\ast}}$with respect to normal stars. We provide parametric limits as a function of theclosest antistar mass, velocity, and surrounding matter density. We also employa novel Monte~Carlo method to set limits for a few hypotheses about theantistar population. For a population with properties equivalent to those ofregular stars concentrated in the Galactic disk we obtain $f_{\bar{\ast}} < 2.5\times 10^{-6}$ at 95\% confidence level, which is 20 times more constrainingthan limits previously available. For a primordial population of antistarsdistributed in the Galactic halo we obtain new local upper limits whichdecrease as a function of antistar mass $M$ from $f_{\bar{\ast}} < 0.2$ at 95\%confidence level for $M = 1 \; M_\odot$ to $f_{\bar{\ast}} < 1.6 \times10^{-4}$ at 95\% confidence level for $M = 10 \; M_\odot$. By combining theselimits with existing microlensing constraints for lighter objects in theMagellanic clouds, we infer that a primordial population of halo antistars musthave a density lower than $\mathcal{O}(10^{-5}\;\text{pc}^{-3})$ to$\mathcal{O}(10^{-2}\;\text{pc}^{-3})$ depending on their masses. Our limitscan constrain models for the origin and propagation of antinuclei in cosmicrays.

Constraints on the antistar fraction in the Solar system neighborhood from the 10-years Fermi Large Area Telescope gamma-ray source catalog