  The Fermi Large Area Telescope (LAT) has revolutionized high-energy (HE)
astronomy, and is making enormous contributions particularly to gamma-ray
pulsar science. As a result of the many new pulsar discoveries, the gamma-ray
pulsar population is now approaching 100. Some very famous millisecond pulsars
(MSPs) have also been detected: J1939+2134 (B1937+21), the first MSP ever
discovered, as well as J1959+2048 (B1957+20), the first black widow pulsar
system. These, along with other MSPs such as PSR J0034-0534 and J2214+3000, are
rare among the pulsar population in that they exhibit nearly phase-aligned
radio and gamma-ray light curves (LCs). Traditionally, pulsar LCs have been
modelled using standard HE models in conjunction with low-altitude conal beam
radio models. However, a different approach is needed to account for
phase-aligned LCs. We explored two scenarios: one where both the radio and
gamma-ray emission originate in the outer magnetosphere, and one where the
emission comes from near the polar caps (PCs) on the stellar surface. We find
best-fit LCs using a Markov chain Monte Carlo (MCMC) technique for the first
class of models. The first scenario seems to be somewhat preferred, as is also
hinted at by the radio polarization data. This implies that the phase-aligned
LCs are possibly of caustic origin produced in the outer magnetosphere, in
contrast to the usual lower-altitude conal beam radio models. Lastly, we
constrain the emission altitudes with typical uncertainties of ~10% of the
light cylinder radius. The modelled pulsars are members of a third gamma-ray
MSP subclass, in addition to two others with non-aligned radio and gamma-ray
LCs.
