An Asteroid Belt Interpretation for the Timing Variations of the Millisecond Pulsar B1937+21

Pulsar timing observations have revealed companions to neutron stars that include other neutron stars, white dwarfs, main-sequence stars, and planets. We demonstrate that the correlated and apparently stochastic residual times of arrival from the millisecond pulsar B1937+21 are consistent with the signature of an asteroid belt having a total mass less than approximately 0.05 Earth masses. Unlike the solar system's asteroid belt, the best fit pulsar asteroid belt extends over a wide range of radii, consistent with the absence of any shepherding companions. We suggest that any pulsar that has undergone accretion-driven spin-up and subsequently evaporated its companion may harbor orbiting asteroid mass objects. The resulting timing variations may fundamentally limit the timing precision of some of the other millisecond pulsars. Observational tests of the asteroid belt model include identifying periodicities from individual asteroids, which are difficult; testing for statistical stationarity that become possible when observations are conducted over a longer observing span; and searching for reflected radio emission.