Download Cooling neutron stars: Theory and observations

COOLING NEUTRON STARS: THEORY AND
OBSERVATIONS
D.G. Yakovlev
Ioffe Physical Technical Institute, St.-Petersburg, Russia
Main collaborators:
• A.D. Kaminker, Ioffe Institute
• A.Y. Potekhin, Ioffe Institute
• Introduction
• Neutrino emission
• Cooling theory
• Phenomenological concept
• Theory and observation
• Connections
• Conclusions
Hirschegg – January – 2009
Cooling Theory: Primitive and complicated at once
Basic Ideas
Heat content:
UT ~ 1048 T92 ergs
PRE-PULSAR HISTORY
Stabler (1960) – PhD, First estimates of X-ray surface thermal
emission
Chiu (1964) – Estimates that neutron stars can be discovered
from observations of thermal X-rays
Morton (1964) , Chiu & Salpeter (1964), Bahcall & Wolf (1965) –
First simplified cooling calculations
Tsuruta & Cameron (1966) – Basic formulation of all elements
of the cooling theory
Neutrino Emission Processes in Neutron Star Cores
Direct Urca, N/H
n  p  e  e p  e  n   e
Pion condensate
N  N  e  e N  e  N  e
Fast
erg cm-3 s-1
Outer core
Inner core
Slow emission Fast emission
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STANDARD
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Kaon condensation
B  B  e  e
B  e  B  e
Or quark matter
d  u  e  e
Modified Urca
nN  pNe
u  e  d  e
pNe  nN
NN bremsstrahlung
N  N  N  N  
Enhanced emission in inner cores of
massive neutron stars:
Everywhere in neutron star cores:
QFAST  Q0FT96
LFAST  L0FT96
QSLOW  Q0ST98
LFAST  L0ST98
THREE COOLING STAGES
Stage
Duration
Physics
Relaxation
10—100 yr
Crust
Neutrino
10-100 kyr
Core, surface
Photon
infinite
Surface, core,
reheating
INITIAL THERMAL RELAXATION:
LOOK FROM INSIDE AND OUTSIDE
OBSERVATIONS AND BASIC COOLING CURVE
Nonsuperfluid star
Nucleon core
EOS PAL (1988)
Modified Urca
neutrino emission:
slow cooling
1=Crab
2=PSR J0205+6449
3=PSR J1119-6127
4=RX J0822-43
5=1E 1207-52
6=PSR J1357-6429
7=RX J0007.0+7303
8=Vela
9=PSR B1706-44
10=PSR J0538+2817
11=PSR B2234+61
12=PSR 0656+14
13=Geminga
14=RX J1856.4-3754
15=PSR 1055-52
16=PSR J2043+2740
17=PSR J0720.4-3125
Talks by Frank Haberl and Slava Zavlin
MODIFIED AND DIRECT URCA PROCESSES
1=Crab
2=PSR J0205+6449
3=PSR J1119-6127
4=RX J0822-43
5=1E 1207-52
6=PSR J1357-6429
7=RX J0007.0+7303
8=Vela
9=PSR B1706-44
10=PSR J0538+2817
11=PSR B2234+61
12=PSR 0656+14
13=Geminga
14=RX J1856.4-3754
15=PSR 1055-52
16=PSR J2043+2740
17=PSR J0720.4-3125
M MAX  1.977 M
c  2.578 1015 g/cc
M D  1.358 M
c  8.17 1014 g/cc
From 1.1 M to 1.98 M with step M  0.01 M
BASIC PHENOMENOLOGICAL CONCEPT
Neutrino emissivity function
Neutrino luminosity function
BASIC PARAMETERS:
QSLOW , QFAST , 1 ,  2  LSLOW , LFAST , M 1 , M 2
Problems:
• To discriminate between neutrino mechanisms
• To broaden transition from slow to fast neutrino
emission
MODIFIED AND DIRECT URCA PROCESSES:
SMOOTH TRANSITION
MODIFIED AND DIRECT URCA PROCESSES:
SMOOTH TRANSITION
2p proton SF
1=Crab
2=PSR J0205+6449
3=PSR J1119-6127
4=RX J0822-43
5=1E 1207-52
6=PSR J1357-6429
7=RX J0007.0+7303
8=Vela
9=PSR B1706-44
10=PSR J0538+2817
11=PSR B2234+61
12=PSR 0656+14
13=Geminga
14=RX J1856.4-3754
15=PSR 1055-52
16=PSR J2043+2740
17=PSR J0720.4-3125
M VELA  1.61 M ?
MODIFIED AND DIRECT URCA PROCESSES:
SMOOTH TRANSITION -- II
2p proton SF
Mass ordering is the same!
M VELA  1.47 M ?
Neutron stars with strongproton and mild neutron superfluidities in the
cores
TESTING THE LEVELS OF SLOW AND FAST NEUTRINO EMISSION
Slow neutrino emission:  Q(Mod Urca) / 30
Fast neutrino emission:  Q(Mod Urca)  30
Two other parameters are totally not
constrained
Broadening of threshold for fast neutrino emission
Superfluidity:
Suppresses ordinary neutrino
processes
Initiates Cooper-pairing neutrino
emission
Should be:
Strong in outer core to
suppress modified Urca
Penetrate into inner core to
broaden direct Urca threshold
Can be: proton or neutron
E.,g. pion
polarization
Voskresensky &Senatorov (1984, 1986)
Schaab et al. (1997)
Nuclear physics effects
Magnetic broadening Baiko & Yakovlev (1999)
Effects of accreted envelopes and surface magnetic fields
Different mass M / M of
accreted material on the surface
Dipole magnetic field
in heat blanketing layer
Summary of cooling regulators
Regulators of neutrino emission in neutron star cores
EOS, composition of matter
Superfluidity
Heat content and conduction in cores
Heat capacity
Thermal conductivity
Thermal conduction in heat blanketing envelopes
Thermal conductivity
Chemical composition
Magnetic field
Internal heat sources (for old stars and magnetars)
Viscous dissipation of rotational energy
Ohmic decay of magnetic fields, ect.
CONNECTION: X-ray transients
1
2
3
4
5
6
7
8
9
Direct Urca
Aql X-1
4U 1608-522
RX J1709-2639
KS 1731-260
Cen X-4
SAX J1810.8-2609
XTE J2123-058
1H 1905+000
SAX 1808.4-3658
Pion condensate
Data collected by
Kseniya Levenfish
Talk by
Rudy Wijnands
Kaon condensate
CONNECTION: Magnetars
Kaminker et al. (2006)
SUMMARY OF CONNECTIONS
Objects
Physics which is tested
Middle-aged isolated NSa
Neutrino luminosity function
Composition and B-field in heat-blanketing envelopes
Young isolated NSs
Crust
Quasistationary XRTs
Neutrino luminosity function
Composition and B-field in heat-blanketing envelopes
Deep crustal heating
Quasipersistent XRTs
KS 1731—260; MXB 1659—29
Crust
Deep crustal heating
Superbursts
Crust
Magnetars after outbursts
Crust
Magnetars in quasistationary
states
??
CONCLUSIONS
Today
Cooling neutron stars
Soft X-ray transients
• Constraints on slow and fast neutrino emission levels
• Mass ordering
Future
• New observations and good practical theories of dense matter
• Individual sources and statistical analysis
CONCLUSIONS
Ordinary cooling isolates neutron stars of age 1 kyr—1 Myr
• There is one basic phenomenological cooling concept
(but many physical realizations)
• Main cooling regulator: neutrino luminosity function
• Warmest observed stars are low-massive; their neutrino luminosity
seems to be <= 1/30 of modified Urca
• Coldest observed stars are more massive; their neutrino luminosity
should be > 30 of modified Urca (any enhanced neutrino emission would do)
• Neutron star masses at which neutrino cooling is enhanced are not constrained
• The real physical model of neutron star interior is not selected
Connections
• Directly related to neutron stars in soft X-ray transients (assuming deep crustal
heating). From transient data the neutrino luminosity of massive stars
is enhanced by direct Urca or pion condensation
• Related to magnetars and superbusrts
Future
• New observations and accurate theories of dense matter
• Individual sources and statistical analysis
CONCLUSIONS
The case is not solved
Plenty of work ahead
Neutrino Emission Processes in Neutron Star Cores
Enhanced emission in inner cores of massive neutron stars
QFAST  Q0FT96
Model
LFAST  L0FT96
Q0 [erg cm 3 s 1 ]
Process
N/H direct Urca
B  B  e  e
B  e  B  e
1026  3 1027
Pion condensate
N  N  e  e
N  e  N  e
1023  1026
Kaon condensate
B  B  e  e
B  e  B  e
1023  1024
Quark matter
d  u  e  e
u  e  d  e
1023  1024
Everywhere in neutron star cores
QSLOW  Q0ST98
LFAST  L0ST98
Modified Urca
nN  pNe
pNe  nN
Bremsstrahlung
N  N  N  N  
1020  3 1021
1019  1020
Analytical estimates
Thermal balance of
cooling star with
isothermal interior
dT
C (T )
  L (T )  L (Ts )  LHEAT
dt
L  4 R 2Ts4
L  L (1  rg /R )
Heat blanketing envelope: Ts  Ts (T )
T (t )  T (r , t ) exp( (r ))
Slow cooling via
Modified Urca
process
Fast cooling via
Direct Urca
process
tSLOW
1 year
~
T96
T ~ 1.5 108 K in t  105 yrs
tFAST
1 min
~
T94
T ~ 107 K in t  200 yrs
MAIN PHYSICAL MODELS
Problems:
• To discriminate between neutrino mechanisms
• To broaden transition from slow to fast neutrino
emission
Direct Urca Process
Lattimer, Pethick, Prakash, Haensel (1991)
n  p  e  e ,
p  e  n  e
 n  n  e  e
p
Q  2 wi  f  f n (1  f p )(1  f e ) d
e
  
m
457 2
n m p me
2
Q
G (1  3g A ) 10 3 T 6 npe
10080
 c
Q ~ 3 1027 T96 erg cm3 s 1 
46
6
9
L ~ 10 T
erg s
n
1
e
Is forbidden in outer core by momentum conservation:
  0  pFn  330 MeV/c, pFe  pFp  120 MeV/c, p ~ kBT / c ~ 0.1T9 MeV/c
Threshold:
pFn  pFp  pFe
 ~2 0
Similar processes with muons
Similar processes with hyperons, e.g.
n
In inner cores
of massive stars
Welcome to the Urca World - I
Gamow and Shoenberg: Casino da Urca in Rio de Janeiro
Neutrino theory of stellar collapse, Phys. Rev. 59, 539, 1941:
Unrecordable cooling agent
Photo and
Story by
R. Ruffini
Welcome to the Urca World - II