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PHYS3281 Star and Planet Formation > Accretion Disks > Flashcards

Accretion Disks Flashcards

disk properties, observational evidence for disks around young stars, direct imaging, infrared spectra

1
Q

Basic Facts About Accretion Disks

A
  • material falling onto a protostar will have substantial angular momentum, as a consequence, an accretion disk forms
  • accretion disks are modelled as geometrically thin, H
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2
Q

Keplerian Azimuthal Velocity

A

vφ = √[GM*/R] ∝ R^(-1/2)

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3
Q

Why are they called ‘accretion disks’?

A

-the protostar is fed material from the collapsing envelope through the accretion disk

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4
Q

Accretion Disks and Viscosity

A
  • viscosity in the disk causes:
  • -mass transfer inwards
  • -angular momentum transfer outwards
  • the exact mechanism behind this viscosity is unknown but the two best candidates are:
  • -turbulence
  • -magnetic fields
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5
Q

Viscous Evolution of a Ring in the Accretion Disk over Time

A
  • considering a plot of ~disk surface density against radius
  • as time passes, the peak moves inwards as there is more mass closer to the centre
  • the curve flattens
  • some mass moves inwards feeding the star and some moves outwards transferring angular momentum
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6
Q

How can we observe accretion disks?

A

-accretion disks around young stars can be observed directly (via imaging) or indirectly (via excess emission at infrared wavelengths)

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7
Q

Alternative Names for Accretion Disks

A
  • accretion disks
  • circumstellar disks
  • protoplanetary disks (usually used for latter stages after envelope is gone)
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8
Q

Direct Evidence for Accretion Disks

A
  • spatially-resolved thermal emission from dust grains
  • spatially- and/or spectrally-resolved molecular line emission
  • reflected/scattered light
  • in silhouette against bright nebular background
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9
Q

Observational Evidence for Accretion Disks

Spatially Resolved Thermal Emission

A
  • for a disk ~100AU, sub arc-second resolution is required
  • only radiation right at the centre is hot enough to see in optical and IR
  • the rest is cooler and therefore invisible at these wavelengths, it emits at radio and sub-mm
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10
Q

Observational Evidence for Accretion Disks

Spectrally-Resolved Molecular Lines

A
  • exploitation of knowledge of Keplerian rotation can reveal orbiting molecular disks via double-peaked lin profile
  • if the disk is tilted to the line of sight then it appears as an ellipse shape
  • as it is rotating, material on one side is moving away and therefore red-shifted, material on the other side is moving towards us and therefore blue-shifted
  • so there are two peaks in the spectrum, the blue-shifted peak and the red-shifted peak
  • the smaller the angle that the disk is inclined at, the closer the distance between the two peaks
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11
Q

Observational Evidence for Accretion Disks

Spatially-Resolved Molecular Lines

A
  • ALMA has enabled a huge step forward in spatial resolution, ~10-100AU in the nearest protoplanetary disks
  • spatially-resolved molecular line emission give us position-position-velocity information
  • we can also inspect the channel-by-channel image, i.e. the positons of material moving at a certain velocity
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12
Q

Observational Evidence for Accretion Disks

Reflected/Scattered Light

A
  • HST near-IR images revealed the first resolved disks in reflected light, i.e. a face down view of the disk
  • modern optical/near IR telescopes now employ coronagraphs to see scattered starlight from the disk
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13
Q

Observational Evidence for Accretion Disks

Disks in Silhouette

A

-HST also observed disks in silhouette against bright nebula

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14
Q

Indirect Evidence for Accretion Disks

SEDs

A

-the presence of dusty disks (and/or envelopes) around young stars can also be inferred indirectly via measurement of the spectral energy distributions (SEDs)

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15
Q

Accretion Disk Spectrum

Etot

A

-consider an annulus of material in the disk of mass dm at radius r in a disk of mass M and radius R
-the total energy is the sum of kinetic and potential energies
Etot = - 1/2 * GMdm/r

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16
Q

Accretion Disk Spectrum

Rate of Change of Energy

A

dE/dt ~ GMM’/2r² dr

  • where M’=dm/dt is the mass accretion rate
  • assume all energy goes into radiation
17
Q

Accretion Disk Spectrum

Dependence of T on r

A

T = (GMM’/8πσr³)^(1/4)
-so
T ∝ r^(-3/4)
-hotter closer to the centre

18
Q

Accretion Disk Spectrum

Graph

A
  • the emergent disk spectrum can be seen as the sum of a number of blackbody spectra, each with a temperature corresponding to the temperature of a ring at a distance R form the star, i.e. summing over multiple annuli
  • stetches from mm to optical/UV with peak in IR
19
Q

What makes the accretion disk spectrum shallower?

A

-caused by heating from a host star

20
Q

What makes the accretion disk spectrum steeper?

A
  • mass is accreting through the disk to the star so over time the mass of the disk is decreasing over time
  • the primary heat source is then the host star
21
Q

Emission from Surrounding Dust Clouds / Envelope

Description

A
  • when first formed, stars are still embedded in the infalling dusty envelope
  • any UV/optical radiation from the star (or accretion shock) is absorbed by dust and re-radiated in the IR
  • presence of the envelope causes the peak to shift to longer wavelengths
  • the star peak is no longer present since the optical/UV radiation from the star is efficiently absorbed and reradiated at IR by the envelope
22
Q

Emission from Surrounding Dust Clouds / Envelope

Equations Steps

A
  • consider a single dust grain, radius a, in the envelope, energy absorbed by the star is equal to the energy is emitted
  • energy in is equal to the integral over optical/UV of πa²QvIv
  • the energy out is equal to the integral over IR of 4πa²QvBv(T)
23
Q

Emission from Surrounding Dust Clouds / Envelope

Dependence of T on r

A

T = (L/[16πσ(210^(-4))r²])^(1/5)
-thus
T ∝ r^(-0.4)
-for 10

24
Q

Evolution of Infrared Spectra From Young Stars

A
  • in the early stages of formation, the dusty envelope is very optically thick, even at IR wavelengths: spectrum peaks in far-IR
  • as the envelope clears, the peak shifts to shorter wavelengths until light from the star disk is revealed
  • eventually, the disk is dispersed, leaving behind emission from the star only

PHYS3281 Star and Planet Formation (13 decks)

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