Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 59
ature then stays almost constant for a long time until photon cooling
from the surface begins to dominate. In this scenario the cooling curve
depends sensitively on the “on switch” set by the occurrence of the direct
URCA process anywhere in the star, and by the “off switch” from
superfluidity. As the occurrence of these effects depends on fine points
of the equation of state as well as on the density and thus the stellar
mass there may not be a universal cooling curve for all neutron stars.
Another effect which would accelerate cooling is the occurrence of
a meson condensate (Sect. 4.9.1) because of the increased efficiency of
neutrino emission. Again, this effect depends sensitively on the equation
of state and thus on the density and the stellar mass. The most
recent numerical study of neutron-star cooling with a pion condensate
was performed by Umeda, Nomoto, and Tsuruta (1994).
2.3.4 Cooling by Particle Emission
The emission of novel particles would also accelerate the cooling of
neutron stars. Iwamoto (1984) considered axion emission e + (Z, A) →
(Z, A) + e + a in the crust and found unacceptably fast cooling unless
α ′ < ∼ 10 −25 where α ′ is the axionic fine-structure constant (Chapter 3).
However, this result is quite uncertain, notably in view of the above
Pethick and Thorsson (1994) band-structure suppression of the bremsstrahlung
rate. Moreover, in view of the white-dwarf and globularcluster
bounds of α ′ < ∼ 10 −26 it appears that crust cooling by axions is
not important in neutron stars.
In the interior of neutron stars, axions can be emitted by the neutron
bremsstrahlung process nn → nna (Sect. 4.2). With a numerical
implementation of Iwamoto’s (1984) bremsstrahlung rate Tsuruta and
Nomoto (1987) found a limit g < an ∼ 10 −10 for the axion-neutron Yukawa
coupling, based on a comparison with the 10 3 yr old sources. In their
calculation the effect of superfluidity apparently was not included which
would diminish the bound. Conversely, including protons in a regime
where neither protons nor neutrons are superfluid would increase the
emission rate (Sect. 4.2.6). Of course, the more recent ROSAT results
suggest that thermal surface emission has not been observed for any of
the 10 3 yr old sources anyway.
Most recently, Iwamoto et al. (1995) considered the plasma decay
process γ → νν in the crust under the assumption of a large neutrino
magnetic dipole moment. They found that for µ ν of order 10 −10 µ B a
significant effect would obtain, but that a value as large as 5×10 −7 µ B
would be consistent with current data. In view of the globular-cluster