1. Supporting the Obscuring Torus by Radiation Pressure Julian Krolik Johns Hopkins University

2. Typical AGN Have Toroidal Obscuration Spectropolarimetry of “type 2” objects Ionization cones warm IR spectra X-ray absorption

3. The Basic Problem N(type 2) ~ N(type 1) implies ΔΩ obscured ~ ΔΩ unobscured which in turn implies h obscured ~ r But h/r ~ Δv/v orb, with v orb ~ 100 km/s If Δv = c s, then T ~ 10 5 K >> T subl (dust) If 10 5 K is too hot, what supports the obscuring matter?

4. Candidate Mechanisms Bouncing magnetized clouds stirred by orbital shear (K. & Begelman 1988, Beckert & Duschl 2004) Clumping avoids immediate thermal destruction But is this degree of elasticity plausible? And their collision rate must not be >> the orbital frequency Warped thin disk (Sanders et al. 1989) But well-formed ionization cones are seen close to the center, IR interferometry shows a thick structure at ~1 pc in NGC 1068, and dust cannot survive closer Magnetic wind (Königl & Kartje 1994) But origin of large-scale field? And mass-loss rate can be very large: 10 N H24 (h/r)(v r100 )r pc Msun/yr

5. Another Candidate Mechanism: Radiation Pressure (Pier & K. 1992) If thermal continuum is created by dust reprocessing, there must be a large radiation flux through the obscuration κ midIR (dust) ~ 10—30 κ T (Semenov et al. 2003) so (L/L E ) eff ~ (10–30)L/L E

6. What is the Internal Flux? All previous calculations of flux have guessed the density distribution: Pier & K. (1993): constant density, rectangular envelope Granato & Danese (1994): density a power-law in r, exponential in cos(  ) Efstathiou & Rowan-Robinson (1996): density a power- law in r, exponential in  Nenkova, Ivezic & Elitzur (2002): probability of a clump a power-law in r, independent of , approximate treatment of diffuse radiation Hoenig et al. (2006): probability of a clump a power-law in r, Gaussian in z, transfer like Nenkova et al.

7. Radiation Transfer and Dynamics Must Be Consistent F rad moves dusty gas, altering radiation transfer. New transfer solution changes F rad Additional forces (magnetic, collisions,...) further complicate the problem A difficult calculation!

8. Qualitative Character of Solution Greater optical depth in equatorial direction than in (half-) vertical direction guarantees most flux upward; some radial component remains, decreasing outward from the inner edge

9. Possible Dynamical Elements Gravity Radiation pressure Rotational support (j(r) not necessarily = j Kep (r)) Random motions/thermal pressure At inner surface, a drastic phase change flux primarily UV, not IR, so much larger opacity temperature much higher than in torus body rocket effect from evaporating matter Treat this separately!

10. The Simplest Self-Consistent Picture Forces: Gravity Rotational support Radiation pressure Assume hydrostatic balance

11. The Simplest Self-Consistent Picture Assumptions: 2-d, axisymmetric, time-steady thermally-averaged opacity independent of T, diffusion approximation (smooth density distribution) no sources of infrared inside the torus l/l Kep = j(r)

12. Boundary Conditions Must specify available matter: choose  (r,z=0) =  in (r/r in ) -  After finding  (r,z), locate photosphere: insist on F ~ cE by varying  Must also have E > 0 also by varying  Location of inner boundary left undetermined

13. Solution: Entirely Analytic Step 1: Hydrostatic balance + diffusion equilibrium + absence of internal radiation sources leads to r dj 2 /dr + 2(1- α) j 2 = 3 - 2α for α = - d ln Ω/d ln r, so that j 2 (r) = [j in 2 + f(α)](r/r in ) 2(α-1) – f(α) In other words, If Frad,z ~ Fgrav,z in a geometrically thick disk, then Frad,r ~ Fgrav,r likewise So the orbiting matter must have sub-Keplerian rotation if it is to remain in equilibrium; magnetic angular momentum redistribution?

14. A)To fix the quantity of available matter---  (r,z=0) = (  * /  r in )(r/r in ) -  B) To match the diffusion solution to its outgoing flux--- F ~ cE at the dust photosphere (which determines  ) Step 2: Requiring both components of force balance to give a consistent density leads to (∂E/∂z)/(zΩ 2 ) – (∂E/∂r)/{rΩ 2 [1-j 2 (r)]} = 0 which is analytically solvable by characteristics: E = constant on (almost) elliptical surfaces Step 3: Apply boundary conditions:

15. Free Parameters Q ' ¿ ¤ M ( < r i n ) M BH · T · L E L » 1 ¡ 10 ® = ¡ dl n ­ = dl nr ¿ ¤ = ·½ i n r i n » 10 ¡ 30 As Q increases,  increases

16. Example Solution for α = 3/2;  * = 10; Q=3, so L/L E = 0.1—0.3 radiation energy densitygas density

17. The X-ray Column Density Distribution Predicted by the Example Solution

18. What About Internal Heating? Two plausible possibilities: Compton recoil from hard X-rays Stellar heating if there is intense star-formation / L 4 ¼ ( r 2 + z 2 ) ( L X = L ) f reco i l /½ 3 = 2 ( r ; z )

19. Solutions with Internal Heating (L X /L)f comp = 0.02 L * /L = 0.05 radiation energy densitygas density

20. Range of Q and  Permitted X = 0.01 or P = 0.005 X = 0.1 or P = 0.25

21. Conclusions Tori convert optical/UV flux to IR; there must therefore be a large IR flux through them Mid-IR opacity/mass ~ 10—30 Thomson, increasing the effective F/F E by that factor With some simplifying assumptions, a self- consistent hydrostatic equilibrium and 2-d diffusive transfer solution can be found The torus becomes geometrically thick when L/L E ~ 0.03—0.3 and the midplane  T ~ 1