Radiation of neutron stars produced by superfluid core
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We find a new mechanism of neutron star radiation wherein radiation is produced by the stellar interior. The main finding is that the neutron star interior is transparent for collisionless electron sound, the same way as it is transparent for neutrinos. In the presence of the magnetic field the electron sound is coupled with electromagnetic radiation; such collective excitation is known as a fast magnetosonic wave. At high densities such waves reduce to the zero sound in electron liquid, while near the stellar surface they are similar to electromagnetic waves in a medium. We find that zero sound is generated by superfluid vortices in the stellar core. Thermally excited helical vortex waves produce fast magnetosonic waves in the stellar crust that propagate toward the surface and transform into outgoing electromagnetic radiation. The magnetosonic waves are partially absorbed in a thin layer below the surface. The absorption is highly anisotropic; it is smaller for waves that in the absorbing layer propagate closer to the magnetic field direction. As a result, the vortex radiation is pulsed with the period of star rotation. The vortex radiation has the spectral index α ≈-0.45 and can explain nonthermal radiation of middle-aged pulsars observed in the infrared, optical, and hard X-ray bands. The radiation is produced in the star interior, rather than in the magnetosphere, which 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 × 108 K, while the core temperature of PSR B0656+14 and Geminga exceeds 2 × 108 K. This is the first measurement of the temperature of a neutron star core. The temperature estimate rules out equations of state incorporating Bose condensations of pions or kaons and quark matter in these objects. The estimate also allows us to determine the critical temperature of triplet neutron superfluidity in the Vela core, Tc = (7.5 ± 1.5) × 109 K, which agrees well with the value of critical temperature in a core of a canonical neutron star calculated based on recent data for behavior of strong interactions at high energies. We also find that in the middle-aged neutron stars the vortex radiation, rather than thermal conductivity, is the main mechanism of heat transfer from the stellar core to the surface. The core radiation opens a possibility to study composition of neutron star crust by detection of absorption lines corresponding to the low-energy excitations of crust nuclei. Bottom layers of the crust may contain exotic nuclei with the mass number up to 600, and the core radiation creates a perspective to study their properties. In principle, zero sound can also be emitted by other mechanisms, rather than vortices. In this case the spectrum of stellar radiation would contain features corresponding to such processes. As a result, zero sound opens a perspective of direct spectroscopic study of superdense matter in the neutron star interior.