Modeling light curves of the phase-aligned gamma-ray millisecond pulsar subclass

The gamma-ray population of millisecond pulsars (MSPs) detected by the Fermi Large Area Telescope (LAT) has been steadily increasing. A number of the more recent detections, including PSR J0034−0534, PSR J1939+2134 (B1937+21; the first MSP ever discovered), PSR J1959+2048 (B1957+20; the first black widow system), and PSR J2214+3000, exhibit an unusual phenomenon: nearly phase-aligned radio and gammaray light curves (LCs). To account for the phase alignment, we explore geometric models where both the radio and gamma-ray emission originate either in the outer magnetosphere near the light cylinder (RLC) or near the polar caps (PCs). We obtain reasonable fits for the first three of these MSPs in the context of “altitudelimited” outer gap (alOG) and two-pole caustic (alTPC) geometries. The outer magnetosphere phase-aligned models differ from the standard outer gap (OG) / two-pole caustic (TPC) models in two respects: first, the radio emission originates in caustics at relatively high altitudes compared to the usual low-altitude conal radio beams; second, we allow the maximum altitude of the gamma-ray emission region as well as both the minimum and maximum altitudes of the radio emission region to vary within a limited range. Alternatively, there also exist phase-aligned LC solutions for emission originating near the stellar surface in a slot gap (SG) scenario (“low-altitude slot gap” (laSG) models). We find best-fit LCs using a Markov chain Monte Carlo (MCMC) maximum likelihood approach [30]. Our fits imply that the phase-aligned LCs are likely of caustic origin, produced in the outer magnetosphere, and that the radio emission may come from close to RLC. We lastly constrain the emission altitudes with typical uncertainties of ∼ 0.3RLC. Our results describe a third gamma-ray MSP subclass, in addition to the two (with non-aligned LCs) previously found [50]: those with LCs fit by standard OG / TPC models, and those with LCs fit by pair-starved polar cap (PSPC) models