outflows & jets: theory & observations - mpia.de · 2007-01-28 · outflows & jets:...

Lecture winter term 2006/2007

Henrik Beuther & Christian Fendt

Outflows & Jets: Theory & Observations


20.10 Introduction & Overview (H.B. & C.F.)

27.10 Definitions, parameters, basic observations (H.B.)

03.11 Basic theoretical concepts & models I (C.F.): Astrophysical models, MHD

10.11 Basic theoretical concepts & models II (C.F.): MHD, derivations, applications

17.11 Observational properties of accretion disks (H.B.)

24.11 Accretion disk theory and jet launching (C.F.)

01.12 Outflow-disk connection, outflow entrainment (H.B.)

08.12 Outflow-ISM interaction, outflow chemistry (H.B.)

15.12 Theory of outflow interactions: instabilities & shocks (C.F.)

22.12, 29.12 & 05.01 Christmas & New Year break

12.01 Outflows from massive star-forming regions (H.B.)

19.01 Radiation processes in jets & outflows (H.B. & C.F.)

26.01 AGN jet theory (C.F.): black holes, superluminal motion, beaming, boosting

02.02 Observations of AGN jets (Guest speaker: Klaus Meisenheimer)

09.02 Summary, outlook, questions (H.B. & C.F.)


Standard model of jet formation

collimation and acceleration of a disk wind into a jet ?

ejection of disk material into wind?

accretion of matter? generation of magnetic field?

jet propagation / interaction with ambient medium

--> jets are collimated disk winds, launched / accelerated / collimated by magnetic forces (MHD / ED)

The standard model of jet formation:

--> 4 basic questions of jet theory:


Extragalactic jets – nomenclature

Nomenclature of radio double sources:

- core: central source, active nucleus

(supermassive BH + disk)

- jets: relativ. hot, magnetized plasma

- hot spots: jet plasma becomes shocked

- cocoon: surrounding layer of backflow

- lobes: bow-like structures beyond hot spot

Historical classification:

comparison of radio surface brightness

& source size (Fanaroff & Riley 1974)

-> ratio RFR ~ distance (bright) / size (faint)

-> two classes: FR 1 : RFR < ½

FR 2 : RFR > ½

-> lobe dominated <-> core dominated

example Cyg A (233Mpc) as FR 2

-> FR correlation with spectral radio luminosity

-> spectral index α : S(ν) ~ ν^α : core: α ~ 0 (flat), jets: α ~ 0.6 (steep)

hot spots: α ~ 0.5...1.0

Unified model of all AGN (viewing angle) max resolution 0.00015 '' ~0.1pc = 130 lightdays


Extragalactic jets – propagation

Proper motion of jet knots

Example 1:

M87 inner knots by HST:

apparent superluminal motion

(Biretta et al. 1999)

-- > v ~ 6c

Note: optical resolution sufficient for

nearest e-g jet source (16 Mpc),

other sources: radio interferometry

Velocity of extragalactic jets



Velocity of extragalactic jets

Proper motion of jet knots

Example 2:

Blazars & Quasars:

jets pointing towards the observer;

high variability, strong beaming

3C 345: v ~7c (period 5 yrs)

0827+243: Lorentz factor γ ~20

Note: Highest resolution with VLBA radio

interferometry


Galactic relativistic jets

Micro quasars:

detected in radio emission: ejection of knots with superluminal motion (Mirabel & Rodriguez 1994)

jet sources: (# ~ 20) Galactic high energy sources : High Mass X-ray Binaries

model : similar to AGN/quasars: black hole + accretion disk

central mass ~ 10 M_o

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: 12 kpc

velocities: v = 0.92 c v_j_app = 1.25 c v_cj_app = 0.65 c

inclination: 70 deg

source mass: M_bh = 14 M_o

( Fender 1999, Greiner et al. 2002)



Superluminal motion ( geometric / apparent effect ):

--> consider relativistic motion towards observer --> time t = 0 when 1st signal is emitted

time t = ∆t when 2nd signal is emitted --> arrival of 1st signal: t1 = D/c --> projected travel path of emitters

_|_ to l. o. s. -> d = β ∆t sinθ || to l. o. s. -> d' = β ∆t cosθ --> arrival of 2nd signal:

t2 = ∆t + ( D – d' ) / c =

∆t + D / c – ∆t β cosθ



Superluminal motion ( geometric / apparent effect ):

--> apparent velocity _|_ l. o. s.

--> β_app maximized at dβ_app / dθ = 0

--> cos(θ_max) = β

with β_[app,max] = γ β

--> β_[app,max] > 1 if b > 1 / sqrt(2)

app=d

t 2 t 1

=

sin 1cos


Extragalactic jets – radiation

Doppler shift

consider radiation source moving with β ~1 , inclination φ

--> time lapse (dilatation) between co-moving frame (ν) and observer's frame (ν'):

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

--> radiation source has travels:

--> earlier arrival times of photons:

--> observed frequency:

--> relativistic Doppler factor:

--> note relativistic γ --> strong function of aspect angle

=1 t=

1 t '

=

'

s=v t cos

t arr= t 1 cos

obs=1

t arr

=

' 1 cos

D1

1 cos



Boosting & beaming

--> “one can show ” that concerved quantity under Lorentz transformation: ( co-moving (source) frame primed, observer's frame un-primed )

--> ; time interval (frequency) :

--> Doppler boosting: --> for isotropic distribution of flux from sphere: note that ; solid angle

--> similar for power law spectrum α : --> in general: with p=3 for sphere, p=2 for continuous jet in case of syncrotron radio spectrum: --> Beaming of radiation: --> radiation isotropically emitted in co-moving frame into region (-π/2, +π/2), half opening angle θ' = π/2 --> relativistic aberation θ' -> θ : (coordinate transformation for angles) --> decrease in opening angle: --> for γ >> 1

I 3 =

I ' '

' 3

I =D3 I ' ' ' =D '

=D 2 '

S =D3 S ' '

S =D p S ' '

S ~ , 0.31

tan =sin '

cos '

tan =1

1

S = d I

S =D3 S ' '



Doppler boosting

application example:

--> appearance of intrinsically symmetric jets in case of l. o. s. viewing angle φ

--> boosting of approaching jet, de-boosting of receding counter-jet

--> flux ratio

--> example: radio α = 0.5, jet n=2+α, γ >> 1/φ >> 1 --> S1 / S2 ~ (2/φ)5

--> factor 1000 for φ = 30° --> counter-jets very diffcult to observe ( note that this argument does not hold for protostellar jets ) --> AGN jets often observed as one-sided (“core-dominated” sources ) --> AGN kpc jets one-sided in spite of two lobes observed --> strong & rapid variability in light curves due to changes in beaming geometry (?)

S 1

S 2

=

1 cos1 cos

n

= app2D 2

n

; n= 2 , 3 , ...


Extragalactic jets – radiation, particle processes

Radiation processes in relativistic jets

--> pair creation/anihilation --> heating / particle acceleration --> synchrotron radiation --> Compton scattering

last lecture ???


Standard model of jet formation

collimation and acceleration of a disk wind into a jet ?

ejection of disk material into wind?

accretion of matter? generation of magnetic field?

jet propagation / interaction with ambient medium

--> jets are collimated disk winds, launched / accelerated / collimated by magnetic forces (MHD / ED)

The standard model of jet formation:

--> 4 basic questions of jet theory:


Extragalactic jets – central black hole (BH)

Evidence for central black holes in AGN jet source:

(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 η < 10 -10 for chem. reaction; η < 10 -3 for H-He fusion (3) superluminal (ie. highly relativistic) speed of jets --> expected if originating in relativistically deep potential well (4) stellar velocity disperion close to nucleus ~ 10 -3 c (5) rotation curve in NGC 4258; orbital motion of stars in Galactic center (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

L M c 2 0.1

Nandra et al. 1997:FeKα emission line in Seyfert galaxies


Extragalactic jets – central BH

Example NGC 4258: inner molecular diskWater maser (22GHz) spectroscopy, polarimetry --> resolution 0." 0006 ~ 0.017 pc (Miyoshi et al. 1995) --> “perfect” Keplerian orbit -> central mass (r< 0.13 pc) 3.3 x 10 7 Mo --> concentrated within r < 0.012 pc --> accretion model: accretion rate 10 - 3.7 Mo/yr


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 --> diffraction-limited 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.; www.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) --> “ cosmic censorship “: singularity will always be hidden (Penrose 1969), not settled ...BH parameters: --> “ no hair ” theorem (Wheeler): BH characterised solely by three parameters: --> mass M, angular momentum a = J/Mc, charge --> radius of horizon ( convention G=c=1 ): --> Schwarzschild radius (a=0): r_s = 2M --> gravitational radius (a=1): r_g = M --> metric usually described by Boyer-Lindquist coordinates (singular at horizon):

--> “ frame dragging “ ω : angular velocity of space: ( -> ZAMO angular velocity, ω = ( dφ / dt )_ZAMO ) --> “ red shift “, “ lapse function “ α : gravitational time lapse: ( -> time lapse ZAMO proper time t <--> global time t, α = ( dτ / dt )_ZAMO )

r H = M M 2a 2

ds 2=

2 c 2 dt 2 r

2 d dt 2 / dr 2

2 d 2

2 r 2

a 2 cos 2 r 2

2G M r / c 2a 2

2 r 2

a 2 2a 2

sin 2 r / sin

r , 2 a G M r / c 2

r ,



BH orbits:

--> Schwarzschild metric independent of φ, t--> conservation of energy & angular momentum

--> e. o. m. (similar to Newtonian case):

with effective potential

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

--> least stable circular orbit: marginally stable orbit at , defines inner edge of acc disk binding energy

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

V r = 12M / r 1h 2/ r 2

(from MIT physics 8.033)

e 2 V r min

r ms =3 r s

r ms = r g r ms =9 r g

e =u 0 = 12M / r dt / d

h =u= r 2 d / d

dr / d = e 2V r

V r ms = 1e ms =0.057



Ergosphere of rotating BH: --> Kerr metric --> stationary observer, fixed (r,θ), rotation Ω = dφ / dt --> normalization of 4-velocity --> implying static limit for rotating BH:

--> observer is enforced to rotate, Ω_min > 0 ! --> for , BH angular velocity

--> ergoshpere: region between r_h and r_E --> Penrose process (1969) orbits with e < 0 exist crossing the horizon --> reduce BH mass /energy by extracting spin energy --> Hawking radiation: area of horizon cannot decrease --> define irreducible mass --> reducible mass:

(from Soshichi Uchii)r r E = M M 2

a 2 cos 2

u j u j =1minmax

r r h : min =maxh =a

r h2a 2

M M irr0.29 M

A =8 M r h

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

8 M irr



Energy extraction from rotating BH:

--> Blandford-Znajek mechanism: electromagnetic coupling to BH --> 4 thought experiments

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 τ ~ r_g / c

--> if BH endowed with resistance R_h (i.e. not perfect conductor )

--> with Maxwell's eqs:

--> R_h = 4 π = 377 Ohm (exact!!, Znajek 1978)

B t= x E

Er g

j Rh

r g

B Rh

4 r g

B

(from Blandford 1990)




--> Blandford-Znajek mechanism: electromagnetic coupling to BH --> 4 thought experiments

c) Schwarzschild BH , constant magnetic field,

connected to battery (battery emf is V ) --> electric current I = V / R_h 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 Ψ across the BH --> if electric current is able to flow externally from pole to equator --> dissipation, work on external gas --> energy extraction from BH spin

(from Blandford 1990)

V h M 2 Bh




--> Blandford-Znajek mechanism: --> power estimate by Ohmic heating maximum external power for R_h ~ R_ext --> --> applied to AGN: --> magnetic field provided by accretion disk, equipartition (P_gas ~ P_mag) field strength 10 4 G

--> electric potential: --> power of rotating BH (a<<M)

--> comparison: “ free energy “ (a<<M):

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

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

L BZ I 2 Rh I 2 Rext

L BZ I 2 Rext r g2 B 2

/ Rh

V r g B=10 19 M10 8 M o

B10 4 G

Volts

L BZ10 45 aM

2

M10 8 M o

2

B10 4 G

2

erg s1

M M irr ~4 M 3h

25 x 10 61 a

M

2

M10 8 M o

erg


20.10 Introduction & Overview (H.B. & C.F.)27.10 Definitions, parameters, basic observations (H.B.)03.11 Basic theoretical concepts & models I (C.F.): Astrophysical models, MHD10.11 Basic theoretical concepts & models II (C.F.) : MHD, derivations, applications17.11 Observational properties of accretion disks (H.B.)24.11 Accretion disk theory and jet launching (C.F.)01.12 Outflow-disk connection, outflow entrainment (H.B.)08.12 Outflow-ISM interaction, outflow chemistry (H.B.)15.12 Theory of outflow interactions: instabilities & shocks (C.F.)22.12, 29.12 & 05.01 Christmas & New Year break

12.01 Outflows from massive star-forming regions (H.B.)19.01 Radiation processes in jets & outflows (H.B. & C.F.)26.01 AGN jet theory (C.F.): black holes, superluminal motion, beaming, boosting02.02 Observations of AGN jets (Guest speaker: Klaus Meisenheimer) 09.02 Summary, outlook, questions (H.B. & C.F.)

outflows & jets: theory & observations - mpia.de · 2007-01-28 · outflows & jets:...

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