Barcelona, September 26, 2014,
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
NEUTRON STAR COOLING AS A PROBE
OF FUNDAMENTAL PHYSICS
NEUTRINO EMISSION IN NEUTRON STARS
Main features: • unobserved regulates cooling
• complete transparency
QdVL
Q
]c [erg luminosity neutrino and
]scm [erg emissivity neutrino :quantity acticalPr
1
13
e
ep
n
, e e e en p e p e n n n
27 6 3 1
9
46 6 1
9
~ 3 10
~ 10
Q T erg cm s
L T erg s
FeFpFn ppp 02 ~
Direct Urca Process
Lattimer, Pethick, Prakash, Haensel (1991)
Threshold: Can be open in
inner cores
of massive stars Similar processes with muons
In outer core – is forbidden by momentum conservation:
0 9 330 MeV/c, 120 MeV/c, ~ / ~ 0.1 MeV/cFn Fe Fp Bp p p p k T c T
SLOW NEUTRINO EMISSION PROCESSES
EVERYWHERE IN NEUTRON STAR CORES
, e en N p N e p N e n N
8 8
SLOW 0S 9 SLOW 0S 9 Q Q T L L T
MODIFIED URCA [N=n or p = nucleon-spectator]
NUCLEON-NUCLEON BREMSSTRAHLUNG
N N N N
n n n n
n p n p
p p p p
{
Bahcall and Wolf (1965), Friman and Maxwell (1979), Maxwell (1987),
Yakovlev and Levenfish (1995)
Friman and Maxwell (1979)
Any neutrino
flavor
Enhanced emission in inner cores of massive neutron stars
Everywhere in neutron star cores
Neutrino Processes in Neutron Star Cores
6 6
FAST 0F 9 FAST 0F 9 Q Q T L L T
Model Process
Direct Urca
3 1
0 [erg cm s ]Q
e en p e p e n 26 2710 3 10
8 8
SLOW 0S 9 SLOW 0S 9 Q Q T L L T
Modified Urca
Bremsstrahlung
nN pNe pNe nN
N N N N
20 2110 3 10
19 2010 10
Direct Urca
Neutrino emission from cores of non-superfluid NSs
Outer core Inner core
Slow emission Fast emission
}
} }
e en p e p e n
Modified Urca
nN pNe pNe nN
NN bremsstrahlung
N N N N
Enhanced emission in inner cores of
massive neutron stars:
Everywhere in neutron star cores:
6 6
FAST 0F FAST 0F Q Q T L L T
8 8
SLOW 0S SLOW 0S Q Q T L L T
STANDARD
Fast
erg
cm
-3 s
-1
NS with nucleon core:
N=n, p
n n
n p
p p
FAST AND SLOW NEUTRINO COOLING
FAST AND SLOW NEUTRINO COOLING
SUN
M 31
Effects of superfluidity on neutrino emission
Two effects:
1. Suppresses traditional neutrino processes
2. Creates specific neutrino emission due to Cooper pairing of nucleons
Neutrino emission due to Cooper pairing
Flowers, Ruderman and
Sutherland (1976)
Voskresensky and Senatorov
(1987)
Schaab et al. (1997)
n n
Temperature dependence of
neutrino emissivity due to
Cooper pairing
Features:
• Efficient only for
triplet-state pairing
of neutrons
•Non-monotonic
T-dependence
• Strong many-body
effects
Leinson (2001) Leinson and Perez (2006)
Sedrakian, Muether, Schuck
(2007)
Kolomeitsev, Voskresensky
(2008)
Steiner, Reddy (2009)
Leinson (2010)
Physics:
Jumping over cliff
from branch A to B
A
B
Neutrino emission due to Cooper pairing
Neutrino luminosity due to Cooper pairing
8)10010(~ TLL MurcaCooper
Gusakov et al. (2004)
Minimal and maximal cooling paradigms
Consider neutron stars with nucleon cores (simplest composition)
Minimal cooling paradigm: no direct Urca in all stars
Maximal cooling paradigm: direct Urca in heavy stars
Pradigm SF SF
Minimal cooling off on
Maximal cooling off on
Four cases
Minimal cooling theory:
Page, Lattimer, Prakash, Steiner (2004)
Gusakov, Kaminker, Yakovlev, Gnedin (2004)
Minimal and maximal cooling paradigms
Minimal
cooling
Maximal
cooling
SF off SF on
~ (10 100)Cooper MurcaL L
Minimal cooling. SF on
Non-superfluid star
with nucleon core
Standard Murca cooling
Add strong proton super-
fluidity
Very slow cooling
Add moderate neutron
superfluidity:
CP neutrino outburst
nn nn
np np
pp pp
nN pNe pNe nN
nN pNe pNe nN
np np
pp pp
nn nn
~ 0.01 MurcaL L MurcaL L
nN pNe pNe nN
nn nn
np np
pp pp
nn
MAXIMAL COOLING
EXAMPLE OF SUPERFLUID REDUCTION OF NEUTRINO EMISSION
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
STRONG PROTON AND MILD NEUTRON SUPERFLUIDITY
Summary of neutrino emission properties
Neutrino emission from neutron star cores is strongly regulated by
(1)Temperature
(2)Composition of the matter
(3)Superfluidity
These regulators may affect the emissivity in a non-trivial way
(enhance or suppress)
What is their effect? Next lecture
REFERENCES
U. Lombardo, H.-J. Schulze. Superfluidity in neutron star matter.
In: Physics of Neutron Star Interiors, edited by D. Blaschke,
N. Glendenning, A. Sedrakian, Berlin: Springer, 2001, p. 30.
D.G. Yakovlev, K.P. Levenfish, Yu.A. Shibanov. Cooling of neutron
stars and superfluidity in their cores. Physics – Uspekhi 42, 737, 1999.
D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel.
Neutrino emission from neutron stars. Phys. Rep. 354, Nums. 1,2, 2001.
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 STAGES
After 1 minute of proto-neutron star stage
( ) ( ) ( )ii i s
dTC T L T L T
dt
2 44 (1 / )
Heat blanketing envelope: ( )
( ) ( , ) exp( ( ))
s g
s s
i
L R T L L r R
T T T
T t T r t r
Analytical estimates
Thermal balance of
cooling star with
isothermal interior
Slow cooling via
Modified Urca
process SLOW 6
9
1 year~
i
tT
8 5~ 1.5 10 K in 10 yrsiT t
Fast cooling via
Direct Urca
process FAST 4
9
1 min~
i
tT
7~ 10 K in 200 yrsiT t
Roberto Turolla
Roberto explained how to detect thermal emission of neutron stars
THERMAL RADIATION FROM ISOLATED NEUTRON STARS
These data are now incomplete, a few more sources can be added
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
15
MAX c
14
D c
1.977 2.578 10 g/cc
1.358 8.17 10 g/cc
From 1.1 to 1.98 with step 0.01
SUN
SUN
SUN SUN SUN
M M
M M
M M M M
Does not explain
the data
MAXIMAL COOLING: STRONG 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: STRONG PROTON SF
This model explains the
data but such explanation is not
unique
MINIMUM AND MAXIMUM COOLING
SF on
Gusakov et al. (2004, 2005)
Minimum cooling
Gusakov et al. (2004)
Minimum-maximum cooling
Gusakov et al. (2005)
MYSTERIOUS COMPACT CENTRAL OBJECT IN Cas A SNR
Very bright radio source
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
Distance: 3.4 kpc (Reed et al. 1995)
Age: 330 yrs => 1680
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
Main features:
1. Rather warm neutron star
2. Consistent with standard
cooling
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 NS:
1. Warm as for standard cooling
2. Cools much faster
ln0.1
ln
sd Ts
d t
ln1.35 0.15 (2 )
ln
sd Ts
d t
Standard
cooling
curve slope
Superfluid cooling neutron star?
APR EOS
Neutrino emission peak: ~80 yrs ago
Superfluid Cas A NS:
D. Page, M. Prakash, J.M. Lattimer, A.W. Steiner, PRL, 106, 081101 (2011)
P.S. Shternin, D.G. Yakovlev, C.O. Heinke, W.C.G. Ho, D.J. Patnaude, MNRAS Lett., 412,
L108 (2011)
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
Is there rapid cooling of Cas A NS real (2013)?
K. G. Elshamouty,
C. Heinke et al.
B. Posselt,
G. Pavlov,
V. Suleimanov,
O. Korgaltsev
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 heating Cooling of initially
hot star
Objects Physics which is tested
Middle-aged isolated NSa Neutrino luminosity function
Composition and B-field in heat-blanketing envelopes
Young isolated NSs Crust
Quasistationary XRTs Neutrino luminosity function
Composition and B-field in heat-blanketing envelopes
Deep crustal heating
Quasipersistent XRTs
KS 1731—260; MXB 1659—29
Crust
Deep crustal heating
Superbursts Crust
Magnetar outbursts Crust
Magnetars in quasistationary
states
Crustal heating
Main Cooling Objects
Vela pulsar, M=1.4 MSUN, APR I EOS
Greatest headache: heat blankets
Chemical composition of heat
blanketing envelope is basically
unknown =>
extracting neutrino cooling rate
from observations is basically uncertain =>
internal neutrino cooling is disguised by
by unknown thermal insulation
Important issue: to study composition of
envelopes (Bildsten et al.)
56.8 10 KsT
CONCLUSIONS
THEORY
• Main cooling regulator: neutrino luminosity function
• Warmest observed stars INSs are low-massive; their neutrino luminosity
<= 0.01 of modified Urca
• Coldest observed stars INSs are massive; their neutrino luminosity
>= 100 of modified Urca
OBSERVATIONS
•Include sources of different types
• Observations seem more important that theory
•Are still insufficient to solve NS problem
Evidence for SF from NS cooling •Warmest observed isolated INSs and NSs in quasi-stationary XRTs
require very slow cooling => consistent with strong proton
superfluidity which suppresses many neutrino processes
•Unusual cooling behavior of Cas A NS
CONCLUSIONS
Future
•New observations => good practical theories of dense matter
• Proper inclusion of B-field, rotation, superfluidity
• Independent measurements of masses, radii, etc.
• Good luck
Warning
• Do not expect from cooling theory more than it can give
• Cooling theory by itself will hardy allow accurate mass and radius
measurements – it has to be calibrated by independent measurements
and/or reliable theory of nuclear matter
• Info on internal neutrino emission is disguised by unknown
composition of heat blanket
Start. 1960s. To discover NSs
as cooling X-ray objects
Now. INSs
XRTs
Magnetars
Magneto-rotational evolution
Rotational-chemical evolution
Bursts and outbursts
Glitches
Internal and magnetospheric activity
etc.
FROM CINDERELLA TO REAL BEAUTY