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

Scheme of the lamp-post geometry ◮ central black hole – mass, spin h = 1 . 5 Γ 0.8 3.0 ◮ accretion disc 2.5 F E [ L X / keV ] 0.6 2.0 → Keplerian, geometrically thin, optically thick → Novikov-Thorne thermal emission 0.4 ( T NT , M , ˙ M = L b η c 2 , a , f c ) 0.2 ◮ compact corona with isotropic emission → height, luminosity, size (radius), 0 0 0.5 1 1.5 2 optical depth ( h , L X or L obs , R , τ ) E [keV] ◮ up-scattering in the corona observer → nthcomp (E; Γ , E c , T BB ) a ◮ relativistic effects: corona → Doppler and gravitational energy shift → light bending (lensing) h → aberration (beaming) δ i δ e black hole M ∆Φ M = 10 7 M ⊙ , L b = L Edd , r in Ω a = 0 . 998, η = 32 . 4 % , f c = 2 . 4 r accretion disc out

Thermal photon flux arriving at corona 4 N E P h [GM/c 2 ] E P 10 N 1.2 E BB E BB 1.5 f BB × d S d / d Ω n [ × 10 32 s -1 ] 3 T BB N T BB 2.4 5.1 E [keV] 1 Newton 2 1 0.1 0 1 2 3 4 5 10 1 2 3 4 5 10 20 30 r [GM/c 2 ] h [GM/c 2 ] r out T BB = E peak E BB = F in E P = L X f in = 8 πζ ( 3 ) k 3 d r r d Ω L � 2 . 82 , , ( gT NT ) 3 f in f out c h 3 c 2 f 4 d S d r in F th ( E peak ) = MAX [ F th ( E )] r out 4 π 5 k 4 d r r d Ω L � ( gT NT ) 4 F in = c 15 h 3 c 2 f 4 d S d ∞ r in � f out = nthcomp ( E ;Γ , E c , T BB ) d E d Ω n = h g = E L D 3 , 0 d S d E d

Size of the corona - components ( 1 − e − τ ) f in d S L = f out � 1 g L f out R = 1 − e − τ π f in 100 10 R [GM/c 2 ] 1 Newton energy shift 0.1 change of area light bending Einstein 0.01 1 2 3 4 5 10 20 30 h [GM/c 2 ]

Size of the corona – constant intrinsic luminosity 100 1.0 0.8 10 R [GM/c 2 ] 0.6 F e / L X 1 0.4 Γ Γ 3.0 0.1 2.0 2.5 0.2 2.5 2.0 3.0 R max 0.01 0.0 1 2 3 4 5 10 20 30 1 2 3 4 5 10 20 30 h [GM/c 2 ] h [GM/c 2 ] F e = 1 − F in f out L X = 0 . 031 L Edd Γ τ L X L X f in ( L obs = 0 . 02 L Edd at h = 10 GM / c 2 ) 2 0.85 2.5 0.4 ( 1 − e − τ ) f in d S L = f out Σ e = τ ∼ 10 23 − 10 24 cm − 2 3 0.2 σ t � 1 g L f out computed with R = n e = Σ e ∼ 10 9 − 10 12 cm − 3 1 − e − τ compps π f in l

Size of the corona – constant observed luminosity 100 1 10 0.1 R [GM/c 2 ] L obs / L X 1 0.01 Γ 3.0 0.1 0.001 2.5 2.0 R max 0.01 0.0001 1 2 3 4 5 10 20 30 1 2 3 4 5 10 20 30 h [GM/c 2 ] h [GM/c 2 ] L obs d Ω L L obs = 0 . 001 L Edd = g 2 L L X d Ω o What size of the corona is needed for the given observed luminosity if the corona is at height h ?

Application to 1H0707-495 ◮ dotted red → size for the minimum L obs 40 L X / L Edd L obs / L Edd ◮ solid red → size for the light bending 36 R max 0.470 0.0027 scenario, L X set from the minimum L obs 32 1.900 0.0760 at h = 1 . 5 28 0.012 0.2700 ◮ dotted dark green → size for the R [GM/c 2 ] 24 maximum L obs 20 ◮ dotted blue → size for the average L obs 16 ◮ solid blue → size for the light bending 12 scenario, L X set from the average L obs at h = 2 8 ◮ solid green → size for the light bending 4 scenario, L X set from the minimum L obs 0 at h = 3 . 5 → pure light bending 1 2 3 4 5 6 7 8 scenario cannot reach maximum L obs h [GM/c 2 ] ∞ � E nthcomp ( E ;Γ , E c , T BB ) d E F o ( 0 . 3 − 10keV ) = 0 L obs = 4 π D 2 F o ( 0 . 3 − 10keV ) 2 × 10 − 13 − 2 × 10 − 11 10 / g L � erg cm − 2 s − 1 E nthcomp ( E ;Γ , E c , T BB ) d E 0 . 3 / g L

Conclusions General conslusions: ◮ for reasonable assumptions the corona is not tiny but still may be quite small (even of the order of 1 − 10 r g ), ◮ 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 30 R g ) at low height (2 R g ), ◮ 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 L Edd ),

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 (2 r g at height 2 − 3 r g ) and maybe the maximum flux could be explained by changing corona size and geometry, e.g. by extending it further outside (20 r g at height 2 − 3 r g )? ◮ 3D computations with non-spherical geometry and corona rotation are needed for more accurate estimations.