Outflows & Jets: Theory & Observations

Outflows & Jets: Theory & Observations Lecture winter term 008/009 Henrik Beuther & Christian Fendt

10.10 17.10 4.10 31.10 07.11 14.11 1.11 8.11 05.1 1.1 19.1 6.1 09.01 16.01 3.01 30.01 Introduction & Overview ("H.B." & C.F.) Definitions, parameters, basic observations (H.B.) Basic theoretical concepts & models I (C.F.): Astrophysical models, MHD Basic theoretical concepts & models II (C.F.) : MHD, derivations, applications Observational properties of accretion disks (H.B.) Accretion, accretion disk theory and jet launching (C.F.) Outflow-disk connection, outflow entrainment (H.B.) Outflow-ISM interaction, outflow chemistry (H.B.) Theory of outflow interactions; Instabilities (C.F.) Outflows from massive star-forming regions (H.B.) Radiation processes - 1: forbidden emission lines (C.F.) and 0.01 Christmas and New Year's break Radiation processes - (H.B.) Observations of AGN jets (C.F.) Some aspects of AGN jet theory (C.F.): superluminal motion, beaming, black holes Summary, Outlook, Questions (H.B. & C.F.)

Extragalactic jets proper motion Velocity of extragalactic jets Proper motion of jet knots: Example 1: M87 inner knots by HST: > v ~ 6c apparent superluminal motion (Biretta et al. 1999) Note: optical resolution sufficient for nearest extragalactic jet source (16 Mpc), > other sources: radio interferometry

Extragalactic jets proper motion Velocity of extragalactic jets Example : Blazars & Quasars: jets pointing towards the observer; high variability, strong beaming 3C 345: ~7c (period 5 yrs) 087+43: Lorentz factor ~0 > highest resolution with VLBA radio interferometry

Galactic relativistic jets Velocity in micro quasars : Galactic sources of relativistic velocity > detected in radio emission: ejection superluminal knots (Mirabel & Rodriguez 1994) > jet sources: (# ~ 0) Galactic high energy sources : High Mass X ray Binaries > model: similar to AGN/quasars: black hole (neuron star) + accretion disk > central mass < 10 Mo > laboratory for AGN processes: > time scale reduced for physical processes (Kepler, free fall, instabil.) > accessible for observations: 4 MQ weeks < > 10 AGN years GRS 1915+105 propagation: jet 17.6 mas/d c jet 9.0 mas/d distance: 1 kpc velocities: v = 0.9 c vj,app = 1.5 c vcj,app = 0.65 c inclination: 70 deg source mass: MBH = 14 Mo ( Fender 1999, Greiner et al. 00)

Extragalactic jets propagation Source, t=0 Apparent superluminal motion: For relativic motion = v/c towards observer: Source, t= t time t = t when nd signal emitted -> arrival of 1st signal: t 1=D /c -> projected path of source: _ _ to l.o.s. to l.o.s. Distance -> time t = 0 when 1st signal emitted d = t sin( d' = t cos( -> arrival of nd signal: D d ' D t = t = t t cos c c Observer

Extragalactic jets propagation Apparent superluminal motion: d sin = Apparent velocity _ _ to l.o.s.: app = t t 1 1 cos

Extragalactic jets propagation Apparent superluminal motion: Apparent velocity _ _ to l.o.s.: For fixed v/c : Then: d app =0 d with = app and 1 1 Superluminal motion app,max 1 possible if 1/ app = d sin = t t 1 1 cos is maximal for cos max = app,max =

Extragalactic jets radiation Doppler shift: consider radiation source moving with ~1, inclination > time lapse (dilatation) between co moving frame ( ) and observer's frame ( '): 1 1 ' = = = t t ' > since v~c > difference in photon arrival times: > radiation source has traveled: > earlier arrival times of photons: > observed frequency: s=v t cos t arr = t 1 cos 1 ' obs = = t arr 1 cos > relativistic Doppler factor: D 1 1 cos > note relativistic > strong function of aspect angle

Extragalactic jets radiation Doppler shift: > relativistic Doppler factor: D 1 1 cos

Extragalactic jets radiation Doppler boosting/beaming: > one can show that a concerved quantity under Lorentz transformation is: phase space density of photons I 3 > with Doppler factor =D ' = I ' ' ' 3 ( observer's frame un primed ) > intensity boost: I =D 3 I ' ' ' > Doppler boosting of flux: 3 > in case of isotropic flux from sphere: S =D S ' ' note that S = I d with solid angle =D ' > numbers: = 0.97, ~ 4 > D3 ~ 1000 > similar for power law spectrum : S =D 3 S ' ' > in general: S =D p S ' ' with p=3 for sphere, p= for continuous jet > in case of synchrotron radio spectrum: S ~, 0.3 1

Extragalactic jets radiation Doppler boosting/beaming: > Beaming of radiation: > radiation isotropically emitted in co moving frame into region ( /, + /), half opening angle ' = / > relativistic aberation ' > : tan = sin ' cos ' (coordinate transformation for angles) > decrease in opening angle: 1 tan = 1 > for >> 1 :

Extragalactic jets radiation Doppler boosting: > application: appearance of intrinsically symmetric jets for l. o. s. viewing angle > boosting of approaching jet, de boosting of receding counter jet > flux ratio S 1 1 cos n n = = app D ; S 1 cos n=, 3,... > example: radio = 0.5, jet n=+, >> 1/ >> 1 > S1 / S ~ (/ )5 > factor 1000 for = 30 > counter jets very diffcult to observe ( of course not applicable for protostellar jets with = 1 ) > one sided AGN jets ( core dominated sources ) one sided AGN jets on kpc in spite of two lobes observed The cause of one sidedness in... jets of otherwise symmetrical... radio sources is a subject of... controversy. During a study... polarization properties of powerful radio sources, it became clear that in... sources with one sided jets, depolarization with increasing wavelength is... weaker for the lobe containing the jet. One... interpretation is... depolarization is caused by differential Faraday rotation through... magnetoionic medium surrounding... source. The side with... stronger jet closer to us, is seen through a smaller amount of material and therefore shows less depolarization. Laing, Nature 331, 1988 However: > strong & rapid variability in light curves due to changes in beaming geometry (?)

Extragalactic jets variability Jet of 3C79 time series 1995 001: ejection of knots from core correlated with luminosity flares > knots in radio > flares in IR, X > knot velocity ~ 4c

Extragalactic jets radiation Outlook: comparison of models with observations: MHD provides time dependent dynamics of propagation Radiation field follows from density, velocity etc > Intensity maps to be compared with observations Simulation of highly resolved radio observations of 3C79. time evolution of radio knots at GHz. resolution 0.15 mas. Apparent jet velocity 5c (Lindfors et al. 006)

Standard model of jet formation MHD model of jet formation: > jets are collimated disk/stellar winds, launched, accelerated, collimated by electro magnetic forces > 5 basic questions of jet theory: collimation & acceleration of a disk/ stellar wind into a jet? ejection of disk/stellar material into wind? accretion disk structure? generation of magnetic field? jet propagation / interaction with ambient medium Nssss

Extragalactic jets central black hole (BH) Evidence for central black holes in center of AGN: (1) rapid variability < 1 min (Rees 1977) > light crossing time ~ Schwarzschild radius of 107 Mo BH > characteristic time scale increases with luminosity () high efficiency of rest mass energy conversion in radiation > L M c 0.1 > compare to < 10 10 for chem. reaction, < 10 3 for H He fusion (3) superluminal (ie. highly relativistic) speed of jets > expected if originating in relativistically deep potential well (4a) rotation curve in NGC 458: Water maser GHz > resolution 0." 0006 ~ 0.017pc (Miyoshi et al. 1995) > perfect Keplerian orbit, central mass 3.3x10 7 Mo concentrated within r < 0.01 p (4b) orbital motion of stars in Galactic center

Extragalactic jets central black hole (BH) Evidence for central black holes in centers of AGN: (5) stellar velocity disperion close to nucleus ~ 10 3 c (6) radio jet orientation constant for > 10 7 yrs > compact spinning high mass object (7) broad emission lines (optical & X ray) > relativistic motion of radiation source (inner accretion disk) in relativistic potential well Nandra et al. 1997: FeK emission line in Seyfert galaxies

Extragalactic jets central BH ESO Example: center of Milky Way: > orbital motion of central stellar cluster (Schödel et al. 00, Ghez et al. 005) > stars close to GC as test particles to probe central mass > orbits imply 3.7 x 10 6 solar mass dark matter within r < 0.000 pc (= 6 lh or 600 RS ) > exceeds volume averaged mass densities inferred for any other galaxy > massive central black hole 1 pc Ghez et al.; www.astro.ucla.edu/~ghezgroup/gc/ > diffraction limited Keck imaging > mapping the GC w/ sufficient angular resolution (Chez et al 003, '05) > stars move at 1,000 km/sec

Extragalactic jets black holes BH definition: > solution to general relativistic field equations with asymptoically flat space time and horizon > horizon separates visible and invisble events; encloses singularity (of classical physics) > hypothesis of cosmic censorship : singularity will always be hidden (Penrose 1969); not finally settled (quantum gravity...) BH parameters: > no hair theorem (Wheeler): BH characterised solely by three parameters: > mass M, angular momentum a = J/Mc, charge Q > radius of horizon ( convention G = c = 1 ): r H = M M a > Schwarzschild radius (a=0): rs = M > gravitational radius (a=1): rg = M

Extragalactic jets black holes BH metric: > metric often described by Boyer Lindquist coordinates (singular at horizon): ds = c dt r d dt / dr d r a cos r G M r / c a r a a sin r / sin > frame dragging : angular velocity of space: r, a G M r / c > ZeroAngularMomentumObserver angular velocity, = ( d / dt )ZAMO > red shift, lapse function : gravitational time lapse: r, > time lapse of ZAMO proper time < > global time t, = ( d / dt )ZAMO ) > Kerr Schild coordinates avoid horizon singularity > applied in numerical simulations > Reissner Nordstroem metric for non rotating, charged BH > Kerr Newman metric for rotating, charged BH

Extragalactic jets black holes BH orbits: > Schwarzschild metric independent of, t > conservation of energy & angular momentum: > e. o. m. (similar to non relativistic case): e= u 0= 1 M / r dt / d h=u =r d / d dr / d = e V r with effective potential V r = 1 M / r 1 h / r (from MIT physics 8.033)

Extragalactic jets black holes BH orbits: > e. o. m. (similar to non relativistic case): dr / d = e V r > solve problem of test particle motion in potential well: stable circular orbits at radii minimising V(r) non circular orbits not closed for e V r min (oscillations in radius around minimum) instable circular orbits at radii maximising V(r) (from MIT physics 8.033) > last stable circular orbit: marginally stable orbit at r ms =3r s ( inner edge of disk) binding energy V r ms = 1 ems =0.057 > Kerr metric: case a=1: r ms =r g (direct orbit), r ms =9 r g (retrograde orbit)

Extragalactic jets black holes Ergosphere of rotating BH: > Kerr metric > stationary observer, fixed (r, ), angular velocity = d / dt > normalization of 4 velocity: u j u j = 1 > constraint on rotation law: min max > implying static limit for rotating BH: (from Soshichi Uchii) r r E = M M a cos > observer is enforced to rotate, min > close to the horizon: r r h : min = max h= a r h a, BH angular velocity

Extragalactic jets black holes Ergosphere of rotating BH: > ergoshpere: region between rh and re > Penrose process (1969): orbits with e < 0 exist crossing the horizon > reduce BH mass /energy by extractingbh spin energy > Hawking radiation: area of horizon (from Soshichi Uchii) A=8 M r h cannot decrease > defines irreducible mass: M irr = A/16 = M r h / ; (cannot be lost by classical processes) > reducible mass: M M irr 0.9 M H 1 8 M irr

Extragalactic jets black holes Energy extraction from rotating BH: > Blandford Znajek mechanism (1973): electromagnetic coupling to BH > 4 thought experiments, involving membrane paradigm a) BH in constant electric field > solve Maxwell equations for E in Schwarzschild metric > BH is electric conductor with horizon as equipotential surface b) BH in magnetized (B,E) cloud > accretion of magnetized plasma (from Blandford 1990) > B,E fluctuations, decay time ~ rg / c > if BH endowed with resistance RH (i.e. not perfect conductor ) > with Maxwell's eqs: B jr BR E B e t = x E > RH = 4 Ohm, rg h rg exact!!, Znajek (1978) h 4 rg

Extragalactic jets black holes Energy extraction from rotating BH: > Blandford Znajek mechanism (1973): electromagnetic coupling to BH > 4 thought experiments, involving membrane paradigm c) Schwarzschild BH, constant magnetic field, connected to battery (battery emf is V ) > electric current I = V / RH across B > Lorentz force ~ j x B > torque ~ I B spins up BH d) Inverse case: rotating BH, constant B (from Blandford 1990) > BH is conductor > unipolar induction ( E ~ v x B ) causes potential difference V h M B h from pole to equator with magnetic flux across the BH > if electric current is able to flow from pole to equator externally > dissipation, work on external gas > energy extraction from BH spin

Extragalactic jets black holes Energy extraction from rotating BH: > Does BZ work? power estimate by Ohmic heating: L BZ I Rh I Rext maximum external power for RH ~ Rext > L BZ I Rext r g B / R h > application to AGN: magnetic field provided by accretion disk, equipartition, Pgas ~ Pmag, B ~ 104 G M B 19 Volts > electric potential: V r g B=10 8 4 10 M o 10 G > power of rotating BH (a<<m): L BZ 10 45 a M M 8 10 M o B 4 10 G 1 erg s 3 M M irr ~4 M h 5 x 10 61 a M M erg 8 10 M o > available even for low accretion rate, as electro magnetically extracted by BZ > comparison to free energy (a<<m): NOTE: BZ is heavily debated: causality issues, boundary conditions, matter inertia issues; ongoing MHD & ED simulations tend to support feasibility of BZ mechanism

Extragalactic jets black holes Energy extraction from rotating BH: Simulations of BZ: (taken from Komissarov 008) Koide et al. (1999): BL coordinates, thin disk, short run, transient ejection from the disk (?) Komissarov (001): BL coordinates; wind from disc; outflow in magnetically dominated funnel (BZ process?) McKinney&Gammie (004), McKinney (005): KS coordinates, outflow in magnetically dominated funnel > clear indications of the BZ process Hirose et al. (004 006): BL coordinates; outflow in funnel (BZ process?), but Punsly (006): MHD Penrose process or computational errors? dissipative layer horizon ergosphere Field lines entering the ergosphere are set in rotation. Dissipative layer in equatorial plane acts as energy source. (emits negative energy photons that fall into BH) > Energy is extracted from the space between the horizon and the ergosphere! (from Komissarov 004)