Issue |
A&A
Volume 521, October 2010
|
|
---|---|---|
Article Number | A77 | |
Number of page(s) | 12 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361/200913861 | |
Published online | 22 October 2010 |
Rotochemical heating in millisecond pulsars: modified Urca reactions with uniform Cooper pairing gaps
Departamento de Astronomía y Astrofísica, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
Received:
13
December
2009
Accepted:
3
March
2010
Context. When a neutron star's rotation slows down, its internal density increases, causing deviations from beta equilibrium that induce reactions, heating the stellar interior. This mechanism, named rotochemical heating, has previously been studied for non-superfluid neutron stars. However, the likely presence of superfluid nucleons will affect the thermal evolution of the star by suppressing the specific heat and the usual neutrino-emitting reactions, while at the same time opening new Cooper pairing reactions.
Aims. We describe the thermal effects of Cooper pairing
with spatially uniform and isotropic energy gaps of neutrons
and protons
, on the rotochemical heating in millisecond pulsars (MSPs) when only
modified Urca reactions are allowed. In this way, we are able to determine the amplitude
of the superfluid energy gaps for the neutron and protons needed to
produce different thermal evolution of MSPs.
Methods. We integrate numerically, and analytically in some approximate cases, the neutrino reactions for the modified Urca processes with superfluid nucleons to include them in the numerical simulation of rotochemical heating.
Results. We find that the chemical imbalances in the star grow up to the
threshold value = min (
+ 3
, 3
+
),
which is higher than the quasi-steady
state achieved in the absence of superfluidity. Therefore, the superfluid MSPs
will take longer to reach the quasi-steady state than their nonsuperfluid
counterparts, and they will have a higher a luminosity in this state, given
by
= (1–4) × 1032(
/MeV)
(
/
) erg s-1, where
is the period derivative in units
of 10-20 and
is the period in milliseconds.
We are able to explain the UV emission of the PSR J0437-4715 for
0.05 [MeV] ≲
≲ 0.45 [MeV].
These results are valid if the energy gaps are uniform and isotropic.
Key words: stars: neutron / dense matter / stars: rotation / pulsars: general / pulsars: individual: PSR J0437-4715
© ESO, 2010
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