Minimum X-ray source size for a lamppost corona in light-bending - - PowerPoint PPT Presentation

Minimum X-ray source size for a lamppost corona in light-bending models for AGN

Michal Dovˇ ciak Chris Done

Astronomical Institute

• f the Czech Academy of Sciences, Prague

Durham University From the Dolomites to event horizon: Sledging down the Black Hole potential well (3rd ed.) Sexten Center for Astrophysics, Sesto, Italy 13th–17th July 2015

Scheme of the lamp-post geometry

r

in

r

• ut

δi δe

a

Ω

corona accretion disc black hole

• bserver

∆Φ

h M

◮ central black hole – mass, spin ◮ accretion disc

→ Keplerian, geometrically thin, optically thick → Novikov-Thorne thermal emission (TNT, M, ˙ M = Lb

ηc2 , a, fc) ◮ compact corona with isotropic emission

→ height, luminosity, size (radius),

• ptical depth (h, LX or Lobs, R, τ)

◮ up-scattering in the corona

→ nthcomp(E; Γ, Ec, TBB)

◮ relativistic effects:

→ Doppler and gravitational energy shift → light bending (lensing) → aberration (beaming)

0.2 0.4 0.6 0.8 0.5 1 1.5 2 FE [ LX / keV ] E [keV] Γ 3.0 2.5 2.0

h = 1.5

M = 107M⊙, Lb = LEdd, a = 0.998, η = 32.4%, fc = 2.4

Thermal photon flux arriving at corona

1 2 3 4 1 2 3 4 5 10 fBB × dSd / dΩn [×1032 s-1] r [GM/c2] h [GM/c2] 1.2 1.5 2.4 5.1 Newton 0.1 1 10 1 2 3 4 5 10 20 30 E [keV] h [GM/c2] EP EBB TBB EP

N

EBB

N

TBB

N

fin = 8πζ(3)k3 f 4

c h3 c2 rout

• rin

dr r dΩL dSd (gTNT)3 Fin = 4π5k4 f 4

c 15h3 c2 rout

• rin

dr r dΩL dSd (gTNT)4 dΩn dSd = h D3 , g = EL Ed TBB = Epeak 2.82 , EBB = Fin fin , EP = LX fout Fth(Epeak) = MAX[Fth(E)] fout =

∞

• nthcomp(E;Γ,Ec,TBB)dE

Size of the corona - components

(1−e−τ)findSL = fout R =

• 1

π gL 1−e−τ fout fin 0.01 0.1 1 10 100 1 2 3 4 5 10 20 30 R [GM/c2] h [GM/c2] Newton energy shift change of area light bending Einstein

Size of the corona – constant intrinsic luminosity

0.01 0.1 1 10 100 1 2 3 4 5 10 20 30 R [GM/c2] h [GM/c2] Γ 3.0 2.5 2.0 Rmax 0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 10 20 30 Fe / LX h [GM/c2] Γ 2.0 2.5 3.0

LX = 0.031LEdd (Lobs = 0.02LEdd at h = 10GM/c2) Σe = τ σt ∼ 1023 −1024 cm−2 ne = Σe l ∼ 109 −1012 cm−3 Γ τ 2 0.85 2.5 0.4 3 0.2 computed with

compps

Fe LX = 1− Fin LX fout fin (1−e−τ)findSL = fout R =

• 1

π gL 1−e−τ fout fin

Size of the corona – constant observed luminosity

0.01 0.1 1 10 100 1 2 3 4 5 10 20 30 R [GM/c2] h [GM/c2] Γ 3.0 2.5 2.0 Rmax 0.0001 0.001 0.01 0.1 1 1 2 3 4 5 10 20 30 Lobs / LX h [GM/c2]

Lobs = 0.001LEdd Lobs LX = g2

L

dΩL dΩo

What size of the corona is needed for the given observed luminosity if the corona is at height h?

Application to 1H0707-495

4 8 12 16 20 24 28 32 36 40 1 2 3 4 5 6 7 8 R [GM/c2] h [GM/c2]

LX / LEdd Lobs / LEdd 0.470 1.900 0.012 0.0027 0.0760 0.2700 Rmax

Fo(0.3−10keV) = 2×10−13 −2×10−11 erg cm−2 s−1 Lobs = 4πD2Fo(0.3−10keV)

∞

• E nthcomp(E;Γ,Ec,TBB) dE

10/gL

• 0.3/gL

E nthcomp(E;Γ,Ec,TBB) dE

◮ dotted red → size for the minimum Lobs ◮ solid red → size for the light bending

scenario, LX set from the minimum Lobs at h = 1.5

◮ dotted dark green → size for the

maximum Lobs

◮ dotted blue → size for the average Lobs ◮ solid blue → size for the light bending

scenario, LX set from the average Lobs at h = 2

◮ solid green → size for the light bending

scenario, LX set from the minimum Lobs at h = 3.5 → pure light bending scenario cannot reach maximum Lobs

Conclusions

General conslusions:

◮ for reasonable assumptions the corona is not tiny but still may be

quite small (even of the order of 1−10rg),

◮ in light bending scenario with inverse Compton the corona has to

change size (geometry), it scales with height,

◮ for larger Γ we need smaller τ and both increase R, ◮ point-source approximation is not valid, 3D computations with

non-spherical geometry and corona rotation are needed for more accurate corona size (and shape) estimation.

Conclusions

Conslusions on 1H0707-495:

◮ due to high observed flux in 1H0707-495, in the pure light bending

scenario the small spherical patch of corona does not fit above the horizon,

◮ Wilkins & Fabian (2012) reproduce the steep radial emissivity with

an extended corona (up to 30Rg) at low height (2Rg),

◮ such an extended corona probably cannot change its emissivity to

100× larger luminosity either through light bending scenario or by extending it even further outside,

◮ thus could the inner accretion have higher temperature to produce

more photons? (the disc in our assumptions already shines at LEdd),

Conclusions

◮ however, the steep decrease of radial emissivity might be artificial

due to wrong assumptions on local emission directionality and radial decrease of ionisation, see Svoboda et al (2012) and his poster,

◮ thus the extension may be much smaller (2rg at height 2−3rg) and

maybe the maximum flux could be explained by changing corona size and geometry, e.g. by extending it further outside (20rg at height 2−3rg)?

◮ 3D computations with non-spherical geometry and corona

rotation are needed for more accurate estimations.