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Jets, Disks, and Protostars 5 May 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low How does collapse proceed? • Singular isothermal spheres have constant 3 accretion rates M 0.975cs G • 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 self2 2 gravity, radial force eqn: r r GM r • So long as M large, Ω ~ r -3/2 (Kepler’s law) d 3 • Shear in Keplerian disk r dr 2 d • Define a shear stress tensor πr r dr • If viscosity ν 0, torque is exertedT 2 r rπr dz • angular momentum transport is then dJ T M d , where mass accretion M d 2 rvr dr r Alpha disk models • Viscous accretion a diffusion process, with 2 acc r • 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 π r vr v – for subsonic turbulence, δv ~ αcs – in MHD flow, Maxwell stress π r Br B • B-H inst. numerically gives αmag ~ 10-2 – where πrφ = – αmag Pmag 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 c B • 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 2 2 k 2cs2 2 G k where is the disk surface density, and 1 d 2 2 the square of the epicyclic frequency 3 r r dr – from linearization of fluid equations in rotating disk – angular momentum decreasing outwards ( 2 0 ) 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 unstable 1/2 1 λ / λT Shu, Gas Dyn. Q T T 4 2G 1 0, where T 4 2 4 cs cs and the Toomre parameter Q = T G 2 2 • 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” Effective potential along a field line 2 GM 1 r r0 r, z 2 2 r0 2 r0 r z where r0 is the footpoint of the field line • If field lines tilted less than 60o 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 ff G ~ 1 hr for Sun • Kelvin-Helmholtz time scale (thermal relaxation: radiation of gravitational energy) 1 2 KH • Nuclear timescale GM 2 ~ 3 107 yr for Sun RL N EH He MxH ~ 1010 yr for Sun L 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 H2 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)