III- Star-disc interaction: ejections

1. III- Star-disc interaction: ejections

2. Anumericalcoincidence… Shu et al 94 • Stellar spin down => zero torque condition • Jet asymptotics (if connected to disc) Vjet ~ 200 to 500 km/s => J ~ 3 to 14 => f ~ 0.07 to 0.4 So, YSO jets seem to allow « naturally » a spin equilibrium… if they are causallyconnected to the star AND the disc

3. Two simple configurations Camenzind90 Shuet al 94a, 95 Matt & Pudritz05 • Assumes Rt= Rco • « X-wind»: assumed to possibly spin down the protostar (or in spin equilibrium) Rt (Uchida & Low 81, Hirose 97) Ferreira, Pelletier, Appl 00 - Assumes Rt< RX = Rco - « ReconnectionX-winds » at the magneticneutral line: very efficient stellar spin down (but unsteadywind = bullets) RX

4. III.1- Steady-stateX-winds

5. X-winds : back to basics Shu et al 94a,b Shu et al 95 Najita & Shu 94, Shang et al 98,02 Cai et al 08 Ostriker & Shu 95 Mohanty & Shu 08 • Y-typemagnetic interaction (scenario for the origin of B) • Magnetosphereisassumed to bepotential • Cold windcalculations: super-SM flow from point source to A surface (prescribed), matched to cylindricalasymptotics; • unknownmethod (interpolation of invariants?): Shang et al • Variationalmethod: Cai et al 08 (Seealso Rosso & Pelletier 94)

6. Shu et al 94c • Open questions: • Can the disc afford the imposed mass flux and fieldgeometry? • Is the transfiedequilibriumsatisfied? • How isenergytransferred to the MHD wind ? Shang et al 98, 02

7. Cold fan-shapedwinds: T-winds, M-winds Ferreira & Casse 12, in press Terminal or T-wind Magnetospheric or M-wind Look at all a-disc + jet equations and verify if boundary conditions canbesatisfied: mi ~1, me <<1 and 3 cases for M-winds: ri < rco: « regular » ri > rco: « propeller » ri < rco: « X-wind »

8. GoverningMHD equations, applied on a thin disc annulus • Mass • Momentum • Energy • Perfect gas • Diffusion Bp • Induction Bf With 3 anomalous transport coefficients: viscosity (nv), magneticdiffusivity (nm, nm’)

9. The magnetic configuration Given the fan geometry, the dominant cemftermis At the surface (ideal MHD) The magneticshearistherefore Steady-stateOhm’slaw: with The magneticbendingis Jf

10. The poloidal structure Sincem< 1 in the annulus by assumption: - Radial balance mostlykeplerianin a thin disc (annulus) - Quasi- MHS vertical balance

11. Properties of stationaryfan-shapedwinds Spherical dilution of the magnetic flux SinceonlypublishedF-shapedwindisX-wind, use same notations where The definition of the disc magnetizationbrings (mass + mg flux conservation) Angularmomentum: Specificenergy (Bernoulli)

12. F-wind power and velocity Wind power is where Thus, Defining an average jet velocity: Wind withkeplerian speed requires q ~ Dr/r = h/r << 1 Najita & Shu 94, Cai et al 08

13. Energy budget of the annulus (1/4) Local energy conservation writes for a cold flow: Integrated over the volume Accretion power ri re Note: in X-windtheory f = 0.1 to 0.4 and 2Pwind ≈ GMMa/2ri Dr/r=h/r= 0.05

14. Energy budget of the annulus (2/4) Viscous power « difference factor » Note: in SAD theory, torque assumed =0 at ri and re >> ri To get power, a F-Windrequires D>0 and of orderunity => Energy must beflowingfrom the innerradiithroughviscous (turbulent) means, more efficientlythanitleaks out at the outer radius ri re

15. Energy budget of the annulus (3/4) Disc luminosity (dissipation) The viscous contribution is The magnetic contribution (Joule heating) => Negligiblewrtviscous dissipation The total power lost by the annulus ri re

16. Energy budget of the annulus (4/4) The power available to the windcanbederived by applying the energy budget On the other hand, ideal MHD equations for the windgive Combining the twoprovides the relations, valid for all fan-shapedwinds ri re

17. M-windsbelowco-rotation • Weidentify ri < rco as the base of the columns • Stellarmagnetic torque brakes down the disc • Boundary conditions: • Rm,i~r/h • Re,e= 3/2 • Unless Pm>> 1, D <0: unphysicalsituation • Relax steady-state approximation or allow for re~ri (but not a fan shapeanymore…) • NB: Same conclusion for T-winds

18. M-windsbeyondco-rotation • Situation withrco < rt < ri • No accretioncolumns (propellerregime) • In that case, steady-stateonly for f=1 • viscous stress must transport angularmomentumfromrt to ri : viscous torque accelerates the disc Theenergyfeeding the windis the rotationalenergy of the star, if D > ½ namely comparable viscosities. Ok. But to redirectentirely the accretion flow, mass conservation requires an incomingvelocityue ~Cs. Sinceue ~ avCs h/r, thisimpliesav~r/h >> 1

19. M-windsatco-rotation: X-winds • Situation withrt < ri ≈rco • Accretioncolumns possible below ri => f <1 • Possibility to bepowered by stellar rotation • viscous stress must transport angularmomentumfromrt to ri : viscous torque accelerates the annulus (zi~r/h and <0) • Magnetic torque due to X-winddecceleratesit, sothat the actual disc accretion speed istiny (1) This requires an almostperfectmatchingbetween the two torques (2) All modelscomputedwith b~ unity, J between 2 and 7 => q = 1/a’m ~ h/r

20. Comments on X-wind (1) All considerationshere are consistent withideal MHD winddynamicspublished Differences are - Induction equation for Bj (q) not used in X-windtheory - Disc angularmomentum conservation not used (2) M-winds (whatever) neverobtained in simulations: but out of range of parameterspace (3) CouldX-windsberealized ? - issue of turbulence - issue of allowingaccretioncolumn formation (needs ms~ 1 whereas ms ~ (h/r)2) (4) Note: YSO jet kinematicsinconsistentwithcurrent (published) windcalculations(Ferreira et al 06, Cabrit et al 07) - range in poloidal speeds not explained - steepdecline in speddtowards jet edge not explained

21. III.2- ReX-winds

22. Reconnection X-winds: Interplay of dynamo + fossil fields • Protostellar core at break-up (Class 0) • Bipolar fossil field • t=0: dynamo produces a dipole field • Magnetic neutral line at RX= R* • Contraction of the protostar, spin-down by the ReX-wind + accretion funnels • rx≈ rco increases (magnetosphere expands) • Accretion rate onto the star is regulated • Stellar open field increases (Class I, II?)

23. The global picture Ferreira, Pelletier, Appl 00, MNRAS Stationary extended disc wind, providing open magnetic flux to the star Unsteady ejection above the reconnection zone, allowing to brake down the contracting protostar Basic features remain if stellar dipole is inclined (precessing bullets channeled by the outer disc wind)

24. The role of a reconnectionbelt Ferreira, Pelletier, Appl 00 Shu et al 94a Ostriker & Shu 95 • Both configurations require an equatorialreconnection zone (interesting for energydissipation and CAI in chondrules-Calcium Aluminium Inclusions-Gounelleet al 06) • « ReX-wind » model:enforced, due to opposedlydirectedmagneticfields (disc+star) • « X-wind » model: no justification (?) • Severalnumericalattempts but large scalereconnectionis major issue

25. Governingequations (L3 level) Consider a sphere of mass M*initiallyatbreak-up R*=rco, with a dynamo, evolvingfollowing the Hayashitrack (T*=Cte), embedded in an ambiant magneticfield, surrounded by an accretion disc in JED state. • (1) Virialtheorem: • (2) Energy conservation with • Provides the contraction rate of the protostar • (3) Mass conservation • (4) Angularmomentum conservation • withalwaysverified on long (KH) time scales

26. Governingequations • The co-rotation radius isassumed to followrco= rX • Rxis the reconnection line withso a prescription for the field must beused • Disc field (equipartition): • Depends on Ma. If star spins down, rco= rxincreases, so must do BMAES, hence Ma • Stellarfield: • where n free parameter and Bclis the closed (initiallydipolar) magneticfieldlinking the star to the disc. • Normalized to the t=0 values, one has • whereis the stellarclosedmagnetic flux. • whichneeds to beprescribed in time…(or impose some time evolution for Ma).

27. The stellarmagnetic flux The total stellarmagnetic flux (open+closed) Assuming dynamo contribution to open flux negligible with (BMAES varies as r-b, b=3/4). This contribution of the open stellar flux grows in time as What about Fcl(t) ? - scenario 1: dynamo providesclosed flux atsame rate - scenario 2: no dynamo at all, closed flux isonly the inital flux whichcanbeparametrized by whereis a measure of the amount of closed flux at t=0

28. Stellar spin evolution Free parameters: (+ a in the no-dynamo scenario) n > 3 magneticfieldexponent f = Mx/Ma mass flux in ReX-wind l= (rA/rx)2magnetic lever arm parameter

29. ReconnectionX-winds Dynamo scenario T* = 3000 K Stellarfield n = 4

30. ReconnectionX-winds Dynamo scenario T* = 3000 K Stellarfield n = 4

31. ReconnectionX-winds Dynamo scenario T* = 3000 K n=4 l = 3 Influence of f solid : f=0.01 dashed: f=0.027 dotted: f=0.07 dash-dot: f= 0.19 Long-dash: f=0.5

32. ReconnectionX-winds a=0.01 NO-dynamo scenario T* = 3000 K a=0.5 Stellarfield n = 3

33. Momentum flux Vs Bolometric luminosity Class 0 103 yr 104 yr Class I 105 yr Ferreira et al. 00 Bontemps et al. 95

34. Saturation mechanism for B*? • ReX-windis not a « wind » (or only in a very long time averagedsense) • power diminishes in time withW* • The disc magnetic flux F must belimitedotherwise B*too large, W*toolow • If disc magnetic flux ceases, both Disc wind + ReX-wind stop (but APSW dominant) • One wouldexpect a correlationbetweenW*and F • Does the weak dispersion instellarperiodsreflect a weak dispersion in disc magnetic flux ? (rememberF  M) n = 4

35. III.3- Steady-stateconicalwinds

36. Rt < rco Rt > rco: propeller Romanova et al 09 Konigl et al 11 Lii et al 12 • « discovery » of conical jets alongopenedstellarfieldlines • dense flow attached to the disc (= conicalwind) • stellarwind (= fast axial jet) • stellarmagnetosphereiscompressed: m ~1 • high mass flux Mw/Ma ~10-30% • flow driven by gradient of toroidalmagneticfield (== dense config) • propeller case: rapid spin down of the protostar • Accretor case: spin up of the protostar • depending on turbulence parameters, steady-statewind or not • => A new class of ejections ?

37. Romanova et al 09

38. Time normalized to keplerianperiodat r=1 Nq =50, NR =120

39. Lii et al 12 Same as in Romanova et al 09, but computationaldomain 3 times larger => launching + collimation studies Simulations donewith Pm= 2-3, typicalav=0.3 and am=0.1 No stellarwindallowedthis time.

40. Launching zone requiresequipartition large scale (open) field • same as in disc winds • magnetictopologydifferentfromM-wind (no fan: Pm toolow) • The outer part is not a SAD: mslarger, due to open fieldlines Lii et al 12

41. Lii et al 12 • - Accretion rate onto the star, expelled in the wind (no stellarwindhere) • Ang mom. fluxes measuredat the stellar surface (red) AND at R=20 (green). • Star spins up • Wind ismatterdominated: resembles a « warm disc wind » • Note: Steady-stateis « demonstrated » by thesecurves, not by showing invariants

42. Projection of the forces: • windaccelerationisdoneat the expense of poloidalcurrentIp • Wind collimation idem (currentclosureoutside the box)

43. The conicalwindsremainaxisymmetricevenwithinclineddipole Romanova et al 09

44. Onto the star Comments Onto the wind Romanova et al 09 (Appendix D2) am=1 Pm=0.3 : no wind am=0.3 Pm=1 : steady-stateconicalwind am=0.1 Pm=3 : « oscillations » am=0.01 Pm=30: ?? Steady-stateconicalwinds are formedwhenever Pm>1, but large viscosityrequired: sharemanyproperties of « warm disc winds » (steady, familiardynamics, axisymmetric) But the oscillations wereunexplained…

45. III.4- Magnetospheric Ejections

46. ME = MagnetosphericEjections Zanni & Ferreira 12, in press • simulation withav=0.3 and am=0.1 • MEs+ stellarwindprovide efficient spin-down of the star • MEs are time-dependent and depend on stellarfield structure (variability, asymmetry).Collimation depends on outer disc wind • Time unit= stellarperiod • NR x Nq = 214 x 100 (twiceresolution R09)

47. Mass fluxes: Onto the star In the MEs Dot: disc wind Long dash: ME, from star Dash: Stellar Wind

48. Forces from disc surface to cusp Forces fromstellar surface to cusp • ME’s are loadedfrombothsides (but most of the mass from disc) • (plots= time average over 54 stellarperiods) • From disc: centrifugal + magnetic • From star: « thermal » push • at r=7, stellarmaterialencounters disc materia • magneticfieldisazimuthalyacceleratingmaterial: magneticslingshot

49. Ejecta transport away a significant fraction of the disc angularmomentum => hugedecrease of the accretion torque onto the star

50. Torques on the star Accretion Dash: ME Dot: Stellarwind • Combination of ME + Stellarwindalows a net spin down torque • But does not compensate for contraction… • Need to rely on more massive ejecta and/or somepropeller phases