Pulsar motion effect and Geminga's high braking index

Abstract

THE pulsar braking index, n, is a dimensionless quantity describing the rate at which a magnetized neutron star loses rotational energy¹. It can be determined from pulsar timing measurements, and for distant pulsars is found to lie close to n = 3 (ref. 2), as predicted by theoretical models of pulsar emission mechanisms^3–5. In contrast, the timing parameters—in particular the second derivative of the pulsation frequency—of the nearby pulsar Geminga^6–11 indicate an extremely large braking index of about 10-30. To understand this property of Geminga, we consider here the effect on the measured timing parameters of a pulsar's motion through space. We find that the Doppler effect alone can give a high apparent braking index, but only if the pulsar is very close and has an abnormally high velocity (>1000kms^-1). A more likely (but related) cause of the high braking index is the pulsar's proper motion: failure to correct for changes in the source coordinates with time can greatly influence the higher derivatives of the pulsar frequency, and lead to an erroneous value of n. A self-consistent analysis of the timing data, which account for both the proper motion and the Doppler effect, should permit a reliable estimate of the distance to Geminga.