Timing the Geminga Pulsar with Gamma-Ray Observations

We present the COS-B/EGRET 1997 ephemeris for the rotation of the Geminga pulsar. This ephemeris is derived from high-energy gamma-ray observations that span 24 yr. The recently obtained accurate position and proper motion are assumed. A cubic ephemeris predicts the rotational phase of Geminga with errors smaller than 50 milliperiods for all existing high-energy gamma-ray observations that span a 24.2 yr timing baseline. The braking index obtained is 17 +/- 1. Further observation is required to ascertain whether this high value truly reflects the rotational energy loss mechanism, or whether it is a manifestation of timing noise. The ephemeris parameters are sufficiently constrained so that timing noise will be the limitation on forward extrapolation. If Geminga continues to rotate without a glitch, as it has for at least 23 yr, we expect this ephemeris to continue to describe the phase, with an error of less than 100 milliperiods, until 2008. Statistically significant timing residuals are detected in the EGRET data that depart from the cubic ephemeris at a level of 30 milliperiods. Although this could simply be an additional manifestation of timing noise, the EGRET timing residuals appear to have a sinusoidal modulation that is consistent with a planet of mass 1.7/sin i solar mass, orbiting Geminga at a radius of 3.3 AU.