Metallicity as a source of dispersion in the SNIa bolometric light curve luminosity-width relationship
E. Bravo, I. Dominguez, C. Badenes, L. Piersanti, O. Straniero
aa r X i v : . [ a s t r o - ph . C O ] F e b Metallicity as a source of dispersion in the SNIa bolometric lightcurve luminosity-width relationship
E. Bravo , I. Dom´ınguez , C. Badenes , , L. Piersanti , O. Straniero ABSTRACT
The recognition that the metallicity of Type Ia supernova (SNIa) progenitorsmight bias their use for cosmological applications has led to an increasing interestin its role on the shaping of SNIa light curves. We explore the sensitivity ofthe synthesized mass of Ni, M ( Ni), to the progenitor metallicity startingfrom Pre-Main Sequence models with masses M = 2 − ⊙ and metallicities Z = 10 − − .
10. The interplay between convective mixing and carbon burningduring the simmering phase eventually rises the neutron excess, η , and leadsto a smaller Ni yield, but does not change substantially the dependence of M ( Ni) on Z . Uncertain attributes of the WD, like the central density, have aminor effect on M ( Ni). Our main results are: 1) a sizeable amount of Ni issynthesized during incomplete Si-burning, which leads to a stronger dependenceof M ( Ni) on Z than obtained by assuming that Ni is produced in materialthat burns fully to nuclear statistical equilibrium (NSE); 2) in one-dimensionaldelayed detonation simulations a composition dependence of the deflagration-to-detonation transition (DDT) density gives a non-linear relationship between M ( Ni) and Z , and predicts a luminosity larger than previously thought at lowmetallicities (however, the progenitor metallicity alone cannot explain the wholeobservational scatter of SNIa luminosities), and 3) an accurate measurement ofthe slope of the Hubble residuals vs metallicity for a large enough data set ofSNIa might give clues to the physics of deflagration-to-detonation transition inthermonuclear explosions. Subject headings: distance scale — nuclear reactions, nucleosynthesis, abun-dances — stars: evolution — supernovae: general Dept. F´ısica i Enginyeria Nuclear, Univ. Polit`ecnica de Catalunya, Carrer Comte d’Urgell 187, 08036Barcelona, Spain; [email protected] Depto. F´ısica Te´orica y del Cosmos, Univ. Granada, 18071 Granada, Spain; [email protected] Benoziyo Center for Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel; [email protected] INAF - Osservatorio Astronomico di Teramo, via mentore Maggini snc, 64100 Teramo, Italy
1. Introduction
In addition to the mass, metallicity is one of the few progenitor attributes that canleave an imprint on the observational properties of SNIa by affecting the synthesized massof Ni, with important consequences for their use as cosmological standard candles. Up tonow, attempts to measure Z directly from supernova observations have been scarce and theirresults uncertain (Lentz et al. 2000; Taubenberger et al. 2008). Measuring Z from the X-rayemission of supernova remnants is a promising alternative but as yet has been only applied toa single supernova (Badenes et al. 2008). An alternative venue is to estimate the supernovametallicity as the mean Z of its environment (Badenes et al. 2009). Hamuy et al. (2000)looked for galactic age or metal content correlations with SNIa luminosity, but their resultswere ambiguous. Ellis et al. (2008) looked for systematic trends of SNIa UV spectra withmetallicity of the host galaxy, and found that the spectral variations were much larger thanpredicted by theoretical models. Cooper et al. (2009), using data from the Sloan Digital SkySurvey and Supernova Survey concluded that prompt SNIa are more luminous in metal-poorsystems. Recently, Gallagher et al. (2008, hereafter G08) and Howell et al. (2009, hereafterH09), using different methodologies to estimate the metallicity of SNIa hosts, arrived toopposite conclusions with respect to the dependence of supernova luminosity on Z .There is a long history of numerical simulations of SNIa aimed at predicting the im-pact of metallicity and explosive neutronization on their yields (e.g. Bravo et al. 1992;Brachwitz et al. 2000; Travaglio et al. 2005; Badenes et al. 2008). Dom´ınguez et al. (2001,hereafter DHS01) found that the offset in the calibration of supernova magnitudes vs lightcurve (LC) widths is not monotonic in Z and remains smaller than 0 . m for Z ≤ . M ( Ni) and Z . The conclusions of TBT03 relied on two main assumptions: first,that most of the Ni is synthesized in material that burns fully to NSE and, second, thata fiducial SNIa produces a mass M η Fe ∼ . ⊙ of Fe-group nuclei whose η is not modi-fied during the explosion. Piro & Bildsten (2008) and Chamulak et al. (2008), based on thesame assumptions as TBT03, extended their analysis taking into account the neutronizationproduced during the simmering phase.In this paper, we show that the first assumption of TBT03 does not hold for mostSNIa. Indeed, for a SNIa that produces M η Fe ∼ . ⊙ the fraction of Ni synthesizedout of NSE exceeds ∼ ⊙ . This range cannot be accounted for by 3 –metallicity variation within reasonable values. Accordingly, our working hypothesis is thatthe yield of Ni in SNIa is governed by a primary parameter different from Z . In our one-dimensional models the primary parameter is the DDT density, ρ DDT , although in natureit may be something else such as the expansion rate during the deflagration phase. Theinitial metallicity is a secondary factor that can give rise to scatter in the value of M ( Ni)either directly ( linear scenario ), by affecting the chemical composition of the ejecta for agiven value of the primary parameter, or indirectly ( non-linear scenario ), by modifying theprimary parameter itself. The understanding of which one of these two characters is actuallybeing played by Z is of paramount importance.
2. The effect of metallicity on the yield of Ni We explore the sensitivity of M ( Ni) to the progenitor metallicity, starting from Pre-Main Sequence models of masses, M , in the range 2 − ⊙ and metallicities, Z , from 10 − to 0.10, as given in the first column of Table 1. The initial mass fractions of all the isotopeswith A & Z ⊙ = 0 . M core , and chemical structure of the C-O core left behind. Afterwards,an envelope of the appropriate size to reach the Chandrasekhar mass, M Ch , has been addedon top of the C-O cores, and these structures have been fed as initial models to a supernovahydrocode. Finally, the explosive nucleosynthesis has been obtained with a post-processingnucleosynthetic code.The hydrostatic evolution has been computed by means of the FRANEC code (Chieffi et al.1998). With respect to the calculations of DHS01, the code has been updated in the inputphysics. For the purposes of the present paper, the most important changes concern the C ( α, γ ) O reaction rate, which is calculated according to Kunz et al. (2002) instead ofCaughlan et al. (1985), and the treatment of convective mixing during the late part of thecore-He burning (Straniero et al. 2003).The presupernova model is a Chandrasekhar mass WD built in hydrostatic equilibriumwith a central density ρ c = 3 × g cm − . The composition of the envelope of mass M Ch − M core is the same as that of the outermost shell of the C-O core. Thus, insteadof assuming C/O=1, as in DHS01, we adopt the C/O ratio obtained as a result of He-shell burning during the AGB phase. The effect of changing ρ c and the composition of theenvelope has been tested in several models, as explained later. We leave aside other eventualcomplexities of pre-supernova physics like rotation (Piersanti et al. 2003; Yoon & Langer 4 –2004).The internal composition of the WD is eventually modified during the simmering phase,due to the combined effects of convective mixing, carbon burning and electron captures. Thefirst two phenomena affect the carbon abundance within the core, while the latter leads to anincrease of η . The average (within the WD) carbon consumption and neutron excess increaseduring the simmering phase are ∆ Y ( C) ≈ − . × − mol g − and ∆ η = − ∆ Y ( C)(Chamulak et al. 2008). We assume that convective mixing is limited to the C-O core, whichimplies that the change in the neutron excess within the core is ∆ η ≈ . × − M Ch /M core .We have also exploded several models disregarding the simmering phase, to which we willrefer in the following as stratified models .The supernova hydrodynamics code we have used is the same as in Badenes et al. (2003).As in DHS01, the present models are based on the delayed-detonation paradigm (Khokhlov1991). To address the linear scenario we take ρ DDT independent of Z . In this case, ρ DDT =3 × g cm − , although simulations with ρ DDT in the range 1 − × g cm − are alsoreported.For the non-linear scenario we have adopted the criterion that a DDT is induced whenthe laminar flame thickness, δ lam , becomes of the order of the turbulent Gibson length l G (R¨opke & Niemeyer 2007), with the flame properties (velocity and width) depending on theabundances of C (eq. 22 in Woosley 2007) and Ne (Chamulak et al. 2007), and hence on Z and η . Townsley et al. (2009) concluded from 2D simulations of SNIa that the metallicitydoes not affect the dynamics of the explosion, and so the turbulence intensity is independentof Z . Thus, for a given turbulent intensity a change in Z can be compensated by a changein ρ DDT in order to recover the condition δ lam /l G ≈ ρ DDT ∝ X ( C) − . (1 + 129 η ) − . . (1)In order to introduce an η dependence in the above expression we have assumed, for simplic-ity, that the bulk of neutronized isotopes synthesized during the simmering phase acceleratesthe carbon consumption rate the same way Ne does.
The results of the hydrostatic evolution of our presupernova models are shown in Table 1.For each M and Z we give: M core , the central abundance of C and η in stratified models, X c ( C) and η c , and the same quantities in the models accounting for the simmering phase, 5 – X sim ( C) and η sim . In comparison with DHS01, the present models span a larger range of Z , as DHS01 computed models with Z . Z ⊙ . In the common range of Z and M the resultsare comparable, although the adopted rate of the C ( α, γ ) O reaction leads to a slightlylarger carbon abundance than in DHS01. The differences in M core between our models andthose of DHS01 are smaller than 0 .
06 M ⊙ . The central carbon to oxygen ratio and M core weobtain, and their dependencies with Z and M , agree as well with Umeda et al. (1999). M ( Ni) ejected
The results of the explosion simulations are summarized in Figs. 1 and 2. Figure 1 showsthe dependence of M ( Ni) on Z . For the stratified models, we obtain the same range ofvariation of M ( Ni) with respect to M at given Z as DHS01: 0.06 M ⊙ , although the Niyields do not match with DHS01 because they used different values of ρ c = 2 × g cm − and ρ DDT = 2 . × g cm − . The models accounting for the simmering phase behave likethe stratified models with respect to variations in M and Z , although with a smaller total M ( Ni) due to electron captures during the simmering phase. The dependence of M ( Ni)on Z can be approximated by a linear function: M ( Ni) ∝ f ( Z ) = 1 − . ZZ ⊙ , (2)while stratified models can be approximated by: M ( Ni) ∝ − . Z/Z ⊙ , i.e. the slopeof the linear function is quite insensitive to the carbon simmering phase.To explore the non-linear scenario we have computed models accounting for the sim-mering phase with fixed M = 5 M ⊙ . Introducing a composition dependent ρ DDT producesa qualitatively different result because the relationship between M ( Ni) and Z is no longerlinear, especially at low metallicites for which a larger ρ DDT is obtained, implying a muchlarger M ( Ni). Our results can be fit by a polinomial law: M ( Ni) ∝ f ( Z ) = 1 − . ZZ ⊙ (cid:18) − . ZZ ⊙ (cid:19) . (3)Both the central density at the onset of thermal runaway and the final C/O ratio in theaccreted layers have a minor effect on M ( Ni) within the explored range.TBT03 proposed a linear relationship between M ( Ni) and Z : M ( Ni) ∝ − . Z/Z ⊙ (dotted line in Fig. 1). In all of our present models we find a steeper slope. The reason forthis discrepancy lies in the assumption by TBT03 that most of the Ni is synthesized inNSE. In our models a sizeable fraction of Ni is always synthesized during incomplete Si-burning, whose final composition has a stronger dependence on Z than NSE matter. As 6 –Hix & Thielemann (1996) showed, the mean neutronization of Fe-peak isotopes during in-complete Si-burning is much larger than the global neutronization of matter because neutron-rich isotopes within the Si-group are quickly photodissociated, providing free neutrons thatare efficiently captured by nuclei in the Fe-peak group, favouring their neutron-rich isotopes.Figure 2 shows that up to ∼
60% of M η Fe can be made out of NSE, the actual fraction de-pending essentially on the total mass of Fe-group elements ejected. Thus, the less M ( Ni)is synthesized, the larger fraction of it is built during incomplete Si-burning and the strongeris its dependence on Z .
3. Discussion
The results presented in the previous section show that the metallicity is not the pri-mary parameter that allows to reproduce the whole observational scatter of M ( Ni), fora reasonable range of Z . We have also shown that a possible dependence of the primaryparameter on Z , would lead to a non-linear relationship between M ( Ni) and Z , as in Eq. 3.However, as we will show in the following, it would be possible to unravel the way M ( Ni)depends on Z by means of future accurate measurements of SNIa properties.We start analysing the amount of the scatter induced by the dependence of M ( Ni) on Z given by Eq. 3. For simplicity we follow the procedure of M07 to estimate the supernovaluminosity and LC width. The peak bolometric luminosity, L , is determined directly by themass of Ni synthesized (in the following, all masses are in M ⊙ and energies are in 10 ergs): L (cid:2) M ( Ni) (cid:3) = 2 × M ( Ni) erg s − , (4)while the bolometric LC width, τ , is determined by the kinetic energy, E k , and the opacity, κ : τ ∝ κ / E − / . The kinetic energy is given by the difference of the WD initial bindingenergy, | BE | , and the nuclear energy released, the latter being related to the final chemicalcomposition of the ejecta: E k ≈ . M ( Ni) + 1 .
74 [ M Fe − M ( Ni)] + 1 . M IME − | BE | , where M Fe is the total mass of Fe-group nuclei and M IME is the mass of intermediate-mass elements (IME). The opacity is provided mainly by Fe-group nuclei and IMEs: κ ∝ M Fe + 0 . M IME . We have taken | BE | = 0 .
46, which is a good approximation given the smallvariation of binding energy with initial central density: | BE | is in the range 0 . − .
47 for ρ c = 2 − × g cm − . To reduce the number of free parameters we further link M IME to M Fe imposing that the ejected mass is the Chandrasekhar mass ( M Ch ≈ .
38 M ⊙ in ourmodels), and that the amount of unburned C+O scales as M CO ≈ . M , as deduced fromour models. Thus, M Fe + M IME + 0 . M = M Ch . Furthermore, the mass of Ni is linkedto the mass of Fe-group nuclei by M ( Ni) = M η Fe × f ( Z ) = ( M Fe − M ec ) × f ( Z ), where 7 – f ( Z ) is given by Eq. 3 or a similar function, and M ec is the mass of the neutron-rich Fe-group core (due to electron captures during the explosion). We have taken M ec ≈ .
14 M ⊙ ,which is representative of the range of masses obtained in our models: 0 . − .
16 M ⊙ for ρ c = 2 − × g cm − . Finally, to compare with observed values a scale factor of 24.4 isapplied to the value of τ thus obtained, as in M07. Putting all these together, we obtain thefollowing expression for the bolometric LC width (in days) as a function of M ( Ni) and Z : τ (cid:2) M ( Ni) , Z (cid:3) = 21 . ( M ( Ni) f ( Z ) − .
027 + 0 . s − . M ( Ni) f ( Z ) ) / ((cid:18) . f ( Z ) − . (cid:19) M ( Ni) − .
46 + 2 . s − . M ( Ni) f ( Z ) ) / . (5)The relationship between L and τ derived from Eqs. 3, 4 and 5 is displayed in Fig. 3 forthree different metallicities along with observational data. There are also represented therelationships obtained by substituting Eq. 3 by the M ( Ni) vs Z dependences proposedby TBT03 and Eq. 5 in H09. Our Eq. 3 gives a wider range of M ( Ni), which accountsbetter for the scatter of the observational data. Indeed, if real SNIa follow Eq. 3, derivingsupernova luminosities from Z -uncorrected LC shapes might lead to systematic errors of upto 0.5 magnitudes.To estimate the bearing that the metallicity dependence of M ( Ni) can have on cos-mological studies that use a large observational sample of supernovae, we have generated avirtual population of 200 SNIa that has been analyzed following the same methodology asG08 and H09. Each virtual supernova has been randomly assigned a progenitor metallicity,from a uniform distribution of log( Z ) between Z min = 0 . Z ⊙ and Z max = 3 Z ⊙ , and an M Fe ,uniformly distributed in the range from 0.31 to 1.15 M ⊙ . The minimum and maximum M ( Ni) thus obtained (computed with Eq. 3 and M ec = 0 .
14 M ⊙ ) are 0 . ⊙ , andthe bolometric LC width, τ , lies in the range 15 −
24 days. A Z -uncorrected mass of Ni, M ⊙ , has then been obtained as the value of M ( Ni) that would give the same τ if Z = Z ⊙ .The M ⊙ so computed gives an idea of the effect of fitting an observed SNIa LC with atemplate that takes no account of the supernova metallicity. From Eq. 4, we estimate theHubble Residual, HR, of each virtual SNIa at: HR = 2 . (cid:0) M ⊙ /M ( Ni) (cid:1) . As a final stepwe have added gaussian noise with σ = 0 . Z ), to simulate the effect ofobservational uncertainties.A linear relationship HR = α + β log( Z ) has then been fit to the noisy virtual databy the least-squares technique, as in G08 and H09. Figure 4 shows the results for 10,000realizations of the noisy virtual dataset. The histogram gives the number counts of the slope 8 – β in the 10,000 realizations. The whole process has been repeated by using Eq. 2 (i.e. the linear scenario ) to represent the dependence of M ( Ni) on Z and the results are also shownin Fig. 4. From the Figure it is clear that, for a large enough set of SNIa whose luminosityand metallicity are measured with small enough errors, it is possible to discriminate betweenthe linear and non-linear scenarios . In our numerical experiment, the mean value of β is 0.13in the first case and 0.26 in the second case, both with a standard deviationof 0.02.Figure 4 shows also the observational results obtained by G08, who approximated themetallicities of the SNIa in their sample by the Z of the host galaxy, obtained from anempirical galactic mass-metallicity relationship. The striking match between our resultsbased on the non-linear scenario and those of G08 must be viewed with caution in viewof the observational uncertainties involved in measuring supernova metallicities and thelimitations of our models (i.e. the assumption of spherical symmetry). Recently, using adifferent method of determination of the SNIa metallicity, H09 arrived to a result oppositeto that of G08, i.e. they found that HR is uncorrelated with Z , leading to a distributioncentered around β ≈
0. Thus, until such discrepancies are resolved it is not possible todraw any firm conclusion about the metallicity effect on SNIa luminosity. However, it isworth stressing that the simultaneous measurement of supernova luminosity and metallicityfor a large SNIa set would strongly constrain the physics of the deflagration-to-detonationtransition in thermonuclear supernovae, one of the key standing problems in supernovatheory.This work has been partially supported by the MEC grants AYA2007-66256 and AYA2008-04211-C02-02, by the European Union FEDER funds, by the Generalitat de Catalunya, andby the ASI-INAF I/016/07/0. CB thanks Benoziyo Center for Astrophysics for support
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This preprint was prepared with the AAS L A TEX macros v5.2.
11 –Table 1. Properties of CO cores at the beginning of TPs Z a M M core X c ( C) η c X sim ( C) η sim (M ⊙ ) (M ⊙ )10 − (0.23) 3 0.801 0.28 8 . × − . × − − (0.23) 5 0.903 0.25 8 . × − . × − − (0.23) 6.5 1.052 0.20 8 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − Initial metallicity (and helium abundance) 12 –
Fig. 1.— Ni yield vs initial metallicity for different initial masses and explosion parameters.Black triangles: stratified models with ρ c = 3 × g cm − and ρ DDT = 3 × g cm − . Red(filled) circles: models exploded with the same parameters but accounting for the simmeringphase. Blue (empty) circles: the same as red circles except that ρ DDT is a function of thelocal (at flame position) Z through X ( C) and η (Eq. 1) . Blue crosses and blue stars:the same as blue circles except that ρ c = 2 × g cm − (crosses) or ρ c = 4 × g cm − (stars). Blue squares: the same as blue circles except that the composition of the envelopeis composed by equal amounts of carbon and oxygen, i.e. C/O = 1 as compared to valuesranging from C/O = 1.5 to 2.3 as taken from the He-shell burning during the TP phase. Thelines represent the linear relationship between M ( Ni) and Z proposed in TBT03 (dottedline), and our Eq. 3 (dashed line). 13 – Fig. 2.— Fraction of Fe-group elements (from Ti to Zn) synthesized in layers experiencingincomplete Si-burning ( T max ≤ . × K) as a function of the total mass of Fe-groupelements ejected. The filled square is a reference model with ρ DDT = 3 × g cm − , Z = 10 − , and M = 5M ⊙ , that accounts for the simmering phase. The empty squaresbelong to models with varying ρ DDT , from 2 . × to 10 g cm − . All the above modelsare linked by a solid line to help guiding the eye. The rest of models show the sensitivity todifferent model parameters with respect to the reference model, as follows: crosses, varying Z ; empty circles, varying M ; stars, varying ρ c
14 –
24 22 20 18 16 1442.543 LC width (days)
Fig. 3.— Sensitivity of the bolometric light curve luminosity-width relationship to the initialmetallicity. The solid lines belong to Eq. 3 of the present work for Z = 0 . Z ⊙ (green), Z = Z ⊙ (blue), and Z = 3 Z ⊙ (red). There are also shown the curves obtained using the M ( Ni) vsZ relationships of TBT03 (dotted lines) and H09 (dashed lines). The stars represent SNIafrom Contardo et al. (2000), whose light-curve width has been computed as in M07, whilethe asterisks represent SN1999ac (Phillips et al. 2006), SN2003du (Stanishev et al. 2007),and SN2005df (Wang et al. 2009) (by order of decreasing LC width), estimated from thepublished bolometric light curves 15 –
Fig. 4.— Number distribution of the slope, β , of the least-squares fit to the Hubble residualvs metallicity. The statistics used 10,000 data sets, each one obtained adding gaussian noise( σ = 0 . Z ) to a virtual random population of 200 SNIa generatedusing either the quadratic M (56