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Since the launch of the Fermi Gamma-Ray Space Telescope, several hundredgamma-ray pulsars have been discovered, some being radio-loud and someradio-quiet with time-aligned radio and gamma-ray light curves. In the secondFermi Pulsar Catalogue, 117 new gamma-ray pulsars have been reported based onthree years of data collected by the Large Area Telescope on the Fermisatellite, providing a wealth of information such as the peakseparation~$\Delta$ of the gamma-ray pulsations and the radio lag~$\delta$between the gamma-ray and radio pulses. We selected several radio-loudmillisecond gamma-ray pulsars with period~$P$ in the range 2-6~ms and showing adouble peak in their gamma-ray profiles. We attempted to constrain the geometryof their magnetosphere, namely the magnetic axis and line-of-sight inclinationangles for each of these systems. We applied a force-free dipole magnetospherefrom the stellar surface up to the striped wind region -- well outside thelight cylinder -- to fit the observed pulse profiles in gamma-rays,consistently with their phase alignment with the radio profile. In decidingwhether a fitted curve is reasonable or not, we employed a least-square methodto compare the observed gamma-ray intensity with that found from our model,emphasising the amplitude of the gamma-ray peaks, their separation, and thephase lag between radio and gamma-ray peaks. We obtained the best fits andreasonable parameters in agreement with observations for ten millisecondpulsars. Eventually, we constrained the geometry of each pulsar described bythe magnetic inclination~$\alpha$ and the light-of-sight inclination~$\zeta$.We found that both angles are larger than approximately~$45^{\rm o}$.

Constraining millisecond pulsar geometry using time-aligned radio and gamma-ray pulse profile