THERMAL EVOLUTION OF NTHERMAL EVOLUTION OF NEUTRON STEUTRON STAARRS:S:Theory and observationsTheory and observations
D.G. Yakovlev
Ioffe Physical Technical Institute, St.-Petersburg, Russia
Catania, October 2012,
1. Formulation of the Cooling Problem 2. Superlfuidity and Heat Capacity 3. Neutrino Emission 4. Cooling Theory versus Observations
Stage Duration Physics
Relaxation 10—100 yr Crust
Neutrino 10-100 kyr Core, surface
Photon infinite Surface, core,reheating
THREE COOLING STAGESAfter 1 minute of proto-neutron star stage
( ) ( ) ( )ii i sdTC T L T L Tdt
2 44 (1 / )
Heat blanketing envelope: ( )( ) ( , )exp( ( ))
s g
s s
i
L R T L L r R
T T TT t T r t r
Analytical estimates
Thermal balance of cooling star with isothermal interior
Slow cooling viaModified Urca process
SLOW 69
1 year~i
tT
8 5~ 1.5 10 K in 10 yrsiT t
Fast cooling viaDirect Urca process
FAST 49
1 min~i
tT
7~ 10 K in 200 yrsiT t
OBSERVATIONS: MAIN PRINCIPLES
S
pin
axi
s B- axis
Isolated (cooling) neutron stars – no additional heat sources:Age tSurface 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
Chandraimage of the Velapulsarwind nebulaNASA/PSUPavlov et al
Chandra XMM-Newton
MULTIWAVELENGTH SPECTRUM OF THE VELA PULSAR
4(1.1 2.5) 10 yr
0.65 0.71 MKS
t
T
THERMAL RADIATION FROM ISOLATED NEUTRON STARS
OBSERVATIONS AND BASIC COOLING CURVENonsuperfluid starNucleon coreModified Urca neutrino emission:slow cooling
Minimal cooling; SF off – does not explain all data
MAXIMAL COOLING; SF OFFMODIFIED AND DIRECT URCA PROCESSES
1=Crab2=PSR J0205+64493=PSR J1119-61274=RX J0822-435=1E 1207-526=PSR J1357-64297=RX J0007.0+73038=Vela9=PSR B1706-4410=PSR J0538+281711=PSR B2234+6112=PSR 0656+1413=Geminga14=RX J1856.4-375415=PSR 1055-5216=PSR J2043+274017=PSR J0720.4-3125
15MAX c
14D c
1.977 2.578 10 g/cc
1.358 8.17 10 g/ccFrom 1.1 to 1.98 with step 0.01
M M
M MM M M M
Does not explain the data
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”)
VELA 1.61 ?M M
MAXIMAL COOLING: SRTONG PROTON SF
MAXIMAL COOLING: STRONG PROTON SF – II
VELA 1.47 ?M M
Mass ordering is the same!
MINIMUM AND MAXIMUM COOLING SF on
Gusakov et al. (2004, 2005)
Minimum coolingGusakov et al. (2004)
Minimum-maximum coolingGusakov et al. (2005)
Cassiopeia A supernova remnant
Cassiopeia A observed by the Hubble Space Telescope
Very bright radio sourceWeak in optics due to interstellar absoprtion
Distance: kpc (Reed et al. 1995)
Diameter: 3.1 pc
No historical data on progenitor
Asymmetric envelope expansionAge yrs => 1680 from observations of expanding envelope (Fesen et al. 2006)
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 observationsLater 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 pulsations2.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, 671Fitting the observed spectrum with carbon atmosphere model gives the emission from the entire neutron star surface
Neutron star parameters
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)
Conclusion:Cas A SNR contains cooling neutron star with carbon surfaceIt is the youngest cooling NS whose thermal radiation is observed
Main features:1. Rather warm neutron star2. Consistent with standard cooling3. Not interesting for cooling theory!!! (Yakovlev et al. 2011)
Heinke & Ho, ApJL (2010): Surface temperature decline by 4% over 10 years
Ho & Heinke 2010
New observation
Standard cooling
“Standard cooling” cannot explain these observations
M, R, d, NH are fixed
Observed cooling curve slope
REVOLUTION: Cooling Dynamics of Cas A NS!
Cas A neutron star:1.Is warm as for standard cooling2.Cools much faster than for standard cooling
ln 0.1ln
sd Tsd t
ln 1.35 0.15 (2 )ln
sd Tsd t
Standard cooling curve slope
Neutron superfluidity:
Proton superfluidity:
Together:
Faster cooling because of CP neutrino emission
Slower cooling because of suppression of neutrino emission
Sharp acceleration of cooling
Effects of Superfluidity on 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 agoWhat for? suppresses neutrino emission
before the appearance of neutron superfluidity
produces neutrino outburst
Example: Cooling of 1.65 Msun StarAPR EOS
Neutrino emission peak: ~80 yrs ago
Neutron stars of different masses
Only Tcn superfluidity I explains all the sources
One model of superfluidity for all neutron stars
Alternatively: wider profile, but the efficiency of CP neutrino emission at low densities is weak
Gusakov et al. (2004)
Cas A neutron star among other isolated neutron stars
Slope of cooling curve
logMeasure ( )~ infer log
s ss
d TT t t sd t
1 /121 / 8
sss
= standard cooling (Murca)
= slope of cooling curve
= enhanced cooling (Durca)
>> 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)
Deep crustal heating:Theory: Haensel & Zdunik (1990) Applications to XRTs:Brown, Bildsten & Rutledge (1998)
INSs XRTs Magnetars
Magnetic heatingCooling of initially hot star
CONCLUSIONS (without Cas A)
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
OBSERVATIONS
•Include sources of different types
•Seem more important than theory
•Are still insufficient to solve NS problem
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???