Mitch Begelman & Eric Coughlin JILA, University of Colorado ARE RELATIVISTIC JETS ALWAYS MAGNETIC?
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Transcript of Mitch Begelman & Eric Coughlin JILA, University of Colorado ARE RELATIVISTIC JETS ALWAYS MAGNETIC?
![Page 1: Mitch Begelman & Eric Coughlin JILA, University of Colorado ARE RELATIVISTIC JETS ALWAYS MAGNETIC?](https://reader030.fdocuments.net/reader030/viewer/2022032703/56649cfa5503460f949cc73c/html5/thumbnails/1.jpg)
Mitch Begelman & Eric CoughlinJILA, University of Colorado
ARE RELATIVISTIC JETS ALWAYS MAGNETIC?
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Why we assume relativistic jets are propelled by large-scale B-fields:
• Only way to tap BH spin (?)– OK, good point
• Rel. electrons cool too rapidly so thermal pressure won’t work– Could use ion pressure if coupling to electrons weak
• Radiation drag due to aberration limits acceleration by radiation pressure– Only applies at low optical depth (cf. fireball models of GRBs)
• Need super-Eddington flux for radiative acceleration
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The Magnetic Flux/Spin Paradigm- strict requirements here as well
cLJ
22
~
Magnetic flux threading Magnetic flux threading engineengine
Angular velocity of Angular velocity of engineengine
Jet power limited by amount of flux available
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Tidal Disruption Event
A star ventures inside the tidal radius of a black hole and is torn apart
**,RM
hM
stars type-solarfor
47cm107
radius Tidal3/2
63/1
612
3/1**
g
ht
rMM
MMRr
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Tidal forces …
... unbind ~half the debris
… throw the other half into highly eccentric orbits
Semi-major axis:
g
ht
i
rM
M
MMr
r
3/16
3/26
14
3/1*
2400
cm104
2
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Energy pumped into the stellar debris by tides …
Simulations by Guillochon & Ramirez-Ruiz 2013
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yr1.0fallback for timerise Initial 2/16Mti
Edd2/3
5
Edd2/3
6
-1Sun
2/16
2400
80
yrM2 ratefallback Peak
MM
MM
MM i
2EddEdd 10 cLM
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yr1.0fallback for timerise Initial 2/16Mti
Edd2/3
5
Edd2/3
6
-1Sun
2/16
2400
80
yrM2 ratefallback Peak
MM
MM
MM i
Simulations by Guillochon & Ramirez-Ruiz 2013
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BH 1010for
yr31~for Eddington -super
as decaysFallback
Sun65
2.23/5
M
ttM
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Common wisdom says that matter falling back in excess of ṀE should be blown away:
R> (Ṁ/Ṁ)Rg:
thin Keplerian disk
R> (Ṁ/Ṁ)Rg:
regulates L~LE
Shakura & Sunyaev 73
const. M
RM
… but this may not always happen
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Super-Eddington TDE Swift J1644+57
Edd100~ L
Edd~ L
Tchekhovskoy et al. 2014
•Swift + Chandra light curves•L corrected for beaming•Radio “re-brightening” after ~ 4 months
l
Swift J2058+05 a second case?Cenko et al. 2012
Bloom et al. 2011
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Swift J1644+57 outburst suggestive of a beamed, relativistic flow = jet
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Do TDEs have enough magnetic flux?Transient accretion events have access to a fixed amount of flux…
Tidal Disruption Event candidate Swift J1644+57:
Jet power: Lj > 1045 erg s-1 ~ 100 LE
Flux needed: > 1030 G-cm2
Flux available: ~ 1025 B3 (R/R)2 G-cm2
Collapsar Gamma-Ray Burst:
Jet power: Lj > 1050 erg s-1 ~ 1011 LE
Flux needed: > 1028 G-cm2
Flux available: ~ 1025 B3 (R/R)2 G-cm2
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An alternate approach
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geff
MRI
Powered by dissipation of turbulent B
““Empty” funnelEmpty” funnel
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geff
MRI
Powered by dissipation of turbulent B
““Empty” funnelEmpty” funnel
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geff
Reconnection
MRI
Reconnection converts energy to radiation
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geff
Reconnection
MRI
Entrainment (by rad’n force)
Mass-loading, collimation and acceleration
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geff
Reconnection
MRI
Entrainment (by rad’n force)
Self-shielding (from drag) few~
Self-shielding from radiation drag
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Max. of a radiation-propelled jet:• Jet power Lj = l LE
• “Terminal” Lorentz factor = Lj/Ṁjc2
– based on available energy
• Increase by decreasing Ṁjc2
– but if Ṁ too small photons leak out before is reached
(for conical flow; 2/7 instead of 1/4 for paraboloidal)
41
max ,minj
Rees & Meszaros 2005Rees & Meszaros 2005
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Radiative self-shielding:
STATIONARY
Lj, j
pressure pDrag important if
12
rel
c
rpD
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Radiative self-shielding:
STATIONARY
Lj, j
pressure pDrag important if
Boundary layer dragged by jet radiation, retarded by radiation from wall
12
rel
c
rpD
2/1~ jBL
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Radiative self-shielding:
STATIONARY
Lj, j
pressure pDrag important if
Boundary layer dragged by jet radiation, retarded by radiation from wall
BL1 for rays impinging on boundary layer
12
rel
c
rpD
2/1~ jBL
BLr ~
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Radiative self-shielding:
STATIONARY
Lj, j
pressure pDrag important if
BL can be dominated by kinetic energy:
12
rel
c
rpD
2/1~ jBL
22
~ BLBL
BL
BL
DRad
KE
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Radiative self-shielding:
STATIONARY
Lj, j
pressure pDrag important if
Ratio of BL to jet energy:
12
rel
c
rpD
2/1~ jBL
j
BL
j
BL DL
L
1~
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Radiation-driven jet is pressure-confined
• Spherical envelope with pressure pa~r-
– > 2 jet blows up envelope– > 2 envelope crushes jet
• Need evacuated funnel held open by rotation• … but not too wide a funnel (otherwise
radiation can drive circulation or slow wind)WHERE MIGHT WE FIND SUCH FUNNELS?WHERE MIGHT WE FIND SUCH FUNNELS?
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Slim Disk Models of Hyperaccretion
• Radial pressure force significant• Angular momentum below Keplerian• H/r ~ few tenths• Vertical and radial structure coupled
– Can be modeled in 1D– 2D models more reliable
Only possible if l/lKep large enough
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l/lKep
disk
ope
ning
ang
le
const.M
rM 0.74 0.88
A clue from self-similar slim disk models
• Gyrentropes: s(l)• Quasi-Keplerian• Disk closes up at l close to lKep
What is going on?
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Case with mass loss …• Assume scaling for radial transport:
• Add radial pressure balance
2
2
13
2~
KR
GMp
2/32/1 RpR
KKR
GMB
88.0013
10
6
13~
2
2
(ADIOS scaling)
RM
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• Dynamical conditions don’t allow a bound disk-like flow• Flow “closes up” to axis as B 0
• Flow becomes “star-like” (with a rotational funnel)• Less disk “surface” to lose energy via wind• Flow reduces B instead by steepening density/pressure
profiles
Answer: l is too small to set up a flow with 0
2
2
Hv
B
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rd
d
ln
ln
B=0
Less l steeper higher accretion L
Flow blows up or finds way to vent excess energy equilibrium with B~0 (B<< GM/R)
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Summary:• Some low-l accretion flows unavoidably produce
hyper-Eddington luminosities– TDEs, GRBs, maybe quasi-stars
• Magnetic flux available might be too small to drive electromagnetic jets with adequate power
• Radiation pressure is an alternative to driving relativistic jets under these conditions – Can drive the fastest jets: max~(L/LE)1/4 – Self-shield from drag: boundary layer can carry
substantial energy flux– BLs slower (~j
1/2) but wider beaming angle
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