dynamics of astrophysical discs - damtp

Dynamics of Astrophysical Discs

Henrik Lattere-mail: hl278@cam.ac.uk

16 lectures, 3 example classes

http://www.damtp.cam.ac.uk/user/hl278/DAD.html

Course Outline

• Introduction: Discs in the Universe

• Orbital dynamics

• Viscous accretion discs

• Vertical disc structure

• Local disc models (shearing sheet)

• Inertial waves, vortices, particles

• Density waves and gravitational instability

• Planet-disc interactions

• Magneto-rotational instability (MRI)

16 lecturesTu. Th. 10

Office: F1.19hl278@cam.

ac.uk

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• Usually circular, thin

• Usually Keplerian

• Celestial mechanics

• Fluid mechanics

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• Usually circular, thin

• Usually Keplerian

• Celestial mechanics

• Fluid mechanics

• It accretes!

Angular momentum

Mass

Discs in the Universe

Discs in the Universe

Discs in the Universe

Discs in the Universe

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Discs come in different sizes:

• Galactic discs: ~1020 m (~10000 ly)• AGN disc: ~1014 m (~1000 AU)• Protoplanetary disc: ~1013 m (~100 AU)• X-ray binary star: ~109 m (~R⊙)• Planetary ring: ~108 m (~R�)

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Discs have different compositions:

• Galactic discs: stars, gas, dark matter • Protoplanetary disc: weakly ionised gas, solids

• X-ray binary star: dense H/ He plasma

• Planetary ring: metre-sized iceballs

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Relevant descriptions:

•Gravitational collisionless dynamics (stars, dark matter, solids)•Gas dynamics (neutral, ideal gas)•Magnetohydrodynamics (ionised, ideal gas)•Kinetic theory (low density gas, particle gas)

+ relativity, radiation forces where needed

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: Saturn’s rings

Galileo (1610): “I have seen the most distant planet to have a triple

form”

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: Saturn’s rings

Huygens (1656): “It is surrounded by a thin flat ring, nowhere touching, and

inclined to the ecliptic”

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: Saturn’s rings

Cassini spacecraft (2004 - )Moons creating structure

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: protoplanetary discs

Jets: evidence for accretionGaps, possibly by satellites

PP disks: Gaps

(HL Tauri)

H Latter Discs in the Universe

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: binary star discs

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: Dwarf Novae

Luminosity variability (orbital time)

IY UMa

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: Dwarf Novae

Outbursts (days-weeks)

SS Aur

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: X-ray binaries

Complicated variability

Cyg X-1

1996 2008

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: AGN & galactic discs

Active galaxies: jets, accretion onto supermassive black holes

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Observations: Galactic discs

Spiral density waves, gravitational instability

Messier 101

Discs in the Universe

•Disc-like structures are ubiquitous•Are long-lived (many orbits)•Evidence for accretion•Observations of waves•Perturbations by satellites

Discs in the Universe

•Disc-like structures are ubiquitous•Are long-lived (many orbits)•Evidence for accretion•Observations of waves•Perturbations by satellites

•Implicated in •star formation•planet formation •galactic structure•ICM structure (AGN feedback)

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Formation:

•Consequence of angular momentum conservation•Disc is much smaller than original structure•Example: collapse of molecular cloud

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Formation:

•Molecular cloud (1018 m) collapses to disc (1013 m)•Material speeds up•Has to become flatter

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Formation:

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Formation:

slowly rotating

rapidly rotating centrifugallysupported

Gravitationalforce

Centrifugal force

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

Formation:

•Orbital ang. mom. binary much larger than ang. mom. gas close to black hole

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

•Discs are all about angular momentum•Ubiquity of disks because of

•gravitational collapse (accretion) •Angular momentum conservation

•Subsequent accretion because of transport (how?)•Importance of instabilities and turbulence

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• Discs are strange objects

• Balance between gravity and centrifugal force

• Circular velocity increases towards center

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• Consider circular orbits only

• 2 spaceships on same orbit

• What do I have to do to overtake?

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• Breaking = accelerating (!)

• All because of balance between gravity and centrifugal force

• Energy of acceleration is more than compensated for by climbing out of potential well of star

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• Breaking = accelerating

• Bonus question: what if the spaceships are connected by a spring?

• Related to MHD turbulence in discs...

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• What is the structure of astrophysical discs?

• How do they evolve?

• What is driving accretion?

• What happens to embedded objects? (particles, moons, planets, black holes)

Main questions:

Discs in the Universe

Disc: (continuous) medium in orbit around a massive central body

• Beautiful Cassini images (www.ciclops.org)

• Formation of extrasolar planets

• Quasars: most distant galaxies

Discs are “hot”:

Course Outline

• Introduction: Discs in the Universe

• Orbital dynamics

• Viscous accretion discs

• Vertical disc structure

• Local disc models (shearing sheet)

• Inertial waves, vortices, particles

• Density waves and gravitational instability

• Planet-disc interactions

• Magneto-rotational instability (MRI)

16 lecturesTu. Th. 10

Office: F1.19hl278@cam.

ac.uk