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The Cooling ofNeutron Stars
Dany PageInstituto de Astronomía, UNAM, Mexico
KIAS - APCTP International Symposium in Astro-Hadron Physic Seoul, Korea, 10 - 14 November 2003
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Neutrino Emission ScenariosPrologue ...
The previously denominated “Standard Cooling Model”
Nucleon pairing introducesanother neutrino process due to the
FORMATION and BREAKING of COOPER PAIRSFlowers, Ruderman & Sutherland, Ap. J. 205 (1976), 541
Voskresenskii & Senatorov, Zh. Eksp. Teor. Fiz. 90 (1986), 1505 [JETP 63 (1986), 885]
Voskresenskii & Senatorov, Yad. Fiz. 45 (1987), 657 [Sov. J. Nucl. Phys. 45 (1987), 411]
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Minimal Coolingof
Neutron Stars
Dany PageInstituto de Astronomía, UNAM
Ongoing collaboration with:
•J.H. Lattimer (SUNY Stony Brook)
•M. Prakash (SUNY Stony Brook)
•A. Steiner (UM, Mineapolis)
Revised version of the “Standard Model”
PART I
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Motivation:Many new observations of cooling neutron stars
with CHANDRA and XMM-NEWTON.
Some have low estimates of Te
Do we have any strong evidence for the presence of some “exotic” component in the
core of some of these neutron stars ?
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ATMOSPHERE: a few cm thick.Determines the spectrum: distribution of
observable flux as a function of photon energy Measurement of “surface” temperature
ENVELOPE: a few tens of meter thick.Blanket which controls the outgoing heat flux
Luminosity
CRUST: only important for the early cooling, little effect later on.
OUTER CORE: n, p, e, essential for neutrino emission, and
thermal energy content
INNER CORE: mystery. Assumed not to exist for now.
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The Supranuclear
Equation of State (EOS)
for the
Minimal Model
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•APR: Akmal & Pandharipande, Phys. Rev. C56 (1997), 2261
Akmal, Pandharipande & Ravenhall, Phys. Rev. C58 (1998), 1804 [AV18 potential + UIX 3body interaction + vb boost]
•WFF3: Wiringa, Fiks & Fabrocini, Phys. Rev. C38 (1988), 1010 [UV14 potential + TNI 3body interaction]
•BPAL21 & BPAL31: Bombaci, Prakash, Ainsworth & Lattimer, Phys. Rep. 280, 1 (1997) [Parametric EOS which reproduces saturation properties, with S ~ n1/2]
Selection criteria for the supranuclear EOS: • The only present baryons are neutrons and protons. (No meson condensate, no hyperons, no quark matter, no ...)• The proton fraction is sufficiently low that DURCA is not allowed.
Point 2 eliminates most Effective Field Theoretical (EFT) models andrelativistic Dirac-Brückner-Hartree-Fock (DBHF) models
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PRESSURE vs. DENSITY
0 1 2 3 4 5 6
nB/n0n0 = saturation density
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Neutron Star MASS vs. RADIUS
At 1.4 Mo :
R ~ 11 – 12 km
At MMax:
R ~ 9.5 – 10.5 km
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NUCLEON EFFECTIVE MASS
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Conclusions:
Within the Minimal Model the EOS is pretty well defined.
• 1.4 Mo neutron stars have radii ~ 11 - 12 km• MMax neutron stars have radii ~ 9.5 – 10.5 km
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The Envelope: (outer boundary condition)
•Sensitivity Strip
•Magnetic field
•Chemical composition
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Temperature profile in the envelope:the “sensivity strip”
Gudmundsson, Pethick & Epstein, Ap. J. 259 (1982), L19 and Ap. J. 272 (1983) 286
2/1 s
8b
6s
TT
and K 10 TK when 10T
b∝
≈≈
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“Te – Tb relationship” for dipolar and dipolar+quadrupolar fields
Page & Sarmiento, 1996
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Menv = 0
Light elements in the envelope
Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99
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Menv = 10-17 Mo
Light elements in the envelope
Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99
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Menv = 10-15 Mo
Light elements in the envelope
Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99
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Menv = 10-13 Mo
Light elements in the envelope
Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99
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Menv = 10-11 Mo
Light elements in the envelope
Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99
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Menv = 10-9 Mo
Light elements in the envelope
Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99
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Menv = 10-7 Mo
Light elements in the envelope
Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99
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€
dEth
dt = CV
dTdt
= −Lν − Lγ
€
dTdt
= − qν 0
cV 0
×T 7 ⇒ t − t0 = A 1T 6 − 1
T06
⎡ ⎣ ⎢
⎤ ⎦ ⎥ ⇒ T ∝ t−1/6
€
CV = 43 πR3 cV0 ×T
Lν = 43 πR3 qν 0 ×T 8
Lγ = 4πR2 Te4 ∝T 2+α [α <<1]
Neutrino Cooling era: L >> L
Photon Cooling era: L << L
€
dTdt
∝ −T 1+α ⇒ t − t0 = B 1T α − 1
T0α
⎡ ⎣ ⎢
⎤ ⎦ ⎥ ⇒ T ∝ t−1/α
Basic Cooling: neutrino vs photon cooling eras
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)(TTT ee =
Effect of envelope chemical compositions
Light elements envelope
Iron-like envelope
€
Lγ = 4πR2 Te4 ∝T 2+α
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Neutron and Proton
Pairing
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Predictions for the NEUTRON 1S0 gap
WAP: Wambach, Ainsworth & Pines, Nulc. Phys. A555 (1993), 128
CCDK: Chen, Clark, Davé & Khodel, Nucl. Phys. A555 (1993), 59
SCLBL: Schulze, Cugnon, Lejeune, Baldo & Lombardo, Phys. Lett. B375 (1996), 1
SFB: Schwenk, Friman & Brown, Nucl. Phys. A717 (2003), 191
Crust-core transition
Important feature:Medium polarization effects reduce Tc by a factor three
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Predictions for the PROTON 1S0 gap
T: Takatsuka, Prog. Thero. Phys. 50 (1970), 905
CCY: Chao, Clark & Yang, Nucl. Phys. A179 (1972), 320
AO: Amundsen & Osgaard, Nucl. Phys. A437 (1985), 487
BCLL: Baldo, Cugnon, Lejeune & Lombardo, Nucl. Phys. A536 (1992), 349
CCDK: Chen, Clark, Davé & Khodel, Nucl. Phys. A555 (1993), 59
EEHO: Elgaroy, Engvik, Horth-Jensen & Osnes, Nucl. Phys. A604 (1996), 466
Important features:
All vanish at pF >1.3 fm-1
and most at pF > 1 fm-1
Expected maximum Tc ~ 1 - 2 x 109 K
Medium polarization effects seem to reduce Tc by a factor three
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Predictions for the NEUTRON 3P2 gap
0: Hoffberg, Glassgold, Richardson & Ruderman, Phys. Rev. Lett. 24 (1970), 775
1: Amundsen & Osgaard, Nucl. Phys. A442 (1985), 4163
2: Takatsuka, Prog. Theor. Phys. 48 (1972), 1517
a, b, c:Baldo, Elgaroy, Engvik, Horth-Jensen & Schulze,
Phys. Rev. C58 (1998), 1921
Important feature:
WE DO NOT REALLY KNOW WHAT IT IS
Medium polarization effects were expected to increase the 3P2 gap while they probably strongly suppress it.
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Specific Heat
and its
Suppression by Pairing
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Distribution of Cv in the core among constituents
At T=109 K
€
CV = N(0) π 2
3 kB2T N (0) = m* pF
π 2h3
€
CVpaired =
CVnormal × M (T /Tc )
≈ CVnormal × e−Δ(T ) /kT
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Pairing and neutrino emission:
•Supression
•Cooper pair formation and destruction
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Suppression of MURCA et al. by pairingnormalpaired )phase;/( qTcTSq =
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Neutrino emission through the formation and breaking of Cooper pairs
Flowers, Ruderman & Sutherland, Ap. J. 205 (1976), 541
Voskresenskii & Senatorov, Zh. Eksp. Teor. Fiz. 90 (1986), 1505 [JETP 63 (1986), 885]
Voskresenskii & Senatorov, Yad. Fiz. 45 (1987), 657 [Sov. J. Nucl. Phys. 45 (1987), 411]
89
21MUrca
79
22Coop
T 10
T )phase;/( 10
≈
≈
q
TcTFq
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Cooper pair neutrino luminosities for p 1S0 and n 3P2 gaps (APR 1.4 Mo)
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Cooper Pair Neutrino Luminosities vs MURCA and Photons in complete realistic evolutionary calculations (APR 1.4 Mo)
Neutron 3P2 gap “a” Neutron 3P2 gap “b” Neutron 3P2 gap “c”
Proton 1S0 gap from Amundsen & Ostgaard
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Variations on a theme:
•Varying the star´s mass
•Varying the EOS
•Cranking up the MURCA rate
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Varying the star´s mass
EOS: APR
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Varying the EOS
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Cranking up the MURCA rate
(à la Friman & Maxwell)
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Putting things together:
Minimal Model(and all its uncertainties)
vs.
DATA(and all their uncertainties)
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Everything together:
All possible neutron and proton gapsLight element envelopes
Heavy element envelopes
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Heavy element envelopes
All possible neutron and proton gaps
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Predictions for the NEUTRON 3P2 gap
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Heavy elements envelopesNeutron 3P2 gap = 0 All possible n & p 1S0 gaps
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Heavy elements envelopesNeutron 3P2 gap = "a" (Tc ~109 K) All possible n & p 1S0 gaps
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Heavy elements envelopesNeutron 3P2 gap = "b" (Tc ~3x109 K) All possible n & p 1S0 gaps
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Heavy elements envelopesNeutron 3P2 gap = "c" (Tc ~1010 K) All possible n & p 1S0 gaps
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Heavy elements envelopes All possible n & p gaps
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Light element envelopes
All possible neutron and proton gaps
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Light elements envelopesNeutron 3P2 gap = 0 All possible n & p 1S0 gaps
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Light elements envelopesNeutron 3P2 gap = "a" (Tc ~109 K) All possible n & p 1S0 gaps
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Light elements envelopesNeutron 3P2 gap = "b" (Tc ~3x109 K) All possible n & p 1S0 gaps
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Light elements envelopesNeutron 3P2 gap = "c" (Tc ~1010 K) All possible n & p 1S0 gaps
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Light elements envelopesAll possible n & p gaps
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Light element envelopes
Iron envelopes
Summary: Temperature vs Time
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Summary: Luminosity vs Time
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CONCLUSIONSabout the
THEORY • EOS quite well determined
• The mass of the star has little impact
• The dominant neutrino emission process is from the formation and breaking of Cooper pairs from the neutron 3P2 gap (unless this gap is very small)
• Possibility of the presence of light elements in the envelope allows to accomodate a range of Te at a given age
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CONCLUSIONSabout
COMPARISON with DATA • Neutron 3P2 pairing with Tc ~ 109 K and various envelope composition may be marginally acceptable.
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CONCLUSIONSabout
COMPARISON with DATA • Neutron 3P2 pairing with Tc > 3x109 K and various envelope composition seems to be marginally inacceptable.
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CONCLUSIONSabout
COMPARISON with DATA • Neutron 3P2 pairing with Tc ~ 0 is inacceptable and would requiere a more elaborate model
but a vanishing neutron 3P2 gap is a
serious problem
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Fast Coolingof
Neutron Stars
PART II
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ATMOSPHERE: a few cm thick.Determines the spectrum: distribution of
observable flux as a function of photon energy Measurement of “surface” temperature
ENVELOPE: a few tens of meter thick.Blanket which controls the outgoing heat flux
Luminosity
CRUST: only important for the early cooling, little effect later on.
OUTER CORE: n, p, e, essential for neutrino emission, and
thermal energy content
INNER CORE: mystery. ==> Strong neutrino emission
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Neutrino Emission Scenarios
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Fast Cooling with Direct Urca Process
“The Cooling of Neutron Stars by the Direct Urca Process”, Page & Applegate, ApJ 394, L17 (1992)
Critical mass for Durca:
1.35 Mo
Notice: the 1.4 Mo star has a "Durca pit" of 0.04 Mo !
<- Arbitrary, we DO NOT KNOW what it really is
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Fast Cooling with Direct Urca Process
“The Cooling of Neutron Stars by the direct Urca Process”, Page & Applegate, ApJ 394, L17 (1992)
With pairing (e.g., n 3P2) the cooling can be temporarily stopped at practically any temperature, depending on the value of Tc in the "Durca pit"
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Fast Cooling with a Kaon Condensate
“Strangeness Condensation, Nucleon Superfluidity, and Cooling of Neutron Stars”, Page & Baron, ApJ 354 L17 (1990)
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Fast Neutrino Emission Scenarios
Q =
T erg s-1 cm-3
[K- condensate]
T erg s-1 cm-3
- condensate
T erg s-1 cm-3
[Direct URCA]
From: D. Page, “Thermal Evolution of Isolated Neutron Stars”,in The Many Faces of Neutron Stars [NATO ASI, Lipari, 1996]
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“Prospects of Detecting Baryon and Quark Superfluidity from Cooling Neutron Stars”, Page, Prakash, Lattimer & Steiner, PRL 85, 2048 (2000)
A "Maximal Model"Direct Urcas with Nucleons, Hyperons and Quarks
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€
H (t) = J44 ×1040 t + τ 0
100 yrs ⎛ ⎝ ⎜
⎞ ⎠ ⎟−3/2
erg s-1
J44= differential angular momentum in the frictionally coupled inner crust neutron superfluid, in units of 1044 g cm2 rad s-1
Fast Cooling with a Kaon Condensate with frictional heating and light element envelopes
“Fast Cooling of Neutron Stars: Superfluidity versus Heating and Accreted Envelope”, Page, ApJ 479, L43 (1997)
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