Stars as Laboratories for Fundamental Physics - MPP Theory Group

58 Chapter 2
open circle in Fig. 2.15). Such a high temperature is not compatible
with the total x-ray luminosity unless the radius of the neutron star is
very small (3−4 km). Either way, it may be premature to reach definite
conclusions regarding neutron star cooling on the basis of Vela.
At still larger ages, ROSAT measurements of the surface temperature
of the pulsars PSR 0656+14, PSR 1055–52, and Geminga have
been reported which lie close to the theoretical standard cooling curves.
However, the inferred temperature values depend sensitively on the assumed
circumstellar atmospheric models which can modify the spectrum
and thus lead to an erroneous temperature assignment. Still, the
old isolated pulsars give one a first realistic observational handle at the
issue of neutron star cooling.
2.3.3 Nonstandard Cooling and Heating Effects
The so-called “standard” neutron star cooling scenario should be called
a “reference” or “minimal” scenario because there are many effects that
will alter the cooling history; no doubt at least some of them will be in
operation in some or all neutron stars. For reviews see Tsuruta (1986,
1992), for recent numerical cooling curves including various nonstandard
effects see Umeda, Tsuruta, and Nomoto (1994).
The occurrence of nucleon superfluidity slows the neutrino emission
by the URCA process (Sect. 4.8). However, the cooling curves including
superfluidity (Nomoto and Tsuruta 1987) do not seem to differ significantly
from the reference curves at ages above a few hundred years
unless extreme assumptions are made.
When nucleon superfluidity is important, νν bremsstrahlung emission
by electrons in the crust dominates. However, electron bandstructure
effects may suppress this process, and the crust mass may be
smaller than previously thought (Pethick and Thorsson 1994). Therefore,
the cooling may be slowed even further. Slowed cooling may also
occur by a number of heating effects (accretion, polar cap heating, vortex
creep, and others), although such effects become important only
for relatively old neutron stars (t > ∼ 10 4 yr). Of course, heating effects
related to accretion will not be important in isolated pulsars which thus
are preferred laboratories to study neutron star cooling.
The cooling is accelerated if the equation of state provides enough
protons to allow for the direct URCA process (Sect. 4.8). In this case
the surface temperature drops catastrophically at an age of about 100 yr
(Page and Applegate 1992; Lattimer et al. 1994) until superfluidity sets
in which essentially stops neutrino cooling from the core. The temper-