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Collapse of protostellar cores into protoplanetary disks

Collapse of protostellar cores into protoplanetary disks. Ascona 2008 Origin and Evolution of Planets Ralph Pudritz, McMaster Uni. Outline: 1. Core formation 2. Filamentary flow and disk formation 3. Outflows from early disks

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Collapse of protostellar cores into protoplanetary disks

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  1. Collapse of protostellar cores into protoplanetary disks Ascona 2008 Origin and Evolution of Planets Ralph Pudritz, McMaster Uni.

  2. Outline: 1. Core formation 2. Filamentary flow and disk formation 3. Outflows from early disks 4. Ambipolar diffusion and disk decoupled zones 5. Implications for planet formation. Collaborators: Robi Banerjee (ITA), Dave Anderson (McMaster), Dennis Duffin (McMaster) David Tilley (McMaster, Notre Dame)

  3. Cores, and CMF in Pipe dark cloud (Alves et al 2007): - Same as IMF except for offset factor of 3 lower in mass 1. Core formation Core Mass Functions (CMFs) – to the IMF? (Motte et al 1998, Testi & Sargent 1998, Johnstone et al 2000, Andre et al 2007,..) Grey line – IMF of Trapezium cluster (Alves et al 2007)

  4. Clouds, to cores, to disks: • Supersonic turbulence: - produce filaments and cores; cloud support - CMF: lognormal at lower mass; power-law at high (eg. Hennebelle & Chabrier 2008) - core angular momentum distribution -> origin of disks [Simulations; Porter et al 1994, Klessen & Burkert 2001, Padoan et al 2001, reviews by MacLow & Klessen 2004, McKee & Ostriker 2007, .. ] • Gravity: - collapse of rotating, dense cores into disks - gravitational torques in disks • B fields: - brake rotating cores; cloud support - outflows: disk torques - core dispersal (eg. Matzner & McKee 2000) • Thermal physics - characteristic stellar mass scale + disk accretion shock

  5. Core Formation a. Hydro turbulence + gravity (Tilley & Pudritz 2004) - Initial Kolomogorov or Burger’s velocity field – decaying turbulence - initial uniform density; - ZEUS 3D + good gravity solver; - periodic B.C.; 256 or 512 cubed simulations; - Truelove (1997): resolve local Jeans length with at least 4 pixels

  6. Initial properties of cluster forming, clump simulation (based on Orion cloud data (Lada & Lada 1991):

  7. Core Mass Spectrum (CMF) • Mass spectrum (eg. Padoan & Nordlund 2000, Hennebelle & Chabrier 2008) • Width given by Mach no. • High mass slope; from turbulent spectrum Bound cores

  8. Core specific angular momentum distribution Spin arises via vorticity production in oblique shocks (Jappsen & Klessen 2004) - natural scale: - High spin -> binary fragmentation In physical units

  9. b. MHD turbulence - role in core formation… One new parameter: gravitational and magnetic energies scale in same way with scale, L -> Ratio - the mass to flux ratio: Supercritical (>1): gravity wins Subcritical (<1) B supports Tilley & Pudritz 2007

  10. More Jeans masses: Turbulence breaks up clouds into dense cores in which stars form before big sheet is organized…

  11. Close-up: spinning cores emit flux of Alfven waves extracting some angular momentum Stage set for magnetized collapse…

  12. CMFs: - Numerical data compared with Padoan & Nordlund (2002) models - Shape OK, but PN02 misses peaks of numerical CMFs, roughly at Jeans mass in turbulent pressured medium. FORM OF CMF in strong B: - Bimodal - Fragmentation reduced

  13. Core Magnetization Function: Tilley & Pudritz (2007) - poorly magnetized clouds -> strongly magnetized, local cores (with large dispersion)!

  14. The data: Zeeman measurements of B in cores (Crutcher, 2008): THE POINT: • Cores GET strongly magnetized in turbulence (eg. Padoan & Nordlund 2002, TP07) – B support cannot be avoided….. • Exactly opposite to “ambipolar diffusion” model of star formation (Shu et al 1987) - cores form where magnetization LOST

  15. 2. Filamentary flow and disk formationFLASH – Adaptive Mesh Refinement (AMR) simulations (Banerjee, Pudritz, & Anderson, MNRAS 2006): start with TP04 - Dynamically, self adjusting grid - resolve local Jeans length (Truelove et al 1997); we use 12 pixels - Add coolants - including molecular + dust cooling, H2 formation and dissociation, heating by cosmic rays, radiative diffusion for optically thick gas, etc.

  16. Filamentary structure: from 0.1 pc down to sub AU scale - Large scale filamentary collapse onto a growing disk: (x-z plane)

  17. Origin of disk angular momentum: (Cut through disk midplane, x-y) • an off-centre sheath of material impacting disk provides angular momentum of the disk. • highest resolution shows spiral wave structure

  18. Filamentary collapse and formation of a protostellar disk. - Filamentary flow draws material from very large scales. - Disk surprisingly “regular” in spite of highly non-uniform formation conditions.

  19. Temperature structure and cooling: First shock set by dust cooling – on 10 AU scale Second shock arising from H2 dissociation…

  20. Spiral waves in disk – appear to connect to a central bar • Strong gravitational torque reduces central specific ang. Momentum..

  21. Evolution of radial temperature profile Sharp transition to warm gas occurs at few 10s AU – marks the boundary of first accretion shock.

  22. Outside-in collapse: as generally expected for objects with non-singular density profiles – as in Bonner-Ebert spheres (Larson-Penston) Accretion rate exceeds SIS (no turbulence) model by 1,000 – and Bonner-Ebert sphere collapse by 20

  23. Evolution of radial column and volume density profiles during collapse:

  24. Evolution of angular momentum profiles Left: specific angular momentum jz: stable… Right: Angular momentum per mass shell decreases with time: extraction by spiral wave torque

  25. 3. Outflows from early disks (MHD simulations of collapsing, magnetized B-E spheres - FLASH AMR MHD code) • Uniform, magnetic field:  = 84 on midplane, molecular cooling, threading rotating BE sphere Low mass model: M = 2.1 solar masses, R = 12,500 AU, T = 16K; free-fall time 67,000 yr. (Banerjee & Pudritz 2006, ApJ) (3D cylinrical collapse and outflow: Tomisaka (1998, 2002) Barnard 68 (Alves et al 2001): excellent fit with Bonner-Ebert model

  26. Onset of large scale outflow:100 AU scales… magnetic tower flow (eg. Lynden-Bell )

  27. Magnetic tower flow – 10 AU scales

  28. Jets as disk winds (eg. review Pudritz et al 2007) - launch inside 0.07 AU (separated by 5 month interval) - jets rotate and carry off angular momentum of disk - spin of protostellar core at this early time?

  29. 3D Visualization of field lines, disk, and outflow:- Upper; magnetic tower flow on larger scales- Lower; zoomed in by 1000, centrifugally driven disk wind on smaller scales

  30. Protodisk and close binary system: side and top views inside of 0.1 AU Jets are initiated even though central object(s) are only 1/100th of a solar mass… jets are true products of disk accretion

  31. Physical quantities across disk.- Hiyashi law for disk column density - Ideal MHD -> predicts strong disk field

  32. 4. Ambipolar diffusion – decoupled zones.(Duffin & Pudritz 2008 a, submitted) • Since ρion << ρneutral can usesingle fluid approx. • Ions: ρion ~ (ρneutral)1/2 • Valid up to about ngas = 1010 cm-3 ( multiple species: Tassis & Mouschovias 2007, Nakano et al. 2002) • Implemented into FLASH AMR code as a MHD sub-module • Expectation: decoupling of field at high density; accretion flow through surface layers (via wind or magnetic torques).

  33. Ideal MHD (density left, infall speed right): adjustment Initially uniform, spheres; initial density 300; 30 solar masses. AD MHD (density left, infall speed right): collapse

  34. Collapse and disk evolution under AD:(initial magnetized, rotating BE sphere) • New results: • Layered accretion (through surface active zone) • Outflow from surface coupled zone • Decoupled zone at midplane..

  35. Disk fragmentation (low mass model): ideal vs AD MHD • Upper: ideal, fragment separation: 2-3 AU • Lower: AD, fragment separation 10 AU • Effective loss of pressure support leads to more fragmentation (compare Banerjee et al. 2004 and Banerjee & Pudritz 2006)

  36. 5. Implications for planet formation Early disks inherit characteristics from cores: - disk mass + magnetization - size determined by first shock + rotation - disk fragmentation suppressed by B field - early outflow exerts disk torque competitive with spiral torque -> angular momentum evolution - decoupled zone and layered surface flow Planet formation inherits characteristics from disks: - planetary mass (depend on disk mass) – eg. Matsumura’s talk) - B affects gravitational fragmentation to giant planets - disk winds affect angular momentum flow -> planetary accretion + migration - “quiet” decoupled zone -> planetesimal formation

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