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Дата индексирования: Mon Oct 1 22:00:01 2012
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Log N Log S of close-by young NSs:
an independent test for cooling curves
Sergei Popov
University of Padua, Italy
Sternberg Astronomical Institute, Russia
Collaborators: H. Grigorian, R. Turolla, D. Blaschke
Plan of the talk
Introduction.
T t-test.
Overview. Pro et contra.
Log N - Log S. An overview.
Local population of cooling NSs.
Ingredients of population synthesis.
Stars in the solar proximity. The Gould Belt.
Mass spectrum of close-by NSs.
Atmospheres and other emission properties.
Log N Log S of cooling NSs.
A toy model.
Effects of different ingredients.
Comparison of different cooling curves.
Pro et contra of Log N - Log S.
Age-distance diagram.
Conclusions.

TtT Temperature-age test.
Neutron P gap = 0
3
2
Neutron P gap = "a"
3
2
Neutron P gap = "b"
3
2
Light elements
envelopes
Heavy elements
envelopes
Neutron P gap = 0
3
2
Neutron P gap = "a"
3
2
Neutron P gap = "b"
3
2
Figure from Page et al. 2004 [astro-ph/0405196].

T-t Test. Pro et contra.
Pro
The most natural plot.
Perfect illustration.
Does not care about uncertainties of the third parameters. Only
internal uncertainties of the model are important.
Contra
Uncertainties in t.
Very often an age is determined by p= _
p, or as a SNR age.
Uncertainties in T . Atmospheres etc.
Comparison of calculations with observations.
Temperature is not measured directly, it is always obtained as a fit.
Non-uniform data set.
Data samples of coolers are non-uniform. There are sources of differ-
ent types. The sample is nor flux, neither volume limited.

Log N - Log S Test. Pro et contra.
Pro
Uses uniform sample of objects.
Takes into account populational effects.
No unsertainties in properties of observed objects!
Contra
There are many uncertainties of the scenario.
Initial distribution of progenitors.
Mass spectrum.
Emission properties.
There can be unknown correlations between parameters of synthesis.
(For example mass-magnetic field due to fall-back;
velocity-internal structure due to deconfinement).
Finite sample. It is difficult to take into account statistical fluctua-
tions if a data sample is small.
Hidden population (unobserved objects).

Ingredients of the population synthesis model.
Initial spatial distribution.
Velocity distribution.
Cooling curves.
Mass spectrum of NSs.
Emission model (atmospheres etc.).
Interstellar absorption.

Why population synthesis is important?
Each part by itself can be perfect, but all together do not fit!
It is necessary to analyse how fitting proceedure for some particular
objects influences the whole population of sources of that type.
It is necessary to analyse (if possible) uniform data samples.

Mass spectrum.
Here we use bins at low masses since without the low-mass NSs in several model it is impossible to
interprete data on the T t (temperature age) plot (see Blaschke et al. 2004).
Each bin corresponds to one of the calculated curve. On the vertical axis percentage of stars in
each bin (i.e. contribution of each curve) is shown. Masses are not equaly spaced, so widths of bins
are different.
We use eight cooling curves for M = 1.1, 1.25, 1.32, 1.4, 1.48, 1.6, 1.7, 1.76 M . Each curve has a
statistical weight: 2.54, 2.06, 0.88, 2.25, 0.07, 0.09, 0.06, 0.05 according to the mass spectrum.

Table 1: List of models
Model Ref. figure Comments
I 21 Cooling of NS configuration with superfluid nuclear matter
with medium effects and with pion condensation.
The gaps are taken from Takatsuka & Tamagaki (2004),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is given by a fit.
II 13 Cooling of NS configuration with superfluid nuclear matter
with medium effects but without pion condensation.
The gaps are taken from Yakovlev et al. (2003),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is given by the Tsuruta law.
III 15 Cooling of NS configuration with superfluid nuclear matter
with medium effects and with pion condensation.
The gaps are taken from Yakovlev et al. (2003),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is given by a fit.
IV 12 Cooling of NS configuration with superfluid nuclear matter
with medium effects but without pion condensation.
The gaps are taken from Yakovlev et al. (2003),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is given by a fit.
V 16 Cooling of NS configuration with superfluid nuclear matter
with medium effects and with pion condensation.
The gaps are taken from Yakovlev et al. (2003),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is given by the Tsuruta law.
VI 14 Cooling of NS configuration with superfluid nuclear matter
with medium effects but without pion condensation.
The gaps are taken from Yakovlev et al. (2003),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is from Yakovlev et al. (2003), = 4 10 16 .
VII 18 Cooling of NS configuration with superfluid nuclear matter
with medium effects and with pion condensation.
The gaps are taken from Yakovlev et al. (2003),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is given by a fit.
The proton gap is suppressed by a factor 0.5.
VIII 19 Cooling of NS configuration with superfluid nuclear matter
with medium effects and with pion condensation.
The gaps are taken from Yakovlev et al. (2003),
the neutron gap 3P 2 is additionally suppressed.
The T s -T in relation is given by a fit.
The 1S 0 neutron gap suppressed by a factor 0.5
and 1S 0 proton gap by a factor 0.2.
The neutron 3P 2 gap is remained to be suppresed by 0.1.

Cooling curves for model I.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
0.501
1.000
1.100
1.250
1.320
1.400
1.480
1.600
1.700
1.750
1.930
Cooling for HJ EoS (AV18)
Our crust , with medium effects, 3P 2 *0.1 p cond
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects and with pion
condensation. The gaps are taken from Takatsuka & Tamagaki (2004), the neutron gap 3P 2 is
additionally suppressed. The T s -T in relation is given by a fit.

Cooling curves for model II.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
0.501
1.250
1.350
1.370
1.390
1.400
1.420
1.437
1.452
1.480
1.700
1.930
Cooling for HJ EoS (Y)
Turuta crust, with medium effects, 3P 2 *0.1
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects but without pion
condensation. The gaps are taken from Yakovlev et al. (2003), the neutron gap 3P 2 is additionally
suppressed. The T s -T in relation is given by the Tsuruta law.

Cooling curves for model III.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
0.501
1.000
1.250
1.390
1.400
1.420
1.443
1.452
1.480
1.700
1.930
Cooling for HJ EoS
our crust, with medium effects, p cond. 3P 2 *0.1
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects and with pion
condensation. The gaps are taken from Yakovlev et al. (2003), the neutron gap 3P 2 is additionally
suppressed. The T s -T in relation is given by a fit.

Cooling curves for model IV.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
0.501
1.000
1.250
1.390
1.400
1.420
1.452
1.480
1.700
1.839
1.840
1.841
1.930
Cooling for HJ EoS (Y)
our crust, with medium effects, 3P 2 *0.1
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects but without pion
condensation. The gaps are taken from Yakovlev et al. (2003), the neutron gap 3P 2 is additionally
suppressed. The T s -T in relation is given by a fit.

Cooling curves for model V.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
0.501
1.000
1.250
1.320
1.370
1.390
1.400
1.420
1.435
1.445
1.452
1.480
1.930
Cooling for HJ EoS (Y)
Turuta crust, with medium effects, p cond, 3P 2 *0.1
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects and with pion
condensation. The gaps are taken from Yakovlev et al. (2003), the neutron gap 3P 2 is additionally
suppressed. The T s -T in relation is given by the Tsuruta law.

Cooling curves for model VI.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
0.501
1.000
1.250
1.320
1.350
1.390
1.400
1.420
1.435
1.452
1.480
1.700
1.930
Cooling for HJ EoS (Y)
Yakovlev crust (h = 4.0*10 16
), with medium effects, 3P 2 *0.1
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects but without pion
condensation. The gaps are taken from Yakovlev et al. (2003), the neutron gap 3P 2 is additionally
suppressed. The T s -T in relation is from Yakovlev et al. (2003), = 4 10 16 .

Cooling curves for model VII.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
1.000
1.100
1.320
1.350
1.370
1.390
1.400
1.420
1.430
1.452
1.930
Cooling for HJ EoS
our crust, with medium effects, p cond. 3P 2 *0.1, proton 1S 0 *0.5
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects and with pion
condensation. The gaps are taken from Yakovlev et al. (2003), the neutron gap 3P 2 is additionally
suppressed. The T s -T in relation is given by a fit. The proton gap is suppressed by a factor 0.5.

Cooling curves for model VIII.
0 1 2 3 4 5 6 7
log(t[yr])
5.6
5.8
6
6.2
6.4
log(T
s
[K])
RX
J082243
1E
120752
RX
J0002+62
PSR
0656+14
PSR
105552
RX
J18653754
Vela Geminga
PSR
J0205+64
in
3C58
Crab
0.501
1.000
1.250
1.320
1.340
1.350
1.390
1.400
1.420
1.452
1.930
Cooling for HJ EoS
our crust, with medium effects, p cond. neutron 3P 2 *0.1, 1S 0 *0.5 and proton !S 0 *0.2
From Blaschke et al. (2004); astro-ph/ 0403170.
Cooling of NS configuration with superfluid nuclear matter with medium effects and with pion
condensation. The gaps are taken from Yakovlev et al. (2003), the neutron gap 3P 2 is additionally
suppressed. The T s -T in relation is given by a fit. The 1S 0 neutron gap suppressed by a factor 0.5
and 1S 0 proton gap by a factor 0.2. The neutron 3P 2 gap is remained to be suppresed by 0.1.

Log N - Log S for model I.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).

Log N - Log S for model II.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).

Log N - Log S for model III.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).
Dashed line R belt = 500 pc, mass spectrum is not cutted.

Log N - Log S for model IV.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).

Log N - Log S for model V.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).

Log N - Log S for model VI.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).
Dashed line R belt = 500 pc, mass spectrum is not cutted.

Log N - Log S for model VII.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).
Dashed line R belt = 500 pc, mass spectrum is not cutted.

Log N - Log S for model VIII.
Solid line R belt = 300 pc, mass spectrum is not cutted.
Dotted line R belt = 500 pc, mass spectrum is cutted (no M = 1:1 M ).

Conclusions.
Log N - Log S distribution of close-by NSs can be a potential test for
cooling curves.
Main difficulties are connected with uncertainties in:
Mass spectrum of NSs
Emission model (atmospheres etc.)
Log N - Log S as a test is free from many disadvantages of the T t
test.
As Log N - Log S has its own problems and uncertainties two test
should be used together
5