Multi-dimensional
Radiation-hydrodynamics modelingsof interaction-powered SNe
Akihiro Suzuki (U. Tokyo)
Refs.
Suzuki, A., Moriya, T.J., & Takiwaki, T. (2019) ApJ 887, 249
Suzuki, A., Moriya, T.J., & Takiwaki, T. (2021) ApJ 899, 565
Suzuki, A., Nicholl, M., Moriya, T.J., & Takiwaki, T. (2021) ApJ 908, 995

MIAPbP workshop on interacting supernovae, 2023/02/06-03/03

SNe and interaction-powered transients2

RSG‣ supernova spectral classi cation
no

yes

Bang!

Hydrogen

He starType II
Ca, Si, Fe, Co, Ni

Type I

no

yes
Bang!

SiliconType Ianoyes

Ca, Si, Fe, Co, Ni

thermonuclear SNe

HeliumType Ic

Type Ibfi+broad-lined Ic (Ic-BL)

striped envelope SNeBang!

CO starSNe and interaction-powered transients3

RSG‣ supernova spectral classi cation
no

yes

Bang!

Hydrogen

He starType II→ Type IIn
Ca, Si, Fe, Co, Ni

Type I

no

yes
Bang!

SiliconType Ianoyes

Ca, Si, Fe, Co, Ni

thermonuclear SNe→ Type Ia-CSM

HeliumType Ic

Type Ib→ Type Icn→ Type Ibn
fi+broad-lined Ic (Ic-BL)

striped envelope SNeBang!

CO starSNe and interaction-powered transients

4

RSG

Margutti+(2019)‣ supernova spectral classi cation

AT 2018cow, Perley+(2019)

no

yes

Bang!

Hydrogen

He starType II→ Type IIn
Ca, Si, Fe, Co, Ni

Type I

no

yes
Bang!

SiliconType Ianoyes

Ca, Si, Fe, Co, Ni

thermonuclear SNe→ Type Ia-CSM

HeliumType Ic

Type Ib→ Type Icn→ Type Ibn
fi+broad-lined Ic (Ic-BL)

striped envelope SNeBang!

CO star5

SN ejecta - CSM collision‣ SN ejecta: Ekin~1051[erg] and Erad~1049[erg]‣ collision of SN ejecta with a massive CSM e ciently converts Ekin to Erad: the reverse
shock propagation into the ejecta (interaction-powered SNe)free expansion: v=r/t
ρejecta mass: Mejejecta energy: Esn

CSM
Mcsm, Rcsm

ρ~v-1
ρ~v-10inner
ejecta

CSM mass: Mcsm
CSM radius: Rcsm

outerejectaSN ejecta
Mej, Esn(optically thick)

ρ~r-2
CSM
r=vmaxt

r=Rcsmrtalks by L. Dessart, T. Moriya, and many others

ffi

r=vbrt6

SN ejecta - CSM collision‣ SN ejecta: Ekin~1051[erg] and Erad~1049[erg]‣ collision of SN ejecta with a massive CSM e ciently converts Ekin to Erad: the reverse
shock propagation into the ejecta (interaction-powered SNe)free expansion: v=r/t
ρreverse shock

CSM
Mcsm, Rcsm

ρ~v-1
ρ~v-10inner
ejectaSN ejecta
Mej, Esn

forward shockouter
ejectathermal radiation
ρ~r-2(optically thick)CSM
r=vmaxt

r=Rcsmrtalks by L. Dessart, T. Moriya, and many others

ffi

r=vbrtSpecial-relativistic radiation-hydrodynamic simulations‣ gray approximation (frequency-integrated quantities) + LTE‣ moment method: temporal evolutions of radiation energy density and‣yxzux (Er, Fr , Fr , Fr )ij
ij
M1-closure scheme for the Eddington tensor: Pr = Er D

Yan-Fei Jiangʼs talk this morning

Radiative transfer equations∂Er ∂Fri4i+ i = Γρ̄κ̄a(arTg − Ēr) − Γρ̄(κ̄a + κ̄s)βiF̄r
∂t
∂x
i
ij
2
∂Fr ∂PrΓji
4ii+ j = − ρ̄(κ̄a + κ̄s)F̄r + Γρ̄κ̄a(arTg − Ēr)β −ρ̄(κ̄a + κ̄s)β βjF̄r
∂t
∂x
Γ+1
ρ̄, Tg, β i, Γ : gas density, temperature, velocity, Lorentz factor

M1 closure scheme

Prij 1 − χ ij 3χ − 1 FriFrj
=
δ +
Er
2
2 | Fr |2i2
3 + 4Fr Fr,i /Erχ=
5 + 2 4 − 3FriFr,i /Er2

Ēr, F̄r: comoving radiation energy density and uxκ̄a: comoving absorption opacity (Kramersʼ type; free-free)κ̄s: comoving scattering opacity (e--scattering)+ SR hydro equations
flfle.g., Livermore (1984)

7

8

Adaptive mesh re nement‣ SN ejecta is gradually expanding in an ambient medium‣ Automatic tracking of the ejecta expansion by an adaptive mesh re nement (AMR)
technique (Berger & Corella 1989)‣ small structures produced at the CSM-ejecta interface are also covered by AMRfifigreen rectangle = 32x32 AMR block9

Adaptive mesh re nement‣ SN ejecta is gradually expanding in an ambient medium‣ Automatic tracking of the ejecta expansion by an adaptive mesh re nement (AMR)
technique (Berger & Corella 1989)‣ small structures produced at the CSM-ejecta interface are also covered by AMRfifigreen rectangle = 32x32 AMR block10

What is the origin of CSM ?
‣ normal wind mass-loss from single massive stars DOES NOT expect the highly elevatedmass-loss rate (dM/dt ~ 0.1Msun/yr).

‣ unknown stellar activity 1-100yrs from gravitational collapse?
‣ Luminous Blue Variable (LBV)-like giant eruption?
‣ wave-driven mass-loss due to convective oxygen/silicon burning?
‣ some binary interaction? common-envelope evolution?
HST image of η Carinae (©NASA)SN observations and theoretical modelings
can shed lights on the mysterious origin of massive CSMs
Topics covered in 1st and 2nd week…

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SN ejecta - CSM collision in multi-D‣ Question: how such massive CSMs are created?
‣ Galactic luminous blue variables (LBVs) surely exhibit
giant eruption: an immediate progenitor of SLSNe-II?

‣ less luminous optical transients have also been
discovered: SN imposters, luminous Red Novae
SN 2011iqb

HST image of η Carinae (©NASA)+ C. Franssonʼs talk on SN 1987A last week
(see, also some early 2D,3D numerical studies; van Marle+2010,
Vlasis+2016,McDowell+2018,Kurfurst&Krticka2019 )+ Anjashaʼs talkSmith+ (2014)

1170

J. Mauerhan et al.

12

SN ejecta - CSM collision in multi-D‣ Galactic luminous blue variables (LBVs) surely exhibit
giant eruption: an immediate progenitor of SLSNe-II?

‣ less luminous optical transients have also been
discovered: SN imposters, luminous Red Novae
Figure 2. Total flux, fractional de-biased polarization Pdb , and position
angle θ for SN 2009ip during its 2012 outburst, at epochs between Sep. 21
and Dec. 6. The three Kuiper/SPOL epochs (red) have been averaged forclarity. The Sep. 21 and 24 MMT/SPOL data (light blue) have been averaged
and binned to 300 Å; all other epochs are binned to 50 Å. Note the ∼90◦
offset in θ between the 2012a phase and the peak of 2012b.

+ C. Franssonʼs talk on SN 1987A last week
(see, also some early 2D,3D numerical studies; van Marle+2010,
Vlasis+2016,McDowell+2018,Kurfurst&Krticka2019 )Spectropolarimetry of SN 2009ip

2009ip occupies a compact portion of the Q–U plane, in quadrant II.
The points form a slightly elongated cluster that shows a continuous
trend in wavelength, with the bluest points exhibiting the lowest position angle in the Q–U plane. The cluster as a whole exhibits a small
but non-negligible spread in position angle, which corresponds toa range of ∼10◦ on the sky. The dilution in polarization associatedwith intermediate-width Hα emission is apparent as a protrusionfrom the cluster of data points which roughly points towards theorigin. Note that our binning causes the line to be unresolved, and1177

MNRAS 442, 1166–1180 (2014)

Figure 9. Illustration of a potential SN/CSM configuration during the 2012aevent (not to scale), before the onset of intense CSM interaction. The presence of broad P-Cygni lines implies a rapidly expanding photosphere. The
detection of significant continuum polarization at this phase suggests an

Figure 10. Illustration of a possible configuration for the 2012b phase, after the onset of intense CSM interaction. A toroidal distribution of dense
CSM gives rise to strong shocks, electron scattering, and a luminous polarized continuum (marked by a bold-faced ‘P’). At the same time, diluted yet

2012 event of SN imposter 2009ip

Mauerhan+ (2014)

Downloaded from https://academic.oup.com/mnras/article-abstra

HST image of η Carinae (©NASA)polarization vectors from the 2012a and 2012b components, as thelatter rises in luminosity.
By Oct. 11, the source has risen to peak flux. The spectrum hasretained the overall appearance of Oct. 5, while the continuum becomes less blue and broad-line P-Cygni absorption becomes apparent for He I/NaD. Our Lick/Kast and Kuiper/SPOL measurements
on Oct. 14 show that P has risen to a maximum of ∼1.7 per centand θ has reached ∼72◦ . At this time, strong deficits in polarization
are seen for the intermediate-width emission components of Hαand, to a lesser extent, Hβ. This is likely to be the result of dilution
from the strong, intrinsically unpolarised emission lines in the outer
CSM. Meanwhile, a slight increase in P is seen at 5600–5800 Å,
suggesting a potential association with broad He I λ5876 or NaD
P-Cygni lines.
Fig. 4 (top panels) shows the Stokes spectra and the data distribution in the Q–U plane for the Oct. 14 Lick epoch, binned to 100 Å.
For reference, we also show scaled logarithmic flux spectra in thesame figure, which has been normalized with a low-order spline(avoiding the strongest emission features for the spline nodes). On
Oct. 14, near peak brightness, the entire optical spectrum of SN

Figure 3. Upper panel: temporal evolution of the total V-band (5050–
5950 Å) polarization for SN 2009ip during the 2012a and 2012b phases.
For reference, an arbitrarily scaled version of the V-band light curve isplotted in the background. Lower panel: evolution in the Q–U plane. ISP isconstrained to <0.2 per cent, illustrated by the black dot near the origin. The
dashed lines represent the position angles θ V = 166◦ and 72◦ measured at
the first epoch on Sep. 21 and peak polarization on Oct. 14, respectively. Ourlatest continuum measurement (5200–5500 Å) for Dec. 6 is marked with a
red cross near the origin, consistent with our ISP limit. The approximate
point-reflection symmetry between 2012a and the peak of 2012b suggests
two separate and roughly orthogonal components of polarization on the sky.
Note the temporary shift in θ associated with the bump in the light curve at∼30 d past peak.

Downloaded from https://academic.oup.com/mnras/article-abstract/442/2/1166/980021 by National Astronomical Observatory of Japan user on 22 October 2018

‣ Question: how such massive CSMs are created?

SN ejecta - CSM collision in multi-D

Brethauer+(2022)‣ Question: how such massive CSMs are created?
‣ Galactic luminous blue variables (LBVs) surely exhibit
giant eruption: an immediate progenitor of SLSNe-II?

‣ less luminous optical transients have also been
discovered: SN imposters, luminous Red Novae
Transitional SN 2014C(Milisavljevic+2015, Margutti+2017, Tinyanont+2019)
Thomas+ (2022)

HST image of η Carinae (©NASA)+ C. Franssonʼs talk on SN 1987A last week
(see, also some early 2D,3D numerical studies; van Marle+2010,
Vlasis+2016,McDowell+2018,Kurfurst&Krticka2019 )13

SN ejecta - CSM collision in multi-D‣ Question: how such massive CSMs are created?
‣ Galactic luminous blue variables (LBVs) surely exhibit
giant eruption: an immediate progenitor of SLSNe-II?

‣ less luminous optical transients have also been
discovered: SN imposters, luminous Red Novae‣ binary interaction, such as the common-envelope
mass ejection is also a promising way to expel amassive starʼs envelope(see, also some early 2D,3D numerical studies; van Marle+2010,
Vlasis+2016,McDowell+2018,Kurfurst&Krticka2019 )3D simulations of common-envelope mass ejection
Macleod+(2018)

14

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spherical SN ejecta - spherical CSM collision‣ 2D cylindrical coordinate (r,z)‣ SN ejecta(10Msun, Ekin=1051[erg]) + wind-like CSM (0.1, 1, and 10Msun within 5x1015cm)
density distribution

Suzuki, Moriya, & Takiwaki (2019)gas
energydensity~5days~10days~20days~50days~100daysspherical SN ejecta - spherical CSM collision
Suzuki, Moriya, & Takiwaki (2019)‣ Even for spherical SN + spherical CSM, theshocked layer experiences(radiation-)hydrodynamic instabilities

Forward shock

Reverseshock‣ Rayleigh-Taylor instability for the contact
surface‣ Thin-shell instability (Vishniac 1983) for thecold dense shell (with radiative loss isimportant)‣ Impact on emission line pro les at late
L. Dessartʼs talk last week
cold
dense
shell

fi

epochs?

16

spherical SN ejecta - spherical CSM collision

17

1, and 10Msun within 5x1015cm)‣ SN ejecta(10Msun, Ekin=1051[erg]) + wind-like CSM (0.1,
The Astrophysical Journal, 887:249 (27pp), 2019 December 20
The Astrophysical Journal, 887:249 (27pp), 2019 December 20

Suzuki, Moriya, & Takiwaki

Suzuki, Moriya, & Takiwaki (2019)Ne
indensitygasenergydensityradiationenergydensity

ex
an
art
im
Th
en
en
ind
in
de

wi
30
ge
alo
inc
cu
sim
de
ati
are
int
ce

SN ejecta with disk-like CSM

symmetry
axis

18

Θobs

‣ CSM disk (Mcsm=0.1, 1, 10Msun, andopening angle θ=10, 20[deg])
CSM disk‣ SN ejecta with M=10Msun andSN ejecta

E=1051[erg]~5days~10days~20days

Suzuki, Moriya, & Takiwaki (2019)~50days~100daysSN ejecta with disk-like CSM

symmetry
axis

19

Θobs

‣ CSM disk (Mcsm=0.1, 1, 10Msun, andopening angle θ=10, 20[deg])
CSM disk‣ SN ejecta with M=10Msun andSN ejecta

E=1051[erg]disk-like CSM with Mcsm=1.0M◉, θdisk=20 deg~5days~10days~20days

Suzuki, Moriya, & Takiwaki (2019)~50days~100daysSN ejecta with disk-like CSM‣ CSM disk (Mcsm=0.1, 1, 10Msun, andopening angle θ=10, 20[deg])‣ SN ejecta with M=10Msun anddensity

E=1051[erg]symmetryaxis
Θobs

CSM disk

SN ejecta

gas
energydensityradiationenergydensitySuzuki, Moriya, & Takiwaki (2019)disk-like CSM with Mcsm=1.0M◉, θdisk=20 deg~5days~10days~20days~50days20~100daysSN ejecta with disk-like CSM‣ CSM disk (Mcsm=0.1, 1, 10Msun, andopening angle θ=10, 20[deg])‣ SN ejecta with M=10Msun and
E=1051[erg]symmetryaxis
Θobs

CSM disk

SN ejecta

Suzuki, Moriya, & Takiwaki (2019)disk-like CSM with Mcsm=1.0M◉, θdisk=20 deg

21SN ejecta with disk-like CSM

disk-like CSM with Mcsm=1.0M◉, θdisk=20 deg‣ CSM disk (Mcsm=0.1, 1, 10Msun, andopening angle θ=10, 20[deg])‣ SN ejecta with M=10Msun and
E=1051[erg]symmetryaxis

large viewing angle(edge-on)

Θobs

CSM disk

small viewing angle(face-on)SN ejecta

Suzuki, Moriya, & Takiwaki (2019)

22

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SN ejecta with disk-like CSM‣ CSM disk (Mcsm=0.1, 1, 10Msun, andopening angle θ=10, 20[deg])θdisk=10 deg Mcsm=0.1M◉‣ SN ejecta with M=10Msun and
E=1051[erg]symmetryaxis
Θobs

θdisk=20 deg

CSM disk

SN ejecta

Suzuki, Moriya, & Takiwaki (2019)

Mcsm=1.0M◉

Mcsm=10M◉

24

SN ejecta with disk-like CSM
Lsymmetry axis

CSM disk

small viewing angle- steep rise- modest decaytime

CSM disk

CSM disk

SN ejecta

large viewing angle- slow rise
- slow decayL

CSM disktime
SN ejecta

Summary: SN modeling by RHD simulations‣ radiation-hydrodynamic simulations as a powerful tool of modeling SN ejecta‣ light curve tting by RHD: properties of the progenitor, the SN ejecta, and theenvironment(CSM)‣ multi-dimensional RHD modeling of interaction-powered SNe: keys to the origin offi

massive CSMs around the progenitor

25

26

Backup slides

Test simulations: light bulb
‣ a uniform sphere emitting radiation with a constant absorption opacity‣ analytic solution for the monochromatic intensity

27

28

Test simulations: advection-diffusion‣ advection and di usion of radiation in uniform density and velocity elds
‣ uniform scattering opacity with no absorptionfiff‣ case with static medium

29

Test simulations: advection-diffusion‣ advection and di usion of radiation in uniform density and velocity elds
‣ uniform scattering opacity with no absorptionfiff‣ case with medium moving with (vx/c, vy/c)=(0.9/ 2, 0.9/ 2)

Test simulations: 1D non-relativistic radiative shocks‣ sub-critical shock‣ super-critical shock30

Test simulations: StaNdaRT‣ S. Blondin+(2022): “a repository of standardized test models and outputs for supernova
radiative transfer”‣ toy06: 1Msun, 1051erg SN ejecta with 0.6Msun 56Ni

31

Test simulations: StaNdaRT‣ S. Blondin+(2022): “a repository of standardized test models and outputs for supernova
radiative transfer”‣ toy06: 1Msun, 1051erg SN ejecta with 0.6Msun 56Ni

32

33

SN ejecta with disk-like CSM
Lsymmetry axis

small viewing angle- steep rise- modest decaytime

CSM disk

SN ejecta

large viewing angle- slow rise
- slow decay
L

time

34