X-ray polarization by reflection from accretion disc in AGN Michal - PowerPoint PPT Presentation

X-ray polarization by reflection from accretion disc in AGN Michal Dovˇ ciak Astronomical Institute of the CAS Prague Marin & Goosmann Svoboda & Karas Matt Muleri Di Lalla Strasbourg Astronomical Astronomical Institute University IASF INFN Observatory Prague Roma Tre Rome Pisa 10 th International Workshop on Astronomical X-ray optics 4 th –7 th December 2017,Prague, Czech Republic

Scheme of the lamp-post geometry ◮ central black hole → mass, spin Corona: P p , χ p ◮ accretion disc Disc: P loc , χ loc → Keplerian, geometrically thin, → Chandrasekhar (1960) optically thick and neutral Relativistic effects: χ o , χ d , χ do ◮ compact corona → isotropic power-law emission → static (or slow motion) observer → height, photon index a ◮ relativistic effects: corona → Doppler and gravitational energy shift → light bending (lensing) → aberration (beaming) h δ i δ e black hole ◮ references: → Matt (1993) M ∆Φ r → Dovˇ ciak, Muleri, Goosmann, in Ω Karas & Matt (2011) r accretion disc out

Stokes parameters at infinity � � S ( P p , χ p ) = S ( 0 , − )+ P p [ S ( 1 , 0 ) − S ( 0 , − )]cos 2 χ p +[ S ( 1 , π / 4 ) − S ( 0 , − )]sin 2 χ p � I ( E ) = G p I p ( E / g p ) + Σ d S G I loc ( E / g ) Q ( E ) = G p P p ( E / g p ) I p ( E / g p ) cos 2 [ χ p ( E / g p )+ χ o ] + � Σ d S G P loc ( E / g ) I loc ( E / g ) cos 2 [ χ loc ( E / g )+ χ do ] U ( E ) = G p P p ( E / g p ) I p ( E / g p ) sin 2 [ χ p ( E / g p )+ χ o ] + � Σ d S G P loc ( E / g ) I loc ( E / g ) sin 2 [ χ loc ( E / g )+ χ do ] I loc , P loc and χ loc depend on: ◮ local geometry of scattering ( µ i , µ e , ∆ ϕ ) ◮ incident polarisation properties ( P p , χ p , χ d )

Relativistic effects – lamp to observer 15 tan χ o = a β − h sin θ o inclination a 2 sin θ o + β h 30 ° 12 60 ° relativistic change 85 ° χ o [deg] 9 of polarisation angle χ o : ◮ is relatively small 6 (and zero for non-rotating BH) 3 ◮ has counter-clockwise direction 0 ◮ increases with 1 10 100 h [GM/c 2 ] → inclination → BH spin → lower height

Relativistic effects – lamp to disc 30 Relativistic change of polarisation angle χ d : 0 ◮ is quite large -30 (especially close χ d [deg] to the BH) height ◮ has mostly clockwise -60 1.1 direction 1.5 ◮ special relativistic effects -90 3 important (aberration) ◮ for highly spinning BH 50 -120 and very low heights, 1 10 100 1000 gravitational dragging r [GM/c 2 ] causes rotation in counter-clockwise direction

Change of polarization angle and transfer function → important when integrating over the disc surface → polarization angle changes due to aberration and light bending → emission is amplified due to beaming and lensing → depolarization around the critical point

Unpolarised primary radiation → importance of the local polarization properties → geometry of scattering (incident, emission and relative azimuthal angles) → source height, observer inclination and black hole spin → formation of additional depolarizing critical points → illumination pattern depends on height of the source

Energy dependence θ o =30 ° , h=3, P L =0% θ o =30 ° , h=3, P L =100%, χ L =0 ° θ o =30 ° , h=3, P L =100%, χ L =45 ° 6 100 100 Spin a=0 a=1 90 90 4 80 80 P [%] P [%] P [%] 70 70 2 60 60 Spin Spin a=0 a=0 a=1 a=1 0 50 50 1 10 1 10 1 10 E [keV] E [keV] E [keV] θ o =30 ° , h=3, P L =0% θ o =30 ° , h=3, P L =100%, χ L =0 ° θ o =30 ° , h=3, P L =100%, χ L =45 ° 2 50 10 45 χ [ °] χ [ °] χ [ °] 0 0 40 Spin Spin Spin a=0 a=0 a=0 a=1 a=1 a=1 -10 -2 35 1 10 1 10 1 10 E [keV] E [keV] E [keV] ◮ polarisation changes with energy → primary power-law decrease and reflection Compton hump ◮ features at the energies of spectral lines and edges

Dependence on height θ o = 30 ◦ P L =0% P L =100%, χ L =0 ° P L =100%, χ L =45 ° 9 100 100 2-6 keV 6-10 keV 10-20 keV 20-50 keV 75 75 6 P [%] P [%] P [%] 50 50 3 25 25 2-6 keV 2-6 keV 6-10 keV 6-10 keV 10-20 keV 10-20 keV 20-50 keV 20-50 keV 0 0 0 1 10 100 1 10 100 1 10 100 h [GM/c 2 ] h [GM/c 2 ] h [GM/c 2 ] ◮ larger changes in polarisation and de-polarisation for higher energies ◮ larger effect for higher spin ◮ largest polarisation for small heights ( h � 10) ◮ significant de-polarisation for all heights

Dependence on inclination h = 3GM / c 2 P L =0% P L =100%, χ L =0 ° P L =100%, χ L =45 ° 100 100 2-6 keV 6-10 keV 15 10-20 keV 20-50 keV 75 75 10 P [%] P [%] P [%] 50 50 5 25 25 2-6 keV 2-6 keV 6-10 keV 6-10 keV 10-20 keV 10-20 keV 20-50 keV 20-50 keV 0 0 0 0 30 60 90 0 30 60 90 0 30 60 90 θ o [ ° ] θ o [ ° ] θ o [ ° ] ◮ larger changes in polarisation and de-polarisation for higher energies ◮ larger effect for higher spin ◮ largest polarisation for inclinations 55 ◦ � θ o � 75 ◦ ◮ usually significant de-polarisation for all inclinations

Reflection versus absorption – MCG-6-30-15 6 6 6 Polarization degree [%] Polarization degree [%] Polarization degree [%] reflection1 reflection1 reflection2 reflection2 absorption absorption 4 4 4 2 2 2 reflection1 reflection2 absorption 0 0 0 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 E [keV] E [keV] E [keV] 15 15 15 Polarization angle [deg] Polarization angle [deg] Polarization angle [deg] 10 10 10 5 5 5 0 0 0 -5 -5 -5 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 E [keV] E [keV] E [keV] Absorption scenario – clumpy wind : 30 ◦ Inclination: → constant polarisation degree and angle Spin: a = 0 , a = 1 Photon index: Γ = 2 Reflection scenario : h = 2 . 5GM/c 2 Height: → energy dependent polarisation degree and angle Primary pol. deg: P = 0 , 2 , 4 % Primary pol. ang: χ = 0 ◦ see Marin et al. (2012) MNRAS, 426, L101

Simulation of the reflection in MCG-6-30-15

Reflection versus absorption – NGC-1365 10 10 10 Polarization degree [%] Polarization degree [%] Polarization degree [%] reflection1 reflection1 reflection1 reflection2 reflection2 reflection2 8 8 8 absorption absorption absorption 6 6 6 4 4 4 2 2 2 0 0 0 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 E [keV] E [keV] E [keV] 20 20 20 Polarization angle [deg] Polarization angle [deg] Polarization angle [deg] 15 15 15 10 10 10 5 5 5 0 0 0 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 E [keV] E [keV] E [keV] Absorption scenario – obscuring circumnuclear clouds : 60 ◦ Inclination: → constant polarisation degree and angle Spin: a = 0 , a = 1 Photon index: Γ = 2 Reflection scenario : h = 2 . 5GM/c 2 Height: → energy dependent polarisation degree and angle Primary pol. deg: P = 0 , 2 , 4 % Primary pol. ang: χ = 0 ◦ see Marin et al. (2013) MNRAS, 436, 1615

Simulation of the reflection in NGC-1365

Summary of results ◮ relativistic effects from the lamp to the observer are small ◮ relativistic effects from the lamp to the disc are large even for high heights and large radii ◮ largest polarisation degree for high spin, low heights, inclinations of 55 ◦ − 75 ◦ and high energy ◮ expected variation of polarisation angle with energy is ∆ χ � 10 ◦ ◮ polarisation by reflection in AGN will probably not be observable with near future polarimetry missions such as IXPE or eXTP Advertisement: Codes KYNBB and KYNLPCR usable inside XSPEC with polarisation computations included are available at https://projects.asu.cas.cz/stronggravity/kyn