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Protostellar spin evolution

Protostellar spin evolution. 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. Dynamo field: Magnetic torque: Accretion torque: Equation of motion:.

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Protostellar spin evolution

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

  2. Stellar spin evolution: results 3 B0,sun=30 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. 250 B(ref) = 300 G 200 B(ref) = 100 G Equatorial velocity on ZAMS (km/sec) 150 100 50 0 -2.5 -2 -1.5 -1 -0.5 Log (Mass accreted / Msun) 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. N The distribution of disc masses inferred for CTTS from 1.3 mm continuum fluxes can be approximated by a log-normal distribution: -3 -2 -1 Log (Macc/ Msun) The resulting distribution of projected equatorial rotation speeds resembles the peak-and-tail distribution found in the  Per (50 Myr) and Pleiades (70 Myr) clusters. N 0 50 100 150 v sin i (km/sec) 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):  ~ t–1/2. • 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. Parker’s 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. 1.4 -2.8 -2.9 1.2 -3 -3.2 1 -3.1 0.8 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Isothermal wind solutions • Integrate: “Solar wind” solution passes smoothly through sonic point; putting u=cs and r=rc gives C = -3. Constant of integration. u/cs “Solar wind” C u/cs “Breezes” r/rc r/rc

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