Ionising Stellar Feedback with Phantom and CMacIonize Maya Petkova - PowerPoint PPT Presentation

Ionising Stellar Feedback with Phantom and CMacIonize Maya Petkova Supervisor: Ian Bonnell Collaborators: Guillaume Laibe, Bert Vandenbroucke, Jim Dale

SPH and MCRT JHK Spitzer/IRAC Herschel/PACS Herschel/Spire Bonnell, Bate & Vine (2003) Robitaille (2011) 0.2pc Smoothed ParPcle Monte Carlo Hydrodynamics RadiaPve Transfer

MCRT Recap

SPH and MCRT ParPcle posiPons, density structure SPH MCRT Moves parPcles Propagates light to new posiPons through a density based on forces. grid. Thermal energy deposited in the parPcles

SPH and MCRT ParPcle posiPons, density structure SPH MCRT Moves parPcles Propagates light to new posiPons through a density based on forces. grid. Thermal energy deposited in the parPcles

Lagrangian vs Eulerian Cloud SPH MCRT

Voronoi tessellaPon

Voronoi tessellaPon Hubber, Ercolano & Dale (2016)

An SPH parPcle and its kernel ⎧ 2 3 1 − 1.5 r ⎜ ⎞ ⎛ + 0.75 r ⎛ ⎜ ⎞ , r ≤ h ⎪ ⎟ ⎟ ⎝ h ⎠ ⎝ h ⎠ ⎪ ⎪ 3 ⎪ ⎛ ⎞ W ( r , h ) = 1 0.25 2 − r , h ≤ r ≤ 2 h ⎨ ⎜ ⎟ h 3 π ⎝ h ⎠ ⎪ ⎪ 0, r ≥ 2 h W ⎪ ⎪ 0.30 ⎩ 0.25 0.20 0.15 0.10 0.05 r 0.5 1.0 1.5 2.0 2.5 3.0 h

SPH density sum N ρ ( ! m i W ( ! r − ! ∑ r ) = r i , h ) i = 1

Voronoi cell density

How do we integrate a spherically symmetric funcPon over the volume of any random polyhedron?

Can How do we integrate a spherically symmetric funcPon over the volume of any random polyhedron? (analy&cally)

Yes. And this is how. Divergence Green’s Theorem Theorem b ∫ f ( x ) dx = F ( b ) − F ( a ) a

Divergence Theorem ∇⋅ ! ! ∫ ∫ F ⋅ ˆ F dV ndA = V ∂ V ⎧ 2 3 ⎜ ⎞ ⎛ ⎜ ⎞ ⎛ 1 − 1.5 r + 0.75 r , r ≤ h ⎪ ⎟ ⎟ h h ⎝ ⎠ ⎝ ⎠ ∇⋅ ! ⎪ ⎪ 3 ⎪ W ( r ) = 1 0.25 2 − r ⎛ ⎞ ∫ ∫ W dV F dV = , h ≤ r ≤ 2 h ⎨ ⎜ ⎟ h 3 π ⎝ h ⎠ ⎪ V V ⎪ 0, r ≥ 2 h ⎪ ⎪ ⎩ ! r ˆ F = F r ⎧ 1 10 h 2 r 5 + 1 3 3 r 3 − 8 h 3 r 6 , r ≤ h ⎪ ⎪ ⎛ ⎞ ⎪ 6 h 3 r 6 − h 3 r = 1 = 1 1 1 3 r 3 − 3 8 h r 4 + 6 5 h 2 r 5 − 1 r 2 W ( r ) dr ∫ F ⎟ , h ≤ r ≤ 2 h ⎨ ⎜ r 2 r 2 h 3 π 4 15 ⎝ ⎠ ⎪ ⎪ h 3 ⎪ 4 , r ≥ 2 h ⎩

Green’s Theorem ∇⋅ ! ! " ∫ ∫ ⋅ ˆ H dA H mdl = A ∂ A ! ∇⋅ ! ! ! H = H R R ∫ ∫ F ⋅ ˆ ndA H dA = ∂ V A µ = cos θ = r 0 r ⎧ 2 3 1 6 µ − 2 − 3 ⎛ r ⎞ µ − 4 − 1 ⎛ r ⎞ µ − 5 + B 3 , µ ≥ r 0 0 1 0 ⎪ ⎜ ⎟ ⎜ ⎟ 40 ⎝ h ⎠ 40 ⎝ h ⎠ r h ⎪ 0 ⎪ ⎛ ⎞ 2 3 − 3 3 ⎪ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ H R = 1 = 1 r 1 4 3 µ − 2 − r ⎟ µ − 3 + 3 r µ − 4 − 1 r µ − 5 + 1 r ⎟ + B 2 3 , r 2 h ≤ µ ≤ r ∫ F r sin θ dR 0 0 0 0 0 0 0 ⎜ µ ⎟ ⎨ ⎜ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ h 3 π R R 4 ⎝ h ⎠ 10 ⎝ h ⎠ 30 ⎝ h ⎠ 15 ⎝ h ⎠ r h ⎪ ⎝ ⎠ 0 ⎪ − 3 − 1 ⎛ r ⎞ µ + B 3 3 , µ ≤ r ⎪ 0 0 ⎜ ⎟ ⎪ 4 ⎝ h ⎠ r 2 h ⎩ 0

Final soluPon I 0 = ϕ + C ⎛ ⎞ 2 3 3 1 = r 4 − 2 3 + 3 ⎛ r ⎞ − 1 ⎛ r ⎞ B 0 ⎜ 0 0 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ 10 ⎝ h ⎠ 10 ⎝ h ⎠ 2 1 + r ⎝ ⎠ 2 cos 2 ϕ ⎜ 0 ⎟ R 0 ⎜ ⎟ ⎧ 2 3 − 2 I 1 = − sin − 1 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ − 2 3 + 3 r − 1 r − 1 r + C 0 0 0 ⎜ ⎟ , r 0 ≤ h 2 ⎪ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 1 + r 3 ⎪ 10 h 10 h 5 h 0 B 2 = r ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎜ ⎟ ⎜ ⎟ 0 2 ⎨ R 0 ⎝ ⎠ 4 2 3 − 3 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎪ − 4 3 + r ⎟− 3 r + 1 r − 1 r 0 0 0 0 , h ≤ r 0 ≤ 2 h ⎜ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 2 ⎪ I − 2 = ϕ + r ⎝ h ⎠ 10 ⎝ h ⎠ 30 ⎝ h ⎠ 15 ⎝ h ⎠ ⎩ 0 2 tan ϕ + C R 0 ⎧ 2 3 − 2 − 2 3 + 3 ⎛ r ⎞ − 1 ⎛ r ⎞ + 7 ⎛ r ⎞ 0 0 0 , r 0 ≤ h 2 4 ⎪ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ I − 4 = ϕ + 2 r 2 tan ϕ + 1 r ( ) + C 4 tan ϕ sec 2 ϕ + 2 0 0 10 ⎝ h ⎠ 10 ⎝ h ⎠ 5 ⎝ h ⎠ ⎪ R 0 3 R 0 ⎪ 2 3 − 3 − 2 3 ⎪ B 3 = r − 4 3 + r ⎛ ⎟− 3 ⎞ ⎛ r ⎞ + 1 ⎛ r ⎞ − 1 ⎛ r ⎞ + 8 ⎛ r ⎞ 0 0 0 0 0 0 , h ≤ r 0 ≤ 2 h ⎨ ⎜ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 4 ⎝ h ⎠ 10 ⎝ h ⎠ 30 ⎝ h ⎠ 15 ⎝ h ⎠ 5 ⎝ h ⎠ ⎪ ⎪ − 3 ⎛ ⎞ r ⎪ 0 , r 0 ≥ 2 h ⎜ ⎟ ⎝ h ⎠ ⎪ ⎩ ⎧ 2 3 6 I − 2 − 3 1 ⎛ r ⎞ I − 4 − 1 ⎛ r ⎞ I − 5 + B 3 I 0 , µ ≥ r 0 0 1 0 ⎪ ⎜ ⎟ ⎜ ⎟ 40 ⎝ h ⎠ 40 ⎝ h ⎠ r h ⎪ α = R 0 0 ⎪ ⎛ 2 3 − 3 ⎞ 3 ⎪ = r 1 4 3 I − 2 − r ⎛ ⎟ I − 3 + 3 ⎞ ⎛ r ⎞ I − 4 − 1 ⎛ r ⎞ I − 5 + 1 ⎛ r ⎞ ⎟ + B 2 3 I 0 , r 2 h ≤ µ ≤ r r ∫ 0 0 0 0 0 0 0 0 H R Rd ϕ ⎜ I 1 ⎟ ⎨ ⎜ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ h 3 π 4 ⎝ h ⎠ 10 ⎝ h ⎠ 30 ⎝ h ⎠ 15 ⎝ h ⎠ r h r ⎪ ⎝ ⎠ 0 0 cos ϕ ⎪ R 0 − 3 − 1 ⎛ r ⎞ I 1 + B 3 3 I 0 , µ ≤ r µ = ⎪ 0 0 ⎜ ⎟ 2 1 + r ⎪ 4 ⎝ h ⎠ r 2 h 2 cos 2 ϕ ⎩ 0 0 R 0 u = 1 − (1 + α 2 ) µ 2 I − 3 = α (1 + α 2 ) ⎛ ⎞ ⎛ ⎞ 2 u ⎟ + α ) + tan − 1 u ( 1 − u 2 + log(1 + u ) − log(1 − u ) 2 log(1 + u ) − log(1 − u ) ⎟ + C ⎜ ⎜ 4 ⎝ ⎠ ⎝ α ⎠ I − 5 = α (1 + α 2 ) 2 ⎛ 10 u − 6 u 3 ⎞ ⎟ + α (1 + α 2 ) ⎛ 2 u ⎞ ) + tan − 1 u ⎛ ⎞ ⎟ + α (1 − u 2 ) 2 + 3 log(1 + u ) − log(1 − u ) ( ) 1 − u 2 + log(1 + u ) − log(1 − u ) 2 log(1 + u ) − log(1 − u ) ( ⎟ + C ⎜ ⎜ ⎜ 16 4 ⎝ ⎠ ⎝ α ⎠ ⎝ ⎠

Graphic RepresentaPon of the SoluPon Petkova et al. 2018 ParPcle posiPon r 0 Voronoi cell φ R 0 wall Voronoi cell vertex

Graphic RepresentaPon of the SoluPon Petkova et al. 2018 ParPcle posiPon Voronoi cell wall

Graphic RepresentaPon of the SoluPon Petkova et al. 2018 ParPcle posiPon Voronoi cell wall

Kernel IntegraPon in 2D Petkova et al. 2018

Kernel IntegraPon in 3D Petkova et al. 2018 h\ps://github.com/mapetkova/kernel-integraPon

Numerical Tests Petkova et al. 2018

Comparison with the Common Density CalculaPon Methods Petkova et al. 2018 Disk galaxy Uniform cube SN shock Clumpy cloud

Density CalculaPon Timing Tests Petkova et al. 2018

ParPcle posiPons, density structure SPH MCRT Moves parPcles Propagates light to new posiPons through a density based on forces. grid. Thermal energy deposited in the parPcles

Live radiaPon hydrodynamics SPH: Phantom (Price et al. 2017) + MCRT: CMacIonize (Vandenbroucke & Wood, in press) + Density mapping: Petkova et al. 2018

Live radiaPon hydrodynamics (test): D-type expansion of an H II region Bisbas et al. 2015

Live radiaPon hydrodynamics (test): D-type expansion of an H II region Bisbas et al. 2015

Live radiaPon hydrodynamics (test): D-type expansion of an H II region Bisbas et al. 2015

Live radiaPon hydrodynamics (test): D-type expansion of an H II region Bisbas et al. 2015

Live radiaPon hydrodynamics (test)

Live radiaPon hydrodynamics (test)

Soon to come… Dale et al. 2012

MulPple sources

Open QuesPon: ResoluPon Koepferl et. al (2016)

Summary ParPcle posiPons, density structure SPH MCRT Moves parPcles Propagates light to new posiPons through a density based on forces. grid. Thermal energy deposited in the parPcles