Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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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)

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 Presentation

Transcript of Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

Page 1: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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)

Page 2: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars
Page 3: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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

Page 4: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars
Page 5: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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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

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1015 1016 1017 1018 1019

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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

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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

Page 8: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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

Page 9: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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10

20

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Teff

= 1.93 107 K log g = 14.0 F

shock = 0.9 F

total

m0 = 3 g / cm2

T

,

keV

m , g / cm2

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1021

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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

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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

Page 12: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars
Page 13: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars
Page 14: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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

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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).

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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

Page 17: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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

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Page 19: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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

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0.1 1 10 100

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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

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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 ):

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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:

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+ 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:

Page 24: Importance of Compton scattering on X-ray spectra of Millisecond Pulsars and Intermediate Polars

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