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Protoplanetary Disks as Accretion Disks. Roman Rafikov (Princeton). Outline. Origin of protoplanetary disks Observational properties Spectra and their formation Angular momentum transport Emphasize differences and similarities with disks around compact objects. Origin. Dispersion relation. - PowerPoint PPT Presentation
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Protoplanetary Disks as Accretion Disks
Roman Rafikov (Princeton)
Outline• Origin of protoplanetary disks• Observational properties• Spectra and their formation• Angular momentum transport
Emphasize differences and similarities with disks around compact objects
Origin
OriginCollapse of Jeans-unstable dense clumps of molecular gas. A single time event – disk is not fed externally for a long time.
2/1
34
2/1
10102.0
cmn
KTpcJ - Jeans length
2/1
34
2/3
10103
cmn
KTMM SunJ - Jeans mass
leads to Gkc 4222 Dispersion relation
Typical accretion rate and time scale
,10
102/3
16
KTyrMM Sun
2/1
345
10102
cmnyrtcollapse
Rotational Support
2
115
2/3
34
2/1
10101030
scmn
KTAUR G
disk
Machida et al (2007)
Collapsing cloud slowly rotates at
11510~ sG
Conservation of angular momentum leads to disk formation
Likely that most of the stellar mass has been processed through the disk. B fields may have been important.
Observational properties
Observational properties
• Sizes• Ages• • Spectra• Masses• Mass distribution• Temperatures
M
Observational properties: sizes
Determined via• Hi-res imaging in the visible of scattered (by dust) stellar light• IR, submm or mm imaging of disk’s own thermal emission• IR interferometry can resolve sub-AU details• SED modellingDisks sizes range between tens to thousands of AU, consistent with expectations
2 mm
Kitamura et al (2002)
Observational properties:
M
Calvet et al 1999
• Obtained by measuring the excess continuum or line emission due to gas accretion onto the star• Disk emission does not probe • Requires knowledge of stellar M and R• Measurements are highly uncertain• Clear correlation (decay) with the age
M
Observational properties: disk lifetimes
Hillenbrand 2005• Disk age = stellar
age• Determine average disk lifetimes by looking at fraction of stars with disks in groups of different ages• This fraction decays with age• Typical lifetimes are of order 1-10 Myrs. Disappear due to photoevaporation.
Observational properties: spectra
Chiang & Goldreich 1997
• Protoplanetary disks are usually passive – their own accretion luminosity is small compared to the irradiation by the central star
1~
Rh
LL
FF
accvisc
irr at r > 1 AU
7/27/32
4 /~,,4
rrhrTr
LT
• Irradiated disk is flared:
Observational properties: spectra
Dullemond et al 2007
Spectrum of a flat disk
Disk flaring plays very important role in shaping disk spectrum
Observational properties: masses
Kitamura et al (2002)
• Outer parts of protoplanetary disks (beyond tens of AUs) have low enough surface density and T (meaning low dust opacity) to be optically thin • Their IR and sub-mm luminosity probes total dust mass in the optically thin region• Using dust-to-gas conversion get • Range between
diskM
SunM1.010 3
Minimum Mass Solar NebulaProtoplanetary Disks
y1Py12P y250P
)AU(r
Surf
ace
dens
ity (g
cm
-2)
d88P
Goldreich & Sari
Based on smearing out the refractory content in SS planets
Angular momentum transport
Possible angular momentum transport mechanisms
• Accretion implies outward angular momentum transport – need some kind of viscosity• Keplerian disks are hydrodynamically stable• Convection does not provide outward angular momentum• Magneto-rotational Instability (MRI) is the most likely agent, BUT
- Unlike the disks around compact objects protostellar disks are poorly conducting- MRI gets modified by resistivity in important ways (especially at small scales)
MRI with resistivityLundquist Number
• Protoplanetary disks around 1 AU are too cold for thermal ionization• External sources are shielded
This gives rise to a “dead zone” near the disk midplane (Gammie 1996)
Mark Wardle
exT /2/1Neal Turner
“Dead” zone Fleming & Stone 2003
In these calculations
was enough to quench MRI operation
10010~ MRIS
“Dead” zone• While magnetic stress virtually dies out in the dead zone, Reynolds stress gets transmitted (albeit at low levels) into this zone maintaining some transport there.• Accretion rate is not constant in the dead zone - long term steady state is not possible
Fleming & Stone 2003
Other things to worry about
Dust• Small dust grains are efficient charge absorbers• Abundance of small dust grains is poorly known• Dust can grow and sediment towards midplane• This can lead to streaming instabilities and turbulencePlanets• Density waves lead to outward angular momentum transport
Other non-ideal MRI effects• Ambipolar diffusion• Hall effect
Comparison with disks around compact objectsSimilarities
Accretion disks, transport - MRI
Differences
Compact Objects• High T• Significant thermal ionization• Ideal MRI• Long-term steady state possible
Young stars• Low T• Weak thermal ionization, some external is possible• Non-Ideal MRI• Transient objects, likely dynamic in the dead zones
Conclusions• Protoplanetary disks are cold, massive accretion
disks surrounding young stars• Stars likely form via fast accretion in the initial phases of the disk life• They are likely transient objects – lifetimes ~ 1-10 Myrs• They are passive, heated mainly by their central stars, emit mainly in the IR and sub-mm range• Accretion is likely due to MRI, which is significantly modified by the non-ideal effects• Low ionization makes resistivity very low and damps MRI in some parts of the disks creating “dead zones”