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