ralph pudritz physics 778 – star formation - 2009
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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). - PowerPoint PPT PresentationTRANSCRIPT
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, rotating, Bonner-Ebert sphere sec/108.2
1.0
5.6
15 rad
t ff
Initial Conditions:
- Pressure confined, rigidly rotating, B-E model
- Rotation in range given by observations
- MOLECULAR COOLING, using data from Neufeld et al. (1995)
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
451.6max
2
Gcs /47 3
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=..
Collapse & disk formation: Density
Collapse & disk formation: Mach number
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…
)(log/)(log pddeff
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
Same initial conditions;except faster initial rotation:
3.0 fft
Ring formation… (t=20)
Which then fragments into binary, each with a disk (t=49)
Block structure for AMR Temperature distribution
B. MHD simulations of collapsing, magnetized B-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 4.0 fft
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?
Magnetized disk properties: radial profiles
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
1;1/ dff tt
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