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 mechanisms3–5. In contrast, the timing parameters—in particular the second derivative of the pulsation frequency—of the nearby pulsar Geminga6–11 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.