Transcript Slide 1

Observations of the BL Lac Jet
Acceleration/Collimation Region
Review of Marscher et al. (2008) and
Related Theoretical Papers
David Meier (JPL)
Outline
• Review of Hydrodynamics (waves, causality,
wind principles)
• Introduction to Magneto-Hydrodynamics
(waves, causality, jet principles)
• Self-similar jet models (cold, warm; slow, fast)
• The Marscher et al. paper (results,
interpretation, and significance)
HYDRODYNAMICS
Non-dispersive HD (Sound) Waves
Dispersion Relation
for Sound Waves
Adiabatic
Sound Speed
HD Causality
• Any k is valid, so
– Sound waves are isotropic
– But they are Doppler shifted in direction of flow when V  0
• a) Subsonic Flow (V < cs):
– Points A and B can both affect each other
– The entire region is causally connected
• b) Supersonic Flow (V > cs):
Bogovalov (1994)
– Point A can affect point B
– But, point B cannot affect point A
– Information flows downstream only
• Mach Cones and Caustics
– Mach cone is similar to light cone: divides the sonic past
from the sonic future
– Caustic is a vector, tangent to the Mach cone, pointing
toward sonic future
– Mach cones & caustics appear only when V exceeds cs
HD Winds
moving
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The velocity in a single streamline in a smoothly-accelerating wind will eventually
pass through the Sonic Point, where V = cs
The full set of such streamlines creates a “Sonic Surface” (SS)
Caustics and Mach cones appear (or disappear) at sonic surfaces
In order for the flow across the sonic surface to be “regular”, an implicit “regularity
condition” must be satisfied: the numerator of the wind equation also must = 0
there, or
rs = GM/2cs2
IDEAL
MAGNETOHYDRODYNAMICS
Non-dispersive MHD Waves: 1. Alfven
transverse
(Alfvén)
longitudinal
(magneto-acoustic)
Full Dispersion Relation
Alfvén Velocity Vector
Alfvén Dispersion
Relation
Non-dispersive MHD Waves: 2. Magneto-acoustic
Magneto-acoustic
Dispersion Relation
Fast Magneto-acoustic
Speed
Slow Magneto-acoustic
Speed
Phase Speeds along
Magnetic Field
MHD Causality
• Phase velocity remarks
– Slow magneto-acoustic velocity is
• cs along the magnetic field (sound wave!)
• Zero normal to the magnetic field
– Fast magneto-acoustic velocity is
• VA along magnetic field (but still compressive,
not Alfven)
• cms = (VA2 + cs2)1/2 normal to the magnetic field
• Group velocity remarks
– Friedrich’s (polar) diagrams used to
determine caustics:
• Pick fluid velocity point (magnitude & direction)
• Draw tangents from branch curve to point
• Sub(magneto)sonic velocities produce no
tangents, hence no caustics; flow at that speed
is fully causally connected
– Special branch of the slow mode (the
“cusp” wave)
• Transmits information BACKWARD
• ITS caustics disappear when V < Vc = cs VA / cms
MHD Winds (Linearly Accelerating)
• Assume that V || B
• A linearly-accelerating MHD wind
consists of 5 regions:
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V < Vc
(A)
Vc < V < VS
(B, C)
VS < V < VA(D)
VA < V < VF(E)
VF < V
(F, G, H)
• There are three sonic surfaces where caustics appear or disappear
• Cusp surface (CS)
• Slow Magnetosonic Surface (SMS)
• Fast Magnetosonic Surface (FMS)
• At the Alfven Surface caustics do not appear/disappear
• But, they do change sign
• The Alfven Surface, therefore, is a “separatrix surface”
MHD Winds (Collimating Jets)
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From Bogovalov (1994)
Adding curvature (collimation) to the
MHD wind lifts the degeneracy at the
SMS & FMS
Each splits into
– A magnetosonic surface and
– A separatrix surface, where caustics
change direction
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Separatrix surfaces
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There are, therefore, three important separatrix surfaces that determine the nature of
an accelerating, collimating jet
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CS
Are physical, not mathematical, surfaces
Are generated by the causal nature of MHD
Act as initial hypersurfaces or internal boundaries
Need to have conditions specified on them that propagate throughout the entire flow
The Alfven Surface (AS)
The Slow Magnetosonic Separatrix Surface (SMSS)
The Fast Magnetosonic Separatrix Surface (FMSS)
And there are still three additional and distinct sonic surfaces (CS, SMS, FMS)
However, note this important point:
• The FMS is no longer the “horizon”, where information flow is downstream only
• The actual magnetosonic horizon in a collimating jet is the FMSS
AXISYMETRIC, IDEAL
MAGNETOHYDRODYNAMICS
AXISYMMETRIC, STATIONARY, IDEAL
MAGNETOHYDRODYNAMICS
• Like all conservation laws, MHD is a function of the event point in spacetime
(r, θ, ϕ, t)
• Full 3-D, time-dependent simulations are the most realistic (Nakamura,
Spitkovsky, McKinney, Anninos & Fragile, etc.)
• Many have performed 2-D, axisymmetric simulations (∂/∂ϕ = 0), which still
afford some realism (r, θ, t)
• Time-Independent (stationary; ∂/∂t = 0) MHD studies offer perhaps the best
compromise:
– Steady-state view of a 2-D, axisymmetric system
– Semi-analytic insight into large regions of parameter space
• The axisymmetric, stationary equations of ideal MHD are a special and VERY
useful set and used for pulsars, jets, black holes, etc.
• They have the following properties (not derived here today) …
AXISYMMETRIC, STATIONARY, IDEAL
MAGNETOHYDRODYNAMICS (cont.)
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If Ω ≠ 0, they produce rotation-driven, outflowing wind (or inflowing accretion)
Along a given magnetic field line, several physical quantities are constant:
– Angular velocity of the magnetic field line:
Ω = Ωf
– The local magnetic flux in a given poloidal area: B  dSp
– The local mass flux in a given poloidal area: 4π ρ γ V  dSp
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This leads to an extraordinary result, independent of field strength
(Chandrasekhar 1956, Mestel 1961): the poloidal magnetic field and velocity are
parallel with the proportionality constant
k = 4π ρ γ Vp / Bp
… leading to a closed form for the plasma velocity in terms of the magnetic field
V = k B / 4π ρ γ + R Ω eϕ
This is a special case of the “frozen-in field”: in the poloidal plane
– Plasma flows along the field and
– The field is carried along by the flow
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Additional quantities are conserved along B:
– Angular momentum per unit mass (including field a.m.)
– Total energy (Bernoulli constant)
– The adiabatic coefficient KΓ
SELF-SIMILAR,
AXISYMMETRIC, STATIONARY, IDEAL
MAGNETOHYDRODYNAMICS:
The MHD Jet Analogy to the Parker Wind
Table of Important Self-Similar MHD Jet Papers in the Last ¼ Century
Thermal / Relativistic
Properties
Non-Relativistiic
Relativistic
Cold (p = 0)
Blandford & Payne (1982)
(2 singular points: AS, FMSS)
Li, Chiueh, Begelman (1992)
(2 singular points)
Warm (0 < p < B2/8π)
Vlahakis et al. (2000)
(3 singular points: add SMSS)
Vlahakis & Konigl (2003)
(3 singular points)
THE SELF-SIMILAR ASSUMPTION and
SELF-SIMILAR MHD JET EQUATIONS
• Removes one more degree of freedom, turning the 2-D partial differential
equations into 1-D ordinary differential equations
• Possible self-similarity assumptions:
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Cylindrical Z: presupposes a collimated vertical jet structure
Cylindrical R: useful for accretion disk structure, not jets
Spherical θ:
similar to spherical wind (NO collimation)
Spherical r:
only choice with equations that allow collimation
• Blandford & Payne (1982) chose the latter:
– r-self-similarity; θ structure same for every field line
– Reduces MHD to only two ordinary differential equations in θ
• Standard procedure for deriving any (MHD) wind/jet equation:
– Derive the (algebraic) conservation of energy (Bernoulli) equation; then differentiate it to obtain
a1 dM / dθ + b1 dψ / dθ = c1
where M is the Alfven Mach number and ψ is the local magnetic field/velocity angle
– Derive another equation that is skew, if not orthogonal, to the differentiated Bernoulli eq. (BP
used the Z-component of the momentum equation) to obtain the “cross-field” equation:
a2 dM / dθ + b2 dψ / dθ = c2
– Solve for dM / dθ and dψ / dθ to get 2 coupled ordinary differential equations. For example…
THE SELF-SIMILAR ASSUMPTION and
SELF-SIMILAR MHD JET EQUATIONS (cont.)
dM / dθ = N / D = (c1 b2 - c2 b1 ) / (a1 b2 - a2 b1 )
– Integrate numerically w.r.t θ, applying the regularity condition N = 0 at any θ where D = 0
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Blandford & Payne’s equation was only slightly different:
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DNR = 0 at two points:
– Alfven “point” (where a single field line crosses the Alfven surface): MNR = ±1 or
Vθ = ± Bθ / (4πρ)1/2
 Vp = ± Bp / (4πρ)1/2
– “Modified Fast Point” (single field line crosses the Fast Magnetosonic Separatrix Surface [FMSS])
Vθ = ± B / (4πρ)1/2
– VERY IMPORTANT: The MFP occurs where the collimation speed toward the axis (Vθ) equals the fast
magneto-acoustic speed!
– This can occur VERY FAR from the black hole (e.g., 104-5 rg)
RECAP SO FAR: SELF-SIMILAR
JET ACCELERATION AND COLLIMATION THEORY
Supersonic
Solar Wind
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After launching, jet continues to be accelerated and
collimated by the rotating magnetic field
The process is similar to the Parker solar wind
Hydrostatic
Solar Wind
MHD jets have 3 singular points (Blandford & Payne
1982; Vlahakis & Konigl 2004): MSP, AP, MFP
Modified Fast Point
(Vθ = -Vfast)
Alfven Point
(Vjet = VAlfven)
What happens beyond the MFP?
Modified
Slow Point
(Vθ = Vslow)
Vjet = Vfast = (VA2+cS2)1/2 Poynting Flux
(not a singular point)
Dominated
Collimation Shock !!
Kinetic Energy Flux
Dominated
SMSS
AS
FMSS
• Side Notes:
• FR II jets appear to be Kinetic Energy Flux Dominated
 Strong collimation shock disrupted jet in the nucleus at ~MFP (i.e., 104-5 rg)
• Some FR I jets appear to be Poynting Flux (magnetically) Dominated
 Weak or absent MFP
• But, FR I sources are likely to be a very heterogeneous lot
SELF-SIMILAR MHD JET MODELS
• Blandford & Payne (1982) summary:
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Assumed cold plasma (p = 0), so did not have a Modified Slow Point (SMSS)
Assumed Keplerian rotation at the base of the outflow, so had a specific Ω(R) and Bϕ(R) at base
Assumed final jet was cylindrical, so there never was a true MFP either (i.e., θMFP = 0)!
I.e., the solution had only an Alfven point
Typical model results:
• Jet Total Luminosity:
• Jet Mass Loss Rate:
• Jet Torque (A.M. loss):
LT
≈ 2.4 Ψ2out Ωout / R0,max
= 2.4 B2out R30,max Ωout
ΔM
≈ 0.02 Ψ2out / R30,max Ωout
= 0.02 B2out R0,max / Ωout
≈ 0.51 Ψ2out / R0,max
= 0.51 B2out R30,max
G
• Li, Chiueh, & Begelman (1992) summary:
– Added relativistic flow; NOTE: self-similarity assumption was NOT compatible with gravity (not
even Newtonian gravity); So, gravity is not included in relativistic self-similar MHD
– Used a true cross-field equation, instead of Z-component momentum equation
– Similar denominator to BP, but with relativistic expressions for Alfven and Fast speeds;
also much more complex numerator; ALSO sought cylindrical solutions and ignored the MFP
– Obtained Lorentz factors up to  ~ 50
– Typical results similar to BP, but with R0,max replaced with RL,out; that is, scale radius is now the
LIGHT CYLINDER radius of the outermost magnetic field line
• Jet Total Luminosity: LT
• Jet Mass Loss Rate: ΔM
≈ 1.6 Ψ2out Ωout / RL, out
= 1.6 B2out R4L, out Ω2out / c
≈ 0.08 Ψ2out / R3L, out Ωout
= 0.08 B2out c / Ω2out
(BZ expression)
SELF-SIMILAR MHD JET MODELS (cont.)
• Vlahakis, Tsinganos, Sauty, & Trussoni (2000) summary:
– Assumed warm plasma (0 < p < B2/8π), so did have a Modified
Slow Point (SMSS):
D  Vθ4 - Vθ2 cms2 + cs2 V2A,θ
– Also achieved a true Modified Fast Point (FMSS)
– So, the solution had all three singular points
– Actually used the polar angle θ as the dependent variable, rather
than Z or R
– MFP
Specific Energy
vs. Z Diagram
Bogovalov-type
Causality
Diagram for
MHD Jet Model
SELF-SIMILAR MHD JET MODELS (cont.)
• Vlahakis & Konigl(2003,2004) summary:
– Can be considered to be a combination of Li et al. (1992) and Vlahakis et al. (2000):
relativistic AND warm flow, with MSP and MFP
– These are the models to use for AGN, microquasars, etc.
 
40
Model for 3C 345:
Specific Energy and
Velocity Components
vs. R Diagrams
SELF-SIMILAR MHD JET MODELS: SUMMARY
• Basic Model:
– Three separatrix surfaces (manifested as modified singular surfaces in the equations)
– Three sonic surfaces (cusp, classical slow, classical fast)
Modified Fast Point
(Vθ = -Vfast)
Alfven Point
(Vjet = VAlfven)
What happens beyond the MFP?
Vjet = Vfast = (VA2+cS2)1/2 Poynting Flux
(not a singular point)
Dominated
Collimation Shock !!
SMSS
(SMP)
AS
(AP)
FMSS
(MFP)
Kinetic Energy Flux
Dominated
• What happens after the MFP is a mystery; at least 2 possibilities:
– Convergence creates a strong collimation shock, converting magnetic energy to particle energy
and jet to kinetically dominated
– Flow remains magnetically dominated (bounce instead of shock)
Poynting Flux
Dominated
OBSERVING THE JET
ACCELERATION & COLLIMATION
REGION
QUESTIONS TO TRY TO ANSWER WITH OBSERVATIONS
• Is the MHD model at all viable?
– Can we detect a helical, well-ordered magnetic field in this region?
– Is there any evidence of rapid rotation of the jet plasma or features?
• Where does the gamma-ray emission come from? Shocks?
Emission deep in the collimation or launching region?
• What happens at the MFP and beyond?
– Does a strong, field-destroying shock develop?
– Or is there a gentler transition, leaving the jet still in a Poynting flux/magnetically-dominated
state?
– Does this answer depend on the type of source (e.g., FR I, FR II)
• NOTES:
– FR I jets are expected to collimate slowly  collimation regions 103-5 rg in length or more
• M87
• Cen A
• BL Lac
 1.4 – 140 mas in size
 0.6 – 60 mas in size
 0.006 – 0.6 mas in size (foreshortened)
– FR II jets are expected to collimate quickly  collimation regions 10 - 100 rg in length, AND BE
FARTHER AWAY
• Cyg A
• 3C 35
 1 – 10 μas in size
 0.4 – 4 mas in size
MARSCHER et al. (2008, Nature, 452, 966)
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Observed BL Lac with VLBA, UMRAO/Metsahovi, Steward/Crimea, XTE, & ?? (TeV)
2 γ-ray flares (~2005.82, 2005.88) detected
Outbursts also seen in radio, optical (R-band), & X-ray during γ-ray flaring period
Particularly important results:
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γ-ray flaring period occurs during the birth of a new VLBI component
First γ-ray flare occurs simultaneously with a 240 degree polarization rotation in the optical
Optical polarization reaches 15%  VERY strong magnetic field
Unfortunately, 2nd γ-ray flare has no optical polarization data
2005.82 2005.88
MARSCHER et al. (cont.)
• Marscher et al.’s interpretation:
– Very similar to self-similar jet model picture, but with time-dependent features
– The birth of a VLBI component generates a ‘pulse’ that travels along the jet that produces a
“Moving emission feature”
– Rotating R-band polarization feature is this pulse rotating around in its helical path through
the rotating helical magnetic field
– First γ-ray flare is a beaming event of the “moving emission feature”
– Second γ-ray flare occurs when pulse passes through a “standing shock”
– Acceleration & collimation region is between 104 and 105 rg
– Gamma-rays are produced by shocks in the jet, not near the central engine
MARSCHER et al. (cont.)
• My additions:
– The “moving emission feature” is actually an MHD slow-mode shock, which is constrained
to travel ONLY along the helical magnetic field (recall properties of slow-mode waves)
– The coherent 240 degree polarization swing is strong evidence for a well-ordered helical
magnetic field; knowing the “beaming angle” we could calculate the field pitch angle
– The “standing shock” is probably a collimation shock produced near the MFP, and
represents the place where the jet nozzle ends and free jet flow begins
– However, the lack of polarization data during and after 2nd flare is a severe loss
– We cannot tell whether plasma is strongly magnetized or becomes turbulent and,
therefore, cannot tell for certain whether a true MFP exists or not
– BL Lac’s parent is probably an FR I; FR II objects are likely to be quite different
They don’t know this
to be the case!!
MARSCHER et al. (cont.)
•
Importance and significance of the Marscher et al. (and future such) observations
– First time we have peered into the “central jet engine” and seen a little bit of how it works
– This is the ONLY method we have (probably for decades) to probe the acceleration &
collimation region of ANY ASTROPHYSICAL JET (AGN, protostellar, microquasar, symbiotic, GRB,
SN, nor PN)
– The high-resolution imaging of the VLBA is essential for determining the location of optical/X/γ-ray features
– Multi-wavelength observations, esp. optical & hard X-/γ-ray are essential for probing the
internal structure of the jet
– Space VLBI will provide even higher resolution, allowing perhaps a probe of an FR II-class object
– One of the most important mysteries to solve is why are FR II sources so kinetically dominated,
if all jets are magnetically accelerated and collimated?
– Where is the magnetic energy converted into non-thermal internal energy? (In the MHD model
it’s converted into kinetic energy in the acceleration/collimation region.
– Our old, bright VLBI source friends are probably the best candidates for this type of work:
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They are bright, giving very good S/N
We are peering down jet engine nozzle
Helical field easily identified with multi-frequency polarization observations
They evolve on relatively short time scales
All we need is the highest angular VLBI resolution and best (u,v)-coverage possible