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