Transcript Lecture 4

THERMAL EVOLUTION OF NEUTRON STARS:
Theory and observations
D.G. Yakovlev
Ioffe Physical Technical Institute, St.-Petersburg, Russia
1. Formulation of the Cooling Problem
2. Superlfuidity and Heat Capacity
3. Neutrino Emission
4. Cooling Theory versus Observations
Catania, October 2012,
THREE COOLING STAGES
After 1 minute of proto-neutron star stage
Stage
Duration
Physics
Relaxation
10—100 yr
Crust
Neutrino
10-100 kyr
Core, surface
Photon
infinite
Surface, core,
reheating
Analytical estimates
Thermal balance of
cooling star with
isothermal interior
dTi
C (Ti )
  L (Ti )  L (Ts )
dt
L  4 R 2Ts4
L  L (1  rg /R )
Heat blanketing envelope: Ts  Ts (T )
Ti (t )  T ( r, t ) exp( ( r ))
Slow cooling via
Modified Urca
process
Fast cooling via
Direct Urca
process
tSLOW
1 year
~
Ti 69
Ti ~ 1.5  108 K in t  105 yrs
tFAST
1 min
~
Ti 94
Ti ~ 107 K in t  200 yrs
Spin
axis
OBSERVATIONS: MAIN PRINCIPLES
Isolated (cooling) neutron stars – no
additional heat sources:
Age t
Surface temperature Ts
MEASURING DISTANCES:
parallax; electron column density from radio data;
association with clusters and supernova remnants;
fitting observed spectra
MEASURING AGES:
pulsar spin-down age (from P and dP/dt);
association with stellar clusters and supernova remnants
MEASURING SURFACE TEMPERATURES:
fitting observed spectra
OBSERVATIONS
Chandra
image of
the Vela
pulsar
wind nebula
NASA/PSU
Pavlov et al
Chandra
XMM-Newton
MULTIWAVELENGTH SPECTRUM OF THE VELA PULSAR
t  (1.1  2.5) 104 yr
TS  0.65  0.71 MK
THERMAL RADIATION FROM ISOLATED NEUTRON STARS
OBSERVATIONS AND BASIC COOLING CURVE
Nonsuperfluid star
Nucleon core
Modified Urca
neutrino emission:
slow cooling
Minimal cooling; SF off – does not explain all data
MAXIMAL COOLING; SF OFF
MODIFIED AND DIRECT URCA PROCESSES
1=Crab
2=PSR J0205+6449
3=PSR J1119-6127
4=RX J0822-43
5=1E 1207-52
6=PSR J1357-6429
7=RX J0007.0+7303
8=Vela
9=PSR B1706-44
10=PSR J0538+2817
11=PSR B2234+61
12=PSR 0656+14
13=Geminga
14=RX J1856.4-3754
15=PSR 1055-52
16=PSR J2043+2740
17=PSR J0720.4-3125
Does not explain
the data
M MAX  1.977 M
c  2.578 1015 g/cc
M D  1.358 M
c  8.17 1014 g/cc
From 1.1 M to 1.98 M with step M  0.01 M
MAXIMAL COOLING: SRTONG PROTON SF
Two models for proton superfluidity
Neutrino emissivity profiles
Superfluidity:
• Suppresses modified Urca process in the outer core
• Suppresses direct Urca just after its threshold (“broadens
the threshold”)
MAXIMAL COOLING: SRTONG PROTON SF
M VELA  1.61 M ?
MAXIMAL COOLING: STRONG PROTON SF – II
Mass ordering is the same!
M VELA  1.47 M ?
MINIMUM AND MAXIMUM COOLING
SF on
Gusakov et al. (2004, 2005)
Minimum cooling
Gusakov et al. (2004)
Minimum-maximum cooling
Gusakov et al. (2005)
Cassiopeia A supernova remnant
Very bright radio source
Weak in optics due to interstellar absoprtion
Distance:
kpc (Reed et al. 1995)
Diameter: 3.1 pc
No historical data on progenitor
Asymmetric envelope expansion
Age
yrs => 1680
from observations of expanding envelope
(Fesen et al. 2006)
Cassiopeia A observed by
the Hubble Space Telescope
MYSTERIOUS COMPACT CENTRAL OBJECT IN Cas A SNR
Various theoretical predictions:
e.g., a black hole (Shklovsky 1979)
Discovery: Tananbaum (1999)
first-light Chandra X-ray observations
Later found in ROSAT and Einstein
archives
Later studies (2000-2009):
Pavlov et al. (2000)
Chakrabarty et al. (2001)
Pavlov and Luna (2009)
Main features:
1. No evidence of pulsations
2. Spectral fits using black-body model
or He, H, Fe atmosphere models
give too small radius R<5 km
Conclusion: MYSTERY –
Not a thermal X-ray radiation emitted
from the entire surface of neutron star
A Chandra X-ray Observatory image of
the supernova remnant Cassiopeia A.
Credit: Chandra image:
NASA/CXC/Southampton/W.Ho;
illustration: NASA/CXC/M.Weiss
COOLING NEUTRON STAR IN Cas A SNR
Ho and Heinke (2009) Nature 462, 671
Fitting the observed spectrum
with carbon atmosphere model
gives the emission from the entire
neutron star surface
Conclusion:
Cas A SNR contains cooling neutron
star with carbon surface
It is the youngest cooling NS whose
thermal radiation is observed
Neutron star parameters
Main features:
1. Rather warm neutron star
2. Consistent with standard
cooling
3. Not interesting for cooling
theory!!! (Yakovlev et al. 2011)
OBSERVATIONS
available for
Ho and Heinke (2009)
Heinke and Ho (2010):
16 sets of Chandra
observations in
2000, 2002, 2004, 2006,
2007, 2009
totaling 1 megasecond
(two weeks)
REVOLUTION: Cooling Dynamics of Cas A NS!
Heinke & Ho, ApJL (2010): Surface temperature decline by 4% over 10 years
“Standard cooling”
cannot explain these
observations
Observed
cooling
curve slope
Ho & Heinke 2010
New observation
Standard cooling
M, R, d, NH are fixed
Cas A neutron star:
1. Is warm as for standard cooling
2. Cools much faster than for
standard cooling
s
Standard
cooling
curve slope
d ln Ts
 1.35  0.15 (2 )
d ln t
s
d ln Ts
 0.1
d ln t
Effects of Superfluidity on Cooling
Neutron superfluidity:
Faster cooling because of CP neutrino emission
Proton superfluidity:
Slower cooling because of
suppression of neutrino emission
Together:
Sharp acceleration of cooling
Superfluidity naturally explains observations!
Both, neutron and proton, superfluids are needed
Superfluidity
Strong proton
Moderate neutron
Tc – profile
>3x109 K, profile unimportant
maximum: TCn(max)~(5-9)x108 K
and wide Tc –profile over NS core
Appears
Early
a few decays ago
What for?
suppresses neutrino emission
before the appearance of
neutron superfluidity
produces neutrino outburst
Example: Cooling of 1.65 Msun Star
APR EOS
Neutrino emission peak: ~80 yrs ago
Neutron stars of different masses
Cas A neutron star among other isolated neutron stars
One model of
superfluidity
for all neutron
stars
Only Tcn superfluidity I explains all the sources
Gusakov et al. (2004)
Alternatively: wider
profile, but the
efficiency of CP neutrino emission
at low densities is weak
Slope of cooling curve
Measure Ts (t )~t  s
{
d log Ts
 infer s  
d log t
= slope of cooling curve
s  1 / 12 = standard cooling (Murca)
s  1 / 8 = enhanced cooling (Durca)
s >> 0.1 => something extraordinary!
Theoretical model for Cas A NS
Shternin et al. (2011)
Now: s = 1.35 = very big number
=> unique phenomenon!
Happens very rarely!
Measurements of s in the next decade
confirm or reject this interpretation
Cooling objects – connections
• Isolated (cooling) neutron stars
• Accreting neutron stars in X-ray transients (heated inside)
• Sources of superbursts
• Magnetars (heated inside)
INSs
Cooling of initially
hot star
XRTs
Deep crustal heating:
Theory: Haensel & Zdunik (1990)
Applications to XRTs:
Brown, Bildsten & Rutledge (1998)
Magnetars
Magnetic heating
CONCLUSIONS (without Cas A)
OBSERVATIONS
•Include sources of different types
•Seem more important than theory
•Are still insufficient to solve NS problem
THEORY
•Too many successful explanations
• Main cooling regulator: neutrino luminosity
• Warmest observed stars are low-massive; their neutrino luminosity
<= 0.01 of modified Urca
• Coldest observed stars are more massive; their neutrino luminosity
>= 100 of modified Urca
CONCLUSIONS about Cas A
• Observations of cooling Cas A NS in real time – matter of good luck!
• Natural explanation: onset of neutron superfluidity in NS core about 80 years ago;
maximum Tcn in the core >~7 x 108 K
• Profile of critical temperature of neutrons over NS core should be wide
• Neutrino emission prior to onset of neutron superfluidity should be 20-100 times smaller
than standard level  strong proton superfluidity in NS core?
• To explain all observations of cooling NSs by one model of superfluidity, Tcn profile has
to be shifted to higher densities
• Prediction: fast cooling will last for a few decades
• Cooling of Cas A NS  direct evidence for superfluidity?
Two Cas A teams
Minimal cooling theory:
Page, Lattimer, Prakash, Steiner (2004)
Gusakov, Kaminker, Yakovlev, Gnedin (2004)
Superfluid Cas A neutron star:
D. Page, M. Prakash, J.M. Lattimer, A.W. Steiner, PRL, vol. 106, Issue 8, id. 081101 (2011)
P.S. Shternin, D.G. Yakovlev, C.O. Heinke, W.C.G. Ho, D.J. Patnaude, MNRAS Lett., 412,
L108 (2011)
Doubts
Carbon atmosphere: why?
Theory: probability to observe is small (too good to be true)
Theory: to explain observations of all cooling neutron stars one needs
unusual Tcn – profile over neutron star core
Observations: data processing???