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Jonathan Ferreira. Mass loss in YSOs and star-disc interactions. Collaborators : C Zanni, F. Casse, G. Murphy, S. Cabrit , C. Dougados , N. Bessolaz , P. Garcia. O utline. I - Star-disc interaction: the disc locking scenario The rotational problem in low-mass star formation
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Jonathan Ferreira Mass loss in YSOs and star-disc interactions Collaborators: C Zanni, F. Casse, G. Murphy, S. Cabrit, C. Dougados, N. Bessolaz, P. Garcia
Outline I - Star-disc interaction: the disc locking scenario • The rotationalproblem in low-mass star formation • The Ghosh & Lamb model and disc-lockingparadigm • Issues and numerical simulations II- Mass lossfromYSOs • Jets in YSOs • MHD equations and steady-state jet models • Disc winds: how do theywork? The JEDs and the magnetichistory of discs • Stellarwinds: their revival III- Star-disc interaction: ejections • X-winds, M-winds, T-winds… • Conicalwinds • ReX-winds • Magnetospheric Ejections (or EpisodicMagnetospheric Inflation) IV- Conclusion
Rotationalevolution of PMS stars THE SAMP (TWO problems): • T Taurirotateat 10% break-up speed (Bertout 89) • Velocitydispersion requires disc interaction (« disc locking » paradigm) Bouvier et al. 97
Muzzerolle et al 01 • free-fallinggas in dipole, temperatureobtainedwithad-hocvolumetricheatingterm and coolingfunction • All kineticenergyat the shockassumed to beconvertedinto BB radiation Courtesyof R. Kurosawa
Model fit for BP tau Muzzerolle et al 01 • Reproduces inverse P-cygni profiles, blueasymmetry • reasonablefits for severalobjects: a success (given the simplifications) Courtesy of R. Kurosawa
3D magneticfield reconstructions Donati et al, MAPP collaboration
Somemilestones 1990’s: A magneticstar-disc interaction and the disc-lockingparadigm The Ghosh & Lamb (77) model applied for YSOs: - Camenzind 90, Konigl 91 - Cameron & Campbell 93, Armitage & Clarke 96 Calculations of the magneticfield structure: - Lovelace, Romanova & Bisnovatyi-Kogan 95 - Bardou & Heyvaerts 96, Agapitou & Papaloizou 00 - Uzdensky, Konigl & Litvin 02 2000’s: Numerical MHD simulations First attempts: - Hayashi 96, Miller & Stone 97, Hirose et al 97 - Goodson et al 97, 99, Kueker et al 03 - Romanova et al 02, 03,04, 05, Long et al 05 Controlled simulations, comparison to detailed observations: - 2D: Bessolaz et al 08, Zanni & Ferreira 09,12 - 3D: Long et al 07,08, 10, Kurosawa et al 11, Romanova et al 11,12
The disc-lockingparadigm Ghosh & Lamb 77, 79 Konigl 91 Cameron & Campbell 93 Armitage & Clarke 96 Li & Wickramasinghe 97 Matt & Pudritz 05…12 • The main ingredients are the following: • The disc istruncatedatrt • The existence of an extendedmagnetosphere: rout >> rin = rt • Accretioncolumns /curtains (funnel flow) take place mainlyaroundrt • No mass loss • Viscosity transports the excessangularmomentumoutwardly • => Use verticallyintegratedequations for the accretion disc • Whatdeterminesrt? • Whatdeterminesrout ?
Stellardipole: 3 configurations rt < rco: Accretionregime Narrow interaction zone (as in mostnumerical simulations) rt < rco: Accretionregime Extended interaction zone: good star-disccoupling à la Ghosh & Lamb Rt > rco: Propellerregime No accretionallowed (but…?) Matt & Pudritz 05
Stellar spin evolution Axisymmetricangularmomentum conservation: • Integration over the stellar surface involvesseveral zones in the dipolarmagnetosphere: • Closed, not reaching the disc -> neglected • Closed, withfunnelflows -> accretion + magnetic torques • Open, at the interface -> neglected • Open, withstellarwind -> wind torque (later…)
Whenintegrated over the volume of the star: Whichrequiresevaluating the toroidalfieldat the stellar surface Not easy… Anotherwayis to make budgets: materialassumedkeplerianat r=rtand rotatingwith the star at r=R*
The magnetic torque Isorotationimpliesalmost no toroidalfieldat the stellar surface: the shearisdistributedalong the magnetosphericfunnel evaluatedat the disc surface In thissimplifiedapproach, thereshouldbe no net momentum flux on the star: the magnetic torque (distributed over the disc), should balance the accretion torque. This magneticbrings an excess of angularmomentumthat must becompensated by the viscous torque. In most GL models, this (crucial) effect has not been takenintoaccount.
Stellarspin-up In a few 105yrs, a contracting T Tauriwould spin up and all of themshouldbeatbreak-up speed (d=1). Evenworse if one takes contraction intoaccount…
The toroidalmagnetic component In the ideal MHD magnetosphere: Namelyat the disc surface In the resistive MHD disc (in the gas frame) So that in the fixed frame (GL79, Cameron & Campbell 73, Armitage & Clarke 96) NB: for Bz<0 @ r< rco, W> W* and Bf>0
How good is the disc coupling? In a SAD = Standard Accretion Disc, one wouldexpect => Choosingbdefines the regime (Armitage & Clarke 96 usedb=1) and then the strength (and sign) of the overallmagnetic torque WhereBz varies as r-3 (dipole). Another factor is how twisted (max value of q) can the fieldget?
A limit on q: field line opening Aly 84, 91 Van Ballegooijen 94 Lovelace et al 95, 99 Bardou& Heyvaerts 96 Uzdensky et al 02a,b, Matt & Pudritz 05 - Differential rotation between star and disc: generation of Bf - Magneticenergydensityincreases, helicity as well - Magnetic structure relaxes by - plasma acceleration (if loaded) : jet production mechanism - field inflation if force-free (Aly’stheorem) Uzdensky, Konigl, Litwin 2002a, 2002b
Uzdensky, Konigl, Litwin 2002a,b t=0 t=0.5 t=1 t=1.5 Steady state achievedonly for highenoughresistivity, qmax =1 Field inflation isfasterthan radial field diffusion (contrary to Bardou & Heyvaerts 96, Agapitou & Papaloizou 00). Ejecta (with plasma) around 60°
3: the truncation radius 1st criterion (Ghosh & Lamb 79a, Konigl 91): when local mg torque = local viscous torque The disc magnetization (at disc midplane) : Abovecriterion translates into << 1 whichgives an upperlimit for rt
3: the truncation radius 2nd criterion (Romanova et al 02, Koldoba et al 02): when the magneticfielddominates the dynamics (whenfieldstrength comparable to gravity) This criterionisverified in simulations, but is not predictive. Unlessassuming v= Wr The criterion translates into >> 1 namely, a lowerlimiton rt
3: the truncation radius Correct criterion (guessed by Pringle & Rees 72, demonstrated by Bessolaz et al 08): when the magneticfieldreachesequipartition Magnetic torque must be dominant AND brake down the disc (rt< rco) (2) Poloidal flow must behalted by magneticwall: or (3) Disc pressure must be able to up-liftmaterial (4) Maximum magneticshearislimited to q ~ 1
Truncation radius with a dipole For B=140G, M=0.8, R=2, Ma=10-8, P=8 d Surprisingly, whererAisAlfven radius (Elsner & Lamb 77) In litterature, rt=k rA, with k = 0.5 (GL79, Konigl91) to 1 (Ostriker & Shu 95).
Spin equilibrium solution • In the absence of anystellarwind and contraction, an equilibriumrequires • providing • Or, equivalently, • where • independent of radius • requires a strongstellarfield (> kG)… • (C=1 used by Konigl 91, Ostriker & Shu 95) FromMatt & Pudritz 05
Spin evolution of accretingYSOs Matt & Pudritz 05 where x= r/rco Because of qc, thereis a rinand rout b=1, qc=∞ For bqc=0.5 => rin=0.63, rout=1.3 Truncation radius iswhereTvis<0, calculationsassuming a zero net torque b=1, but qc=1
Net torque on the star Matt & Pudritz 05 Spin equilibrium Log d So, unlessextendedmagnetosphere (b=1, rout=∞), no spin equilibriumwithd=0.1 Failure of the Ghosh & Lamb picture…
The physics of 2.5D funnelflows Zanni & Ferreira 09 av=am=1 Pm=1 Up to 10 P*
Physics of funnelflows Zanni & Ferreira 09 Position of the truncation radius
Fluxes and forces Zanni & Ferreira 09 magn matter star disc Positive flux: goesfrom disc to star Positive force: towards the disc Existence of a SM critical point (accretion flow remainsalwayssub-A) => Flow isdeccelerated by B (both in j and poloidal) not accelerated, whenrt<rco Li & Wilson 96 Koldoba et al 02
Magneticfield redistribution Zanni & Ferreira 09 Magneticfield diffusion, after 55 stellarperiods
Zanni & Ferreira 09 Magneticfield diffusion, after 55 stellarperiods => Decrease of Bzevenfaster, lowersdrastricallyefficiency of disc-lockingmechanism
Torques on the accreting protostar Zanni & Ferreira 09 • Ghosh & Lamb equilibriumis NOT established • Aftersome time, mostfieldlines are disconnectedfrom the star (nm≈ Csh) • Final stage = 2 electric circuitswith star = 2 torques • Positive torque due to accretion (dominant) • Negative torque due to open fieldlines (ready for a stellarwind…)
Spin-up of accreting YSO Zanni & Ferreira 09 Spin up: Solid: Magn torque < rco Dot: kinetic torque Spin down: Dot-dash: stellarwind torque Dash: Magn torque > rco Limited size of physicalconnection + weakerBzfield => magnetic torque smaller by a factor 10 than MP05 estimate Oscillation= mismatchbetween 2 Mdots - viscous torque in disc geometry - magnetic torque in funnel flow (nozzle) onto the star
Effect of boundary conditions Zanni & Ferreira 09 Solid: ZF09 Dot: Bf=0 Dot-dashed: dRBf/dR=0 Dashed: outflow RunwithdRBf/dR=0 => Rcodecreases: the disc feels a star rotatingfaster (as in Long et al 05)
3D simulations: complexfields Addhigherorder components, inclination etc… Marina Romanova’sgroup (world leadership) Cubedsphere (Koldoba et al 02) Romanova et al 03, 04, 11, 12 Long et al 07, 08, 09 Kurosawa et al 08 Etc… Courtesy of M. Romanova
Truncation radius m ~1 Physics of accretioncolumnsseems correct in 3D: truncation radius as expected Angularmomentumtransfer… more worrying. Courtesy of M. Romanova
3D accretion: interchangeinstability Romanova et al. 03, 08 Kulkarni & Romanova 08
Variation in position of accretionshock Romanova et al 04 Time dependentaccretion + complexfieldtopology => variation of position of hot spots (caveat for derivingstellarperiodfromvariability) Courtesy of M. Romanova
Quadrupole + dipolefields Quadrupole: equatorialaccretionbelt -> torque isless efficient -> asymmetryintroduced Courtesy of M. Romanova
Octupole + dipolefield • e.g. as in BP Tau (Donati et al 07) • Dipole 1.2 kG + octupole 1.6kG • The dipoledeterminesrt • The octupole modifies accretionshock Long et al 10