SLIDE 1
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,
- ptically thick and neutral
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 - - PowerPoint PPT Presentation
X-ray polarization by reflection from accretion disc in AGN Michal Dov ciak Astronomical Institute of the CAS Prague Marin & Goosmann Svoboda & Karas Matt Muleri Di Lalla Strasbourg Astronomical Astronomical Institute
SLIDE 2
SLIDE 3
Stokes parameters at infinity
S(Pp,χp) = S(0,−)+Pp
- [S(1,0)−S(0,−)]cos2χp +[S(1,π/4)−S(0,−)]sin2χp
- I(E) = Gp Ip(E/gp)
+
- Σ dS G Iloc(E/g)
Q(E) = Gp Pp(E/gp) Ip(E/gp) cos2[χp(E/gp)+ χo] +
- Σ dS G Ploc(E/g) Iloc(E/g) cos2[χloc(E/g)+ χdo]
U(E) = Gp Pp(E/gp) Ip(E/gp) sin2[χp(E/gp)+ χo] +
- Σ dS G Ploc(E/g) Iloc(E/g) sin2[χloc(E/g)+ χdo]
Iloc, Ploc and χloc depend on:
◮ local geometry of scattering (µi, µe, ∆ϕ) ◮ incident polarisation properties (Pp, χp, χd)
SLIDE 4
Relativistic effects – lamp to observer
3 6 9 12 15 1 10 100 χo [deg] h [GM/c2] inclination 30° 60° 85°
tanχo = a β −h sinθo a2 sinθo +βh
relativistic change
- f polarisation angle χo:
◮ is relatively small
(and zero for non-rotating BH)
◮ has counter-clockwise
direction
◮ increases with
→ inclination → BH spin → lower height
SLIDE 5
Relativistic effects – lamp to disc
- 120
- 90
- 60
- 30
30 1 10 100 1000 χd [deg] r [GM/c2] height 1.1 1.5 3 50 Relativistic change
- f polarisation angle χd:
◮ is quite large
(especially close to the BH)
◮ has mostly clockwise
direction
◮ special relativistic effects
important (aberration)
◮ for highly spinning BH
and very low heights, gravitational dragging causes rotation in counter-clockwise direction
SLIDE 6
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
SLIDE 7
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
SLIDE 8
Energy dependence
2 4 6 1 10 P [%] E [keV] θo=30°, h=3, PL=0% Spin a=0 a=1 50 60 70 80 90 100 1 10 P [%] E [keV] θo=30°, h=3, PL=100%, χL=0° Spin a=0 a=1 50 60 70 80 90 100 1 10 P [%] E [keV] θo=30°, h=3, PL=100%, χL=45° Spin a=0 a=1
- 10
10 1 10 χ [°] E [keV] θo=30°, h=3, PL=0% Spin a=0 a=1
- 2
2 1 10 χ [°] E [keV] θo=30°, h=3, PL=100%, χL=0° Spin a=0 a=1 35 40 45 50 1 10 χ [°] E [keV] θo=30°, h=3, PL=100%, χL=45° Spin a=0 a=1
◮ polarisation changes with energy
→ primary power-law decrease and reflection Compton hump
◮ features at the energies of spectral lines and edges
SLIDE 9
Dependence on height
θo = 30◦
3 6 9 1 10 100 P [%] h [GM/c2] PL=0% 2-6 keV 6-10 keV 10-20 keV 20-50 keV 25 50 75 100 1 10 100 P [%] h [GM/c2] PL=100%, χL=0° 2-6 keV 6-10 keV 10-20 keV 20-50 keV 25 50 75 100 1 10 100 P [%] h [GM/c2] PL=100%, χL=45° 2-6 keV 6-10 keV 10-20 keV 20-50 keV
◮ 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
SLIDE 10
Dependence on inclination
h = 3GM/c2
5 10 15 30 60 90 P [%] θo [°] PL=0% 2-6 keV 6-10 keV 10-20 keV 20-50 keV 25 50 75 100 30 60 90 P [%] θo [°] PL=100%, χL=0° 2-6 keV 6-10 keV 10-20 keV 20-50 keV 25 50 75 100 30 60 90 P [%] θo [°] PL=100%, χL=45° 2-6 keV 6-10 keV 10-20 keV 20-50 keV
◮ larger changes in polarisation and de-polarisation for higher energies ◮ larger effect for higher spin ◮ largest polarisation for inclinations 55◦ θo 75◦ ◮ usually significant de-polarisation for all inclinations
SLIDE 11
Reflection versus absorption – MCG-6-30-15
2 4 6 2 4 6 8 10 Polarization degree [%] E [keV] reflection1 reflection2 absorption 2 4 6 2 4 6 8 10 Polarization degree [%] E [keV] reflection1 reflection2 absorption 2 4 6 2 4 6 8 10 Polarization degree [%] E [keV] reflection1 reflection2 absorption
- 5
5 10 15 2 4 6 8 10 Polarization angle [deg] E [keV]
- 5
5 10 15 2 4 6 8 10 Polarization angle [deg] E [keV]
- 5
5 10 15 2 4 6 8 10 Polarization angle [deg] E [keV] Inclination: 30◦ Spin: a = 0, a = 1 Photon index: Γ = 2 Height: h = 2.5GM/c2 Primary pol. deg: P = 0,2,4% Primary pol. ang: χ = 0◦
Absorption scenario – clumpy wind: → constant polarisation degree and angle Reflection scenario: →energy dependent polarisation degree and angle see Marin et al. (2012) MNRAS, 426, L101
SLIDE 12
Simulation of the reflection in MCG-6-30-15
SLIDE 13
Reflection versus absorption – NGC-1365
2 4 6 8 10 2 4 6 8 10 Polarization degree [%] E [keV] reflection1 reflection2 absorption 2 4 6 8 10 2 4 6 8 10 Polarization degree [%] E [keV] reflection1 reflection2 absorption 2 4 6 8 10 2 4 6 8 10 Polarization degree [%] E [keV] reflection1 reflection2 absorption 5 10 15 20 2 4 6 8 10 Polarization angle [deg] E [keV] 5 10 15 20 2 4 6 8 10 Polarization angle [deg] E [keV] 5 10 15 20 2 4 6 8 10 Polarization angle [deg] E [keV] Inclination: 60◦ Spin: a = 0, a = 1 Photon index: Γ = 2 Height: h = 2.5GM/c2 Primary pol. deg: P = 0,2,4% Primary pol. ang: χ = 0◦
Absorption scenario – obscuring circumnuclear clouds: → constant polarisation degree and angle Reflection scenario: →energy dependent polarisation degree and angle see Marin et al. (2013) MNRAS, 436, 1615
SLIDE 14
Simulation of the reflection in NGC-1365
SLIDE 15