The Cooling of Neutron Stars Dany Page Instituto de Astronomía, UNAM, Mexico KIAS - APCTP International Symposium in Astro-Hadron Physic Seoul, Korea, November 2003

Neutrino Emission Scenarios Prologue... The previously denominated “Standard Cooling Model” Nucleon pairing introduces another neutrino process due to 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]

Minimal Cooling of Neutron Stars Dany Page Instituto 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

Motivation: Many new observations of cooling neutron stars with CHANDRA and XMM-NEWTON. Some have low estimates of T e Do we have any strong evidence for the presence of some “exotic” component in the core of some of these neutron stars ?

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.

The Supranuclear Equation of State (EOS) for the Minimal Model

APR: Akmal & Pandharipande, Phys. Rev. C56 (1997), 2261 Akmal, Pandharipande & Ravenhall, Phys. Rev. C58 (1998), 1804 [AV18 potential + UIX 3body interaction +  v b 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 ~ n 1/2 ] 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 and relativistic Dirac-Brückner-Hartree-Fock (DBHF) models

PRESSURE vs. DENSITY n B /n 0 n 0 = saturation density

Neutron Star MASS vs. RADIUS At 1.4 M o : R ~ 11 – 12 km At M Max : R ~ 9.5 – 10.5 km

NUCLEON EFFECTIVE MASS

Conclusions: Within the Minimal Model the EOS is pretty well defined. 1.4 M o neutron stars have radii ~ km M Max neutron stars have radii ~ 9.5 – 10.5 km

The Envelope: (outer boundary condition) Sensitivity Strip Magnetic field Chemical composition

Temperature profile in the envelope: the “sensivity strip” Gudmundsson, Pethick & Epstein, Ap. J. 259 (1982), L19 and Ap. J. 272 (1983) 286

“T e – T b relationship” for dipolar and dipolar+quadrupolar fields Page & Sarmiento, 1996

M env = 0 Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

M env = M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

M env = M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

M env = M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

M env = M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

M env = M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

M env = M o Light elements in the envelope Chabrier, Potekhin & Yakovlev, ApJ 477 (1997), L99

Neutrino Cooling era: L >> L  Photon Cooling era: L  << L  Basic Cooling: neutrino vs photon cooling eras

Effect of envelope chemical compositions Light elements envelope Iron-like envelope

Neutron and Proton Pairing

Predictions for the NEUTRON 1 S 0 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 T c by a factor three

Predictions for the PROTON 1 S 0 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 p F >1.3 fm -1 and most at p F > 1 fm -1 Expected maximum T c ~ x 10 9 K Medium polarization effects seem to reduce T c by a factor three

Predictions for the NEUTRON 3 P 2 gap 0: Hoffberg, Glassgold, Richardson & Ruderman, Phys. Rev. Lett. 24 (1970), 775 1: Amundsen & Osgaard, Nucl. Phys. A442 (1985), : 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 3 P 2 gap while they probably strongly suppress it.

Specific Heat and its Suppression by Pairing

Distribution of C v in the core among constituents At T=10 9 K

Pairing and neutrino emission: Supression Cooper pair formation and destruction

Suppression of MURCA et al. by pairing

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]

Cooper pair neutrino luminosities for p 1 S 0 and n 3 P 2 gaps (APR 1.4 M o )

Cooper Pair Neutrino Luminosities vs MURCA and Photons in complete realistic evolutionary calculations (APR 1.4 M o ) Neutron 3 P 2 gap “a”Neutron 3 P 2 gap “b”Neutron 3 P 2 gap “c” Proton 1 S 0 gap from Amundsen & Ostgaard

Variations on a theme: Varying the star´s mass Varying the EOS Cranking up the MURCA rate

Varying the star´s mass EOS: APR

Varying the EOS

Cranking up the MURCA rate (à la Friman & Maxwell)

Putting things together: Minimal Model (and all its uncertainties) vs. DATA (and all their uncertainties)

Everything together: All possible neutron and proton gaps Light element envelopes Heavy element envelopes

All possible neutron and proton gaps

Predictions for the NEUTRON 3 P 2 gap

Heavy elements envelopes Neutron 3 P 2 gap = 0 All possible n & p 1 S 0 gaps

Heavy elements envelopes Neutron 3 P 2 gap = "a" (T c ~10 9 K) All possible n & p 1 S 0 gaps

Heavy elements envelopes Neutron 3 P 2 gap = "b" (T c ~3x10 9 K) All possible n & p 1 S 0 gaps

Heavy elements envelopes Neutron 3 P 2 gap = "c" (T c ~10 10 K) All possible n & p 1 S 0 gaps

Heavy elements envelopes All possible n & p gaps

Light element envelopes All possible neutron and proton gaps

Light elements envelopes Neutron 3 P 2 gap = 0 All possible n & p 1 S 0 gaps

Light elements envelopes Neutron 3 P 2 gap = "a" (T c ~10 9 K) All possible n & p 1 S 0 gaps

Light elements envelopes Neutron 3 P 2 gap = "b" (T c ~3x10 9 K) All possible n & p 1 S 0 gaps

Light elements envelopes Neutron 3 P 2 gap = "c" (T c ~10 10 K) All possible n & p 1 S 0 gaps

Light elements envelopes All possible n & p gaps

Light element envelopes Iron envelopes Summary: Temperature vs Time

Summary: Luminosity vs Time

CONCLUSIONS about 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 T e at a given age

CONCLUSIONS about COMPARISON with DATA Neutron 3P2 pairing with T c ~ 10 9 K and various envelope composition may be marginally acceptable.

CONCLUSIONS about COMPARISON with DATA Neutron 3P2 pairing with T c > 3x10 9 K and various envelope composition seems to be marginally inacceptable.

CONCLUSIONS about COMPARISON with DATA Neutron 3P2 pairing with T c ~ 0 is inacceptable and would requiere a more elaborate model but a vanishing neutron 3 P 2 gap is a serious problem

Fast Cooling of Neutron Stars PART II

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

Neutrino Emission Scenarios

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 M o Notice: the 1.4 M o star has a "Durca pit" of 0.04 M o ! <- Arbitrary, we DO NOT KNOW what it really is

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 3 P 2 ) the cooling can be temporarily stopped at practically any temperature, depending on the value of T c in the "Durca pit"

Fast Cooling with a Kaon Condensate “Strangeness Condensation, Nucleon Superfluidity, and Cooling of Neutron Stars”, Page & Baron, ApJ 354 L17 (1990)

Fast Neutrino Emission Scenarios Q         erg s -1 cm -3 [K - condensate]       erg s -1 cm -3  -  condensate        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]

“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

J 44 = differential angular momentum in the frictionally coupled inner crust neutron superfluid, in units of g cm 2 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)