13. Dispersal of the Protoplanetary Disk Flashcards
How does the star evolve from Class II to III?
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
What is the Class III phase also known as?
Debris disk phase
Which are more emissive at IR wavelengths: dust grains or larger objects?
Dust grains
How do we known lifetimes of dusty disks?
Surveys of SEDs of nearby YSOs and measuring IR excess to infer dust mass
How long do disks take to disappear?
10 - 100 million year
What are the two dust removal mechanisms of the disk we look at?
Radiation pressure
Thomas-Poynting Effect
What is the radiation pressure argument for removal of dust from the dusty disk?
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?
Show the radiation pressure argument for dust removal from the disk
See notes
What is extinction efficiency at optical wavelengths?
~ 1
How does changing luminosity affect the dust particle size removed by radiation pressure?
L increased, increase minimum size of dust grains that can survive
(as radiation pressure stronger with luminosity)
How does changing mass of the star affect the dust particle size removed by radiation pressure?
M increased, decrease minimum size of dust grains that can survive
(M increased increases gravitational well)
Whilst it does happen, what are the issues with the radiation pressure dust removal mechanism?
No radius dependence, affects particles at all radii equally ⇒ cannot explain inside-out clearing
Much faster than observed disk
lifetimes of 10 -100 Myr
Why does Poynting-Robertson effect arise?
Photon travelling at c is seen by grain which orbits at more classical velocity
What is the Poynting-Robertson effect?
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
In the Poynting-Robertson effect, where is the photon path for the stellar vs dust frame of reference?
Stellar: Photon path orthogonal to velocity of dust grain
Dust: Path tilted by small angle -> retarding force
Angle in incidence in Poynting-Robertson effect?
ø = v/c
Derive timescale of Poynting-Robertson effect
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
What effect does the tangential radiation pressure on the grain have on the orbit in the Poynting-Robertson effect?
Grain slows, orbit shrinks
What does the Poynting-Robertson equation show?
Further away dust grain, longer lifetime i.e., clears disk from inside out and smallest grains removed first
Equation for Poynting-Robertson effect?
t = 1400 [(a/µm) (R/au)^2] / (L*/Lº) years
How is equation for Poynting-Robertson effect inconsistent with some observations?
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
What does consistencies with Poynting-Robertson effect and observations imply?
Dust grains lost to star are somehow replenished
How might dust grains be replenished to explain difference in observations and Poynting-Robertson effect?
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))
What happens to the dusty disk from Class II to Class III phase?
Disperses from inside out
What do observations of disk lifetimes of 10-100 Myr imply?
Upper limit for timescale of planet formation
