Title:A large age for the pulsar B1757-24 from an upper limit on its proper motion

Abstract: The "characteristic age" of a pulsar usually is considered to approximate its true age, but this assumption has led to some puzzling results, including the fact that many pulsars with small characteristic ages have no associated supernova remnants. The pulsar B1757-24 is located just beyond the edge of a supernova remnant; the properties of the system indicate that the pulsar was born at the centre of the remnant, but that it has subsequently overtaken the expanding blast-wave. With a characteristic age of 16,000 yr, this implies an expected proper motion by the pulsar of 63-80 milliarcsec per year. Here we report observations of the nebula surrounding the pulsar which limit its proper motion to less than 25 mas/yr, implying a minimum age of 39,000 yr. A more detailed analysis argues for a true age as great as 170,000 yr, significantly larger than the characteristic age. From this result and other discrepancies associated with pulsars, we conclude that characteristic ages seriously underestimate the true ages of pulsars.