We find a new mechanism of neutron star radiation wherein radiation is produced by the stellar interior . The source of radiation is oscillating neutron vortices in the superfluid core of a rotating neutron star . Thermally excited helical waves of vortices generate fast magnetosonic waves at the stellar crust . Near the crust bottom such waves reduce to a collisionless zero sound in an electron liquid , while near the stellar surface they behave as electromagnetic waves in a medium . The magnetosonic waves propagate across the crust and transform into electromagnetic radiation at the surface . The vortex contribution has the spectral index \alpha \approx - 0.45 and can explain nonthermal radiation of middle-aged pulsars observed in infrared , optical and hard X-ray bands . Detection of vortex radiation allows direct determination of the core temperature . Comparing the theory with available spectra observations we find that the core temperature of the Vela pulsar is T \approx 8 \times 10 ^ { 8 } K , while the core temperature of PSR B0656+14 exceeds 2 \times 10 ^ { 8 } K. This is the first measurement of the temperature of a neutron star core . The temperature estimate rules out equation of states incorporating Bose condensations of pions or kaons and quark matter in these objects . In principle , zero sound can also be emitted by other mechanisms , rather than vortices , which opens a perspective of direct spectroscopic study of superdense matter in the neutron star interiors .