Emission Mechanisms of Millisecond Radio and Gamma-ray Pulsars

The last decade has seen impressive progress in our understanding of the millisecond pulsar phenomenon. These pulsating powerhouses radiate across the broadband spectrum, exhibiting a rich spectral and temporal phenomenology. The Fermi Large Area Telescope has announced over 250 gamma-ray pulsar detections, about one hundred of them being millisecond pulsars, in addition to 2 500 known radio pulsars and tens detected in optical and X-ray wavebands. These include millisecond pulsars in binary systems that exhibit pulsations on both spin and orbital time scales. New ground-based detections of pulsations from four young and middle-aged pulsars by Cherenkov telescopes in the GeV to TeV band provide novel puzzles to solve, raising the question whether similar spectral components will be uncovered by the Cherenkov Telescope Array (CTA) from millisecond pulsars. Unprecedented constraints inferred by the Neutron Star Interior Composition Explorer (NICER) in the X-ray band on the mass and radius plus surface heating patterns of a couple of millisecond pulsars are adding new information to the valuable and growing library of discoveries. MeerKAT and the future Square Kilometre Array (SKA) will enormously increase our database of radio pulsars and will enable powerful population synthesis techniques to be exploited. I will highlight the utility of multi-band light curves to constrain emission mechanisms and spatial emissivity patterns. Complementary observations and modelling of multi-wavelength spectra and polarisation signatures further probe the complex particle dynamics, electrodynamical environment, and radiation characteristics of the relativistic pair plasma. I will provide an overview of the latest high-energy magnetohydrodynamic (MHD) and particle-in-cell (PIC) models that place the main site of gamma-ray emission in the current sheet beyond the light cylinder, plus others that invoke multipolar magnetic field structures and General Relativistic effects, and finally discuss some open questions that will have to be addressed by continued observations and model development.