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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 Origin Collapse of Jeans-unstable dense clumps of molecular gas. A single time event – disk is not fed externally for a long time. 2 c 2 k 2 4G Dispersion relation leads to 1/ 2 n T J 0.2 pc 4 3 10 K 10 cm 3/ 2 1/ 2 - Jeans length n T M J 3M Sun 4 3 10 K 10 cm 1 / 2 - Jeans mass Typical accretion rate and time scale 3/ 2 6 M 10 M Sun T yr , 10 K 1 n tcollapse 2 10 yr 4 3 10 cm 5 1/ 2 Machida et al (2007) Rotational Support Collapsing cloud slowly rotates at G ~ 10 15 s 1 Conservation of angular momentum leads to disk formation 1/ 2 Rdisk n T 30 AU 4 3 10 K 10 cm 3 / 2 G 15 1 10 s 2 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 • M • Spectra • Masses • Mass distribution • Temperatures 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 modelling Disks sizes range between tens to thousands of AU, consistent with expectations Kitamura et al (2002) 2 mm Observational properties: • Obtained by measuring the excess continuum or line emission due to gas accretion onto the star • Disk emission does not probe M • Requires knowledge of stellar M and R • Measurements are highly uncertain • Clear correlation (decay) with the age M Calvet et al 1999 Observational properties: disk lifetimes • 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. Hillenbrand 2005 Observational properties: spectra • Protoplanetary disks are usually passive – their own accretion luminosity is small compared to the irradiation by the central star Firr L h ~ 1 Fvisc Lacc R Chiang & Goldreich 1997 at r > 1 AU • Irradiated disk is flared: L 3 / 7 T , T r , 2 4r 4 ~ h / r r 2/7 Observational properties: spectra Disk flaring plays very important role in shaping disk spectrum Spectrum of a flat disk Dullemond et al 2007 Observational properties: masses • 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 M disk • Range between 103 0.1 M Sun Kitamura et al (2002) Protoplanetary Disks Surface density (g cm-2) Minimum Mass Solar Nebula P 88 d P 1y P 12 y P 250 y Goldreich & Sari r (AU ) 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 resistivity Lundquist Number Neal Turner T 1/ 2 / xe • Protoplanetary disks around 1 AU are too cold for thermal ionization • External sources are shielded Mark Wardle This gives rise to a “dead zone” near the disk midplane (Gammie 1996) “Dead” zone In these calculations SMRI ~ 10 100 was enough to quench MRI operation Fleming & Stone 2003 “Dead” zone Fleming & Stone 2003 • 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 Other things to worry about Other non-ideal MRI effects • Ambipolar diffusion • Hall effect 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 turbulence Planets • Density waves lead to outward angular momentum transport Comparison with disks around compact objects Similarities Accretion disks, transport - MRI Differences Compact Objects Young stars • High T • Low T • Significant thermal ionization • Weak thermal ionization, some external is possible • Ideal MRI • Non-Ideal MRI • Long-term steady state possible • 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”
