Astrophysical fluid dynamics
Part III Mathematics 2015–16
24 lectures
gio10@cam
Introductory lecture M. W. F. 9
Professor Gordon Ogilvie DAMTP F1.02
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
Lecture materials, including extended notes in preparation:http://www.damtp.cam.ac.uk/user/gio10/afd.html
Revision class (based on past Tripos questions):● Thursday 12 May, 15:00–16:30, MR11
Seminars that may be of interest
DAMTP Astrophysics seminars:● Mondays at 16:00 in MR14
IoA colloquia:● Thursdays at 16:00 in the Sackler Lecture Theatre, IoA
DAMTP Fluid Mechanics seminars:● Fridays at 16:00 in MR2
All listings at http://www.talks.cam.ac.uk
● Tuesdays at 13:00 in MR14
Centre for Exoplanet Research seminars:● Wednesdays at 16:00 in the Ryle Seminar Room, Kavli Institute
Theoretical varieties of AFD
Basic models:
HDNewtonian gas dynamicsnon-relativisticcompressibleideal (inviscid, adiabatic)self-gravitatingperfect gas (usually)
MHD + magnetic fieldideal (perfectly conducting)
Theoretical varieties of AFD
Extensions (beyond this course):● Dissipative fluid (viscosity, thermal conduction, resistivity)
● Chemistry (equation of state, composition, reactions / ionization)● Radiation (various possible treatments)● Relativity
● Plasma physics / multifluid MHD / Hall effect / ambipolar diffusion
Theoretical varieties of AFD
HDMHDRHDRMHDGRHDGRMHDGRRHD...etc.
hydrodynamics
magnetohydrodynamics
radiation hydrodynamics
radiation magnetohydrodynamics
general relativistichydrodynamics
magnetohydrodynamicsgeneral relativistic
general relativisticradiation magnetohydrodynamicsGRRMHDgeneral relativisticradiation hydrodynamics
Examples of observations
Examples of numerical simulations
Useful data (in CGS units)
AU = 1.496� 1013 cm
pc = 3.086� 1018 cm
● Astronomical unit● Parsec
● Solar radius
● Newton’s constant
● Solar mass
● Boltzmann’s constant
● Speed of light● Stefan’s constant
● Solar luminosity
G = 6.674⇥ 10�8 cm3 g�1 s�2
M� = 1.989⇥ 1033 g
L� = 3.846⇥ 1033 erg s�1
R� = 6.955⇥ 1010 cm
k = 1.381⇥ 10�16 ergK�1
Joule / erg conversion: J = 107 erg
� = 5.670⇥ 10�5 erg cm�2 s�1 K�4
● Proton mass mp = 1.673⇥ 10�24 g
c = 2.998⇥ 1010 cm s�1
Some typical numbers (order-of-magnitude estimates)
● Solar-type star:⇢ ⇠ 102 g cm�3, T ⇠ 107 K
photosphere ⇢ ⇠ 10�7 g cm�3, T ⇠ 104 K
corona ⇢ ⇠ 10�15 g cm�3, T ⇠ 106 K
molecular clouds n ⇠ 103 cm�3, T ⇠ 10K
cold medium (neutral) n ⇠ 10� 100 cm�3, T ⇠ 102 K
warm medium (neutral/ionized) n ⇠ 0.1� 1 cm�3, T ⇠ 104 K
hot medium (ionized) n ⇠ 10�3 � 10�2 cm�3, T ⇠ 106 K
centre
● Interstellar medium:
⇢ n(mass density , number density )
Validity of a fluid approach
Equations of HD and MHD are derived under the assumption of smalldepartures from a local Maxwellian velocity distribution of particles
A fluid approach is valid provided that:
mean free path
mean flight time
of particlesbetween collisions
⌧ ⌧ T
� ⌧ L
Collisions tend to produce a local Maxwellian distribution, whilegradients tend to produce departures
characteristic time-scale
characteristic length-scale
of the fluid flow
Estimates: (collisional cross-section )� =1
n�, ⌧ ⇠ �
v̄, v̄ ⇠
rkT
m�