NEUTRON STAR COOLING

NEUTRON STAR COOLING
D.G. Yakovlev, O.Y. Gnedin*, M.E. Gusakov, A.D. Kaminker,
K.P. Levenfish, A.Y. Potekhin
Ioffe Physical Technical Institute, St.-Petersburg, Russia
*Space Telescope Science Institute, Baltimore, USA
Introduction
Theory
Theory versus observations
Conclusions and the end
MSU, September, 2004,

Chandra
image of
the Vela
pulsar
wind nebula
NASA/PSU
Pavlov et al

Basic concepts of the cooling theory
Thermal balance:
dT
C( T ) = −Lν
( T ) − Lγ
( Ts
)
dt
Photon luminosity:
Heat blanketing
envelope:
Heat content:
2 4
L = γ
4πσR
Ts
T = s
Ts
(T )
48 2
U T
~ 10 T
9
ergs
Neutrino emission: slow and/or fast?
Main cooling regulators:
1. EOS
2. Neutrino emission
3. Superfluidity
4. Magnetic fields
5. Light elements on the surface

HISTORY
Old
Stabler 1960
Chiu 1964
Morton 1964
Chiu & Salpeter 1964
Bahcall & Wolf 1965
Tsuruta & Cameron 1966
New
Lattimer, Pethick, Prakash &
Haensel 1991
Page & Applegate 1992
Schaab, Voskresensky,Sedrakian,
Weber & Weigel 1997
Page 1998

Direct Urca (Durca) process
Lattimer, Pethick, Prakash, Haensel (1991)
n → p + e + ,
ν e p + e → n +
n → n +ν + ν
e
Q = ∫ w
→
ε f (1 − f )(1 − f dΓ
e
ν
2
i f ν n p e)
e
p
e
Q
=
457π
G
10080
2
(1 + 3g
2
A
)
m m
∗ ∗
n p
10 3
h
c
m
∗
e
T
6
Θ
npe
n
ν e
Q
~ 3
Threshold:
27 6
−3
−1
× 10 T9
erg cm s
p +
ρ > ~
2ρ
Fn
≤ pFp
pFe
0
Similar processes with muons : produce ν
Similar processes with hyperons, e.g.:
L ν
µ
n → Λ
46
~ 10
T
6
9
erg
s
−1
in the inner cores
of massive stars

Inner cores of massive neutron stars:
Nucleons,
hyperons
Pion
condensates
Kaon
condensates
n →
p + e + ν
p + e → n + ν
n~
→ ~ p + e + ν
e
~ p + e → n~
+ ν
q~
→ q~
+ e + ν
e
q~
+ e → q~
+ ν
e
e
e
e
27 6 erg
Q ~ 3 × 10 T9
3
cm s
24 − 26 6 erg
Q ~ 10 T9
3
cm s
23 − 24 6 erg
Q ~ 10 T9
3
cm s
L
L
L
ν
ν
ν
~ 10
~ 10
~ 10
46
T
42 − 44
41−
42
6
9
T
T
6
9
6
9
erg
s
erg
s
erg
s
Quark
matter
d → u + e + ν
u + e → d + ν
e
e
23 − 24 6 erg
Q ~ 10 T9
3
cm
s
L
ν
~ 10
41−42
T
6
9
erg
s
Everywhere in neutron star cores
Modified
Urca (Murca)
n + N → p + e + N
p + e + N → n + N
+ ν
+ ν
e
e
20 − 22 8 erg
Q ~ 10 T9
3
cm
s
L
ν
38
~ 10
−40
T
8
9
erg
s
Bremsstrahlung
N
+ N → N + N +ν +ν
18 − 20 8 erg
Q ~ 10 T9
3
cm
s
L
ν
36
~ 10
−38
T
8
9
erg
s
ν e, ν µ
, ν τ

Effects of superfluidity
Cooper pairing at T

Welcome to the Urca World
1. Gamow and Shoenberg: Casino da Urca in Rio de Janeiro
Neutrino theory of stellar collapse, Phys. Rev. 59, 539, 1941:
Unrecordable cooling agent
2. Kseniya Levenfish: St.-Petersburg
Direct Urca -- Durca
Modified Urca -- Murca

OBSERVATIONS AND BASIC COOLING CURVE
Nonsuperfluid star
Murca neutrino emission:
slow cooling
Relaxation
Neutrino cooliing
stage
Photon
stage
Yakovlev & Pethick 2004

NONSUPERFLUID STARS: MURCA VERSUS DURCA
Yakovlev & Pethick 2004

Neutron stars with proton superfluidity in the cores

Neutron stars with proton and mild neutron superfluidities in the cores
Harmful
mild
neutron
pairing

SUPERFLUID NUCLEON STARS WITHOUT DURCA
Gusakov, Kaminker, Yakovlev, Gnedin 2004
Page, Lattimer, Prakash, Steiner 2004 –
minimal cooling model
EOS: Douchin & Haensel 2001
Useful mild neutron
pairing

TESTING COOLING MODELS WITHOUT DURCA
Gusakov, Kaminker, Yakovlev, Gnedin 2004

SUPERFLUID NEUTRON STARS WITHOUT DURCA
BUT WITH ACCRETED ENVELOPES
Kaminker, Gusakov, Yakovlev, Gnedin 2004

SIMILAR
THEORY
OF SXRTs
Cooper pairing of
neutrons
Nucleon Durca
pi-condensate
K-condensate

THEORY
versus
OSERVA-
TIONS
Cooper pairing of
neutrons
pi-condensate
Nucleon
Nucleon
Durca
Durca
K-condensate

Theory of thermal
states of SXRTs
Yakovlev, Levenfish
& Haensel, 2003

THEORY
VERSUS
OBSERVATIONS

LEFT BEHIND
Sophisticated EOSs and models: strange stars, color superconductivity,
localized protons, etc
Cooling of young stars (thermal relaxation stage, t1 Myr; reheating mechanisms) – Alpar et al. 1987,
Shibazaki & Lamb 1989
Cooling of neutron stars with magnetic fields and accreted envelopes – thermal
evolution combined with the evolution of magnetic field and burning of
light elements in the surface layers
Symmetry of cooling behavior with respect to exchanging proton and neutron
superfluidities – Kaminker et al. 2004
The effects of crustal superfluidity
Cooling of accreting neutron stars – e.g., in soft X-ray transients with deep
crustal heating of accreted matter – Haensel & Zdunik 1990, Brown et al. 1998

CONCLUSIONS
There are several very different cooling scenarios. All require enhanced neutrino
cooling and can explain the observations.
All scenarios predict the acceleration of cooling with increasing neutron-star
mass – mass ordering
The cooling of middle-aged stars is strongly regulated by EOS and superfluidity
There should be no mild superfluidity in outer neutron star cores
New observations of the coldest and hottest neutron stars are most important
Other observational evidences (cold isolated neutron stars; transiently accreting
neutron stars, measurements of masses and radii, spectral lines, etc) would
be helpful
New theoretical results (EOS, superfluidity, etc) are welcome

THE END