Signatures of strong-field gravity accretion: Relativistic effects in spectra and polarization from black-hole accretion discs

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1 extp meeting Beijing, October 2015 Signatures of strong-field gravity accretion: Relativistic effects in spectra and polarization from black-hole accretion discs Selected topics as science drivers for the new mission proposal Vladimír Karas (Astronomical Institute, Prague) in collaboration with M. Dovčiak, J. Hamerský, D. Kunneriath, F. Marin, J. Svoboda (Prague) F. Muleri (Rome), Wenfei Yu (Shanghai) p.1/25

2 Objects and models Active galactic nuclei Stellar-mass black holes Intermediate-mass black holes (?) p.2/25

3 Objects and models Active galactic nuclei Stellar-mass black holes Intermediate-mass black holes (?) Central black hole emitting Accretion disc BH accretion disc observer emitting corona corona h θ L δi...geometrically thin, planar, non-self-gravitating Spectral features...time-dependent, non-axisymmetric rin δe to the observer rout p.2/25

4 Objects and models Active galactic nuclei Stellar-mass black holes Intermediate-mass black holes (?) Central black hole emitting Accretion disc BH accretion disc observer emitting corona corona h θ L δi...geometrically thin, planar, non-self-gravitating Spectral features...time-dependent, non-axisymmetric rin δe to the observer rout GR effects taken into account Link to a spectrum-fitting procedure (XSPEC) p.2/25

5 High-frequency elmg. waves Basic equations vacuum case: F µν ;ν = 0, F µν ;ν = 0. E α = F αβ u β, F µν 1 2 ε µν ρσ F ρσ An electromagnetic wave is an approximate test-field solution of the Maxwell equations: F αβ = Re [ u αβ e IS(x)]. A fixed background geometry is asssumed. Phase S(x)... rapidly varying function Amplitude u αβ... slowly varying function Wave vector k α S,α... paralel transport, null geodesics k α;β k β = 0, k α k α = 0. p.3/25

6 Polarization tensor Polarization tensor... J αβγδ 1 F F 2 αβ γδ In observer s rest-frame... J αβ J αβγδ u β u δ = E α Ē β Four parameters... S A 1(k 2 αu α ) 2 F A (A = 0,...,3) (F A... constructed by projecting onto a tetrad e α (i) ) On the composition and resolution of streams of polarized light from different sources References: [1] Sir George Stokes (1852), Trans. Cambridge Phil. Soc., 9, 399 [2] Chandrasekhar (1950), Radiative Transfer (Oxford: Clarendon) [3] Cocke & Holm (1972), Nature, 240, 161 [4] Jauch & Rohrlich (1955), The Theory of Photons and Electrons (Reading: Wesley) p.4/25

7 Stokes parameters ) S 0 J αβ (e α (1)e β (1) +eα (2)e β (2) = E (1) 2 + E (2) 2 ) S 1 J αβ (e α (1)e β (1) eα (2)e β (2) = E (1) 2 E (2) 2 ) S 2 J αβ (e α (1)e β (2) +eα (2)e β (1) = E (1) Ē (2) +E (2) Ē (1) ) S 3 IJ αβ (e α (1)e β (2) eα (2)e β (1) = I E (1) Ē (2) E (2) Ē (1) S 1, S 2, and S 3 determine the polarization state. References: [5] Anile (1989), Relativistic fluids and magneto-fluids (Cambridge) [6] Madore (1974), Comm. Math. Phys., 38, 103 [7] Bičák & Hadrava (1975), A&A, 44, 389 [8] Breuer & Ehlers (1980), Proc. Roy. Soc. Lond. A, 370, 389 [9] Broderick & Blandford (2003), MNRAS, 342, 1280 p.5/25

8 Propagation law Normalized Stokes parameters: s 1 = S 1 /S 0, s 2 = S 2 /S 0, s 3 = S 3 /S 0. Degree of polarization: Π l = s 2 1 +s 2 2, Π c = s 3, Π = Π 2 l +Π2 c. Propagation through an arbitrary (empty) space-time: F A ds em = F A ds obs p.6/25

9 Five transfer functions The energy shift (gravitational and Doppler) emitted photons are coming from places with high gravity photons are emitted from rapidly moving matter p.7/25

10 Five transfer functions The energy shift (gravitational and Doppler) emitted photons are coming from places with high gravity photons are emitted from rapidly moving matter The lensing effect the change of solid angle along the light ray p.7/25

11 Five transfer functions The energy shift (gravitational and Doppler) emitted photons are coming from places with high gravity photons are emitted from rapidly moving matter The lensing effect the change of solid angle along the light ray The limb darkening/brightening law the effect of aberration p.7/25

12 Five transfer functions The energy shift (gravitational and Doppler) emitted photons are coming from places with high gravity photons are emitted from rapidly moving matter The lensing effect the change of solid angle along the light ray The limb darkening/brightening law the effect of aberration The light-time effect mutual time delays of photons at detector p.7/25

13 Five transfer functions The energy shift (gravitational and Doppler) emitted photons are coming from places with high gravity photons are emitted from rapidly moving matter The lensing effect the change of solid angle along the light ray The limb darkening/brightening law the effect of aberration The light-time effect mutual time delays of photons at detector The change of polarization angle Polarization vector is parallel transported through gravitational field p.7/25

14 The shift of photon energy, z a = M, θ = 70 Dovčiak et al. (2004), ApJSS, 153, 205 p.8/25

15 The shift of photon energy, z a = M, θ = 70 Dovčiak et al. (2004), ApJSS, 153, 205 p.9/25

16 The shift of photon energy, z Maximum and minimum g-factor for θ o =70 a/m: max (min) g-factor p.10/25

17 Lensing effect, S em /S obs p.11/25

18 Lensing effect, S em /S obs φ Darwin φ E φ MM φ (1) PMS φ B φ KP Bozza Darwin (1959) Einstein (1911) Mutka & Mähönen (2002) Amore & Diaz (2006) Beloborodov (2002) Keeton & Peters (2005) Bozza (2003) Semerák (2015) r 0 In Schwarzschild metric: δφ D = 4 r 0 /(GMΥ) [ F ( π,κ) F (ϕ,κ) ] 2 4GM r G2 M 2 r 2 0 Light deflection and gravitational lensing: exact formula and analytical approximations G3 M 3 +O [ (GM/r 0 ) 4]. r0 3 Amore & Diaz, Phys. Rev. D73 (2006) p.12/25

19 Emission angle, cosδ em p.13/25

20 Light-time effect, δt p.14/25

21 Polarization angle, cosψ p.15/25

22 Wave fronts in a BH spacetime Schwarzschild metric, ds 2 = ( 1 2M r ) dt 2 + ( 1 2M r ) 1 dr 2 +r 2 dω 2. Eikonal equation, ( 1 2M r ) (ψ,r ) 2 + ( 1 2M r ) 1 (ψ,t) 2 r 2 (ψ,φ) 2 = 0. Solved by separation of variables, ψ(t,r,φ) R(r)+αφ ωt, ( 1 2M r ) (R ) 2 = ( 1 2M r ) 1 ω 2 r 2 α 2. Wave front: ψ(t 0 +nδt,r,φ) = ψ(t 0,r 0,0). p.16/25

23 Wave fronts in a BH spacetime Electromagnetic radiation does not influence geometry of the BH spacetime (to first order). Wave fronts do not depend on polarization (in geometrical optics approximation). The analogy: light propagation in a vacuum curved spacetime versus material media in a flat spacetime. The effective permeability: µ = 1 2M/r. Mashoon (1973); Hanni (1977);... p.17/25

24 Wave fronts in a BH spacetime Kerr metric, ds 2 = Σ ( ) 2 dt asin 2 Σ θdφ + dr2 +Σdθ 2 + sin2 θ Σ [ adt (r 2 +a 2 )dφ] 2. The separation of variables and solution for the eikonal equation follow from Carter s solution of the scalar wave equation, ψ = R(r)+T(θ)+αφ ωt. Wave fronts exhibit the frame dragging effect. p.18/25

25 Example 1: Orbiting spot Energy [kev] Time [orbital periods] Reviews: Fabian, Iwasawa, Reynolds, Young, (2000), Broad Iron Lines in Active Galactic Nuclei, PASP, 112, 1145 Reynolds & Nowak (2003), X-rays from active galactic nuclei: relativistically broadened emission lines, Phys. Rep., 337, 389 Karas (2006), Theoretical aspects of relativistic spectral features, Astronomische Nachrichten, 327, 961 p.19/25

26 Example 2: Polarization Thermal emission from an accretion disc can be polarized due to scattering in the disc atmosphere. GR changes the observed polarization at infinity: rotation of the polarization angle. We compute the polarization degree and the angle as functions of energy ( 2 10 kev), view angle of the observer, spin of the black hole, optical thickness of the atmosphere. Connors, Stark, & Piran (1980), ApJ, 235, 224 Dovčiak, Muleri, Goosmann, Karas, & Matt (2008), MNRAS, 391, 32 Li-Xin Li, Narayan, & McClintock (2008), ApJ, in press p.20/25

27 Example 2: Polarization The only positive detection of polarization to date: Crab Nebula (Weisskopf et al. 1978; Dean et al. 2008). Gas Pixel Detector (Costa et al. 2001; Bellazzini et al. 2007) is one of the most advanced project in this field. Two scenarios have been modelled to verify that GR effects will be measurable by the next missions with the GPD on-board (Karas et al. 2011; Dovčiak et al. 2012). Bellazzini et al. (2007), NIMA, 579, 863 Costa et al. (2001), Nature, 411, 662 Dean et al. (2008), Science, 321, 1183 Weisskopf et al. (1978), ApJ, 220, L117 p.21/25

28 Example 2: Polarization Flux [Arbitrary units] θ o =30 θ o =60 a=1 a=0 Polarization degree [%] τ = τ = 2.0 τ = 1.0 τ = 0.5 τ = θ o = E[keV] µ e Left: multicolour black body spectra for the extreme Kerr and Schwarzschild black holes (inclination of 30, 60 and 85 ). Right: The dependence of the local polarization degree on the cosine of the emission angle (different optical depth τ). p.22/25

29 Example 2: Polarization The energy dependence. Top: polarization degree. Bottom: polarization angle. p.23/25

30 Example 2: Polarization A simulated observation of 500 ks by the pathfinder mission. Kerr (solid) and Schwarzschild (dashed) cases, with τ = 1.0, θ 0 = 70. Errors at the 3-σ level. Dovčiak et al. (2008), MNRAS, 391, 32; Karas et al. (2011), HEAD 12, p.24/25

31 Thank you! For further details: Role of environment: waves in a refractive and dispersive media in SFG Flare/spot model in SFG: F var for Schwarzschild vs. Kerr Flares from Sgr A* Signatures of spiral waves in accretion disks in SFG See Additional Material for Discussion p.25/25