## 4. Discussion and resultsFigures 5-8
display density dependence of the neutrino synchrotron
emissivity calculated from Eq. (16) for
the magnetic fields , 10 The high-density (horizontal) parts of the synchrotron curves
correspond to domain (Eq. (7)), where
is density independent. The low-density bends
are associated with transitions either into domain
(where according to
Eq. (6)) or into domain (where
decreases exponentially due to cyclotron
harmonics suppression, Eq. (14)). Domain
is realized only for G and
K in
Figs. 5 and
6.
The low-density bends of in domain are
much steeper than those in domain . These bends
are more pronounced at highest G, at
which domain extends to higher For comparison, we also plot the emissivities produced by other neutrino generation mechanisms: the electron-positron pair annihilation into neutrino pairs, electron-nucleus bremsstrahlung, plasmon decay and photon decay. The pair annihilation in a magnetized plasma has been considered by Kaminker et al. (1992a, b), and Kaminker & Yakovlev (1994). For the parameters of study, the emissivity appears to be weakly dependent on the magnetic field. At G it is very close to the zero-field emissivity (Itoh et al. 1989, 1996). As seen from Figs. 5 and 6, the pair-annihilation emissivity differs slightly from the zero-field one only in a not too hot plasma ( K) at G. The neutrino bremsstrahlung curves are plotted neglecting the influence of the magnetic field. The effect of the field on the bremsstrahlung has not been studied so far but it is expected to be weak, for the parameters in Figs. 5-8 . We use the results of Haensel et al. (1996) to describe the neutrino pair due to Coulomb scattering of electrons by atomic nuclei in the liquid phase of matter. In the solid phase, similar process is known to consist of two parts: the phonon and static lattice contributions. We use the results by Yakovlev & Kaminker (1996) to evaluate the phonon contribution. As for the static lattice contribution, we employ the most recent theory by Pethick & Thorsson (1996) and perform numerical calculation from Eqs. (28) and (29) of their paper (adopting the Debye-Waller factor and the nuclear form-factor which were used by Yakovlev & Kaminker 1996). Numerous jumps of the bremsstrahlung curves in Figs. 5 - 8 are associated either with jump-like changes of nuclear composition of cold-catalyzed matter or with solid-liquid phase transitions (see Haensel et al. 1996 for details). The neutrino emissivities from other processes are determined by the electron and positron number densities which are nearly continuous function of the density. Therefore, all other curves are smooth. The neutrino generation due to plasmon and photon decays in a magnetic field has not been considered in the literature, and we present the field-free results of Itoh et al. (1989, 1996), for illustration. In the case of zero magnetic field, the bremsstrahlung process dominates completely in most dense layers of the NS crust at not too high temperatures K. Plasmon decay, photon decay, and pair annihilation are significant at high temperatures, K, but their emissivities become negligible very soon as temperature decreases. The synchrotron emissivity is, to some extent, similar to the
bremsstrahlung, for it persists over the wide temperature and density
ranges. In the presence of the strong magnetic field
G, the synchrotron emission is seen to
be important and even dominant for any
© European Southern Observatory (ESO) 1997 Online publication: March 24, 1998 |