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Advances in Space Research 38 (2006) 1434–1438

The science of c-ray spectroscopy

J. Isern a,*, E. Bravo b, A. Hirschmann b

a Institut d�Estudis Espacials de Catalunya and Institut de Ciencies de l�Espai (CSIC); Edifici NEXUS, c/Gran Capita 2, 08034 Barcelona, Spainb Institut d�Estudis Espacials de Catalunya and Departament de Fısica i Enginyeria Nuclear (UPC); Diagonal 647, 08028 Barcelona, Spain

Received 21 October 2004; received in revised form 18 July 2005; accepted 19 July 2005

Abstract

The explosion mechanism associated with thermonuclear supernovae (SNIa) is still a matter of debate. Nevertheless, there is awide agreement that high amounts of radioactive nuclei are produced during these events, that are expected to be strong c-ray emit-ters. In this paper we investigate the use of c-rays as a diagnostic tool. For this purpose we have performed a complete study of the c-ray spectra associated with all the different scenarios currently proposed: detonation, deflagration, delayed detonation, pulsatingdelayed detonation and off-center detonation. Our study shows that the c-ray emission from SNIa is, effectively, a promising toolbut that must be carefully used since it can lead to misinterpretations. We also show that 3D effects might be relevant in some cir-cumstances and provide important information about the exploding system and the thermonuclear burning front mechanism if highresolution spectra are obtained.� 2006 Published by Elsevier Ltd on behalf of COSPAR.

Keywords: Supernovae; Nucleosynthesis; c-Rays

1. Introduction

It is commonly accepted that Type Ia supernovae arethe result of the thermonuclear explosion of mass-accret-ing C–O white dwarfs. At present there are several theo-ries to account for these events. Some of them assumethat the thermonuclear runaway starts at the centerand propagates outwards either supersonically – detona-tion – (Arnett, 1969), or subsonically – deflagration –(Nomoto et al., 1984), while others assume that it initiallypropagates as a deflagration and later as a detona-tion, when the density falls below some critical value(Khokhlov, 1991). A version of this theory is the pulsatingdelayed detonation mechanism which assumes that a def-lagration starts at the center of the star producing itsexpansion with the subsequent quenching of the flame

0273-1177/$30 � 2006 Published by Elsevier Ltd on behalf of COSPAR.

doi:10.1016/j.asr.2005.07.037

* Corresponding author. Tel.: +34 932 802 088; fax: +34 932 806395.

E-mail address: isern@ieec.fcr.es (J. Isern).

but, after a period of expansion, the star recontracts andinduces the detonation of the fuel that was left unburned.Finally, another class of models assumes that a CO whitedwarf with a mass below the Chandrasekhar limit accreteshelium from a companion and forms a degenerateenvelope; when the mass of the envelope reaches a criticalvalue, helium ignites and triggers the explosion of theentire star (Ruiz-Lapuente, 1993; Livne and Arnett, 1993;Woosley and Weaver, 1994; Arnett and Livne, 1994).

In all the models high amounts of 56Ni and otherradioactive isotopes are produced during the outburst.The total amount and the distribution of the differentradioactive species as well as the density and expansionprofiles are model dependent. This leads to significativedifferences in the evolution of the properties of thec-ray lines, opening the possibility of using them asdiagnostic tools (Gehrels et al., 1987; Ambwami andSutherland, 1988; Burrows and The, 1990; The et al.,1993; Hoflich et al., 1994; Kumagai and Nomoto,1997; Gomez-Gomar et al., 1998).

0 100 200 3000

Time (days)

DET

PDDa

DDTa

DDTe

DEFf

DEFa

PDDe

Fig. 1. Evolution of the intensity of the 1238 keV line of 56Coassuming a distance of 1 Mpc. The horizontal lines represent the upperbounds imposed by the observations of SN1998bu. The continuousand the dotted lines were obtained according to two different kinds ofanalysis (Georgii et al., 2002).

J. Isern et al. / Advances in Space Research 38 (2006) 1434–1438 1435

2. Models and diagnostic criteria

Supernova explosions, as well as the resulting nucle-osynthesis, have been modeled with the 1D hydrocodedescribed by Bravo et al. (1996) and Badenes et al.(2003). Since at present there is not a self-consistent the-ory for the propagation of the nuclear flames throughthe degenerate interior of white dwarf stars, all the cal-culations rely on a parameterization of the burning frontregime.

Below are the main characteristics of the models.

� Chapman–Jouguet detonations starting from the cen-ter can be disregarded because they convert almost allthe star into iron peak elements that are not observedduring the maximum of the light curve, as would beexpected. Despite that, since the velocity of the burn-ing front only depends, in this case, on the thermody-namic properties of the unburned material, it is usefulto use such explosions as a model for comparison.The model used here is of a 1.38Mx white dwarfcomposed of half carbon and half oxygen plus 1%of 22Ne. The star is initially in hydrostatic equilibriumwith an adiabatic thermal profile. The explosionwas obtained by incinerating the central layer toNSE and allowing the flame to propagate as aChapman–Jouguet detonation.� Deflagration models (DEF) assume that the flame

starts in the central region and initially propagates ina laminar regime. Because of different instabilities(Rayleigh–Taylor, Kelvin–Helmholtz, Landau–Darrieus),the burning front wrinkles and the effective velocityof the flame (defined in terms of burned mass perunit time) increases. There is not at present asatisfactory theory of how this flame propagates.A useful parameterization assumes that the velocityof the flame is given by:

vdef ¼ maxðvl; vRTÞ;

where vl is the laminar velocity and

vRT /rfl

sRT

;

where rfl is the maximum radius of the flame and sRT

is the characteristic time for the Rayleigh–Taylorinstability. In the present calculations, for the con-stant of proportionality, we use values from 0.06(case a) to 0.16 (case f). The initial model is the sameas for the DET case, except that the star isisothermal.� Delayed detonation models (DDT) assume that the

flame initially propagates as a deflagration, but whenthe density drops below a critical value, qtr, the flameaccelerates and becomes a detonation. This critical

density must be smaller than few times 107 g/cm3 toprevent the complete incineration of the material.The extreme cases a and e in Fig. 1 correspond todensities of 3.9 and 1.3 · 107 g/cm3, respectively.The velocity during the deflagration phase is conve-niently parametrized as: vdef = acs, where cs is thesound velocity and a was taken to be 0.03.� The pulsating delayed detonation (PDD) is treated in

the same way, but after the bounce. The extremecases a and e in Fig. 1 correspond to transition den-sities of 4.4 · 107 and 7.7 · 106 g/cm3, respectively.� The sub-Chandrasekhar case assumes a CO white

dwarf that accretes helium at a rate that allows theformation of a degenerate envelope. When this layerreaches a critical value (�0.2�0.3Mx), that slightlydepends on the initial conditions, helium is ignitedat the bottom and induces a detonation that propa-gates outwards, incinerating all the accreted helium,and a shock wave that propagates inwards whichtriggers the detonation of carbon in the centralregions. The initial model was kindly provided by J.Jose. It was obtained from a white dwarf model withthe same composition as before but with an initialmass of 0.8Mx. At the moment of ignition, the sizeof the envelope is 0.2Mx and is a consequence ofthe accretion of helium at a steady rate of3.5 · 10�8Mx year�1.

The c-ray spectra emerging from the different modelshave been computed using the 1D code developed byGomez-Gomar et al. (1998). This allows one to compute

1436 J. Isern et al. / Advances in Space Research 38 (2006) 1434–1438

the spectrum for any profile of composition, velocityand density. This code is based on the Monte Carlomethod technique and includes the radioactive chainsthat are relevant for Type Ia supernovae. It is importantto point out here that this code has passed a test of con-sistency with other independent codes (Milne et al.,2004), and that the main properties are compatible withthose derived by other authors.

The results obtained with the c-ray code can be sum-marized as follows:

� The models involving a prompt or delayed detona-tion display strong lines twenty days after the explo-sion because their high expansion rates induce a rapiddecrease of the opacity. Lines are particularly intensefor those models containing 56Ni and 56Co in theouter layers (pure detonation and sub-Chandrase-khar models). The maximum intensity of these linesdepends strongly on the model through the expansionrate and the distribution of 56Ni. Pure deflagrationmodels only display a continuum since they efficientlycomptonize the high energy c-rays. The shape of thecontinuum at low energies is limited in all the modelsby the competing photoelectric absorption, whichimposes a cut-off below 40–100 keV. The energy ofthe cut-off is determined by the chemical compositionof the external layers where most of the emergentcontinuum is formed at this epoch. Consequently,the continuum of those models containing low Z ele-ments in the outer layers will extend to lower energiesthan those containing high Z elements.� The 56Co lines reach their maximum of intensity

roughly two months after the explosion in all modelsexcept for the pure deflagration one. At maximum,the intensity of the lines, except for the deflagrationmodel, is determined by the total mass of radioactiveisotopes, while the differences in the expansion rateare secondary, and the position of the energy cut-offapproaches 70 keV.� Four months after the explosion, the ejecta are opti-

cally thin in all cases and the intensity of the lines isproportional to the total mass of the parent isotopes.The continuum is faint and is dominated by the pos-itronium annihilation component which shows a stepbelow 170 keV, the energy of the backscattered511 keV. At this epoch, line profiles reveal the distri-bution in velocity of their parent isotopes in all thelayers of the ejecta. The lines corresponding to thepure detonation case are the broadest ones and dis-play a peculiar truncated core produced by theabsence of 56Co in the central layers, while those cor-responding to the sub-Chandrasekhar models displaycharacteristic wings.

It is thus clear that there are noticeable differences be-tween the spectra of these models, specially during the

early epochs when the total amount of radioactive iso-topes and their distribution, the expansion rate andthe composition of the ejecta affect the emission. Thequestion is, however, if these differences provide unam-biguous criteria for rejecting any of the mechanisms.

Fig. 1 displays the evolution of the intensity of the1238 keV line of 56Co with time for the extreme casesof the different explosion models considered here(DET, DEF, DDT, PDD). The luminosity ranges ofsolutions for the different models all overlap, exceptfor the case of a pure detonation, and it would be diffi-cult to disentangle them even if it were possible to obtaina light curve with a good signal-to-noise ratio. For in-stance, Georgii et al. (2002) obtained, with COMPTEL,two upper bounds to the emission of the 1238 keV lineof 56Co during the SN1998bu eruption in M96, whichis placed at 11.3 ± 0.9 Mpc. Depending on the type ofanalysis used, imaging or spectral, they obtained3.2 · 10�5 and 2.3 · 10�5 photons cm�2 s�1, the differ-ence being caused by the background analysis. It is evi-dent from Fig. 1 that with such a measurement it isimpossible to discriminate among the different modelsof explosion and only allows one to constrain theparameters that characterize each family.

3. Three dimensional effects

The low level of polarization and the rather homoge-neous profile of the absorption line of Si II observed inType Ia supernovae indicate that the departures fromspherical symmetry are small, while infrared observa-tions indicate that the total amount of unburnt matterthat is ejected during the explosion is smaller than 10%.

Nevertheless, the attempts to build three dimensionalmodels of Type Ia supernovae show interesting devia-tion from spherical symmetry since 56Ni is localized inpockets distributed along the entire radius of the starand, at the same time, large amounts of unburned car-bon and oxygen are left not only in the outer layers,but also in the inner ones (Reinecke et al., 2002; Gamezoet al., 2003; Garcıa-Senz and Bravo, 2005). This is atodds with the observations. One way to reconcile themis to assume that, when the density falls below a criticalvalue, the burning regime changes from a deflagration toa detonation and converts the unburnt mixture ofcarbon and oxygen into 56Ni, erasing the differencesbetween the burnt and the unburnt regions. One wayto test if this late detonation occurs is to examine theprofile of the c-ray lines. Effectively, if there are blobsof radioactive matter moving at different velocities, theprofile of the c lines will display irregularities due tothe different Doppler shifts, as it can be inferred fromFig. 2a which shows the distribution of 56Ni as afunction of the three velocity components in the caseof a pure deflagration. If the deflagration becomes a

01.2 1.22 1.24 1.26 1.28 1.3

Fig. 3a. The line profile for the 1238 keV emission of 56Co 70 daysafter the explosion for a pure deflagration model. The solid line wasobtained averaging over the solid angle 0 < / < 360, 27 < h < 63, thedotted line over 0 < / < 360, 162 < h < 180, and the dashed–dottedline over all the sphere.

Fig. 2a. Abundance of 56Ni as a function of the components of thevelocity for a pure deflagration model.

J. Isern et al. / Advances in Space Research 38 (2006) 1434–1438 1437

detonation, these blobs disappear, and 56Ni will be dis-tributed more uniformly in the velocity space, as canbe seen in Fig. 2b. These differences concerning the sym-metry of the distribution of 56Ni translate into differ-ences in the c-ray emission, enhancing once more thepossibility of using the properties of c-ray lines as adiagnostic tool for discriminating between differentexplosion mechanisms.

In order to check this possibility we have computedusing a 3D Monte Carlo code whose details will be

Fig. 2b. Abundance of 56Ni as a function of the components of thevelocity for a deflagration model followed by a detonation.

described elsewhere, the profile of the 1238 keV 56Co line,assuming a deflagration (Fig. 3a) and a delayed detona-tion (Fig. 3b). Although these results are still preliminary,it seems that the profile obtained with the delayed detona-tion model is smoother than that obtained with the defla-gration one. Such studies are promising. Once a morecomplete research has been conducted, this propertycould be added to the set of diagnostic criteria obtainedfrom 1D models.

1.2 1.22 1.24 1.26 1.28 1.30

Fig. 3b. The same as Fig. 3a for the case of a delayed detonationmodel.

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Before using these effects as a diagnostic tool of theexplosion mechanism, we must realize that we need notonly good resolution and high signal-to-noise ratio spec-tra, but also a significant sample of supernovae in order todisentangle which properties are due to the flame itselfand which to the lack of symmetry of the scenario (theinfluence of the companion, for instance, in the case ofthe single degenerate scenario). These statements implythat these kind of studies will not be possible before thedevelopment of high performance c-ray detectors, likethe c-ray lens concept described by P. von Balmoos inthese proceedings, able to fulfill these requirements.

4. Conclusions

One dimensional simulations show clear differencesbetween the c-ray spectra of different type Ia supernovamodels. Unfortunately, the similarity of the resultsmakes constructing a unique diagnostic difficult.

Three dimensional simulations indicate that notice-able asymmetries could appear during the explosion,but the detector performances necessary in order to de-tect them may be beyond the capabilities of the presentinstruments.

Acknowledgements

This research has been partially supported by theCIRIT, the MEC programs AYA2002-04094-C03-01/02 and AYA2004-06290-c02-01/02, and by the EUFEDER funds.

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