physical processes in astrophysics - desyhyan/lectures/lect1_fall16.pdf · physical processes in...
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Reference Books:
� Plasma Physics for Astrophysics, Russell M. Kulsrud (2005) � The Physics of Astrophysics, Frank H. Shu (1991) � Physical Processes in the Interstellar Medium, Lyman Spitzer (1978) � The Physics of Fluids and Plasmas, Arnab Raichoudhuri,
(1998) � Plasma Physics, Peter A. Sturrock (1994)
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Outline 1. Interstellar medium: components, phases, interconnection 2. Particle motions 3. Basic MHD 4. Nonlinear Phenomena: Turbulence in magnetized fluids 5. Interaction of high energy particles with turbulent magnetic field 6. Origin of high energy particles 7. Magnetic reconnection 8. Particle acceleration processes in astrophysics 9. Galactic cosmic rays and supernova remnants 10. Magnetohydrodynamic (MHD) processes in star formation 11. Relation to intergalactic media, ϒ ray burst 12. Confronting theory with observations, future perspective
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Lecture I: Interstellar medium: components, phases, interconnection
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90% of the visible matter in the Universe is in plasma state (dilute gas of ions, electrons, atoms, and molecules).
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Interstellar medium: components, phases, interconnection Idealized phases: � Corona gas, f ~ 0.4, T, n~0.003cm-3, shock heated Observed: X ray emission, UV absorption � HII region, f~0.1, T~10^4K, ncm-3
Heated and ionized by photons Observed: optical, radio, UV absorption � HI, f~0.5, warm, T~6000K, n~0.3 cool
Coronal gas
H II region H I region warm cool
Diffuse H2 region
Dense H2
Stellar outflows
f 0.4 0.1 0.5 0.02 0.01 0.0005
T (K) >3x105 104 6000 100 60 10-100
n (cm-3) 0.003 ~0.3-104 0.3 30 20-100 100-106 2(M/10-6M¤yr)(10km s-1/Vwind)
cooling Expansion, X ray emission
Optical lines FIR ([CII] 157μm)
FIR emission [C II]
FIR emission
observed X ray emission, UV absorption lines
Optical, Radio (thermal) continuum, UV absorption lines
HI 21cm Optical & UV absorption lines
HI 21cm, CO 2.6mm, Optical & UV absorption lines
CO 2.6mmm emission, Dust FIR
Radio (HI & CO) Dust FIR emission, optical absorption 6
Magnetic field � Typical interstellar value ~ 3x10-6G, comparable to other form of energies, thermal, turbulence, cosmic rays, etc. � Origin: dynamo (?) � Interacts with: cosmic rays, plasma, partially ionized gas Functions: 1. Glue the components together 2. Influence propagation of polarized radiation 3. Accelerates and scatters cosmic rays 4. Supports clouds against collapse 5. Redistributes angular momentum when a rotating
cloud collapses Relevant to
star formation
{
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Cosmic rays � Accelerated charged particles (1011eV -1019eV) � Coming isotropically
� A number of acceleration mechanisms exist. Most efficient- First order Fermi acceleration in strong shocks and magnetic reconnections.
Galaxy
Halo of cosmic rays + magnetic field
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Matter balance
Intergalactic matter
ISM 5x109M¤
stars
Infall~1M¤yr-1 Star formation 3-10M¤yr-1
Galactic wind? ~ 1M¤yr-1 Stellar ejecta
Energy balance
Extragalactic background
ISM Stars
photons
Cosmic rays
radiation
outflows
Self gravity
Radiative cooling Cold sky
Complex structure of the ISM stems from these energy flows
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Plasma (Levels 0 and 1 same as above)
Level Description of State Dynamical equations
2: Distribution Function 2.5: Two-fluid model 3: One-fluid model
f(x, v, t) ρ(x), T(x), v(x), B(x)
Vlasov eqn. MHD eqn.
Neutral fluids
Level Description of State Dynamical equations
0: N quantum particles 1: N classical particles 2: Distribution Function 3: Continuum (of fluid cells)
ψ(x1, …, xN) (x1…, xN, v1, …, vN) f(x, v, t) ρ(x), T(x), v(x)
Schrödinger eqn. Newton’s Laws Boltzmann eqn. Hydrodynamic eqns.
� =h
p' hp
mkBT,
hn1/3
pmkBT
de Broglie wavelength
>> 1 Quantum memchanical << 1 classical
Ehrenfest’s Theorem
Why can E be ignored?
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Basic properties of plasma
Debye length
�(r) =Q
rexp(�r/�D)
� Saha equation for ionization:
only applies in thermodynamic equilibrium! H II region, e.g., is completely ionized by UV photons!
x
2
x� 1
=
(2⇡me)3/2
(kBT )5/2
h
3pgas
exp(� �
kBT)
Derive it �D =
skBT
4⇡nq2
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Different Plasma systems
Plasma parameter
< 1 for plasma
g ⌘ 1
n�3D
=(4⇡)3/2n1/2e3
(kBT )3/2
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Lecture III: Particle motions
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Motion in uniform B field Motion of individual particles is primarily controlled by magnetic field Important concept: pitch angle, guiding center
� Ions’ motion about B is clockwise � electrons’ motion about B is anticlockwise
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Motion in a nonuniform B field � Gradient drift
Magnetic moment (right hand grip rule） For Larmor motion,
vD ⇡ ⇢
Lvth
Only depends on energy, no q or m
dependence
µ ⌘ ~IS =1
2qr⇥ v
Plasma is diagmagnetic!
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~µ ⌘ �W?B
b̂
~µ
Potential energy Force To balance this force with qvDB/c, again is needed! Similarly, external forces also produce the drift in the same fashion! General expression
U ⌘ �~µ ·B
vD ⇡ ⇢
Lvth
vD = cF⇥B
qB2
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F = �rU = r(~µ ·B)
Curvature drift
Figure 2.5: Curvature and Centrifugal Force
Take |B| constant; radius of curvature Re.
To 1st order the particle just spirals along the field.
In the frame of the guiding center a force appears because the plasma is rotating about the center ofcurvature.
This centrifugal force is Fcf
Fcf = mv||
2
Rc pointing outward (2.38)
as a vector
Fcf = m v||2Rc
Rc2
(2.39)
[There is also a coriolis force 2m(ω ∧v) but this averages to zero over a gyroperiod.]
Use the previous formula for a force
vd = 1qFcf ∧B
B2 =
m v||2
q B2
Rc ∧B
Rc2
(2.40)
This is the "Curvature Drift".
It is often convenient to have this expressed in terms of the field gradients. So we relate Rc to ∇B etc. asfollows:
Figure 2.6: Differential expression of curvature
(Carets denote unit vectors)
From the diagram
db =^b 2 −
^b 1 = −
^R c α (2.41)
and
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1st adiabatic invariant
� magnetic momentμ (assignment: please use the force exerted by the to prove) Requirement:
Application: magnetic mirror, sin2θC=B/Bmax
rBk
|Tc
B· @B@t
| ⌧ 1, |Rc ·rB
B| ⌧ 1
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Formation of the Van Allen belt
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Cool solar corona
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2nd adiabatic invariant & Fermi acceleration
Magnetic “clouds”
Fermi (1949)
Requirement: Much more stringent than the condition for the 1st adiabatic invariant!
|Tl
B· @B@t
| ⌧ 1
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