Spectra of the spreading layers on the neutron star surface and constraints on the neutron star equation of state

Spectra of the spreading layers on the neutron star surface are calculated on the basis of the Inogamov-Sunyaev model taking into account general relativity correction to the surface gravity and considering various chemical composition of the accreting matter. Local (at a given latitude) spectra are similar to the X-ray burst spectra and are described by a diluted blackbody. Total spreading layer spectra are integrated accounting for the light bending, gravitational redshift and the relativistic Doppler effect and aberration. They depend slightly on the inclination angle and on the luminosity. These spectra also can be fitted by a diluted blackbody with the colour temperature depending mainly on a neutron star compactness. Owing to the fact that the flux from the spreading layer is close to the critical Eddington, we can put constraints on a neutron star radius without the need to know precisely the emitting region area or the distance to the source. The boundary layer spectra observed in the luminous low-mass X-ray binaries, and described by a blackbody of colour temperature T_c = 2.4 +/- 0.1keV, restrict the neutron star radii to R = 14.8 +/- 1.5km (for a 1.4-M_solar star and solar composition of the accreting matter), which corresponds to the hard equation of state.