Collaborators:
Ken’ichi Nomoto (Kavli IPMU)
Miho Ishigaki (Kavli IPMU)
Sergey Blinnikov (ITEP)
Shigehiro Nagataki (RIKEN)
Nozomu Tominaga (Konan Univ)
Sung-Chul Yoon (SNU)

Simulations of Supernova Light Curves and Spectra
Using Multigroup Radiation Hydrodynamics
Alexey Tolstov (Kavli IPMU, Tokyo Univ)
alexey.tolstov@ipmu.jp
RESCEU-RIKEN-IPMU Joint Meeting

7/8/2014

Contents
Introduction
Shocks in supernovae. Supernova shock breakouts.
I. Numerical solution of relativistic radiation transfer equation
Development of algorithm for solving a problem of radiation transfer in
fluids moving with high values of Lorentz factor
Calculation of radiation fluxes for the distant observer
II. Supernova light curves and spectra modeling
Shock breakout model for type I b/c supernovae using multigroup radiationhydrodynamics
The influence of relativistic and geometric effects of radiation propagation
to the distant observer on light curves and spectra
Numerical modeling in application for data analysis and interpretation ofcosmic observations

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Role of shock breakouts in astrophysics• The most reliable predictions for SN outbursts in observations• The theory of radiation hydrodynamics can be improved
including the case of the ejecta moving with high value ofLorentz factor• Stellar evolution problems resolution, e.g. unknown numberof outbursts
collapsing I b/c supernovae hard for detection.
SN Type II:SNLS-04D2dc• Better description of the connection of SNe with GRBs
• For nearby supernovae (in our galaxy), correlation with thedetection of gravitational waves and neutrinos.
• Improvements of new direct measurements of distance in the
Universe, aimed at studying the evolution of the dark energy.
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SN classification

Radioactive decays
56Ni → 56Co
(following D.K.
Nadyozhin)

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The luminescence due
to shock interacting withmedium can last tens of
thousand of years

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Supernova light curves

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Supernova shock breakout (by N. Tominaga)

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Supernova shock breakout (SB) observations
SN2008D, Type Ib/c, WR candidate progenitor, Swift

SN Type II:SNLS-04D2dc

SNLS-04D2dc, Type II RSG progenitor, GALEX

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Subaru/Hyper Supreme Camera (HSC)

SN Type II:SNLS-04D2dc

Supernova remnant of Cassiopia A• The detection of transients such as shock breakoutof SNe is one of the most important missions of HSC
Interpretation of early light curves and spectra – explanation of the nature of exploding stars.
From Swift , GALEX to Subaru/HSC, PTF, LOSS, CRTS, KWFC, Skymapper, DES, Pan-STARRS, LSST,
KMTNetTheoretical models are in demand!
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KMTNet (Korea Microlensing Telescope Network)
The KASI plans to build a network of wide-field photometric survey systems called Korea
Microlensing Telescopes Network (KMTNet), funded by the government of Korea, in thesouthern hemisphere (Chile, South Africa, and Australia).
http://www.kasi.re.kr/english/project/KMTNet.aspx

SN Type II:SNLS-04D2dc

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Supernova remnant of Cassiopia A

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Supernova shock breakout (by B. Katz)

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SN Shock Breakout Summary• The phenomenon of a supernova in most cases should start with abright flash, caused by a shock wave emerging on the surface of thestar after the phase of collapse or thermonuclear explosion in interiors.
• The detection of such outbursts associated with SN SBO can be used
to obtain information about explosion properties and presupernova
parameters.
Supernova remnant of Cassiopia A• For an accurate treatment of the shock wave propagation near thesurface of a presupernova it is necessary to perform numericalcalculations.
• In some cases, e.g. in compact type Ib/c presupernovae, shock waves
reach relativistic velocities. Then one has to include into consideration
a number of relativistic effects.

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Numerical simulation of relativistic radiation transfer

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Numerical algorithms STELLA and RADA
STELLA (STatic Eddington-factor Low-velocity Limit
Approximation) (Blinnikov et al., 1998)• 1D Lagrangian NR Hydro + Radiation Moments Equations,
VEF closure, multigroup (100-300 groups)• Opacity includes photoionization, free-free absorption, lines andelectron scattering (Blandford, Payne 1981). Ionization –Saha’s approximation• STELLA was used in modeling of many SN light curves:
SN 1987A, SN 1993J and many others (Blinnikov et al. 2006)• STELLA shows good agreement with observations in case of
SNLS-04D2dc. (Tominaga et al. 2009, 2011)t δR= t diff :For Ib/c model STELLA is not accurate!
RADA (fully Relativistic rADiative transfer Approximation)(Tolstov, Blinnikov, 2003)• 1D Relativistic Radiative Transfer in comoving frame (McCrea &Mitra 1936, Mihalas, 1980)• Relativistic transformation of fluxes from the source to the observer
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7/8/2014l – photon mean free pathδR - the distance from the shock to thephotosphereD – shock front velocityc – speed of light13
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Hydrodynamics
STELLA hydro equations:

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Comoving radiation transfer (Mihalas, 1980)
Transfer equation:

Moments equation:

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SRRHD. Non-relativistic strong shockSemi-analytic relativistic hydro +Relativistic radiation transfer(no closure condition)
Shock tube configuration(Farris et al., 2008), Pr/Pg ≈ 0.001

Closure condition: P = fE
• Eddington approximation: f = 1/3• M1-closure (Levermore, 1984)
f = f(E,F) joins “optically thin”
and “thick” cases• Photon Boltzmann equation

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SRRHD. Strong shock and relativistic wave
• Mildly Relativistic Strong Shock (Test 2)

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• Relativistic Strong Shock (Test 3)

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SRRHD. Radiation-dominated mildly-relativistic shock wave
Semi-analytic relativistic hydro +Relativistic radiation transfer(no closure condition)
Shock tube configuration(Farris et al., 2008), Pr/Pg ≈ 10

Closure condition: P = fE
• Eddington approximation: f = 1/3• M1-closure (Levermore, 1984)
f = f(E,F) joins “optically thin”
and “thick” cases• Photon Boltzmann equation

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Radiative shocks

Discontinuity disappears if radiation energy and pressure exceeds gas energy
and pressure.
Theoretical estimations (Belokon, 1959, Imshennik, Morozov, 1964):

Pr / Pg ~ 8.5

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1

Shock wave structure for strong shock

Closure condition: P = fE
• Eddington approximation: f = 1/3• M1-closure~• Photon Boltzmann equation

Pr / Pg ~ 8.5
Diffusion approximation:

Pr / Pg ~ 8.5
4.65
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Transformation of fluxes from source to observer’s frame

Allowance of time delay, Doppler effect and aberration
Flux F in the point of observation – integral of intensity I0 over the surface:3  0 
2F ( t obs )  2    p I 0 ( R(  ),    , cos  0 (cos  ))   d 
min
 
 0 
1

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Effects of Lorentz covarianceTransfer equation Lorentz covariance, Doppler effect and aberration:lead to the following visible effects in moving to radiation sources:
1. Radiation flux increases
2. Spectrum becomes harder
3. The space moves towards the direction of motion

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Transformation of fluxes from source to observer’s frame
Lorentz covariance, Doppler effect and aberration•••

Radiation flux increases
Spectrum becomes harder
The space shrinks towards the direction of motion

V=0

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V = 0.5 c

Г = 107/8/2014

Г = 100

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STELLA RADA Integration
Algorithm RADA turns on before shock breakout starts
STELLA uses Lagrangian grid over mass coordinate, RADA – short characteristics withphysical quantities interpolationdI ( s )   b   J
   s  I ( s )  sI ( s )
s
s



I ( s )  I 0  e        e   e  ( s')ds' ,   0.5  s 2   s
0



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I b/c Shock Breakout Simulations

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SN 1987A shock breakout

The black and blue lines
represent, respectively, the
STELLA and RADA
calculations in the comoving
frame of reference.
Red line - RADA calculations
in observer’s frame ofreference taking into accountradiation time delay.

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SN 1987A shock breakout spectra

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The hardest semi-relativistic model, the SN Ib/c model• Evolutionary calculation of
KEPLER program for amain sequence star
(Woosley et al., 1995)• STELLA provides a shock
velocity at breakout up to
0.6с (Blinnikov, 1998)• M = 3.199 M
R = 1.41 1011 сm
E = 0.9 1051 erg

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SN Ibc shock breakout modeling (Tolstov et al. 2013)
Explosion energy = 1.8 foe,
Shock velocity at shock breakout ≈ 0.5с•Radiation Transfer – Short Characteristic Method(about 90% of calculation time)•

Radius х Angle x Energy = 350 * 100 * 200 == 7 000 000 for 1 time step•

200 steps of RADA , 10000 steps of STELLA,
3 days of calculation

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Spectra in observer’s frame of reference
Instantaneous spectra for various times at the epoch of SBO.

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SN I b/c model light curves

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Scattering is important!
Like for the 14E1X2 version above we switched off the thermalization of photons at thefirst scattering and increase the number of frequency bins for the version s1b7a2X. The
maximum temperature becomes enormous (~ 1010 K), but small admixture of true “gray”(i.e. frequency-independent) absorption, 10−6 of the Thomson scattering in an SN Ib
progenitor, makes the temperature lower for several orders of magnitude (the version
s1b7a2Xm6)

Matter temperature for the version s1b7a2X (left) and s1b7a2Xm6 (right) at shock
breakout versus Lagrangian mass Mr measured from the surface. The time in seconds is
given near the curves. The temperature peak is at an optical depth ∼ 200; 50; 4; 1; 0 attimes 67.0, 67.5, 67.9, 68.1, 68.9 s.
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Modeling of XRO080109/SN2008DRESCEU-RIKEN-IPMU Joint Meeting

7/8/2014

XRO080109/SN2008D• On 2008 Jan 9 at 13:32:49 UT, we serendipitously
discovered an extremely bright X-ray transient
during a scheduled Swift X-ray Telescope (XRT)
observation of the galaxy NGC 2770 (d = 27 Mpc).
Previous XRT observations of the ﬁeld just twodays earlier revealed no pre-existing source at thislocation. The transient, hereafter designated as Xray outburst (XRO) 080109, lasted about 400 s,
and was coincident with one of the galaxy’s spiralarms (Soderberg A. et al. Nature, Volume 453,
Issue 7194, pp. 469-474 (2008))• Drawing on optical, UV, radio, and X-ray
observations shows that the progenitor wascompact (R ≈ 1011cm) and stripped of its outer
Hydrogen envelope by a strong and steady stellar
wind. These properties are consistent with those of
Wolf-Rayet (WR) stars, the favored progenitors ofType Ibc SNe.
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XRO080109/SN2008D in the Model of SNIb
How to explain the duration and spectrum of the outburst?
External medium is optically thin to affect the radiation(Chevalier, Roger A., Fransson, Claes, 2008, ApJ, 683L, 135C)

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XRO080109/SN2008D in the Model of SNIb with the Stellar Wind
Can we explain the observational data by ‘natural’ model (WR star + wind)?
1.
2.

The growth of photosphere
Changes in absorption/emission of the perturbed wind

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XRO080109/SN2008D Spectra and Light Curves• X-Ray light curves and spectra, averaged over the duration of the flash,of XRO 080109 in Swift/XRT band (0.3-10 keV) for 10A presupernova model• No extinction

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XRO080109/SN2008D Spectra and Light Curves (extinction)• X-Ray light curves and spectra, averaged over the duration of the flash,of XRO 080109 in Swift/XRT band (0.3-10 keV) for 10A presupernova model• NH = 22 × 1021 cm−2, XRT response• EK = 262.5 foe (Tanaka et al. 2009) in modeling of SN2008D light curve
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Ibc models. Variations of stellar wind parameters

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XRO080109 Spectrum Evolution

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SN2008D light curve modeling, E=2 foe

Tanaka M. et al., 2009, Bersten M. 2013

STELLA
STELLA+RADA
SN2008 data

Density modulations of circumstellar medium
OR

Chemical composition of the progenitorOR

Jet geometry

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Current projects and Future plans

RESCEU-RIKEN-IPMU Joint Meeting

7/8/2014

IPMU: The First Stars (2014-2016)• 400 million years after the Big Bang
• Light curves and spectra of First
Direct insight into the age of galaxy formation
Supernovae (including shock breakout)• Chemical enrichment of the early
Universe• 2nd generation (low mass) extremely
metal-poor (EMP) stars: abundance
pattern and distribution (mixing)• Abundance pattern of EMP stars provides
constraints on Mass, Explosion energy ofFirst supernovae• Elemental abundance ratio in EMP stars(Iwamoto et al., 2003,2005)• Low 56Ni mass, low E faint supernovae• Observational signature of First
Supernovae (M, E, abundance) expectedfrom first stars: no metal blue supergiant
progenitor of First SNe
Understanding of the earliest starformation and the chemicalenrichment history of the Universe!
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Objectives• Analyses, prediction and interpretation of data of Subaru
Hyper-Suprime Cam (HSC) using SB templates for SN type Ib/c
New serveys: Palomar Transient Factory (PTF), Lick Observatory
Supernova Search (LOSS), Catalina Real-Time Transient Survey(CRTS), Kiso/Kiso Wide Field Camera (KWFC), Skymapper, Dark
Energy Survey (DES), Pan-STARRS, Subaru/HSC, Large Synoptic
Survey Telescope (LSST), KMTNet• Research and development of new and effective numericalmethods for calculating the radiation of relativistic gas dynamics• Numerical Improvements in SRRHD code:• Relativistic radiation hydrodynamics in 1D• Relativistic radiation hydrodynamics in 2D-3D• Scattering processes and radiation mechanisms
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SN Ibc Shock Breakout at High Redshift• Cosmological parameters(Komatsu et al. 2009):
H0 = 70.5 km s−1 Mpc−1k=0
Ωλ = 0.726
ΩM = 0.274• Dilated and redshifted multigroup
LCs with the g bandpass of the
Subaru/HSC• The horizontal line − 5σ detection
limit in the g-band for the
Subaru/HSC 1 hr integration• No extinction and no IGM
absorption

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Current status of Radiation Hydrodynamics calculations
RHD Technique\
Spacial Dim

1D

2D

3D

Single Energy(Relativistic code
/ Nonrelativisticcode)

RRMHD Codes(Farris, Zanotti,
Roedig, Sadowski,
Takahashi) Edd
ApproxHerant (1994)

SNSPH (Fryer 2006) , HARMRAD(McKinley 2013)

Multi Energy

STELLA (Blinnikov
1998, VEF), Hoflich,
VEF (1993)

FLD by Burrows(1995)RAGE (Frey 2013)

Multi Energy +Multi Angle

RADA (+ HD static)(Tolstov 2013)

ZEUS (Norman)
Muller, Janka 2012
(GR, Neutrino 2D but“ray-by-ray-plus”(1D))

ZEUS, Code by Jiang et al. (2013)(VEF,LTE, no AV, only tests)
Kuroda 2012 (GR, fEdd approx,
low-res), Ott 2013 (GR) “ray-byray”, ATHENA (Davis, 2012)

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Conclusions• Our numerical calculations provides us the opportunity tobuild templates for the analysis and interpretation of the SN
observations• The phenomenon of XRO080109/SN2008D may well be
explained qualitatively by the explosion of a conventional
WR-star surrounded by a stellar wind. SN2008D light curve
must be modeled for the optimal model• For the accurate consideration of not very strong radiation
dominated shock waves it is necessary to solve radiationtransfer equation (Eddington and M1 closure are not good
approximations)

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Thank you!

E-mail: alexey.tolstov@ipmu.jp
7/8/2014

Shock wave discontinuity

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