  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 gamma-ray 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 (R_LC) or near the
polar caps (PCs). We obtain reasonable fits for the first three of these MSPs
in the context of "altitude-limited" 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. 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 R_LC. We lastly constrain the emission
altitudes with typical uncertainties of ~0.3R_LC. Our results describe a third
gamma-ray MSP subclass, in addition to the two (with non-aligned LCs)
previously found.
