Jets, Disks, and Protostars

1. Jets, Disks, and Protostars 5 May 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low

2. How does collapse proceed? • Singular isothermal spheres have constant accretion rates • Observed accretion rates appear to decline with time (older objects have lower Lbol) • Flat inner density profiles for cores give better fit to observations. • Collapse no longer self-similar, so shocks form.

3. Yorke et al. 1993 Accretion shocks • Infalling gas shocks when it hits the accretion disk, and again when it falls from the disk onto the star • Stellar shock releases most of the luminosity • Disk shock helps determine conditions in flared disk.

4. Accretion disks • Form by dissipation in accreting gas • Observed disks have M ~ 10-3 M << M* • Inward transport of mass and outward transport of angular momentum energetically favored. • How can gas on circular orbits move radially? • Either microscopic viscosity or macroscopic instabilities must be invoked. • Balbus-Hawley instabilities can provide viscosity • gravitational instability produces spiral density waves on macroscopic scales • Gravitational instability will act if B-H remains ineffective while infall continues.

5. Shu, Gas Dynamics Disk Structure • Nelecting pressure (Ωr >> cs) and disk self-gravity, radial force eqn: • So long as M large, Ω ~ r -3/2(Kepler’s law) • Shear in Keplerian disk • Define a shear stress tensor • If viscosity ν  0, torque is exerted • angular momentum transport is then

6. Alpha disk models • Viscous accretion a diffusion process, with • molecular ν = λmfpcs; in a disk with r ~ 1014 cm, • λmfp ~ 10 cm, cs~ 1 km s-1 => ν ~ 106 cm2 s-1 • so τacc = 1022 s ~ 3  1014 yr! • Some anomalous viscosity must exist. Often parametrized as πrφ = – αP • based on hydro turbulent shear stress • for subsonic turbulence, δv ~ αcs • in MHD flow, Maxwell stress • B-H inst. numerically gives αmag ~ 10-2 • where πrφ = – αmag Pmag

7. Magnetorotational instability • First noted by Chandrasekhar and Velikhov in 1950s • ignored until Balbus & Hawley (1991) rediscovered it... • Driven by magnetic coupling between orbits • instability criterion dΩ/dr < 0 (decreasing ang. vel., not ang. mntm as for hydro rotational instability) • most unstable wavelength • so long as λc > λdiss even very weak B drives instability • if B so strong that λc>> H, instability suppressed • Field geometry appears unimportant • May drive dynamo action in disk, increasing field to strong-field limit

8. MRI in protostellar disks • MRI suppressed in partly neutral disks if every neutral not hit by ion at least once per orbit (Blaes & Balbus 1998) • Inside a critical radius Rc ~ 0.1 AU collisional ionization maintains field coupling (Gammie 1996) • Outside, CR ionization keeps surface layer coupled • Accretion limited by layer Gammie 1996

9. time less ionization Mac Low et al. 1995 Simulations of MRI suppression Hawley & Stone 1998 Sheet formation occurs in partially neutral gas

10. Shu, Gas Dynamics Gravitational Instability in Disks • Important for both protostellar and galactic disks • Axisymmetric dispersion relation • from linearization of fluid equations in rotating disk • angular momentum decreasing outwards ( ) produces hydro instability • Differential rotation stabilizes Jeans instability • if collapsing regions shear apart in < tffthen stable

11. Q ω2 > 0 stable Toomre Criterion 1 stabilized by rotation stabilized by pressure • Disks with Toomre Q < 1 subject to gravitational instability at wavelengths around λT ω2 < 0 unstable λ / λT Shu, Gas Dyn. 0 1/2 1

12. Accretion increases surface density σ, so protostellar disk Q drops • Gravitational instability drives spiral density waves, carrying mass and angular momentum. • Will act in absence of more efficient mechanisms • Very low Q might allow giant planet formation. • direct gravitational condensation proposed • may be impossible to get through intermediate Q regime though, due to efficient accretion there. • standard giant planet formation mechanism starts with solid planetesimals building up a 10 M core followed by accretion of surrounding disk gas • Brown dwarfs may indeedform from fragmentation during collapse (“failed binaries”).

13. Jets • Where does that angular momentum go? • Surprisingly (= not predicted) much goes into jets • lengths of 1-10 pc, inital radii < 100 AU • velocities of a few hundred km s-1 (proper motion, radial velocities of knots) • carry as much as 40% of accreted mass • cold, overdense material • CO outflows carry more mass • driven either by jets, or associated slower disk winds • velocities of 10-20 km s-1 • masses up to a few hundred M

14. Herbig-Haro objects • Jets were first detected in optical line emission as Herbig-Haro objects • H-H objects turn out to be shocks associated with jets • bow shocks • termination shocks • internal knots • tangential & coccoon shocks • line spectrum can be used to diagnose velocity of shocks

15. Jet Observations

16. CO outflows Gueth & Guilleteau 1999 High resolution interferometric observations reveal that at least some CO outflows tightly correlated with jets. Others less collimated. Also jets?

17. C. Fendt Blandford-Payne disk winds • Gas on magnetic field lines in a rotating disk acts like “beads on a wire” • If field lines tilted less than 60o from disk, no stable equilibrium => outflow

18. Jet Propagation • Collimation • Gas dynamical jets are self-collimating • However, hydro collimation cannot occur so close to source • Toroidal fields can collimate MHD jets quickly • Knots in jets • knots found to move faster than surrounding jet • variability in jet luminosity seen at all scales • large pulses overtake small ones, sweeping them up simulated IR from M.D. Smith “Hammer Jet”

19. Time Scales • Free-fall time scale • Kelvin-Helmholtz time scale (thermal relaxation: radiation of gravitational energy) • Nuclear timescale

20. Termination of Accretion • exhaustion of dynamically collapsing reservoir? • masses determined by molecular cloud properties? • competition with surrounding stars for a common reservoir? • termination of accretion? • ionization • jets and winds • disk evaporation and disruption

21. Protostar formation • Dynamical collapse continues until core becomes optically thick (dust) allowing pressure to increase. n ~ 1012 cm-3, 100 AU • Jeans mass drops, hydrost. equil. reached • radiation from dust photosphere allows quasistatic evolution • Second dynamical collapse occurs when temperature rises sufficiently for H2 to dissociate • Protostar forms when H- becomes optically thick. • Luminosity initially only from accretion. • Deuterium burning, then H burning

22. C. Fendt z • deeply embedded, most mass still accreting • disk visible in IR, still shrouded • T-Tauri star, w/disk, star, wind • weak-line T-Tauri star

23. Pre-Main Sequence Evolution • Protostar is fully convective • fully ionized only in center • Large opacity, small adiabatic temperature gradient • Energy lost through radiative photosphere, gained by grav. contraction until fusion begins • Fully convective stars with given M, L have maximum stable R, minimum T • Hayashi line on HR diagram • Pre-main sequence evolutionary calculations must include non-steady accretion to get correct starting point (Wuchterl & Klessen 2001)