The Energy Dependence of Neutron Star Surface Modes and X-ray Burst Oscillations

We calculate the photon energy dependence of the pulsed amplitude of neutron star (NS) surface modes. Simple approximations demonstrate that it depends most strongly on the bursting NS surface temperature. This result compares well with full integrations that include Doppler shifts from rotation and general relativistic corrections to photon propagation. We show that the energy dependence of type I X-ray burst oscillations agrees with that of a surface mode, lending further support to the hypothesis that they originate from surface waves. The energy dependence of the pulsed emission is rather insensitive to the NS inclination, mass and radius, or type of mode, thus hindering constraints on these parameters. We also show that, for this energy-amplitude relation, the majority of the signal (relative to the noise) comes in the 2-25 keV band, so that the current burst oscillation searches with the Rossi X-Ray Timing Explorer are close to optimal. The critical test of the mode hypothesis for X-ray burst oscillations would be a measurement of the energy dependence of burst oscillations from an accreting millisecond pulsar.