Introductory lecture

Astrophysical fluid dynamics
Introductory lecture
Professor Gordon Ogilvie
Part III Mathematics 2015–16
24 lectures
M. W. F. 9
DAMTP F1.02
gio10@cam
Provisional synopsis
● Overview of astrophysical fluid dynamics and its applications
● Equations of ideal gas dynamics and MHD
● Physical interpretation of MHD
● Conservation laws, symmetries and hyperbolic structure
● Stress tensor and virial theorem
● Linear waves in homogeneous media
● Nonlinear waves, shocks and other discontinuities
● Spherically symmetric steady flows: stellar winds and accretion
● Axisymmetric rotating magnetized flows: astrophysical jets
● Stellar oscillations: introduction to asteroseismology and tides
● Local dispersion relation
● Internal waves and instabilities in stratified rotating bodies
Practical arrangements
Lectures:
● Mondays, Wednesdays and Fridays at 9:00 in MR11
Example classes (based on four example sheets):
● 1. Thursday 29 October, 14:00–15:30, MR11
● 2. Thursday 19 November, 14:00–15:30, MR11
● 3. Thursday 3 December, 14:00–15:30, MR11
● 4. Thursday 14 January, 14:00–15:30, MR15
Revision class (based on past Tripos questions):
● Thursday 12 May, 15:00–16:30, MR11
Lecture materials, including extended notes in preparation:
http://www.damtp.cam.ac.uk/user/gio10/afd.html
Seminars that may be of interest
DAMTP Astrophysics seminars:
● Mondays at 16:00 in MR14
● Tuesdays at 13:00 in MR14
DAMTP Fluid Mechanics seminars:
● Fridays at 16:00 in MR2
IoA colloquia:
● Thursdays at 16:00 in the Sackler Lecture Theatre, IoA
Centre for Exoplanet Research seminars:
● Wednesdays at 16:00 in the Ryle Seminar Room, Kavli Institute
All listings at http://www.talks.cam.ac.uk
Theoretical varieties of AFD
Basic models:
HD
Newtonian gas dynamics
non-relativistic
compressible
ideal (inviscid, adiabatic)
self-gravitating
perfect gas (usually)
MHD
+ magnetic field
ideal (perfectly conducting)
Theoretical varieties of AFD
Extensions (beyond this course):
● Dissipative fluid (viscosity, thermal conduction, resistivity)
● Plasma physics / multifluid MHD / Hall effect / ambipolar diffusion
● Chemistry (equation of state, composition, reactions / ionization)
● Radiation (various possible treatments)
● Relativity
Theoretical varieties of AFD
HD
MHD
RHD
RMHD
GRHD
GRMHD
GRRHD
GRRMHD
...etc.
hydrodynamics
magnetohydrodynamics
radiation hydrodynamics
radiation magnetohydrodynamics
general relativistic
hydrodynamics
general relativistic
magnetohydrodynamics
general relativistic
radiation hydrodynamics
general relativistic
radiation magnetohydrodynamics
Examples of observations
Examples of numerical simulations
Useful data (in CGS units)
● Newton’s constant
● Boltzmann’s constant
● Stefan’s constant
● Speed of light
G = 6.674 ⇥ 10
8
= 5.670 ⇥ 10
5
k = 1.381 ⇥ 10
3
cm g
16
1
erg cm
2
c = 2.998 ⇥ 1010 cm s
24
● Proton mass
● Solar mass
M = 1.989 ⇥ 1033 g
● Solar luminosity
● Parsec
● Astronomical unit
Joule / erg conversion:
L = 3.846 ⇥ 1033 erg s
pc = 3.086
1018 cm
AU = 1.496
1013 cm
J = 10 erg
1
g
R = 6.955 ⇥ 1010 cm
7
s
erg K
mp = 1.673 ⇥ 10
● Solar radius
1
1
s
2
1
K
4
Some typical numbers (order-of-magnitude estimates)
● Solar-type star:
centre
photosphere
corona
⇢ ⇠ 102 g cm
⇢ ⇠ 10
⇢ ⇠ 10
7
3
g cm
15
, T ⇠ 107 K
3
, T ⇠ 104 K
3
g cm
, T ⇠ 106 K
● Interstellar medium:
molecular clouds
cold medium (neutral)
warm medium (neutral/ionized)
hot medium (ionized)
n ⇠ 103 cm
n ⇠ 10
n ⇠ 0.1
n ⇠ 10
3
, T ⇠ 10 K
100 cm
3
1 cm
3
10
2
(mass density ⇢ , number density n )
3
, T ⇠ 102 K
, T ⇠ 104 K
cm
3
, T ⇠ 106 K
Validity of a fluid approach
Equations of HD and MHD are derived under the assumption of small
departures from a local Maxwellian velocity distribution of particles
Collisions tend to produce a local Maxwellian distribution, while
gradients tend to produce departures
A fluid approach is valid provided that:
characteristic time-scale
mean flight time
of particles
between collisions
⌧ ⌧T
⌧L
characteristic length-scale
mean free path
Estimates:
1
=
, ⌧ ⇠ , v̄ ⇠
n
v̄
of the fluid flow
r
kT
m
(collisional cross-section
)