Mellinger Lesson 8 Star Formation Toshihiro Handa Dept. of Phys. & Astron., Kagoshima University Kagoshima Univ./ Ehime Univ. Galactic radio astronomy

Mellinger Collapse of a molecular cloud ▶ Collapse by self gravity ■ Potential energy  thermal energy ■ Radiation with infrared : isothermal collapse ■ Small gas pressure with enough cold and rare gas ▶ Timescale ■ dynamical time ■ free fall time

Mellinger Dynamical time ▶ T dyn : Time falling in uniform gas sphere with M d 2 r/dt 2 =-(G/r 2 )(4  /3) r 3  ■ Solve it with r=R, dr/dt=0 at t=0 r=R cos(t(4  G  /3) 1/2 ), ■ It gives T dyn =(3  ) 1/2 /4 (G  ) -1/2 Mass M density  Radius R

Mellinger Free fall time(1) ▶ T ff : Time falling with gravity of object with M d 2 r/dt 2 =-GM/r 2 ■ solve it with r=R, dr/dt=0 at t=0 (u-1) 1/2 /u+arctan((u-1) 1/2 )=At/R, where u=R/r 、 A=(2GM/R) 1/2 ■ Therefore, T ff =1/2 3/2 (G  M ) -1/2 R 3/2 ■ Define  =3M/(4  R 3 ), T ff =(3  /32) 1/2 (G  ) -1/2 mass M=4  R 3 /3 radius R

Mellinger Free fall time(2) ▶ T ff for each shell is independent of initial pos. ▶ It is controlled by avr. density inside it pos. T ff =(3  /32) 1/2 (G  ) -1/2 ■ Outside shell never overpasses the inside shell! ▶ Whole sphere collapse with this time. T ff =2 -1/2 T dyn ▶ These timescales differ only by a factor.

Mellinger Collapse time of a Molecular cloud ▶ Free fall = negligible internal pressure ▶ Typical density of a molecular cloud n(H 2 )=10 3 cm -3 means  = 3.4× g cm -3 ▶ It gives T ff =(3  /32) 1/2 (G  ) -1/2 =1.1×10 9 yr ▶ Time should be much longer. ■ ∵ too short lifetime! ▶ Self gravity vs turbulent motion

Mellinger From Mol. cloud to star formation ▶ Density inhomogenity ▶ Grow by self gravity (?) ▶ Molecular cloud core ■ Observe with high density tracer ■ CS, NH 3 ▶ Collapse by self gravity ▶ Accelerating collapse  adiabatic collapse  heat up ▶ Become a protostar after ionization

Mellinger Mol. cloud & cloud core ▶ e.g. S252(Monkey Head Nebula) Imura 2010 Master Thesis 13 CO NH 3

Mellinger Star forming site ▶ elephant trunk

Mellinger Bipolar outflow and protostar ▶ Gas flow in both sides ▶ Rotating gas disk at its foot

Mellinger Gas outflow from a protostar(1) ▶ Observe the root of jet

Mellinger Gas outflow from a protostar(2) ▶ Maser spot ▶ Herbig-Haro object

Mellinger Acceleration of bipolar outflow ▶ mechanism ▶ Characteristic around a protostar ■ Compact object (protostar) + a lot of gas ■ Magnetic field

Mellinger Magnetic field ▶ Distribution of ion sands around a magnet ▶ Force line connect two poles = magnetic line 大阪市立科学館

Mellinger Characteristic of magnetic field ▶ Magnetic line = B to understand intuitively ■ Repulse two parallel magnetic lines ■ Shortened along a single magnetic line ▶ Magnetic field and line ■ Direction of the line = direction of field ■ Density of the line = field strength ▶ Magnetic line  magnetic flux

Mellinger Electromagnetism and field line ▶ Electric current makes magnet ▶ Field line around a current

Mellinger Magnetic line and electric current ▶ Attract or Repulse two currents ▶ Force to magnetic line from current ▶ Fleming’s left hand rule

Mellinger Electron and magnetic line ▶ Electric current = electron current ▶ Electron motion and mag. line ▶ Spiral motion ▶ Never apart from the line ▶ “Frozen-in” to field line

Mellinger Twist of B by accretion disk ▶ Windup a sprint  pop up a spring 富坂による計算結果

Mellinger Another model ▶ Magnetic-centrifugal force model ■ Rotating magnetic field by an accretion disk ■ Accelerated along magnetic lines