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.
Dense matter
• Equilibrium:
• Fermi sphere:
• Non-interacting particles (not a great approx.):
• Charge neutrality:
• Relevant regime:
• Combining:
• Relativistic limit:
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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
Momentum conservation?
forbidden! are processes aDirect Urc
gas) Fermi ginteractin-non (including
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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
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)
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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
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.
Yakovlev & 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 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 ),(
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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:
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
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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
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
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)
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