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We computed accurate atmosphere models of rotation-powered millisecondpulsars in which the polar caps of a neutron star (NS) are externally heated bymagnetospheric return currents. The external ram pressure, energy losses, andstopping depth of the penetrating charged particles were computedself-consistently with the atmosphere model, instead of assuming a simplifieddeep-heated atmosphere in radiative equilibrium. We used exact Comptonscattering formalism to model the properties of the emergent X-ray radiation.The deep-heating approximation was found to be valid only if most of the heatoriginates from ultra-relativistic bombarding particles with Lorentz factors of$\gamma \gtrsim 100$. In the opposite regime, the atmosphere attains a distincttwo-layer structure with an overheated optically thin skin on top of anoptically thick cool plasma. The overheated skin strongly modifies the emergentradiation: it produces a Compton-upscattered high-energy tail in the spectrumand alters the radiation beaming pattern from limb darkening to limbbrightening for emitted hard X-rays. This kind of drastic change in theemission properties can have a significant impact on the inferred NS pulseprofile parameters as performed, for example, by Neutron star InteriorComposition ExploreR. Finally, the connection between the energy distributionof the return current particles and the atmosphere emission properties offers anew tool to probe the exact physics of pulsar magnetospheres.

Magnetospheric return-current-heated atmospheres of rotation-powered millisecond pulsars