Radiative-transfer Modeling of Supernova Spectra and Light CurvesApplication to Massive-star Explosions In collaboration with Roni Waldman & Eli Livne (Racah Inst., Jerusalem) Luc Dessart1 and D. John Hillier2 1 :Laboratoire d’Astrophysique de Marseille, France 2 :University of Pittsburgh, USA General Aims: Infer SN ejecta properties Radiative Transfer Connect to Progenitor properties Stellar Evolution Connect to Explosion mechanisms Grav. Collapse, Explosive burning etc.
Synopsis • General context and relevance • Observational Background: SN typing, SN diversity • Theory Background: Stellar evolution, Explosion mechanisms • Radiative-transfer modeling: Method, processes, approximations, dependencies, e.g. line blanketing & opacity, electron-scattering, non-LTE, time-dependence, decay energy & non-thermal processes • Application to SN light-curves and spectra: II-P, II-pec, IIb, Ib, Ic
Core-collapse Supernovae (CCSNe): Key phenomena of modern astrophysics • Associated with massive-star death (M>8Mcollapse) • Progenitors of stellar-mass compact objects: SN connection (II,I, dark SNe)? • Explosion mechanism ? Theoretical challenge. Upper mass cut? Robustness? • Extreme r/T => Neutrino and GRW emitters (quest for a galactic SN). • Light-curve/spectral diversity heterogeneous progenitor/explosion properties • Luminous phenomena: Probes of distant Universe, cosmology (Ia) • Connection to Long-duration GRBs & highly-energetic Type Ic CCSN explosion. • Connection to observed super-luminous SNe, faint transients, interacting SNe? • Prime targets of current/future deep blind surveys for transients: PTF, Pan-STARRS, Sky-Mapper, LSST (2015+)
SN typing: Based purely on spectral signatures Type I SN: absence of hydrogen lines Ib: no-HI, HeI Ic: no-HI, no-HeI Fe-core collapse of an evolved (H-deficient) massive star => Wolf-Rayet Ia: no-HI, no-HeI, SiII 6300A feature Thermonuclear runaway in envelope of accreting Chandrasekhar-mass white-dwarf in binary system Type II SN: presence of hydrogen lines Fe-core collapse of an initially less massive star => BSG-RSG => SN typing reflects diversity of progenitor properties
Finer classification of CCSNe Light-curve morphology • II-Plateau: RSG progenitor (most common) • II-pec: BSG progenitor (rare; e.g.: 87A) • II-L: Mysterious set. Incudes the most luminous SNe known. Smith et al. (2011) Line-profile morphology • IIn, Ibn: Narrow HI/HeI lines Spectral evolution • IIb, i.e. II Ib Connection to GRB • Ic/GRB: SN with -ray emission
Diversity of Light curves • Car • duringoutburst
Diversity of Spectra Variations in composition, ionization, excitation, T, V(m)
Multiple paths to massive-star death. • Envelope stripping: wind mass loss and/or mass transfer. Key for SN diversity • Single star: Mdot is f(M,L,Z) => RSG/BSG/WNh/WN/WC/WO II-P/II-pec - IIb – Ib – Ic • Rotation influences transition between RSG & WR at death, i.e., II & Ibc SNe • Binary stars: Mdot via mass transfer! « WR » from 10-25 M progenitors • dM/dt, DL/dt = f(Z) => Type II vs. Type I SNe, Ib vs. Ic, GRB/SN, hypernovae without GRBs? • Puzzle: LBVs as progenitors of CCSNe? • => HUGE MESS! Wide range of properties at death due to: M,dM/dt,Z, (single) + mass transfer (binaries) (Courtesy of Doug Leonard)
Core evolution to gravitational collapse and explosion • Stellar evolution: progression toward increasing c and Tc ; Binding energy ladder: H He C O Ne Mg Si Fe => degenerate core • Electron capture (producing neutrinos) + photo-dissociation => Pressure deficit • Collapse when M>Mch=5.83 (Ye)2 M on dynamical timescale (10-100 ms) • Collapse halted at nuclear densities (~2x1014g/cm3), bounce, shock formation • Fe white dwarf -> p,n,e-,e+, neutron star: Gain of 1053 erg of grav. energy. • Energy losses at core bounce (photo-dissociation + neutrino losses): Shock wave stalls • Explosion requires shock revival: • Neutrino-driven explosion: • Magneto-rotational explosion: MRI. Fast rotating progenitor Fe core • Energy liberated ~ 0.1-10B; Explosive nucleosynthesis: ~0.001-0.1M of 56Ni Diversity of CCSNe: reflects complexities of stellar evolution (envelope & core properties) & variations in explosion mechanism/properties
Chronology of events in the life of a CCSN • 1 sec: Core collapse, bounce, shock revival • 1 min to 1 day: shock propagates and breaks out (1st EM signature). Fallback? NS vs. BH formation? • At breakout: Erad~Ekin ; Erad>>Eth ; cont ~106 • Mins to days: Final ejecta acceleration to homology (VR) • Ejecta properties: Ekin~1051erg, Mejecta~ few M, Vexp~3000km/s, M(56Ni) ~ 0.1M • Generic subsequent Evolution controlled by Cooling (Expansion & Radiative losses) versus Heating (Radioactive decay & Recombination). modulo Transport (dynamic radiative diffusion --- opacity/composition/ionization, dT/dr!) Their variations cause the diversity of CCSN Light Curves and Spectra • Weeks to months: Photospheric phase (1) • After a (few) month(s): Transition to Nebular phase (1) • 1-10n years: SNR, CSM interaction, light echoes
Radiative-transfer conditions: Before shock emergence Shock emergence (shock breakout) tSBO ~ 70s (R/R) (vs/104km/s)-1 tSBO~ 1min (WR), few mins (BSG), ~1d (RSG) R★~1-103R vshock~104km/s Rarefaction 1D radiation-hydrodynamics simulations (Dessart et al. 2010) Post-shock region: vr~3000km/s, T~106K, r ~ const. Radiation-dominated shock (P~aT4) Radiation trapped behind shock
Radiative-transfer conditions: Shock emergence 106 10 1 Envelope Atmosphere/Wind • Before explosion: Big M -> Big ~ M/R2 ~ 106-11 -> Big tdiff ~ 3 R / c ~ 103-5yr. • At large tshock << tdiff : Photons are trapped in the flow • Diffusion wave initiated when tshock ~ tdiff or c /3vshock ~ 10 • Radiative Precursor / Burst @1010-1011L • Duration: function of H R =>1-103s • High-energy radiation: X-ray (Ib/c; e.g., SN 2008D) or far-UV (II-pec,II-P) Eddington factor: fEdd=1/3 fEdd~1 Mean free path: p << R p ~ R tshock >> tdiff tshock << tdiff tshock ~ tdiff Rphot
At breakout: Erad ~ Ekin • Within minutes to days: dPrad/dr Etot ~ Ekin • homologous expansion: RSN >> R★; v(m) = const.; r(m) = r0(m)(texpl/t)3 • Subsequent evolution controled by cooling, heating & transport Radiative-transfer conditions: After Shock emergence 1.2B RSG explosion Dessart et al. (2010)
SN radiation influenced by cooling • Cooling through expansion primarily • dE=dQ-PdV ; Prad >> Pgas: E=aT4V, P=E/3 • => if dQ=0 then dT/T=-1/3 dV/V. Since dV/V=3dR/R => T ≈ 1/R • Explosion of a WD: R0=108cm, RSN=1015cm => RSN/R0=107 • => T drops from 109K to room T in ~2 weeks! Velocity [km/s] Velocity [km/s]
SN radiation influenced by heating • Recombinationenergy: e.g. 13.6eV per HI (weak). • Radioactive decayenergy: 56Ni 56Co 56Fe (g-rays,n, positrons). Key for Type I Sne! 56Ni 56Co : 1.75MeV per decay, half-life=6.07d 56Co 56Fe : 3.74MeV per decay, half-life=77.22d 3. Exceptionalcircumstances: Magnetarspin-down (Eth), interaction (EkinEth) Treatment of -rays: • Monte-Carlo code to follow -rays trough ejecta subject to Compton Scattering and photoelectric absorption • >>1: assume local deposition as heat. • <1: non-local, non-thermal
SN radiation influenced by transport • Fdiff ~ -dB/dt ; B is the Planck function (B~T4) • => Radiative Diffusion driven by dT/dR and inhibited by opacity c • t= R/l. Random walk requires t2steps so tdiff = t2l/c = tR/c • Note: For the sun, tdiff ~105years, <l>~0.1cm • tdiff is a characteristic time scale for energy leakage from SN ejecta • tdiff : function of expansion rate, mass, scale, opacity, ionisation etc. • Diffusion ≠ Trapping! No diffusion if dT/dt but trapping is t>1
Supernova Radiative-transfer Homology: V ~ R Outer boundary Free streaming Spectrum Formation Region trTlines, scattering, non-LTE Flux~const. trTLTE Edep, DJ/Dt, DF/dt Thermalization depth: J ~ B Phot. (~1015cm, 8kK, 5000km/s) Cont. Radiation escapes (t=2/3)
Non-LTE Time-Dependent Radiative Transfer Modeling with CMFGENCo-moving frame formulation for homogously-expanding ejecta (MKH75) Rate Equation: Gas & charge conservation Energy Equation: + Dedecay/Dt Coupling where (Excitation + Ionization) Radiation RTE 0th moment: RTE 1st moment:
1-D Non-LTE time-dependence using CMFGEN(Hillier & Miller 1998; Dessart & Hillier 2005,2008, 2010,2011ab; Hillier & Dessart 2012) • Simultaneously solves the radiative-transfer equation in the CMF frame, the statistical-equilibrium and the energy equations; Fully implicit solver; partial linearization of SEE. • Accurate description of I/J/H: moments of RTE with all important terms in v/c, /t, /,/, /r • RTE solved for at ~105frequency points(with coupling). Coverage:~10A to ~5m • Detailed description of the gas: 25 species & 15 ionization stages. Non-LTE D/Dt ionization • Large model atom: few 10000 levels and few 100000 transitions. • Approximation: Use of Super-Levels. Easy check on approx by switching to full levels. • Non-LTE: All important radiative + collisional rates included explicitly. • Non-LTE line blanketing: All continuum and line opacity sources included explicitly • Solution of Spencer-Fano equation for non-thermal heating/ionization/excitation rates • Adaptive grid:~7 pts per -decade at each time (asset over hydro: mass grid); [10-8 to 106 ]
1-D Non-LTE time-dependence using CMFGEN(Hillier & Miller 1998; Dessart & Hillier 2005,2008, 2010ab) • Physical consistency: stellar-evolution + hydro input: Xi(m), T(m), (m), v(m) r(m) => use SN light to constrain pre-SN evolution and explosion • Full-ejecta simulation, e.g. no “artificial” boundary conditions, Xi stratification • Decay energy: Computed with Monte Carlo -ray transport code(local or non-local) • Model requires ~5-10Gb, i.e. (NT=2000) x (ND=100) x (NBNDS+1=4) x 8 • Time step: t = 0.1t => 45-50 steps to go from 0.3 to 21d, or 10 to 1000d => 3 months SN II-P SN1987A
Application to Supernovae1) Steady-state mode2) Time-dependent mode
Non-LTE Steady State ApproachApplication: Modeling of Young Type II SNeThe case of the Type II-P SN 2005cs in NGC 5194 (Dessart et al. 2008) Steady-state models good at early times to constrain the Reddening, composition, expansion rate, distance/radius (EPM)
Study Dependencies! Degenerate effect of E(B-V) and T. Use lines • Z modulates metal-line blanketing • (v) modulates line and cont • H/He in SN II-P: influences UV flux but HI lines poorly sensitive
Spatial grid • Use optical-depth scale, not mass scale (e.g. hydro code) • Good resolution of photosphere; Eddington factors 1/3 1 • Naturally adjusts to resolve recombination fronts • Converged results with ~100 depth points. Dessart & Hillier (2010) HeI HI
Model atom --- Line Blanketing • Many species: H, He, CNO, IME, IGE • Many ions (I-VII) treated simultaneously • Huge model atom to account for all species/ions and sources of opacities (lines and continuum). • Sources of atomic data: Opacity project etc. Essential. • In non-LTE, need for all rates (radiative & collisional) • Strong line blanketing
Model atom --- Line Blanketing • Difficult to obtain converged results, especially in UV, UB bands • Accuracy of atomic data? • Illustration for importance of FeI, NiII and larger FeII model (big huge atom)
Effects associated with Electron-scattering:Frequency redistribution • photon scattering with free electrons causes frequency redistribution • Non-coherent scattering in CMF caused by the thermal motion of scatterers: Vthermal • Coherent scattering in CMF due to expansion, Redshift in Observer’s frame: Vexpansion • Vexpansion > Vthermal the redshift dominates: P-Cygni profile with enhanced red-wing flux • Vexpansion < Vthermal non-coherent redshift/blueshift dominates: Symmetric profile (SNe IIn) Effect of varying Vphot on H morphology
Electron-scattering: Flux ‘’Dilution’’ Mihalas book; Dessart & Hillier (2005b) • Scattering-dominated atmosphere => << => = • Eddington Approximation and dB/d =const. => Flux 2√ B(1/ √3 ) -> 1/ √3 : thermalization depth -> 2√ : Factor of “dilution” (<<1) • Introduce of ‘’dilution’’ factor Fobs= (Rphot/D2 B(TC) ; (Rphot -> Rphot) Gezari et al. (2008) Example with early post-breakout models: SEDs fitted with B(Tth) and ~0.6
Non-LTE effects • Solution of the statistical-equilibrium equations using all collisional/radiative rates. About 2000 levels/variables => Yields non-LTE level populations, ionization, line-blanketing • High density => Strong collision & weak scattering => LTE • Low density => weak collision: Dominance of scattering => Drives gas out of LTE • Large departure coefficients in regions of 1 but we recover LTE at depth! Dessart & Hillier (2011) Non-LTE LTE
non-LTE effects: HeI lines in young SNe II Eastman & Kirshner (1989) LTE Models non-LTE: Account of radiative rates in the determinations of level populations non-LTE allows good fit to HeI lines using a ‘’standard’’ BSG/RSG He abundance at early times non-LTE key for abundance determinations Flux SN87A obs Dessart et al. (2008) non-LTE model for 05cs Dessart & Hillier (2005): non-LTE model for SN87A
Spectral Modelling: time-dependent effects Dessart & Hillier (2008) Utrobin & Chugai (2005) D/Dt: No D/Dt: Yes D/Dt: Yes • High V, low trec ~ R/V time-dependent effects (UC05, DH08) • Retain D/Dt terms in SSE and Energy equations • Key to yield strong recombination lines in the absence of Lyman/Balmer flux • H strength at recombination epoch sensitive to Ne rather than profile
-ray escape and the nebular-phase decline rate • Fneb supports full -ray trapping in SNe II-P and II-pec up to few 100d => Higher mass • Fneb suggests -ray escape as early as ~50d in SNe IIb/Ib/Ic => Lower mass Dessart et al. (2011)
Non-LTE time-dependent Radiative transfer Full-Ejecta Simulations Dessart & Hillier 2010,2011; Dessart et al. 2011ab SN II-pec (87A): evolution from 0.3 to 21d of BSG-progenitor model lm18a7Ad (Woosley, priv. comm.) SN II-P: evolution from 10 to 1000d of 1.2B explosion of 15 and 25M RSG progenitors. SNe IIb/Ib/Ic: evolution from 1 to 100d of 1.2B explosion of (quasi) hydrogen-less cores produced from binary-star evolution (Yoon et al. 2010).
Light-curve evolution of SNe II-P, II-pec, Ib: Radiative-transfer simulations on full ejecta using physical input models Inputs (DH10,DH11a; Dessart et al. 2011) • Rapid fading after shock breakout • Post-breakout plateau: LPlateau function of R • Possible re-brightening from 56Ni/56Co decay. Delay function of mixing. • High-brightness phase function of M (large ), R (cooling), M56Ni (heating) • Transition to nebular phase when ~1; Lnebular function of M56Ni and -ray trapping • Not considered: binary (Kasen 2010) or CSM interaction, Magnetar radiation (Maeda et al. 07) Confrontation of simulations to observations => M*, R*, Eexpl, 56Ni LCs are degenerate/ambiguous: confusion Ia/b/c, difference M & Mejecta etc.
Comparison to observations of SN1987A Agreement at 10% level except in the blue (opacity issue) Supports 18MBSG progenitor, R~50R, and Eexpl~1.2B Observation Simulation Dessart & Hillier (2010a)
Simulations of SNe II-P: 15 and 25M RSG progenitor starsDessart & Hillier (2011) Spectral Evolution Photospheric phase Photospheric Composition vs. Time: Probe from surface to core! Nebular phase LP ~ 2-3 x larger than <Lobs>~3x108L => progenitors R-M too large?
Comparison to SN 1999em (II-P) spectra • General agreement at all times: supports RSG progenitor • Specific disagreement with H at nebular times: neglect of non-thermal processes • [OI]: emission from core + envelope; Key CCSN feature! 40d 300d H [CaII] 70d [OI]
SN II-P ejecta kinematics: Vphot vs. [OI] width • Smartt, van Dyk and Co. find SNe II-P stem from MRSG of 8-17M • Use nebular [OI] to constrain the main-sequence mass MMS • MMS Mhe , but dM/dt => Same final mass but bigger core! => Higher-mass progenitors eject oxygen at a larger velocities • Observations: v(OI) < 1500km/s => MMS < 20M Dessart et a.l. (2011)
Study of SNe IIb/Ib/Ic. What distinguishes them from Type II CCSNe? Main-sequence mass? Rotation? Metallicity? Explosion mechanism etc.?
Wolf-Rayet-star Properties • Single WR stars have long been proposed as progenitors of SNe Ibc • Properties of WR stars: 106L, Mdot~10-5M/yr, v∞=103km/s, M≥10M. • Emission line spectra => Easy detection out to few Mpcs! (WR search by Crowther/Bibby) • Final masses ≥10M for most WR, higher for WN, and even higher for WNh? WR Masses in binaries Crowther (2007)
Single WRs as progenitors of SNeIIb/Ib/Ic? • CCSN Rates: 48% of II-P, but 14% of Ic, 7% of Ib, and 10.6% of IIb (Smith et al. 2010) => Not an IMF reflection but calls for a binary component • Non-detection of any Ibc progenitor conflicts with single luminous WR stars • Problems with SN IIb/Ib/Ic observations: • difficulty to produce low-mass cores at death for Type I CCSNe. • 2) difficult to produce He-rich envelopes (with residual H) for Ib (IIb).
(Low-mass) Binary channel • Binary-star evolution naturally produces low-mass stars with degenerate Fe cores from 10-25M main-sequence stars (Yoon et al. 2010). Favored by IMF. • Progenitor properties: low L, weak winds, no emission lines => NOT genuine WR stars! • He up to 50% of the total mass. • Low-binding energy and similar core as 15M RSG => common exposion mech.? • Brighter and more massive companion when primary explodes. Naturally explains the existence of SNe Ibc in high luminosity region, even for low-mass binaries. He 56Ni O
Observed SN IIb/Ib/Ic Light curves Drout et al. (2010) • Nearly always discovered on the rise (suspicious). • Rise time to peak of ~20 days --- Same as a SN Ia! • Narrow peak (20d). • Faster decline than for full g-ray trapping (not shown) • SNe IIb, Ib, and Ic have similar LC properties. • Scatter in peak brightness. Similar magnitude of scatter for SNe II-P.
SN IIb/Ib/Ic LC - Simulations • Ensman & Woosley (1988) using artificially stripped 15-25Mprogenitors explode hydrogen-less cores and reproduce the basic morphology of SNeIb LC - no discussion of spectra though. • Dessart et al. (2011,2012): Simulations of both spectra and light curves based on (realistic) binary-star progenitors. Prediction of post-breakout plateau, early peak, narrow peak, fast decline at nebular times. Some agreement with obs. => SNeIIb/Ib/Ic have LOW-MASS ejecta! EW88
The case of SNeIIb Dessart et al. (2011) • Binary-star progenitor model • M=18M, Mejecta= 2.91M, M(H) = 0.0007M, • X(H) = 0.1 at 50000 km/s • X(H) < 0.001 at 10000 km/s • M(56Ni)=0.18M (unmixed) H • SNeIIb and Ib have similar LCs. Diff. is HI lines • Our work: HI easy to reproduce even with very little hydrogen (=> Large rate of IIb?) => Low-mass ejecta with little H excludes known WNh stars => Supports close low-mass binaries
SN Ib: Position of the « problem » • SNe Ib: Strong HeI lines at 10000km/s from a few days to peak and beyond • Issue: HeI ionization/excitation potential really high => difficult to excite levels or photoionize/recombine at a cool photosphere. • Non-thermal processes are key (Lucy 1991). • Origin: radioactive decay -> Compton scattering -> high-energy (non-thermal) electrons. Subdominant in number compared to thermal electrons with Maxwellian distribution at local T of a few 1000K but key non-thermal ionization/excitation effects. • Magnitude of non-thermal processes conditioned by distribution of g-ray energy deposition. • Problem: 56Ni produced at the highest r and T at base of ejecta in the first second. Velocity initial ~ 1000 km/s BUT HeI lines seen with 10000km/s width. => Non-local edep. But gamma-ray mean free path short for several weeks throughout most of the ejecta.
Mixing is essential. • Large scale asymmetry of explosion: propels 56Ni along 1-2 directions. • Small scale asymmetry: RT but weak in Type I SNe. Intrinsic structure of SN shock with 56Ni fingers etc. Very likely the favored option since fundamental property of the SN mechanism as we know it (SASI, convection, KH, RT instabilities). Lg / R Velocity [km s-1]
1D to multi-D: Hydro. Instabilities => Mixing • Shock fundamentally aspherical on large scale • Instabilities (RT, shocks, convection) => small scale clumps, fingers Main source of mixing in Type I b/c Sne • Strong RT when shock meets H/He interface in Type II SNe. • Impacts SN radiation for low-mass ejecta Kifonidis et al. (2006)
Effects of Mixing: Numerical Exploration Grid of models based on the SAME ejecta but with different levels of MIXING. 4.4M progenitor model -> Ejecta with 3M, 1.2B, 0.15M of 56Ni. Increasing mixing from x0 to x4