30
The Broad Fe Kα Line in MCG-6-30-15 Jörn Wilms (U Warwick/IAA Tübingen) http://astro.uni-tuebingen.de/~wilms in collaboration with R. Staubert C.S. Reynolds (UMD), M.C. Begelman (JILA), E. Kendziorra (IAAT), J. Reeves (GSFC), S. Molendi (Milano)

Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

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Page 1: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

The Broad Fe Kα Linein

MCG−6-30-15

Jörn Wilms (U Warwick/IAA Tübingen)http://astro.uni-tuebingen.de/~wilms

in collaboration with

R. Staubert

C.S. Reynolds (UMD), M.C. Begelman (JILA), E. Kendziorra (IAAT),

J. Reeves (GSFC), S. Molendi (Milano)

Page 2: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Contents 1

Structure

• Kα Line Diagnostics

– Accretion geometry

– Compton reflection and Fe Kα generation

– Line transfer close to the BH

• MCG−6-30-15

– Simultaneous XMM-Newton/RXTE Observations

– Soft X-ray spectrum

– Observations of a Broad Line

– Interpretation and Caveats

• Summary

Page 3: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Testing Relativity in AGN 1

Kα Line Diagnostics

Hot Corona

Thin Accretion Disk

BLR

BH

RS

AU

10 100Energy [keV]

1

10

100

Flu

x [a

rbitr

ary

units

]

Γ=1.9

AGN X-Ray Spectrum:

• Comptonization of soft X-rays from

accretion disk in hot corona (T ∼ 108 K):

power law continuum.

Page 4: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Testing Relativity in AGN 2

Kα Line Diagnostics

Hot Corona

Thin Accretion Disk

BLR

BH

RS

AU

10 100Energy [keV]

1

10

100

Flu

x [a

rbitr

ary

units

]

Γ=1.9

AGN X-Ray Spectrum:

• Comptonization of soft X-rays from

accretion disk in hot corona (T ∼ 108 K):

power law continuum.

• Thomson scattering of power law photons in

disk: Compton Reflection Hump

Page 5: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Testing Relativity in AGN 3

Kα Line Diagnostics

Hot Corona

Thin Accretion Disk

BLR

BH

RS

AU

10 100Energy [keV]

1

10

Fe K

Fe K

100

Flu

x [a

rbitr

ary

units

]

Γ=1.9

α

β

AGN X-Ray Spectrum:

• Comptonization of soft X-rays from

accretion disk in hot corona (T ∼ 108 K):

power law continuum.

• Thomson scattering of power law photons in

disk: Compton Reflection Hump

• Photoabsorption of power law photons in

disk: fluorescent Fe Kα Line at ∼6.4 keV

Page 6: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Testing Relativity in AGN 4

Kα Line Diagnostics

∆Φ

0

2

4

6

8

I νo [

arb

itra

ry u

nits]

4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Energy [keV]

−0.15−0.05 −0.100.000.100.200.30

z=(E e/Eo) − 1

Total observed line profile affected by

• grav. Redshift

Page 7: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Testing Relativity in AGN 5

Kα Line Diagnostics

0

2

4

6

8

I νo [

arb

itra

ry u

nits]

4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Energy [keV]

−0.15−0.05 −0.100.000.100.200.30

z=(E e/Eo) − 1

5o

10o

20o

30o

40o

50o

60o

70o

80o

Total observed line profile affected by

• grav. Redshift

• Light bending

• rel. Doppler shift

Page 8: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Testing Relativity in AGN 6

Kα Line Diagnostics

Line

Em

issi

vity constant

power law

0.0

0.2

0.4

0.6

0.8

1.0

I νo [a

rbitra

ry u

nits]

4.5 5.0 5.5 6.0 6.5 7.0 7.5Energy [keV]

−0.15−0.05 −0.100.000.100.200.30

z=(E e/Eo) − 1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

io= 40o

Total observed line profile affected by

• grav. Redshift

• Light bending

• rel. Doppler shift

• emissivity profile

Page 9: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Testing Relativity in AGN 7

Kα Line Diagnostics

rotating Black Holeve

loci

ty

velo

city

nonrotating Black Hole

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

I νo [a

rbitra

ry u

nits]

4.5 5.0 5.5 6.0 6.5 7.0 7.5Energy [keV]

−0.15−0.05 −0.100.000.100.200.30

z=(E e/Eo) − 1

0.00

0.25

0.50

0.75

0.9981

io= 40o

Total observed line profile affected by

• grav. Redshift

• Light bending

• rel. Doppler shift

• emissivity profile

• spin of black hole

Page 10: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

MCG−6-30-15 1

MCG−6-30-15, IL

ine

flu

x (

10

ph

/s/k

eV

/cm

)

−5

2

05

10

15

0.4 1.41.21.00.80.6

ν/ν 0

MCG−6-30-15 (z = 0.008): first AGN with relativistic disk line

Tanaka et al. (1995): time averaged ASCA

spectrum: line skew symmetric

=⇒ Schwarzschild black hole.

Page 11: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

MCG−6-30-15 2

MCG−6-30-15, IIL

ine

flu

x (

10

ph

/s/k

eV

/cm

)

−5

2

05

10

15

0.4 1.41.21.00.80.6

ν/ν 0

0.4 0.6 0.8 1.21.0 1.4

ν/ν 0

010

15

Lin

e flu

x (

10 ph/s

/keV

/cm

)

−5

2

5

MCG−6-30-15 (z = 0.008): first AGN with relativistic disk line

Tanaka et al. (1995): time averaged ASCA

spectrum: line skew symmetric

=⇒ Schwarzschild black hole.

Iwasawa et al. (1996): “deep minimum

state”: extremely broad line

=⇒ Kerr Black Hole.

Page 12: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

MCG−6-30-15 3

MCG−6-30-15, IIIL

ine

flu

x (

10

ph

/s/k

eV

/cm

)

−5

2

05

10

15

0.4 1.41.21.00.80.6

ν/ν 0

0.4 0.6 0.8 1.21.0 1.4

ν/ν 0

010

15

Lin

e flu

x (

10 ph/s

/keV

/cm

)

−5

2

5

MCG−6-30-15 (z = 0.008): first AGN with relativistic disk line

Tanaka et al. (1995): time averaged ASCA

spectrum: line skew symmetric

=⇒ Schwarzschild black hole.

Iwasawa et al. (1996): “deep minimum

state”: extremely broad line

=⇒ Kerr Black Hole.

Later confirmed with BeppoSAX (Guainazzi et al., 1999) and RXTE (Lee et al., 1999).

Page 13: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

XXX

Page 14: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

MCG−6-30-15 5

XMM-Newton Data, II

Two long XMM-Newton Observations of MCG−6-30-15 available:

June 2000 : (rev 108), 100 ksec

(Wilms et al. 2001, Reynolds et al., 2003)

• overall flux ∼ ASCA “deep minimum”

• source strongly variable

• broad Fe Kα line

July/August 2001 : (rev 301–303), 315 ksec

(Fabian et al. 2002, Vaughan et al. 2003, Ballantyne et al. 2003)

• source 70% brighter than in June 2000

• similar variability

• broad Fe Kα line

Page 15: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

MCG−6-30-15 6

Data Extraction

0

2

4

6

8

10

12

14

Cou

nt r

ate

[cps

]

0 6 12 18 0 6 12 182000 July 11 2000 July 12

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2

JD−2451736

XMM−Newton EPIC pn (singles)

RXTE PCA (normalized to 1 PCU)

XMM-Newton and RXTE lightcurves, ∆t = 100 s.Total XMM-Newton exposure∼100 ksec.

Overall flux ∼ ASCA “deep minimum” (F2−10 = 2.3 × 10−11 erg s−1 cm−2)To avoid possible pile-up, use data from < 14 cps in EPIC pn onlyfor MOS: Ring 10′′, 35′′, pattern 0–12.

Page 16: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

MCG−6-30-15 7

Spectral Analysis

10-2

10-1

10 0

10 1

coun

ts s

-1 k

eV-1

Single Events

Double Events

Energy [keV]

0.60.81.01.21.41.61.8

data

/mod

el

1.0 5.0 10.0

MCG-6-30-15EPIC pn

X-ray spectrum very

complex:

• warm absorber at

. 1.5 keV

• power-law continuum

• reflection continuum

• relativistic iron line

• narrow iron line

Low energy end of

spectrum: warm absorber

=⇒ RGS.

Then Fe line analysis with

EPIC data.

Page 17: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

MCG−6-30-15 8

RGS Data

0

1

2

3

RG

S c

ount

s s-1

keV

-1

Energy [keV]

-5

0

5

∆χ2

0.5 1.0

MCG-6-30-15RGS

RGS1

RGS2

(red: RGS1, blue: RGS2; χ2red = 1.4).

• absorption edges of

C V (400), O VII (740),

O VIII (870), and

Ne X (1362 eV),

• blended resonance

absorption lines below O VII

and O VIII edges,

• four moderately broad, weak

Gaussian emission features

at 0.885 keV, 0.935 keV,

0.995 keV, and 1.06 keV

(lab frame; no interpretation).

(model similar to Lee et al. 2001)

Analysis à la Branduardi-Raymont et al. (2001) gives similar results for Fe line.

Page 18: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Iron Line 1

Iron Line, I

1 10Energy [keV]

0.8

0.9

1.0

1.1

1.2

data

/mod

el

χ2/dof = 2852/1718

Continuum model:

1. empirical “warm absorber model”,

2. power law (Γ = 1.94 ± 0.02),

3. relativistically smeared reflection from a

possibly ionized accretion disk (i = 30,

Ω/2π = 1–1.5).

4. narrow Fe line (EW ∼ 40 eV)

=⇒Clear deviations in the 2–7 keV band

=⇒ relativistically broadened iron line.

Page 19: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Iron Line 2

Iron Line, II

1 10Energy [keV]

0.8

0.9

1.0

1.1

1.2

data

/mod

el

χ2/dof = 2852/1718

Energy [keV]

0.8

0.9

1.0

1.1

1.2

data

/mod

el

2 10

χ2/dof = 1506/1312

Continuum model:

1. empirical “warm absorber model”,

2. power law (Γ = 1.94 ± 0.02),

3. relativistically smeared reflection from a

possibly ionized accretion disk (i = 30,

Ω/2π = 1–1.5).

4. narrow Fe line (EW ∼ 40 eV)

=⇒Clear deviations in the 2–7 keV band

=⇒ relativistically broadened iron line.

5. relativistically broadened Gaussian:

E = 6.95+0−0.15 keV, WKα = 582 eV; with

emissivity IFe(r) ∝ r−β: β = 4.6 ± 0.3

Page 20: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Iron Line 3

Observational Summary

0.6

0.8

1.0

1.2

1.4

1.6

1 100.8

0.9

1.0

1.1

1.2

1.3

data

/mod

el

2 3 4 5 6 7 8 9Energy (keV)

6

8

10

12

14

16

ν f ν

(10

-3 k

eV c

m-2

s-1

)

a

b

c

a pure PL fit,

b Setting the normalization of the lines

to zero reveals the extreme width

and skewed profile of the Fe line,

c Components of the final fit

Page 21: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Iron Line 4

Other XMM Observations

Lin

e fl

ux (

10 keV

/cm

/s

/keV

)2

−4

82

46

4 6 8

0

Energy (keV)

after Fabian et al. (2002)

July/August 2001 315 ksec

observation

(Fabian et al., 2002)

• Strong narrow line

• broad line clearly present

• emissivity profile very steep forradii close to rin

IFe Kα ∝

r−5.5±0.3 for r < 6.1+0.8−0.5rg

r−2.7±0.1 outside

(Fabian & Vaughan, 2003)

Page 22: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Caveats 1

Caveats

Broad line obviously depends on assumed continuum

• ionized reflection models not yet very realistic!but would require big change at low E, rather improbable. . .

=⇒ Ballantyne & Fabian models give same result for line!

• absorption in ionized gas? attempts of including this generally unsuccessful. . .

• partial covering? so far, all partial covering models we tried failed in the RXTE-PCA. . .

• simple PL continuum usedexpected from Comptonization; fitting realistic Comptonization models to XMM/RXTE data

results in large β and kTe & 70 keV =⇒ PL

• Continuum variabilityΓ changes with flux, might mimic broadening

=⇒ time dependent analysis shows line remains broad

Page 23: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Caveats 2

Alternative Continuum Models

• Partial covering à la Pounds et al.

(2002) does not work with PCA!

• ionized reflection, as assumed

here, works with PCA!

Page 24: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Caveats 3

Observational Summary

3 4 5 6 7 8Energy [keV]

0

5

10

15

Pho

ton

Flu

x [1

0−5 p

h cm−

2 s−

1 ke

V−

1 ] MCG−6−30−15Tanaka et al. (1995)

1 10 100Energy [keV]

10−3

10−2

ν f ν

[keV

2 c

m−

2 s−

1 keV

−1

Tanaka et al., 1995 Wilms et al., 2001, 2003

XMM-Newton: MCG−6-30-15 has broadest Fe Kα line seen in all AGN

Width of the line: Kerr Black Hole is required (Confirming ASCA and BeppoSAX )

The emissivity index, β, is large =⇒ Line from centralmost regions!

Page 25: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Interpretation 1

Interpretation

Shape of line profile depends on

radial line emissivity

XMM-Newton: IFe Kα ∝ r−4.6

line emissivity ∝ flux irradiated on disk

∝ downward coronal flux

∝ local disk emissivity

∝ local energy dissipation rate1 10 100

Energy [keV]

10−3

10−2

ν f ν

[keV

2 c

m−

2 s−

1 keV

−1

BUT: Accretion theory: dissipation rate ∝ r−3!

XMM-Newton observations show that more energy dissipated in disk

than predicted from theory =⇒ additional energy source required!

Page 26: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Interpretation 2

Interpretation

Hypothesis: Magnetic couple between BH

and accretion disk:

1. Magnetic connection between inner disk

and plunging region (Agol & Krolik, 2000)

2. Magnetic connection between inner disk

and rotating event horizon (Li, 2000, 2002,

2003).

“torqued disks”

Complications:• Magnetic field structure for r < rin: connection

btw. plunging region and disk too weak forenergy release required? (Li, 2003) [but:contradicts numerical simulations, e.g., Hawley& Krolik, 2001]

• Corona might be suppressed by torquing (Merloni & Fabian, 2003)• gravitational focussing of X-rays? Petrucci & Henri (1997) show that in this case central source needed

as well (but see Martocchia, Matt & Karas 2002).• relativistic outflow? Proposed by Titarchuk, no comparison with data yet. . .• limb darkening law of accretion disk? (Beckwith & Done, 2004, no fits yet).

Page 27: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Line Profiles 1

Realistic (?) Line Profiles

Payne & Thorne (1994) accretion disk, torqued at

r = rms (Agol & Krolik, 2000), including returning

radiation

χ2/dof = 2075/2104

=⇒Fits need large increase of inner disk radiative

efficiency to explain line profile, are dominated

by torquing.

Reynolds, Wilms, et al. (2004)

Page 28: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

Summary 1

Summary

• XMM-Newton observations show extremely broad line.

• Line profile implies very steep emissivity profile.

• Steep emissivity profile also seen in longer observation of Fabian et al.

(2002).

• Shakura & Sunyaev type disks cannot explain inferred emissivity profile.

• Plausible explanation by elimination of other alternatives:

spin extraction from a magnetized black hole

=⇒More theoretical work on line emissivity profiles from (Kerr) black

holes is needed!

And the future?

• more deep AGN observations with XMM-Newton

• Simbol-X

• XXX-XEUS

=⇒ enough to do for age 65 – 85. . .

Page 29: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

1–1

*

Bibliogr

Page 30: Jörn Wilms (U Warwick/IAA Tübingen)...Testing Relativity in AGN 1 Kα Line Diagnostics Hot Corona Thin Accretion Disk BLR BH R S AU 10 100 Energy [keV] 1 10 100 Flux [arbitrary units]

1–1 BIBLIOGRAPHY

Agol, E., & Krolik, J. H., 2000, ApJ, 528, 161

Branduardi-Raymont, G., Sako, M., Kahn, S. M., Brinkman, A. C., Kaastra, J. S., & Page, M. J., 2001, A&A, 365, L140

Fabian, A. C., et al., 2002, MNRAS, 335, L1

Guainazzi, M., et al., 1999, A&A, 341, L27

Iwasawa, K., et al., 1996, MNRAS, 282, 1038

Lee, J. C., Fabian, A. C., Brandt, W. N., Reynolds, C. S., & Iwasawa, K., 1999, MNRAS, 310, 973

Lee, J. C., Ogle, P. M., Canizares, C. R., Marshall, H. L., Schulz, N. S., Morales, R., Fabian, A. C., & Iwasawa, K., 2001, ApJ, 554, L13

Martocchia, A., Matt, G., & Karas, V., 2002, A&A, 383, L23

Petrucci, P. O., & Henri, G., 1997, A&A, 326, 99

Tanaka, Y., et al., 1995, Nature, 375, 659

Wilms, J., Reynolds, C. S., Begelman, M. C., Reeves, J., Molendi, S., Staubert, R., & Kendziorra, E., 2001, MNRAS, 328, L27