Time Lags Due to Thermal and Bulk Comptonization

8/8/2019 Time Lags Due to Thermal and Bulk Comptonization

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Time lags due tothermal and bulk

ComptonizationJuan C Luna

George Mason University


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Variable Sources

AGN (Active Galactic Nucleus)

Neutron Star / White Dwarf

Black Hole Candidate


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Compact Objects


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White Dwarf (Mira)


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Neutron StarAfter a supernova explosion, the central region of the star collapses

combining protons and electrons and forcing them to produce neutrons. A

pulsar is a rotating neutron star.


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Black HoleThe star collapse up to a point of infinite mass an zero volume,

becoming a singularity.


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Black Holes


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Telescopes

Rossi XTEXMM NewtonChandra

1


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Slide 8

j1 Rossi XTEjcl,10/3/2006


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Tools & Files

FTOOLS

CIAO 3.1

XSPEC

Sherpa

Xronos


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Xspec output:

Spectrum and Light Curve


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Accretion Disc


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Accretion Models

Standard Disk(Shakura & Sunyaev 1973)

optically thick, geometrically thin,energy produced by viscousheating emitted locally asblackbody radiation (cool disk)

Two temperature Disks

(Shapiro, Lightman & Eardley1976)

The inner region of the disk is hot

geometrically thicker than the cooldisk, but optically thin to absorption(gas pressure is dominant hotdisk)


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Advection Dominated Accretion FlowAccretion flow in which as the gas spirals in and gets very

hot, it does not radiate its heat energy efficiently. Instead

of radiating and cooling down, the gas remains hot and

spirals in to the center. The heat energy released byviscous dissipation is not radiated immediately, as in a

thin disk, but is stored in the gas as thermal energy and

advected with the flow Narayan 06


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Main spectral states of

accreting black holesunabsorbed spectra

predicted detection by

Z. & Gierliski 2004


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black

holecold accretion

disk

active region soft seed

photonsreflectedphotons

scattered

hard

photons

Spectral States:

A. Zdziarski 05

cold outer disk

direct soft

photonsscattered

hard photonsreflected

photons

hot inner disk

variable inner radius

gravity +

Coulomb

black hole

outflow/jet

emitting

radio/IR/...

Soft State

Hard State


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cold outer disk

direct softphotons scatteredhard photonsreflected

photons

hot inner disk

variable inner radius

gravity +

Coulomb

black hole

outflow/jet

emittingradio/IR/...


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Power Spectra(Powspec & FFT)

QPO: quasiperidodical oscillationsFFT & PSD StatisticsTerms:

Power Spectral Density (PSD) FFT of

the auto-correlation function

Cross Spectral Density (CSD) FFT of

the Cross-correlation function


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Phase Info (autocorrelation FFT):

Time Lag

Difference in Photon Arrival times gives us information about source

size and propagation speed


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Advection model references

Blandford & Begelman (1999)

non-relativistic advection dominated inflow-outflow solution

Becker, Subramanian & Kazanas (2001)

pseudo-newtonian process in the event horizon RADIOS (self-similar relativistic advection dominated inflow-outflow solution)

Truong V. Le & Becker (2005)

relativistic outflows in advection dominated accretion disks withshocks

Becker & Wolff (2006)

Thermal and Bulk Comptonization in accretion powered X-raypulsars


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Transport Equation

2 2 0 0 0 02 2 2 20 0

( ) ( ) ( )1 1v v

3 4

N r r t t f f d f f r r

t r r dr r r r r

H H I I H I O

I T I

x x x x x !

x x x x x

First order Fermi energization Diffusion term

4

2 2

1e T

e

e

n cf ff kT

t m c

WI

I I I

x x x x x x -

Kompaneets Equation

Recoil

lossesStochastic energization

by thermal electrons


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2 2 0 0 0 02 2 2 20 0

( ) ( ) ( )1 1v v

3 4

N r r t t f f d f f r r

t r dr r r r r r

H H I I H I

I I

x x x x x

x x x x x

0

9 31/ 21/ 4 2

0 00

3 30 0

0 0

3 2, , exp

1 18 2 1

x

t

xx x xN eF x w I

xxr xxF

\I \I

I \ \T I T \

!

-

% %

% %%

0( ) 21

( , )2

iw t t

eF t dt observed fluxe I I

T

g

g

* ! %

22

2

164 81 9

ln4 2 1

AB

AB

v

v

\T \

N \T \

! -

%

% %%%

% %


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5 10 15 20

-2.25

-2

-1.75

-1.5

-1.25

-1

-0.75

-0.5

M. Van Der Klis et Al. 1987


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Future Work

4

2 2

1e

B e

e

n c f f k T

c

W

II II

x x x x -

2 2 40 0 0 02 2 2 2 2 20 0

( ) ( ) ( )1 1 1v v

3 4

e T

B e

e

N r r t t n c f f d f f fr r f k T

t r dr r r r r r m c

H H I I H WI

I

I I I I I

x x x x x x x

x x x x x x x -

Add stochastic energization by thermal

electrons, and the effect of the electrons

recoil (Kompaneets equation)The transport equation has to be

solved considering a disc geometry.

Kompaneets equation term


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References

The Why & How of X-Ray timing

Z. Arzoumanian. 2003 X-Ray Summer School

X-Ray Timing Analysis

Michael Novak- Chandra X-Ray Science Center / MIT

Chandra X-ray Observatory

http://chandra.harvard.edu/ Dr. Rita M. Sambruna Class Notes

Dr. Peter Becker- Class Notes, Verbal Communication

Dr. Lev Titarchuk- Class Notes, Seminars

[1] A Catalog of Candidate Intermediate-luminosity X-rayObjects V2. ApJS 2002. E.J.M Colbert, and A.F. Ptak.

Gravitys Fatal AttractionMitchell Begelman

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Time Lags Due to Thermal and Bulk Comptonization