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Pulse profiles of accreting millisecond pulsars can be used to determineneutron star (NS) parameters, such as their masses and radii, and thereforeprovide constraints on the equation of state of cold dense matter. Informationobtained by the Imaging X-ray Polarimetry Explorer (IXPE) can be used todecipher pulsar inclination and magnetic obliquity, providing ever tighterconstraints on other parameters. In this paper, we develop a new emission modelfor accretion-powered millisecond pulsars based on thermal Comptonization in anaccretion shock above the NS surface. The shock structure was approximated byan isothermal plane-parallel slab and the Stokes parameters of the emergentradiation were computed as a function of the zenith angle and energy fordifferent values of the electron temperature, the Thomson optical depth of theslab, and the temperature of the seed blackbody photons. We show that ourCompton scattering model leads to a significantly lower polarization degree ofthe emitted radiation compared to the previously used Thomson scattering model.We computed a large grid of shock models, which can be combined with pulseprofile modeling techniques both with and without polarization included. Inthis work, we used the relativistic rotating vector model for the oblate NS inorder to produce the observed Stokes parameters as a function of the pulsarphase. Furthermore, we simulated the data to be produced by IXPE and obtainedconstraints on model parameters using nested sampling. The developed methodscan also be used in the analysis of the data from future satellites, such asthe enhanced X-ray Timing and Polarimetry mission.

Polarized radiation from an accretion shock in accreting millisecond pulsars using exact Compton scattering formalism