Transcript Lecture 2. Thermal evolution and surface emission of neutron stars

Thermal evolution and
population synthesis of
neutron stars
Sergei Popov (SAI MSU)
Evolution of neutron stars. I.:
rotation + magnetic field
Ejector → Propeller → Accretor → Georotator
1 – spin down
2 – passage through a molecular cloud
3 – magnetic field decay
astro-ph/0101031
See the book by Lipunov (1987, 1992)
Evolution of NSs. II.: temperature
Neutrino
cooling stage
Photon
cooling stage
First papers on the thermal
evolution appeared already
in early 60s, i.e. before
the discovery of radio pulsars.
[Yakovlev et al. (1999) Physics Uspekhi]
Early evolution of a NS
(Prakash et al. astro-ph/0112136)
NS Cooling
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
NSs are born very hot, T > 1010 K
At early stages neutrino cooling dominates
The core is isothermal
dEth
dT
 CV
  L  L
dt
dt
Photon luminosity
Neutrino luminosity
L  4 R 2 Ts4 , Ts  T 1/ 2 (   1)
Core-crust temperature relation
Page et al. astro-ph/0508056
Cooling depends on:
1.
2.
3.
4.
5.
Rate of neutrino emission from NS interiors
Heat capacity of internal parts of a star
Superfluidity
Thermal conductivity in the outer layers
Possible heating
(see Yakovlev & Pethick 2004)
Depend on the EoS
and composition
Main neutrino processes
(Yakovlev & Pethick astro-ph/0402143)
Fast Cooling
(URCA cycle)
n  p  e   e
p  e  n  e

Slow Cooling
(modified URCA cycle)
n  n  n  p  e   e
n  p  e  n  n  e

p  n  p  p  e  e

p  p  e   p  n  e
 Fast cooling possible only if np > nn/8
 Nucleon Cooper pairing is important
 Minimal cooling scenario (Page et al 2004):
 no exotica
 no fast processes
 pairing included
pp
pn
pe
pn<pp+pe
Equations
Neutrino emissivity
heating
After thermal relaxation
we have in the whole star:
Ti(t)=T(r,t)eΦ(r)
At the surface we have:
(Yakovlev & Pethick 2004)
Total stellar heat capacity
Simplified model of a cooling NS
No superfluidity, no envelopes and magnetic fields, only hadrons.
The most critical moment is the onset of direct URCA cooling.
ρD= 7.851 1014 g/cm3.
The critical mass
depends on the EoS.
For the examples below
MD=1.358 Msolar.
Simple cooling model for low-mass NSs.
Too hot ......
Too cold ....
(Yakovlev & Pethick 2004)
Nonsuperfluid nucleon cores
Note “population
aspects” of the right
plot: too many NSs
have to be explained
by a very narrow
range of mass.
For slow cooling at the neutrino cooling stage tslow~1 yr/Ti96
For fast cooling
tfast~ 1 min/Ti94
(Yakovlev & Pethick 2004)
Slow cooling for different EoS
For slow cooling there is nearly no dependence on the EoS.
The same is true for cooling curves for maximum mass for each EoS.
(Yakovlev & Pethick 2004)
Envelopes and magnetic field
Non-magnetic stars
No accreted envelopes, Envelopes + Fields
Thick lines – no envelope
different magnetic fields.
Envelopes can be related to the fact that we see a subpopulation of hot NS
Thick lines – non-magnetic
in CCOs with relatively long initial spin periods and low magnetic field, but
do not observed representatives of this population around us, i.e. in the Solar vicinity.
Solid line M=1.3 Msolar, Dashed lines M=1.5 Msolar
(Yakovlev & Pethick 2004)
Simplified model: no neutron superfluidity
Superfluidity is an important ingredient
of cooling models.
It is important to consider different types
of proton and neutron superfluidity.
There is no complete microphysical
theory whiich can describe superfluidity
in neutron stars.
If proton superfluidity is strong,
but neutron superfluidity
in the core is weak
then it is possible
to explain observations.
(Yakovlev & Pethick 2004)
Neutron superfluidity and observations
Mild neutron pairing in the core
contradicts observations.
(Yakovlev & Pethick 2004)
Minimal cooling model
“Minimal” Cooling Curves
“minimal” means
without additional cooling
due to direct URCA
and without additional heating
Main ingredients of
the minimal model
•
•
•
•
Page, Geppert & Weber (2006)
EoS
Superfluid properties
Envelope composition
NS mass
Luminosity and age uncertainties
Page, Geppert, Weber
astro-ph/0508056
Uncertainties in temperature
• Atmospheres
(composition)
• Magnetic field
• Non-thermal
contributions
to the spectrum
• Distance
• Interstellar
absorption
• Temperature
distribution
(Pons et al. astro-ph/0107404)
NS Radii
A NS with homogeneous surface temperature
and local blackbody emission
L  4 R  T
L
2
4
F
 R / D   T
2
4 D
2
4
From X-ray
spectroscopy
From dispersion
measure
NS Radii - II

Real life is a trifle more complicated…
Strong B field
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Photon propagation different
Surface temperature is not homogeneous
Local emission may be not exactly planckian
Gravity effects are important
Atmospheres
Local Surface Emission

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

Much like normal stars NSs are covered by
an atmosphere
Because of enormous surface gravity,
g ≈ 1014 cm/s2, Hatm ≈ 1-10 cm
Spectra depend on g, chemical composition
and magnetic field
Plane-parallel approximation (locally)

Free-free absorption dominates
   3 , h  kT

High energy photons decouple deeper in the atmosphere where
T is higher
Zavlin & Pavlov (2002)
Gravity Effects
 Redshift
 Ray bending
L  4 R  T
2

4

2
2
1
0
0
0
4 T   d  d  du
4

2

E , 2
E ,1
dE I ( E, B, cos , Ts ,  )
STEP 1
Specify viewing geometry
and B-field topology;
compute the surface
temperature distribution
STEP 2
Compute emission from
every surface patch
STEP 4
Predict lightcurve and
phase-resolved spectrum
Compare with observations
STEP 3
GR ray-tracing to obtain
the spectrum at infinity
CCOs
1.
2.
3.
4.
Found in SNRs
Have no radio or gamma-ray counterpats
No pulsar wind nebula (PWN)
Have soft thermal-like spectra
Known objects
New candidates
appear continuosly.
(Pavlov et al. astro-ph/0311526)
New population?
Gotthelf & Halpern (arXiv:0704.2255) recently suggested that
1E 1207.4-5209 and PSR J1852+0040 (in Kes 79) can be
prototypes of a different subpopulation of NSs born with
low magnetic field (< few 1011 G) and
relatively long spin periods (few tenths of a second).
These NSs are relatively hot, and probably not very rare.
Surprisingly, we do not see objects of this type in our vicinity.
In the solar neighbourhood we meet a different class of object.
This can be related to accreted envelopes
(see, for example, Kaminker et al. 2006).
Sources in CCOs have them, so they look hotter,
but when these envelopes disappear, they are colder
than NSs which have no envelopes from the very beginning.
So, we do not see such sources among close-by NSs.
M 7 and CCOs
Both CCOs and M7 seem to be
the hottest at their ages (103 and 106 yrs).
However, the former cannot evolve
to become the latter ones!
Temperature
CCOs
M7
Age
• Accreted envelopes
(presented in CCOs,
absent in the M7)
• Heating by decaying magnetic field
in the case of the M7
(Yakovlev & Pethick 2004)
Accreted envelopes, B or heating?
It is necessary to make population synthesis studies to test all these possibilities.
The Seven X-ray dim Isolated NSs
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Soft thermal spectrum (kT  50-100 eV)
No hard, non-thermal tail
Radio-quiet, no association with SNRs
Low column density (NH  1020 cm-2)
X-ray pulsations in all 7 sources (P 3-10 s)
Very faint optical counterparts
The Magnificent Seven
Source
kT (eV)
P (s)
Amplitude/2
Optical
RX J1856.5-3754
60
7.06
1.5%
V = 25.6
RX J0720.4-3125 (*)
85
8.39
11%
B = 26.6
RX J0806.4-4123
96
11.37
6%
-
RX J0420.0-5022
45
3.45
13%
B = 26.6 ?
RX J1308.6+2127
(RBS 1223)
86
10.31
18%
m50CCD = 28.6
RX J1605.3+3249
(RBS 1556)
96
6.88?
??
m50CCD = 26.8
104
9.43
4%
-
1RXS J214303.7+065419
(RBS 1774)
(*) variable source
Featureless ? No Thanks !

RX J1856.5-3754 is convincingly featureless
RX J0720.4-3125 (Haberl et al 2004)
(Chandra 500 ks DDT; Drake et al 2002; Burwitz et al 2003)

A broad absorption feature detected in all other
ICoNS (Haberl et al 2003, 2004, 2004a; Van Kerkwijk et al 2004;
Zane et al 2005)
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
Eline ~ 300-700 eV; evidence for two lines with E1 ~
2E2 in RBS 1223 (Schwope et al 2006)
Proton cyclotron lines ? H/He transitions at high B
?
Period Evolution
.

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
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RX J0720.4-3125: bounds on Pderived by Zane et al.
(2002) and Kaplan et al (2002)
Timing solution by Cropper et al (2004), further
improved by Kaplan & Van Kerkwijk (2005):
.
-14 s/s, B = 2x1013 G
=
7x10
P
13 -1014 G
B
~
10
RX J1308.6+2127: .timing solution by Kaplan & Van
Kerkwijk (2005a), P = 10-13 s/s, B = 3x1013 G
Spin-down values of B in agreement with absorption
features being proton cyclotron lines
Source
Energy
(eV)
EW
(eV)
Bline
(Bsd)
(1013 G)
Notes
RX J1856.5-3754
no
no
?
-
RX J0720.4-3125
270
40
5 (2)
Variable line
RX J0806.4-4123
460
33
9
-
RX J0420.0-5022
330
43
7
-
RX J1308.6+2127
300
150
6 (3)
-
RX J1605.3+3249
450
36
9
-
700
50
14
-
1RXS
J214303.7+065419
ICoNS: The Perfect Neutron Stars
ICoNS are key in neutron star astrophysics:
these are the only sources for which we have
a “clean view” of the star surface
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Information on the thermal and magnetic
surface distributions
Estimate of the star radius (and mass ?)
Direct constraints on the EOS
Pulsating ICoNS
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RX J0420.0-5022 (Haberl et al 2004)
Quite large pulsed
fractions
Skewed lightcurves
Harder spectrum at pulse
minimum
Phase-dependent
absorption features
The Optical Excess
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RX J1605 multiwavelength SED (Motch et al 2005)
In the four sources with a
confirmed optical counterpart
Fopt  5-10 x B(TBB,X)
Fopt  2 ?
Deviations from a RayleighJeans continuum in RX J0720
(Kaplan et al 2003) and RX J1605 (Motch
et al 2005). A non-thermal power
law ?
RX J1856.5-3754 - I
Blackbody featureless
spectrum in the 0.1-2 keV
band (Chandra 500 ks DDT, Drake et al
2002); possible broadband
deviations in the XMM 60 ks
observation (Burwitz et al 2003)
RX J1856 multiwavelength SED (Braje & Romani 2002)
Thermal emission from NSs is not expected to be a featureless
BB ! H, He spectra are featureless but only blackbody-like
(harder). Heavy elements spectra are closer to BB but with a
variety of features
RX J1856.5-3754 - II


A quark star (Drake et al 2002; Xu 2002; 2003)
A NS with
caps
and cooler
Whathotter
spectrum
?
equatorial
region
(Pons
The optical
excess
? et al 2002; Braje &
Romani 2002; Trűmper et al 2005)

A bare NS (Burwitz et al 2003; Turolla, Zane &
Drake 2004; Van Adelsberg et al 2005; PerezA perfect
BB ? 2005)
Azorin, Miralles
& Pons
Bare Neutron Stars
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At B >> B0 ~ 2.35 x 109 G atoms
attain a cylindrical shape
Turolla, Zane & Drake 2004
Formation
of molecular chains by
covalent bonding along the field
direction
RX J0720.4-3125
Interactions between molecular
chains can lead to the formation of a
RX J1856.5-3754
3D condensate
Critical
condensation
temperature
Fe
H
depends on B and chemical
composition (Lai & Salpeter 1997; Lai 2001)
Spectra from Bare NSs - I
The cold electron gas approximation. Reduced
emissivity expected below p (Lenzen & Trümper
1978; Brinkmann 1980)
Spectra are very close
to BB in shape in the
0.1 - 2 keV range, but
depressed wrt the BB at
Teff. Reduction factor
~ 2 - 3.
Turolla, Zane & Drake (2004)
Spectra from Bare NS - II
Proper account for damping of free electrons
by lattice interactions (e-phonon scattering; Yakovlev
& Urpin 1980; Potekhin 1999)
Spectra deviate more
from BB. Fit in the
0.1 – 2 keV band still
acceptable. Features
may be present.
Reduction factors
higher.
Turolla, Zane & Drake (2004)
Is RX J1856.5-3754 Bare ?
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
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Fit of X-ray data in the 0.15-2
keV band acceptable
Radiation radius problem eased
Optical excess may be
produced by reprocessing of
surface radiation in a very
rarefied atmosphere (Motch, Zavlin
& Haberl 2003; Zane, Turolla & Drake
2004; Ho et al. 2006)

Details of spectral shape
(features, low-energy behaviour)
still uncertain
Long Term Variations in
RX J0720.4-3125

A gradual, long term
change in the shape of the
X-ray spectrum AND the
pulse profile (De Vries et al
2004; Vink et al 2004)
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
Steady increase of TBB
and of the absorption
feature EW (faster during
2003)
Evidence for a reversal of
the evolution in 2005 (Vink
et al 2005)
De Vries et al. 2004
A Precessing Neutron Star ?



Evidence for a periodic modulation in the spectral
parameters (Tbb, Rbb) but no complete cycle yet
Phase residuals (coherent timing solution by Kaplan & Van Kerkwijk
2005) show periodic behavior over a much longer timescale
Haberl et al. 2006
(> 10 yrs)
Periods consistent within the errors, Pprec ~ 7.1-7.7 yr (Haberl
et al. 2006)
M7 and RRATs
Similar periods and Pdots
In one case similar thermal properties
Similar birth rate?
(arXiv: 0710.2056)
M7 and RRATs: pro et contra
Based on similarities between M7 and RRATs it was proposed that they can be
different manifestations of the same type of INSs (astro-ph/0603258).
To verify it a very deep search for radio emission (including RRAT-like bursts)
was peformed on GBT (Kondratiev et al.).
In addition, objects have been observed with GMRT (B.C.Joshi, M. Burgay et al.).
In both studies only upper limits were derived.
Still, the zero result can be just due to unfavorable orientations
(at long periods NSs have very narrow beams).
It is necessary to increase statistics.
(Kondratiev et al, in press, see also arXiv: 0710.1648)
M7 and high-B PSRs
Strong limits on radio emission from the M7
are established (Kondratiev et al. 2008: 0710.1648 ).
However, observationally it is still possible that
the M7 are just misaligned high-B PSRs.
Are there any other considerations
to verify a link between these
two popualtions of NSs?
In most of population synthesis studies of PSRs
the magnetic field distribution is described as a
gaussian, so that high-B PSRs appear to be not
very numerous.
On the other hand, population synthesis of the
local population of young NSs demonstrate that
the M7 are as numerous as normal-B PSRs.
So, for standard assumptions
it is much more probable, that
high-B PSRs and the M7
are not related.
INSs and local surrounding
Massive star population in the Solar vicinity (up to 2 kpc)
is dominated by OB associations.
Inside 300-400 pc the Gould Belt is mostly important.
De Zeeuw et al. 1999
Motch et al. 2006
Population of close-by young NSs
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Magnificent seven
Geminga and 3EG J1853+5918
Four radio pulsars with thermal emission
(B0833-45; B0656+14; B1055-52;
B1929+10)
Seven older radio pulsars, without
detected thermal emission.
To understand the origin of these populations and predict future detections
it is necessary to use population synthesis.
Population synthesis: ingredients
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Birth rate of NSs
Initial spatial distribution
Spatial velocity (kick)
Mass spectrum
Thermal evolution
Interstellar absorption
Detector properties
Task:
To build an artificial model
of a population of some
astrophysical sources and
to compare the results of
calculations with observations.
The Gould Belt
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Poppel (1997)
R=300 – 500 pc
Age 30-50 Myrs
Center at 150 pc from the
Sun
Inclined respect to the
galactic plane at 20 degrees
2/3 massive stars in 600 pc
belong to the Belt
Mass spectrum of NSs
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Mass spectrum of local young NSs
can be different from the general one
(in the Galaxy)
Hipparcos data on near-by massive
stars
Progenitor vs NS mass:
Timmes et al. (1996);
Woosley et al. (2002)
astro-ph/0305599
Progenitor mass vs. NS mass
Woosley et al. 2002
Log of the number of sources
brighter than the given flux
Log N – Log S
calculations
-3/2 sphere:
number ~ r3
flux
~ r-2
-1 disc:
number ~ r2
flux
~ r-2
Log of flux (or number counts)
Cooling of NSs
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Direct URCA
Modified URCA
Neutrino bremstrahlung
Superfluidity
Exotic matter (pions,
quarks, hyperons, etc.)
(see a recent review in astro-ph/0508056)
In our study for illustrative purposes
we use a set of cooling curves calculated by
Blaschke, Grigorian and Voskresenski (2004)
in the frame of the Nuclear medium cooling model
Some results of PS-I:
Log N – Log S and spatial distribution
Log N – Log S for closeby ROSAT NSs can be
explained by standard
cooling curves taking into
account the Gould Belt.
Log N – Log S can be
used as an additional test
of cooling curves
More than ½ are in
+/- 12 degrees from
the galactic plane.
19% outside +/- 30o
12% outside +/- 40o
(Popov et al. 2005
Ap&SS 299, 117)
Population synthesis – II.
recent improvements
Spatial distribution of progenitor stars
We use the same
normalization for
NS formation rate
inside 3 kpc: 270 per Myr.
Most of NSs are born in
OB associations.
a) Hipparcos stars up to 500 pc
[Age: spectral type & cluster age (OB ass)]
b) 49 OB associations: birth rate ~ Nstar
c) Field stars in the disc up to 3 kpc
For stars <500 pc we even
try to take into account
if they belong to OB assoc.
with known age.
Population synthesis – II.
recent improvements
Spatial distribution of ISM (NH)
instead of :
now :
Modification of the old one
NH inside 1 kpc
(see astro-ph/0609275 for details)
Hakkila
50 000 tracks, new ISM model
Predictions for future searches
Candidates:
Agueros
Chieregato
radiopulsars
Magn. 7
Age and distance distributions
0.01 < cts/s < 0.1
Age
New cands.
Distance
0.1 < cts/s < 1
1 < cts/s < 10
Different models: age distributions
Bars with vertical lines:
old model for Rbelt=500 pc
White bars: new initial dist
Black bars:
new ISM (analyt.) and
new initial distribution
Diagonal lines:
new ISM (Hakkila) and
new initial distribution
Different models: distance distr.
Where to search for more cowboys?
We do not expect to find much more candidates at fluxes >0.1 cts/s.
Most of new candidates should be at fluxes 0.01< f < 0.1 cts/s.
So, they are expected to be young NSs (<few 100 Mys) just outside the Belt.
I.e., they should be in nearby OB associations and clusters.
Most probable candidates are Cyg OB7, Cam OB1, Cep OB2 and Cep OB3.
Orion region can also be promising.
Name
l-
l+
b-
b+
Cyg OB7
84
96
-5
9
Cep OB2
96
108
-1 12
700
Cep OB3
108
113
1
700-900
7
Dist., pc 130
L=110
90
10
600-700
0
-10
Cam OB1 130
153
-3
8
800-900
(ads.gsfc.nasa.gov/mw/)
Standard test: temperature vs. age
Kaminker et al. (2001)
Log N – Log S as an additional test

Standard test: Age – Temperature
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Log N – Log S
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Sensitive to ages <105 years
Uncertain age and temperature
Non-uniform sample
Sensitive to ages >105 years
(when applied to close-by NSs)
Definite N (number) and S (flux)
Uniform sample
Two test are perfect together!!!
astro-ph/0411618
List of models (Blaschke et al. 2004)
Pions Crust
Blaschke et al. used 16 
sets of cooling

curves.

They were different in
three main respects: 
1. Absence or presence 
of pion condensate 

2. Different gaps for
superfluid protons

and neutrons

3. Different Ts-Tin
Model I. Yes
Model II. No
Model III. Yes
Model IV. No
Model V. Yes
Model VI. No
Model VII. Yes
Model VIII.Yes
Model IX. No
C
D
C
C
D
E
C
C
C
Gaps
A
B
B
B
B
B
B’
B’’
A
Model I
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

Pions.
Gaps from Takatsuka &
Tamagaki (2004)
Ts-Tin from Blaschke, Grigorian,
Voskresenky (2004)
Can reproduce observed Log N – Log S
(astro-ph/0411618)
Model II
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

No Pions
Gaps from Yakovlev et al.
(2004), 3P2 neutron gap
suppressed by 0.1
Ts-Tin from Tsuruta (1979)
Cannot reproduce observed Log N – Log S
Sensitivity of Log N – Log S
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
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Log N – Log S is very sensitive to gaps
Log N – Log S is not sensitive to the crust if it is
applied to relatively old objects (>104-5 yrs)
Log N – Log S is not very sensitive to presence or
absence of pions
We conclude that the two test complement each other
Mass constraint
• Mass spectrum has to be taken
into account when discussing
data on cooling
• Rare masses should not be used
to explain the cooling data
• Most of data points on T-t plot
should be explained by masses
<1.4 Msun
In particular:
• Vela and Geminga should not be
very massive
Phys. Rev .C (2006)
nucl-th/0512098
(published as a JINR preprint)
Cooling curves from
Kaminker et al.
Conclusions
• Studies of cooling NSs is a unique opprtunity to learn something about
very high density matter physics
• Different populations of cooling NSs are observed: CCOs, normal radio pulsars,
Magnificent seven, one of the RRATs, ....
• Population synthesis studies of cooling NSs can be a useful test for models
of their thermal evolution
• Population synthesis can be useful in planning how to search for more INSs
• Joint studies of different populations can help to understand reasons for
their diversity and evolutionary links between them