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Most challenges of calculating thermonuclear burning in supernova are resolved
Doron Kushnir
(Weizmann)
With: Boaz Katz (Weizmann)
8/8/19
~10% accuracy is required to resolve the type Ia supernova problem
§ Could
0.6 0.8 1 1.2 1.4 1.6 1.8 2
10-1
100
We want to calculate the ejecta from first principles
§ Collision of two 0.64 Msun CO WDs with an impact parameter of 0.2(R1+R2).
We want to calculate the ejecta from first principles
§ Collision of two 0.64 Msun CO WDs with an impact parameter of 0.2(R1+R2).
§ FLASH4.0, Δx≈8 km.
We want to calculate the ejecta from first principles
§ Collision of two 0.64 Msun CO WDs with an impact parameter of 0.2(R1+R2).
§ FLASH4.0, Δx≈8 km. § 13 isotope ⍺-net.
We want to calculate the ejecta from first principles
§ Collision of two 0.64 Msun CO WDs with an impact parameter of 0.2(R1+R2).
§ FLASH4.0, Δx≈8 km. § 13 isotope ⍺-net. § With burning limiter.
Log10(Normalized integrated mass)
We can directly measure the 56Ni distribution in the ejecta with nebular spectra
Log10(Normalized integrated mass) § Assume we have an isolated emission line
We can directly measure the 56Ni distribution in the ejecta with nebular spectra
Log10(Normalized integrated mass)
θ=0
§ Assume we have an isolated emission line
ϕ=135°
We can directly measure the 56Ni distribution in the ejecta with nebular spectra
Log10(Normalized integrated mass)
θ=0
θ=30°
§ Assume we have an isolated emission line
ϕ=135°
We can directly measure the 56Ni distribution in the ejecta with nebular spectra
Log10(Normalized integrated mass)
θ=0
θ=30° θ=60°
§ Assume we have an isolated emission line
ϕ=135°
We can directly measure the 56Ni distribution in the ejecta with nebular spectra
Log10(Normalized integrated mass)
θ=0
θ=30° θ=60°
θ=0
§ Assume we have an isolated emission line
ϕ=135°
ϕ=90°
We can directly measure the 56Ni distribution in the ejecta with nebular spectra
§ [CoIII] line profile near 5900 Å is the 56Ni distribution
SN2007ontakenbyFolatellietal.2013
Dong et. at, 2014
Double peak features are observed
§ [CoIII] line profile near 5900 Å is the 56Ni distribution
§ 2007on is a collision
SN2007ontakenbyFolatellietal.2013
Dong et. at, 2014
Double peak features are observed
§ [CoIII] line profile near 5900 Å is the 56Ni distribution
§ 2007on is a collision § 4/20 SNe have non-single-peak profile
SN2007ontakenbyFolatellietal.2013
Dong et. at, 2014
Double peak features are observed
§ [CoIII] line profile near 5900 Å is the 56Ni distribution
§ 2007on is a collision § 4/20 SNe have non-single-peak profile ⇒ 4 SNe are collisions, possibly consistent with all them being collisions (viewing angle effect).
SN2007ontakenbyFolatellietal.2013
Dong et. at, 2014
Double peak features are observed
§ [CoIII] line profile near 5900 Å is the 56Ni distribution
§ 2007on is a collision § 4/20 SNe have non-single-peak profile ⇒ 4 SNe are collisions, possibly consistent with all them being collisions (viewing angle effect).
SN2007ontakenbyFolatellietal.2013
Dong et. at, 2014
Double peak features are observed
See also Vallely+ 2019
100IAS survey
100IAS survey § Aims to systematically observe the nebular spectra of a complete sample of (100) low-z SNe (PI Dong).
100IAS survey § Aims to systematically observe the nebular spectra of a complete sample of (100) low-z SNe (PI Dong).
§ We have measured the 56Ni mass distribution in ~90 SNe.
Dong et. at, 2018
100IAS survey § Aims to systematically observe the nebular spectra of a complete sample of (100) low-z SNe (PI Dong).
§ We have measured the 56Ni mass distribution in ~90 SNe.
§ Can we compare it to calculations?
Dong et. at, 2018
Simulated 56Ni mass do not agree R
atio
to S
hen
et a
l. po
st-p
roce
ssed
Shen et al. 2018 hydro
Sim et al. 2010 Blondin et al. 2017
Shen et al. 2018 Townsley et al. 2016 method
Moll et al. 2014 Shigeyama et al. 92
Sub-Chandra - central ignition of a detonation wave
Shen et al. 2018
Simulated 56Ni mass do not agree R
atio
to S
hen
et a
l. po
st-p
roce
ssed
Shen et al. 2018 hydro
Sim et al. 2010 Blondin et al. 2017
Shen et al. 2018 Townsley et al. 2016 method
Moll et al. 2014 Shigeyama et al. 92
Sub-Chandra - central ignition of a detonation wave
• In order to compare to nebular observations, we must be able to accurately calculate the 56Ni distribution (to ~10%).
Shen et al. 2018
Major problems:
Major problems:
1. The burning length scale is small (~1 cm)
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
2. NSE scale can be small
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
2. NSE scale can be small
3. Many (>100) isotopes are required
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
2. NSE scale can be small
3. Many (>100) isotopes are required
Simulations cannot resolve the detonation wave § Detonation wave scale – 1-10 cm <<<< WD scale 10000 km ⇒ unfeasible for simulations. Imshennik & Khokhlov 84
Khokhlov 89
106 107 108
100
102
104
106
108
1010
1012
Simulations cannot resolve the detonation wave § Detonation wave scale – 1-10 cm <<<< WD scale 10000 km ⇒ unfeasible for simulations. Imshennik & Khokhlov 84
Khokhlov 89
Dynamical scale
12C burning
Typical resolutions in multi-D simulations
106 107 108
100
102
104
106
108
1010
1012
Simulations cannot resolve the detonation wave § Detonation wave scale – 1-10 cm <<<< WD scale 10000 km ⇒ unfeasible for simulations. Imshennik & Khokhlov 84
Khokhlov 89
Dynamical scale
12C burning
Typical resolutions in multi-D simulations
§ Implication:
Ø free parameters for the location/time of ignition are introduced.
§ To ignite a detonation you need:
burning region > sound travelling distance
Ignition is achieved by fast burning
§ To ignite a detonation you need:
burning region > sound travelling distance
Inject nuclear energy
Ignition is achieved by fast burning
Inject nuclear energy
Burning time × speed of sound
No ignition
§ To ignite a detonation you need:
burning region > sound travelling distance
Ignition is achieved by fast burning
Ignition is achieved by fast burning
Inject nuclear energy
Burning time × speed of sound
Ignition
§ To ignite a detonation you need:
burning region > sound travelling distance
Planar
geometry
Temperature
Temperature
§ Converged Lagrangian 1D toy model
Hydrodynamical
Shock
50 km
upstream downstream
The ignition scale is 50 km
Temperature
[109 K]
12C depletion
[10%] Distance from contact surface [103 km]
§ Converged Lagrangian 1D toy model
Hydrodynamical
Shock
50 km
upstream downstream
The ignition scale is 50 km
Temperature
[109 K]
12C depletion
[10%] Distance from contact surface [103 km]
§ Converged Lagrangian 1D toy model
Hydrodynamical
Shock
50 km
upstream downstream
The ignition scale is 50 km
Temperature
[109 K]
12C depletion
[10%] Distance from contact surface [103 km]
§ Converged Lagrangian 1D toy model
Runaway! Δt=5 ms 2Δt×cs≈50 km
Hydrodynamical
Shock
50 km
upstream downstream
The ignition scale is 50 km
Temperature
[109 K]
12C depletion
[10%] Distance from contact surface [103 km]
The ignition scale is 50 km § Converged Lagrangian 1D toy model
Runaway! Δt=5 ms 2Δt×cs≈50 km
Hydrodynamical
Shock
Temperature
[109 K]
12C depletion
[10%]
50 km
upstream downstream Convergence can be achieved in 2D and 3D
Distance from contact surface [103 km]
1 mm detonation width is irrelevant for ignition
§ Detonation wave accelerates ⇒ higher T ⇒ faster burning ⇒ narrower width reaching 1 cm scale.
1 mm detonation width is irrelevant for ignition
§ Detonation wave accelerates ⇒ higher T ⇒ faster burning ⇒ narrower width reaching 1 cm scale.
§ irrelevant for the ignition.
1 mm detonation width is irrelevant for ignition
§ Detonation wave accelerates ⇒ higher T ⇒ faster burning ⇒ narrower width reaching 1 cm scale.
§ irrelevant for the ignition.
§ If your simulation resolves 50 km, then it is not OK to ignite by hand anymore.
Be Careful of false ignition at low resolution
Inject nuclear energy
Burning time × speed of sound
Numerical ignition - not physical
Numerical cell
§ e.g., Hawley, Athanassiadou, Timmes 2012 (Δx=130 km)
Be Careful of false ignition at low resolution
Inject nuclear energy
Burning time × speed of sound
Numerical ignition - not physical
Numerical cell
§ e.g., Hawley, Athanassiadou, Timmes 2012 (Δx=130 km)
§ A solution is to use a burning limiter (DK et al. 2012):
burning time > Δx/cs
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
2. NSE scale can be small
3. Many (>100) isotopes are required
106 107 108
100
102
104
106
108
1010
1012
Heavy elements synthesis scale can be smaller than a cell size
Dynamical scale
12C burning
Typical resolutions in multi-D simulations
Iron group synthesis
106 107 108
100
102
104
106
108
1010
1012
Heavy elements synthesis scale can be smaller than a cell size
Dynamical scale
§ Implication:
Ø Impose detonation speed and burning from steady state solutions.
12C burning
Typical resolutions in multi-D simulations
Iron group synthesis
106 107 108
100
102
104
106
108
1010
1012
Heavy elements synthesis scale can be smaller than a cell size
Dynamical scale
§ Implication:
Ø Impose detonation speed and burning from steady state solutions. Ø Ignore this.
12C burning
Typical resolutions in multi-D simulations
Iron group synthesis
We first need the exact (ODE) solution
We first need the exact (ODE) solution Upstream density = 3×108 g cm-3
We first need the exact (ODE) solution
§ Khokhlov 89 used an erroneous EOS (twice the radiation pressure).
Upstream density = 3×108 g cm-3
We first need the exact (ODE) solution
§ Khokhlov 89 used an erroneous EOS (twice the radiation pressure).
§ Good comparison to Townsley et al. 2016.
10-2 100 102 104 106 1081.5
2
2.5
3
3.5
4
Upstream density = 3×108 g cm-3 Upstream density = 107 g cm-3
ρ/ρ0
10-210-1 100 101 102 103 104 105 106 107 1080
1
2
3
4
5
Resolved scales are accurate with burning limiter
178 isotopes
§ The exact solution with a limiter is compared to a hydro code:
ρ/ρ0
X(56Ni)×10
10-210-1 100 101 102 103 104 105 106 107 1080
1
2
3
4
5
Resolved scales are accurate with burning limiter § The exact solution with a limiter is compared to a hydro code:
ρ/ρ0
X(56Ni)×10
FLASH 178 isotopes
Δx=8 km
Resolved scales are accurate with burning limiter § The exact solution with a limiter is compared to a hydro code:
10-210-1 100 101 102 103 104 105 106 107 1080
1
2
3
4
5
ρ/ρ0
X(56Ni)×10
FLASH
new scheme (unlimited distance)
178 isotopes
Δx=8 km
Resolved scales are accurate with burning limiter
§ The small-length-scale problem of thermonuclear detonation waves is efficiently solved with a burning limiter.
§ The exact solution with a limiter is compared to a hydro code:
10-210-1 100 101 102 103 104 105 106 107 1080
1
2
3
4
5
ρ/ρ0
X(56Ni)×10
FLASH
new scheme (unlimited distance)
178 isotopes
Δx=8 km
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
2. NSE scale can be small
3. Many (>100) isotopes are required
Solution:
Limiter
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
2. NSE scale can be small
3. Many (>100) isotopes are required
Solution:
Limiter
106 107 108
100
102
104
106
108
1010
1012
NSE scale can be smaller than the dynamical scale
Dynamical scale
12C burning
Typical resolutions in multi-D simulations
Iron group synthesis
NSE
T=6×109 K
106 107 108
100
102
104
106
108
1010
1012
NSE scale can be smaller than the dynamical scale
Dynamical scale
12C burning
Typical resolutions in multi-D simulations
Iron group synthesis
NSE
T=6×109 K
§ The burning calculation becomes both extremely slow and inaccurate.
106 107 108
100
102
104
106
108
1010
1012
NSE scale can be smaller than the dynamical scale
Dynamical scale
§ Implication:
Ø Impose NSE at some arbitrary conditions.
12C burning
Typical resolutions in multi-D simulations
Iron group synthesis
NSE
T=6×109 K
§ The burning calculation becomes both extremely slow and inaccurate.
106 107 1080
1
2
3
4
5
The solution is to group isotopes in detailed balance
ρ/ρ0+0.5
106 107 1080
1
2
3
4
5
The solution is to group isotopes in detailed balance
0 10 20 30 400
5
10
15
20
25
30
§ This is done adaptively at each time step (ASE). The number of effective isotopes (n) reduces dramatically (generalization of Hix+ 2007).
ρ/ρ0+0.5
log10(n)
cell 1
106 107 1080
1
2
3
4
5
The solution is to group isotopes in detailed balance
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
ρ/ρ0+0.5
log10(n)
cell 1 cell 2
§ This is done adaptively at each time step (ASE). The number of effective isotopes (n) reduces dramatically (generalization of Hix+ 2007).
106 107 1080
1
2
3
4
5
The solution is to group isotopes in detailed balance
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
ρ/ρ0+0.5
log10(n)
cell 1 cell 2
cell 3
§ This is done adaptively at each time step (ASE). The number of effective isotopes (n) reduces dramatically (generalization of Hix+ 2007).
106 107 1080
1
2
3
4
5
The solution is to group isotopes in detailed balance
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
ρ/ρ0+0.5
log10(n)
cell 1 cell 2
cell 3 cell 4
§ This is done adaptively at each time step (ASE). The number of effective isotopes (n) reduces dramatically (generalization of Hix+ 2007).
The solution is to group isotopes in detailed balance
106 107 1080
1
2
3
4
5
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
0 10 20 30 400
5
10
15
20
25
30
§ The code is more accurate and faster by orders of magnitude.
ρ/ρ0+0.5
log10(n) log10(told/tnew)
cell 1 cell 2
cell 3 cell 4
§ This is done adaptively at each time step (ASE). The number of effective isotopes (n) reduces dramatically (generalization of Hix+ 2007).
Major problems:
1. The burning length scale is small (~1 cm)
• Ignition
• Detonation propgation
2. NSE scale can be small
3. Many (>100) isotopes are required
Solution:
Limiter
Solution:
ASE
Summary § We have developed a novel algorithm to calculate supernovae explosions:
Summary § We have developed a novel algorithm to calculate supernovae explosions:
§ Accurate
Summary § We have developed a novel algorithm to calculate supernovae explosions:
§ Accurate
§ Efficient
Summary § We have developed a novel algorithm to calculate supernovae explosions:
§ Accurate
§ Efficient
§ Can be easily implemented in multi-dimensional codes.
Summary § We have developed a novel algorithm to calculate supernovae explosions:
§ Accurate
§ Efficient
§ Can be easily implemented in multi-dimensional codes.
§ Large nuclear networks.
Summary § We have developed a novel algorithm to calculate supernovae explosions:
§ Accurate
§ Efficient
§ Can be easily implemented in multi-dimensional codes.
§ Large nuclear networks.
§ Next step: apply it to different scenarios.
