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

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

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?

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

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

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.

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!

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

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!

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

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)

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

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?

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:

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

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

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

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 )

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

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

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