Doron Kushnir (Weizmann) - CASbps.ynao.cas.cn/xzzx/201908/W020190820419301094697.pdf · Doron...

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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.

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