Accretion Disks Flashcards
disk properties, observational evidence for disks around young stars, direct imaging, infrared spectra
Basic Facts About Accretion Disks
- 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
Keplerian Azimuthal Velocity
vφ = √[GM*/R] ∝ R^(-1/2)
Why are they called ‘accretion disks’?
-the protostar is fed material from the collapsing envelope through the accretion disk
Accretion Disks and Viscosity
- 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
Viscous Evolution of a Ring in the Accretion Disk over Time
- 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
How can we observe accretion disks?
-accretion disks around young stars can be observed directly (via imaging) or indirectly (via excess emission at infrared wavelengths)
Alternative Names for Accretion Disks
- accretion disks
- circumstellar disks
- protoplanetary disks (usually used for latter stages after envelope is gone)
Direct Evidence for Accretion Disks
- spatially-resolved thermal emission from dust grains
- spatially- and/or spectrally-resolved molecular line emission
- reflected/scattered light
- in silhouette against bright nebular background
Observational Evidence for Accretion Disks
Spatially Resolved Thermal Emission
- 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
Observational Evidence for Accretion Disks
Spectrally-Resolved Molecular Lines
- 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
Observational Evidence for Accretion Disks
Spatially-Resolved Molecular Lines
- 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
Observational Evidence for Accretion Disks
Reflected/Scattered Light
- 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
Observational Evidence for Accretion Disks
Disks in Silhouette
-HST also observed disks in silhouette against bright nebula
Indirect Evidence for Accretion Disks
SEDs
-the presence of dusty disks (and/or envelopes) around young stars can also be inferred indirectly via measurement of the spectral energy distributions (SEDs)
Accretion Disk Spectrum
Etot
-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
Accretion Disk Spectrum
Rate of Change of Energy
dE/dt ~ GMM’/2r² dr
- where M’=dm/dt is the mass accretion rate
- assume all energy goes into radiation
Accretion Disk Spectrum
Dependence of T on r
T = (GMM’/8πσr³)^(1/4)
-so
T ∝ r^(-3/4)
-hotter closer to the centre
Accretion Disk Spectrum
Graph
- 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
What makes the accretion disk spectrum shallower?
-caused by heating from a host star
What makes the accretion disk spectrum steeper?
- 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
Emission from Surrounding Dust Clouds / Envelope
Description
- 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
Emission from Surrounding Dust Clouds / Envelope
Equations Steps
- 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)
Emission from Surrounding Dust Clouds / Envelope
Dependence of T on r
T = (L/[16πσ(210^(-4))r²])^(1/5)
-thus
T ∝ r^(-0.4)
-for 10
Evolution of Infrared Spectra From Young Stars
- 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
