Dispersal of the Protoplanetary Disk

Question 1

What happens as stars move towards the main sequence?

Answer 1

• major accretion and outflows have ended

- remnant (debris) disk around the young star

Question 2

What happens as a star evolves?

Answer 2

• inner region of the disk disappears first
• disk loses dust and becomes fainter overtime
• cool, black body hence a weaker emitter

Question 3

Lifetime of the Dusty Disk

Answer 3

• using measurements of infra-red ‘excess’, it can be deduced that disks disappear after 10-100 million years
• as the disk is only around for ~10 million years, planets must form on this timescale

Question 4

Momentum of a Photon

Answer 4

p = E/c

Question 5

List two dust removal mechanisms

Answer 5

• radiation pressure

- Poynting-Robertson effect

Question 6

Dust Removal - Radiation Pressure

Force on a Dust Particle from Radiation

Answer 6

Fr = (flux of radiation / c) * projected area of a dust particle
Fr = Qoptπa²L*/4πr²c
-where Qopt is the extinction at optical wavelength, ~1 and a is the dust grain radius

Question 7

Dust Removal - Radiation Pressure

Force on a Dust Particle due to Gravity

Answer 7

Fg = GMm/r² = 4/3 πa³ρGM/r²

-where ρ is the bulk density of the dust grain material

Question 8

Dust Removal - Radiation Pressure

Blow-Out

Answer 8

-consider the balance of radiation and gravitational force on a dust grain
-if Fr>Fg, the grain will be blown out
-this process doesn’t depend on r at all:
a = 0.3 L(L☉)/M(M☉) μm
-dust particles ≤1μm will be blown out of a solar-like system, this is a very fast process, ~10^4yr

Question 9

What are the issues with radiation pressure for explaining dust removal?

Answer 9

• the equation has no dependence on radius, it affects particles at all radii equally so cannot explain inside-out clearing
• the process is much faster than observed disk lifetimes of 10-100Myr

Question 10

Dust Removal - Poyting-Robertson Effect

Relativistic Effects

Answer 10

-for a particle with Fr<

Question 11

Dust Removal - Poyting-Robertson Effect

Rate of Change of Angular Momentum

Answer 11

-there is a tangential radiation pressure on the grain:
p = v/c pphot = vE/c²
-angular momentum:
L = mwr² = mvr
-rate of change of angular momentum:
dL/dt ∝ L/r²

Question 12

Dust Removal - Poynting-Robertson Effect

Description

Answer 12

• the dust grain due to the relativistic effect is experiencing a small retarding force so is loosing angular momentum
• we are ultimately interested in how long it takes for the dust grain to spiral into the centre of the star

Question 13

Dust Removal - Poynting-Robertson Effect

Time

Answer 13

t = 1/2 R² 2mc²/L*a²
= 1400 (a/μm)(R/AU)²/(L*/L☉) yr
-time is proportional:
t ∝ aR²/L*
-Poynting-Robertson effect clears the disk from the inside out and the smallest grains first

Question 14

What are the problems with the Poytning-Robertson effect?

Answer 14

• it is inconsistent with some observations
• micron wavelength emission comes from micron-sized grains, too large, too cold grains otherwise
• fits imply disk sizes of the order of ~100au
• while few images actually show disks ~100au and smaller
• this implies that dust grains lost to the star are somehow replenished

Question 15

How are dust grains replenished?

Answer 15

• best explanation is colliding asteroid, planetesimals etc. breaking down into smaller material
• there is evidence for this in the solar system (E.g. craters in th moon)