Transcript Neutron Stars 3: Thermal evolution Andreas Reisenegger ESO Visiting Scientist Associate Professor, Pontificia Universidad Católica de Chile.

Neutron Stars 3:
Thermal evolution
Andreas Reisenegger
ESO 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
n  p  e  e
• Equilibrium:

and p  e  n  e
 n   p  e
• Fermi sphere: pF  (3 2n)1 3
• Non-interacting particles (not a great approx.):  
(mc 2 ) 2  p F2 c 2
• Charge neutrality: np  ne  pFp  pFe
• Relevant regime:
• Combining:
me c  (mn  mp )c  pFp  mp c
 1030 cm-3  np  1040 cm-3
3
  
nn

 3 2 nn  0.01


38
3
nn  2mp c 
 3 10 cm 
np
• Relativistic limit:
( pFp  mpc  np  10 cm )
40
-3
pFn  2 pFp
np
1


nn
8

Direct Urca processes
Why 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  
n  p  e  e ,
p  e  n  e
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
Direct Urca rates
Energy/time/volume emitted as  e ,  e
(excerpts from Yakovlev et al. 2001)
Momentum conservation?

 | pk |  pFk (k  n, p, e)

~ kT   k  | p , |  kT c  pFk
Ek   k
E ,
Momentumconservation :
can only be satisfiedif
or equivalently



p n  p p  pe
pFp  pFe  pFn 2
n p  ne  nn 8
Not satisfiedin most neutronstar models!
(including non - interacting Fermigas)
 Direct Urca processesare forbidden!
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:
N  n  N  p  e  e , N  p  e  N  n  e
• In this case, momentum conservation can
always be satisfied.
Modified Urca rates
(excerpts from Yakovlev et al. 2001)
cf. direct Urca:
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)
T 

Tint  1.3 10 
 g14 
8
4
s6
0.455
K
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 nonsuperfluid 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
Yakovlev & Pethick 2004
Cooling with
modified
Urca & no
superfluidity
vs.
observations
Direct vs. modified Urca
Yakovlev & Pethick 2004
Effect of exotic particles
Yakovlev & Pethick 2004
Superfluid games - 1
Yakovlev & Pethick 2004
Superfluid games - 2
Yakovlev & 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.
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
n  p  (e, )  n   p  e
• Compressing or expanding a fluid element perturbs
e.g., n   p  e
equilibrium
• Non-equilibrium reactions tend to restore
equilibrium
n  p  e  e
• “Chemical” energy released as neutrinos & “heat”
Reisenegger 1995, ApJ, 442, 749
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   n   p  e,  0
 non-equilibrium reactions n  p  (e, )  e,
 internal heating
 possibly detectable thermal emission
Idea & order-of-magnitude calculations: Reisenegger 1995
Detailed model: Fernández & Reisenegger 2005, ApJ, 625, 291
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)
Yakovlev & Pethick 2004
Thermo-chemical evolution
Variables:
•Chemical imbalances ηe,μ
•Internal temperature T
 μ n  μ p  μ e,μ
Both are uniform in diffusive equilibrium.
d  increasethrough  decreasethrough
  

 
n  pe
dt  com pression  

dT  increasethrough  decreasethrough
  

 
dt  n  p  e   radiation:  ,  
Internal
temperature
Stationary
state
Chemical
imbalances
Fernández & R. 2005
MSP evolution
Magnetic dipole spin-down (n=3)
with P0 = 1 ms; B = 108G;
modified Urca
Insensitivity to initial temperature
 )8 / 7
Lthermal  (
Fernández & R. 2005
For a given NS model, MSP temperatures can be
predicted uniquely from the measured spin-down rate.
PSR
J0437-4715:
the nearest
millisecond
pulsar
SED for PSR J0437-4715
HST-STIS far-UV observation (1150-1700 Å)
Kargaltsev, Pavlov, & Romani 2004
 constrainton R 2T
PSR J0437-4715: Predictions vs. observation
Observational constraints
Modified Urca
Theoretical models
M  1.58  0.18 M Sun
Direct Urca
(vanStratenet al. 2001)
Fernández & R. 2005
Old, classical pulsars:
sensitivity to initial rotation rate
B  2.5 10 G
11
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
– α EM  e2 c (Webb et al. 2001; disputed)
– mp me (Reinhold et al. 2006)
 See how NSs constrain d/dt of αG  Gmn2 c
Previous constraints on dG/dt
Method
Solar System planet and
satellite orbits
Binary pulsar orbit
Rotation of isolated PSRs
(var. moment of inertia)
White dwarf oscillations
Paleontology:
Earth's surface temp.
vs. prehistoric fauna
Binary pulsar masses
(Chandrasekhar mass at
time of formation)
Helioseismology
(Solar evolution models)
Globular clusters
(isochrones vs. age of the
Universe)
CMB temperature
fluctuations (WMAP
vs. specific models)
Big Bang Nucleosynthesis
(abundances of D, He, Li)
G'/G [yr^(-1)] Timespan[yr]
Reference
1E-12
24
Williams
et al (1996)
5E-12
10
Kaspi et al (1994)
6E-11
10
Goldman (1990)
3E-10
20
Benvenuto et
al. (2004)
Eichendorf &
Reinhardt (1977)
2E-11
4E+09
2E-12
2E+09
Thorsett (1996)
2E-12
5E+09
7E-12
1E+10
Guenther et
al. (1998)
Degl'Innocenti
et al. (1996)
1E-13
1E+10
Nagata
et al. (2004)
2E-13
1E+10
Copi
et al. (2004)
Gravitochemical heating
dG/dt (increasing/decreasing gravity)
 density increase/decrease
  n   p  e,  0
 chemical imbalance
n

p

(
e
,

)
 non-equilibrium reactions
 internal heating
 possibly detectable thermal emission
Jofré, Reisenegger, & Fernández 2006, Phys. Rev. Lett., 97, 131102
Most general constraint
from PSR J0437-4715
10
-1

| G | / G  2 10 yr
“Modified Urca”
reactions (slow )
PSR J0437-4715
Kargaltsev et al. 2004 obs.
“Direct Urca”
reactions (fast)
Constraint from PSR J0437-4715
assuming only modified Urca is allowed
12
-1

| G | / G  4 10 yr
Modified Urca
PSR J0437-4715
Kargaltsev et al. 2004 obs.
Direct Urca
Constraint from PSR J0437-4715:
12
1

G / G  4 10 yr
...if only modified Urca processes are allowed,
and the star has reached its stationary state.
Required time: teq  90 Myr
Compare to age estimates: tspin -down  4.9 Gyr
t WD cooling  2.5  5.3 Gyr
(Hansen & Phinney 1998)
Method
Solar System planet and
satellite orbits
Binary pulsar orbit
Rotation of isolated PSRs
(var. moment of inertia)
White dwarf oscillations
Now:
Gravitochemical heating
of NSs (PSR J0437-4715)
MOST GENERAL
Gravitochemical heating
of NSs (PSR J0437-4715)
ONLY MODIFIED URCA
Paleontology:
Earth's surface temp.
vs. prehistoric fauna
Binary pulsar masses
(Chandrasekhar mass at
time of formation)
Helioseismology
(Solar evolution models)
Globular clusters
(isochrones vs. age of the
Universe)
CMB temperature
fluctuations (WMAP
vs. specific models)
Big Bang Nucleosynthesis
(abundances of D, He, Li)
G'/G [yr^(-1)] Time [yr]
Reference
1E-12
24
Williams
et al (1996)
5E-12
10
Kaspi et al (1994)
6E-11
10
Goldman (1990)
3E-10
20
2E-10
1E+05
Benvenuto et
al. (2004)
Jofré et al. (2006)
4E-12
9E+07
Jofré et al. (2006)
2E-11
4E+09
Eichendorf &
Reinhardt (1977)
2E-12
2E+09
Thorsett (1996)
2E-12
5E+09
7E-12
1E+10
Guenther et
al. (1998)
Degl'Innocenti
et al. (1996)
1E-13
1E+10
Nagata
et al. (2004)
2E-13
1E+10
Copi
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:
 (not 
)
L
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)