Modelling Star Formation with AMR* Simulations

Robi Banerjee, FLASH Workshop, Hamburger Sternwarte, Feb 15th 2012

Sink Particles and Applications for FLASH

Christoph Federrath (Monash University)Paul Clark (University of Heidelberg)Thomas Peters (Zurich University)Philipp Girichidis (University of Hamburg)Daniel Seifried (University of Hamburg)...

Robi BanerjeeHamburger Sternwarte


Why Sink Particles?

• modeling of dense regions in collapse simulations, e.g. star formation (M.Bate et al. 1995)• ‘controlled’ violation of the Truelove criterion (Truelove et al. 1997): preventing artificial fragmentation by resolving the Jeans length• allows long term runs of star forming regions: binaries, stellar clusters, outflows also: feedback, drag forces, ... • BUT: ‘arithmetic’ part of the system, i.e. ⇒ physical interpretation?


ImplementationBased Paul Ricker’s particle module in FLASH• handles boundaries• moves particles across CPUs/blocks• mapping of grid variables onto particles and vice versa• advances particles

Extensions / modifications:• creation of particles on the ‘fly’• gravity: use 1/r2 force for particle contribution• time dependent particle masses: accretion / loss• momentum transfer onto the particles• back-reaction onto the grid (feedback)• MPI communication of global particle list


Implementation• Gravity

originally:1. mapping of particle density onto grid (CIC, NGP, TSC)2. solve Poisson’s equation with gas-density + particle-density3. map acceleration to particle4. advance particle (Euler, Leapfrog)

Sink Particle Module:• use direct acceleration from particles ⇒ more accurate (e.g. binary system)

⇒ faster for small particle numbers


Implementation• Gravity

with 1/r2 → f(r,rsoft) : gravitational softening

particles

grid


Implementation

• Gravitational softening

Linear


Sub-Cycling

• close “binary” interaction can limit time step:

⇒ sub-cycle on particle-particle interaction till:


Sub-Cycling

• after 10 orbits

Federrath et al. 2010


Sub-Cycling

• after 1000 orbits (two particles around the common center)


• Particle creation

Implementation

Conditions by gravitational collapse:

0. Density criterion (within accretion radius raccr):

ρgas > ρcrit (ρcrit parameter)

⇒ choose ρcrit so that Truelove criterion is not violated:

λJ > NJ Δxmin

Jeans refinement condition available (λJ = (πc2/Gρ)1/2)



Implementation

Federrath, RB, Clark, Klessen, ApJ 2010

Conditions by gravitational collapse:

0. Density criterion: ρgas > ρcrit (ρcrit parameter)



Implementation


• Mass accretion / momentum transfer

Implementation

• Mass accretion from excess gas density within ri < raccr :

Mi = Mi + Σj ΔVolj (ρj − ρcrit)

• Check for convergent flow, i.e. vrad < 0• Mass conservation ensured

• linear momentum conservation:

Pi = Pi + Σj Δmj vj


• angular momentum

Implementation

no unique solution for angular momentum conservation:

⇒ internal spin:

use for sub-grid modelling, e.g. outflows from young stars


• Particle merging (optional)

Implementation

dynamicalmerging

• merged particle at center of mass • ensures conservation of mass, momentum and spin


• Inter CPU communication

Implementation

Communicate global particle list (Module GetInfoAllParticle)

CPU1 CPU2

raccr

Sink

Use global list• to find particles• for gas-sink interaction• sink-sink interaction• “integrate” quantities (e.g. mass within sink-radius)


Tests

• sinks in an external potential (SIS density profile)• sink refinement


Tests

• sinks in an external potential (SIS density profile)• sink refinement• sub-cycling necessary


• Star cluster formation (Philipp Girichidis)• Self-consistent jet-launching (Daniel Seifried)

+ Feedback (sub-grid models):• radiation feedback (Thomas Peters, Mikhail Klassen)• Jets/Outflows (Martin Schrön)• Supernovae• gas drag ....

Applications


Comparison to SPH implementation

• collapse of turbulent cloud cores (see also Philipp Girichids’ talk)


Comparison to SPH implementation

• good agreement• differences due to hydro ⇒ SPH slightly more dissipative

⇒ cluster more centrally condensed

Federrath et al. 2010


Applications

feedback from ionizing radiation by Thomas Peters

disc formation and jet launching by Daniel Seifried


Outflows form YSOs

Sub-grid modelling


SN Feedback


Particle-Gas drag

• “easy” implementations of gas-particle interaction• e.g. particle-gas drag via elastic scattering


Outlook• prospect for many more applications: e.g. planets in viscous disks, ...• further intrinsic properties

• chemical properties for chemical networks• sticking properties: build up of planetesimals• non rigid body for angular momentum exchange• ...

• more flexible interfaces to use for sub-grid modelling (so far: only one big module)• combine with Tree-Gravity Code (Richard Wünsch) ⇒ faster gravity

Modelling Star Formation with AMR* Simulations

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