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Photon-axion mixing can create observable signatures in thermal spectra ofisolated, cooling neutron stars. Their shape depends on the polarizationproperties of the radiation, which, in turn, are determined by the structure ofstellar outermost layers. Here we investigate the effect of mixing on thespectrum and polarimetric observables, polarization fraction and polarizationangle, using realistic models of surface emission. We focus on RX J1856.5-3754,the only source among the X-ray dim isolated neutron stars for whichpolarimetric measurements in the optical band were performed. Our results showthat in the case of a condensed surface in both fixed and free-ion limits, themixing can significantly limit the geometric configurations which reproduce theobserved linear polarization fraction of 16.43%. In the case of an atmosphere,the mixing does not create any noticeable signatures. Complementing ourapproach with the data from upcoming soft X-ray polarimetry missions will allowto obtain constraints on $g_{\gamma a} \sim 10^{-11}$ GeV$^{-1}$ and $m_a\lesssim 10^{-6}$ eV, improving the present experimental and astrophysicallimits.

Towards constraining axions with polarimetric observations of the isolated neutron star RX J1856.5-3754