Formation of lamp-post coronae in Seyfert Galaxies and X-ray binaries

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1 NASA/NuSTAR, Wilkins et al 2015 Formation of lamp-post coronae in Seyfert Galaxies and X-ray binaries Yajie Yuan (Spitzer Fellow, Princeton) In collaboration with: Roger Blandford, Dan Wilkins (Stanford) and Anatoly Spitkovsky, Alex Chen (Princeton)

2 Outline Observations and puzzles Possible scenarios for the compact X-ray corona: Gap at the base of the jet (?) Tangling of small scale flux tubes near the axis Summary and perspectives

3 X-ray coronae in Seyfert Galaxies Spiral galaxies, M ~ M, Radio quiet L ~ LEdd LX ~ LO/UV Uttley+2014

4 X-ray coronae in Seyfert Galaxies Spiral galaxies, M ~ M, Radio quiet L ~ LEdd LX ~ LO/UV typical local reflection spectrum MCG Reynolds+1997 Uttley+2014

5 Lamppost coronae? ➊ Figure from E. Kara Reverberation mapping emissivity profile modeling Microlensing Iron K lag in NGC 4151 ➋ Zoghbi+2012 Kara+2016

6 Lamppost coronae? Wilkins & Fabian 2012 Reverberation mapping emissivity profile modeling Microlensing Mrk 335, Wilkins & Gallo 2015

7 Lamppost coronae? Reverberation mapping emissivity profile modeling Microlensing Morgan+2008; Chartas+2009; Mosquera+2013; Reis&Miller2013

8 Questions to answer Why is the corona so compact, and located at such a special place (a few gravitational radii above the BH)? Why is the X-ray luminosity so high? Is this relevant to the radio loud/quiet dichotomy?

9 Scenario 1: gap at the jet base

10 Reynolds+1997 Scenario 1: gap at the jet base MCG L O/UV 0.1L Edd erg s 1 u s 10 8 erg cm 3 s,max 100 ev thr m e c 2 / s,max 10 4 B B Edd 10 5 G 0.4 MeV E 4 2 P diss L jet If there are already plenty of MeV photons, gaps may not need to form What if gap is the sole source for X-rays and MeV emission? 3e Does the strong radiative drag on particles help enhancing the dissipation? T u s, E B 10 4 Ejr3 g B 2 r 2 gc E B 10 4 Too small!

11 Scenario 2: tangling of small scale flux tubes near the axis

12 Scenario 2: tangling of small scale flux tubes near the axis

13 Scenario 2: tangling of small scale flux tubes near the axis

14 Scenario 2: tangling of small scale flux tubes near the axis

15 Force-free configuration in Kerr spacetime Force-free, axisymmetric, steady state: Grad- Shafranov equation Earlier works: Uzdensky 2004, 2005, low spin regimes My new relaxation method, can also handle outer light surfaces for favorable configurations As field lines can slip on the BH, closed field lines linking the hole and the disk can exist in steady state! What determines the extent of the closed zone?

16 Effect of external pressure d = r ISCO (1/r 0 1/r) d =(r r 0 )/r ISCO d =(r 2 r 2 0)/r 2 ISCO

17 Foot point on the disk d =(r r 0 )/r ISCO r 0 =1.5r ISCO r 0 =2r ISCO r 0 =4r ISCO Consistent with Uzdensky 2005

18 Effect of BH spin d =(r r 0 )/r ISCO r 0 =3r ISCO max height r 0 =2r ISCO a =0.999, r 0 =3r ISCO

19 Steady state approach is missing a few important things: Stability Possible non-axisymmetric modes Time evolution and dissipation Need 3D time-dependent simulations! cf. Parfrey+2015

20 A test case We use the time-dependent, relativistic force-free code originally developed by Anatoly Spitkovsky (2006) Mimicking the electromagnetic effect of the black hole using a rotating, resistive membrane in flat spacetime On the membrane, B =4πK, E =RK=4πK=B, where K is the surface current, R is the surface resistivity flat spacetime Kerr

21 A test case A rotating resistive membrane disk ( BH ) surrounded by a perfectly conducting, non-rotating disk ( accretion disk ) Marginal confinement case: m=1 instability

22 Confined situation A test case

23 Unconfined situation A test case

24 Energetics estimation Typical magnetic field strength: B Edd = p 8 p Edd = Power extraction from the black hole: s 2L Edd 3cr 2 g = s m p c 2 r 2 er g = M 1/2 6 G Voltage: V! 1 ac/r g a(b/b Edd )M 6 V Power: P V 2 /Z a 2 c 2 /(r 2 gz 0 ) a 2 (B/B Edd ) 2 M 2 6 erg s 1 Angular momentum flux: P/! 3 2 ac/(r g Z 0 ) Dissipation due to reconnection: P diss 1 L Edd 12 vrec c r r g P diss B 2 r 2 v rec /8 2 B B Edd 2

25 Summary Compact, Lamppost-like coronae seem typical from observations Possible dissipation mechanisms: Electrostatic gap at the jet base is not favored based on energetics Reconnection due to tangled small scale flux tubes near the axis may be a viable mechanism This can be tested using relativistic force-free simulations, and maybe MHD simulations in the future.

26 A comment on mass loading Highly magnetized situation: particles behave like beads on a wire Lagrangian L = 1 2 (g tt + 2 g t + 2 g ) 1 dt 2 K d t = u 0 + u is conserved (Super-)Hamiltonian 2 + D dt d H = dt d ds d b2 2 +(g 0 2 ds + g )b dt d d D K t K s 2(D 2 Kb 2 ) Inside the light surfaces, effective potential is t 2K V e = 2 t 2K ds d b2 ds d 2

27 A comment on mass loading