Jets Disks and Protostars 5 May 2003 Astronomy

Jets, Disks, and Protostars 5 May 2003 Astronomy G 9001 - Spring 2003 Prof. Mordecai-Mark Mac Low

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.

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.

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.

Disk Structure Shu, Gas Dynamics • Nelecting pressure (Ωr >> cs) and disk selfgravity, 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

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 cm 2 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

Magnetorotational instability • First noted by Chandrasekhar and Velikhov in 1950 s – 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

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

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

Gravitational Instability in Disks Shu, Gas Dynamics • 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 < tff then stable

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

• 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”).

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

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

Jet Observations

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?

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 60 o from disk, no stable equilibrium => outflow C. Fendt

• Collimation Jet Propagation – 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 “Hammer Jet” simulated IR from M. D. Smith

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

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

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 H 2 to dissociate • Protostar forms when H- becomes optically thick. – Luminosity initially only from accretion. – Deuterium burning, then H burning

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

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)