# AS 4002 Star Formation & Plasma Astrophysics Protostellar spin evolution Solve equation of motion numerically Use a stellar evolution code (Eggleton 1992)

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AS 4002 Star Formation & Plasma Astrophysics 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:

AS 4002 Star Formation & Plasma Astrophysics Stellar spin evolution: results 4 5 6 7 8 Log (Age in y) 3 2 1 0 Log  sun M acc =.002 M sun M acc =.01 M sun M acc =.05 M sun B 0,sun =30 G

AS 4002 Star Formation & Plasma Astrophysics Disc mass and ZAMS rotation rate Models which accrete more than 0.01 M sun arrive on the ZAMS with a low rotation rate that is almost independent of disc mass.

AS 4002 Star Formation & Plasma Astrophysics The ZAMS rotation distribution The distribution of disc masses inferred for CTTS from 1.3 mm continuum fluxes can be approximated by a log-normal distribution: N -3 -2 -1 Log (M acc / M sun ) N 0 50 100 150 v sin i (km/sec) 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.

AS 4002 Star Formation & Plasma Astrophysics 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

AS 4002 Star Formation & Plasma Astrophysics Parker’s isothermal wind solution Spherically symmetric Steadily expanding Isothermal Mass continuity Equation of motion Equation of state

AS 4002 Star Formation & Plasma Astrophysics The sonic point Eliminate  using: To get: Sonic point: both LHS and RHS vanish at critical point where:

AS 4002 Star Formation & Plasma Astrophysics Isothermal wind solutions Integrate: Constant of integration. r/r c “Solar wind” u/c s C r/r c “Solar wind” solution passes smoothly through sonic point; putting u=c s and r=r c gives C = -3. “Breezes”

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