Huirong Yan

Uni Potsdam & Desy

Email: huirong.yan@desy.de

Physical Processes in Astrophysics

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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) �  Order of Magnitude Physics, Peter Goldreich (1999)

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Outline 1.  Interstellar medium: components, phases, interconnection 2.  Dimensional Analysis, diffusivity and viscosity 3.  Motion of particles 4.  Basic MHD 5.  MHD waves, instabilities 6.  Magnetic topology, reconnection 7.  Nonlinear Phenomena: Turbulence in magnetized fluids 8.  Interaction of high energy particles with turbulent magnetic field 9.  Origin of high energy particles   10.  Particle acceleration processes in astrophysics 11.  Galactic cosmic rays and supernova remnants 12.  Magnetohydrodynamic (MHD) processes in star formation 13.  ϒ ray burst  

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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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30 2 Definition of the Plasma State

to distinguish the electron and ion gas by individual densities, ne and ni. Moreover,plasmas are often in a non-equilibrium state with different temperatures, Te andTi of electrons and ions. Such two-temperature plasmas are typically found in gasdischarges. The solar plasma (in the interior and photosphere), on the other hand, isa good example for an isothermal plasma with Te = Ti.

Plasmas exist in an environment that provides for a large number of ionizationprocesses of atoms. These can be photoionization by an intense source of ultra-violet radiation or collisional ionization by energetic electrons. Impact ionization isthe dominant process in gas discharges because of the ample supply of energeticelectrons. Photoionization is found in space plasmas where the electron and atomdensities are low but a large number of ultraviolet (UV) photons may be present.These processes and their reciprocal processes can be written in terms of simplereaction equations, as summarized in Table2.1.

Besides recombination by these volume processes, electrons and ions can effec-tively recombine at surfaces, which may be the walls of discharges or embeddedmicroparticles. In thermodynamic equilibrium, each of these volume processes isbalanced by the corresponding reciprocal process (i.e., photoionization and two-body recombination, or impact ionization and three-body recombination.) Becausethe ionization energy of neutral atoms lies between 3 and 25eV, plasmas produced byimpact ionization typically exist at high temperatures. Photoionized plasmas requireshort wavelength radiation, typically in the UV region. There are also situations, inhot and dilute plasmas, where collisional ionization is efficient but electrons are toofew for three-body recombination. Then, a steady state can be reached, in which two-body recombination balances the impact ionization. The solar corona is an examplefor such a plasma that is in a non-thermodynamic equilibrium.

As a final remark, it is worth mentioning that some plasmas are not governed bylocal equilibria but by non-local processes. The properties of the solar wind at theEarth orbit, for example, are mostly determined by the emission process at the Sun’ssurface and by heating processes (e.g., shocks) during the propagation from Sun toEarth. We will see in Chap.11 that a negative glow is also produced by electrons thathave gained their energy at a different place.

Table 2.1 Ionization andrecombination processes

e+ A → A+ + 2e Collisional ionization

hν + A → A+ + e Photoionization

A+ + 2e → A + e Three-body recombination

A+ + e → A + hν Two-body recombination

Ionization can be as low as 0.01%!

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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 (? Galactic rotation? Turbulence?) �  Interacts with: cosmic rays, plasma (incl. 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

EGCRs

Radiation, GCRs

outflows

Self gravity

Radiative cooling Cold sky

Complex structure of the ISM stems from these energy flows

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The Milky Way “Haze” in radio (CSIRO)

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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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Is there any system always

on level 0?

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 and Saha eq. doesn’t apply!

x2

x� 1=

(2⇡me)3/2(kBT )5/2

h3pgasexp(� �

kBT)

Derive it �D =

skBT

4⇡nq2

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Different Plasma systems

Within Debye length, particles interact collectively. Plasma parameter < 1 for plasma

Interaction amongst particles is weaker, but a large number of them interact simultaneously

g ⌘ 1

n�3D

=(4⇡)3/2n1/2e3

(kBT )3/2

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< P.E. >

< K.E. >⇡ e2n1/3

kBT/ g2/3

For a pair of nearby particles

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Dimensional Analysis w. Example fluid viscosity

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Buckingham Pi Theorem: A system described by n variables, built from r independent dimensions, is described by n-r independent dimensionless groups

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A.1 Basic concepts A.1.1 Thermal diffusivity of liquids and solids

In solids, heat is carried by vibrational waves, or phonons; the heat diffusion is therefore diffusion of phonons.

Random walk

The time for traveling a distance L is ⌧ ⇠ L2

��cs

= L2

�cs

= 13�cs

physical parameter determined by the properties of the substance, thermal diffusivity

L =pN�

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A.2.2 Diffusivity and viscosity of gas

• Diffusivity ϰ: Heat is carried by gas molecules rather than sound waves

For air at room temperature, thus

• viscosity �: momentum diffusion coefficient Prandtl number

=13�v,

� ⇠ 1/(n�)

� ⇠ a2, a ⇠ 3A, n ⇠ 3⇥ 1019cm�3, v ⇠ 3⇥ 104cm/s

⇠ 13

3·104cm/s3·1019cm�3⇥10�15cm2 ⇠ 0.3cm2/s

Pr ⌘ ⌫

Molecular motion dominates both momentum and energy transfer, and therefore Pr is ∼ 1, but can be very different in other cases (eg., w. diffusion of magnetic field).