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”