The Emissivity Profiles of AGN Accretion Discs

Dan WilkinsInstitute of Astronomy, University of Cambridge

Supervisor: Andy Fabian

High Energy View of Accreting Objects, Crete 2010

1. Concept of emissivity profiles

• So what?

2. Determination from observed spectra

• 1H 0707-495

3. Test with self-consistent XSPEC model

4. Theoretical emissivity profiles

• Link to source parameters

Outline

2

‘Lamppost’ Model

3

PLC

RDC

X-ray source in corona around BHIC scattering of seed photons

Reflection from accretion discatomic lines/absorption imprinted (reflionx)

Emissivity Profile

4

• Reflected power per unit area from disc.

• Flux received at point on disc falls off with distance from X-ray source.

1e-05

0.0001

0.001

0.01

0.1

1

10

0.1 1 10 100r

Emissivity Profile

4

• Reflected power per unit area from disc.

• Flux received at point on disc falls off with distance from X-ray source.

F ∝ 1d2

=1

r2 + h2

d

h

• e.g. Euclidean space

r

Emissivity Profile - So What?

5

• Depends on

• Source location/height

• Source extent

• Source/disc geometry

• Typically assume a (broken) power law emissivity profile.

Emissivity Profiles from Spectra

6

(r) ∝ r−α

• Typically assume a (broken) power law emissivity profile.

Emissivity Profiles from Spectra

6

(r) ∝ r−α

• Instead, can we determine the emissivity from observed spectra?

• Constrain properties of X-ray source...

1 100.5 2 5

12

3

ratio

Energy (keV)

1H0707 495 Emission Lines• Narrow emission line in disc frame.

• To observer, broadened by relativistic effects:• Doppler shift/beaming• Gravitational redshift

• Transfer function:

Broadened Emission Lines

7

F0(ν0) =

Ie(re,ν0

g)T (re, g)dgredre

105

050

010

00

norm

aliz

ed c

ount

s s

1 keV

1

Energy (keV)

Broadened Emission Lines

8

• Line profiles different from successive radii.

• Total line is sum (integral) over disc

• Photon count from each annulus

• Get emissivity from photon counts from successive annuli (divided by projected area).

Emissivity from Broad Lines

9

F0(ν0) =

T (re, g)redre(re)

N(r) ∝ A(r)(r)

• Model spectrum

• In iron K band (3-10 keV), dominant components are power law continuum and disc reflection.

• Model parameters from best fit model of Zoghbi+10 for 1H 0707-495.

• Fit for photon count from each radius (norm) in XSPEC.

Emissivity from Broad Lines

10

powerlaw +

kdblur⊗ reflionx

10 3

0.01

norm

aliz

ed c

ount

s s

1 keV

1

data and folded model

105

0.8

1

1.2

ratio

Energy (keV)drw 20 May 201

χ2 = 255.48

χ2 / NDoF = 1.1255

1H 0707-495

11

XMM-NewtonEPIC pn500ks(Zoghbi+10)

! = 3.3

! = 6

" /

arbi

trar

y u

nits

10#10

10#9

10#8

10#7

10#6

10#5

10#4

10#3

0.01

r / RG

1 10 100

1H 0707-495 Emissivity Profile

12

3-10 keV

! = 3.3

! = 6

" /

arbi

trar

y u

nits

10#10

10#9

10#8

10#7

10#6

10#5

10#4

10#3

0.01

r / RG

1 10 100

1H 0707-495 Emissivity Profile

12

3-10 keV

?

! = 3.3

! = 6

" /

arbi

trar

y u

nits

10#10

10#9

10#8

10#7

10#6

10#5

10#4

10#3

0.01

r / RG

1 10 100

! = 0

! = 7.8

" /

arbi

trar

y u

nits

10#12

10#9

10#6

10#3

r / RG

1 10 100

1H 0707-495 Emissivity Profile

12

3-10 keV 3-5 keV

?

• Fit one reflection component with continuous emissivity profile over disc.

• Twice broken power law

• kdblur3 blurring kernel.

• Fit for slopes and break points.

Test with XSPEC Model

13

kdblur2 kdblur3

Index 1 4.82 7.83

R break 1 6.85RG 5.60RG

Index 2 2.09 7.84x10-5

R break 2 — 34.75RG

Index 3 — 3.30

χ2 287.52 264.32

χ2 / Ndof 1.11 1.04

3-10keV : powerlaw + kdblur⊗reflionx

10 3

0.01

norm

aliz

ed c

ount

s s

keV

105

0.8

1

1.2

ratio

Energy (keV)

10 3

0.01

norm

aliz

ed c

ount

s s

keV

105

0.8

1

1.2

1.4ra

tio

Energy (keV)

Fits to 1H 0707-495 Iron K Line

14

kdblur3 kdblur2

powerlaw + kdblur⊗reflionx

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

1 10 100 1000

/ ar

bitra

ry u

nits

r / rg

kdblur3kdblur2

1H 0707-495 Emissivity Profile

15

16

0.6

0.7

0.8

0.9

1

1.1

1 10 100 1000

F( <

r )

/ F(

<40

0rg

)

r / rg

F (< r) =

r

1.235rg

(r) rdr

17

Reflected Flux Distribution

• Isotropic point source above the disc plane.

• Either on or orbiting the rotation axis.

• Trace rays from source until they hit disc plane.

• Emissivity – number of photons hitting disc per unit area.

18

Theoretical Emissivity ProfilesFollowing Miniutti+03, Suebsuwong+06

e(t) = v

The Source

19

e(a) · e

(b) = η(a)(b)

• Source frame basis (flat)

• Rays at equal intervals in solid angle.

• Calculate initial conditions by transforming to global basis.

• Isotropic Point Source• Equal power radiated

into equal solid angle, in source frame.

dΩ = d(cos α)dβα

βei

e’i

θϕ

r

dΩ’

• Propagate photons using (null) geodesic equations as affine parameter advances.

Photon Propagation

20

• Accretion disc (equatorial plane) divided into radial bins.

• When photons hit disc (θ=π/2), record radial bin.

• Emissivity given by photons per bin (per bin area, with relativistic effects).

-4-2

0 2

4

-4

-2

0

2

4

0

1

2

3

4

5

1e-06

1e-05

0.0001

0.001

0.01

0.1

1 10 100r

• Flat, Euclidean spacetime.

• Flux falls off as inverse square of distance from source.

• Projected normal to the disc plane.

Classical Case

21

(r) ∝ 1

d2cosϑ =

1

h2 + r2h√

h2 + r2

d

h

r

r-3

constant

ϑ

• Gravitational light bending towards black hole• Focusses more rays onto inner disc – steepens emissivity

profile.

• Relativistic beaming if source is moving• More emission onto regions of disc on/below orbit.

• Proper area of radial bins (GR and length contraction)

• A/dr increases in inner disc – shallower profile.

• Time dilation/gravitational redshift• Proper time elapses slower at inner disc so greater flux

measured in disc frame per ray – significant steepening.

Relativistic Effects

22

∼ t2

Relativistic Effects (2)

23

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / RG

r = 3r = 6

r = 10r = 20r = 50

rs

Theoretical Emissivity Profiles (1)

24

StationaryAxialSource

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / RG

r = 3r = 6

r = 10r = 20r = 50

rs

Theoretical Emissivity Profiles (1)

24

StationaryAxialSource

α~7

α~3.3

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / RG

x = 5, h = 1.235x = 5, h = 3x = 5, h = 5

x = 5, h = 10x = 5, h = 20x = 5, h = 50

!"

"

Theoretical Emissivity Profiles (2)

25

‘Co-rotating’Ring Source(height)

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / RG

x = 1.235, h = 5x = 3, h = 5x = 5, h = 5

x = 10, h = 5

Theoretical Emissivity Profiles (3)

26

!"

"

‘Co-rotating’Ring Source(radius)

0.01

0.1

1

10

100

1000

10000

1 10 100 1000

/ ar

bitra

ry u

nits

r / RG

x = 20, h = 2

Theoretical Emissivity Profiles (4)

27

!"

"

‘Co-rotating’Ring Source

0.01

0.1

1

10

100

1000

10000

1 10 100 1000

/ ar

bitra

ry u

nits

r / RG

x = 20, h = 2

Theoretical Emissivity Profiles (4)

27

!"

"

‘Co-rotating’Ring Source Break point at outer

extent (rise as close to disc)

0.01

0.1

1

10

100

1000

10000

1 10 100 1000

/ ar

bitra

ry u

nits

r / RG

x = 20, h = 2

Theoretical Emissivity Profiles (4)

27

!"

"

‘Co-rotating’Ring Source Break point at outer

extent (rise as close to disc)

Steepening – close to disc/BH

• Simulations of point sources explain basic form of emissivity profile.

• Steep inner part due to time dilation/gravitational redshift.

• Flattening in middle region (h » r).• Constant index slightly steeper than classical (3).

Theoretical Results

28

• Outer break radius (flat to constant index outer disc) lies approximately below the source.

• Greater steepening at inner disc for sources closer to the black hole.

• Either source radius or height above disc.

Theoretical Results (2)

29

Extended Sources

30

• Sum point sources.

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / rg

• Vertical ‘jet’

• Constant power with h

Extended Sources

30

• Sum point sources.

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / rg

Extended source, 1.235<x<20, h=10Ring source, x=20, h=10• Radially

extended

• Constant power with r

Extended Sources (2)

31

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / rg

Extended source, 1.235<x<20, h=10Ring source, x=20, h=10• Radially

extended

• Constant power with r

Extended Sources (2)

31

Break point at outer extent

0.01

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

/ ar

bitra

ry u

nits

r / rg

Extended source, 1.235<x<20, h=10Ring source, x=20, h=10• Radially

extended

• Constant power with r

Extended Sources (2)

31

Break point at outer extent

Steepening from inner/height

-4-2

0 2

4

-4-2

0 2

4 0

1

2

3

4

5

• Reflected radiation from one part of disc can be bent by black hole back on to disc.

• More radiation on inner disc – steeper profile.

Return Radiation

32

Cunningham 1976, Ross & Fabian 2002

• Determined emissivity profile of 1H 0707-495 without a priori assumption of its form.• Twice broken power law.• Steep (α~7.8) in inner disc, flat 5.6–34.8RG, α~3.3 over outer

disc.

• Consistent with XSPEC fit to reflection spectrum using one continuous emissivity profile.

• Form of emissivity profile agrees with theoretical prediction.• Understand form in terms of physics (relativistic effects).

• Can constrain properties of hard X-ray source...

Conclusions

33