On Measuring the Metallicity of a Type Ia Supernova's Progenitor
Broxton J. Miles, Daniel R. van Rossum, Dean M. Townsley, F. X. Timmes, Aaron P. Jackson, Alan C. Calder, Edward F. Brown
SSubmitted to the Astrophysical Journal on August 24, 2015. Accepted on April 9, 2016
Preprint typeset using L A TEX style emulateapj v. 04/17/13
ON MEASURING THE METALLICITY OF A TYPE IA SUPERNOVA’S PROGENITOR
Broxton J. Miles , Daniel R. van Rossum , Dean M. Townsley , F. X. Timmes Aaron P. Jackson , Alan C.Calder , and Edward F. Brown Submitted to the Astrophysical Journal on August 24, 2015. Accepted on April 9, 2016
ABSTRACTIn Type Ia Supernovae (SNe Ia), the relative abundances of chemical elements are affected by theneutron excess in the composition of the progenitor white dwarf. Since these products leave signaturesin the spectra near maximum light, spectral features may be used to constrain the compositionof the progenitor. We calculate the nucleosynthetic yields for three SN Ia simulations, assumingsingle degenerate, Chandrasekhar mass progenitors, for a wide range of progenitor metallicities, andcalculate synthetic light curves and spectra to explore correlations between progenitor metallicity andthe strength of spectral features. We use two 2D simulations of the deflagration-detonation-transitionscenario with different Ni yields and the W7 simulation to control for differences between explosionmodels and total yields. While the overall yields of intermediate mass elements (16 < A ≤
40) differbetween the three cases, trends in the yields are similar. With increasing metallicity, Si yieldsremain nearly constant, Ca yields decline, and Ti and Fe yields increase. In the synthetic spectra,we identify two features at 30 days post explosion that appear to deepen with progenitor metallicity:a Ti feature around 4200 ˚A and a Fe feature around 5200 ˚A. In all three simulations, their pseudoequivalent widths show a systematic trend with progenitor metallicity. This suggests that these twofeatures may allow differentiation among progenitor metallicities of observed SNe Ia and potentiallyhelp reduce the intrinsic Hubble scatter.
Keywords: nuclear reactions, nucleosynthesis, abundances – radiative transfer – stars: abundances –supernova: general INTRODUCTIONType Ia supernovae are generally considered to be theresult of the thermonuclear disruption of carbon-oxygenwhite dwarfs in binary star systems. Although the pathwhich leads to these explosions is uncertain, the resultsare easily seen and quite useful. Powered by the radioac-tive decay of Ni (Colgate & McKee 1969), SNe Ia haveluminosities on the order of ∼ × L (cid:12) . This ex-treme luminosity in conjunction with a generally wellfollowed correlation between peak brightness and declinerate (Phillips 1993; Phillips et al. 1999) allow SNe Iato be used as standard candles out to redshifts of z ≈ Department of Physics & Astronomy, University of Alabama,Tuscaloosa, AL; [email protected] Department of Astrophysics, The University of Chicago,Chicago, IL Department of Physics & Astronomy, The State Universityof New York - Stony Brook, Stony Brook, NY New York Center for Computational Sciences, The StateUniversity of New York - Stony Brook, Stony Brook, NY Department of Physics & Astronomy, Michigan State Uni-versity, East Lansing, MI The Joint Institute for Nuclear Astrophysics School of Earth and Space Exploration, Arizona State Uni-versity, Tempe, AZ duced in the explosion with a portion of this materialbeing radioactive Ni. Explosions with lower amounts ofiron-group material, and thus lower amounts of Ni, areredder, dimmer, and have faster decline times than thosewith higher amounts of iron-group material. One factorthat can affect the production of stable and radioactiveiron-group material is the metallicity of the progenitor.Higher metallicity progenitors have larger abundances ofneutrons causing greater amounts of stable iron-groupmaterial to be produced and less radioactive Ni (Timmeset al. 2003).Studies of explosion models used in this work (de-scribed below) confirm this result holds when consideringthe effect of the metallicity on the flame speed in addi-tion to composition (Townsley et al. 2009; Jackson et al.2010). The capability to observationally constrain themetallicity of SN Ia progenitors would reduce some ofthe uncertainty caused by intrinsic variations betweenindividual events. In this study, we seek possible spec-tral features that could serve as indicators of progenitormetallicity.Observationally, it has been clear for some time thatenvironment plays a role in the observed behavior ofSNe Ia. Hamuy et al. (2000) saw in a sample of 62SNe Ia that brighter, slower declining events preferen-tially occurred in spiral galaxies, while elliptical galax-ies were host primarily to quickly declining, dim events.Also, they find that metal-poor environments producedbrighter SNe Ia. Kelly et al. (2010) find that SNe Ia thatoccur in larger, more massive galaxies were 10% brighterthan other SNe Ia with similar light curve shapes. Theyclaim that this trend could be caused by a correlation be-tween galaxy mass and metallicity, older progenitors in a r X i v : . [ a s t r o - ph . H E ] M a y higher mass galaxies, or other factors such as dust. Addi-tionally, Ellis et al. (2008) found that for 36 intermediate-redshift SNe Ia the differences between observed UVspectra could not be accounted for by dust alone requir-ing some other environmental factors such as metallicityto play a role. And, Howell et al. (2009a) found thatSNe Ia that occured in host galaxies with higher metallic-ities produced up to 10% less Ni. These observationalstudies all use host galaxy metallicity as a proxy for theprogenitor metallicity. However as metallicity can varyby location and time in galaxies, it would be more effec-tive to have an indicator of the individual progenitor’smetallicity in the SN Ia spectrum itself.There have been a number of investigations into the re-lationship between spectra and brightness (e.g. Nugentet al. 1995; Bailey et al. 2009; Blondin et al. 2011a,b,2012), mostly with the broad aim of improving the cali-bration of SN absolute brightness and thereby decreasingthe scatter from the Hubble law. In this present study,we do not attempt to resolve this broader question, butinstead focus on evaluating, from theory, candidate in-dicators of the metallicity of the progenitor that are nottoo blended or obscured by neighboring features. Sincemetallicity is thought to be mostly a secondary param-eter relating to the SN brightness, the next step wouldbe to attempt to separate it from the primary param-eter. Given our limited sampling of theoretical modelsand their current uncertainty, we refrain from addressingprimary variation in brightness directly here, and insteadlimit our study to searching for candidate spectral indi-cators of metallicity.Past theoretical studies have focussed on metallicity ef-fects on synthetic spectra, in particular the UV flux, bymaking sensible ad hoc modifications to the abundanceprofiles of explosion models (see Brown et al. (2015), andreferences therein). Generally, such modifications are notnecessarily self-consistent with different levels of progen-itor metallicity. For example, this type of modificationdoes not account for the effect of progenitor metallic-ity on the Ni production, which affects post explosionejecta temperatures, and therefore the shape and colorof synthetic light curves and spectra. De et al. (2014)have shown that the production of intermediate mass el-ements is also affected by progenitor metallicity in a waythat is expected to be fairly model independent. Thesechanges in the yields of the intermediate mass elements(IMEs, with atomic mass number 16 < A ≤
40) shouldalso have visible effects on the observed spectra. Theyfind the greatest change to be in the abundance of Cawith the least amount of change in the abundance of Si.This indicates that the characteristic SiII line at 6150 ˚Amay remain fairly static with metallicity, but the fea-tures from other IMEs should vary in such a way thatthe progenitor metallicity could possibly be measured.Here, we use multi-dimensional simulations of SNe Iausing the deflagration-to-detonation transition paradigmwith the FLASH hydrodynamics code in conjunctionwith particle post-processing and the 1-D radiative trans-fer code PHOENIX to examine the effects of progenitormetallicity on nucleosynthetic yields, light curves, andspectra. In section 2, we outline the SN Ia models weare using as well as a description of the hydrodynamic,particle post-processing, and radiative transfer calcula- tions. In section 3, we discuss the nucleosynthesis re-sults, synthetic light curves, and spectra. We also com-pare our results to Foley & Kirshner (2013) and Grahamet al. (2015), who examined SN2011by and SN2011fe,two spectroscopically normal SNe Ia which had nearlyidentical decline times and optical spectra, but interest-ing differences in the NUV region. Finally, in section4, we give our conclusions and discuss the possibilityof using spectral features as an indicator of progenitormetallicity. SN Ia EXPLOSION SIMULATIONSWe consider two types of explosion simulations, bothvariations of the delayed-detonation model for SNe Ia(Khokhlov 1991). The main model is a 2-dimensionalsimulation of a Chandrasekhar-mass WD exploding viathe deflagration-detonation transition (DDT) mecha-nism. These simulations are identical to those we haveperformed previously to study systematic variation inthis scenario (Krueger et al. 2010; Jackson et al. 2010;Krueger et al. 2012). For comparison, we also computenucleosynthetic yields, spectra, and light-curves for thewell-studied, 1-dimensional W7 model (Nomoto et al.1984). We briefly describe our 2D explosion model andpost-processing here.2.1.
Hydrodynamic Simulations
We chose two realizations of a CO white dwarf witha central density 2 × g/cm . Krueger et al. (2012)created 5 CO white dwarf progenitors with central den-sities that ranged from 1 × to 5 × g/cm . Foreach progenitor, 30 realizations were created by apply-ing initial conditions in the form of random perturba-tions on the initial burned region. This was done to bet-ter understand potential systematic biases such as howthe morphology of the initial conditions might influencethe results. Many of their progenitors produced higheryields of Ni than is typical in SNe Ia. In light of this,we selected realizations R01 and R10 due to their lowerestimated Ni yields, 0.8 M (cid:12) and 0.7 M (cid:12) respectively,which are closer to typical values for SN Ia (Howell et al.2009b). In this paper we refer to these two simulationsas DDT-high and DDT-low.We recalculated the simulations because the origi-nal simulations did not feature tracer particles that areneeded for this work (see below). For this work we useda newer version of the FLASH code, version 4.0. Thesimulation results are nearly identical to the those pub-lished in Krueger et al. (2012), with some small changesdue to changes to the hydrodynamics method in the in-tervening FLASH releases. The overall software consistsof the publically available version of the FLASH softwareinstrument along with added components for efficientmodeling of carbon-oxygen flames and detonations de-veloped during our previous work (Calder et al. 2007;Townsley et al. 2007, 2009; Jackson et al. 2010; Kruegeret al. 2012) as well as software for computing nucleo-synthesis in post-processing (Townsley et al. 2015) . Inaddition to the hydrodynamics itself, the current publicFLASH software release includes the advection-diffusion available from http://flash.uchicago.edu available from http://astronomy.ua.edu/townsley/code rogenitor Metallicity from SN Ia Spectra will also be included in a futurepublic release of the FLASH software instrument.Our simulations begin at the end of the core convectionphase of the runaway just after the ignition of a propa-gating thermonuclear flame (see Nonaka et al. 2012 fora discussion of this ignition process). We make the as-sumption that the flame is ignited in such a way that itspreads in the center of the star before plumes rise tolower densities. This is an analog of the “multi-point”ignition scenarios explored by other authors in 3D (e.g.Seitenzahl et al. 2013 for an example). Nonaka et al.(2012) suggests that multi-point ignitions are likely dis-favored by nature. Nevertheless, as others have shownpreviously and we demonstrate again in this work, thisdoes lead to an explosion that reproduces spectral obser-vations of normal SNe Ia fairly well. Our simulations fol-low the nuclear and hydrodynamic evolution of the flamewithin the star until it reaches a density of 10 . g cm − ,at which point it is assumed that a detonation is ignitedby a DDT mechanism (Khokhlov 1991; Poludnenko et al.2011). This detonation is ignited with the introductionof a small heated region since all burning fronts, andtherefore any physical DDT processes, are unresolved inour full-star simulations. The complete incineration ofthe star by the detonation then ensues. Active burningfronts cease due to the expansion of the star by about 1.8seconds and then we follow the expansion of the star to4 seconds, at which point it is already close to force-freeexpansion.Our model of carbon-oxygen burning used in hydrody-namics is a three-level burning model that is calibratedagainst steady state deflagrations and detonations. Theresulting temperature, T , and density, ρ , in the explosionsimulation enable post-processing of Lagrangian tracerparticles (see next section) to obtain abundances behindthe reaction front with an accuracy of 5-10% (Townsleyet al. 2015). The global energy deposition based on theburning model is consistent with the yields obtained frompost-processing to within 10%.2.2. Lagrangian Tracer Particles
During the explosion simulations, the temperature-density histories of a set of 100,000 Lagrangian tracerparticles are recorded. These tracer particles are inac-tive, meaning that they do not affect the hydrodynamicsbut are only advected with the flow, recording the his-tory of local fluid variables. During the burning phase ofthe explosion, the histories are recorded every time step,giving the full time resolution data which is needed for ac-curate post-processing (Townsley et al. 2015). The equalmass particles are distributed randomly. After the hydro-dynamic simulation is complete, we use the TORCH software instrument to compute the evolution of a setof 225 nuclides subject to the conditions recorded for agiven fluid element. This post-processing step allows thecomputation of detailed nucleosynthetic yields withouthaving to compute the reaction or advection of all ofthese species in the main hydrodynamic simulation.The density and temperature histories for W7 were Available at http://cococubed.asu.edu; Our version availableat http://astronomy.ua.edu/townsley/code obtained from Friedel Thielemann (priv comm). Theseconsist of about 500 time steps for 175 zones out to 4.15seconds. These histories were treated in the same manneras Lagrangian tracks from our 2D simulations. Similaryields were used by De et al. (2014) to investigate the de-pendence of Si-group yields on metallicity in comparisonto trends expected from quasi-equilibrium calculations.2.3.
Nucleosynthesis
The nucleosynthetic yields from the explosion simu-lations are determined by post-processing the historiesof Lagrangian tracer particles. The reaction networkcalculation, described in Townsley et al. (2015), deter-mines mass fractions for each particle. As described inTownsley et al. (2015), for fluid that is processed by thedeflagration we reconstruct, in post-processing, a por-tion of the Lagrangian history in order to obtain a morerealistic ρ ( t ), T ( t ) near the artificially thickened flamefront. We do not do so for detonations or for the W7element histories, instead using the ρ ( t ), T ( t ) history di-rectly. After post-processing, radioactive products withhalf-lives smaller than 5 days, according to beta decayrates in TORCH, have their calculated abundances con-verted into their decay products. Three important decaychains of three isotopes are calculated during the radi-ation transport simulations: Ni, Fe, and Cr. Thedecay chain of Ni to Fe is well understood to be crit-ical in the powering of SNe Ia light curves. Ni has ahalf-life of 6.075 days and transitions by beta decay to Co. Co has a half-life of 77.236 days and transi-tions by beta decay to Fe. The decay of Fe to Cr iscomplex. Fe has a half-life of 8.275 hours and tran-sitions by beta decay to the 2+ excited state of Mn.The excited state has a half-life of 21.1 minutes , buthas two possible decay branches. 98.25% will transitionby beta decay to Co, and the remaining 1.75% decaysto the ground state of Mn via internal transition. Theground state has a half-life of 5.591 days (Dessart et al.2014; Huo et al. 2007). However, we do not track thissmall amount of Mn due to its negligible influence onspectral features. Cr has a half-life of 21.56 hours and decays to V. The V has a much longer half-lifeat 15.9735 days , therefore its presence and changingabundance is important throughout the radiation trans-port calculations.The particles are then mapped onto a 1D sphericallysymmetric velocity grid with 100 cells to match the map-ping of the radiation transport calculations, using thefinal velocities each particle has at the end of the sim-ulation. The mass fractions in each cell of the velocitygrid follow from the average mass fractions of all parti-cles in that cell. These mass fractions per cell, togetherwith a spherically symmetrized density profile from thehydro simulation and the geometrical volume of eachcell, give the total yields (in gram) per species.If a velocity grid cell contains many particles we limitthe number of particles that are post-processed to 100,selected randomly. This reduces the amount of timeneeded for post-processing. An independently selected This is done with Nathan Hearn’s QuickFlash analysis tools,using the latest checkpoint from the hydro simulation for whichthe ejected material has not begun to run off the grid. set leads to abundances that differ on the order of 10%in velocity grid cells that contain greater than 100 parti-cles, and total yields that differ by less than 5%.2.4.
Progenitor White Dwarf Abundances
The progenitor white dwarf is comprised broadly oftwo regions: a convective core, the inner 0.8 M (cid:12) of thestar, and a non-convective outer region. Our progeni-tor abundances are constructed to be similar to those inDom´ınguez et al. (2001), as well as to account for pre-explosion carbon burning (Piro & Chang 2008).In this work, the progenitor metallicity is varied bychanging the initial abundance state of the tracer par-ticles, not by calculating separate hydro simulations fordifferent initial abundances, because the energy releaseby carbon-oxygen burning is only marginally modifiedby the metallicity variations. The hydrodynamic initialmodel is at a single metallicity of Z/Z (cid:12) = 1.33. Thethree parameters that control the carbon-oxygen burn-ing model used in the hydro stand for the abundances of C, O, and Ne. We choose the convective core to bemade up of 40% C, 3% Ne, with the remaining 57%as O; the envelope is 50% C, 48% O, and 2% Ne.The Ne is a stand-in for the neutron excess contributedfrom the metallicity in both the core and the outer lay-ers (Timmes et al. 2003). In the convective region theadditional 1% of Ne stands in for the neutron excessfrom the products of pre-detonation simmering (Piro &Bildsten 2008; Chamulak et al. 2008).When post-processing the particles with a large nuclearnetwork, more complete and realistic progenitor abun-dances can be used. Figure 1 shows how the materialaffected by metallicity and the simmering ashes are dis-tributed through the star for both the reduced abundanceset and the abundances used for post-processing. A par-ticle’s initial location is used to determine whether or notthe particle began in the convection region, and thus theinitial C fraction and the relative contributions frommetallicity and simmering. The initial abundances forpost-processing are then set using 4 components: • The mass fraction X C is set to the value at theparticle’s initial position in the hydrodynamic pro-genitor. • The abundance of all other nuclides are first set toscaled solar abundances based on
Z/Z (cid:12) and abun-dances from Anders & Grevesse (1989). In doingthis, we assume all metals lighter than O, i.e. C, N, and O are converted into Ne and arethus added to that abundance instead. • A simmering contribution is added to some abun-dances for particles that are initially in the con-vective region. We approximate that the simmer-ing ashes, of a fraction X sim determined below, aremade up of an even mix of C, O, Ne, and Ne (Chamulak et al. 2008). • Once the C, C, Ne, Ne, Ne and all heav-ier metal abundances are set in this fashion, theremainder of the material is assumed to be O.For this study, the contribution from simmering ashesis held fixed as the metallicity is varied. Changing themetallicity thus affects the second and fourth step.
M(r)/M tot -2 -1 M a ss F r a c t i o n Temp C O Ne Ne sim Ne Z T e m p e r a t u r e [ K ] tot -3 -2 -1 M a ss F r a c t i o n C C O Ne Ne Ne Fe0.1 Z/Z fl fl fl Figure 1.
Top : The initial composition and temperature (black)profile of the progenitor white dwarf used in the hydrodynamiccalculations. This reduced set of nuclides consists of C (red), O (blue), Ne (green). Ne is a stand in for the contribu-tions from the simmering ashes (dashed), only present in the con-vective region, and the metallicity (dash-dot) present throughoutthe star.
Bottom:
Initial composition profile used in the post-processing showing a small subset of 225 species used, with valuesshown for different metallicities. C (orange), Ne (brown), and Ne (cyan) are all components of the simmering ashes held atequal fixed abundances in the convective region, and consequently,overlap one another. Outside of the convective region, Ne alsocontributes as a component of the metals.
The amount of simmering ashes, X sim , is set to obtainconsistency with the progenitor metallicity of Z/Z (cid:12) =1 .
33 used in the hydrodynamics, based on the Y e , Y e = (cid:88) i X i Z i A i , (1)in the outer layers. Here Z i and A i are the number ofprotons and number of nucleons in species i . Matching Y e between the progenitor and the initial abundances usedfor post-processing gives X O , prog
816 + X C , prog
612 + X Ne , prog X O
816 + X C
612 + X Z Y e,Z + X sim (cid:18)
816 + 613 + 1020 + 1023 (cid:19) (2)where abundances with the “prog” subscript are thosefound at the initial particle position in the progeni-tor used in the hydrodynamics, X Z is the sum of thescaled solar abundances of all material in the metallicity-scaled component, including Ne, Y e,Z is the Y e of themetallicity-scaled component, and equal abundances ofthe 4 simmering products have been assumed. For thehydrodynamic abundances given above, Z/Z (cid:12) = 1 . X O = 1 − X sim − X Z − X C , Equation (2) gives X sim = 0 . X sim = 0 out- rogenitor Metallicity from SN Ia Spectra X sim is then used to construct theinitial abundances for post-processing at all metallicities.2.5. Radiation Transport Simulations
We calculate light curves and spectra using
Phoenix . Phoenix is a stellar atmosphere and radiation transportsoftware instrument (Hauschildt & Baron 1999, 2004;van Rossum 2012a).
Phoenix numerically solves thespecial relativistic radiative transfer equation using theefficient and highly accurate short characteristic and op-erator splitting methods. It samples millions of atomiclines individually.
Phoenix solves for the time evolu-tion using the radiation energy balance method. Thecode does not use the Sobolev approximation, diffusionapproximations or opacity binning approximations. Weoperate
Phoenix in one dimension, assuming sphericalsymmetry.The deterministic radiation transport method em-ployed in
Phoenix calculates spectra without the noisethat is inherent to Monte Carlo methods. This allowsthe study of small effects of individual atomic transi-tion lines on the calculated spectrum through knockoutspectra (van Rossum 2012b). Knock-out spectra are cal-culated by post-processing a normal calculation of lightcurves and spectra. For the calculation of knockout spec-tra, the opacity of individual transition lines is artificiallyset to zero while keeping the temperatures, electron den-sities, and atomic occupation numbers fixed to the valuesdetermined in the original calculation. The difference be-tween the original spectrum and a knockout spectrum isattributed to the same line opacity that was artificiallyset to zero. Here, as a diagnostic, we use knockout spec-tra to identify which chemical elements are responsiblefor the differences that metallicity changes cause in thecalculated spectra.We note that a spectrum is not merely a linear combi-nation of individual lines. When multiple knockout spec-tra are shown together in one plot each of the knockoutspectra is interpreted as described above, but there is nouseful interpretation to a linear combination of knockoutspectra. RESULTS3.1.
Nucleosynthetic Yields
The total yields for six different progenitor metallici-ties, Z/Z (cid:12) ∈ [0.1, 0.5, 1.33, 2.0, 3.0, 4.0], of each of thethree explosion simulations are listed in Table 1.The yields are grouped into Carbon and Oxygen (CO, A = 12 and A = 16), intermediate mass elements (IME,16 < A ≤ A > Ni is also included in the table because of its impor-tance as energy source for light curves and spectra. Ta-ble 1 shows that the amount of radioactive Nickel de-creases with increasing progenitor metallicity while thetotal yields of iron-group elements increases due to theincreased neutronization.The relative change in abundances with progenitormetallicity is plotted in Figure 2. The effect of pro-genitor metallicity on the nucleosynthetic yields of theexplosion are fairly similar among the three models formost elements, especially for the DDT-high and DDT-low models. The most marked difference between W7and the 2D DDT models is that the Ne and Na yields
He O Na Al P Ar Sc V Mn Co Ni56Chemical Element0.30.20.10.00.10.20.30.40.50.6 l o g ( Y i e l d R a t i o ) Z=2 / Z=0.5C Ne Mg Si S Ca Ti Cr Fe NiHe O Na Al P Ar Sc V Mn Co Ni56Chemical Element0.30.20.10.00.10.20.30.40.50.6 l o g ( Y i e l d R a t i o ) Z=2 / Z=0.5C Ne Mg Si S Ca Ti Cr Fe NiHe O Na Al P Ar Sc V Mn Co Ni56Chemical Element0.30.20.10.00.10.20.30.40.50.6 l o g ( Y i e l d R a t i o ) Z=2 / Z=0.5C Ne Mg Si S Ca Ti Cr Fe Ni
Figure 2.
Ratios of the nucleosynthetic yields of high (Z=2 Z (cid:12) )versus low (Z=0.5 Z (cid:12) ) progenitor metallicities for the DDT-highmodel (top), the DDT-low model (middle), and W7 (bottom) ona logarithmic scale. A value close to 0, like Si, means that thesame nucleosynthetic yields were obtained for different progeni-tor metallicities. The effect of progenitor metallicity on the totalnucleosynthetic yields of the explosion are fairly similar betweenthe two DDT models. The affects on W7 are fairly consistent insign with the DDT models except for a number of elements abovescandium. Table 1
Nucleosynthetic yields grouped by atomic mass in M (cid:12) for three simulations and six progenitor metallicities.Z/ Z (cid:12) a b c Ni 0.848 0.831 0.800 0.775 0.738 0.703DDT-lowCO 0.076 0.077 0.077 0.076 0.076 0.075IME 0.385 0.382 0.375 0.369 0.360 0.351IGE 0.906 0.909 0.916 0.922 0.932 0.941 Ni 0.771 0.756 0.726 0.703 0.669 0.637W7CO 0.166 0.166 0.165 0.163 0.161 0.159IME 0.306 0.304 0.300 0.297 0.292 0.288IGE 0.889 0.890 0.896 0.900 0.907 0.913 Ni 0.698 0.684 0.658 0.638 0.607 0.577 a CO: A = 12 and A = 16 b IME: 16 < A ≤ c IGE:
A > fl T o t a l M a ss ( M fl ) Si, DDT-high Ca*10, DDT-high Fe, DDT-high Si, DDT-low Ca*10, DDT-low Fe, DDT-low Si, W7 Ca*10, W7 Fe, W7
Figure 3.
Total yields in M (cid:12) of Si (red), Fe (green), Ca(black) as a function of metallicity for the two realizations, DDT-high (circles, solid line) and DDT-low(squares, dashed lines), aswell as W7 (triangles,dash dot lines) increase more with metallicity in the W7 model.Figure 3 shows the integrated yields of Si, Ca, and Fe for the six progenitor metallicities. We find thatwith increasing metallicity, the overall yields of Si stayrelatively constant. Conversely, the total yields of Cadecrease and Fe increase with increasing metallicitysimilar to the trends seen in De et al. (2014) with de-creasing Y e . The relatively flat trend in the Si yieldsmakes this species a useful reference for comparing thetrends in the yields of other species between the threemodels. The ratios of Ca and Fe relative to Si are fl F e : S i DDT-highDDT-lowW7 fl C a : S i DDT-highDDT-lowW7
Figure 4.
Ratio of Fe to Si yields (top) and Ca to Si yields(bottom) from the 2D DDT and the W7 simulations. The ratiosof these abundances show similar smooth trends with progenitormetallicity for these three models. shown in Figure 4. As expected from Figure 2, the trendsare similar among the models, though the absolute ratioof Ca to Si is different in the W7 model due to Cabeing produced in higher amounts at a wider extent inthe DDT models (Figure 5). The trends are also smoothover the metallicity range that we are studying.Figure 5 shows the chemical abundance profiles in ve-locity space from the DDT-high, DDT-low, and W7 mod-els for two metallicities: Z=0.5 and 2.0 Z (cid:12) . Differencesin explosion model produce differences in the profiles fora single metallicity. While all three models feature a Ni rogenitor Metallicity from SN Ia Spectra A b un d a n c e [ n o r m a li z e d ] heconemgalsipsarcamnfeconicuni56DDT-high, Z=0.5 0 5000 10000 15000 20000 25000 30000 35000Velocity [km/s]10 A b un d a n c e [ n o r m a li z e d ] heconenamgalsipsclarcacrmnfeconicuni56DDT-high, Z=20 5000 10000 15000 20000 25000 30000 35000Velocity [km/s]10 A b un d a n c e [ n o r m a li z e d ] heconemgalsipsarcamnfeconicuni56DDT-low, Z=0.5 0 5000 10000 15000 20000 25000 30000 35000Velocity [km/s]10 A b un d a n c e [ n o r m a li z e d ] heconenamgalsipsarcacrmnfeconicuni56DDT-low, Z=20 5000 10000 15000 20000 25000 30000 35000Velocity [km/s]10 A b un d a n c e [ n o r m a li z e d ] heconemgalsipsarcacrmnfeconicuni56W7, Z=0.5 0 5000 10000 15000 20000 25000 30000 35000Velocity [km/s]10 A b un d a n c e [ n o r m a li z e d ] heconenamgalsipsarcacrmnfeconicuni56W7, Z=2 Figure 5.
Chemical abundance profiles in 1D spherical velocity space of the DDT-high model (top row), the DDT-low model (middlerow), and the W7 model (bottom row) for two different initial metallicities, Z=0.5 and Z=2. core that extends to approximately 1 . × cm/s, W7is the only model that has a “nickel hole”, which is aknown characteristic of 1-D models. In the higher ve-locity portion of the ejecta, from ≈ . × cm/s to2 . × cm/s, the W7 model’s ejecta consist of unburntC, O, and Ne, much simpler than that produced in theDDT-high and DDT-low models. In this region of thematerial, the DDT-high and DDT-low models’ profilesconsist of predominantly C and O, with (cid:46)
10% of Si,Mg, Ne, S, Ni, Ar, and Ca. At the highest velocities, (cid:38) . × cm s − , the DDT-high and DDT-low ejectatake on a similar configuration to that of the outer layersof W7, unburnt C, O, and Ne. At intermediate veloci-ties, between 1 . × cm/s and 1 . × , Si peaks inall three models. This is also the location of other IMEpeaks such as S, Ar, and Ca.Examining the same explosion models at differentmetallicites presents additional features. At Z = 2 Z (cid:12) , Ni makes up less of the total Ni yield in the three ex-plosion models, though there is little change in the over-all mass fraction of Ni. Overall, the Fe mass fractionincreases with the increased metallicity. However, notonly is the mass fraction of Fe higher, the Fe rich layersextend further outward into the higher velocity ejecta.In all three modes, the Fe rich layer reaches into thematerial that is mostly intermediate mass elements. Theincrease in metallicity also causes the Ca peak to be bothlower and narrower. The Si peak is largely unaffected bythe increase in metallicity. This is also reflected in howlittle the overall Si abundance varies in Figure 3, and thesmall change in the Si ii spectral feature at 6150 ˚A withmetallcity as shown in section 3.3.Figure 6 shows the abundance profiles of Si and Tiin the DDT and W7 models 30 days post explosion.It demonstrates how the Ti production is sensitive tothe progenitor metallicity while the Si production islargely unaffected. The variation of Ti with metallicity isstrongest in the region of incomplete Si burning and theunburned regions. A shift in the quasi-equilibrium abun-dances due to metallicity is expected in the Si-burning re-gion (De et al. 2014). The direct Ti production is mainlyin the form of Ti, which has a half-life of 60 years ,while the progenitor metallicity contributes mainly Ti.Any Cr produced during the explosion will decay witha half-life of 21.56 hours to V, which will decay fur-ther with a half-life of 15.97 days to stable Ti. Weshow the profile at day 30 post explosion to facilitatediscussion of Ti spectral features at this epoch in Sec-tion 3.3. At this time, 71% of the Cr produced duringthe explosion has decayed to Ti so that the Ti curvesin Figure 6 in some regions are higher than the “directTi” curves. 3.2.
Light Curves
The bolometric light curves for the three explosionmodels with two extreme metallicities are shown in Fig-ure 7. Higher progenitor metallicities systematicallymake the bolometric light curve rise more slowly andpeak lower. The slower rise is caused by the higherabundance of metals in the outer layers of the ejecta,which raise the opacity, and make radiation diffuse out A b un d a n c e [ n o r m a li z e d ] Z=4Z=2Z=1.33Z=0.5Z=0.1TiSiDirect TiDDT-high0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Velocity [cm/s] 1e910 A b un d a n c e [ n o r m a li z e d ] Z=4Z=2Z=1.33Z=0.5Z=0.1TiSiDirect TiDDT-low0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Velocity [cm/s] 1e910 A b un d a n c e [ n o r m a li z e d ] Z=4Z=2Z=1.33Z=0.5Z=0.1TiSiDirect TiW7
Figure 6.
Radial abundance profiles of Si and Ti at day 30 postexplosion in the DDT-high model (top), DDT-low model (middle),and the W7 model (bottom). Different line colors represent dif-ferent initial metallicities. The Ti yield (solid line) in the outerregions of the burning zone is sensitive to the progenitor metal-licity, while the Si production (dashed line) is largely unaffected.Also shown, for each metallicity, is the portion of the Ti that is nota product of Cr decay (direct Ti, dotted lines). rogenitor Metallicity from SN Ia Spectra A b s o l u t e B o l o m e t r i c M a g n i t u d e DDT-high, Z=0.1DDT-high, Z=4DDT-low, Z=0.1DDT-low, Z=4W7, Z=0.1W7, Z=4
Figure 7.
Bolometric light curves of the DDT-high (solid lines),DDT-low (dashed lines), and W7 (dotted lines) explosion simula-tions at two extreme progenitor metallicities of 0.1 (blue lines) and4 times solar (green lines). The light curves of explosion simula-tions with high metallicity progenitor are brighter at peak thanthose with low metallicity progenitors because the former have ahigher Ni yield. more slowly from the hot Ni-rich core. The lower peakbrightness is caused by the lower total Ni mass in themodels with higher progenitor metallicities, as shown inTable 1.In Figure 8 shows the UBVRI-band model lightcurvescompared to the light curves from the data drivenmodel MLCS Jha et al. (2007). The systematic trendwith progenitor metallicity in most light curves is smallbut significant, especially in the UBV-bands. This isapparent in Figure 9, where the light curve shape pa-rameters, peak brightness and decline rate ∆M (B), areplotted, along with the Phillips et al. (1999) relation (seealso Mandel et al. 2011). The model light curves haveslightly brighter peak magnitudes than the bulk of ob-served SNe Ia at the same ∆ m ( B ). We find for thetwo 2D DDT cases used here, which have above-averageyields, that the changes in ignition conditions that leadto different Ni yields cause the shape parameters tochange perpendicular to the Phillips et al. (1999) rela-tion. This confirms a similar result found by Seitenzahlet al. (2013) using 3D DDT models. This failure of mul-tidimensional DDT models to reproduce the Phillips re-lation in the expected way makes it difficult to makecomparisons with empirical metallicity-luminosity rela-tions. In contrast, the progenitor metallicity introducesa change in the B-band light curve shapes that roughlyfollows the observed width-luminosity relation.The bottom panel of Figure 9 shows the bolometricpeak magnitude and decline rate. While higher metal-licity leads to lower bolometric peak magnitudes, just asit leads to lower B -band peak, the effect on ∆ M (bol)is very small. This indicates that the range of ∆ M ( B )(top panel of Figure 9) spanned by metallicity is dueentirely to a color effect, in which the B-band light de-creases more quickly at higher metallicity while the de-cline rate of the total energy output is mostly unchanged.∆ M (bol) is even slightly slower at higher metallic-ity, the opposite of ∆ M ( B ). In reality, any color ef- A b s o l u t e M a g n i t u d e bolUBVRI Z=0.5Z=2MLCSDDT-high0 10 20 30 40 50Time post explosion [day]20.019.519.018.518.017.517.0 A b s o l u t e M a g n i t u d e bolUBVRI Z=0.5Z=2MLCSDDT-low0 10 20 30 40 50Time post explosion [day]20.019.519.018.518.017.517.0 A b s o l u t e M a g n i t u d e bolUBVRI Z=0.5Z=2MLCSW7 Figure 8.
Bolometric and UBVRI-band light curves of the DDT-high (top), DDT-low (middle) and the W7 model (bottom), com-paring progenitor metallicities of Z=0.5 (solid lines) and Z=2(dashed lines). As a reference, MLCS light curves are plotted fora value of MLCS ∆ = 0 (dash-dotted lines). The models are simi-lar in brightness and color evolution, especially the DDT-high andDDT-low simulations. The biggest difference is the peak brightnessin the U-band between the 2D DDT simulations and W7. (B))20.019.519.018.518.017.5 P e a k B b a n d M a g n i t u d e ( M B ) DDT-high, Z=0.1DDT-high, Z=0.5DDT-high, Z=1.33DDT-high, Z=2DDT-high, Z=4 DDT-low, Z=0.1DDT-low, Z=0.5DDT-low, Z=1.33DDT-low, Z=2DDT-low, Z=4 W7, Z=0.1W7, Z=0.5W7, Z=1.3W7, Z=2W7, Z=4 ( ) )-19.5-19-18.5 P k B o l M a g ( M ) Figure 9.
Peak B-band magnitude ( M B ) vs. B-band decline rate(∆ M ( B )) ( top panel ) and peak bolometric magnitude vs. bolo-metric decline rate ( bottom panel ), for the DDT-high, DDT-low,and W7 models with initial metallicities of 0.1, 0.5, 1.33, 2, and 4times solar. The Phillips et al. (1999) relation is plotted in gray,with the shaded regions indicating the 1 and 2 σ observed variationalso from that work. The range in ∆ M is present in the B-bandbut not the bolometric light curves showing that this is a coloreffect, as pointed out by Kasen & Woosley (2007) fects caused by progenitor metallicity would be convolvedwith environmental factors such as extinction from dust.Light curve modeling techniques such as MLCS (Riesset al. 1996; Jha et al. 2007) and BayeSN (Mandel et al.2011) are able to separate the two, allowing them to havethe possibility of properly capturing the effects of theprogenitor metallicity. 3.3. Spectra
Model spectra, calculated for W7 and the two DDTsimulations, with different progenitor metallicities, andat four different epochs post explosion, are shown in Fig-ures 10 through 13.The model spectra are compared against the Hsiaoet al. (2007) spectral templates. These templates rep-resent the typical spectral shape of normal SN Ia, asthey are constructed as an average over many observedspectra. We set day 0 of the Hsiao07 templates (whichis the time of maximum brightness) to the time that theB-band luminosity peaks in the model spectra, averagedover the set of progenitor metallicities, and fit a “dis-tance” to the imaginary source of the Hsiao07 templatesto simultaneously fit the spectra of all epochs. We donot apply any other corrections, such as stretch or colorcorrections, to the Hsiao07 templates.The model spectra generally agree reasonably well withthe templates, but there are a few significant discrepan-cies. First, none of the model spectra reproduce the farUV flux below 2500 ˚A as it is observed on Day 10 and 20 post explosion (pe). Second, although the Si ii featureat 6150 ˚A is present in the model spectra none of themaccurately reproduces the observed shape of this feature.It is unclear whether this is a consequence of an underor over produced nucleosynthetic yield or a missing lineor combination of lines from the radiative transfer calcu-lation. Third, the W7 model spectra do not reproducethe observed strong absorption feature around 3300 ˚A atday 10 pe.Different progenitor metallicities give rise to variationsin the model spectra. These variations change with time.Generally, the variations appear to affect the flux moreon the blue side of the spectrum than on the red sideand, over time, the range in which variations are stronggradually extends further to longer wavelengths. At day10 pe, the DDT and W7 spectra are most effected in the2600–3600 ˚A range. At days 20 and 30 pe that windowextends to 2600–4500 ˚A and 2600–5200 ˚A, respectively.In the latest spectra, at day 40 pe, the effect of progenitormetallicity presents only a small amount of variation.The systematic decrease of blue (short-wavelength)flux with progenitor metallicity is correlated in part tothe decline in total Ni yield with metallicity. Thismakes it more difficult to use this region as an indicatorof metallicity that is independent of overall Ni yield.The total Ni yield affects the brightness of the lightcurve as well as the temperature of the radiating ejecta,and thus the spectral color. At the same time, the pro-genitor metallicity affects the composition of the SN Iaejecta, which may affect the strength of individual spec-tral features.In order to help demonstrate the difference be-tween the Ni-mass–temperature–color effect and thecomposition–feature-strength effect, Figure 14 comparesspectra at similar Ni yields. From the top panel spec-tra at days 10 and 20 pe, we see that the region of thespectrum around 3000 ˚A does not show as strong a metal-licity variation in this comparison as it does in Figure 10.The case in the bottom panel with slightly higher yieldand lower metallicity, shows more metallicity variationin this region. Together these comparisons show that itwill be necessary to carefully control for total Ni yieldin order to use a metallicity indicator from this spectralregion.Features that vary consistently in both Figures 10and 14 are good candidates for robust metallicity in-dicators that may not require careful control for Niyield, which renders the feature useless if the Ni yieldis not known. Two features that clearly vary with pro-genitor metallicity at day 30 pe in Figure 14 as well asin all spectra in Figure 10 are 1) an absorption fea-ture around 4200 ˚A, and 2) an absorption feature around5200 ˚A. These two features are potential spectral indi-cators of progenitor metallicity . We will examine thesefeatures more below.There are a couple of other features that are promising,but their variation with metallicity is less consistent forboth varying (Figure 10) and fixed (Figure 14) Ni. Thevariation with metallicity around 4400 ˚A at day 20 pe inFigure 10 is much less clear in Figure 14. The featurearound 5500 ˚A at day 20 pe that appears to vary in Fig-ure 14 does not vary in the same way in Figure 10. For rogenitor Metallicity from SN Ia Spectra F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) Figure 10.
Model spectra of the DDT-high model ( top ) and DDT-low model ( bottom ) for five different progenitor metallicities at day10, 20, 30, and 40 post explosion (pe). For comparison against observational data, the Hsiao et al. (2007) spectral templates are plottedin grey. The spectral feature in the black box around 4200 ˚A and 5200 ˚A at day 30 pe are potential spectral indicators for the progenitormetallicity (see text). F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) Figure 11.
Spectra of Figure 10 extended to the IR range rogenitor Metallicity from SN Ia Spectra F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) Figure 12.
Model spectra of the W7 model for five different pre-explosion metallicities at day 10, 20, 30, and 40 post explosion (pe). Forcomparison against observational data, the Hsiao et al. (2007) spectral templates are plotted in grey. The spectral features in the blackboxes around 4200 ˚A and 5200 ˚A at day 30 pe are potential spectral indicators for the progenitor metallicity (see text). F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) Figure 13.
Spectra of Figure 12 extended to the IR range F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) F l u x [ e r g / s / a n g ] ( w i t h o ff s e t ) Figure 14.
Model spectra at similar Ni yields, 0.7 M (cid:12) ( top ) and 0.77 M (cid:12) ( bottom ), from different DDT models at different progenitormetallicities. This comparison, together with Figure 10, helps to determine which variations in the spectra are due to changes in theabundance profiles of species other than Ni. The most characteristic feature that robustly varies with progenitor metallicity, even atconstant Ni mass, are the absorption features highlighted with black boxes around 4200 ˚A and 5200 ˚A at day 30 pe. rogenitor Metallicity from SN Ia Spectra p E W DDT-highDDT-lowW7 pEW (4200 )pEW (5200 )
Figure 15.
The pseudo equivalent width (pEW) of the spectralfeatures around 4000–4400 ˚A (solid lines) and 4900–5400 ˚A (dashedlines) as measured in the synthetic spectra of three explosion mod-els DDT-high (blue), DDT-low (green), and W7 (red) at day 30 pe(see Figures 10 and 14). Using the three models investigated inthe paper, these two absorption features gradually become strongerwith increasing progenitor metallicity, making them good potentialcandidates for spectral indicators of SN Ia progenitor metallicity. this latter feature it appears that the two DDT mod-els produced different amounts of the chemical elementsthat are responsible for these features, and so this is nota simple effect of progenitor metallicity.The Si ii P-Cygni feature at 6150 ˚A is present in theDDT and W7 model spectra at peak brightness and be-fore. Even though, as noted before, the observed shapeof this feature is not very accurately reproduced in themodel spectra, the change in metallicity has very littleeffect on both the depth of the absorption wing and theheight of the emission wing. This is in agreement withthe observation in Figures 2 and 3, namely that the Siabundance remains relatively static by changes in theprogenitor metallicity. This allows for its use as a pos-sible calibration when examining the strengths of otherfeatures.3.4.
Analysis of Spectral Features Around 4200 ˚A and5200 ˚A
Two spectral features were identified above as potentialspectral indicators of progenitor metallicity, in all threemodels: 1) an absorption feature around 4200 ˚A, and 2)an absorption feature around 5200 ˚A; both at day 30 pe.Both of these features become systematically strongerwith increasing progenitor metallicity. Figure 15 showsthe trend of the feature strength with progenitor metal-licity, with the pseudo equivalent width pEW as measurefor feature strength.pEW = (cid:90) λ b λ a F pCont ( λ ) − F ( λ ) F ( λ ) dλ, (3)where F pCont is the pseudo continuum flux level as ap-proximated by a linear interpolation between the fluxlevels F at beginning and end points of integration λ a and λ b . The interpolation range for the two features ischosen as [4000, 4400] and [4900, 5400] in units of ˚A. While the dependence of the pEW on metallicityis promising, the variation across metallicities in the Z/Z (cid:12) =0.5 to 2 range is similar to that among the threeexplosion models considered here. This means that, inorder to use a plot like Figure 15 to determine the metal-licity, it is necessary to obtain a control variable that dis-tinguishes among the models. Unfortunately the mostaccesible control variable ∆ m ( B ) does not appear tofill this role well. The DDT-high model at Z/Z (cid:12) = 0 . Z/Z (cid:12) = 2 have both verysimilar ∆ m ( B ) and very similar 4000-4400 ˚A pEWs.Our limited sample of explosions available here does notallow us to robustly test control parameters. However,we are hopeful that a larger sample, theoretical or ob-servational, may be able to exploit the trends in pEWshown here to calibrate a measure of metallicity.In order to investigate which chemical species are re-sponsible for these two specific characteristic features weuse knockout spectra (see Section 2.5). Figures 16 and 17displays a series of knockout spectra for the DDT-low andthe W7 model at day 30 pe for Z/ Z (cid:12) = 0.1, 1.33 and 4.These knockout spectra are created by removing theopacity from all transition lines of a single chemical ele-ment from the radiative transfer calculation and repeat-ing the simulation with fixed temperatures, electron den-sities, and population numbers as in the original calcu-lation. The recalculated spectra show the effect of theabsence of opacity. This allows us to identify what andhow strongly different elements are involved in formingspecific spectral features.In the knockout spectra, Figures 16 and 17, the fullspectra are represented by the solid black line. The colorpatches represent the knockout effect that each elementhas on the full spectrum. Patches below the spectra indi-cate emission features: the flux level is that much lowerin the absence of opacity from that species. In the sameway, patches above the full spectrum represent absorp-tion features.Using the knockout spectra, we see that the two identi-fied spectral indicators of progenitor metallicity, around4200 ˚A and 5200 ˚A at day 30 pe, can be associated withTitanium and Iron production, respectively. The higherthe progenitor metallicity the stronger the Titanium andIron abosption features appear in the spectra. Iron alsoshows a shift from emission to absorption in this featureas metallicity increases. Looking back at Figures 5 and 6,we see that indeed the Ti and Fe abundances increasewith the progrenitor metallicity in the outer regions ofthe ejecta, i.e., at velocities > cm/s.3.5. Spectra Ratios
Foley & Kirshner (2013), and more recently, Grahamet al. (2015) investigated the two SNe Ia SN 2011fe andSN 2011by. These two objects exhibited remarkably sim-ilar optical spectra and decline times, and even peakbrightnesses after accounting for possible errors in themeasured distance to 2011by. Thus the two objects be-come nearly identical. However, the two objects dis-play differences in the near UV regions of their spectra.Graham et al. (2015) propose that one possible sourceof these differences could be a difference in progenitormetallicity. To investigate this proposal, they first nor-6 F l u x [ e r g / s / a n g ] + D e l t a s s t a c k e d F l u x [ e r g / s / a n g ] + D e l t a s s t a c k e d F l u x [ e r g / s / a n g ] + D e l t a s s t a c k e d Figure 16.
Knock-out spectra for the DDT-low model with metallicity Z/ Z (cid:12) =0.1 (top), 1.33 (middle), and 4.0 (bottom) at day 30 pe.Contributions from line opacity of individual elements to the full spectrum (black solid lines) are represented by colored patches. Theseare calculated by removing the line opacities from a single element and recalculating the spectra while keeping the temperatures andpopulation numbers fixed. Emission contributions are represented by colored patches below the full spectra, and absorption contributionsare represented by patches above the full spectra. The spectral features highlighted with black boxes are two potential spectral indicatorsfor progenitor metallicity. rogenitor Metallicity from SN Ia Spectra F l u x [ e r g / s / a n g ] + D e l t a s s t a c k e d F l u x [ e r g / s / a n g ] + D e l t a s s t a c k e d F l u x [ e r g / s / a n g ] + D e l t a s s t a c k e d Figure 17.
Like Figure 16 but for the W7 model. Ni mass) areallowed to vary independently.In Figure 18, we take 4 pairs of spectra from our mod-els at day 20 pe and follow a similar procedure as Gra-ham et al. (2015). Two pairs, DDT-high Z = 0.5 Z (cid:12) & DDT-low Z = 2.0 Z (cid:12) and DDT-high Z = 2.0 Z (cid:12) & DDT-low Z = 4.0 Z (cid:12) , have similar decline times asshown in Figure 9. The other two pairs, DDT-high Z= 2.0 Z (cid:12) & DDT-low Z = 0.1 Z (cid:12) and DDT-high Z =4.0 Z (cid:12) & DDT-low Z = 4.0 Z (cid:12) , have similar opticalspectral features at day 20 pe. Each of the spectra arenormalized across the 4000 – 5500 ˚A region. The topand middle panels of the left column of Figure 18 showthe normalized spectra in log space of each pair selectedfor similar decline times. The top and middle panels ofthe right column of Figure 18 show the normalized spec-tra in log space of each pair selected for similar opticalfeatures. Also included in the top and middle panels ofboth columns of Figure 18 are the spectra of SN2011feat -2 days from peak brightness (Mazzali et al. 2014) andSN2011by at -1 day (both Melissa Graham, priv. comm.).These spectra were first binned in increments of 5 ˚A andthen normalized in the same way as our calculated spec-tra. Our calculated spectra share a similar sequence offeatures, especially blueward of about 3000 ˚A, with thesetwo observed spectra. However, the features in the modelspectra are both stronger and located at slightly shorterwavelengths. Also the overall relative flux level bluewardof about 2700 ˚A is about a factor of 10 lower in the modelspectra.The bottom panels of both columns in Figure 18 showthe ratios taken between each pair as well as the ratio ofSN2011fe to SN2011by. One of the most prevalent differ-ences in the model spectra is in the 3000 ˚A region, whichis one of the regions most strongly effected by varyingmetallicity. The model pairs selected to have the samedecline time show a factor of 4-6 ratio in this region,while the observed pair shows no significant difference.Comparing the ratios of pairs, DDT-high Z = 0.5 Z (cid:12) & DDT-low Z = 2.0 Z (cid:12) (Figure 18, bottom left panel,red curve) and DDT-high Z = 4.0 Z (cid:12) & DDT-low Z= 4.0 Z (cid:12) (Figure 18, bottom right panel, green curve),demonstrates the difficulty in separating metallicity from Ni yield variations. The location of the peaks in thesetwo pairwise comparisons is similar, having ratio peaksat about 1900, 2350, 2500, and 3600 ˚A. However, whilethe first pair are at different metallicities, the second pairare at the same metallicity but with different Ni yields.A possible factor in the similarity can be seen in the Ni yields. Looking at Table 1, it is clear that none ofthe four cases produced equal amounts of Ni, thoughthe ratios of Ni produced in each pair are very similarat ≈ Ni yield. Since changesin spectral features from this temperature effect occuralongside changes from the varying ejecta composition,isolating the two effects by taking spectral ratios appearschallenging. A more conclusive comparison will requiremodel spectra that are more similar to the observationsin this spectral range. CONCLUSIONS AND DISCUSSIONWe have utilized a combination of multidimensionalhydrodynamics calculations, nucleosynthetic particlepost-processing calculations, and radiative transport cal-culations in a preliminary investigation into the role thatprogenitor metallicity plays in the chemical compositionof SN Ia ejecta, and the consequences that has for theirlight curves and spectra. These calculations were per-formed on two 2-dimensional DDT models, as well as onthe 1-dimensional W7 model. Lagrangian tracer particleswere produced for the two DDT models using the FLASHhydrodynamics software instrument. These tracer par-ticles as well as the W7 temperature-density historieswere then post-processed using TORCH with a 225 mem-ber nuclear reaction network to calculate nucleosyntheticyields and ejecta abundance profiles. We have used thePHOENIX radiation transport software to compute lightcurves and spectra for these ejecta profiles. With this ap-proach we examine the effects of progenitor metallicityon the nucleosynthetic yields of the explosion and on thesynthetic light curves and spectra.Our approach is different from past theoretical stud-ies that have focussed on the effects of metal content inthe ejecta on synthetic spectra (see Brown et al. (2015),and references therein) in two ways. First, we calculateself-consistent nucleosynthetic yields from explosion sim-ulations by changing the progenitor metallicity instead ofmaking modifications to post-explosion abundance pro-files. This takes into account any effects of progenitormetallicity on the Ni production, which affects post ex-plosion ejecta temperatures, and therefore the shape andcolor of synthetic light curves and spectra, and in partic-ular in the UV. Second, instead of focussing on the UVflux, we explore the effect of progenitor metallicity on thestrength of spectra features in the optical. The UV fluxhas been found to be sensitive not only to metal contentin the ejecta, but also to other properties like the densitystructure and the type of explosion model (Brown et al.2015, and references therein), a finding that is confirmedalso in this paper.We find that two aspects of SN Ia spectra present chal-lenges to finding spectral indicators of progenitor metal-licity or neutron excess. The first is that SN Ia spectraare formed by a large number of blended lines from a va-riety of species. This makes isolating individual featureschallenging, more so in some spectral ranges than oth-ers. The second challenge is that while the abundances ofboth the unburned material and the IME material varysystematically with metallicity, as expected, the result-ing variation in spectral features is confused with thevariation of the total Ni yield with metallicity. Ourinclusion of explosions with different yields allows us to rogenitor Metallicity from SN Ia Spectra l o g N o r m a li z e d F l u x DDT-high, 0.5 Z fl DDT-low, 2 Z fl SN2011feSN2011by2000 2500 3000 3500 4000Wavelength [ ]65432101 l o g N o r m a li z e d F l u x DDT-high, 2 Z fl DDT-low, 4 Z fl SN2011feSN2011by2000 2500 3000 3500 4000Wavelength [ ]02468101214 F l u x R a t i o DDT-high 0.5 Z fl :DDT-low 2 Z fl DDT-high 2 Z fl :DDT-low 4 Z fl SN2011fe:SN2011by 2000 2500 3000 3500 4000Wavelength [ ]65432101 l o g N o r m a li z e d F l u x DDT-high 2 Z fl DDT-low 0.1 Z fl SN2011feSN2011by2000 2500 3000 3500 4000Wavelength [ ]65432101 l o g N o r m a li z e d F l u x DDT-high 4 Z fl DDT-low 4 Z fl SN2011feSN2011by2000 2500 3000 3500 4000Wavelength [ ]02468101214 F l u x R a t i o DDT-high 2 Z fl :DDT-low 0.1 Z fl DDT-high 4 Z fl :DDT-low 4 Z fl SN2011fe:SN2011by
Figure 18.
Top and middle : The normalized maximum light NUV spectra of pairs of spectra chosen for their similar decline times (left)and similar optical spectral features at maximum brightness (right). The spectra of SN2011fe and SN2011by are also shown for comparison.
Bottom : Ratios of the maximum light NUV spectra of each pair chosen for similar decline times (left) and similar optical spectral features(right) with the ratio of SN2011fe to SN2011by included for comparison. Ratios are shown for the top panel pair (red) and middle panelpair (green). explore this ambiguity. Higher metallicity, which pro-vides a larger neutron excess (Timmes et al. 2003), leadsto a lower yield of Ni, instead favoring stable Fe-groupyields. This reduction in the energy source for the pho-tospheric phase causes a lowering of the ejecta temper-ature, and reduces the overall flux in the UV. Isolatingindividual features, which vary due to changes in yieldswith metallicity, from this overall shift in flux intensityis challenging, especially in the early-time UV spectrum.Despite these challenges, we find two spectral featuresthat show promise as potential robust spectral indica-tors of progenitor metallicity. These features stand outas metallicity indicators even when comparing explosionswith similar total Ni, a comparison for which manyother features are the same (see Figure 14). The mostpromising feature we have found is a Ti feature at day 30post explosion that extends from 4000-4400 ˚A, based onthe knock-out spectrum. The pEW for this feature (Fig-ure 15) shows a robust and mostly consistent variationwith metallicity for each of the three explosion simula-tions studied here. However, a control for overall yieldwill still be necessary for this to be used as a precisionindicator of metallicity. The small sample of explosionmodels computed here does not allow evaluation of asuitable control variable, but a broader set of computedcases or an observational collection of spectra may.Our 2D DDT models of SNe Ia produce spectra that are similar to those of observed SNe Ia in many respects(Figure 10), in some regions better than the spectrum ofW7 (Figure 12). It is important to note that we are notfitting spectra, so that a precision match is not the goal,rather similar overall spectral features. One of the maindifferences between the 2D DDT and W7 is apparent inFigure 5, where the DDT models have intermediate massand iron-group material extending out to higher veloci-ties than W7. This appears to make the absorption andemission features in the 2D DDT spectrum, especially inthe blue portion of the spectrum, more similar to thosein observed SNe Ia.There are several trends in yields that result fromchanging progenitor metallicity. Table 1 shows that forall three models, increasing metallicity causes a declinein the production of intermediate mass elements and anincrease in the production of iron-group material. How-ever, as is expected with the increased neutronization,the increased production of these stable iron-group ele-ments comes at the cost of reduced production of Ni.Also at higher metallicities, the iron-group material pro-duced in incomplete Si burning extends further out intothe IME layers of the ejecta. The combination of theincreased opacity from the iron-group material and thereduced production of Ni results in light curves thatare both slower rising and dimmer than those of lowermetallicities. However, we find only an ∼ .
10 mag de-0pendence of the peak luminosity between the lowest andhighest progenitor metallicities, and with our small sam-ple size we are hesitant to make strong comparisons withobservations such as Kelly et al. (2010). Although theoverall yield of intermediate mass elements declines withincreasing metallicity, the yield and distribution of Siremain relatively static. Consequently, the SN Ia char-acteristic Si P-Cygni feature at 6150 ˚A remains mostlyunchanged with metallicity.This work is supported in part at the Universityof Chicago by the National Science Foundation undergrant AST-0909132, and under grant PHY-0822648 forthe Physics Frontier Center “Joint Institute for Nu-clear Astrophysics” (JINA). ACC acknowledges supportfrom the Department of Energy under grant DE-FG02-87ER40317. Some of the software used in this work wasin part developed by the DOE-supported ASC/AlliancesCenter for Astrophysical Thermonuclear Flashes at theUniversity of Chicago. We thank Nathan Hearn for mak-ing his QuickFlash analysis tools publicly available athttp://quickflash.sourceforge.net.REFERENCES10 mag de-0pendence of the peak luminosity between the lowest andhighest progenitor metallicities, and with our small sam-ple size we are hesitant to make strong comparisons withobservations such as Kelly et al. (2010). Although theoverall yield of intermediate mass elements declines withincreasing metallicity, the yield and distribution of Siremain relatively static. Consequently, the SN Ia char-acteristic Si P-Cygni feature at 6150 ˚A remains mostlyunchanged with metallicity.This work is supported in part at the Universityof Chicago by the National Science Foundation undergrant AST-0909132, and under grant PHY-0822648 forthe Physics Frontier Center “Joint Institute for Nu-clear Astrophysics” (JINA). ACC acknowledges supportfrom the Department of Energy under grant DE-FG02-87ER40317. Some of the software used in this work wasin part developed by the DOE-supported ASC/AlliancesCenter for Astrophysical Thermonuclear Flashes at theUniversity of Chicago. We thank Nathan Hearn for mak-ing his QuickFlash analysis tools publicly available athttp://quickflash.sourceforge.net.REFERENCES