Hydrodynamical Model for Strongly Lensed SN Refsdal and Time-Delay Measurements Between Its Multiple Images

Hydrodynamical model for strongly lensed SN Refsdal and time-delay measurements between its multiple images

Petr Baklanov, N. Lyskova, K. Nomoto, S. Blinnikov

Kavli IPMU

February 04, 2020

ITEP [email protected] 1/38 SN Refsdal: discovery

A strongly lensed supernova was found in the MACS J1149.6+2223 galaxy cluster eld on 11 November 2014 Kelly et al. arxiv:1411.6009 Cluster MACS J1149.5+2223 and SN Refsdal

MACS J1149.5+2223 Members (Treu, 2015): 0.520 < z < 0.570 DL = 3.14 Gpc Da = 1.32 Gpc The light travel time is 5.235 Gyr.

SN Refsdal is located at the

outer spiral arm (Rc 7 kpc) ∼ z = 1.49 DL = 11 Gpc Da = 1.771 Gpc The light travel time is 9.380 Gyr. by NASA, ESA Cluster MACS J1149.5+2223 and SN Refsdal

by NASA, ESA by T.Treu (2016) Image SX Motivation

I It is very exciting to study the most distant supernovae type IIP at z = 1.49 To learn the properties of the peculiar core-collapse supernova explosion at high redshifts.

I Try to get the time delays and the magnication ratios between multiple images of the supernova. Constraints for the structure of dark matter halos in galaxies? Measuring the Hubble constant? Facts about SN Refsdal

I Fact 1: This is the rst SN to get its own name since the Late Renaissance.

I Fact 2: This is the rst SN with multiple images due to strong gravitational lensing.

I Fact 3: This is the rst SN for which the place and time of its appearance was predicted. Refsdal, S. (1964). On the Possibility of Determining Hubble's Parameter and the Masses of Galaxies from the Gravitational Lens Eect. Monthly Notices of the Royal Astronomical Society, 128(4), 307310. Facts about SN Refsdal

I Fact 1: This is the rst SN to get its own name since the Late Renaissance.

I Fact 2: This is the rst SN with multiple images due to strong gravitational lensing.

I Fact 3: This is the rst SN for which the place and time of its appearance was predicted. Facts about SN Refsdal

I Fact 1: This is the rst SN to get its own name since the Late Renaissance.

I Fact 2: This is the rst SN with multiple images due to strong gravitational lensing.

I Fact 3: This is the rst SN for which the place and time of its appearance was predicted. Observations: LC of SN Refsdal

The multi-color photometric data were obtained for 400 days following the discovery. There is a slow rise to maximum light (over 150 days). ∼

by Rodney et.al.(2015) arxiv:1512.05734 Observations: the spectra of SN Refsdal

d Spectrum of Hα taken −47 by HST WFC3 Grism

Hα P-Cygni expansion velocity

d Spectrum of Hα taken 16 by the VLT

by Kelly+2015, arxiv:1512.09093 The analysis of observations

These are the conclusions of Rodney+2016, arxiv:1512.05734

I The hydrogen lines are shown in SN Refsdal's spectra so it should be SN II.

I SN Refsdal's slow rise to maximum light (over 150 days) is clearly inconsistent with the rise times for the most common∼ SN types (e.g., Ia, Ib/c, II-P, and II-L).

I SN Refsdal observations have been compared with these normal SN classes, using a library of 42 templates drawn from the Supernova Analysis software suite unsuccessfully

I Rodney et.al. have concluded that the peculiar SN 1987A-like sub-class provides the best matches to the observed shape of the SN Refsdal light curve. Theoretical light curves: code STELLA

The optical light curves of SN Refsdal are analyzed with the multienergy group radiation hydrodynamics code STELLA developed at ITEP (S. Blinnikov, E. Sorokina, P. Baklanov). Model assumptions

I The equations were written in one-dimensional spherical geometry. I The levels and ions populations are computed under LTE. I Our total opacity included contributions from photoionization, bremsstrahlung, lines, and electron scattering. I The line opacity with expansion eect in lines was computed using atomic data from the Kurucz's list with approximately 150,000 lines. I Multigroup radiative transfer coupled with hydrodynamics enables to derive the spectral energy distributions (SEDs) self-consistently. stella solves the time-dependent equations implicitly for the angular moments of intensity averaged over xed frequency bands. No assumption of radiative equilibrium

ITEP [email protected] 11/38 The progenitor model: chemical composition

We have used as initial model the evolutionary model of Nomoto & Hashimoto (1988)

Density as a function of the interior mass Abundance distribution as a function of and radius enclosed mass for the ejecta nommixa nommixa 5 ] 3 0

[g/cm 1e−01 , ρ −5 −10

0.0e+00 5.0e+11 1.0e+12 1.5e+12 2.0e+12 2.5e+12 3.0e+12 3.5e+12 i

R, [cm] X 1e−03 5 ] 3 H Ca 0 He Ar C Fe [g/cm O Ni , 1e−05 Si Ni56 ρ −5

2 5 10 −10

5 10 15 M_r [Solar mass]

M [Msun] 51 SN 1987A: E = 1.7 10 ergs, M = 16.6 M , M56 = 0.078 M × Ni Modeling Light curves of the supernovae:

with SN 1987A with SN Refsdal ts= z=0.00 D=5.14e+04 mu=1.0 Ebv ts=-56950 z=1.49 D=1.10e+10 mu=15.4 ebv=0.00 U lvl14E1nommixaa R lvl14E1nommixaa R SN 1987A U SN 1987A F105W lvl14E1nommixaa F160W lvl14E1nommixaa F105W obs. F160W obs. 0 B lvl14E1nommixaa I lvl14E1nommixaa B SN 1987A V SN 1987A F125W lvl14E1nommixaa F606W lvl14E1nommixaa F125W obs. F435W obs. V lvl14E1nommixaa I SN 1987A F140W lvl14E1nommixaa F814W lvl14E1nommixaa F140W obs. F814W obs.

4 Magnitude Magnitude 28

0 50 100 150 200 0 100 200 300 400 Time [days] Time [days] Good t! A bad agreement with the observations The path to the best model

We have increased the ejected mass to make the cupola longer.

er tt be It's The path to the best model

We have increased the explosion energy to make the photospheric velocities higher.

er tt be It's The path to the best model

56 We have increased the mass of Ni: M56 = 0.078 0.116 M Ni →

er tt be It's The path to the best model

We've increased the degree of 56Ni mixing

er tt be It's The path to the best model

We've decreased the metallicity Z Z(SN 1987A)/10 →

er tt be It's Q: How to choose the best model?

The path to the best model

To evaluate the best-t model which simultaneously reproduces multi-band SN Refsdal light curves, we computed the set of the radiation-hydrodynamical supernova models.

The parameter space of our 181 SN models

R [R ] M [M ] Ni56 [M ] E [Foe] Z [Z ] min 30 16 0.077 1 1 ...... max 100 27 0.42 7 0.1 The path to the best model

To evaluate the best-t model which simultaneously reproduces multi-band SN Refsdal light curves, we computed the set of the radiation-hydrodynamical supernova models.

The parameter space of our 181 SN models

R [R ] M [M ] Ni56 [M ] E [Foe] Z [Z ] min 30 16 0.077 1 1 ...... max 100 27 0.42 7 0.1

Q: How to choose the best model? Model tting and selection

The likelihood function is a Gaussian where summation was performed for time and the broad-band lters of HST (F105W, F125W, F160W):

 2  mo − mm (t + ∆t ) − ∆m 1 X I ,F I ,F I I I log p = −  + log(σ2 + σ2 ) + log(2π) 2  σ2 + σ2 o m,F  t,F o m,F , where σo the observational MCMC (emcee, arxiv: 1202.3665) +2.68 td = 72.24 2.32 uncertainties, − −

σm,S the model uncertainties, dt, dm time delay, magnication +0.03 dm = 2.57 0.03 − − 5 1. F105W refE5R50M26Ni2m2b5m3Z01 − 0 F125W refE5R50M26Ni2m2b5m3Z01 2. − 23 dm F160W refE5R50M26Ni2m2b5m3Z01 5 2. F105W SN Refsdal, image: S1 − .0 F125W SN Refsdal, image: S1 3 +0.04 − sig+F105W = 0.14 0.03 F160W SN Refsdal, image: S1 − 00 1.

75 24 0.

50 0. sig+F105W 25 ∆m ∝ µ 0. +0.05 sig+F125W = 0.17 0.04 − .2 25 1 9 0.

.6 Magnitude 0

sig+F125W 3 0. +0.04 sig+F160W = 0.11 0.02 26 − 00 1.

75 0.

∆t .50 0 sig+F160W 25 27 0.

90 80 70 60 .0 .5 .0 .5 25 50 75 00 .3 .6 .9 .2 25 50 75 00 3 2 2 1 0. 0. 0. 1. 0 0 0 1 0. 0. 0. 1. − − − − − − − − 0 100 200 300 400 td dm sig+F105W sig+F125W sig+F160W Time [days] The models

There are the 8 best-t models selected by criteria BayesianEvidence > 0.001.

The parameters of the top best-t models

56 Model log RMtot M( Ni) Eburst Evidence (R ) (M ) (M ) (E51) ref1 50.0 26.3 0.245193 5.0 0.7096 ref2 50.0 20.6 0.373069 3.0 0.165 ref3 50.0 26.0 0.243826 5.0 0.0891 ref4 45.0 25.0 0.118098 6.0 0.0253 ref5 50.0 26.3 0.245193 3.0 0.0048 ref6 40.0 26.0 0.119082 5.5 0.0022 ref7 50.0 26.0 0.243826 4.0 0.0021 ref8 50.0 26.0 0.243826 3.0 0.0012 The models

There are the 8 best-t models selected by criteria BayesianEvidence > 0.001.

The parameters of the top best-t models

The light curves for S1-S4 Images

24 24 24 24 S1 S2 S3 S4 refE5R50M26Ni2m2b5m3Z01 25 25 25 25 25 20

26 26 26 26 MJD pik= 190 15

Magnitude Magnitude Magnitude Magnitude 10 prob = 0.7140 prob = 0.7140 prob = 0.7140 prob = 0.7140 27 2.6 0.02 1.9 0.02 27 2.3 0.02 27 6.5 0.04 27 dt = 72.12.2 dm = 2.570.03 dt = 9.92.1 dm = 0.140.02 dt = 4.22.3 dm = 0.020.02 dt = 30.48.1 dm = 1.160.05 − 0.04 − 0.04− 0.05− 0.08 σF 105W = 0.140.03 σF 105W = 0.190.03 σF 105W = 0.210.04 σF 105W = 0.210.07 5 Velocity [1e+03 km/s] 0.04 0.03 0.03 0.07 σF 125W = 0.160.03 σF 125W = 0.140.02 σF 125W = 0.160.03 σF 125W = 0.340.06 0.03 0.02 0.02 0.06 28 σF 160W = 0.110.02 σF 160W = 0.080.02 28 σF 160W = 0.090.02 28 σF 160W = 0.080.05 28 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time [days] Time [days] Time [days] Time [days] Time [days] LCs for the broadband lters with merged data for images S1-S4.

F105W F125W F160W 24.5 24.5 24.5

25.0 25.0 25.0

25.5 25.5 25.5 Magnitude 26.0 26.0 26.0

S1 S3 26.5 26.5 26.5 S2 S4 S1: dt= -77.52 dm= -2.52 S2: dt= 9.56 dm= -0.14 S3: dt= 4.19 dm= -0.01 50 0 50 100 150 200 250 50 0 50 100 150 200 250 50 0 50 100 150 200 250 − MJD - 57000 [days] − MJD - 57000 [days] − MJD - 57000 [days] Best model: refR50M26Ni2m2b5m3Z01

24 S1 refE5R50M26Ni2m2b5m3Z01 25 The SN model: 25 20

MJD pik= 190 R 26 15 R0 = 50

Magnitude 10 Mtot = 26 M 27

5 Velocity [1e+03 km/s] M56Ni = 0.13 M (mixed) 28 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Z = 0.1 Z(SN 1987A) Time [days] Time [days] E = 5 1051 ergs × According to our modelling, the SN Refsdal SN 1987A velocities is a more massive and energetic version of SN 1987A. Summary of Time Delays and Magnications

To estimate the time delays and magnications we use the Bayesian model averaging (BMA) method, where the model parameters are averaged to the weight corresponding to this model.

Time delay and Magnication Ratio Measurements

Parameter SN t Template LC Fitsa Polynomial Curve Fitsa 2.5 d d d MJDpk 571392.3 57138 ± 10 57132 ± 4 2.0 d d d ∆tS2:S1 9.62.2 4 ± 4 7 ± 2 2.3 d d d ∆tS3:S1 4.32.3 2 ± 5 0.6 ± 3 7.1 d d d ∆tS4:S1 29.87.6 24 ± 7 27 ± 8 0.02 µS2/S1 1.140.02 1.15 ± 0.05 1.17 ± 0.02 0.02 µS3/S1 1.010.02 1.01 ± 0.04 1.00 ± 0.01 0.02 µS4/S1 0.350.01 0.34 ± 0.02 0.38 ± 0.02 Notes a Values given in Rodney et al. 2016 in Table 3. Constraints for lens models

We used our best model for measuring time delays and magnication ratios.

Q: Can we oer any constraints on the parameters of lens models? Lens models VS SN t

Comparison of the model S2 S2 tting time delays and magnication ratios (gray color) against values predicted by lensing models and template&polinomial tting. S3 S3 Summary of Models (Treu, 2016) Nickname Team Die-a Diego et al. Gri-g Grillo et al.

S4 S4 Ogu-g Oguri et al. Ogu-a Oguri et al. ogu-g ogu-a Sha-g Sharon et al. gri-g Sha-a Sharon et al. sha-g sha-a obs-tmp Rodney et al. die-a obs-tmp obs-pol Rodney et al. obs-pol 20 0 20 40 60 80 0.5 1.0 1.5 2.0 2.5 ∆t : S1 [days] µ : S1 Fitting of the SX LCs

Unfortunately, we have only three observation points. We used our 8 best models to t LCs of SX image.

25.0 refE5R50M26Ni2m2b5m3Z01: refE3R50M20Ni3m2b1m2Z01: niCatR50 M26 Ni023 E50: ref R45 M25 Ni007 E60: 25.5 dt= 317.00 dm= -0.828 dt= 313.98 dm= -0.674 dt= 319.75 dm= -0.847 dt= 307.54 dm= -1.350 26.0 26.5 27.0

Magnitude 27.5 28.0 28.5 350 400 450 500 550 600 650 350 400 450 500 550 600 650 350 400 450 500 550 600 650 350 400 450 500 550 600 650 Time [days] Time [days] Time [days] Time [days]

25.0 refE3R50M26Ni2m2b5m3Z01: ref R40 M26 Ni007 E55: niCatR50 M26 Ni023 E40: niCatR50 M26 Ni023 E30: 25.5 dt= 300.61 dm= -1.020 dt= 301.43 dm= -1.432 dt= 310.48 dm= -0.900 dt= 301.47 dm= -1.024 26.0 26.5 27.0

Magnitude 27.5 28.0 F125W niCatR50M26Ni023E30 F160W niCatR50M26Ni023E30 28.5 F125W SN Refsdal, image: SX F160W SN Refsdal, image: SX 350 400 450 500 550 600 650 350 400 450 500 550 600 650 350 400 450 500 550 600 650 350 400 450 500 550 600 650 Time [days] Time [days] Time [days] Time [days] Fitting of the SX LCs

We used our best model for measuring time delays and magnication ratios.

59 0.12 ∆tSN (SX /S1) = 31684 days, µ(SX /S1) = 0.210.06

Kelly+2016b 0.5 BMA ogu-g ogu-a gri-g 0.4 sha-g sha-a die-a 0.3 SX/S1 magniﬁcation 0.2

0.1 59 0.12 dt = 31684 days µ(SX/S1) = 0.210.06 150 200 250 300 350 400 450 SX-S1 time delay The time delay of gravitational lens and H0

 

1 + zl Dl Ds  1 2  ∆t(θ) =  (θ − β) − ψ(θ) c Dls  2  |grav{z } | geom{z } c(1 + z) Z z dz0 D = A 0 H0 0 E(z ) q 3 2 E(z) = ΩM (1 + z) + Ωk (1 + z) + ΩΛ D D 1 ∆t(θ) ∝ l s ∝ Dls H0

To measure the Hubble constant H0 we need:

I The time delays

I The lens mass models The Hubble constant

To derive H0, we follow the approach proposed in Vega-Ferrero+2018, where the Hubble constant is obtained via rescaling the time delays predictions of the lens models to match the observed values.

base H0 base Plens (∆t, µ|H0) = Plens ( ∆t, µ|H0 , GL) H0

The probability of P(H0|D) is the product of the observed probability distribution of the observed time delay and magnication times the probability distribution from the individual models.

Z P(H0|D) ∝ P(H0) P(D|H0) ∝ P(H0) d∆t dµ · pobs (∆t, µ) · plens (∆t, µ|H0),

The time delay (µ) of multiple images of Contribution of each lens model SN Refsdal predicted the dierent lens models. predictions to the posterior model dt(S2) µ(S2) dt(SX) µ(SX ) distribution P+(H0|D). ogu-g 8.70.7 1.10.24 311.024.0 0.30.05 Gri-g 0.7 0.24 24.0 0.05 0.008 Ogu-g ogu-a 9.41.1 1.10.17 335.621 0.30.03 Ogu-a 1.1 0.17 21 0.03 0.006 Sha-g D)

3.0 0.52 27 0.09 | Sha-a gri-g 10.6 0.9 361.0 0.4 0

6.2 0.43 19 0.11 H 0.004 sha-g 5 0.06 21 0.02 P( 6.06 0.80.18 277.011 0.20.05 sha-a 5 0.19 13 0.04 0.002 8.07 0.80.2 233.046 0.20.01 die-a 19 0.79 55 0.1 0.000 −17.019 1.90.79 262.055 0.30.1 0 25 50 75 100 125 150 H0, km/s/Mpc The Hubble constant

Contribution of each lens model predictions The total posterior distribution P+(H0|D) to the posterior distribution P+(H0|D). dened from observations of images S2 and SX. Grey area shows 68% CL.

0.0030 Gri-g 0.008 Ogu-g 0.0025 Ogu-a Sha-g 0.0020 0.006 D) | 0 D)

| Sha-a 0 H

( 0.0015 H 0.004 + P P( 0.0010 0.002 0.0005

0.000 0.0000 0 25 50 75 100 125 150 0 25 50 75 100 125 150 H0, km/s/Mpc H0, km/s/Mpc We average the probabilities of the models P+(H0|D).

The best value for H0 resulting from the combined analysis of S2 and SX images is +16.7 km s−1 Mpc−1 . H0 = 71.2−11.6 Conclusions

I Our major result is that SN Refsdal was the massive and high-energy version of SN 1987A. It is amazing that the progenitors of the closest (SN 1987A) and the most distant SN IIP are the BSG stars. I The progenitor of SN Refsdal was the BSG with next parameters:

R0 = 50 R

Mtot = 26 M M M56Ni = 0.13 (mixed) Z = 0.1 Z (SN 1987A) E = 5 × 1051 ergs

I We get the time delays and magnication ratios between multiple images of the supernova.

I The best value for H0 resulting from the combined analysis of S2 and SX images is +17 km s−1 Mpc−1 . 71−12 I Potential bias errors: reddening E(B − V ) > 0, microlensing? I Thank you! Appendix SX - S1 Time Delay (Observer-Frame Days)

by Kelly et.al.(2015) arxiv:1512.04654 Observations: LC of SN Refsdal

The multi-color photometric data were obtained for 400 days following the discovery. There is a slow rise to maximum light (over 150 days). ∼

by Rodney et.al.(2015) arxiv:1512.05734 SN Refsdal: tting the observations

Rodney S. et.al. SN Refsdal: photometry and time delay measurements of the rst einstein cross supernova, arxiv:1512.05734

Results of tting the SN Refsdal Results of the template ts to the light curves using a cubic spline SN Refsdal light curves using the best-matching template, which is the SN 1987A-like Type II SN 2006 V. Models of Lenses

Diego, 2016 Credit: NASA, Colley, Turner, and Tyson

The surface mass density is described by the combination of two β = θ − α(θ, Σ) components: θ is the observed position (i) A soft (or diuse) component that is parametrized as a of the source, α is the super- position of Gaussians on a grid of constant width (regular deection angle,Σ is the grid) or varying width (adaptive grid). surface mass density of (ii) A compact component that accounts for the mass associated the cluster at the position with the individual haloes (galaxies) in the cluster. This θ and β is the position of component is modelled either as Navarro Frenk and White the background source proles with a mass proportional to the light of each galaxy or adopting directly the light prole (in one of the IR bands). Lens mass

Summary of Models (Table 5) Short name Team Type rms Images Die-a Diego et al. Free-form 0.78 gold+sil Gri-g Grillo et al. Simply param 0.26 gold Ogu-g Oguri et al. Simply param 0.43 gold Sha-g Sharon et al. Simply param 0.16 gold Zit-g Zitrin et al. Light-tr-mass 1.3 gold The lens equation

Z β = θ − α, Σ(θ) = ρ(θ, z)dz

4GM R α(θ, Σ) = ∇ ψ(θ, Σ), ∼ = 2 sc θ c2p p  

1 + zl Dl Ds  1 2  ∆t(θ)=  (θ − β) − ψ(θ) c Dls  2  |grav{z } | geom{z } θ dθ µ = β dβ

θ is the observed position of the source, α is the deection angle,Σ(θ) is the surface mass density of the cluster at the position θ, β is the position of the background source, Dl , Ds and Dls are the angular diameter distances to the lens, the source and from the lens to the source. geom: time delay due to the extra path length of the deected light ray relative to an unperturbed null geodesic grav: time delay due to general relativistic time dilation, Shapiro time delay Magnication & Time delay (Treu+2016)

Magnication: θ dθ µ = β dβ

Source µ(S1) µ(S2) µ(S3) µ(S4) µ(SX ) Diego+(2015) µ(Si )/µ(S1) 1.89 ± 0.79 0.64 ± 0.19 0.35 ± 0.11 0.31 ± 0.1 Sharon+(2015) +6.4 7.5 +19.1 +6.9 18.5−4.5 14.4−5.5 20.5−3.9 11.0−4.2 Oguri+(2015) 15.4 ± 1.6 17.7 ± 1.9 18.3 ± 1.9 9.8 ± 1.4 4.2 ± 0.3 Grillo+(2016) +17.4 7.9 +19.2 +3.7 +4.5 13.5−10.3 12.4−18.8 13.410.3 5.7−8.1 4.8−5.3

Time delay: ∆t(θ) = 1+zd Dd Ds 1 (θ β)2 ψ(θ) c Dds 2 − −

Source ∆t(S2 − S1) ∆t(S3 − S1) ∆t(S4 − S1) ∆t(SX − S1) Diego+(2015) 17 ± 19 −4.3 ± 27 73 ± 43 262 ± 55 Sharon+(2015) +10 13 +16 +37 2.0−6 −5.0−7 7.0−3 237−50 Oguri+(2015) 9.4 ± 1.1 5.6 ± 0.5 20.9 ± 2.0 335.6 ± 20.7 Grillo+(2016) +7.6 3.0 +34 +334 10.6−16.8 4.8−8.0 25.9−21.6 361−381