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 L bol ) Flat inner density profiles for cores give better fit to observations. Collapse no longer self-similar, so shocks form.

3. Accretion shocks Yorke et al. 1993 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. Disk Structure Nelecting pressure (Ωr >> c s ) and disk self- gravity, radial force eqn: So long as M large, Ω ~ r -3/2 (Keplers law) Shear in Keplerian disk Define a shear stress tensor If viscosity ν 0, torque is exerted angular momentum transport is then Shu, Gas Dynamics

6. Alpha disk models Viscous accretion a diffusion process, with molecular ν = λ mfp c s ; in a disk with r ~ 10 14 cm, – λ mfp ~ 10 cm, c s ~ 1 km s -1 => ν ~ 10 6 cm 2 s -1 –so τ acc = 10 22 s ~ 3 10 14 yr! Some anomalous viscosity must exist. Often parametrized as π rφ = – αP –based on hydro turbulent shear stress –for subsonic turbulence, δv ~ αc s –in MHD flow, Maxwell stress B-H inst. numerically gives α mag ~ 10 -2 –where π rφ = – α mag P mag

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 λ c > λ diss even very weak B drives instability if B so strong that λ c >> 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 R c ~ 0.1 AU collisional ionization maintains field coupling ( Gammie 1996) Outside, CR ionization keeps surface layer coupled Accretion limited by layer Gammie 1996

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

10. 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 < t ff then stable Shu, Gas Dynamics

11. Toomre Criterion Disks with Toomre Q < 1 subject to gravitational instability at wavelengths around λ T Q λ / λ T 1 01/21 ω 2 > 0 stable ω 2 < 0 unstable Shu, Gas Dyn. stabilized by rotation stabilized by pressure

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

17. Blandford-Payne disk winds C. Fendt Gas on magnetic field lines in a rotating disk acts like beads on a wire If field lines tilted less than 60 o 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 ~ 10 12 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 H 2 to dissociate Protostar forms when H - becomes optically thick. –Luminosity initially only from accretion. –Deuterium burning, then H burning

22. z C. Fendt 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)