Neutron Stars 3: Thermal evolution

Andreas ReiseneggerDepto. de Astronomía y Astrofísica

Pontificia Universidad Católica de Chile

Outline

• Cooling processes of NSs:

– Neutrinos: direct vs. modified Urca processes, effects of superfluidity & exotic particles

– Photons: interior vs. surface temperature

• Cooling history: theory & observational constraints

• Accretion-heated NSs in quiescence

• Late reheating processes:

– Rotochemical heating

– Gravitochemical heating & constraint on dG/dt

– Superfluid vortex friction

– Crust cracking

Bibliography

• Yakovlev et al. (2001), Neutrino Emission from Neutron Stars, Physics Reports, 354, 1 (astro-ph/0012122)

• Shapiro & Teukolsky (1983), Black Holes, White Dwarfs, & Neutron Stars, chapter 11: Cooling of neutron stars (written before any detections of cooling neutron stars)

• Yakovlev & Pethick (2004), Neutron Star Cooling, Ann. Rev. A&A, 42, 169

General ideas

• Neutron stars are born hot (violent core collapse)

• They cool through the emission of neutrinos from their interior & photons from their surface

• Storage, transport, and emission of heat depend on uncertain properties of dense matter (strong interactions, exotic particles, superfluidity)

• Measurement of NS surface temperatures (and ages or accretion rates) can allow to constrain these properties

• Very old NSs may not be completely cold, due to various proposed heating mechanisms

• These can also be used to constrain dense-matter & gravitational physics.

“Urca processes”NS cooling through emission of neutrinos & antineutrinos

• Direct Urca:

– Rates depend on available initial & final states

• Much slower than free n decay because of Pauli

• Still very fast on astrophysical scales

– Require high fraction of protons & electrons for momentum conservation: possibly forbidden

• Modified Urca:

– Rates reduced because additional particle must be present at the right time, but always allowed

Why Urca: These processes make stars lose energy as quickly as George Gamow lost his money in the “Casino da Urca” in Brazil...

ee , nepepn

ee , nNepNepNnN

Surface temperature

Model for heat conduction through NS envelope

(Gudmundsson et al. 1983)

K103.1455.0

14

4s68

int

g

TT Potekhin et al. 1997

Cooling (& heating)

• Heat capacity of non-interacting, degenerate fermions C T (elementary statistical mechanics)– Can also be reduced through Cooper pairing: will be dominated by non-

superfluid particle species

• Cooling & heating don’t affect the structure of the star (to a very good approximation)

Observations

Thermal X-rays are:

• faint

• absorbed by interstellar HI

• often overwhelmed by non-thermal emission

difficult to detect & measure precisely

D. J. Thompson, astro-ph/0312272

Cooling with modified

Urca & no superfluidity

vs. observations

Direct vs. modified UrcaYakovlev & Pethick 2004

Effect of exotic particlesYakovlev & Pethick 2004

Superfluid games - 1 Yakovlev & Pethick 2004

Superfluid games - 2Yakovlev & Pethick 2004

Heating neutron star matter by weak interactions

• Chemical (“beta”) equilibrium sets relative number densities of particles (n, p, e, ...) at different pressures

• Compressing a fluid element perturbs equilibrium

• Non-equilibrium reactions tend to restore equilibrium

• “Chemical” energy released as neutrinos & “heat”

Reisenegger 1995, ApJ, 442, 749

epnepn ),(

epn

eepn

Possible forcing mechanisms

• Neutron star oscillations (bulk viscosity): SGR flare oscillations, r-modes – Not promising

• Accretion: effect overwhelmed by external & crustal heat release – No.

• d/dt: “Rotochemical heating” – Yes

• dG/dt: “Gravitochemical heating” - !!!???

“Rotochemical heating”

NS spin-down (decreasing centrifugal support) progressive density increase chemical imbalance non-equilibrium reactions internal heating possibly detectable thermal emission

Idea & order-of-magnitude calculations: Reisenegger 1995Detailed model: Fernández & Reisenegger 2005, ApJ, 625, 291

0, epn

,),( eepn

Yakovlev & Pethick 2004

Recall standard neutron star cooling:

No thermal emission after 10 Myr.

Thermo-chemical evolution

,:radiation

throughdecrease

epn

throughincrease

dt

dT

epn

throughdecrease

ncompressio

throughincrease

dt

d

Variables:•Chemical imbalances•Internal temperature TBoth are uniform in diffusive equilibrium.

μe,pnμe, μμμη

MSP evolutionMagnetic dipole spin-down (n=3)

with P0 = 1 ms; B = 108G; modified Urca

Internal temperature

Chemicalimbalances

Stationary state

Fernández & R. 2005

Insensitivity to initial temperature

Fernández & R. 2005

For a given NS model, MSP temperatures can be predicted uniquely from the measured spin-down rate.

7/8thermal )( L

PSR J0437-4715: the nearest millisecond

pulsar

SED for PSR J0437-4715HST-STIS far-UV observation (1150-1700 Å)

Kargaltsev, Pavlov, & Romani 2004

TR2onconstraint

PSR J0437-4715: Predictions vs. observation

Fernández & R. 2005

Observational constraints

Theoretical models

2001) al.et Straten (van

18.058.1 SunMM Direct Urca

Modified Urca

Old, classical pulsars: sensitivity to initial rotation rate

G105.2 11B

D. González, in preparation

dG/dt ?• Dirac (1937): constants of nature may depend on

cosmological time.• Extensions to GR (Brans & Dicke 1961) supported

by string theory • Present cosmology: excellent fits, dark mysteries,

speculations: “Brane worlds”, curled-up extra dimensions, effective gravitational constant

• Observational claims for variations of– (Webb et al. 2001; disputed) – (Reinhold et al. 2006)

See how NSs constrain d/dt of

ce 2EMα

ep mm

cGm 2nGα

Gravitochemical heating

dG/dt (increasing/decreasing gravity) density increase/decrease chemical imbalance non-equilibrium reactions internal heating possibly detectable thermal emission

Jofré, Reisenegger, & Fernández 2006, Phys. Rev. Lett., 97, 131102

),( epn

0, epn

-110 yr102/|| GGMost general constraintfrom PSR J0437-4715

PSR J0437-4715Kargaltsev et al. 2004 obs.

“Modified Urca”reactions (slow )

“Direct Urca”reactions (fast)

-112 yr104/|| GGConstraint from PSR J0437-4715assuming only modified Urca is allowed

PSR J0437-4715Kargaltsev et al. 2004 obs.

Modified Urca

Direct Urca

Main uncertainties• Atmospheric model:

– Deviations from blackbody• H atmosphere underpredicts Rayleigh-Jeans tail• B. Droguett

• Neutrino emission mechanism/rate: – Slow (mod. Urca) vs. fast (direct Urca, others)– Cooper pairing (superfluidity):

• Reisenegger 1997; Villain & Haensel 2005• C. Petrovich, N. González

– Phase transitions:• I. Araya

Not important (because stationary state):

– Heat capacity– Heat transport through crust

Other heating mechanisms

Accretion of interstellar gas – Only for slowly moving, slowly rotating and/or unmagnetized stars– Does not seem to be enough to make old NSs observable

(conclusion of Astro. Estelar Avanzada 2008-2)

Vortex friction (Shibazaki & Lamb 1989, ApJ, 346, 808)– Very uncertain parameters– More important for slower pulsars with higher B:

Crust cracking (Cheng et al. 1992, ApJ, 396, 135 - corrected by Schaab et al. 1999, A&A, 346, 465)– Similar dependence as rotochemical; much weaker

)not ( L