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

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Ionising Stellar Feedback with Phantom and CMacIonize

Maya Petkova

Supervisor: Ian Bonnell Collaborators: Guillaume Laibe, Bert Vandenbroucke, Jim Dale

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SPH and MCRT

Bonnell, Bate & Vine (2003)

Herschel/PACS 0.2pc Herschel/Spire JHK Spitzer/IRAC

Robitaille (2011)

Monte Carlo RadiaPve Transfer Smoothed ParPcle Hydrodynamics

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MCRT Recap

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SPH MCRT

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

SPH and MCRT

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SPH MCRT

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

SPH and MCRT

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Lagrangian vs Eulerian Cloud

SPH MCRT

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Voronoi tessellaPon

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Voronoi tessellaPon

Hubber, Ercolano & Dale (2016)

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An SPH parPcle and its kernel

W(r,h) = 1 h3π 1−1.5 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

+ 0.75 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

,r ≤ h 0.25 2 − r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

,h ≤ r ≤ 2h 0,r ≥ 2h ⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪

0.5 1.0 1.5 2.0 2.5 3.0 r h 0.05 0.10 0.15 0.20 0.25 0.30 W

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SPH density sum

ρ(! r) = miW(! r − ! r

i,h) i=1 N

∑

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Voronoi cell density

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

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

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• Yes. And this is how.

Divergence Theorem Green’s Theorem

f (x)dx = F(b)− F(a)

a b

∫

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Divergence Theorem

F

r = 1

r2 r2W(r)dr

∫

= 1 r2 1 h3π 1 3r3 − 3 10h2 r5 + 1 8h3 r6,r ≤ h 1 4 8 3r3 − 3 h r4 + 6 5h2 r5 − 1 6h3 r6 − h3 15 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟,h ≤ r ≤ 2h h3 4 ,r ≥ 2h ⎧ ⎨ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ W(r) = 1 h3π 1−1.5 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

+ 0.75 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

,r ≤ h 0.25 2 − r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

,h ≤ r ≤ 2h 0,r ≥ 2h ⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪

∇⋅ ! F dV

V

∫

= ! F ⋅ ˆ ndA

∂V

∫

W dV

V

∫

= ∇⋅ ! F dV

V

∫

! F = F

r ˆ

r

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Green’s Theorem

HR = 1 R F

r sinθ dR

∫

= 1 R r

3

h3π 1 6 µ−2 − 3 40 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

µ−4 − 1 40 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

µ−5 + B

1

r

3 ,µ ≥ r

h 1 4 4 3 µ−2 − r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟µ−3 + 3 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

µ−4 − 1 30 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

µ−5 + 1 15 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−3

µ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟+ B2 r

3 , r

2h ≤ µ ≤ r h − 1 4 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−3

µ + B3 r

3 ,µ ≤ r

2h ⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪

∇⋅ ! H dA

A

∫

= ! H

∂A

" ∫

⋅ ˆ mdl

! F ⋅ ˆ ndA

∂V

∫

= ∇⋅ ! H dA

A

∫

! H = HR ! R µ = cosθ = r r

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Final soluPon

I0 =ϕ +C I1 = −sin−1 1+ r

2

R0

2 cos2ϕ

1+ r

2

R0

2

⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ +C I−2 =ϕ + r

2

R0

2 tanϕ +C

I−4 =ϕ + 2 r

2

R0

2 tanϕ + 1

3 r

4

R0

4 tanϕ sec2ϕ + 2

( )+C

α = R0 r µ = r R0 cosϕ 1+ r

2

R0

2 cos2ϕ

u = 1−(1+α 2)µ 2 I−3 = α(1+α 2) 4 2u 1−u2 + log(1+u)− log(1−u) ⎛ ⎝ ⎜ ⎞ ⎠ ⎟+ α 2 log(1+u)− log(1−u)

( )+ tan−1 u

α ⎛ ⎝ ⎜ ⎞ ⎠ ⎟+C I−5 = α(1+α 2)2 16 10u− 6u3 (1−u2)2 +3 log(1+u)− log(1−u)

( )

⎛ ⎝ ⎜ ⎞ ⎠ ⎟+ α(1+α 2) 4 2u 1−u2 + log(1+u)− log(1−u) ⎛ ⎝ ⎜ ⎞ ⎠ ⎟+ α 2 log(1+u)− log(1−u)

( )+ tan−1 u

α ⎛ ⎝ ⎜ ⎞ ⎠ ⎟+C B

1 = r 3

4 − 2 3 + 3 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

− 1 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ B2 = r

3

4 − 2 3 + 3 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

− 1 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

− 1 5 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−2

,r

0 ≤ h

− 4 3 + r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟− 3 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

+ 1 30 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

− 1 15 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−3

,h ≤ r

0 ≤ 2h

⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ B3 = r

3

4 − 2 3 + 3 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

− 1 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

+ 7 5 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−2

,r

0 ≤ h

− 4 3 + r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟− 3 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

+ 1 30 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

− 1 15 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−3

+ 8 5 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−2

,h ≤ r

0 ≤ 2h

r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−3

,r

0 ≥ 2h

⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ HRRdϕ

∫

= r

3

h3π 1 6 I−2 − 3 40 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

I−4 − 1 40 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

I−5 + B

1

r

3 I0,µ ≥ r

h 1 4 4 3 I−2 − r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟I−3 + 3 10 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

I−4 − 1 30 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

3

I−5 + 1 15 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−3

I1 ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟+ B2 r

3 I0, r

2h ≤ µ ≤ r h − 1 4 r h ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

−3

I1 + B3 r

3 I0,µ ≤ r

2h ⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪

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Graphic RepresentaPon of the SoluPon

Petkova et al. 2018

Voronoi cell vertex Voronoi cell wall ParPcle posiPon r0 R0 φ

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Graphic RepresentaPon of the SoluPon

Petkova et al. 2018

ParPcle posiPon Voronoi cell wall

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Graphic RepresentaPon of the SoluPon

Petkova et al. 2018

ParPcle posiPon Voronoi cell wall

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Kernel IntegraPon in 2D

Petkova et al. 2018

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Kernel IntegraPon in 3D

Petkova et al. 2018 h\ps://github.com/mapetkova/kernel-integraPon

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Numerical Tests

Petkova et al. 2018

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Comparison with the Common Density CalculaPon Methods

SN shock Uniform cube Clumpy cloud Disk galaxy Petkova et al. 2018

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Density CalculaPon Timing Tests

Petkova et al. 2018

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SPH MCRT

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

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Live radiaPon hydrodynamics

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

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Live radiaPon hydrodynamics (test): D-type expansion of an H II region

Bisbas et al. 2015

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Live radiaPon hydrodynamics (test): D-type expansion of an H II region

Bisbas et al. 2015

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Live radiaPon hydrodynamics (test): D-type expansion of an H II region

Bisbas et al. 2015

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Live radiaPon hydrodynamics (test): D-type expansion of an H II region

Bisbas et al. 2015

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Live radiaPon hydrodynamics (test)

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Live radiaPon hydrodynamics (test)

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Soon to come…

Dale et al. 2012

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MulPple sources

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Open QuesPon: ResoluPon

Koepferl et. al (2016)

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SPH MCRT

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

Summary