A&A 443, 1007-1011 (2005)
DOI: 10.1051/0004-6361:20052883

Metallicity effect in multi-dimensional SNIa nucleosynthesis

C. Travaglio1,2 - W. Hillebrandt2 - M. Reinecke2


1 - Istituto Nazionale di Astrofisica (INAF) - Osservatorio Astronomico di Torino, via Osservatorio 20, 10025 Pino Torinese (Torino), Italy
2 - Max-Planck Institut für Astrophysik, Karl-Schwarzschild Strasse 1, 85741 Garching bei München, Germany

Received 15 February 2005 / Accepted 18 July 2005

Abstract
We investigate the metallicity effect (measured by the original 22Ne content) on the detailed nucleosynthetic yields for 3D hydrodynamical simulations of the thermonuclear burning phase in type Ia supernovae (SNe Ia). Calculations are based on post-processes of the ejecta, using passively advected tracer particles. The nuclear reaction network employed in computing the explosive nucleosynthesis contains 383 nuclear species, ranging from neutrons, proton, and $\alpha$-particles to 98Mo. we use the high resolution multi-point ignition (bubbles) model b30_3d_768, and we cover a metallicity range between $0.1\times Z_\odot$ and $3\times Z_\odot$. We find a linear dependence of the ejected 56Ni mass on the progenitor's metallicity, with a variation in the 56Ni mass of $\sim$25% in the metallicity range explored. The largest variation in 56Ni occurs at metallicity greater than solar. Almost no variations are shown in the unburned material 12C and 16O. The largest metallicity effect is seen in the $\alpha$-elements. Implications for the observed scatter in the peak luminosities of SNe Ia are also discussed.

Key words: hydrodynamics - nuclear reactions, nucleosynthesis, abundances - supernovae: general

1 Introduction

The understanding of the influence of an exploding white dwarf's initial composition on the nucleosynthesis, light curve, and spectra of type Ia supernovae is an important tool to evaluate the origin of their observed diversity. It is widely accepted that SNe Ia are thermonuclear explosions of C+O white dwarfs, although the nature of the progenitor binary system and the details of the explosion mechanism are still under debate. Over the last decades, one-dimensional spherically symmetric models have been used to predict spectra, light curves and nucleosynthesis. Moreover, the dependence of the 56Ni ejected on the progenitor's metallicity as well as on the initial C/O composition has been investigated in the literature (Höflich et al. 1998; Iwamoto et al. 1999; Umeda et al. 2000; Höflich et al. 2000; Dominguez 2001; Timmes et al. 2003). More recently it has become possible to perform multidimensional simulations of exploding white dwarfs (see Reinecke et al 2002, and references therein; Gamezo et al. 2003). Also a detailed study of nucleosynthesis using multi-dimensional SNIa models has been performed for a solar metallicity initial composition (Travaglio et al. 2004). The nucleosynthetic yields of multi-dimensional Eulerian hydrodynamic calculations of SNIa explosions have been obtained by post-processing the ejecta, using the density and temperature history of passively advected tracer particles.

Starting with the highest resolution pure deflagration SNIa model presented by Travaglio et al. (2004), b30_3d_768 (a 3D model with ignition in 30 bubbles and grid size of 7683), we explore in this work the metallicity effect on nucleosynthesis. We are also performing a detailed parameter study of the variation of the central density and of the initial carbon/oxygen ratio of the SNIa progenitor. This will be presented elsewhere (Röpke et al. 2005). In Sect. 2 of this work we demonstrate that the mass of 56Ni depends linearly on the initial metallicity of the progenitor, in agreement with recent results from Timmes et al. (2003). We also discuss our results for the detailed nucleosynthetic composition of the SNIa models analyzed, and we compare them with the W7 calculations by Brachwitz et al. (2000) and Thielemann et al. (2003). In Sect. 3 we summarize our results.

2 Effects of variations in 22Ne progenitor abundance

In order to simulate a solar metallicity SNIa, for the initial white dwarf composition we use 0.475 $M_\odot $ of 12C, 0.5 $M_\odot $ of 16O and 0.025 $M_\odot $ of 22Ne (these values are indicated in mass fraction). This is in agreement with the standard W7 initial composition (Iwamoto et al. 1999). As soon as the flame passes through the fuel, 12C, 16O and 22Ne are converted into ash with different composition depending on the initial temperature and density. We simulate a metallicity effect changing the initial 22Ne abundance (and the 12C initial mass as a consequence). The reason is that the metallicity mainly affects the initial CNO abundances in a star. They are converted during pre-explosive H burning to 14N and He burning to 14N($\alpha$,$\gamma$)18F($\beta^+$)18O($\alpha$,$\gamma$)22Ne to heavier nuclei. Therefore a change of 22Ne abundance simulates the metallicity effect. Temperature and density profiles were calculated using the energy released by burning matter of solar metallicity. This seems to be a fair approximation because the metallicity is unlikely to influence the velocity of the flame front (which is independent of the microphysics in the case of strong turbulence), and also the energy production depends only weakly on the metallicity. A mixture of more 22Ne and less 12C should give less energy, due to the differences in binding energies. However, this effect is small as long as the 22Ne abundance is of the order of a few percent only.


  \begin{figure} \par\includegraphics[width=7.8cm,clip]{2883fig1.eps} \end{figure} Figure 1: 56Ni ejected mass by the b30_3d_768 model as a function of the initial metallicity $Z_{\rm CNO}$.
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For the models mentioned above, we use the following initial composition: 0.4975 $M_\odot $ of 12C, 0.5 $M_\odot $ of 16O and 0.0025 $M_\odot $ of 22Ne for the model b30_3d_768_d10; 0.425 $M_\odot $ of 12C, 0.5 $M_\odot $ of 16O and 0.075 $M_\odot $ of 22Ne for the model b30_3d_768_p3.

A complete view of our nucleosynthesis calculations for the models b30_3d_768 (Travaglio et al. 2004), b30_3d_768_d10 and b30_3d_768_p3 is reported in Table 1 (synthesized masses for the main radioactive species from 22Na up to 63Ni), and in Table 2 (synthesized masses for all the stable isotopes up to 68Zn). In both Tables we also include (in Col. 2) for comparison the calculations for the W7 model (from Thielemann et al. 2003, and Brachwitz et al. 2000). In Fig. 2 we show the yields obtained for the models b30_3d_768_d10 and for b30_3d_768_p3, normalized to the "standard'' b30_3d_768 case.

Table 1: Synthesized mass ($M_\odot $) for radioactive species in SNIamodels.


  \begin{figure} \par\includegraphics[width=8.4cm,clip]{2883fig2.eps} %\end{figure} Figure 2: Nucleosynthetic yields (in mass fraction) for the model b30_3d_768 with $Z_{\rm CNO} = 0.1 ~Z_\odot$ ( solid lines and filled dots) and for the model b30_3d_768 with $Z_{\rm CNO} = 3x ~Z_\odot$ ( dotted lines and open dots). Both are normalized to the b30_3d_768 model with solar metallicity.
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The mass fraction of 56Ni depends linearly on the initial metallicity, that can be fitted by the simple following linear equation

\begin{eqnarray*}M(^{56}{\rm Ni}) \simeq 0.45~ M_\odot - 0.031~ Z_{\rm CNO}/Z_\odot. \end{eqnarray*}


Since 22Ne scales with $Z_{\rm CNO}$, we scaled $Z_{\rm CNO}$ rather than $Z_{\rm Fe}$, and we use this notation for the whole paper. As one can see from Table 1, varying the metallicity from $Z_{\rm CNO} = 0.1$ to 3 $Z_\odot$ the 56Ni mass ejected changes by $\sim$25%. This is in a good agreement with the results presented by Timmes et al. (2003) (they found a variation of 56Ni mass ejected by $\sim$25% in a metallicity range 1/3 up to 3 $Z_\odot$). Also in agreement with Timmes et al. (1998) we find that the largest variation in the mass of 56Ni occurs at metallicity greater than solar ($\sim$15%). In contrast, previous investigations of the effect of variations of 22Ne by Höflich et al. (1998) and Iwamoto et al. (1999) do not agree on the 56Ni mass produced. Höflich et al. (1998) found that a metallicity variation from 0.1 to 10 $Z_\odot$ produces only a $\sim$4% variation in the 56Ni mass ejected. Instead Iwamoto et al. (1999) found that a variation of metallicity from zero to solar decreases the 56Ni mass by $\sim$10%. Much smaller 56Ni variations with metallicity can be explained as a difference in temperature profiles, i.e. if temperatures are higher in a large part of the inner white dwarf the electron captures could hide the metallicity effect. Alternatively, the delayed detonation effect produces much 56Ni in the outer layers and the outcome should depend on the 22Ne distribution.

Table 2: Synthesized mass ($M_\odot $) in SNIa models.

Still concerning our results for the 56Ni mass, the amplitude of its variation cannot account for all the observed variation in peak luminosity of SNIa (Pinto & Eastman 2001). The observed scatter in the peak brightnesses may be even larger when more distant SNe are included (Hamuy et al. 1996; Riess et al. 1998; and more recently including type Ia Supernova discoveries at z > 1 from the Hubble Space Telescope and from the Canada-France-Hawaii Telescope, Riess et al. 2004 and Barris et al. 2004, respectively).

Strong metallicity effects are also shown in the variations of the alpha elements (see Table 2), like Mg and Al isotopes. Instead almost no variations are seen in the Ti and V region. The behavior of 54Fe, is discussed in detail by Höflich et al. (1998) and Timmes et al. (2003). As described by Travaglio et al. (2004), when T and $\rho$ are high enough, neutron-rich nuclei are built up due to electron captures and 56Fe is partly replaced by 54Fe and 58Ni. We find that 56Fe is anti-correlated with 54Fe and 58Ni ejected, i.e. 54Fe and 58Ni increase with increasing metallicity. The largest effect is shown by the variation of 54Fe, a decrease by a factor of $\sim$3 for the model b30_3d_768_d10 and an increase by a factor of $\sim$2 for the model b30_3d_768_p3. Therefore subluminous SNe Ia will tend to have larger 54Fe/56Fe ratios than brighter ones.

3 Summary and conclusions

In this paper we discussed the results of detailed nucleosynthesis calculations obtained from coupling 3D hydrodynamics of SN Ia explosion to post-processes of the ejecta using a tracer particle method. Nucleosynthesis and hydrodynamic calculations for the high resolution multi-point ignition model b30_3d_768 discussed here are explained in detail by Travaglio et al. (2004). The purpose of the present work is to investigate the metallicity effects on the nucleosynthesis, obtained by changing the original 22Ne content. We presented here our results for two metallicities (0.1 $Z_\odot$ and 3 $Z_\odot$, model b30_3d_768_d10 and b30_3d_768_p3 respectively), compared to the solar metallicity case b30_3d_768. We also discuss them in comparison with the standard W7 SNIa model (Iwamoto et al. 1999; Brachwitz et al. 2000; Thielemann et al. 2003). The approach is not fully consistent because the metallicity may also affect the C/O of the WD at explosion. However it has been shown recently (Roepke & Hillebrandt 2004) that the C/O ratio does not change the Ni-production and, thus, the peak luminosity of a type Ia supernovae by much if all other properties are kept constant. So we believe that our model catches the essential effect.

We find that the 56Ni mass produced decreases linearly with metallicity, with a variation of 56Ni of $\sim$25% in the metallicity range explored. The largest variation ($\sim$15%) is seen at $Z_{\rm CNO} = 3~Z_\odot$, the highest metallicity investigated in this study. We also discussed the behavior of all the other isotopes with a code that includes 383 isotopes. Interesting changes are shown for isotopes of Mg and Al, and particular attention was paid to the 54Fe and 58Ni isotopes in comparison to 56Fe.

Metallicity effects on the nucleosynthesis using different hydrodynamical SN Ia models are presented by Röpke et al. (2005). A detailed parameter study of the central density and of the initial carbon/oxygen ratio of the SN Ia progenitor with the effect on the nucleosynthesis has been presented by Röpke et al. (2005).

Acknowledgements
C.T. thanks the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research, and the Programme for Investment in the Future (ZIP) of the German Government, and the Max-Planck Institute für Astrophysik (Garching bei München), for their financial support. This work was supported in part by the "Sonderforschungsbereich 375-95 für Astro-Teilchenphysik'' der Deutschen Forschungsgemeinschaft and the European Commission under grant HPRN-CT-2002-00303.

References

 
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