PoS(SUPERNOVA)006 http://pos.sissa.it/ ce. unt for part of the observational ed to explore the conditions under lk of the so-called normal Type Ia m are largely unknown. Most current C ption of massive white dwarfs made of nor a delayed transition to a supersonic ned, and their consequences ive Commons Attribution-NonCommercial-ShareAlike Licen detonation. Although both mechanisms can coexist, and acco carbon and oxygen, but the details of theexplosion explosion models mechanis invoke either a pure turbulent deflagratio sample, only delayed detonations seemsupernovae. able Here to we explain report the on bu two numericalwhich experiments a aim deflagration-to-detonation transition can be obtai Type Ia supernovaeare the result of the thermonucleardisru Copyright owned by the author(s) under the terms of the Creat c Supernovae: lights in the darkness October 3-5, 2007 Mao (Menorca) Eduardo Bravo and Domingo García-Senz Department of Physics and Nuclear Engineering (UPC) and IEE Small steps in thermonuclear supernova research Inmaculada Domínguez Departamento de Física Teórica y del Cosmos, Univ. Granada PoS(SUPERNOVA)006 (García- ⊙ ergs). 51 2M . 10 0 ≡ ∼ f is disrupted by a ther- ing at low velocities (Mar- [2002], Baron et al. [2008]). foe (1 foe al. [2005]). servations of supernovae and exceeding ational data related to Type Ia ali et al. [2008]). ver, even admitting that a perfect 0]), current multidimensional hy- cs of the interstellar medium and proaches the Chandrasekhar-mass or the double degenerate scenario, tly related to the explosion mecha- rophysics. A satisfactory model of range of nickel masses synthesized upernovae, which in turn have pro- e in computer technology, have per- ible models of the explosion always iate rate to avoid the nova instability. s not to be expected, there are a series on of SNIa and those deduced on the h [1997], Saio & Nomoto [1998]). lations. Admitting that at least part of urrent zoo of explosion mechanisms is s that rely on spherical symmetry, and e Galaxy. Nowadays, the favored SNIa al objections (e.g. Nugent et al. [1997], lain even the gross features of the spec- Type Ia supernovae or to make it possi- he light curve and spectra, it is certainly osion simulations in order to elucidate the , after neutronization due to electron captures ⊙ 2 1M ∼ Ni and other Fe-group elements should not be present at the 56 Ni should reach 56 photosphere at the time of maximum brightness (Thomas et al. Large clumps of radioactive Senz et al. [2007]). The ejecta should be chemicallyremnants stratified, (Badenes as et demanded al.[2006], by Gerardy ob et al.[2007], Mazz Intermediate-mass elements should be generated in amounts is properly taken into account (Mazzali et al. [2007]). The final kinetic energy should be on the order or larger than 1 The ejected mass of There should be no more than a few tenths of unburnt carbon mov ion et al. [2003], Baron, Lentz & Hauschildt [2003], Kozma et The knowledge of the physical mechanism by which a white dwar The huge increase in number, quality and diversity of observ • • • • • • monuclear explosion is relevant tothe many explosion topics becomes of crucial modern to ast found better implications understand in Type cosmology Iathe and s chemical in evolution studies of of galaxies.involve the the Although thermonuclear dynami the disruption more of a plaus still white dwarf, too the large c to be useful in cosmological applications of Thermonuclear supernovae 1. Introduction ble to understand the details of the chemical evolution of th model is the thermonuclear explosionlimit of owing to a accretion white from a dwarfOther companion that types star ap at of the models, appropr suchalthough as not the completely sub-Chandrasekhar ruled out, models either aretrum not and light able curve to of exp normal supernovae,Napiwotzki or et face al. theoretic [2002], Segretain, Chabrier & Mochkovitc supernovae (SNIa) in recent years,suaded combined modelers with to the leave advanc the phenomenologicalattempt calculation more physically meaningful multidimensionalthe simu diversity shown by thenism Type Ia of supernovae a sample Chandrasekhar-mass is whitedrodynamical direc dwarf calculations (Hatano should et be al. ablein to [200 different allow events. for Lacking a multidimensional wide risky studies to of interpret t the results of theexplosion three mechanism dimensional expl and discriminate betweenmatch models. between the Howe observed luminositybase and of spectral angle-averaged versions evoluti of the 3Dof explosion tests models that i a good normal SNIa model should pass: PoS(SUPERNOVA)006 cm, 8 , where 10 C nuclear × 8 12 sound . v 1 C+ 01 and the detona- − . 12 3 0 7 . − 1 ≃ ∼ r g cm 8 r the Chandrasekhar-mass 10 agration-to-detonation tran- supersonic velocities which, × hokhlov, & Oran [2004, 2005], deflagration models, preserving 5 . 2 emeyer [2007] explored the range und the center and thermonuclear ate selection of the optimal initial ediate-mass elements synthesized. tabilities. Many exploratory stud- 000]). Although the flame velocity He. The context of our work, the tion of a non-uniformly preheated at the combustion entered the dis- of Gamezo et al. [2005] produced a ce had to be estimated because the in a few hot bubbles. They used a rbulence fluctuations at the scale of to blow away the star. Accounting ter shells, at ≥ energetic explosion, but still far be- mics have shown that the key point ed by the screened on. Later, we show the results from t dden transition from a subsonic defla- d to consistent results with respect to e center. ar. In these models the starting point hokhlov [1991]), i.e. the multidimen- ne [1994], Livne [1999], Golombek & re the DDT occurs. ρ ydrostatic, stages due to the stochastic ation of the velocity of the combustion ly incinerated region probably does not , ition is not well understood. In Gamezo f the problems of pure deflagration mod- scenario aimed to discern the sensitivity 3 (Timmes & Woosley [1992]), it is quite subsonic: 1 − is the sound speed. These velocities are far below the nearly There have been several attempts to bypass the weaknesses of Nowadays the best models involve a white dwarf with a mass nea In this work we have explored the conditions under which a defl The essential feature of detonation initiation is the forma sound et al. [2005] the adopted transition density was rather high physics behind the deflagration-to-detonation (DDT) trans els. The density at which the jump to the detonation takes pla at the same time many of theirgration advantages, by to postulating a a supersonic su detonation (Ivanovasional et version of al. the delayed detonation [1974], model:Niemeyer K Arnett [2005] & in Liv 2D; García-SenzRöpke & & Bravo Niemeyer [2003], [2007] Gamezo, in 3D. K Insatisfactory particular, thermonuclear the explosion, recent thus work solving many o according to many one-dimensional simulations,for turbulent are acceleration needed of thelow flame what can is help needed obtaining toconditions an explain at bright the thermal SNIa, runaway even (Röpke after et an al. [2007]). accur v reaction in degenerate conditions. Thekeep shape the of spherical the symmetry initial thatnature characterizes of previous, ignition h and toies the carried role out played in byto the achieve hydrodynamic past a ins using successful one-dimensional explosion reliesfront hydrodyna (Niemeyer in & the Woosley proper [1997], estim Hillebrandt &is large, Niemeyer close [2 to 100 km s Thermonuclear supernovae tion was induced near the centerof of explosions the that white would dwarf. result Röpke if & the Ni DDT took place in the ou limit in which a nuclearcombustion fuel propagates ignites henceforth in through one theof or rest hydrodynamical many of calculations sparks the is aro st the thermal runaway caus after a huge expansion duephysically to motivated criterion subsonic to combustion switch initiated tributed regime, on in a which DDT, mixing namelythe of th flame burnt width and fresh might fuel triggerthe by a final tu detonation. kinetic This energy criterion andIt le to also the allowed mass the of almost Fe-group complete and depletion of interm carbon in th sition can arise withinmethodology, C-O and matter the contaminated results by arethree-dimensional traces presented simulations of in of the the delayed-detonation next Secti of the explosion properties on the location of the region whe 2. The role of He in deflagration-to-detonation transition PoS(SUPERNOVA)006 r, Ia ut (2.2) (2.1) . cap of He would ⊙ 01 M . 0 for reasonable assumptions. ∼ 3 s: adiabatic pre-compression in he moment of carbon runaway, ssary conditions for a DDT are energy than carbon. Actually, a a DDT in unconfined conditions r the typical maximum expected of a ion as a way to increase the flame laminar flame velocity by a factor g/cm ollowing a deflagration phase. For C-O matter is to mix it with a small his helium might accumulate from f subsonic flames against interaction ness. This criteria was fulfilled for eflagration wave. Up to the present, s identification is problematic since 7 ex geometrical structure of the flame he binary system. This helium could t constant, for instance if it dropped es with fresh fuel (Khokhlov [1991]), om the nuclear processing of accreted . The thermal gradient needed is given 994, 1994] detected indications of two and chemical composition such that a hat can be expected from turbulence at is the induction time at the temperature 10 ioning has received the most attention. meyer & Woosley [1997]). Among the ˙ T × i / 5 τ i T T τ − T = ln ln 2 i Θ sound ). ∂ ∂ τ 3 4 < Av − 0, . ρ < 5 = g/cm < T − Θ 8 3 2 ∇ . 10 0 × g/cm ∼ m in the spectra of the spectroscopically normal SN 1994D. 2 a DDT transition is quite unlikely (Khokhlov et al. [1997], b 6 A µ 3 ∼ 100 km/s (Lisewski, Hillebrandt & Woosley [2000]). Moreove 10 m has been since detected in the early spectra of many other SN ρ µ ∼ × g/cm 8 3 orders of magnitude smaller than required for a DDT to occur ∼ 05 is the Frank-Kameneetskii factor: m and 1.052 . 0 µ − 04 . 0 ∼ is a numerical coefficient, Θ A Such fluctuacions could be produced by a variety of mechanism One way to favor a deflagration-to-detonation transition in Small-scale simulations are needed to ascertain if the nece , and At densities in excess of 10 improve the match of calculatedthe and surrounding observed accretion light disk curves.below if the T the critical rate accretion for rate steadyHe were burning. Cumming I no et lines al. at [1 2.04 Thermonuclear supernovae region with a level of fluctuations of temperature, density, sufficiently large mass burns before a sonicby wave (Khokhlov can [1991]): cross it T The absorption feature at 1.05 (see Nomoto et al. [2003], Pignata et al [2008]), although it proposed mechanisms of transition, turbulenceKhokhlov, pre-condit Oran & Wheeler [1997] determined the criteria for front of a deflagration wave, shock heating,accumulation mixing of of pressure hot waves ash due tofront, a or topologically transition compl to the distributed burning regime (Nie such as those realized duringa the DDT expansion to of be a feasible, white1-8 the dwarf at turbulent f a velocity lengthscale has comparableflame to to densities exceed in the the the detonation range wave 5 thick where Niemeyer [1999] estimated that the sizethe of critical the densities fluctuations is t see Zingale & Dursi [2007]surface who and pointed facilitate to a bubbles DDT at fragmentat quantity of He, whichvery both small is cap more made reactive ofas and He a might releases result rest more of atop previous of accretioneither the from have been white the accreted companion dwarf directly star at from inhydrogen. t a t Höflich He & star Khokhlov or [1996] result suggested fr the pressence actually reached during a white dwarfsuch studies explosion seem driven to by disfavor a a DDT d inwith view of vortical the robustness flow o (Röpke,velocites Hillebrandt at & the integral Niemeyer scale, [2004]) fo PoS(SUPERNOVA)006 6 02 . g, 0 29 , and the He erformed the pri 10 M × 3 sound crossing time 6 pri M f He with the predominant 6 oosley & Hillebrandt [2007]. g ak et al. [2008]). Even though ernal He layer with the C-O be- al chances to mix with the outer rtunity arises during the convec- cineration of the hot primer but, 25 eyer & Woosley [1997]. We have on in a white dwarf, following a nes if a detonation is successfully rtly before the explosion (Khulen, atano et al. [1999]). An interesting ely in scenarios in which the transi- fects: on the one hand it expanded g), meaning that as the primer mass a thermal profile characterized by a namical and nuclear evolution of a merical experiments, as well as the oosley [1997]. Once the sphere was aracterized by four parameters: the ng a small mass fraction of He. This 10 y that helped keeping a high value io, one cannot discard the possibility er that is prone to detonate in a DDT ermost layers of the white dwarf, the rom magnesium and, possibly, other 29 iation conditions in He-contaminated ode instabilities of the star that would × e dwarf, e.g. those described in Plewa, ermal gradient up to a lagrangian mass K, and remained constant at this value rtunity for mixing He within C-O layers of ashes that destabilize the whole white 10 -O matter (50% each by mass) are given bulence and, especially, Rayleigh-Taylor ucture and hence it is easier to start such a 8 × , while a range has been explored for the , the mass of the primer, K, 3 3 3 ρ − 9 = 10 pri of He might remain hidden this way (Mazzali & 5 × g cm M ⊙ 8 6 . 1 10 6 × 01 M c . 5 T 0 . 1 6 ∼ g) to 0.3 s ( = K 25 ρ 9 10 10 × × 3 0 . = , the uniform sphere density, c pri . In order to limit the dimensionality of the problem we have p T ) M He ( where the temperature went down to 10 X pri 20. For the extreme values of primer mass considered the ball M . 0 6 ) We have explored the effect due to mixing of a small quantity o If it actually exists, the small cap of helium will have sever He ( ranges from 0.01 s ( calculations at a fixed density: increases there is more time for building the detonation str detonation. The detonation initiation conditionsin in pure Table C 1, while our results concerning the detonation init mass fraction, neath it. Hence, even though itthat may He seem is a present speculative in scenar somemodel. small Mixing mass of fraction He within within the a matt tion detonating region to seems detonation more occurs lik in theCalder outermost & layers Lamb of [2004], the Bravo whit & García-Senz [2006] and Röpke, W instability induce large radial excursions ofdwarf huge volumes and can result once more in the mixing of an eventual ext Lucy [1998]). layers of the surrounding C-Otive rich simmering white phase dwarf. that affectsWoosley One most & first of Glatzmaier oppo the [2006], whiteconvection Piro dwarf during & simmering sho is Bildsten not [2008], expectedassociated to Chamul motion reach can the excite out pulsatingfacilitate and diffusion non-spherical of He m into the C-Ois layers. during Another the oppo deflagration phase of the explosion itself. Tur C-O material upon themethodology conditions similar needed to that to of launch Arnettfollowed & a with Livne a detonati [1994] one-dimensional and supernova Niem uniform code density sphere the made hydrody of C-O inthermonuclear equal bomb amounts was containi provided with acentral primer peak consisting temperature in followed by acoordinate constant negative th rest of the parameters: 1 Thermonuclear supernovae this line could rather be due to Mg II (Wheeler et al. [1998], H possibility is that the Heintermediate-mass I elements. line Up is to blended with other lines f for the remaining of thephysics ball. included, were The alike numerical those setup describedallowed of in to these Niemeyer & nu evolve W it wasand subject cooled to due two opposite to competingon the ef excess the pressure other exerted hand, byof ongoing temperature. the reactions sudden Which released in of nuclearlaunched the energ or two not. effects wins The iscentral numerical what temperature, experiments determi are therefore ch X PoS(SUPERNOVA)006 the abso- 3 − g cm K provided that a 8 9 10 mperatures becomes a − 7 sphere makes detonation 7] and Röpke et al. [2007] K. At lower densities (e.g. imer mass for which a det- 9 10 g show an interesting behavior: e to initiate a detonation, while temperature or as the minimum × 27 2 17 19 20 21 23 24 27 mly distributed through the sphere 10 ough the whole sphere a detonation considered two distributions of He 15 19 23 25 28 re as small as 10 ∼ 10 10 10 10 10 10 10 ure the less primer mass is needed to × a th respect to C-O matter). For a 10% pri 10 10 10 10 10 n the range 10 ined at a given density and mass of the t of the detonation initiation conditions 3 × × × × × × × case the role of He is limited to a larger r the density the harder to initiate a det- M × × × × × 5 1 9 9 5 1 5 = ...... pri M K) (g) 6 9 K, for the same primer mass as before. The results 9 C K and ) is raised. Note that in this case the total mass of He 6.2 2 2 5 2 1 5.2 2 2 4 2 2 3.5 2 2.8 2 2.2 2 2 1 1.9 1 2.3 2 T 9 10 ⊙ 10 M × ) (10 7 7 7 7 6 8 8 7 7 7 7 7 ρ 3 8 4 × . − 10 10 10 10 10 10 10 10 10 10 10 10 − 4 . × × × × × . For a 5% He mass fraction the minimum temperature needed 10 5 3 3 2 3 ⊙ × (g cm M 5 . 5 1 − > Summary of detonation initiation conditions in C-O matter 10 × 5 . Table 1: the primer mass necessary to initiate a detonation at such te 3 − g cm 6 Compiled from Arnett & Livne [1994], Niemeyer & Woosley [199 The data in Table 1 can be interpreted either as the minimum pr As shown in Table 2 addition of a small quantity of He to the C-O ) 10 a ( × Thermonuclear supernovae C-O matter are shown in Table 2. onation is initiated intemperature C-O for which matter a at detonation is aprimer. correspondingly Either given obta way, density the and qualitativeonation trend peak is while, that at the fixed smalle density,detonate the the higher sphere. the From peak Table 1 temperat it stems that at densities i 3 lute minimum temperature needed to initiate a detonation is non-negligible fraction of the star mass,becomes hence increasingly achievemen difficult. initiation far easier.within In the our sphere, numerical either constrained experiments torelease we the of primer have nuclear (in this energy with(thus taking respect also to into pure account C-O)He the mass or larger fraction unifor reactivity a of detonation He is wi feasible even at a temperatu obtained with a peak temperature of 1 large enough primer mass ( to achieve a stable detonation rises to 1 needed is just above 1 a 20% mass fraction ofwith He a modest constrained 10% to He the mass primer fraction was uniformly not distributed thr abl PoS(SUPERNOVA)006 istributed through the whole Detonation? tonation is a highly non-linear ommon deflagration phase. This rticle Hydrodynamics supernova c tion can coexist for a while during ich He facilitates the transition to a delayed detonation scenario and the uniform ew three-dimensional simulations of when a DDT is prone to occur is just ditions can have a large impact on the 3 ion is far below that of the supersonic − rather than because of its larger nuclear ns of the white dwarf and ends when the ivity of the results to the spatial locations tional calculations that explore the range g cm 6 10 He-distribution 7 × 5 b . ) He ( 0.05 primer y 0.05 unif. n 0.10 primer y 0.05 primer n 0.10 unif. y 0.20 primer n 0.10 primer n 0.05 primer n 0.02 primer n 0.10 unif. y 0.10 primer y X 29 27 29 29 27 27 27 27 27 25 29 a pri 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × Detonation initiation in C-O matter with traces of He K) (g) 9 Table 2: 1.8 3 1.8 3 1.4 3 1.4 3 1.4 3 1.4 3 1.4 3 1.4 3 1.4 3 1.4 3 (10 T1.0 M 3 In all the calculations the density was 1 sphere Primer: He concentrated in the primer. Unif.: He uniformly d Local He mass fraction All the delayed detonation models presented here start by a c Given the scarcity of three-dimensional simulations of the To conclude this section we remark that the initiation of a de ) ) ) c a b ( ( ( Thermonuclear supernovae code described in Bravo & García-Senz [2008]. phase begins when the first sparks ignitefirst in the detonation central wave regio appears. Boththe modes detonation of phase burning although propaga the efficiency of the deflagrat of the DDT. The simulations were performed with a Smoothed Pa process in which a modest variationevolution. in the The environmental possibility con that He isone present example. mixed with C-O 3. Delayed detonation simulations complexity of the problem, it is interestingof to initial perform addi conditions of thedelayed DDT. detonations In in white this dwarfs aimed section to we test the present sensit n was obtained. This results suggestdetonation that in the C-O main matter reason is because byenergy of wh release. its larger reactivity PoS(SUPERNOVA)006 . 3 ∼ − . eously 3 cm and g cm − cm were 7 8 8 10 10 10 g cm × ∼ 7 × cm were instan- 7 55 s the average . to . 8 8 10 . 1 3 s approximately 10 − × = 4 × t 3 ∼ . g cm 6 cm and 2 10 8 than 1 with the results from Gamezo × khar-mass white dwarf in me- 10 the detonation. 7 s within radii 1 her than Fe (after radioactive decay) and nergy generation went up steeply he DDT we used alternative pre- × ruding towards the center. As the ge volume within the white dwarf, 56 ∼ n phase. There were several detona- was switched off once a DDT was e Fe-group nuclei are nearly absent 4 ashes from the previous deflagration detonation was formed. Because the leading to a temperature distribution warf, especially too much radioactive . n of the shortcomings of the previous ribed subsonic velocity during the de- emained nearly spherical. Afterwards, ature of the model is that the ashes are yers synthesized intermediate-mass el- mpatible with, but on the low side of, close to the center. However, there are es, the rate of released nuclear energy ter synthesized additional quantities of y obtained in pure deflagration models. to be induced: or regime, encompassing a large fraction ity developed very quickly, which resulted 9 s the burning front displayed the mushroom- . 0 , and the deflagration algorithm was inefficient to 8 3 = − was achieved at t=1.1 s. At t 1 − g cm 7 erg s 10 51 × 10 × 0 the particles contained in a central volume were instantan 3 . = t . 3 − cm were instantaneously incinerated. Their mean density wa 8 g cm 7 10 10 × 0 × . taneously incinerated. The density in these regions was hig Core detonation. All flame particles whose radius were lower Mid-altitude detonation. In this variant all flame particle 2 Atmospheric detonation. All flame particles within 2 2 instantaneously incinerated. Their densities ranged from The initial conditions were that of an isothermal Chandrase To explore the sensitivity of the results to the location of t In either case, after a transient induction period, a stable The results of the simulations are given in Table 3, together • • • Ni, whereas detonations traveling through lower density la Ni. Moreover, the ejecta is not chemically stratified. Stabl artificially induced. Thermonuclear supernovae detonation. In our computations the deflagration algorithm chanical equilibrium. At like shape characteristic of theof non-linear the Rayleigh-Tayl white dwarf mass.until As a a maximum consequence value the of rate of 1 nuclear e incinerated, from this time on theflagration flame phase. propagated at During a the first presc half secondthe the fingers flame characteristic front r of the Rayleigh-Taylorin instabil hot material rising andflame surface cool increased unburnt due carbon to andand the the oxygen hydrodynamic effective int burning instabiliti velocity also did. At flame density was on the order of 2 scriptions to select the particles in which a detonation had propagate the flame. We took this moment as the time of onset of detonation was initiated in athere more followed or a less period uniform of waymuch rapid in more and homogeneous a generalized than lar combustion that of thetion preceding fronts deflagratio cut off from eachphase. other Those because detonation of fronts the56 propagating presence close of to the cen ements. In this way, the DDT alloweddeflagration the stage, partial giving compensatio an improved explosion model. et al. [2005] for comparison purposes. The total amount of intermediate-mass elements ejected in thethe explosion range allowed are by co SNIa observations.not Another concentrated positive in fe large clumps, contraryIn to addition, what there is remains usuall little unburnttoo carbon many Fe-group and elements oxygen close to56 the surface of the white d PoS(SUPERNOVA)006 . 1 Ni ities 56 15 M ∆ max M ) (mag) (mag) 5], our models kinetic ⊙ CO M M lometric light curves of our . The maximum luminosities ) ( kinetic energies that change by 15 ⊙ n Bravo et al. [1993]. The last de and the decline in bolometric ime SNIa, but are still comparable to , together with observational data M M Gamezo et al. assume the DDT to ch the requirements from infrared r models show that the outcome of performed in Fig. 1, where we plot M 15 ∆ 15 foes, whereas the range of -altitude detonations are too broad he effect of the spatial location of the s of the 3D explosion models. The M [2007], Fesen et al.. [2007]). ns were performed in one dimension, t usually achieved in one-dimensional nation model fit nicely with the obser- oup nuclei synthesized is similar. This ) ( upernova explosions obtained with the ∆ ⊙ 56 (Badenes et al. [2003, 2005]). s elements, as a result of a different time l as the atmospheric detonation model, see Röpke M M ⊙ ) ( ⊙ NSE 9 M erg) ( Ni synthesized and K M 1.1 0.94 0.8 0.73 0.8 0.78 56 51 0.33 0.59 0.34 0.09 0.57 -18.54 0.95 0.51 0.69 0.42 0.14 0.45 -18.76 0.66 0.48 0.71 0.43 0.10 0.48 -18.63 0.57 . By contrast, one-dimensional models with transition dens (10 ⊙ Results of 3D delayed detonation simulations a b b Table 3: a b a Ni masses ranging from 0.38 to 0.97 M 56 This work Gamezo et al. [2005] The most energetic 3D deflagration models are able to fit as wel Compared to the 3D DDT models calculated by Gamezo et al. [200 In Table 3 we give as well the results of the calculations of bo Atmospheric detonation Core detonation Mid-altitude detonation Central high-density DDT Off-center DDT Central DDT Model ) ) 1 b a ( ( achieved by our models arenormal small or compared peculiar with underluminous normal SNIa. bright Suchthe a relationship comparison between is the mass of obtained by Stritzinger et al.vational [2006]. data, The whereas atmospheric the deto light curve of the central and mid Thermonuclear supernovae et al. [2007] energy is substantially lower, although thepoints amount to of a Fe-gr quite different productionof of induction intermediate-mas of the DDToccur in at both a classes higher of density models. thanDDT, in In both our general, Gamezo models. et With respect al. tothe models t (central explosion vs is off-center) not and quite ou different sensitive prescriptions to used it. for the The DDTdelayed diversity is of detonations. not s as The rich as kinetic tha energy varies at most in 0. from the low velocity layers of the ejecta, which does not mat observations of SNIa (Motohara et al. [2006], Gerardy et al. masses spans from 0.34 to 0.43 M 3D delayed detonation models. Theseassuming light spherical curve symmetry, calculatio frommethod angle-averaged followed version to calculatetwo the columns light of curve the table wasmagnitude give the during the same maximum the bolometric as first magnitu i 15 days following the maximum, in the same range as0.34 foes we and have explored produce explosions with PoS(SUPERNOVA)006 1.5 1.4 Ni mass and kinetic 1.3 56 els is the chemical profile 1.2 ions of white dwarfs, current lements in the outer layers of the , their larger f undetected lines of C, an incorrect tual light curve calculations of their . [2008]) did isolate several deficien- are easily reproduced by current 3D that would put them out of the trend ic magnitude after maximum than our ypically consist of a smooth, central, 1.1 15 l properties has to be considered as very . The few one-dimensional spectral calcu- M ∆ elayed detonation models 1 Delta M_15 10 . Crosses are data for a sample of well observed SNIa from Ni synthesized in SNIa explosions and the decrease in bolo- 0.9 15 56 M ∆ 0.8 0.7 0.6 Relationship between the mass of 0.5 0

0.1 0.3 0.2 0.6 0.5 0.4 0.8 0.7 0.9

In spite of recent advances in 3D modeling of delayed detonat One of the most interesting questions concerning 3D SNIa mod M(56Ni) metric magnitude 15 days after maximum, Figure 1: Thermonuclear supernovae Stritzinger et al. [2006], circles belong to the present 3D d With respect to the models from Gamezo et al. [2005] in Table 1 of observational data in Fig.models, 1. any However, conclusion in about the their absence predictedspeculative. of observationa ac 4. Conclusions models are still far from passing basic observational tests lations from angle-averaged 3D SNIa models (e.g. Baron et al energy is expected to imply adelayed faster decrease detonation of models, the bolometr hence a smaller value of cies when compared to observed SNIashape spectra: of the formation the o S lines,ejecta. and On an the excessive abundance othermodels of hand, of Fe-group observed SNIa. e bolometric light curves of the ejecta. 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