Protoplanetary Disks as Accretion Disks

1. Protoplanetary Disks as Accretion Disks Roman Rafikov (Princeton)

2. Outline • Origin of protoplanetary disks • Observational properties • Spectra and their formation • Angular momentum transport Emphasize differences and similarities with disks around compact objects

3. Origin

4. Dispersion relation - Jeans length - Jeans mass Origin Collapse of Jeans-unstable dense clumps of molecular gas. A single time event – disk is not fed externally for a long time. leads to Typical accretion rate and time scale

5. Machida et al (2007) Rotational Support Collapsing cloud slowly rotates at 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.

6. Observational properties

7. Sizes • Ages • Spectra • Masses • Mass distribution • Temperatures Observational properties

8. 2 mm Kitamura et al (2002) 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

9. Observational properties: • 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 Calvet et al 1999

10. Hillenbrand 2005 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.

11. Chiang & Goldreich 1997 Observational properties: spectra • Protoplanetary disks are usually passive – their own accretion luminosity is small compared to the irradiation by the central star at r > 1 AU • Irradiated disk is flared:

12. Dullemond et al 2007 Observational properties: spectra Disk flaring plays very important role in shaping disk spectrum Spectrum of a flat disk

13. 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 Kitamura et al (2002) Observational properties: masses

14. Protoplanetary Disks Surface density (g cm-2) Goldreich & Sari Minimum Mass Solar Nebula Based on smearing out the refractory content in SS planets

15. Angular momentum transport

16. 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)

17. MRI with resistivity Lundquist Number

18. Neal Turner • 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)

19. In these calculations was enough to quench MRI operation “Dead” zone Fleming & Stone 2003

20. “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

21. 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

22. Similarities 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 Comparison with disks around compact objects

23. 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”