Mitch Begelman & Eric CoughlinJILA, University of Colorado

ARE RELATIVISTIC JETS ALWAYS MAGNETIC?

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

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

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

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

Energy pumped into the stellar debris by tides …

Simulations by Guillochon & Ramirez-Ruiz 2013

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

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

BH 1010for

yr31~for Eddington -super

as decaysFallback

Sun65

2.23/5

M

ttM

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

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

Swift J1644+57 outburst suggestive of a beamed, relativistic flow = jet

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

An alternate approach

geff

MRI

Powered by dissipation of turbulent B

““Empty” funnelEmpty” funnel

geff

MRI

Powered by dissipation of turbulent B

““Empty” funnelEmpty” funnel

geff

Reconnection

MRI

Reconnection converts energy to radiation

geff

Reconnection

MRI

Entrainment (by rad’n force)

Mass-loading, collimation and acceleration

geff

Reconnection

MRI

Entrainment (by rad’n force)

Self-shielding (from drag) few~

Self-shielding from radiation drag

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

Radiative self-shielding:

STATIONARY

Lj, j

pressure pDrag important if

12

rel

c

rpD

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

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 ~

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

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~

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?

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

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?

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

• 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

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)

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