Signatures of energetic protons in hot accretion flows: Synchrotron cooling of protons in strongly magnetized pulsars

The existence of hot, two-temperature accretion flows is essential to the recent discussions of the low-luminosity, hard X-ray emission from accreting neutron stars and black holes in Galactic binaries and massive black holes in low-luminosity galactic nuclei. In these flows, protons are essentially virialized and relativistic energies for nonthermal protons are likely. Observational confirmation of the energetic protons' presence could further support the two-temperature accretion flow models. We point out that synchrotron emission from nonthermal relativistic protons could provide an observational signature in strongly magnetized neutron star systems. The self-absorbed synchrotron emission from an accreting neutron star with the magnetic moment similar to 10(30) G cm(3) is expected to exhibit a spectrum nu I-nu similar to nu(2) with the luminosity about a few times 10(33) (L-x/10(36) ergs s(-1))(0.4) ergs s(-1) at nu similar to 10(15) Hz, where L-x is the X-ray luminosity from the neutron star surface. The detection of the expected synchrotron signature in optical and UV bands during the low-luminosity state of the pulsar systems such as 4U 1626-67 and GX 1+4 could prove the existence of the hot, two-temperature accretion flows during their spin-down episodes. The detected optical emission in 4U 1626-67 has a spectral shape and luminosity level very close to our predictions.