13. Dispersal of the Protoplanetary Disk

Question 1

How does the star evolve from Class II to III?

Answer 1

Major accretion and
outflows have ended

Remnant (debris) disk
around the young star

As the star evolves:
➡ Inner region of the disk disappears
➡ Disk loses dust and
becomes fainter
➡ Cool black body; hence a weaker emitter

Question 2

What is the Class III phase also known as?

Answer 2

Debris disk phase

Question 3

Which are more emissive at IR wavelengths: dust grains or larger objects?

Answer 3

Dust grains

Question 4

How do we known lifetimes of dusty disks?

Answer 4

Surveys of SEDs of nearby YSOs and measuring IR excess to infer dust mass

Question 5

How long do disks take to disappear?

Answer 5

10 - 100 million year

Question 6

What are the two dust removal mechanisms of the disk we look at?

Answer 6

Radiation pressure

Thomas-Poynting Effect

Question 7

What is the radiation pressure argument for removal of dust from the dusty disk?

Answer 7

Photon momentum p = E/c

Force on dust particle from radiation = (Flux of radiation / c) * Projected area of dust particle

FR > FG, particle blown away

rearrange for a - what size dust grains do we lose for a given system?

Question 8

Show the radiation pressure argument for dust removal from the disk

Answer 8

See notes

Question 9

What is extinction efficiency at optical wavelengths?

Answer 9

~ 1

Question 10

How does changing luminosity affect the dust particle size removed by radiation pressure?

Answer 10

L increased, increase minimum size of dust grains that can survive

(as radiation pressure stronger with luminosity)

Question 11

How does changing mass of the star affect the dust particle size removed by radiation pressure?

Answer 11

M increased, decrease minimum size of dust grains that can survive

(M increased increases gravitational well)

Question 12

Whilst it does happen, what are the issues with the radiation pressure dust removal mechanism?

Answer 12

No radius dependence, affects particles at all radii equally ⇒ cannot explain inside-out clearing

Much faster than observed disk
lifetimes of 10 -100 Myr

Question 13

Why does Poynting-Robertson effect arise?

Answer 13

Photon travelling at c is seen by grain which orbits at more classical velocity

Question 14

What is the Poynting-Robertson effect?

Answer 14

For a particle with FR«FG

A dust grain being hit by a (relativistic) photon sees radiation from the star to be coming from slightly in front of it

Question 15

In the Poynting-Robertson effect, where is the photon path for the stellar vs dust frame of reference?

Answer 15

Stellar: Photon path orthogonal to velocity of dust grain

Dust: Path tilted by small angle -> retarding force

Question 16

Angle in incidence in Poynting-Robertson effect?

Answer 16

ø = v/c

Question 17

Derive timescale of Poynting-Robertson effect

Answer 17

See notes

[Tangential radiation pressure on grain: p=v/cp_photon=v/cE/c

v slows, orbit shrinks

L = mΩr^2 = mvr find out how much L lost by grain due to force

Energy falling onto grain dE/dt

dL/dt (use chain rule)

Integrate R to = for time

Question 18

What effect does the tangential radiation pressure on the grain have on the orbit in the Poynting-Robertson effect?

Answer 18

Grain slows, orbit shrinks

Question 19

What does the Poynting-Robertson equation show?

Answer 19

Further away dust grain, longer lifetime i.e., clears disk from inside out and smallest grains removed first

Question 20

Equation for Poynting-Robertson effect?

Answer 20

t = 1400 [(a/µm) (R/au)^2] / (L*/Lº) years

Question 21

How is equation for Poynting-Robertson effect inconsistent with some observations?

Answer 21

Micron wavelength emission comes from micron-sized grains,
need too large, too cold grains otherwise

Fits imply disk sizes of the order of ~ 100 au

While (few) images indeed show disks ~ 100 au and smaller

Question 22

What does consistencies with Poynting-Robertson effect and observations imply?

Answer 22

Dust grains lost to star are somehow replenished

Question 23

How might dust grains be replenished to explain difference in observations and Poynting-Robertson effect?

Answer 23

Best explanation is colliding asteroids, planetesimals, etc.

(Evidence for this in the Solar System (e.g., moon
craters during late heavy bombardment period, < 500 Myr))

Question 24

What happens to the dusty disk from Class II to Class III phase?

Answer 24

Disperses from inside out

Question 25

What do observations of disk lifetimes of 10-100 Myr imply?

Answer 25

Upper limit for timescale of planet formation