importance of compton scattering on x-ray spectra of millisecond pulsars and intermediate polars
DESCRIPTION
Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars. (Tuebingen University, Kazan State University). V . Suleimanov. In collaboration with. J. Poutanen (Oulu University) M. Falanga (SEA - Saclay). Millisecond Pulsars - PowerPoint PPT PresentationTRANSCRIPT
Importance of Compton scattering on X-ray spectra of Millisecond
Pulsars and Intermediate Polars
V. Suleimanov
(Tuebingen University, Kazan State University)
In collaboration with
J. Poutanen (Oulu University)
M. Falanga (SEA - Saclay)
Millisecond Pulsars LMXB, νspin(NS) ~ 200 – 700 Hz, Porb ~ 40 min – 4.5 hours, B ~ 108 – 109 Gs
Intermediate Polars (IPs)
CV, P spin (WD) < P orb, B ~ 1 – 10 MGs
AD disrupted by magnetic field at some radius RA (Alfven radius)
R A is radius where P ram = P mag
10-5 10-3 10-1 101 103 105
5
10
15
20
25
30
10-5 10-3 10-1 101 103 105
5
10
15
20
25
30
10-5 10-3 10-1 101 103 105
5
10
15
20
25
30
10-5 10-3 10-1 101 103 105
5
10
15
20
25
30
Teff
= 1.88 107 K log g = 14.0 F
shock = 0.0 F
total
m0 = 0 g / cm2
T ,
ke
V
m , g / cm2
T ,
ke
V
m , g / cm2
T ,
ke
V
m , g / cm2
m0 = 3 g / cm2
m0 = 1 g / cm2
Teff
= 1.93 107 K log g = 14.0 F
shock = 0.1 F
total
T ,
ke
V
m , g / cm2
1015 1016 1017 1018 1019
101
103
105
Teff
= 1.88 107 K log g = 14.0 F
shock = 0.0 F
total
m0 = 0 g / cm2
I
, er
g /
cm2 /
s /
Hz
Frequency, Hz
1 keV 10 keV
1015 1016 1017 1018 1019
101
103
105
Teff
= 1.93 107 K log g = 14.0 F
shock = 0.1 F
total
m0 = 1 g / cm2
I
, er
g /
cm2 /
s /
Hz
Frequency, Hz
= 0.953 = 0.769 = 0.5 = 0.231 = 0.047
1 keV 10 keV
1015 1016 1017 1018 1019
101
103
105
Teff
= 1.93 107 K log g = 14.0 F
shock = 0.1 F
total
m0 = 3 g / cm2
I
, er
g /
cm2 /
s /
Hz
Frequency, Hz
1 keV 10 keV
10-5 10-3 10-1 101 103 105
10
20
30
40
50
60
70
Teff
= 1.93 107 K log g = 14.0 F
shock = 0.9 F
total
m0 = 3 g / cm2
T
,
keV
m , g / cm2
1 10 1001020
1021
1022
1023
1024
BB
Teff
= 1.93 107 K log g = 14.0 F
shock = 0.9 F
total
m0 = 1 g / cm2
H
, e
rg /
cm
2 / s
Energy, keV
1 10 1001020
1021
1022
1023
1024
Teff
= 1.93 107 K log g = 14.0 F
shock = 0.9 F
total
m0 = 3 g / cm2
I
, e
rg /
cm
2 / s
Energy, keV
Method of WD mass estimations• Shock wave standing above WD surface• The kinetic energy of the infalling gas is converted to the thermal
energy
• There is a reliable mass-radius relation for WD (Nauenberg 1972)• Maximum temperature after the shock depends on WD mass only• The temperature can be obtained from the fitting of the observed X-
ray spectrum by bremsstrahlung model
Spectrum of IP TV Col obtained with the RXTE observatory. Crosses denote the PCA data, open circles – HEXTE data. Solid line show bestfit model (see below).
Previous investigations
Rotschild et al (1981) - idea
Ishida (1991) – GINGA / LAC observations, isothermal post-shock region (PSR, or accretion column)
• Detail model of PSR (non-isothermal) Aizu (1973), Wu et al (1994), Woelk & Beuermann (1996), Cropper
et al. (1999)
• WD mass determinations using non-isothermal models of PSR
Cropper et al (1999) – GINGA / LAC (2-20 keV)
Ramsay (2000) – RXTE / PCA (3-20 keV)
• First works
The modelbased on Cropper et al (1999)
• Mass continuity equation
• The momentum equation
• The energy equation
• Ideal-gas law
• The cooling rate
• The cooling function from Sutherland & Dopita (1993)
2//, cmsgav
wd
wd
RGM
Pvdzd )( 2
)1(dzdv
PdzdPv
pmkT
P
)(
2
Tm Np
)(TN
Is Compton scattering significant?
0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.01
0.1
1
0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.01
0.1
1
YC
ompt
MWD
/ Msun
- a = 10 g / s / cm2, computed
YC
ompt
MWD
/ Msun
- a = 1 g / s / cm2, computed - analytical
dznTcm
k
cm
kTY ee
e
Te
e
eCompt 22
44
0.1 1 10 100
1014
1015
1016
1017
1018
1019
Te = 6 108 K
e = 2
Tout
= 106 K
E -
F
lux,
e
rg /
s /
cm
2 / k
eV
Photon energy, keV
Method: radiation transfer solving by short characteristic method with Compton scattering taking into consideration (redistribution functions method (Poutanen & Svensson 1996))
2/1)/425.2(5.1 ComptY
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
1E-3 0.01 0.1 1 10 100 1000
1013
1014
1015
1016
1017
BE (T
Bott = 2 105 K)
B = 107 Gs
+ cyclotron radiation
and TBott
= 2 105 K
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
No Compton scatteringCompton scattering
MWD
= Msun
MWD
= 1.2 Msun
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
+ cyclotron radiation
and TBott
= 2 105 K
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
No Compton scatteringCompton scattering
MWD
= Msun
MWD
= 1.2 Msun
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
Results (plane parallel approximation ):
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
TWD
= 2 104 K
No Compton scatteringCompton scattering
MWD
= Msun
MWD
= 1.2 Msun
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
More detail:
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
1 10 1001015
1016
1017
+ cyclotron radiation
and TBott
= 2 105 K
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
Compton scatteringM
WD = M
sun
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
No Compton scattering MWD
= Msun
MWD
= 1.2 Msun
E
HE,
er
g /
s /
cm2
Photon energy, keV
E
HE,
er
g /
s /
cm2
Photon energy, keV
More detail:
Conclusions
• Work is not finished
• It is necessary to improve the “accretion column” model for Millisecond Pulsars
• Compton scattering is significant for high mass Intermediate Polars and it is necessary to take into account