Masahiro Machida (Kyoto Univ.) Shu-ichiro Inutsuka (Kyoto Univ.), Tomoaki Matsumoto (Hosei Univ.)

1. Protostellar Jet in the Collapsing Cloud Core jet Outflow 360 AU 1000 times close-up Masahiro Machida(Kyoto Univ.)Shu-ichiro Inutsuka (Kyoto Univ.), Tomoaki Matsumoto (Hosei Univ.) first core protostar v~5 km/s v~50 km/s

2. Star Formation and Jet / Outflow Before the star formation Just after the star formation Jet /outflow driving phase ? Jet from protostar We cannot observe Molecular Cloud Core Hirano et al. (2006) (Nagoya Univ.) • Stars born in the molecular cloud core • Jet / Outflow always appearsin the star formation process • Jet / Outflow plays crucial roles in the star formation • They are closely related to the stellar mass • They transport the angular momentum from the cloud core ・・・・

3. outflow jet protostellar disk Protostar outflow dark cloud protostar jet Protostellar Outflows and Jets • In star-forming regions, there are two distinct flows: Outflows and Jets ◆Molecular Outflow：low velocity (~10 km/s), wide opening angle ◆Optical Jet: high velocity (~100 km/s), well-collimated structure • Optical Jet is enclosed by Molecular Outflow • But, Mechanism is still unknown Purpose of This Study • Understanding the driving mechanism of Jets / Outflows • Using the numerical simulation, we calculated the cloud evolution from the molecular cloud (n=104 cm-3, r~104 AU)until the protostar (n~1020 cm-3, r ~ 1Rsun) formation HH30, Pety et al. 2006 Velusamy et al. 2007

4. Adiabatic Phase Second Collapse & Protostellar Phases Isothermal Phase Dead regionB dissipation (1012cm-3<n<1015cm-3) B amplification B amplification protostarformation B H2 dissociation B B Adiabatic core(First core)Formation Thermal Evolution in the Collapsing Cloud 1D Radiative Hydrodynamics Larson (1969)Tohline (1982)Masunaga & Inutsuka (2000) Protostar Log T (K) To MS 104 103 cloud core 102 10 Gas Temperature Log n (cm-3) 105 1010 1015 1020 Spatial Scale (AU) 104 100 1 0.1

5. ◆Magnetic Reynolds number h: resistivityv: free fall velocityL: Jeans Length ◆Basic equations Magnetic Evolution B B Resistivity h B ◆Resistivity is fitted as a function of n and T (Nakano et al. 2002) Ohmic dissipation Magnetic Reynolds number Reynolds number Re Well-Coupled Well-Coupled Resistivity Cloud evolution Protostar Cloud • Coupling between the magnetic field and neutral gas (weakly-ionized plasma) • Low density (n<1012 cm-3): Low ionization rate, but well-coupled due to tff > tcol • Moderate density (1012cm-3<n < 1016cm-3)： Ionization rate decreases as density increases　　　　　　　　　　　　　　　　　　　　　　　　　　⇒ Dissipation of B by Ohmic dissipation • High density (n>1016 cm-3)：Some metals are ionized, Well-coupled

6. Ω L=4 Rotation Axis Magnetic Field Line Bonnor-Ebert Sphere B 4.6x104 AU Initial Settings Gas sphere in hydrostatic equilibrium • Critical Bonner-Ebert Sphere + Rotation + Magnetic Field • Magnetic field lines are parallel to the rotation axis: B//W • Parameters: α, ω • α=Bc2/(4prcs2) :magnetic field strength (ratio of the magnetic to thermal pressure) • w=W/(4pGr)1/2: angular velocity normalized by freefall timescale • Initial Value • Number density ：n=104cm-3 • Temperature：T=10K • Cloud scale: 4.6x104AU • Mass： Mtot =14 Msun • (Bx,0, By,0, Bz,0) = (0, 0, (a4prcs2 )1/2) • (Wx,0, Wy,0, Wz,0) = (0, 0, w(4pGr)1/2 )

7. L = 1 L = 2 L = 3 Numerical Methods • 3D Resistive MHD Nested Grid Method • Grid size: 128 x 128 x 64 (z-mirror sym.) • Grid level:lmax=31 (l: Grid Level) • Total grid number: 128 x 128 x 64 x 31For uniform grid, (128x2x1030)x(128x2x1030)x(64x2x1030) ~ (1030)3 cells are necessary • Grid generation: Jeans Condition 同時刻、異なるグリッドスケール At the same epoch but different spatial scales l=1: Lbox = 4 pc, n = 103 cm-3(initial)l=31: Lbox = 0.2 Rsun, n = 1023 cm-3 (final) 10 orders of magnitude in spatial scale 20 orders of magnitude in density contrast Example of Nested Grid Schematic view of Nested Grid L = 31 L=4

8. Initial State Isothermal Collapse First Core Formation Adiabatic Collapse Outflow Driving Magnetic Dissipation Second Collapse Protostar & Jet Cloud Evolution from Molecular Cloud to Protostar nc=104 cm-3 nc=109 cm-3 nc=1011 cm-3 nc=1013 cm-3 nc=1021 cm-3 nc=1017 cm-3 nc=1022 cm-3 nc=1015 cm-3

9. Dissipation by the Ohmic Dissipation Grid level L=14 (Side on view) Magnetic flux against the central density Ideal MHD model 100 AU Resistive MHD model • Magnetic flux is largely removed from the first core for 1012-1016 cm-3 Evolution of the Magnetic field at center of the cloud • n= ~5x1011 cm-3:First core formation, B field begins to be twisted • 1011 cm-3 <n< 1013 cm-3: B field strongly twisted, outflow appears • 1013 cm-3 <n< 1016 cm-3: B Field is dissipated by the Ohmic dissipation (Br, Bf) ⇒ The magnetic field lines are uncoiled (Bz becomes major component) • 1016 cm-3 <n< 1020 cm-3 : Second collapse, B is coupled with the neutral gas, amplified again • n>1020 cm-3: Protostar formation, Br, Bfincrease again

10. Outflow and Jet Driving Phase High-velocity flow from Protostar Low-velocity Flow from First core Two distinct flows appear in the collapsing cloud!! ~1000 timesclose-upof the central area 360 AU 0.35 AU L=22 voutflow~ 5 km/s L=12 vJet~50 km/s • First Core：n~1011 cm-3, r~10-100 AU • Protostar：n~1021 cm-3, r~0.01 AU

11. Driving Phase of Each Flow 1000 times close-up 103-105 yr • Adiabatic core (first and protostarcore) formation ⇒ trot < tcollapse ⇒ Magnetic field lines are twisted ⇒Flow driving • Each core has different scale and different magnetic field strength • First Core does not experience the Ohmic dissipation: Strong field, hourglass • Protostar experiences the Ohmic dissipation: Weak field, straight lines

12. B gradient Disk Wind Weak B Strong B Wide Opening Angle Narrow Opening Angle Collimation • Different degrees of the collimation are caused by different driving mechanisms Driving Mechanism Forces Around First Core (Outflow)Lorenz≒ Centrifugal ≒Thermal Pressure (inflow) Around Protostar (Jet)Centrifugal ≒ Thermal Pressure >> Lorentz(inflow) Magnetocentrifugal wind ⇒ First core, Outflow Magnetic pressure gradient wind+MRI⇒ Protostar, Jet First Core Protostar ・Strong B・flow along B lines・hourglass B ・weak B・Flow along rotation axis・straight B b>1000 b~1-10

13. Flow Speed • Flow speed is determined by gravitational potential of each core (Kepler speed) • First core: ~0.01 Msun, ~1 AU ⇒ vKep~ 5 km/s ⇔ vmax= 5 km/s (simulation) • Protostar: ~0.01 Msun, ~1 Rsun ⇒ vKep~50 km/s ⇔ vmax= 50 km/s (simulation) • We calculated the very early phase of the star formation • Flow speeds increases with core mass • The Kepler speed is proportional to ∝M1/2 • When the first core and protostar grow up to ~1Msun • Outflow ⇒ vKep~ 50 km/s • Jet ⇒ vKep~500 km/s Proto star First core 20 AU

14. Properties of Outflow and Jet • Our simulation could naturally reproduce properties of outflows and jets • Low-velocity outflow is enclosed by the high-velocity Jet Schematic View

15. Summary • To avoid artificial settings around the protostar, we calculated the cloud evolution (or jet driving) from the molecular cloud (n=104 cm-3) until the protostar formation (n~1023 cm-3) • Outflow is directly driven from the first core (not entrainmented by jet) • Two distinct flows: Outflow from the first core, Jet from the protostar • Outflow: wide opening angle and slow speed • Jet: well-collimated structure and high speed • The differences between outflow and jet is caused by different strength of magnetic field, and different depth of gravitational potential • Different strength of magnetic field is caused by the Ohmic dissipation • Deferent depth of the gravitational potential is cause by the thermal evolution of the collapsing cloud

16. Interaction between outflow and molecular cloud unsteady Outflow driving point (small scale) Outflow propagation (middle scale) Interaction between outflow and host cloud (large scale) 500 AU 10000 AU 2000 AU Initial Molecular Cloud Core Bow shock, Cavity, Turbulence 8000 AU Velusamy et al. (2007)HH47