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. 24 2 26 4 Magnitude Magnitude 28 6 30 8 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 2 3 mo − mm (t + ∆t ) − ∆m 1 X I ;F I ;F I I I log p = − 6 + log(σ2 + σ2 ) + log(2π)7 2 4 σ2 + σ2 o m;F 5 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.