Time lags and reverberation in the lamp-post geometry of the compact corona illuminating a black-hole accretion disc Michal Dovˇ ciak Astronomical Institute Academy of Sciences of the Czech Republic, Prague Astrophysics group seminar, Department of Physics, University of Crete, Heraklion, Greece 30 th May 2014
Acknowledgement StrongGravity (2013–1017) — EU research project funded under the Space theme of the 7th Framework Programme on Cooperation Title: Probing Strong Gravity by Black Holes Across the Range of Masses Institutes: AsU, CNRS, UNIROMA3, UCAM, CSIC, UCO, CAMK Webpages: http://stronggravity.eu/ http://cordis.europa.eu/projects/rcn/106556 en.html
Active Galactic Nuclei – scheme Urry C. M. & Padovani P . (1995) Unified Schemes for Radio-Loud Active Galactic Nuclei PASP , 107, 803
Active Galactic Nuclei – X-ray spectrum Fabian A.C. (2005) X-ray Reflections on AGN , in proceedings of “The X-ray Universe 2005”, El Escorial, Madrid, Spain, 26-30/9/2005
Active Galactic Nuclei – lags 1H 0707 � 495 ESO 113 � G010 200 PL Ν � 0.62 Ν � 0.61 � s � 1000 PL Ν � 0.064 Ν � 1.0 � s � M � 1.8 � 10 6 M � M � 7.1 � 10 6 M � 150 Α� 0.32 Α� 0.91 Θ� 27° 500 Θ� 51° 100 h � 2.4 r g h � 8.8 r g TL Ν � s � TL Ν � s � 50 0 0 � 50 � 500 � 100 10 � 4 10 � 3 10 � 4 10 � 3 Ν � Hz � Ν � Hz � Emmanoulopoulos et al. (2014) General relativistic modelling of the negative reverberation X-ray time delays in AGN , MNRAS 439 3931
Active Galactic Nuclei – lags Lag 1 10 Energy (keV) Kara et al. (2014) The curious time lags of PG 1244+026: Discovery of the iron K reverberation lag , MNRAS 439 L26
References ◮ Blandford & McKee (1982) ApJ 255 419 → reverberation of BLR � ∞ − ∞ dt ′ L p ( t ′ )Ψ( v , t − t ′ ) L o ( v , t ) = ◮ Stella (1990) Nature 344 747 → time dependent Fe K α shape ( a = 0) ◮ Matt & Perola (1992) MNRAS 259 433 → Fe K α response and black hole mass estimate → t ∼ GM / c 3 → time dependent light curve, centroid energy and line equivalent width ( h = 6 , 10; a = 0; θ o ) ◮ Campana & Stella (1995) MNRAS 272 585 → line reverberation for a compact and extended source ( a = 0) ◮ Reynolds, Young, Begelman & Fabian (1999) ApJ 514 164 → fully relativistic line reverberation ( h = 10; a = 0 , 1) → more detailed reprocessing, off-axis flares → ionized lines for Schwarzschild case, outward and inward echo, reappearance of the broad relativistic line
References More recent references: ◮ Chainakun & Young (2012) MNRAS 420 1145 → fully relativistic, lamp-post geometry, ionized accretion disc ◮ Wilkins & Fabian (2013) MNRAS 430 247 → fully relativistic, extended corona, propagation effects ◮ Cackett et al. (2014) MNRAS 438 2980 → Fe K α reverberation in lamp-post model (spectral line) ◮ Emmanoulopoulos et al. (2014) MNRAS 439 3931 → Fe K α reverberation in lamp-post model (soft excess)
Why to study toy model of lamp-post geometry? ◮ physical motivation: base of a jet ◮ many effects should be qualitatively similar with this simple geometry ◮ it can give us certain limits on the model (e.g. spin versus height) ◮ we can easily explore the dependence on many parameters (height of the corona, ionization of the disc, ...) ◮ if we want to study the dependence on geometry, we should know how other parameters influence the results (i.e. Is the idea of measuring geometry of the corona via reverberation feasible? )
Scheme of the lamp-post geometry ◮ central black hole – mass, spin ◮ compact corona with isotropic emission → height, photon index ◮ accretion disc → Keplerian, geometrically thin, optically thick → ionisation due to illumination observer ( L p , h , M , a , n H , q n ) a ◮ local re-processing in the disc → REFLIONX with different directional corona emissivity prescriptions ◮ relativistic effects: → Doppler and gravitational energy shift h → light bending (lensing) δ i δ e black hole → aberration (beaming) → light travel time M ∆Φ r in Ω r accretion disc out
Time delay Time delay Total time delay ( a = 1.0000 , θ o = 60° ) ( a = 1.0000 , θ o = 60°, h = 3 ) a = 1 −20 −10 0 10 20 0 8 16 24 32 35 height 10 10 15 30 6 3 25 5 5 t [GM/c 3 ] 20 0 0 y y 15 10 −5 −5 5 −10 −10 0 0 5 10 15 −10 −5 0 5 10 −10 −5 0 5 10 r [GM/c 2 ] x x ◮ total light travel time includes the lamp-to-disc and disc-to-observer part ◮ first photons arrive from the region in front of the black hole which is further out for higher source ◮ contours of the total time delay shows the ring of reflection that develops into two rings when the echo reaches the vicinity of the black hole
Light curve a = 0, h = 3, ∆ t = 1 a = 1, h = 3, ∆ t = 1 0.25 2.5 inclination inclination 85 ° 85 ° 0.2 60 ° 2 60 ° 30 ° 30 ° Photon flux Photon flux 0.15 1.5 0.1 1 0.05 0.5 0 0 0 10 20 30 40 0 10 20 30 40 t [GM/c 3 ] t [GM/c 3 ] ◮ the flux for Schwarzschild BH is much smaller than for Kerr BH due to the hole below ISCO (no inner ring in Schwarzschild case) ◮ the shape of the light curve differs substantially for different spins ◮ the “duration” of the echo is quite similar ◮ the higher the inclination the sooner first photons will be observed ◮ magnification due to lensing effect at high inclinations
Dynamic spectrum – spectral line ◮ signature of outer and inner echo in dynamic spectra ◮ large amplification when the two echos separate ◮ intrinsically narrow K α line can acquire weird shapes
Dynamic spectrum – ionised disc E 2 × F ( E )
Definition of the phase lag F refl ( E , f ) = ˆ ˆ N p ( f ) . ˆ F refl ( E , t ) = N p ( t ) ∗ ψ ( E , t ) ⇒ ψ ( E , f ) where ψ ( E , f ) = A ( E , f ) e i φ ( E , f ) ˆ if ψ ( E ) = A ( E ) e i φ ( E ) N p ( t ) = cos ( 2 π ft ) and ˆ then τ ( E ) ≡ φ ( E ) F refl ( E , t ) = A ( E ) cos { 2 π f [ t + τ ( E )] } where 2 π f F ( E , f ) ∼ ˆ ˆ F ( E , t ) ∼ N p ( t ) ∗ ( ψ r ( E , t )+ δ ( t )) ⇒ N p ( f ) . ( ˆ ψ r ( E , f )+ 1 ) and A r ( E , f ) sin φ r ( E , f ) tan φ tot ( E , f ) = 1 + A r ( E , f ) cos φ r ( E , f )
Parameter values and integrated spectrum a = 1, h = 3, θ o = 30 ° 10 8 M ⊙ M = reflected primary a = 1 ( 0 ) 1000 30 ◦ ( 60 ◦ ) θ o = E 2 x F(E) h = 3 ( 1 . 5 , 6 , 15 , 30 ) L p = 0 . 001 L Edd Γ = 2 ( 1 . 5 , 3 ) 0 . 1 ( 0 . 01 , 50 , 5 , 0 . 2 ) × 10 15 cm − 3 n H = 100 q n = − 2 ( 0 , − 5 , − 3 ) 0.1 1 10 E [keV] Energy bands: soft excess: 0 . 3 − 0 . 8 keV primary: 1 − 3 keV iron line: 3 − 9 keV Compton hump: 15 − 40 keV
Phase lag dependence on geometry ◮ reflected photon flux decreases a = 1, θ o = 30 ° a = 1, θ o = 60 ° with height 0.12 0.25 height [GM/c 2 ] height [GM/c 2 ] ◮ primary flux increases with height 1.5 1.5 0.1 3 3 0.2 6 6 relative photon flux relative photon flux ◮ the delay of response is increasing 15 15 0.08 30 30 0.15 with height 0.06 ◮ the “duration” of the response is 0.1 0.04 longer 0.05 0.02 ◮ the phase lag increases with height, it depends mainly on the 0 0 0 10 20 30 40 50 0 10 20 30 40 50 “average” response time and t [ks] t [ks] magnitude of relative photon flux a = 1, θ o = 30 ° a = 1, θ o = 60 ° ◮ the phase lag null points are 50 20 shifted to lower frequencies for 0 0 higher heights due to longer -20 timescales of response -50 -40 phase lag [s] phase lag [s] -100 ◮ relative photon flux and the phase -60 -80 lag increase with inclination for low -150 height [GM/c 2 ] height [GM/c 2 ] heights -100 -200 1.5 1.5 3 3 -120 ◮ the delay and duration of response 6 6 -250 15 -140 15 30 30 do not change much with the -300 -160 inclination and thus the phase lag 1 10 100 1 10 100 f [ µ Hz] f [ µ Hz] null points frequencies change only slightly
Phase lag dependence on spin and energy band a = 0, h = 3, θ o = 60 ° a = 1, h = 3, θ o = 60 ° 0.02 0.2 energy band energy band ◮ the relative flux in the energy 0.3-0.8 keV 0.3-0.8 keV 1-3 keV 1-3 keV 3-9 keV 3-9 keV band where primary 0.015 0.15 15-40 keV 15-40 keV relative photon flux relative photon flux dominates may in some cases be larger than that in K α and 0.01 0.1 Compton hump energy bands 0.005 0.05 ◮ the magnitude of the phase lag in different energy bands 0 0 0 5 10 15 20 0 5 10 15 20 differs (in extreme Kerr case t [ks] t [ks] the larger lag in SE is due to a = 0, h = 3, θ o = 60 ° a = 1, h = 3, θ o = 60 ° larger ionisation near BH) 5 20 0 ◮ the magnitude of the phase 0 -5 -10 lag is smaller in Schwarzschild -20 phase lag [s] -15 phase lag [s] case due to the hole in the -20 -40 disc under the ISCO -25 -30 -60 -35 ◮ the null points of the phase lag energy band energy band -40 -80 0.3-0.8 keV 0.3-0.8 keV change only slightly with 3-9 keV 3-9 keV -45 15-40 keV 15-40 keV -50 -100 energy and spin 1 10 100 1 10 100 f [ µ Hz] f [ µ Hz]
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