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The formation of stars and planets Day 4, Topic 1: Magnetospheric accretion jets and outflows Lecture by: C.P. Dullemond Boundary layer Assume disk goes all the way down to the stellar surface GM disk r*3 At inner radius of disk: If star rotates at less than breakup speed: disk star Frictional energy release in boundary layer: Ýr GM 1 M 2 Ý (v disk v starsurf ) Lbl M 3 star 2 2 r 2 2 Boundary layer F For non-rotating star: star accr disk ÝM GM Lbl 2r Lvisc bnd layer Friction between disk and star tends to spin up star until disk star Lbl Lvisc This means that star would rotate at breakup speed (almost zero local gravity at the equator) Ae and Be stars rotate fast Most stars, however, rotate far below breakup speed Magnetospheric accretion Alfvén radius ri Ghosh & Lamb (1978) for neutron stars. Camenzind (1990), Königl (1991), Shu et al. (1994), Wang (1995) for TT stars 2 Magnetic pressure: Dynamic pressure: B Pm 8 Pdyn c s2 v 2 Gas is loaded onto magnetic field lines (disk is destroyed) at the radius ri where Pm =Pdyn. 4 /7 1/ 7 Ý2 / 7 r (2GM) M i * Königl (1991) (Here * is stellar magnetic moment, and <1 is a fudge factor, typically =0.5 ) Magnetospheric accretion Spin-up/spin-down GM rco 2 * 1/ 3 Corotation radius Very rough estimate for spin-up/spin-down: ri 0.35rco ri 0.35rco Spin-up Spin-down Ghosh & Lamb (1977,1978,1979) Königl (1991) Equilibrium sets stellar rotation rate (if braking/spin-up time is shorter than stellar formation time) (The concept of magnetic breaking of the sun was already suggested in 1960 by Hoyle, and in a somewhat less plausible way by Alfvén 1954) Magnetospheric accretion Free-fall and accretion shock From rA down to star: matter is in supersonic free-fall. Near the star the matter gets to a halt in a stand-off shock. Free-fall region Accretion shock ri Shock velocity: 2GM r* vs 1 r* ri Dissipated energy (=accretion luminosity from shock): ÝM r* GM Laccr 1 ri r* Magnetospheric accretion Radiation from accretion shock Stellar spectrum Radiation from accretion shock 0.2 0.4 1 (m) 2 Calvet & Gullbring (1998) Measuring the accretion rate • Veiling of atmospheric lines by continuum of the accretion layer • Broad (FWHM ~ 200 km/s) H line emission Bipolar outflows / jets Bipolar outflows HH47 Bipolar outflows HH34 Bipolar outflows Outflows also seen in molecular lines: Molecular outflows Bachiller et al. Bipolar outflows Jets originate from inner regions of protoplanetary disks Hubble Space Telescope image Bipolar outflows • Optically detected jets: – Very collimated streams of gas, moving at supersonic speed (~~100 km/s) – Mostly bipolar, mostly perpendicular to disk – Jet outflow rate typically 10-9... 10-7 M. • Molecular outflows: – Detected in CO lines – Often associated with optical jets (i.e. same origin) – Derived mass: 0.1...170 M: large! • Most of accelerated mass must have been swept up from the cloud core, rather than originating in mass ejected from the star Bipolar outflows Swept-up material (molecular outflow) Terminal shock Hydrodynamic confinement? Hot bubble of old jet material Magnetic confinement Magneto-centrifugal launching (<AU scale) Magnetically threaded disks Suppose disk is treaded by magnetic field: Inward motion of gas in disk drags field inward: B-field aquires angle with disk Disk winds Slingshot effect. Blandford & Payne (1982) (courtesy: C. Fendt) Use cylindrical coordinates r,z GM Gravitational potential: Effective gravitational potential along field line (incl. sling-shot effect): 2 GM 1 r r0 r0 r 2 z 2 2 r0 r2 z2 Disk winds Blandford & Payne (1982) 2 GM 1 r r0 2 2 r0 2 r r z 0 Infall Critical angle: 60 degrees with disk plane. Beyond that: outflow of matter. Outflow Gas will bend field lines Disk + star: X-wind model of Frank Shu Shu 1994 Magnetic field winding - confinement C. Fendt Magnetic field winding - confinement (courtesy: C. Fendt) c j B 4 1 f j B c Right-hand rule: force points inwards Hydromagnetic launch of jet from disk Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. Kudoh, Matsumoto & Shibata (2003) Hydrodynamic structure of jets • Jets are surrounded by cocoon of pressurized gas – Cocoon partly made of old jet material, partly by swept up material from the environment – Jet material moves supersonically • Head of jet (‘hot spot’) drills through ISM: shock • Often knots seen (Herbig-Haro objects) Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“ benötigt. Stone & Norman (1993) Observed knot movement Hydrodynamic confinement in jet: Shock only reduces the velocity component perpendicular to shock front. Therefore obliquely shocked gas is deflected toward the shock plane. Hydrodynamic confinement in jet: Head of the jet: Turbulent mixing between old jet material and swept-up environment (entrainment) Stand-off shock (most of jet energy dissipated here) Contact discontinuity (boundary between jet and external medium) Bow shock Back flow Shocked external medium gas (molecular outflow) Jet flow much faster than propagation of bow shock. Jet material much more tenuous than external medium