Protostellar jets: Theory & models

Protostellar jets:Theory & models Fabien CASSE AstroParticule & Cosmologie (APC) Université PARIS DIDEROT

Seminaire MHD, ENS Paris, 25/09/06 Outline of this talk • Observational facts. • Young stellar objects (YSO), microquasars, active galactic nuclei (AGN) and related outflows: What do we know about them ? • Accretion disks and jets. • Interplay between disk-driven jets and stellar winds. • Concluding remarks.

Seminaire MHD, ENS Paris, 25/09/06 Young stellar objects • YSO (M* ≤ 2 Mo) exhibit large scale jets • Vjet ~ 100 - 400 km/s • Jet rotation ( Baciotti et al. (2003)). • Jet velocity decreases with radius. • Presence of magnetic field Donati et al(2005). • YSO jets seem to have 2 components (central one is hot, external one is cooler and more extended, Dupree et al (2005)). • Jet and disk luminosities seem related Burrows et al.(1996) Cabrit et al(1990)

Seminaire MHD, ENS Paris, 25/09/06 Microquasars • Binary compact objects surrounded by an accretion disk. • Vjet~0.1 to 0.95c • Time-dependent mass ejection. • Multi-wavelength emission from both disk and jets. • Synchrotron emission ~ magnetic field. • Quasi-Periodic Oscillations (QPO) in X-rays, etc … (see e.g. Tagger et al.) Few pc Mirabel et al(1998)

Seminaire MHD, ENS Paris, 25/09/06 Active galactic nuclei • AGN = radio-loud galaxies with twin jets • Central objects: super-massive BH • Vjet ~ 0.1c to  ~ 10 • Non-thermal emission ranging from radio to -rays (synchrotron, SSC, IC) • 2 classes of AGN: FRI and FRII. • FRII jets are likely to have two components(hadrons and/or pairs). • Jets and disk luminosities linked. M87 Serjeant et al(1998)

Seminaire MHD, ENS Paris, 25/09/06 Observations vs. Theory I • In all kind of systems we have: • Vjet ~ (2GM*/R*)1/2 => Jet matter is likely coming from a region close to the central object and gravity is the most probable source of energy. • Magnetic field + plasma => MHD approach has to be considered. • Some jets have two components => Various mechanisms may be working at once. • Same ingredients: central objects + accretion disks… • Axisymmetry seems to be a good approximation as well as symmetry with respect to the accretion disk mid-plane. • Ejection occurs during times ~ many inner disk or objects rotations:

Seminaire MHD, ENS Paris, 25/09/06 Observations vs. Theory II • Three classes of steady-state, axisymmetric models have been considered • Accretion disk driven jets => Velocity distribution is consistent with obs. and it can account for a large radial extension. • Central object driven winds => Hot internal outflow but limited radial extension. • Magnetospheric winds => Limited radial extension but temperature not very different from the one associated to a disk-driven outflow. • Astrophysical jets are likely to be the result of a combination of at least two of them.

Seminaire MHD, ENS Paris, 25/09/06 Models outlines Models Requirements

Disk-driven jets • Disk structure & equilibrium • Magneto-centrifugal acceleration • Self-similar calculations • 2.5D numerical simulations Model based upon the idea of Blandford & Payne (1982)

Seminaire MHD, ENS Paris, 25/09/06 Disk magnetic braking • Stationary accretion: => The disk has to be resistive ! • For non-resistive disks, the accretion is stopped by the advection of poloidal magnetic field. => The disk is prone to MHD turbulence. • The magnetic torque brakes disk material: => Disk angular momentum removal provokes a magnetic twisting (B <0) • Angular momentum is stored in the magnetic field and is transported along the poloidal magnetic field.

Seminaire MHD, ENS Paris, 25/09/06 Disk Equilibrium • Disk vertical balance is made of 3 forces: • Gravity pinching the disk. • Magnetic pinching of the disk • Thermal pressure gradient lifting matter. • In order to lift a small fraction of the disk matter in the jet => Po/B2 1. • The magnetic field has to collimate the outflow so that Po/B2 cannot be >> 1 (Ferreira & Pelletier 1995). Near-equipartition disk seems to be the most promising structure for stationary jet launching !

Seminaire MHD, ENS Paris, 25/09/06 Magneto-centrifugal acceleration I • Poloidal and toroidal magnetic forces are closely related: • In order to accelerate matter, the magnetic torque has to become positive! =>Increase of the centrifugal force • Both magnetic force & centrifugal force speed up matter in the poloidal plane. (JxB).Bp  (JxB).B

Seminaire MHD, ENS Paris, 25/09/06 Magneto-centrifugal acceleration II • The centrifugal force has to overcome the gravitational attraction: • Opening angle of the field lines has to be larger than 30o at the disk surface, in the case of a “cold” plasma. • The magnetic field may collimate the jet. Blandford & Payne (1982)

Seminaire MHD, ENS Paris, 25/09/06 Magneto-centrifugalAcceleration III RB=cst • In a stationary ideal MHD framework => MHD invariants • Frozen-in field • Angular momentum • Specific energy (Bernoulli) • Acceleration takes place if RB decreases (MHD jet) and/or if CS decreases (thermal wind). • RB MHD current => current circuit in accretion-ejection do have a “butterfly” shape.. • Terminal velocity V2max = 2E(a)

Seminaire MHD, ENS Paris, 25/09/06 Self-similar Model • Accretion-ejection structures has to deal with both resistive and ideal MHD equations. • Simplification: writing all quantities as This is inspired from the shape of the driving force: gravity! • Description valid for large launching array.. • We obtain a 1D problem to solve with 3 critical points. • Slow and fast magnetosonic points • Alfvèn point. • Resistivity has to be prescribed as a spatially varying quantity, e.g. as a Shakura-Sunyaev prescription.

Seminaire MHD, ENS Paris, 25/09/06 Self-similar Calculations • Blandford & Payne (1982): 1st cold self-similar jets • Konigl(1989):1st simplified turbulent disks study • Wardle & Konigl (1993),Li(1995,1996):1st disk-jet connections but with huge simplifications in the context of ambipolar diffusion. • Ferreira & Pelletier(1995):1st complete disk-jet connections with prescribed Ohmic resistivity. • Ferreira(1997):1st trans-Alfvenic jets including complete disk structure (Ohmic resistivity). • Casse & Ferreira (2000): implementation of turbulent viscosity in the disk and coronal heating. • Vlahakis et al(2000):1st jet crossing all critical surfaces. • Ferreira & Casse (2004): 1st jet crossing all critical surfaces with complete disk structure.

Seminaire MHD, ENS Paris, 25/09/06 MHD Jet simulations • Jet simulations with various initial conditions • Ustyugova et al. (1995,1998) • Romanova et al. (1997) • Ouyed et Pudritz (1997,1999) • Krasnopolsky et al. (1999,2003) • Fendt & Cemeljic (2002) • Rekowski & Brandenburg (2004) • Anderson el al. (2005), etc… Quasi-stationary jet solutions crossing all critical surfaces. • Accretion disk is treated as a boundary condition. Krasnopolsky et al(1999)

Seminaire MHD, ENS Paris, 25/09/06 Disk-Jet simulations • Some works have tried to described both disk and jet: • Ideal MHD • Shibata & Ushida (1985) • Stone & Norman (1996) • Matsumoto et al. (1996) • Kudoh et al. (1998) • Kato et al.(2002), etc.. • Resistive MHD • Kuwabara et al.(2005) • Resistive disk & Ideal jet • Casse & Keppens (2002,2004) => • 3D simulations have been performed but without reaching steady-state (e.g. Kigure & Shibata 2005).

Seminaire MHD, ENS Paris, 25/09/06 Accretion-ejection Current circuit Casse & Keppens (2004) Poynting flux & Streamlines

YSO Winds andDisk-driven Jets • Stellar winds • X-wind • Magnetospheric winds

Seminaire MHD, ENS Paris, 25/09/06 Stellar Winds • Since solar wind model (Parker 1958), stars are expected to produce outflows. • Stellar winds needs coronal heating at the base of the flow to overcome gravity..  No MHD Poynting flux near the rotation axis !! • MHD stellar outflows may become collimated if the central object is rotating fast enough (e.g. Bogovalov & Tsinganos (1999), Sauty et al. 2004, Matt & Balick 2004). Sauty et al. (2004)

Seminaire MHD, ENS Paris, 25/09/06 Stellar wind & rotation • Low-mass YSO are slow rotators:  No self-induced collimation ! • Disk-driven jets do have a hollow structure. • Coronal heating may be provoked by matter falling onto the star and/or MHD turbulence. • Stellar wind collimation may be provided by the external disk-driven jet. • Protostars can be spun down by the stellar wind if RA>> RSTAR and/or if the wind mass loss rate is large ! Coronal Heating Matt & Pudritz (2005) Hartmann & Stauffer (1989)

Seminaire MHD, ENS Paris, 25/09/06 Two-component YSO jets • Disk-driven jet simulations with inner stellar wind • Study of both collimation and stellar wind heating Meliani, Casse & Sauty (2006) Steady stellar mass ejection • Mass ejected with Vej ~ 0.01 VAlfven • Magnetic field at star surface ~ 2kG • Resistivity in the stellar wind => Ohmic Heating !

Seminaire MHD, ENS Paris, 25/09/06 Two-component YSO jet Stellar wind hot component T~5.105K • Collimation occurs whatever the stellar wind ejection rate (here 10-9 solar mass/yr) ! • Star braking may be efficient since RA/R* ~ few tens.. • No conclusion since we do not have the inner radius of the disk ! Disk-driven cooler component T~ 6.104K Fast-magnetosonic surface Alfven surface MA=10-7M/yr MJet=10-8M/yr MJet/MW=10 Thermal energy released in the wind ~ 35% of accretion energy !! Slow-magnetosonic surface

Seminaire MHD, ENS Paris, 25/09/06 YSO Jet collimation • Stellar wind mass rate 10-7 M/yr • Larger disk-driven jet ejection rate increases as well as the jet radius  more efficient magneto-centrifugal acceleration !! Larger centrifugal force Stellar wind pressure Enhanced accretion

Seminaire MHD, ENS Paris, 25/09/06 X-wind model • X-wind model (Shu et al. 1994,2000): similar to disk-driven jet except for disk magnetic flux (tiny here leads to RIN ROUT). • Magnetic field comes from stellar magnetopshere. • The wind is powered by accreting material ! • X-wind cannot spin down protostars • A viscous torque has to provide accretion rate. • Ejection rate / Accretion rate ~ 1/3 to fit observations. • Collimation is a crucial issue e.g. Pudritz et al. (2006). • Angular momentum budget does not fit observations (so as radial profiles).

Seminaire MHD, ENS Paris, 25/09/06 Magnetospheric ejection • Stellar braking may occur if its magnetosphere is anchored in the disk beyond corotation radius Ejection arises from reconnection points • Parallel Star dipole (ReX-winds): Disk material is lifted by the reconnecting field lines (e.g. Hirose et al. 1997,Ferreira et al. 2000)=> Unsteady ejection • Anti-parallel stellar dipole (e.g. Goodson et al.1997, Matt et al.2002) => “CME-like ejection of coronal matter => Unsteady ejection • This kind of magnetospheric ejection can occur in the hollow part of a disk-driven jet => Presence of a hot, unsteady internal jet component. Ferreira et al.(2006) Anti-parallel dipole ReX-wind

Seminaire MHD, ENS Paris, 25/09/06 Concluding remarks I • YSO disk-driven jets • Launching and collimation mechanisms are now quite understood.  Disk-driven jet is likely to be the external envelope of Yso jets.. • Some observational features can be reproduced by MHD simulations. BUT • Disk magnetic field origin is not yet completely clear:  Dynamo generated and/or dynamically advected? • Yso disk turbulence origin is still unclear as well as turbulence transport coefficients (e.g.equipartition disks):  Relative amplitude of resistivity and/or turbulent viscosity, role of the ambipolar diffusion… • Heating and cooling terms are not fully taken into account in the MHD energy equation :  No direct comparison with observations .. • 3D stability of disk-jet systems is not yet clearly addressed.

Seminaire MHD, ENS Paris, 25/09/06 Concluding remarks II • Yso stellar winds • Stellar winds may carry away star angular momentum • We have to understand how accretion energy may be massively converted into thermal energy in the stellar corona. • Stellar wind may account for inner yso jet hot component since embedding disk-driven jets seem to remain cylindrical. • Magnetospheric winds • “Disk-locking” models spinning-down is inefficient for measured dipolar magnetic field BDIP < 200 G (Johns-Krulls et al. 1999). • Magnetospheric mechanisms likely produce unsteady ejection.  They may contribute for time dependent spectral fluctuations • X-wind models  X-winds cannot spin down the star…  X-wind cannot achieve cylindrical collimation (e.g. Pudritz et al.2006)

Protostellar jets: Theory & models