Neutron Stars 3: Thermal evolution

Neutron Stars 3: Thermal evolution

Andreas ReiseneggerESO Visiting Scientist

Associate Professor,

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.

Neutron decay (again!):(excerpts from Yakovlev et al. 2001)

Dense matter

• Equilibrium:

• Fermi sphere:

• Non-interacting particles (not a great approx.):

• Charge neutrality:

• Relevant regime:

• Combining:

• Relativistic limit:

312 )3( npF

2222 )( cpmc F

epn

ee and

nepepn

FeFpep ppnn

3-40p

3-30

pFppne

cm10cm10

)(

n

cmpcmmcm

3-38n

n2

3

pn

p

cm10301.03

2

nn

cmn

n

8

12)cm10(

n

pFpFn

3-40ppFp n

nppncmp

Direct Urca processes

n, p, e all have degenerate Fermi-Dirac distributions (kT << EF )

Reactants & products must be within kT of their Fermi energies

Emitted neutrinos & antineutrinos must have energies ~kT

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

Fermi-Dirac distribution function (expected # of fermions per orbital)for T = 0 and 0 < kT << EF

Direct Urca rates

(excerpts from Yakovlev et al. 2001)

Energy/time/volume emitted as ee ,

Momentum conservation?

forbidden! are processes aDirect Urc

gas) Fermi ginteractin-non (including

models!star neutron most in satisfiedNot

8ly equivalentor

2if satisfied beonly can

:onconservati Momentum

||~

),,(||

,,

nep

FnFeFp

epn

Fkk

Fkkkk

nnn

ppp

ppp

pckTpkTE

epnkppE

Modified Urca processes

• Let an additional nucleon N (=n or p) participate in the reaction, without changing its identity, but exchanging momentum with the reacting particles:

• In this case, momentum conservation can always be satisfied.

ee , nNepNepNnN

Modified Urca rates

cf. direct Urca:

(excerpts from Yakovlev et al. 2001)

Exotic particles

• At high densities, exotic particles such as mesons or even “free” quarks may be present

• These generally allow for variants of the direct Urca processes, nearly as fast

Superfluid reduction factor

“Cooper pairing” of nucleons (n or p or both) creates a gap in the available states around the Fermi energy, generally reducing the reaction rates.

Yakovlev et al. 2001

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

Yakovlev & Pethick 2004


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

Soft X-ray transients - 1

• Binary systems with episodic accretion

• Material falls onto the NS surface & undergoes several nuclear transformations:

H He C heavier elements

• Most of the energy gets emitted quickly, near the surface of the star, but ~1MeV/nucleon is released deep in the crust

• This energy ( accreted mass) heats the neutron star interior, and is released over ~106yr as neutrinos from the interior & quiescent X-rays from the surface

Soft X-ray transients - 2

Accretion rate vs. quiescent X-ray luminosity: predictions & observations.

Problem: Observe accretion rate only over a few years, need average over millions of years.


Heating neutron star matter by weak interactions

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

• Compressing or expanding 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 e.g.,

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


Recall standard neutron star cooling:

1) No thermal emission after 10 Myr.

2) Finite diffusion time matters only during first few 100 yr.

3) Cooling of young neutron stars in rough agreement with slow cooling models (modified Urca)

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


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


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

González, R., & Fernández, 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

Previous constraints on dG/dtMethod G'/G [yr^(-1)] Timespan[yr] Reference

Solar System planet and 1E-12 24 Williams satellite orbits et al (1996)

Binary pulsar orbit 5E-12 10 Kaspi et al (1994)

Rotation of isolated PSRs 6E-11 10 Goldman (1990)(var. moment of inertia)

White dwarf oscillations 3E-10 20 Benvenuto etal. (2004)

Paleontology: 2E-11 4E+09 Eichendorf &Earth's surface temp. Reinhardt (1977)vs. prehistoric fauna

Binary pulsar masses 2E-12 2E+09 Thorsett (1996)(Chandrasekhar mass attime of formation)

Helioseismology 2E-12 5E+09 Guenther et (Solar evolution models) al. (1998)

Globular clusters 7E-12 1E+10 Degl'Innocenti (isochrones vs. age of the et al. (1996)Universe)

CMB temperature 1E-13 1E+10 Nagata fluctuations (WMAP et al. (2004)vs. specific models)

Big Bang Nucleosynthesis 2E-13 1E+10 Copi(abundances of D, He, Li) et al. (2004)

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

Constraint from PSR J0437-4715:

...if only modified Urca processes are allowed, and the star has reached its stationary state.

Required time:

Compare to age estimates:

112 yr104/ GG

Myr 90eqt

Gyr 3.55.2

Gyr 9.4

cooling WD

down-spin

t

t

(Hansen & Phinney 1998)

Now:

Method G'/G [yr^(-1)] Time [yr] Reference

Solar System planet and 1E-12 24 Williams satellite orbits et al (1996)

Binary pulsar orbit 5E-12 10 Kaspi et al (1994)

Rotation of isolated PSRs 6E-11 10 Goldman (1990)(var. moment of inertia)

White dwarf oscillations 3E-10 20 Benvenuto etal. (2004)

Gravitochemical heating 2E-10 1E+05 Jofré et al. (2006)of NSs (PSR J0437-4715)

MOST GENERAL

Gravitochemical heating 4E-12 9E+07 Jofré et al. (2006)of NSs (PSR J0437-4715)

ONLY MODIFIED URCA

Paleontology: 2E-11 4E+09 Eichendorf &Earth's surface temp. Reinhardt (1977)vs. prehistoric fauna

Binary pulsar masses 2E-12 2E+09 Thorsett (1996)(Chandrasekhar mass attime of formation)

Helioseismology 2E-12 5E+09 Guenther et (Solar evolution models) al. (1998)

Globular clusters 7E-12 1E+10 Degl'Innocenti (isochrones vs. age of the et al. (1996)Universe)

CMB temperature 1E-13 1E+10 Nagata fluctuations (WMAP et al. (2004)vs. specific models)

Big Bang Nucleosynthesis 2E-13 1E+10 Copi(abundances of D, He, Li) et al. (2004)

Main uncertainties• Atmospheric model:

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

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

• R. 1997; Villain & Haensel 2005; work in progress

Not important (because stationary state):

• Heat capacity: steady state• Heat transport through crust

Other heating mechanisms

Accretion of interstellar gas: Only for slowly moving, slowly rotating and/or unmagnetized stars

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

Comparison of heating mechanisms: González, Reisenegger, & Fernández 2007 (in preparation)

)not ( L

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Neutron Stars 3: Thermal evolution