Comparing the Space Densities of Millisecond-Spin Magnetars and Fast X-Ray Transients

Fast X-ray transients (FXTs) are bright X-ray flashes with durations of minutes to hours, peak isotropic luminosities of L_X,peak ~ 10^42-10^47 erg/s, and total isotropic energies of E ~ 10^47-10^50 erg. They have been detected in the soft X-ray band by Chandra, XMM-Newton, Swift-XRT, and, most recently, by Einstein Probe, which has reported more than 50 FXTs in its first year of operation. While several models have been proposed, the nature of many FXTs remains unknown. One model suggests FXTs are powered by the spin-down of newly formed millisecond magnetars, typically produced by binary neutron star (BNS) mergers. However, the BNS volumetric rate, ~10^2 Gpc^-3 yr^-1, barely overlaps with the estimated FXT rate of 10^3-10^4 Gpc^-3 yr^-1. Even within that overlap, BNS mergers would need to produce FXTs at nearly 100% efficiency. We explore whether other millisecond magnetar formation channels could account for this discrepancy. We compile rate densities for several proposed progenitors: accretion-induced collapse of white dwarfs, binary white dwarf mergers, neutron star-white dwarf mergers, and the collapse of massive stars, and convert Galactic event rates into volumetric rates using either the star formation rate or the stellar mass density distributions as a function of redshift. We find that the highest potential formation rates arise from binary white dwarf mergers and massive star collapses. However, both channels face theoretical and observational challenges: the spin and magnetic field properties of the resulting neutron stars are uncertain, and few are expected to satisfy both conditions required for FXT production. Across all scenarios, the fraction of suitable millisecond magnetars is low or poorly constrained. We conclude that they are unlikely to be the dominant progenitors of FXTs and can contribute to at most 10% of the observed FXT population.