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radiation transport, monte carlo and supernova light curves daniel kasen, UC Berkeley/LBNL supernovae and optical the transient light curve universe optical spectrum ns merger ordinary core collapse supernovae type Ia ordinary core

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SLIDE 1

radiation transport, monte carlo and supernova light curves

daniel kasen, UC Berkeley/LBNL

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SLIDE 2

supernovae and the transient universe

  • ptical

light curve

  • ptical

spectrum

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SLIDE 3

ns merger

slide-4
SLIDE 4
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SLIDE 5
  • rdinary

core collapse supernovae

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SLIDE 6
  • rdinary

core collapse supernovae

type Ia

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SLIDE 7

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

type Ia

slide-8
SLIDE 8

supernova light curves

some basic physical scales

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SLIDE 9

supernova light curves

some basic physical scales

assume (conservatively) blackbody emission at T ~ 104 K

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SLIDE 10

if the remnant expanded to this radius over ~20 days

supernova light curves

some basic physical scales

assume (conservatively) blackbody emission at T ~ 104 K

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SLIDE 11

if the remnant expanded to this radius over ~20 days the kinetic energy of the remnant is then (for M ~ Msun)

supernova light curves

some basic physical scales

assume (conservatively) blackbody emission at T ~ 104 K

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SLIDE 12

stellar evolution (>106 years)

(r), T(r), Ai(r) at ignition/collapse

the computational problem

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SLIDE 13

stellar evolution (>106 years)

(r), T(r), Ai(r) at ignition/collapse hydrodynamics, equation of state nuclear burning, neutrino transport

explosion (seconds/hours)

the computational problem

slide-14
SLIDE 14

stellar evolution (>106 years)

(r), T(r), Ai(r) at ignition/collapse hydrodynamics, equation of state nuclear burning, neutrino transport

explosion (seconds/hours)

neutrinos

  • grav. waves

x-rays, -rays

the computational problem

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SLIDE 15

stellar evolution (>106 years) photon transport matter opacity thermodynamics radioactive decay

expanding ejecta (months)

(x,y,z), v(x,y,z), T(x,y,z), Ai(x,y,z) in free expansion (r), T(r), Ai(r) at ignition/collapse hydrodynamics, equation of state nuclear burning, neutrino transport

explosion (seconds/hours)

neutrinos

  • grav. waves

x-rays, -rays

the computational problem

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SLIDE 16

stellar evolution (>106 years) photon transport matter opacity thermodynamics radioactive decay

expanding ejecta (months)

(x,y,z), v(x,y,z), T(x,y,z), Ai(x,y,z) in free expansion (r), T(r), Ai(r) at ignition/collapse

  • ptical spectra

light curves

hydrodynamics, equation of state nuclear burning, neutrino transport

explosion (seconds/hours)

neutrinos

  • grav. waves

x-rays, -rays

the computational problem

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SLIDE 17

white dwarf helium star red giant 1.4 Msun ~5 Msun 10-20 Msun 109 cm 1011 cm 1013 cm 1051 ergs 1051 ergs 1051 ergs type Ia type Ib/Ic type II

how to explode a supernova

simple description

take a dump in

with a mass

and a radius get a

hydro, burning, neutrinos, etc... ~1051 ergs

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SLIDE 18

jet powered supernova

sean couch

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SLIDE 19

jet powered supernova

sean couch

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SLIDE 20

energetics

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SLIDE 21

energetics

immediately after the explosion (e.g., strong shock) total energy is split between kinetic energy and radiation

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SLIDE 22

energetics

radiation energy dominates over gas thermal energy density e.g., explode the sun, with E = 1051 ergs

immediately after the explosion (e.g., strong shock) total energy is split between kinetic energy and radiation

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SLIDE 23

energetics

radiation energy dominates over gas thermal energy density e.g., explode the sun, with E = 1051 ergs

but the radiation can’t escape because a star is opaque. The ejecta expands by a factor of 102-106 in radius before the density drops enough to become translucent

immediately after the explosion (e.g., strong shock) total energy is split between kinetic energy and radiation

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SLIDE 24

initial radiation from supernova explosions

shock breakout x-ray burst from a red super-giant

0.95 1.00 1.05 1.10 radius (5 × 1013 cm) 2 4 6 8 temperature (105 K)

Ex = 1048 ergs

shock breakout

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SLIDE 25

adiabatic expansion

converts Ethermal into Ekinetic as the radiation does work

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SLIDE 26

adiabatic expansion

first law of thermodynamics (with no heat transfer) converts Ethermal into Ekinetic as the radiation does work

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SLIDE 27

adiabatic expansion

first law of thermodynamics (with no heat transfer)

use chain rule and

converts Ethermal into Ekinetic as the radiation does work

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SLIDE 28

adiabatic expansion

first law of thermodynamics (with no heat transfer)

use chain rule and

converts Ethermal into Ekinetic as the radiation does work

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SLIDE 29

adiabatic expansion

first law of thermodynamics (with no heat transfer)

use chain rule and

so the change in energy density as the radius expands is:

converts Ethermal into Ekinetic as the radiation does work

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SLIDE 30

adiabatic expansion

first law of thermodynamics (with no heat transfer)

use chain rule and

so the change in energy density as the radius expands is:

converts Ethermal into Ekinetic as the radiation does work

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SLIDE 31

adiabatic expansion

first law of thermodynamics (with no heat transfer)

use chain rule and

so the change in energy density as the radius expands is:

converts Ethermal into Ekinetic as the radiation does work

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SLIDE 32

adiabatic expansion

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SLIDE 33

adiabatic expansion

basic thermodynamics

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SLIDE 34

adiabatic expansion

basic thermodynamics

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SLIDE 35

adiabatic expansion

basic thermodynamics

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SLIDE 36

adiabatic expansion

now since basic thermodynamics

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SLIDE 37

adiabatic expansion

now since

the energy density drops as ejecta radius expands

basic thermodynamics

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SLIDE 38

adiabatic expansion

now since

the energy density drops as ejecta radius expands

basic thermodynamics

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SLIDE 39

transition to free expansion

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SLIDE 40

right after the explosion shock, the sound speed cs is of order the expansion velocity, but cs drops with adiabatic cooling

transition to free expansion

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SLIDE 41

right after the explosion shock, the sound speed cs is of order the expansion velocity, but cs drops with adiabatic cooling

transition to free expansion

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SLIDE 42

right after the explosion shock, the sound speed cs is of order the expansion velocity, but cs drops with adiabatic cooling after significant expansion from the initial radius we have

transition to free expansion

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SLIDE 43

right after the explosion shock, the sound speed cs is of order the expansion velocity, but cs drops with adiabatic cooling after significant expansion from the initial radius we have

transition to free expansion

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SLIDE 44

right after the explosion shock, the sound speed cs is of order the expansion velocity, but cs drops with adiabatic cooling after significant expansion from the initial radius we have pressure waves can’t communicate forces faster than the ejecta expands, so hydrodynamics freezes out and fluid moves ballistically

transition to free expansion

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SLIDE 45

right after the explosion shock, the sound speed cs is of order the expansion velocity, but cs drops with adiabatic cooling after significant expansion from the initial radius we have pressure waves can’t communicate forces faster than the ejecta expands, so hydrodynamics freezes out and fluid moves ballistically

transition to free expansion

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SLIDE 46

right after the explosion shock, the sound speed cs is of order the expansion velocity, but cs drops with adiabatic cooling after significant expansion from the initial radius we have pressure waves can’t communicate forces faster than the ejecta expands, so hydrodynamics freezes out and fluid moves ballistically

transition to free expansion

negligible

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SLIDE 47

homologous expansion

self-similar ejecta structure expands over time

Si/O

Si/Mg H

56Ni

He

rule of thumb: to reach homology run your hydrodynamics simulations until Rfinal >~ 10 R0 better: Rfinal ~ 100 R0 check, Ethermal << Ekinetic

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SLIDE 48

r a d i u s ~ t

density ~ t-3 adiabatic temp ~ t-1

s

  • l

a r s y s t e m w h i t e d w a r f r e d g i a n t s

  • l

a r r a d i u s

  • ptical

light curve

  • ptical depth ~ t-2
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SLIDE 49

duration of the light curve

since

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SLIDE 50

duration of the light curve

the diffusion time of photons through the optically thick remnant

since

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SLIDE 51

duration of the light curve

the diffusion time of photons through the optically thick remnant

since

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SLIDE 52

duration of the light curve

the diffusion time of photons through the optically thick remnant

since

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SLIDE 53

duration of the light curve

the diffusion time of photons through the optically thick remnant but since the remnant is expanding, R = vt

since

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SLIDE 54

duration of the light curve

the diffusion time of photons through the optically thick remnant but since the remnant is expanding, R = vt

solving for time (i.e., diffusion time ~ elapsed time)

since

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SLIDE 55

duration of the light curve

the diffusion time of photons through the optically thick remnant but since the remnant is expanding, R = vt

e.g., arnett (1979)

solving for time (i.e., diffusion time ~ elapsed time)

since

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SLIDE 56

diffusion in an expanding medium

arnett 1979, 1980, 1982

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SLIDE 57

diffusion in an expanding medium

  • r substituting:

arnett 1979, 1980, 1982

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SLIDE 58

diffusion in an expanding medium

  • r substituting:

gives the scaling relation for light curve duration arnett 1979, 1980, 1982

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SLIDE 59

diffusion in an expanding medium

  • r substituting:

gives the scaling relation for light curve duration mass often tends to be the dominating factor arnett 1979, 1980, 1982

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SLIDE 60
  • pacity terminology
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SLIDE 61
  • pacity terminology
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SLIDE 62
  • pacity terminology
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SLIDE 63
  • pacity terminology
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SLIDE 64
  • pacity terminology

for example

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SLIDE 65
  • pacity terminology

for example

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SLIDE 66

thomson scattering

interaction with free electrons

  • ptical

atomic lines

scattering/absorption from doppler broadened lines

UV/optical bound-free

photo-ionization of atoms

UV free-free

bremsstrahlung (free electron + nucleus)

infrared

sources of supernova opacity

all of these depend sensitively on the composition and ionization state of the ejecta!

see karp (1977) pinto and eastman (2000)

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SLIDE 67

bound-free electron scattering f r e e

  • f

r e e lines

solar composition

T = 104, rho =10-13

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SLIDE 68

bound-free electron scattering f r e e

  • f

r e e lines

pure iron composition

T = 104, rho =10-13

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SLIDE 69

Local Thermodynamic Equilibrium (LTE) non-equilibrium (NLTE) CaII

line interactions

~1/2 GB atomic data

nxn matrix, where n = number

  • f atomic levels (sparsity depends
  • n number of transitions included)
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SLIDE 70

Local Thermodynamic Equilibrium (LTE) non-equilibrium (NLTE) CaII

line interactions

~1/2 GB atomic data

nxn matrix, where n = number

  • f atomic levels (sparsity depends
  • n number of transitions included)
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SLIDE 71

Local Thermodynamic Equilibrium (LTE) non-equilibrium (NLTE) FeII

line interactions

~1/2 GB atomic data

nxn matrix, where n = number

  • f atomic levels (sparsity depends
  • n number of transitions included)
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SLIDE 72

Local Thermodynamic Equilibrium (LTE) non-equilibrium (NLTE) FeII

line interactions

~1/2 GB atomic data

nxn matrix, where n = number

  • f atomic levels (sparsity depends
  • n number of transitions included)
slide-73
SLIDE 73

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

type Ia

slide-74
SLIDE 74

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more massive, opaque (longer diffusion time) type Ia

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SLIDE 75

how to power a supernova light curve

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SLIDE 76

how to power a supernova light curve

  • thermal energy released in the explosion

shock, nuclear burning

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SLIDE 77

how to power a supernova light curve

  • thermal energy released in the explosion

shock, nuclear burning

  • radioactive decay of freshly synthesized

isotopes: 56Ni (52Fe, 48Cr, 44Ti, R-process)

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SLIDE 78

how to power a supernova light curve

  • thermal energy released in the explosion

shock, nuclear burning

  • radioactive decay of freshly synthesized

isotopes: 56Ni (52Fe, 48Cr, 44Ti, R-process)

  • interaction of the ejecta with a dense

surrounding medium

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SLIDE 79

how to power a supernova light curve

  • thermal energy released in the explosion

shock, nuclear burning

  • radioactive decay of freshly synthesized

isotopes: 56Ni (52Fe, 48Cr, 44Ti, R-process)

  • interaction of the ejecta with a dense

surrounding medium

  • energy injection from a rotating, highly

magnetized neutron star (magnetar)

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SLIDE 80

thermally powered supernovae (Type IIP)

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SLIDE 81

luminosity of thermal light curve

energy deposited by the explosion

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SLIDE 82

luminosity of thermal light curve

energy deposited by the explosion

the radiation energy drops in the expanding gas and takes a diffusion time to escape

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SLIDE 83

luminosity of thermal light curve

energy deposited by the explosion

simple estimate of supernova luminosity the radiation energy drops in the expanding gas and takes a diffusion time to escape

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SLIDE 84

luminosity of thermal light curve

energy deposited by the explosion

simple estimate of supernova luminosity the radiation energy drops in the expanding gas and takes a diffusion time to escape

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SLIDE 85

low radiative efficiency if initial radius is small! for a bright thermally powered supernova, must have R0 >> Rsun

luminosity of thermal light curve

energy deposited by the explosion

simple estimate of supernova luminosity the radiation energy drops in the expanding gas and takes a diffusion time to escape

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SLIDE 86

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more massive (longer diffusion time) type Ia

slide-87
SLIDE 87

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more massive (longer diffusion time)

more energetic, larger radius

type Ia

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SLIDE 88

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more massive (longer diffusion time)

more energetic, larger radius

R = 102 Rsun R = 103 Rsun R = 104 Rsun

fixed E/M

type Ia

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SLIDE 89

Type IIP core collapse supernovae

explosion of red supergiant stars

DK & woosley, 2009

1-D models (vary explosion energy)

E = B

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SLIDE 90

recombination wave in Type IIP supernova

  • pacity from electron scattering drops as ejecta cool and become neutral

recombination at T ~ 6000 K

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SLIDE 91

light curve scalings with recombination

gives a Type II plateau light curve

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SLIDE 92

light curve scalings with recombination

gives a Type II plateau light curve

the photosphere forms at the recombination front

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SLIDE 93

light curve scalings with recombination

gives a Type II plateau light curve

where the recombination temperature Ti =~ 6000 K. the photosphere forms at the recombination front

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SLIDE 94

light curve scalings with recombination

gives a Type II plateau light curve

where the recombination temperature Ti =~ 6000 K.

tsn ∝ E−1/6M 1/2

ej R1/6

κ1/6T −2/3

I

Lsn ∝ E5/6M −1/2

ej

R2/3 κ−1/3T 4/3

I

.

see Popov (1993), DK & Woosley (2009)

Using previous results for diffusion time: the photosphere forms at the recombination front

slide-95
SLIDE 95
slide-96
SLIDE 96

radioactivity powered supernovae

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SLIDE 97

radioactively powered light curves

most important chain: 56Ni  56Co  56Fe

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SLIDE 98

radioactive 56Ni decay

Important Gamma-Ray Line for 56Ni and 56Co Decays

56Ni Decay 56Co Decay

Energy (keV) Intensity (photons/100 decays) Energy (keV) Intensity (photons/100 decays) 158............ 98.8 847 100 270............ 36.5 1038 14 480............ 36.5 1238 67 750............ 49.5 1772 15.5 812............ 86.0 2599 16.7 1562.......... 14.0 3240a 12.5

milne et al. (2004)

100% electron capture 81% electron capture 19% positron production

8.8 days 113 days

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SLIDE 99

gamma-ray deposition by compton scattering

since gamma-ray energies (MeV) are much greater than ionization potentials, all electrons (free + bound) contribute

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SLIDE 100

gamma-ray deposition by compton scattering

change in photon wavelength

angle between incoming and outgoing photon directions

since gamma-ray energies (MeV) are much greater than ionization potentials, all electrons (free + bound) contribute

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SLIDE 101

gamma-ray deposition by compton scattering

change in photon energy from inelastic scattering change in photon wavelength

angle between incoming and outgoing photon directions

since gamma-ray energies (MeV) are much greater than ionization potentials, all electrons (free + bound) contribute

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SLIDE 102

gamma-ray deposition by compton scattering

change in photon energy from inelastic scattering

so an MeV (~2 mec2) gamma-ray loses most of its energy after just a few compton scatterings (then it gets photo-absorbed)

change in photon wavelength

angle between incoming and outgoing photon directions

since gamma-ray energies (MeV) are much greater than ionization potentials, all electrons (free + bound) contribute

slide-103
SLIDE 103
  • ptical (thermalized gamma-rays)

escaping gamma-ray

type Ia supernova light curves

slide-104
SLIDE 104

type Ia gamma-ray spectrum

40 days after explosion

slide-105
SLIDE 105

radioactively powered light curves

most important chain: 56Ni  56Co  56Fe

slide-106
SLIDE 106

radioactive supernovae

light curve estimates

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SLIDE 107

radioactive supernovae

light curve estimates

light curve duration given by standard diffusion time

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SLIDE 108

radioactive supernovae

light curve estimates

light curve duration given by standard diffusion time luminosity estimate from radioactive energy deposition

slide-109
SLIDE 109

arnettʼs law

slide-110
SLIDE 110

arnettʼs law

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SLIDE 111

arnettʼs law

slide-112
SLIDE 112

arnettʼs law

assume diffusion approximation for photon loses

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SLIDE 113

arnettʼs law

assume diffusion approximation for photon loses

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SLIDE 114

arnettʼs law

assume diffusion approximation for photon loses find

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SLIDE 115

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

type Ia

slide-116
SLIDE 116

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more massive (longer diffusion time) type Ia

slide-117
SLIDE 117

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more massive (longer diffusion time) more radioactive type Ia

slide-118
SLIDE 118

2006gy

2007bi 2004ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more radioactive type Ia more massive (longer diffusion time)

slide-119
SLIDE 119

MNi = Mej MNi = 0.1 Mej

2006gy

2007bi 2004ap 2008es ptf09cnd scp06f6

  • rdinary

core collapse supernovae

more radioactive type Ia more massive (longer diffusion time)

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SLIDE 120

pulsations and interaction

eta carinae

slide-121
SLIDE 121

“tamped” supernova models

interacting supernovae

slow moving shell

  • f debris from

first ejection second ejection

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SLIDE 122

“tamped” supernova models

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SLIDE 123

density velocity

colliding shell toy model

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SLIDE 124

density velocity

colliding shell toy model

slide-125
SLIDE 125

interacting supernovae

simple estimate of peak luminosity

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SLIDE 126

interacting supernovae

simple estimate of peak luminosity

peak luminosity for shocked debris at shell radius

slide-127
SLIDE 127

interacting supernovae

simple estimate of peak luminosity

peak luminosity for shocked debris at shell radius to reach the highest luminosities, shell must be at radius

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SLIDE 128

interacting supernovae

simple estimate of peak luminosity

peak luminosity for shocked debris at shell radius to reach the highest luminosities, shell must be at radius time between pulses of ejection

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SLIDE 129

pulsational pair SNe

110 Msun star from woosley et al., 2007

first pulse M ~ 25 Msun E ~ 1050 ergs second pulse M ~ 5 Msun E ~ 6x1050 ergs

slide-130
SLIDE 130

MNi = Mej MNi = 0.1 Mej

pair sn?

  • rdinary

core collapse supernovae

type Ia

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

slide-131
SLIDE 131

MNi = Mej MNi = 0.1 Mej

pair sn?

  • rdinary

core collapse supernovae

type Ia

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

interaction?

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SLIDE 132

crab pulsar wind nebula

from gaenslar and slane (2006)

power from neutron star spindown

crab nebula

B ~ 5x1012 g

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SLIDE 133

neutron star spindown

~10% of neutron stars are born as magnetars, with B ~ 1014 - 1015 g

rotational energy spindown timescale

slide-134
SLIDE 134

light curves from magnetars

roughly better (for l = 2)

kasen&bildsten (2010)

high radiative efficiency when B,P give tm ~ td

slide-135
SLIDE 135

bolometric magnetar models

slide-136
SLIDE 136

MNi = Mej MNi = 0.1 Mej

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

MNi = Mej MNi = 0.1 Mej

slide-137
SLIDE 137

MNi = Mej MNi = 0.1 Mej

magnetar theoretical maximum ~ 2x1045 ergs/s

P =1 ms P =5 ms

2006gy

2007bi 2005ap 2008es ptf09cnd scp06f6

MNi = Mej MNi = 0.1 Mej

slide-138
SLIDE 138

Monte Carlo and Numerical Radiation Transport

slide-139
SLIDE 139

solve radiation transport equation for optical photons

calculate matter

  • pacity/emissivity

update matter state

(temperature, density, ionization from thermodynamics)

determine radioactive energy deposition

(gamma-ray transport)

light curve computation

advance time step

(x,y,z), v(x,y,z), T(x,y,z), Ai(x,y,z) from hydro explosion

slide-140
SLIDE 140

radiation specific intensity

a 6 dimensional integro-differential equation coupled through microphysics to matter energy equation

radiation transfer equation

matter emissivity

matter extinction coefficient

absorption emission scattering

where:

slide-141
SLIDE 141

grey flux limited diffusion

ignore ,,  dependence, solve diffusion equation for “seeping” radiation fluid

multi-group flux limited diffusion (MGFLD)

ignore ,, keep  dependence, solve diffusion equation

ray tracing

follow individual trajectories; ignore scattering and diffusive terms

implicit monte carlo transport mixed-frame stochastic particle propagation; retains

the full angle, wavelength, & polarization information

variable Eddington tensor solve moments of the radiation transport equation with closure relation Sn methods, etc....

....

transport methods in astrophysics

slide-142
SLIDE 142

2-D shadow problem

multi-angle transport (monte carlo)

slide-143
SLIDE 143

2-D shadow problem

multi-angle transport (monte carlo)

slide-144
SLIDE 144

2-D shadow problem

diffusion approximation (DD monte carlo)

slide-145
SLIDE 145

2-D shadow problem

diffusion approximation (DD monte carlo)

slide-146
SLIDE 146

special relativistic transport in 1-D radiating flows

e.g., mihalas&mihalas

comoving frame spherical special relativistic transport eq.

slide-147
SLIDE 147

special relativistic transport in 1-D radiating flows

e.g., mihalas&mihalas

comoving frame spherical special relativistic transport eq.

slide-148
SLIDE 148

ulam

monte carlo transport

slide-149
SLIDE 149

calculating pi at the bar

Signal to noise goes like N-1/2 Need to throw N = 10,000 darts to get pi to two significant digits

slide-150
SLIDE 150

Monte Carlo Transport

slide-151
SLIDE 151

Monte Carlo Transport

slide-152
SLIDE 152

monte carlo transport

each particle has a position vector (x,y,z) a direction vector (Dx, Dy, Dz), an energy, wavelength. Evolution is sampled from appropriate probability distributions

slide-153
SLIDE 153

monte carlo transport

probability of traveling a distance x before scattering

where R is a random number sampled uniformly between (0, 1]

each particle has a position vector (x,y,z) a direction vector (Dx, Dy, Dz), an energy, wavelength. Evolution is sampled from appropriate probability distributions

slide-154
SLIDE 154

monte carlo transport

probability of traveling a distance x before scattering

where R is a random number sampled uniformly between (0, 1]

solve for x (distance traveled before scattering) each particle has a position vector (x,y,z) a direction vector (Dx, Dy, Dz), an energy, wavelength. Evolution is sampled from appropriate probability distributions

slide-155
SLIDE 155

e = 1 mec2

e = . 1 m

e

c

2

e = 10 mec2

rejection method for compton scattering

slide-156
SLIDE 156

e = 1 mec2

e = . 1 m

e

c

2

e = 10 mec2

R1 = 80

rejection method for compton scattering

slide-157
SLIDE 157

e = 1 mec2

e = . 1 m

e

c

2

e = 10 mec2

R1 = 80 R2 =0.63

rejection method for compton scattering

slide-158
SLIDE 158

e = 1 mec2

e = . 1 m

e

c

2

e = 10 mec2

R1 = 80 R2 =0.63

rejection method for compton scattering

slide-159
SLIDE 159

e = 1 mec2

e = . 1 m

e

c

2

e = 10 mec2

R1 = 80 R2 =0.63 R1 = 25

rejection method for compton scattering

slide-160
SLIDE 160

e = 1 mec2

e = . 1 m

e

c

2

e = 10 mec2

R1 = 80 R2 =0.63 R1 = 25 R2 = 0.42

rejection method for compton scattering

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SLIDE 161

special relativistic transport in 1-D radiating flows

e.g., mihalas&mihalas

comoving frame spherical special relativistic transport eq.

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special relativistic transport in 1-D radiating flows

e.g., mihalas&mihalas

comoving frame spherical special relativistic transport eq.

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automatically accounts for all aberration, advection, doppler shifts, and adiabatic loses to all orders of v/c

mixed frame monte carlo transport

  • pacities/emissivities calculated in the comoving frame

monte carlo particles propagated in the observer frame lorentz transformation photon four vector at scattering events

lorentz transformations

general relativistic effects (geodesic tracking) can also be included e.g., Dolence et al., (2009), Dexter et al., (2009)

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implicit monte carlo methods

fleck and cummings 1971

implicit methods: particle absorption/re-emission (i.e., creation/destruction) is replaced by “effective scattering”

momentum four-force vector (i.e., radiative heating/cooling, radiative acceleration)

timescale for matter/radiation coupling

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population control and load balancing

black hole radiation source

black hole accretion disk (Nathan Roth, UCB)

For highly asymmetric 3D radiative flows, some zones may be under (over)-sampled by monte carlo particles

strategies

pressure tensor methods russian roulette particle splitting/killing directionally biased emission replicate heavily loaded zones

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SLIDE 166

population control and load balancing

black hole radiation source

black hole accretion disk (Nathan Roth, UCB)

For highly asymmetric 3D radiative flows, some zones may be under (over)-sampled by monte carlo particles

strategies

pressure tensor methods russian roulette particle splitting/killing directionally biased emission replicate heavily loaded zones

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SLIDE 167

discrete diffusion monte carlo

gentile 2001, densmore et al 2007

For regions of high opacity, monte carlo is very inefficient. Instead, sample from the diffusion approximation:

jump probabilities

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monte carlo parallelization strategies

using hybrid MPI/open MP, run on 10,000-100,000 cores using Cray XE6 (Hopper @ NERSC), Cray XT5 (Jaguar @ ORNL) Blue Gene/P (Intrepid @ ALCF)

full replication

each core holds entire model and propagates particles independently; MPI all reduce of radiation/matter coupling terms after each time step. Memory limited (2D, low resolution 3D).

domain decomposed

spatial grid partitioned over cores particles leaving local domain communicated via MPI to neighbors

hybrid

use openMP threading to do additional particles on shared memory node, can fully replicate certain domains on additional nodes to extend scaling and manage load balancing.

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weak scaling: 2D transport calculation

full replication -- embarrassingly paralell

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domain decomposed monte carlo transport

hybrid MPI/open MP BoxLib AMR framework

  • n Hopper XE6 (NERSC)

2 twelve-core AMD “Mangy-Cours” (4 NUMA “nodes” of 6 cores) 2.1 GHz processors per node

@ 49,152 cores (2048 nodes)

total particles = 1.8 x 1011

total cells = 4.5 x 107

wavelength points = 10,000 total memory = 65 TB

weak scaling

3-D unigrid, constant density

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