  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 -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=8*10^8K, while the core
temperature of PSR B0656+14 exceeds 2*10^8K. 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.
