Protostellar spin evolution

1
Protostellar spin evolution
Dynamo field Magnetic torque Accretion
torque Equation of motion

• Solve equation of motion numerically
• Use a stellar evolution code (Eggleton 1992) to
  compute the moment of inertia and convective
  turnover time at each timestep.

2
Stellar spin evolution results
3
B0,sun30 G
2
Log????sun
Macc.002 Msun
1
Macc.01 Msun
0
Macc.05 Msun
-1
5 6 7
8 Log (Age in y)
4
3
Disc mass and ZAMS rotation rate

• Models which accrete more than 0.01 Msun arrive
  on the ZAMS with a low rotation rate that is
  almost independent of disc mass.

4
The ZAMS rotation distribution
5
Spin-down on the main sequence

• Stars continue to spin down throughout MS
  evolution
• Rapid spindown of fast rotators in young clusters
• Asymptotic phase (Skumanich 1972) ? t1/2.
• Angular momentum loss via hot winds
• low mass-loss rates
• thermally driven at low ?
• centrifugally driven at high ?
• magnetically channelled
• high specific angular momentum

6
Parkers isothermal wind solution

• Spherically symmetric
• Steadily expanding
• Isothermal

Mass continuity
Equation of motion
Equation of state
7
The sonic point

• Eliminate ? using
• To get
• Sonic point both LHS and RHS vanish at critical
  point where

8
Isothermal wind solutions

• Integrate

Solar wind solution passes smoothly through
sonic point putting ucs and rrc gives C -3.
Constant of integration.
u/cs
Solar wind
C
u/cs
Breezes
r/rc
r/rc