Supporting the Obscuring Torus by Radiation Pressure Julian Krolik Johns Hopkins University.
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Transcript of 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 ΔΩobscured ~ ΔΩunobscured
which in turn implies hobscured ~ r
But h/r ~ Δv/vorb , with vorb ~ 100 km/s
If Δv = cs , then T ~ 105 K >> Tsubl (dust)
If 105 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 NH24 (h/r)(vr100)rpc 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
• κmidIR(dust) ~ 10—30 κT (Semenov et al. 2003)
so (L/LE)eff ~ (10–30)L/LE
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
• Frad moves dusty gas, altering radiation transfer.
• New transfer solution changes Frad
• 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 = jKep(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/lKep = j(r)
Boundary Conditions
• Must specify available matter:
choose (r,z=0) = in(r/rin)-
• 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 dj2/dr + 2(1- α) j2 = 3 - 2α for α = - d ln Ω/d ln r,
so that j2(r) = [jin2 + f(α)](r/rin)2(α-1) – f(α)
In other words, If Frad,z ~ Fgrav,z in a geometrically thick disk, then Frad,r ~ Fgrav,r likewiseSo 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) = (*/rin)(r/rin)-
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)/(zΩ2) – (∂E/∂r)/{rΩ2[1-j2(r)]} = 0
which is analytically solvable by characteristics:
E = constant on (almost) elliptical surfaces
Step 3: Apply boundary conditions:
Free Parameters
Q ' ¿¤M (<r in )M B H
· T·
L EL » 1¡ 10
®= ¡ dln =dlnr
¿¤ = · ½inrin » 10¡ 30
As Q increases, increases
What About Internal Heating?
Two plausible possibilities:
Compton recoil from hard X-rays
Stellar heating if there is intense star-formation
/ L4¼(r 2+z2)
(LX =L)f recoil
/ ½3=2(r;z)
Solutions with Internal Heating
(LX /L)fcomp = 0.02
L* /L = 0.05
radiation energy density gas density
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/FE 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/LE ~ 0.03—0.3 and the midplane T ~ 1