Astrophysical Jets from accreting Black Holes€¦ · accreting Black Holes by Max Häberlein. Outline I. Description of astrophysical jets 1. Sources of Jets 2. Formation Mechanism

Astrophysical Jets from accreting Black Holes

by Max Häberlein

OutlineI. Description of astrophysical jets

1. Sources of Jets2. Formation Mechanism3. Structure of Jets

II. Accelaration in Jets1. Fermi Acceleration2. Diffusive Shock Acceleration

III. Deceleration Mechanisms1. Synchrotron Emission2. Inverse Compton Emission3. Other Processes

IV. Phenomena

I.Description of astrophysical jets

● Jets are a tremendous, elongated outflows of plasma● Jets can be observed in a huge spatial and energetic scale reaching

from stellar size to galaxy size● There are many sources for jets● Our universe is full of jets

I.1 Sources of Jets

Accreting BHGRBsAccreting Supermassive BHAGNPhysical SystemObject

Accreting Nucleus or Interacting Winds

Planetary NebulaeRotating NSPulsars (?)Accreting NSLMXBsAccreting NSHMXBsAccreting StarYoung Stellar ObjectsPhysical SystemObject

Extragalactic

Stellar

I.1 Sources of JetsActive Galaxy Nuclei (AGN)

● supermassive black hole in the core of a galaxy

● there are 3 types:1. Seyfert galaxies2. Quasars3. Blazars

● emits ulrarelativistic jets

M~106MSun

V escape≃V jet≃c ;~3M 87

I.1 Sources of JetsMicroquasars

● binary star system consisting of a massive normal star and a black hole bzw neutron star

● timescale proportional to M > evolution of the jets within days (quasars take years)

● jet velocity

artists view of a microquasar

V escape≃V jet≃0.6c

I.1 Sources of JetsGamma Ray Bursts (GRB)

● flashes of gamma ray emitted by heavy stars that collapse

● lifetime ~ s● followed by a longerlived

afterglow● most luminous events in the

sky● jet velocity

V escape≃V jet≃c ;~100

I.2 Structure of Jets

I.3 Formation Mechanism

● not known exactly● there mainly two different

theories● most popular:

the magnetic field lines spin with the BH. As you go to outer regions they get faster than light. This can be handled by a nonstationary model where field lines can be twisted > jet with extreme energy

I.4 Jet Collimination

II. Acceleration in Jets

II.1 Fermi Acceleration

● relativistic particle is reflected by a moving gas cloud● transformations lead to energy gain

EE≈2

ucu2

c2

II.2 Diffusive shock acceleration

● In a uniform magnetic field a freely moving charged particle follows a helical trajectory. The particles pitch is defined as:

so its momenta are

=p⋅BpB

ppara=p

pperp=1−20.5p


● What happens if a small static irregularity is imposed on the uniform field?

● We are using some simplifications in the following slides1. shock normal is parallel to Bfield2. shock is planar3. we are only considering staionary solutions4. individual particle velocity v is much greater than U, the velocity of the up and downstream.


● Momentum is contained because the electric field is identically zero● the pitch changes● describable in phase space by a diffusion equation, which is, considered

the scattering is sufficiently stochastic, isotropic

∂ f∂t=∇ ∇ f


● static irregularities are unrealistic● There are two types of scattering centre motion

1. largescale motions of the background which advects the scattering centres2. motion of the individual centres relative to the background (Fermi II)

∂ f∂t= ∇k ∇ f

∂ f∂ t U⋅∇ f= ∇k ∇ f

∂∂tf x ,p=∂ f

∂x∂ x∂t

U⋅∇ f=U⋅∂ f∂ x


● Liuovilles theorem: phase space density has to be constant along any trajectory

● for every convergence in position space you will need a divergence in momentum space

∂ f∂t= ∇k ∇ f

∂ f∂ t U⋅∇ f= ∇k ∇ f

13∇⋅Up

∂ f∂p

1 1


● motion of the individual centres relative to the background (Fermi II)

∂ f∂t= ∇k ∇ f

∂ f∂ t U⋅∇ f= ∇k ∇ f

13∇⋅Up

∂ f∂p1p2

∂∂pp2D

∂ f∂p

1 1 2


● U(x) = U1 for x < 0U(x) = U2 for x > 0

as a steady solution except for x = 0

⇒U ∂ f∂ x=∂

∂xxx

∂ f∂x


● boundary conditions:1.2. 3. the momentum space distribution has to be continuous4. phase space density is invariant under Lorentztransformations

x−∞⇒ f x ,p f 1p

x∞⇒∣f x ,p ∞∣


● 1+2 gives

{ f 1 pg1p exp∫0x Udx '

g2p = f 2 pf x ,p~


● The anisotropic phase space densitycan be expanded:

where

F x ,p ,

F x ,p ,~ f x ,p−∂ f x ,p∂x

=v3


● Then 3+4 lead to

{F x ,p ,~f 1g1−

3Uvg1

f 2

x=0−

x=0


● it follows with

and hence with

● if a “softer” power law is incoming, a power law with slope a will come out

r−1p∂ f 2∂p=3r f 1− f 2

r=U1

U2

a= 3rr−1

f 2=ap−a∫0

pp 'a−1 f 1p 'dp'


● From shock theorie it follows for the compression ratio

that means for and as for a nonrelativistic plasma

and for in a relativistic plasma

r= 1−1M−2

M∞ =53

r=4⇒a=4⇒N x =∫ 14p '2

f x ,p'dp '~−2

=43

r=7⇒a=3.5⇒N x=∫ 14p'2

f x ,p'dp '~−1.5


● Problem: One doesnt know how the acceleration works on physical grounds

● Answer: Microscopic derivation

II.2 Diffusive shock acceleration● What is the probability for a particle of escaping downstream

towards ?

● What is the probability of crossing the shock front?

probability of not returning

∞

Nesc=nU2

Nuptodown=∫0

1vn d

2=n2v2

⇒

nU2

nv /4=4U2

v


● What is the average momentum gain when crossing the shock front?

pshockfront=p 1U1

v pdownstream=p 1

U1−U2

v

⟨p⟩=p∫0

1[U1−U2

v]2d=

23pU1−U2

v


● In reality p is a random variable, but for v >> U and initial momentum identically

● The probability of crossing the shock front n times is

pn~i=1n p0[1

43

U1−U2

vi]⇒ ln

pnp0~

43U1−U2 i=1

n 1v i

p0

Pn~i=1n1−

4U2

vi⇒ lnPn~−4U2i=1

n 1vi=−3

U2

U1−U2

lnpnp0

⇒Pn=pnp0

−3U2/ U1−U2

=pnp0

−3 /r−1


● With

{

N x.p=∫p∞

4p'2 f x ,p 'dp'

N −∞ , x =

⇒N ∞ , x=U1

U2

N0 pp0

0 pp0N0 pp0


● it follows

N2 pn=PnN p0=U1

U2

pnp0

−3/ r−1

f 2 p=−1

4p2∂N2

∂p=N0

4

3U1

U1−U2

pp0−3r / r−1

=N0

4app0−a


● We again obtain a power law, but unlike other Fermi processes the slope is fixed

● to verify the slope a, we can look at the synchrotron emission if the initial spectum is a power law, the synchrotron spectrum will be a power law with slope

=a−12=0.5


III. Deceleration Mechanisms

● Synchrotron Emission ● Inverse Compton Scattering● proton – proton collision● Bremstrahlung

X X '

X X '

pp'

III.1 Synchrotron Emission

● particles gyrating in the plasma field can emit photons● Synchrotron Loss Time:

● Average Acceleration Time:

sync=6mp ,e

3 c

Tp ,eme2B2

acc=803cU2

r gb−1

r g,maxr g

−1

III.1 Synchrotron Emission

● With acc=sync

⇒max⇒ f max=3⋅10143b

U2

c2Hz

III.2 Inverse Compton Scattering● particles interact with the photonic background● similar as for the sychrotron emission it follows considering both

effects:

where a is the ratio of photonic to magnetic energy density

f max=3⋅10143b

U2

c2 f aHz

III.2 Inverse Compton Scattering

III.3 Other Processes

● 1. proton – proton collision lead to a very fast deceleration2. the probability only gets dominant if the jet for example crosses a gas cloud

● particles emit bremsstrahlung when they cross electric fields

IV Conclusion

● My aim was 1. to present a short overview about the theoretical methods used in jet physics and especially to explain fermi acceleration in a more simple way2. to show where the 2 in the power law spectrum comes from3. to show that there are many things still to be done regarding jets

● My aim for myself was to make a talk about theory interesting, which I found is a hard thing to do and probably will not have worked.. this time


● 3+4 with gives pp'=p 1−Uv

f 1g1= f 2

U1p∂

∂p f 1g13U1g1=U2p

∂

∂pf 2

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Astrophysical Jets from accreting Black Holes€¦ · accreting Black Holes by Max Häberlein. Outline I. Description of astrophysical jets 1. Sources of Jets 2. Formation Mechanism