outflows & jets: theory & observations - mpia.de · 2009-01-24 · > model: similar to...

Lecture winter term 2008/2009

Henrik Beuther & Christian Fendt

Outflows & Jets: Theory & Observations


10.10 Introduction & Overview ("H.B." & C.F.)17.10 Definitions, parameters, basic observations (H.B.)24.10 Basic theoretical concepts & models I (C.F.): Astrophysical models, MHD31.10 Basic theoretical concepts & models II (C.F.) : MHD, derivations, applications07.11 Observational properties of accretion disks (H.B.)14.11 Accretion, accretion disk theory and jet launching (C.F.)21.11 Outflow-disk connection, outflow entrainment (H.B.)28.11 Outflow-ISM interaction, outflow chemistry (H.B.)05.12 Theory of outflow interactions; Instabilities (C.F.)12.12 Outflows from massive star-forming regions (H.B.)19.12 Radiation processes - 1: forbidden emission lines (C.F.)26.12 and 02.01 Christmas and New Year's break09.01 Radiation processes - 2 (H.B.)16.01 Observations of AGN jets (C.F.)23.01 Some aspects of AGN jet theory (C.F.): superluminal motion, beaming, black holes30.01 Summary, Outlook, Questions (H.B. & C.F.)


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

Velocity of extragalactic jets

Extragalactic jets – proper motion

Velocity of extragalactic jets

Example 2: Blazars & Quasars: jets pointing towards the observer; high variability, strong beaming

3C 345: ~7c (period 5 yrs) 0827+243: Lorentz factor ~20

> highest resolution with VLBA radio interferometry

Extragalactic jets – proper motion Outflows & Jets: Theory & Observations


Galactic relativistic jets

Galactic sources of relativistic velocity

> detected in radio emission: ejection superluminal knots (Mirabel & Rodriguez 1994)

> jet sources: (# ~ 20) Galactic high energy sources : High Mass Xray 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 cjet 9.0 mas/d

distance: 12 kpc

velocities: v = 0.92 c vj,app = 1.25 c vcj,app = 0.65 c

inclination: 70 deg

source mass: MBH = 14 Mo

( Fender 1999, Greiner et al. 2002)

Velocity in “micro quasars”:

For relativic motion = v/c towards observer:

-> time t = 0 when 1st signal emitted

time t = t when 2nd signal emitted

-> arrival of 1st signal:

-> projected path of source:

_|_ to l.o.s. d = t sin( || to l.o.s. d' = t cos( -> arrival of 2nd signal:

Observer

Source, t=0

Source, t=t

Dis

tanc

e

t 1=D /c

t 2= tD−d ' c

= tDc− t cos

Apparent superluminal motion:

Extragalactic jets – propagation Outflows & Jets: Theory & Observations

Apparent superluminal motion:Apparent velocity _|_ to l.o.s.: app=

dt 2− t1

=sin

1−cos


Apparent superluminal motion:Apparent velocity _|_ to l.o.s.:

For fixed v/c : is maximal for

Then: and

with

Superluminal motion

possible if

app=d

t 2− t1

=sin

1−cos

=1

1−2

d appd

=0

app cos max =

app ,max=

app ,max1

1/2



Extragalactic jets – radiation

Doppler shift:

consider radiation source moving with ~1 , inclination

> time lapse (dilatation) between comoving frame () and observer's frame ('):

> since v~c > difference in photon arrival times:

> radiation source has traveled:

> earlier arrival times of photons:

> observed frequency:

> relativistic Doppler factor:

> note relativistic > strong function of aspect angle

=1 t

=1

t '= '

s=v t cos

t arr= t 1−cos

obs=1

t arr

= '

1− cos

D≡1

1− cos



Doppler shift: > relativistic Doppler factor:

D≡1

1− cos



Doppler boosting/beaming:

> “one can show ” that a concerved quantity under Lorentz transformation is: phase space density of photons ( observer's frame unprimed )

> with Doppler factor > intensity boost:

> Doppler boosting of flux:

> in case of isotropic flux from sphere: note that with solid angle

> numbers: = 0.97, ~ 4 > D3 ~ 1000

> similar for power law spectrum :

> in general: with p=3 for sphere, p=2 for continuous jet > in case of synchrotron radio spectrum:

I

3=I ' '

'3

I =D3 I ' ' ' =D '

=D2 '

S =D 3S ' '

S =D p S ''

S ~ , 0.3−1

S =∫ I dS =D3 S ' '



Doppler boosting/beaming:

> Beaming of radiation: > radiation isotropically emitted in comoving frame into region (/2, +/2), half opening angle' = /2

> relativistic aberation ' > :

(coordinate transformation for angles) > decrease in opening angle:

> for >> 1 :

tan =sin '

cos '

tan =1

≃1



Doppler boosting:

> application: appearance of intrinsically symmetric jets for l. o. s. viewing angle > boosting of approaching jet, deboosting of receding counterjet

> flux ratioS1

S2

= 1 cos1− cos

n

=app2D2

n; n=2 , 3 ,...



Doppler boosting:

> application: appearance of intrinsically symmetric jets for l. o. s. viewing angle > boosting of approaching jet, deboosting of receding counterjet

> flux ratio > example: radio = 0.5, jet n=2+, >> 1/ >> 1 > S1 / S2 ~ (2/)5 > factor 1000 for = 30° > counterjets very diffcult to observe ( of course not applicable for protostellar jets with = 1 ) > onesided AGN jets (“coredominated” sources ) onesided AGN jets on kpc in spite of two lobes observed

However: The cause of onesidedness 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 onesided 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

> strong & rapid variability in light curves due to changes in beaming geometry (?)

S1

S2

= 1 cos1− cos

n

=app2D2

n; n=2 , 3 ,...

Jet of 3C279

time series 1995 2001:

ejection of “knots” from corecorrelated withluminosity flares

> “knots” in radio> flares in IR, X

> knot velocity ~ 4c


Extragalactic jets – variability

Outlook: comparison of models with observations:

MHD provides timedependent dynamics of propagation

Radiation field follows from density, velocity etc > Intensity maps to be compared with observations

Simulation of highly resolved radio observations of 3C279. time evolution of radio knots at 22 GHz. resolution 0.15 mas. Apparent jet velocity 5c (Lindfors et al. 2006)

Extragalactic jets – radiation Outflows & Jets: Theory & Observations

Nssss

> jets are collimated disk/stellar winds, launched, accelerated, collimated by electromagnetic forces

MHD model of jet formation:

> 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

Standard model of jet formation Outflows & Jets: Theory & Observations


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

(2) high efficiency of rest mass energy conversion in radiation > > compare to < 10 10 for chem. reaction, < 10 3 for HHe fusion

(3) superluminal (ie. highly relativistic) speed of jets > expected if originating in relativistically deep potential well

(4a) rotation curve in NGC 4258: Water maser 22GHz > resolution 0." 0006 ~ 0.017pc (Miyoshi et al. 1995) > “perfect” Keplerian orbit, central mass 3.3x10 7 Mo

concentrated within r < 0.012 p (4b) orbital motion of stars in Galactic center

L≃M c2 0.1


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 & Xray) > 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

Example: center of Milky Way:

> orbital motion of central stellar cluster (Schödel et al. 2002, Ghez et al. 2005)

> stars close to GC as test particles to probe central mass

> diffractionlimited Keck imaging > mapping the GC w/ sufficient angular resolution (Chez et al 2003, '05) > stars move at 12,000 km/sec

> orbits imply 3.7 x 10 6 solar mass dark matter within r < 0.0002 pc (= 6 lh or 600 RS )

> exceeds volume averaged mass densities inferred for any other galaxy > massive central black hole

Ghez et al.;

ww

w.astro.ucla.edu/~ghezgroup/gc/

ESO

1 pc


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 ): > Schwarzschild radius (a=0): rS = 2M > gravitational radius (a=1): rg = M

r H=MM 2−a2



BH metric:

> metric often described by BoyerLindquist coordinates (singular at horizon):

> “ frame dragging “ : angular velocity of space:

> ZeroAngularMomentumObserver angular velocity, = ( d / dt )ZAMO

> “ red shift “, “ lapse function “ : gravitational time lapse:

> time lapse of ZAMO proper time <> global time t, = ( d/ dt )ZAMO )

> KerrSchild coordinates avoid horizon singularity > applied in numerical simulations> ReissnerNordstroem metric for nonrotating, charged BH> KerrNewman metric for rotating, charged BH

ds 2=

2 c2 dt 2−r

2d−dt 2−/dr 2

−2 d 2

2≡r2

a2 cos2 ≡r 2

−2G M r /c2a2

2≡r 2

a2

2−a2

sin2 r≡/sin

r ,≡2aG M r /c2

r ,≡



BH orbits:

> Schwarzschild metric independent of, t> conservation of energy & angular momentum: > e. o. m. (similar to nonrelativistic case):

with effective potential

V r =1−2M /r 1h2

/r 2

(from MIT physics 8.033)

e=−u0=1−2M /r dt /d

h=u=r 2 d/d

dr /d =− e2−V r



BH orbits:

> e. o. m. (similar to nonrelativistic case):

> solve problem of test particle motion in potential well: stable circular orbits at radii minimising V(r) noncircular orbits not closed for (oscillations in radius around minimum) instable circular orbits at radii maximising V(r)

> last stable circular orbit: marginally stable orbit at ( inner edge of disk)

binding energy

> Kerr metric: case a=1: (direct orbit),

(retrograde orbit)

(from MIT physics 8.033)

e2 V r min

r ms=3r s

r ms=r g

r ms=9 r g

dr /d =− e2−V r

V r ms =1−ems =0.057



Ergosphere of rotating BH: > Kerr metric

> stationary observer, fixed (r,), angular velocity = d/ dt

> normalization of 4velocity:

> constraint on rotation law: > implying static limit for rotating BH:

> observer is enforced to rotate, min

> close to the horizon:

, BH angular velocity

(from Soshichi Uchii)

rr E=MM 2−a2 cos2

u j u j=−1

minmax

r r h : min=max≡h=a

r h2a2



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 cannot decrease

> defines irreducible mass: (cannot be lost by classical processes)

> reducible mass:

(from Soshichi Uchii)

M irr= A/16=M r h/ 2 ; H1

8 M irr

M−M irr0.29 M

A=8 M r h



Energy extraction from rotating BH:

> BlandfordZnajek 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 > B,E fluctuations, decay time ~ rg / c > if BH endowed with resistancee RH (i.e. not perfect conductor ) > with Maxwell's eqs:

> RH = 4Ohm, exact!!, Znajek (1978)

∂B∂ t

=−∇ x E≃−Er g

≃−j Rh

r g

≃B Rh

4 r g

≃−B

(from Blandford 1990)




> BlandfordZnajek 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 > BH is conductor > unipolar induction ( E ~ v x B ) causes potential difference 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

(from Blandford 1990)

V≃h M 2 B≃h




> Does BZ work? power estimate by Ohmic heating:

maximum external power for RH ~ Rext >

> application to AGN: magnetic field provided by accretion disk, equipartition, Pgas ~ Pmag, B ~ 104 G

> electric potential:

> power of rotating BH (a<<M):

> comparison to “free energy“ (a<<M):

> available even for low accretion rate, as electromagnetically extracted by BZ

NOTE: BZ is heavily debated: causality issues, boundary conditions, matter inertia issues; ongoing MHD & ED simulations tend to support feasibility of BZ mechanism

LBZ≃I 2 RhI 2 Rext

LBZ≃I 2 Rext≃r g2 B2

/Rh

V≃r g B=1019 M

108 M o B

104 G Volts

LBZ≃1045 aM

2

M108 M o

2

B104 G

2

erg s−1

M−M irr~4 M 3h

2≃5 x1061 a

M 2

M108 M o erg



Energy extraction from rotating BH: Simulations of BZ: (taken from Komissarov 2008)

Koide et al. (1999): BLcoordinates, thin disk, short run, transient ejection from the disk (?)Komissarov (2001): BLcoordinates; wind from disc; outflow in magneticallydominated funnel (BZprocess?)McKinney&Gammie (2004), McKinney (2005): KScoordinates, outflow in magnetically dominated funnel –> clear indications of the BZprocessHirose et al. (2004 2006): BLcoordinates; outflow in funnel (BZprocess?), but Punsly (2006): MHDPenrose process or computational errors?

(from Komissarov 2004)

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!

horizon

ergospheredissipative layer


10.10 Introduction & Overview ("H.B." & C.F.)17.10 Definitions, parameters, basic observations (H.B.)24.10 Basic theoretical concepts & models I (C.F.): Astrophysical models, MHD31.10 Basic theoretical concepts & models II (C.F.) : MHD, derivations, applications07.11 Observational properties of accretion disks (H.B.)14.11 Accretion, accretion disk theory and jet launching (C.F.)21.11 Outflow-disk connection, outflow entrainment (H.B.)28.11 Outflow-ISM interaction, outflow chemistry (H.B.)05.12 Theory of outflow interactions; Instabilities (C.F.)12.12 Outflows from massive star-forming regions (H.B.)19.12 Radiation processes - 1: forbidden emission lines (C.F.)26.12 and 02.01 Christmas and New Year's break09.01 Radiation processes - 2 (H.B.)16.01 Observations of AGN jets (C.F.)23.01 Some aspects of AGN jet theory (C.F.)30.01 Summary, Outlook, Questions (H.B. & C.F.)

outflows & jets: theory & observations - mpia.de · 2009-01-24 · > model: similar to...

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