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The LIGO-Virgo-KAGRA Collaboration recently detected gravitational waves(GWs) from the merger of black-hole-neutron-star (BHNS) binary systems GW200105and GW200115. No coincident electromagnetic (EM) counterparts were detected.While the mass ratio and BH spin in both systems were not sufficient to tidallydisrupt the NS outside of the BH event horizon, other, magnetosphericmechanisms for EM emission exist in this regime and depend sensitively on theNS magnetic field strength. Combining GW measurements with EM flux upperlimits, we place upper limits on the NS surface magnetic field strength abovewhich magnetospheric emission models would have generated an observable EMcounterpart. We consider fireball models powered by the black-hole batterymechanism, where energy is output in gamma-rays over $\lesssim1$~second.Consistency with no detection by Fermi-GBM or INTEGRAL SPI-ACS constrains theNS surface magnetic field to $\lesssim10^{15}$~G. Hence, joint GW detection andEM upper limits rule out the theoretical possibility that the NSs in GW200105and GW200115, and the putative NS in GW190814, retain $\gtrsim10^{15}$~Gdipolar magnetic fields until merger. They also rule out formation scenarioswhere strongly magnetized magnetars quickly merge with BHs. We alternativelyrule out operation of the BH-battery powered fireball mechanism in thesesystems. This is the first multi-messenger constraint on NS magnetic fields inBHNS systems and a novel approach to probe fields at this point in NSevolution. This demonstrates the constraining power that multi-messengeranalyses of BHNS mergers have on BHNS formation scenarios, the magnetic-fieldevolution in NSs, and the physics of BHNS magnetospheric interactions.

Multi-Messenger Constraints on Magnetic Fields in Merging Black Hole-Neutron Star Binaries