Summer term 2011 Henrik Beuther & Christian Fendt · 2011-06-10 · Henrik Beuther & Christian...

Outflows & Jets: Theory & Observations

Lecture plan & schedule

Summer term 2011Henrik Beuther & Christian Fendt

15.04 Today: Introduction & Overview ("H.B." & C.F.)29.04 Definitions, parameters, basic observations (H.B.)06.05 Basic theoretical concepts & models; MHD (C.F.)13.05 MHD & plasma physics; applications (C.F.)20.05 Radiation processes (H.B.) 27.05 Observational properties of accretion disks (H.B.)03.06 Accretion disk theory and jet launching (C.F.)10.06 Theory of interactions: entrainment, Instabilities, shocks (C.F.)17.06 Outflow-disk connection, outflow entrainment (H.B.) 24.06 Outflow-ISM interaction, outflow chemistry (H.B.)01.07 Outflows from massive star-forming regions (H.B.)08.07 Observations of extragalactic jets (C.F.)15.07 Some aspects of relativistic jet theory (C.F.)

Jets are collimated disk/stellar winds, launched, accelerated, collimated by magnetic forces

Energy source: gravity, rotation

MHD model of jet formation:

● ejection of disk/stellar material into wind?

● collimation & acceleration of a disk/stellar wind into a jet

● jet propagation / interaction with ambient medium

● accretion disk structure?

● origin & structure of magnetic field?


Standard model of jet formation

-> 5 basic questions of jet theory:


Disk sources:

Disks commonly found in many astrophysical sources:

-> YSO,-quasars, pulsars, CV (white dwarfs), HMXB, LMXB, AGN-> many of these disk systems have jets-> all jet/outflow sources have disks

Disk summary:

-> mass “infall”, global angular momentum conservation

-> almost Keplerian rotation, almost axisymmetry

-> drift of matter in [-r]-direction (accretion), if angular momentum lost in outward direction

-> angular momentum removal by viscosity / turbulence / disk wind / magnetic field

-> disk heating / luminosity by viscous friction

-> disk temperature profile / spectral energy distribution

Accretion disks


History of accretion disks:

Kant (1755): - “Urnebel”, nebula in stochastic motion, flatened by rotation - collisions -> energy loss -> central condensation (Sun) - planets originate from local concentrations

Laplace (1799): - planet formation from hydrodynamic continuum - rings expelled from solar surface, rings contracts to spherical bullets - no differential rotation, no condensations

Accretion history


History of accretion disks: Kant (1755): Erstes Hauptstück

Von dem Ursprunge des planetischen Weltbaues überhaupt und den Ursachen ihrer Bewegungen ...Wenn demnach ein Punkt in einem sehr grossen Raume befindlich ist, wo die Anziehung der daselbst befindlichen Elemente stärker als allenthalben um sich wirkt: so wird der in dem ganzen Umfange ausgebreitete Grundstoff elementarischer Partikeln sich zu diesem hinsenken.Die erste Wirkung dieser allgemeinen Senkung ist die Bildung eines Körpers... Wenn die Masse dieses Centralkörpers so weit angewachsen ist, dass die Geschwindigkeit, womit er die Theilchen von grossen Entfernungen zu sich zieht, durch die schwachen Grade der Zurückstossung, womit selbige einander hindern, seitwärts gebeugt, in Seitenbewegungen ausschlägt, die den Centralkörper vermittelst der Centerfliehkraft in einem Kreise zu umfassen im Stande sind: so erzeugen sich grosse Wirbel von Theilchen, deren jedes für sich krumme Linien durch die Zusammensetzung der anziehenden und der seitwärtsgelenkten Umwendungskraft beschreibt; ... Indessen sind diese auf mancherlei Art unter einander streitende Bewegungen natürlicher Weise bestrebt, einander zur Gleichheit zu bringen, .... Dieses geschieht erstlich, indem die Theilchen eines des andern Bewegung so lange einschränken, bis alle nach einer Richtung fortgehen; zweitens, dass die Partikeln ihre Verticalbewegung, vermittelst der sie sich dem Centro der Attraction nähern, so lange einschränken, bis sie alle horizontal, d.i. in parallel laufenden Zirkeln um die Sonne als ihren Mittelpunkt bewegt, einander nicht mehr durchkreuzen und durch die Gleichheit der Schwungskraft mit der senkenden sich in freien Zirkelläufen in der Höhe, da sie schweben, immer erhalten ... In diesem Zustande, da alle Theilchen nach einer Richtung und in parallel laufenden Kreisen, nämlich in freien Zirkelbewegungen, durch die erlangte Schwungskräfte um den Centralkörper laufen, ist der Streit und der Zusammenlauf der Elemente gehoben, und alles ist in dem Zustande der kleinsten Wechselwirkung. Dieses ist die natürliche Folge, darein sich allemal eine Materie, die instreitendenBewegungen begriffen ist, versetzt.Dieser Körper in dem Mittelpunkte der Attraction, der diesem zu zufolge das Hauptstück des planetischen Gebäudes durch die Menge seiner versammelten Materie geworden ist, ist die Sonne, ob sie gleich diejenigeflammende Gluth als dann noch nicht hat, die nach völlig vollendeter Bildung auf ihrer Oberfläche hervor bricht.

Accretion history


History of accretion disks:

von Weizsäcker (1943, 1948):

- formation of Sun & planets from gaseous disk - turbulent disk. angular momentum transport outwards

Lynden-Bell, Pringle, Rees (1969, 1972, 1974):

accretion disks in AGN, quasars, compact X-ray sources

Shakura & Sunyaev (1973):

- structure, luminosity, temperature profile of disks - invention of turbulent viscosity parametrisation

Ichimaru (1977) : sub-Eddington and very low opacity disk (~ADAF)

Paczynsky & Wiita (1980): thick disk around black holes

Abramowicz et al. (1988): slim disks

Beckwith et al. (1990): survey (1.3mm) of TT disks -> masses, temperature profiles

Balbus & Hawley (1991): magneto-rotational instability (MRI) causes disk turbulence

Narayan & Yi (1994, 1995): advection dominated accreation disks (ADAFs)

O'Dell, McCaughrean et al. (1993, 1996): direct imaging of disks around young stars

Miyoshi et al. (1995): evidence for 3.6 x107 MO BH in jet source NGC 4258, Kepler disk

Literature: Frank, King, Raine (2002). Accretion power in astrophysics Pringle (1981), Accretion discs in astrophysics, ARA&A 19,137

Accretion history


1) Simplest case of accretion: Free fall: only gravity

2) Radiation from source: Eddington limit: gravity balanced by radiation pressure

-> photon scattered by free electrons (Thompson cross section):

-> momentum of photon with energy E is p = E/c; -> source with luminosity L has photon momentum flux:

-> momentum transfer rate to electron by phtoton is -> radiation < gravitational force for

-> limiting luminosity for mass infall:

Eddington luminosity:

Spherical accretion

dT

d=re sin2

T=83

r e2=6.65×10−25cm2 , re≡

e2

me c2=2.8×10−13cm2

dpdt dA

=L

4cr2

dpdt

=T

dpdt dA

=T

L4cr 2

T

L

4cr2≤

GM mp

r 2

L≤4Gmpc

T

M≡Ledd

Ledd=1.2×1035 MMO erg s−1

=1.2×1043 M108 MO

erg s−1


3) Bondi accretion: (Bondi 1952, Hoyle & Lyttleton 1939, Bondi & Hoyle 1944)

Accretion considering gravity and gas pressure, no rotation (see also Parker wind):

-> stationary HD equations -> mass conservation -> accretion rate: stationary equation of motion: -> integration of e.o.m. (energy conservation):

-> with polytropic gas law and sound speed

Bernoulli equation (wind equation, energy equation):

-> Bondi 1952: different mass flux gives different solution branches of Bernoulli eq.

Interpretation: Infall solution: starts with low speed at large radii, accelerates to high velocity at small radii ( free fall for r -> 0 ) Outflow solution: starts with low speed at small radii

Spherical accretion

M≡4r 2v

v dvdr

=−1

dPdr

−GMr 2

v2

2∫

dP 'P '

−GMr

=const.≡E

P=K

cS2≡

dPd

=P

v2

2

1−1

cS2−

GMr

=E=1

−1cS ,∞

2


Bondi accretion:

(Bondi 1952, Fig.2.)

Velocity u(x), normalised to sound speed

Radius x = r / rB

(Bondi radius)

rS = ½ rB

note := 7/5

> 3 solution branches: one is “physical” ( ie. regular ) accretion solution with critical accretion rate

Spherical accretion

r B=GM / cS,∞2


3) Bondi accretion: (Bondi 1952, Hoyle & Lyttleton 1939, Bondi & Hoyle 1944)

-> re-arrange energy equation and equation of motion:

gives: with

Note: potential singularities in these equations at r = rS

rS is “critical point” -> regularity condition for solution: D1 = D2 = D = 0 at rS

-> at

-> critical point is sonic point

-> mass loss rate derived from integration constant:

->

-> solve for EigenwertS = 0.25 for =5/3

Spherical accretion

1v

dvdr

1

d

dr

2GMr

=0 v dvdr

cS

2

d

dr

GMr 2

=0

dvdr

=D1

D,

d

dr=−

D2

DD1≡

1 2 cS

2

r−

GMr2 , D2≡

1v 2 v2

r−

GMr2 , D≡

1v

v2−cS

2

vS2=cS

2=GM2r S

=2cS ,∞

2

5−3r S=

5−34

GMcS ,∞

2

=∞ cS

cS ,∞2 /−1

M=4∞vS rS2 cS

cS,∞2 /−1

=4S GM

cS ,∞2

2

∞cS ,∞

4) Disk accretion:

-> take into account angular momentum: -> balance between gravity & centrifugal forces: -> stable Keplerian orbits -> no accretion

-> collisions / friction of infalling gas -> exchange of angular momentum -> gas with same specific angular momentum orbits at same radius:

-> gas on Keplerian orbits

-> for accretion: angular momentum transfer within the disk -> e.g. by collisions of disk material -> “friction” -> if outward loss of angular momentum -> mass accretion, accretion rate: (mean density, disk height)

-> angular momentum loss rate required: (outer disk radius rD)

-> for “Keplerian disk”:


Disk accretion

l=l r =GM r

M=ddt

V =dVdt

= A drdt

=2 r hvr

J≃M l r D=MGMr D

v=r≃GM /r≫vr

-> friction force between two orbiting rings of matter:

-> stress:

-> viscous stress tensor: transport of i-momentum in j-direction:

-> kinematic viscosity coefficient (model-dependent) definition of visocity by stress = force/area = F/A =V / L, []: cm2 s-1

-> stress tensor component for angular momentum exchange:

-> Keplerian disk: -> torque between two disk rings:

angular momentum transport outwards if:


Disk accretion

∣F∣=−t r

t ij= ∂v i

∂ x j

∂v j

∂ x i

−23

∇⋅v ij

t r= ∂v

∂r

v

r =r∂r ∂r

t r=−32=−

32GM /r 3

W=∫ r d∫ r t rdz=2 r3∂

∂ r

∂

∂ r0, W0


Concept of “disk height” :

h(r) << r , thin disk: h/r < 0.1

-> average over vertical disk profile: surface density “disk height”:

-> vertical gravitational force:

-> particle with v = cS may reach disk surface h ~ r cS / vK

-> h/r ~ cS / vK

-> condition for thin disk satisfied, if thermal energy < potential energy:

kB T << mP G M / r

-> OK for “cool disks” -> thin disks require efficient radiative cooling

Thin disks

≡∫r ,z dz h=

2

FG ,z=mpG Mz r−3


Time evolution of axisymmetric thin accretion disks:

-> system of HD equations de-couples, vZ = 0:

mass conservation: ->

momentum equation:

angular momentum conservation:

-> accretion velocity:

-> surface density, time evolution:

-> both depend on shear & viscosity

-> needed: model for viscosity: molecular viscosity much too low !!

-> anomalous viscosity (turbulence)

Thin disks

∂t 1r∂r r v r =0∂t ∇⋅v =0

∂t vv⋅∇ v ∇ P∇=∇⋅T

∂t r2∂r r

3vr =

12

∂r W

vr=∂r r

3 ∂r

r ∂r r2

∂t =−1r∂r ∂r r

3∂r

∂r r2


Stationary axisymmetric thin disks:

-> Accretion rate from mass conservation:

->

-> Integrate stationary angular momentum conservation:

-> integration const. defined at some radius ri with

e.g. co-rotation radius / magnetosphere; stellar radius; marginally stable orbit / BH

-> interpretation: C is angular momentum flux and conserved quantity:

-> for Keplerian disk:

-> radial profiles follow from viscosity / turbulence model;

-> M, dM/dt uniquely define stresses required

Thin disks – angular momentum balance

M=dMdt

=ddt

V =dVdt

= A drdt

=−2 r2h vr=−2 r v r∂t

1r∂r r v r =0 M=−2r v r=constant

M

2

Cr 2=−∫t r dz

C=−r i2r iM/2 t r r i=0

M

2Rr =−∫t rdz R r ≡1−r i

r 2r i

r

R r ≡1−r i /r


Thin disks energy balance

Stationary axisymmetric thin disks:

-> energy conservation: accretion = energy gain from potential energy -> orbital rotational energy -> angular momentum transport outwards -> heating due to viscous friction

-> viscous shear locally generates heat Q with rate:

-> Keplerian disk:

-> if heat is radiated away immediately in vertical direction: -> total disk luminosity: integrate from r = infinity to r = ri

(factor ½ is for non-relativistic disks)

Q≡T s= r d

dr 2

=M

2

2 ∣d lnd lnr ∣ 1−r i

r 2r i

r Q=

34

GMMr3 1− r i

r

Ltotal =12

GMMr i


Stationary axisymmetric thin accretion disks:

Spectral energy distribution:

-> assumption LTE -> disk rings emit as black body

-> with it follows:

-> integrate local blackbody:

-> disk spectrum:

Thin disks – disk spectra

S(T(r)), normalized units( Pringle 1981)

Q=T Sr

4

Q=Q T S= 38

GMM r 3 1− r i

r 1 /4

~r−3 /4

BT S r ~3

exp h/kBT S r −1

S~∫r i

rout

BT Sr 2r dr


Shakura Sunyaev (1973): -parametrisation of viscosity -> molecular viscosity too low define an effective, anomalous viscosity l = 10 cm (mean free path), -> viscous accretion time scale ~ r2 / ~ 1015 yrs

-> anomalous viscosity is turbulent viscosity: friction of turbulent cells

-> typical length scale (size of cells): l < h ( = disk heigth ) -> typical velocity scale : v < cS ( = sound speed )

->>

-> parameter < 1 to be adjusted to different sources: “observational parameter” -> can be numerically determined by simulations (Brandenburg et al.) > 0.0001 < < 1; some setup results in negative -> Note: so far, physics of this viscosity not defined, just hidden in -> extremely successful “trick”: - observational proof by some disk systems: “hot disks” in CVs, - not very good fit for protostellar disks (temperature profile): “flared disks”

Thin disks parametrisation

=vlv=vtherm

=cS h

3400 citations as of Nov, 2006 4124 citations as of Nov 11, 2008 5912 citations as of May 31, 2011


Shakura & Sunyaev (1973): a-parametrisation for viscosity

-> application: solve HD equations for thin disk structure:

-> nine equations for nine variables:

-> opacities & pressure contribution -> three regions of solutions: a) inner region: radiation pressure; electron scattering b) intermediate region: gas pressure; electron scattering c) outer region: gas pressure; free-free absorption

plus d) cooler outer regions: dust opacities, atomic/molecular opacities


r ,hr , r ,vr r ,P r ,T r , f r ,r ,F r

=∫dz≃2h , M=2r vr , M

2R r =−∫t rdz , Ltotal=

12

GMMr i

,

h=cS

, f =P , −1 ,T ≃scatt

−1 absorb−1 , P ,T =

2 kBT

mp

13

aT4 , F r ≃acT 4


Shakura & Sunyaev (1973): parametrisation

-> power law profiles for three regions (note: normalization for black holes)



Shakura & Sunyaev (1973): a-parametrisation

-> examples: SS disks of different sources

1) particle density of circumstellar & circumplanetary disks

2) mass density of stellar mass BH disk (quasar)


nr =1.6×1014cm−3−7 /10 M

6×10−5M J yr−1 11 /20

MM J

5 /8

r15 R J

−15 /8

=2.8×1014cm−3−7 /10 M

1.2×10−7 MO yr−1 11/20

MMO

5 /8

r15 RO

−15 /8

r =7.2×10−4gcm−3

0.001 −1

MMedd

−2

r3RS

3 /2

MMO

−1

1− r3RS

−1 /2

−2

Origin of accretion disk viscosity

-> molecular viscosity too low -> viscous accretion time scale ~ r2 / ~ 1015 yrs

-> what causes anomalous (turbulent) viscosity ??

-> Schwarzschild criterium for gravitational instability l2 / r > 0 not satisfied for Keplerian disk

-> Magnetorotational instability, MRI (Balbus & Hawley 1991)

Other suggestions for angular momentum transport / removal in accretion disks:

-> Molecular viscosity (Pringle 1981)

-> Convective turbulence (Lin & Papaloizou 1980, Ryu & Goodman 1992, Stone & Balbus 1996)

-> Outflows (Wardle & Königl 1993)

-> Tidal effects (Vishniac & Diamond 1989)

-> Electron viscosity (Paczynski & Jaroszynski 1978)


Accretion disks disk viscosity


Magnetorotational instability (MRI):

Velikhov (1959): MRI discovered for vertically magnetized Couette flow (diff. rot. cylinders)

Chandrasekhar (1960): MRI generalisation, variational principle (no practical application)

Fricke (1969): application to stars, local instability, dispersion relation

Safranov (1969): turbulisation of accretion disks by magnetic shear instability

Balbus & Hawley (1991, see review Balbus & Hawley 1999):

-> break-through of MRI application in accretion disks:

- shown that MRI manifests itself locally under very general conditions

- give a relatively simple derivation

- provide a detailed explanation of the underlying physical processes

- present limitations of the theory

- suggest MRI as cause for large viscosity in accretion disks

- numerical MHD disk simulations to prove analytical derivations

-> MRI excited by moderate magnetic field strength: - strong fields stabilizes differential rotation, - weak field limit by dissipation (natural length of instability scales inversely with field strength) -> exponential growth till saturation

Accretion disks MRI


Magnetorotational instability: Principle, simplified:

1) Failing-approach maneuvre of spacecraft:

-> spacecraft on inner orbit is faster -> decelerate inner spacecraft -> angular momentum loss -> inner spacecraft sinks to even lower orbit, departs from outer spacecraft

2) Matter on Kepler orbits, connected by a “spring”

-> differential rotation: inner/outer material orbits faster/slower (angular momentum of inner material < a.m. of outer material) -> spring is stretched, shear forces exert decelerating/accelerating torque on inner/outer material -> inner/outer material looses/gains angular momentum, moves inwards/outwards -> differential rotation becomes even stronger -> stronger torques, more angular momentum loss in outward direction

3) In MHD disks: “spring” action delivered by magnetic field

Accretion disks MRI Taken from Andreas Mueller (www.mpe.mpg.de/~amueller/)

http://www.mpe.mpg.de/


Accretion disks – MRI

Magnetorotational instability:

Simulation slice through a magnetized

disk with MRI created turbulence

Blue: gas with less than Keplerian

angular momentum

Red: gas with excess a. m.

“MRI is very effective at creating the angular momentum transport Field line evolution required to make accretion disks accrete” (Balbus & Hawley 1995)


“Other” accretion disks:

-> thick disks : h ~ r ; not local energy balance, heat transport in any direction,

potentially gravitationally unstable

-> rotation not uniquely defined by gravity -> “free” angular momentum distribution

-> not Keplerian anymore; separation of HD eq. in radial & perp. part not possible

-> massive disks in YSO, very hot disks (AGN)

-> ADAFs: advection dominated accretion disks, inefficient cooling, hot disks,

- for BH: matter is accreted into BH before it radiates energy away

- for NS: energy release at NS surface

-> more similar to Bondi accretion than to thin disk , h ~ r, BUT viscous accretion!

-> slim disks: optically thick ADAF, ineffective cooling, advection cooled, super-Eddington

-> ADIOS: adiabatic inflow outflow structures:

ADAF with wind/jet outflow taken into account, ADAF with high viscosity

-> CDAFs: convection dominated advection: ADAF with low viscosity, structure,

very different from ADAFs, e.g. constant angular momentum per volume

-> MDAFs: magnetically dominated advection flows

Accretion disks

Jets are collimated disk/stellar winds, launched, accelerated, collimated by magnetic forces

Energy source: gravity, rotation

MHD model of jet formation:

● ejection of disk/stellar material into wind?

● collimation & acceleration of a disk/stellar wind into a jet

● jet propagation / interaction with ambient medium

● accretion disk structure?

● origin & structure of magnetic field?


Standard model of jet formation

-> 5 basic questions of jet theory:


How to redirect radially accreting material into outflow?

-> launching process is “holy grail” of jet formation theory -> so far mostly steady-state models -> MHD simulations beginning to succeed

“Magnetic accretion-ejection structures” (Ferreira & Pelletier '95-'97): -> investigate disk-jet transition region in stationary self-similar approximation -> jet launching is completely magnetohydrodynamic process (compared to e.g. magneto-centrifugal acceleration ...):

-> disk: quasi-magnetohydrostatic equilibrium,

turbulent magnetic diffusivity

-> magnetic torque in toroidal direction,

-> Lorentz force: use to get ->

-> if FL, _|_ decreases: gas pressure gradient lifts plasma

-> if FL, increases:

centrifugal acceleration of plasma

Jet launching from accretion disks

m=mvA h

F L,= jz Br− jr Bz

Ipr , z =−c2

r B

FL ,=Bp

2 r∇ ∥ Ip

F L, ∥=−B

2r∇ ∥ Ip

F L, ⊥=Bp j

−

B

2 r∇

⊥Ip


“magnetic accretion-ejection structures” (Ferreira et al 1995-1997):

-> disk material 1) diffuses across magnetic field lines, 2) is lifted upwards by MHD forces, then 3) couples to the field, becomes 4) accelerated magnetocentrifugally, and 5) collimated

Jet launching from accretion disks P

oloidal magnetic field lines (thick)

and poloidal streamlines (dashed)



Poloidal velocity as function of distance along the field line.-> super slow- magnetosonic, -> super Alfvenic, and -> marginally fast-magnetosonic (Ferreira 1997)


-> disk material ... 1) diffuses across magnetic field lines, 2) is lifted upwards by MHD forces, then 3) couples to the field 4) accelerated m.-centrifugally, and 5) collimated



Field line structure z(r) for different mass flux per magnetic flux Note: self-similar disk outflows intrinsically re-collimate

(Ferreira 1997)


-> disk material ... 1) diffuses across magnetic field lines, 2) is lifted upwards by MHD forces, then 3) couples to the field, 4) accelerated m.-centrifugally, and 5) collimated


Numerical simulations of disk-jet interaction

Shibata et al. group :Uchida & Shibata 1986 !!!!! -> simulations incl. disk structure: short-term, problem disk evolution-> applications: sun, stars (MHD), BHs (GR-MHD)

Difficult task: - strong gradients in density, gas pressure, magnetic field, velocity - proper disk model? ideal / diffusive MHD, turbulence, radiative transfer,-> mass transfer disk to jet-> disk wind & disk structure



Numerical simulations of disk-jet interaction

Casse & Keppens 2002/04:1st who solved time-dependent jet ejection from disk, long-term evolution until steady state. recent work: Zanni et al 08; Tzefaros et al. 09


Melani et al. 2006

General relativistic simulations: e.g. McKinney (2006): - GR- code HARM (Gammie 2003), Kerr-Schild coordinates - initial magnetic field confined to initial torus, purely poloidal

Poynting dominated jet reaches ~10, fast within < 5°, slow within 30°Disk wind has collimated edge, < 1.5

New “force-free” simulations, low density, reach Lorentz factors of 5000 (Tchekhovskoy, et al 2008)

t ~ 104 tgr ~ 104 rg / 100 rg

rout ~ 10-13 rdisk

Shown is lab frame density + fieldlines

Jet launching from accretion disks Outflows & Jets: Theory & Observations


Lecture plan & schedule

Summer term 2011Henrik Beuther & Christian Fendt

15.04 Today: Introduction & Overview ("H.B." & C.F.)29.04 Definitions, parameters, basic observations (H.B.)06.05 Basic theoretical concepts & models; MHD (C.F.)13.05 MHD & plasma physics; applications (C.F.)20.05 Radiation processes (H.B.) 27.05 Observational properties of accretion disks (H.B.)03.06 Accretion disk theory and jet launching (C.F.)10.06 Theory of interactions: entrainment, Instabilities, shocks (C.F.)17.06 Outflow-disk connection, outflow entrainment (H.B.) 24.06 Outflow-ISM interaction, outflow chemistry (H.B.)01.07 Outflows from massive star-forming regions (H.B.)08.07 Observations of extragalactic jets (C.F.)15.07 Some aspects of relativistic jet theory (C.F.)

Summer term 2011 Henrik Beuther & Christian Fendt · 2011-06-10 · Henrik Beuther & Christian...

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Transcript of Summer term 2011 Henrik Beuther & Christian Fendt · 2011-06-10 · Henrik Beuther & Christian...