Neutron Stars 3: Thermal evolution

1
Neutron Stars 3 Thermal evolution

• Andreas Reisenegger
• Depto. de Astronomía y Astrofísica
• Pontificia Universidad Católica de Chile

2
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

3
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. AA, 42, 169

4
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.

5
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...

6
Surface temperature

• Model for heat conduction through NS envelope
• (Gudmundsson et al. 1983)

Potekhin et al. 1997
7
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 dont affect the structure of
  the star (to a very good approximation)

8
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
9
Cooling with modified Urca no superfluidityvs.
observations
10
Direct vs. modified Urca
Yakovlev Pethick 2004
11
Effect of exotic particles
Yakovlev Pethick 2004
12
Superfluid games - 1
Yakovlev Pethick 2004
13
Superfluid games - 2
Yakovlev Pethick 2004
14
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

15
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 - !!!???

16
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 1995
• Detailed model Fernández Reisenegger 2005,
  ApJ, 625, 291

17
Recall standard neutron star cooling No thermal
emission after 10 Myr.
Yakovlev Pethick 2004
18
Thermo-chemical evolution

• Variables
• Chemical imbalances
• Internal temperature T
• Both are uniform in diffusive equilibrium.

19
MSP evolution
Stationary state
Internal temperature
Chemical imbalances
Fernández R. 2005
Magnetic dipole spin-down (n3) with P0 1 ms B
108G modified Urca
20
Insensitivity to initial temperature
Fernández R. 2005
For a given NS model, MSP temperatures can be
predicted uniquely from the measured spin-down
rate.
21
PSR J0437-4715 the nearest millisecond pulsar
22
SED for PSR J0437-4715
HST-STIS far-UV observation (1150-1700
Å) Kargaltsev, Pavlov, Romani 2004
23
PSR J0437-4715 Predictions vs. observation
Observational constraints
Modified Urca
Theoretical models
Direct Urca
Fernández R. 2005
24
Old, classical pulsars sensitivity to initial
rotation rate
D. González, in preparation
25
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

26
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

27
Most general constraint from PSR J0437-4715
Modified Urca reactions (slow )
PSR J0437-4715 Kargaltsev et al. 2004 obs.
Direct Urca reactions (fast)
28
Constraint from PSR J0437-4715 assuming only
modified Urca is allowed
Modified Urca
PSR J0437-4715 Kargaltsev et al. 2004 obs.
Direct Urca
29
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

30
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, AA, 346,
  465)
• Similar dependence as rotochemical much weaker