Population synthesis of
isolated NSs and
tests of cooling curves
Sergei Popov
(Sternberg Astronomical Institute)
Co-authors: D. Blaschke, H.Grigorian, B. Posselt, R. Turolla
JINR, Dubna, September 01, 2006
Plan of the talk
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Intro. Close-by NSs
Population synthesis
Solar vicinity. Stars
Spatial distribution
Mass spectrum
Two tests of cooling
Brightness constraint
Sensitivity of two tests
Mass constraint
Application to hybrid stars
Future plans
Age-Distance diagram
Final conclusions
2
Isolated neutron stars population:
in the Galaxy and at the backyard
 INSs appear in many flavours
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Radio pulsars
AXPs
SGRs
CCOs
RINSs
RRATs
 Local population of young NSs
is different (selection)
Radio pulsars
Geminga+
3
RINSs
Close-by radioquiet NSs
 Discovery:
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Walter et al. (1996)
Proper motion and
distance: Kaplan et al.
No pulsations
Thermal spectrum
Later on: six brothers
RX J1856.5-3754
4
Magnificent Seven
Name
Period, s
RX 1856
-
RX 0720
8.39
RBS 1223
10.31
RBS 1556
-
RX 0806
11.37
RX 0420
3.45
RBS 1774
9.44
Radioquiet (?)
Close-by
Thermal emission
Long periods
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Population of close-by young NSs
 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.
It is useful to study these stars
using the population synthesis technique
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Population synthesis: ingredients
 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.
A brief review on population
synthesis in astrophysics can
be found in astro-ph/0411792
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Population synthesis – I.
Gould Belt : 20 NS Myr-1
Gal. Disk (3kpc) : 250 NS Myr-1
• Cooling curves by
• Blaschke et al.
• Mass spectrum
ROSAT
18°
Arzoumanian et al. 2002
Gould Belt
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Solar vicinity
 Solar neighborhood is not a
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typical region of our Galaxy
Gould Belt
R=300-500 pc
Age: 30-50 Myrs
20-30 SN per Myr (Grenier 2000)
The Local Bubble
Up to six SN in a few Myrs
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The Gould Belt
 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
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Distribution of open clusters
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(Piskunov et al. astro-ph/0508575)
Surface density of open clusters
(Piskunov et al.)
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Spatial distribution of close-by
open clusters in 3D
Grey contours show
projected density
distribution of young
(log T<7.9) clusters.
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(Piskunov et al.)
Clusters and absorption
Triangles –
Gould Belt
clusters.
(Piskunov et al.)
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Initial spatial distribution
A very simple model for PS-I:
The Gould Belt as a flat inclined disc plus
contribution from the galactic disc up to 3 kpc.
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Some results of PS-I.:
Spatial distribution
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)
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Mass spectrum of NSs
 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)
(masses of secondary objects in NS+NS)
astro-ph/0305599
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Progenitor mass vs. NS mass
Woosley et al. 2002
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Core mass vs. initial mass
Woosley et al.
2002
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Two tests
Age – Temperature
&
Log N – Log S
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Standard test: temperature vs. age
Kaminker et al. (2001)
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Uncertainties in temperature
• Atmospheres
(composition)
• Magnetic field
• Non-thermal
contributions
to the spectrum
• Distance
• Interstellar
absorption
• Temperature
distribution
(Pons et al. astro-ph/0107404)
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Luminosity and age uncertainties
Page, Geppert
astro-ph/0508056
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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)
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Log N – Log S as an additional test
 Standard test: Age – Temperature
 Sensitive to ages <105 years
 Uncertain age and temperature
 Non-uniform sample
 Log N – Log S
 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
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List of models (Blaschke et al. 2004)
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
Pions Crust
 Model I.
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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
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Model I
 Pions.
 Gaps from Takatsuka & Tamagaki
(2004)
 Ts-Tin from Blaschke, Grigorian,
Voskresenky (2004)
Can reproduce observed Log N – Log S
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Model II
 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
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Model III
 Pions
 Gaps from Yakovlev et al.
(2004), 3P2 neutron gap
suppressed by 0.1
 Ts-Tin from Blaschke,
Grigorian, Voskresenky (2004)
Cannot reproduce observed Log N – Log S
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Model IV
 No Pions
 Gaps from Yakovlev et al.
(2004), 3P2 neutron gap
suppressed by 0.1
 Ts-Tin from Blaschke, Grigorian,
Voskresenky (2004)
Cannot reproduce observed Log N – Log S
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Model V
 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
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Model VI
 No Pions
 Gaps from Yakovlev et al.
(2004), 3P2 neutron gap
suppressed by 0.1
 Ts-Tin from Yakovlev et al.
(2004)
Cannot reproduce observed Log N – Log S
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Model VII
 Pions
 Gaps from Yakovlev et
al. (2004), 3P2 neutron
gap suppressed by 0.1.
1P proton gap
0
suppressed by 0.5
 Ts-Tin from Blaschke,
Grigorian, Voskresenky
(2004)
Cannot reproduce observed Log N – Log S
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Model VIII
 Pions
 Gaps from Yakovlev et al.
(2004), 3P2 neutron gap
suppressed by 0.1. 1P0
proton gap suppressed by
0.2 and 1P0 neutron gap
suppressed by 0.5.
 Ts-Tin from Blaschke,
Grigorian, Voskresenky
(2004)
Can reproduce observed Log N – Log S
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Model IX
 No Pions
 Gaps from Takatsuka &
Tamagaki (2004)
 Ts-Tin from Blaschke,
Grigorian, Voskresenky
(2004)
Can reproduce observed Log N – Log S
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HOORAY!!!!
Log N – Log S can select models!!!!!
Only three (or even one!) passed the second test!
…….still………… is it possible just to update
the temperature-age test???
May be Log N – Log S is not necessary?
Let’s try!!!!
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Brightness constraint
 Effects of the crust
(envelope)
 Fitting the crust it is
possible to fulfill the
T-t test …
 …but not the
second test:
Log N – Log S !!!
(H. Grigorian astro-ph/0507052)
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Sensitivity of Log N – Log S
 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
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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.
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Another attempt to test a set of
models: hybrid stars
We studied several models for hybrid stars
applying all possible tests:
- T-t
- Log N – Log S
- Brightness constraint
- Mass constraint
We also tried to present examples when a model successfully passes
the Log N – Log S test, but fails to pass the standard T-t test or fails to
fulfill the mass constraint.
nucl-th/0512098
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Model I
Brightness
- OK
T-t
- OK
Log N – Log S - poor
Mass
- NO
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Model II
Brightness
- OK
T-t
- No
Log N – Log S - OK
Mass
- NO
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Model III
Brightness
- OK
T-t
- poor
Log N – Log S - OK
Mass
- NO
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Model IV
Brightness
- OK
T-t
- OK
Log N – Log S - OK
Mass
- OK
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Resume for HySs
One model among four was able to pass all tests.
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Population sythesis – II.
recent improvements
1. Spatial distribution of progenitor stars
a) Hipparcos stars up to 400 pc
[Age: spectral type & cluster age (OB ass)]
b) Star associations: birth rate ~ Nstar
c) Field stars in the disc up to 3 kpc
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Population synthesis – II.
recent improvements
2. Spatial distribution of ISM (NH)
+ new cross sections & abundances
1kpc
1kpc
instead of :
now :
(by Bettina Posselt)
3. Further improvements:
• Mass spectrum
• fainter XMM EPIC PN count rates
• cooling curves (Grigorian et al. 2005,
Popov et al . 2006)
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First results
The new initial distribution of progenitor stars:
Popov et al. 2005
For comparison: ROSAT, old ISM distribution, masses etc. as before
Count rate > 0.05 cts/s
New
b= +90°
GB 300 pc
GB 500 pc
b= -90°
Outlook
Different log N - log S curve for distinct sky regions
Population synthesis for fainter (XMM) sources
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Age-distance diagram
Detectability of close-by
young NSs strongly
Depends on their ages
and distance from the Sun.
A toy-model: a local
sphere (R=300 pc)
and a flat disk.
visibility
1 source
13 sources
(astro-ph/0407370)
Rate of NS formation
in the sphere is
235 Myr-1 kpc-3
(26-27 NS in Myr in
the whole sphere).
Rate in the disc is
10 Myr-1 kpc-2
(280 NS in Myr up to
3 kpc).
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More realistic age-dist. diagram
Initial distribution
from Popov et al. 2005.
Spatial evolution is not
followed.
For the line of “visibility”
(solid line in the middle)
I assume the limiting
flux 10-12 erg s-1 cm-2
and masses are <1.35
(Yakovlev et al. curves).
In 4.3 Myr in 1 kpc
around the Sun 200 NSs
are expected to be born.
(astro-ph/0407370)
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Realistic age-distance diagram
1
4 13 20
100
Realistic initial distribution.
Spatial evolution is taken
into account.
The line of “visibility” is
drawn as the dotted line.
Five curves correspond to
1, 4 , 13, 20 and 100 NSs.
visibility
At the moment in 1 kpc
only about 10% of NSs
with ages <4-5 Myrs are
observed.
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(astro-ph/0407370)
Resume
 We live in a very interesting region of the Milky Way!
 Log N – Log S test can include NSs with
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unknown ages, so additional sources
(like the Magnificent Seven) can be used
to test cooling curves.
Two tests (LogN–LogS and Age-Temperature) are
perfect together.
Additional considerations (brightness and mass
constraints) have to be taken into account.
More detailed PS models are welcomed.
Age-distance diagram can be used as an additional
tool.
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THAT’S ALL. THANK YOU!
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Radio detection
Malofeev et al. (2005) reported detection of
1RXS J1308.6+212708 (RBS 1223)
in the low-frequency band (60-110 MHz)
with the radio telescope in Pushchino.
In 2006 Malofeev et al. reported radio detection
of another one.
(back)
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NS+NS binaries
Pulsar
B1913+16
B2127+11C
B1534+12
J0737-3039
J1756-2251
Pulsar mass
Companion mass
1.44
1.35
1.33
1.34
1.40
1.39
1.36
1.35
1.25
1.18
(PSR+companion)/2
J1518+4904
J1811-1736
J1829+2456
1.35
1.30
1.25
(David Nice, talk at Vancouver 2005)
(Back)
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