Limits from the soft X-ray background on the temperature of old neutron stars and on the flux of superheavy magnetic monopoles

Using recent observations of the diffuse, soft X-ray background, we obtain upper limits of 49 eV to the average surface temperature and 10³² ergs s⁻¹ to the total photon luminosity of old (∼ 10¹⁰ yr) neutron stars in the Galaxy. If neutron stars are kept hot through monopole-induced nucleon decay, this limit corresponds to a monopole flux limit of FM(σ₀ β) < 3r x 10⁻²³ cm⁻² sr⁻¹ s⁻¹, where the cross section for catalyzed nucleon decay times the monopole-nucleon relative velocity is σ v = 10⁻²⁸(σ₀ βc) cm² (β = v/c), and r=LTOT/Lγ is the ratio of the total luminosity to the photon luminosity of a neutron star whose surface temperature T ≈ 50 eV. For conventional neutron star equations of state r ≈ 1, while for the more exotic ones r can be O(10³-10⁴). Although our temperature limit places a very stringent limit on the monopole flux, it does not significantly constrain other mechanisms for heating old neutron stars.