Physics 778 (2009): 3. Gravitational collapse, early disks and outflows Ralph Pudritz Physics 778 – Star Formation - 2009
A. HYDRO: collapse of rotating B-E spheres (eg. Banerjee, Pudritz, & Holmes 2004) • Initial Conditions: • Pressure confined, rigidly rotating, B-E model • Rotation in range given by observations • MOLECULAR COOLING, using data from Neufeld et al. (1995) Initial, rotating, Bonner-Ebert sphere
BE collapse, 1D: Foster & Chevalier, ApJ 1993. • Key points: - confirm Larson-Penston… radial inflow velocities do indeed reach 3.3cs - study collapse of marginally stable sphere with - collapse formed a protostellar core in 5 free-fall times. - t=0; time of protostellar core formation, -ve times are “collapse” phase, +ve times are “accretion” phase in solutions - max inflow velocity reached just outside edge of inner flattened region of density (defined by isothermal core radius ro). - at larger radii, density - accretion rate depends on radius… NOT a constant. peaking at
3D collapse of BE isothermal sphere: - top: density profiles as a function of time - bottom: radial velocity profiles… note that these are “outside-in” NOT “inside- out” (latter occurs during accretion phase not initial collapse phase Banerjee, Pudritz, & Holmes, MNRAS 2004
Predicted collapse of Barnard 68 (Alves et al), including molecular cooling (from Banerjee, Pudritz, & Holmes 2004) Note; general character of “pure” BE collapse is preserved…
xy: view of disk plane yz: view of vertical section of disk t=.. t=..
Zoomed in view of central region… xy view: rotating bar yz view: vertical collapse + two shock structure
Molecular cooling and “effective” equation of state - Temperature, and effective equation of state; as a function of gas density. - B-E remains isothermal until free-fall time exceeds molecular cooling time scale. After this, collapse *cannot* be modeled with a simple adiabatic index…
Evolution of radial density profile of collapsing, rotating B-E sphere
Evolution of angular momentum profile • Left: specific angular momentum j_z • Right: rotation speed
B. MHD simulations of collapsing, magnetizedB-E spheres • Initial conditions as in hydro; except for addition of additional, uniform, magnetic field: = 84 on midplane • M = 2.1 solar masses, R = 12,500 AU, T = 16K; free-fall time 67,000 yr. • Spin parameter
Propagation of torsional Alfven waves – extracting core angular momentum
Onset of large scale outflow: at 1.86 million yrs, and 1430 yrs later
Jet launch: disk shown inside 0.07 AU separated by 5 month interval - Alfven surface in blue, field lines in green
3D Visualization of field lines, disk, and outflow:- Upper; magnetic tower flow- Lower; zoomed in by 1000, centrifugally driven disk wind
Disk structure: top view- ring formation (left panel) followed by fragmentation into 2 fragments – binary system?
Outflows and the IMF • Stellar mass is the outcome of the competition between collapse and core dispersal (Myers 2008) • Collision times between cores long – so they can remain “isolated” (Evans et al 2009) • Thus, cores can map onto stars (Enoch et al 2008
Wide variety of stellar masses possible… • Self- limiting vs runaway accretion • Depends on free-fall vs dispersal times • Constant CMF/IMF implies td ~ (0.4-0.8)tff Gentle disruption speed required 0.4 km per sec Myers 2008
Early history of disks, outflows, and binary stars (Duffin & Pudritz 2009) - outflows as a consequence of gravitational collapse, (Banerjee & Pudritz 2007)… magnetic tower flows on scale of disks (10s of AU) – low velocity 0.3 -0.4 km/sec - Myers’s dispersal Ideal MHD Ambipolar Diffusion
3. The physics of cores – from low to high mass stars • Going beyond the Singular Isothermal Sphere - Myers & Fuller (1992) “TNT” model - SIS models do not work on large scales, or form massive stars - need model for non-thermal structure on larger scales… - combine observed thermal motions on small scales (<0.01 pc), with non thermal motions (0.1pc) on larger scales. - works for masses 0.2 – 30 solar masses: time formation times (0.1-1.0 million yrs) fall within constraints of later data.
Model: density follows isothermal behaviour at small scales thermal scales, and 1/r at larger nonthermal scales • Accretion rates for massive stars (3-30 solar masses), are 7-10 times larger than low mass stars (0.2 – 3 solar masses) • Truncation by outflows • This paper spawned many other studies… Jijina et al 1999
Limit of massive stars in highly turbulent media – “logatropes” (n ~ 1/r) (McLaughlin & Pudritz 1997) - model for HMS (Osorio et al 1999, 2009) • Intermediate model with adiabatic index (n ~ 1/r^(1.5)) McKee & Tan (2003) McLauglin & Pudritz (1999