The role of radiation pressure and accretion disks in the formation of ...

Rolf Kuiper
The role of radiation pressure
and accretion disks
in the formation of massive stars
Rolf Kuiper
H. Klahr, H. Beuther, T. Henning, C. Dullemond, M. Flock (MPIA),
W. Kley (University of Tübingen), T. Hosokawa (JPL)
ITA colloquium, Heidelberg, May, 12 th 2010
ITA colloquium, Heidelberg May, 12 th 2010

Generalized Eddington limit:
● M → 20 M º
Rolf Kuiper
The radiation pressure problem
not to scale
ITA colloquium, Heidelberg May, 12 th 2010

L *
M *
Rolf Kuiper
What is the radiation pressure problem
= 4G c
in the formation of massive stars?
*
Hosokawa & Omukai (2009)
L *=L accretionL nuclear
Laor & Draine (1993)
ITA colloquium, Heidelberg May, 12 th 2010

Generalized Eddington limit:
● M → 20 M º
Dynamic 1D limit:
● M → 40 M º
Rolf Kuiper
The radiation pressure problem
not to scale
ITA colloquium, Heidelberg May, 12 th 2010

The upper mass limit of spherically symmetric accretion
Rolf Kuiper
ITA colloquium, Heidelberg May, 12 th 2010

Generalized Eddington limit:
● M → 20 M º
Dynamic 1D limit:
● M → 40 M º
Yorke & Sonnhalter (2002):
● “Flashlight effect”
● Frequency dependent
Rolf Kuiper
The radiation pressure problem
● But: shorten disk accretion phases
● M → 43 M º
Krumholz et al. (2007, 2009):
● Non-axially symmetric modes required
● M → 41.5 M º (primary) + 29.2 M º (secondary) + 28.3 M º (disk+envelope)
not to scale
ITA colloquium, Heidelberg May, 12 th 2010

Aim:
● Single yet versatile code to test
the proposed solutions:
● Splitting stellar irradiation
Rolf Kuiper
and thermal dust emission
● Frequency dependent stellar
luminosity feedback
● 1D, 2D, and 3D
Code:
Code development
● Open source Magneto-Hydrodynamics code Pluto (v3.0)
● plus Frequency dependent radiation transport
● plus Poisson-solver
Poisson
PIA cluster at the Garching computing center.
● plus Stellar evolution model (tracks by Hosokawa & Omukai 2009)
● plus Dust model (Laor & Draine 1993)
ITA colloquium, Heidelberg May, 12 th 2010

Conservation of ...
… Mass
… Momentum
… Energy
Eq. of state
Poisson eq.
FLD equation
Rolf Kuiper
∂ t ∇⋅u=0
∂tuu⋅ ∇ u=− ∇ P
∇
− ∇
∂t e ∇⋅[eP u]= u⋅ ∇ −u⋅ ∇
P=−1e
∇ 2 =4G
∂ t E R f c ∇⋅ D ∇ E R= f cQ +
D= c
R f c=
F P ,
4a T 3
c v 1−1
*
= F
* −
Irradiation 0e
= P , r
Q + =− *
∇⋅F P ,
− ∇ F
c
− u⋅ ∇ F
c
=gas density
u=gas u=gas velocity
P=gas pressure
e=internal energy
=adiabatic index
=viscosity tensor
− ∇⋅F
=gravitational potential
G=gravitaty constant
E R=thermal radiation energy
F =flux of total radiation energy
F
D=diffusion coefficient
=-dependent dust opacity
=optical depth
c=speed of light
* =flux of stellar radiation energy
=flux-limiter
R=Rosseland mean opacity
P=Planck mean opacity
a=radiation constant
cv=heat capacity
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
Pluto3.0: A high-order Godunov-solver
For the hydrodynamics we are using the public available MHD-code Pluto3.0:
Godunov-solver: Combining Finite Volume Method (FVM) with Riemann-solvers
Conservative scheme for mass, momentum and energy
Analytic or analytically approximated propagation speed of waves
Full implementation of the viscous stress tensor
Our default configuration:
Runge-Kutta 2 (RK2) in time and spatially
piecewise linear interpolation (Slope-Limiter)
2 nd order in time and space
Harten-Lax-VanLeer (hll) Riemann-solver
Slope-Limiter: MinMod-Limiter, Total Variation Diminishing (TVD) method
No violation of propagation speeds, No post-shock wiggles
Strang operator splitting in multi-dimensions
We added: Self-gravity (Poisson-solver) and Radiation transport (FLD+Ray-tracing),
Dust (Laor & Draine) and Stellar evolution (Hosokawa & Omukai) model
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
The Radiation scheme
not to scale
ITA colloquium, Heidelberg May, 12 th 2010

8
Rolf Kuiper
Domain:
Axial symmetry.
Density setup: r , = 0
Pascucci Radiation Test:
r = 1...1000 AU
= ±90 °
Radial stretched grid (10%).
r d
r
exp−
4
z 2
hr
hr =z d r /r d 1.125
r d =r max /2=500 AU
z d=r max/8=125 AU
Different optical depths via different density normalizations.
2
y [AU]
x [AU]
ITA colloquium, Heidelberg May, 12 th 2010

8
Rolf Kuiper
Domain:
Axial symmetry.
Density setup: r , = 0
Pascucci Radiation Test:
r = 1...1000 AU
= ±90 °
Radial stretched grid (10%).
r d
r
exp−
4
z 2
hr
hr =z d r /r d 1.125
r d =r max /2=500 AU
z d=r max/8=125 AU
Different optical depths via different density normalizations.
=0.1 :
For this most optical thin case, the temperature distribution
is well reproduced via simple gray irradiation (< 2%).
=100 :
The absorption/irradiation temperature distribution is well
reproduced via frequency-dependent irradiation (< 5%).
The deviations in the diffusion run stay below 11%.
2
y [AU]
x [AU]
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
gray
Pascucci Radiation Test:
radial cut
through
midplane
frequency dependent
intermediate layer
polar cut
at r = 2 AU
ITA colloquium, Heidelberg May, 12 th 2010

●Setup:
Rolf Kuiper
Configuration
● Monolithic collapse in spherical coordinates /
Accretion onto a single massive star
Initial conditions:
● Outer radius of 0.1 pc
● Density ~ r -2
● Temperature = 20 K
● Rigid rotation = 1.6*10 -5 yr -1 (in 2 and 3D)
Numerical configuration:
● 2 nd order accurate in space and time
● Semi-permeable inner and outer boundaries
(mass can leave but not enter the domain)
64 x 16 grid:
0.1 pc
100 AU
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
Key features
● Superior frequency dependent ray-tracing step (irradiation)
● Fast and robust flux limited diffusion solver (dust emission)
● Resolution down to 1.27 AU (~10 times higher than before)
● Complete coverage of the accretion phase (10 5 … 10 6 yr) for the first time
● First broad scan of the parameter space (37 simulations analyzed so far)
ITA colloquium, Heidelberg May, 12 th 2010

● Dimension = 1D, 2D, 3D
● Resolution / Convergence
● Sink cell radius = 1 … 160 AU
● Alpha-viscosity (2D) = 0 … 1
● Initial core mass = 60 … 480 M º
Rolf Kuiper
Variations of the 37 simulations
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
Visualization: Global collapse
0.2 pc
ITA colloquium, Heidelberg May, 12 th 2010

Results:
Larger sink cells lead to ...
● longer free fall phases
Rolf Kuiper
Resolving the dust condensation front
=> can be eliminated analytically
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
Resolving the dust condensation front
ITA colloquium, Heidelberg May, 12 th 2010

Results:
Larger sink cells lead to ...
● longer free fall phases
Rolf Kuiper
Resolving the dust condensation front
=> can be eliminated analytically
● diminished shadowing
=> Sink cells in Yorke & Sonnhalter
(2002) were too large!
ITA colloquium, Heidelberg May, 12 th 2010

Breaking through
the upper mass limit of spherically symmetric accretion
Rolf Kuiper
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
Visualization: Non-axial symmetric outflows
~ 200 AU
ITA colloquium, Heidelberg May, 12 th 2010

Results:
Rolf Kuiper
The 3 rd dimension:
Angular momentum transport via self-gravity
● Gravitational instabilities (Toomre: 1 < Q < 2)
● Mean accretion rate ~ viscous disk evolution
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
Visualization: Angular momentum transport
~ 80 AU
ITA colloquium, Heidelberg May, 12 th 2010

Ongoing projects:
Rolf Kuiper
What's next?
● Detailed study of the outflow region in three dimensions
● Consistent stellar evolution modeling (with T. Hosokawa, JPL)
● Broader scan of the parameter space (density profiles, rotation)
Long-term tasks:
● Ionization + radiation pressure feedback
● Radiation Magneto-Hydrodynamics
Magneto
● Sink particles for study of disk fragmentation
ITA colloquium, Heidelberg May, 12 th 2010

Rolf Kuiper
You shall resolve the
dust condensation front!
No “3D Radiative
Rayleigh-Taylor”
instability.
Summary
Disk accretion produces
the most massive stars!
Self-gravity drives a sufficient
angular momentum transport!
ITA colloquium, Heidelberg May, 12 th 2010