An asymmetric explosion as the origin of spectral evolution diversity in type Ia supernovae
K. Maeda, S. Benetti, M. Stritzinger, F.K. Roepke, G. Folatelli, J. Sollerman, S. Taubenberger, K. Nomoto, G. Leloudas, M. Hamuy, M. Tanaka, P.A. Mazzali, N. Elias-Rosa
aa r X i v : . [ a s t r o - ph . C O ] J un An asymmetric explosion as the origin of spectralevolution diversity in type Ia Supernovae
K. Maeda , S. Benetti , M. Stritzinger , , F. K. R¨opke , G. Folatelli , J. Sollerman , ,S. Taubenberger , K. Nomoto , G. Leloudas , M. Hamuy , M. Tanaka , P. A. Mazzali , ,N. Elias-Rosa Published in Nature, 1 July 2010 issue. Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, 5-1-5Kashiwanoha,Kashiwa,Chiba277-8583,Japan: [email protected]. INAF-OsservatorioAstronomicodiPadova,vicolodell’Osservatorio5, I-35122Padova,Italy. CarnegieInstituteforScience,LasCampanasObservatory,ColinaelPinoCasilla601,LaSerena,Chile. Dark Cosmology Centre, Niels Bohr Institute, Copenhagen University, Juliane Maries Vej 30,2100Copenhagen Ø, Denmark. Max-Planck-Institutf¨urAstrophysik,Karl-Schwarzschild-Straße 1, 85741Garching,Germany. UniversidaddeChile, DepartamentodeAstronom´ıa,Casilla36-D, Santiago,Chile. The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, 10691Stockholm,Sweden. Scuola NormaleSuperiore, Piazza Cavalieri 7,56127Pisa, Italy. Spitzer Science Center, California Institute of Technology, 1200 E. California Blvd., Pasadena,CA 91125,USA. 1 ype Ia Supernovae (SNe Ia) form an observationally uniform class of stellar explosions, inthat more luminous objects have smaller decline-rates . This one-parameter behavior al-lows SNe Ia to be calibrated as cosmological ‘standard candles’, and led to the discoveryof an accelerating Universe , . Recent investigations, however, have revealed that the truenature of SNe Ia is more complicated. Theoretically, it has been suggested − that the ini-tial thermonuclear sparks are ignited at an offset from the centre of the white-dwarf (WD)progenitor, possibly as a result of convection before the explosion . Observationally, the di-versity seen in the spectral evolution of SNe Ia beyond the luminosity decline-rate relation isan unresolved issue , . Here we report that the spectral diversity is a consequence of ran-dom directions from which an asymmetric explosion is viewed. Our findings suggest that thespectral evolution diversity is no longer a concern in using SNe Ia as cosmological standardcandles. Furthermore, this indicates that ignition at an offset from the centre of is a genericfeature of SNe Ia. ∼ . M ⊙ ), its central density and temperature increase to a point where a thermonuclear runawayis initiated. The thermonuclear sparks give birth to a subsonic deflagration flame, which at somepoint may make a transition to a supersonic detonation wave that leads to the complete disruptionof the WD , . The thermalization of γ -rays produced from the decay of freshly synthesizedradioactive Ni powers the transient source, known as a SN Ia , . The relationship between theluminosity and the decline-rate parameter ( ∆ m ( B ) , which is the difference between the B -bandmagnitude at peak and that measured 15 days later) is interpreted to be linked to the amount ofnewly synthesized Ni (refs. 15, 16).SNe Ia displaying a nearly identical photometric evolution can exhibit appreciably differentexpansion velocity gradients ( ˙ v Si ) as inferred from the Si II λ , . Morespecifically, objects that show ˙ v Si ∼ >
70 km s − day − are placed into the high-velocity gradient(HVG) group, while those that show smaller gradients are placed in the low-velocity gradient(LVG) group. For normal SNe Ia , which are the predominant population of the total SN Iasample and the main focus of this Letter , ˙ v Si is not correlated with ∆ m ( B ) (ref. 10; Fig. 1a, 1b),thus raising a nagging concern regarding the ‘one-parameter’ description.Late phase nebular spectra can be used to trace the distribution of the inner ejecta . Begin-ning roughly half a year after explosion, as the ejecta expands, its density decreases to the pointwhere photons freely escape. Photons originating from the near/far side of the ejecta are detectedat a shorter/longer (blue-shifted/red-shifted) wavelength because of Doppler shifts. For SNe Ia,3mission lines related to [Fe II] λ λ . These lines show diversity in their central wavelengths– blue-shifted in some SNe Ia and red-shifted in others (see Fig. 1c) – which provides evidencethat the deflagration ashes, therefore the initial sparks, are on average located off-centre. Thewavelength shift can be translated to a line-of-sight velocity ( v neb ) of the deflagration ashes.Figure 2 shows a comparison between ˙ v Si and v neb for 20 SNe Ia. Details regarding the dataare provided in SI §
1. Although the diversities in these observables were discovered independently,Fig. 2 clearly shows that they are connected. Omitting the peculiar SN 2004dt (Fig. 2 Legend; SI § v neb > km s − (i.e., red-shifts), which means that these events areviewed from the direction opposite to the off-centre initial sparks. The 11 LVGs display a widerdistribution in v neb space, but are concentrated to negative values (i.e., blue-shifted), indicating thatthese events are preferentially viewed from the direction of the initial sparks. If HVG and LVGSNe were intrinsically distributed homogeneously as a function of v neb , the probability that just bychance (as a statistical fluctuation) all HVG SNe show v neb > km s − is merely 0.4%; it is thusquite unlikely. Indeed, the probability that by chance 6 HVG SNe are among the 7 SNe showingthe largest red-shift in v neb in our sample of 17 SNe is only 0.06%.This finding strongly indicates that HVG and LVG SNe do not have intrinsic differences, butthat this diversity arises solely from a viewing angle effect. Figure 3 shows a schematic picture.If viewed from the direction of the off-centre initial sparks, an SN Ia appears as an LVG event atearly phases and shows blue-shifts in the late-time emission-lines. If viewed from the opposite4irection, it appears as an HVG event, and shows red-shifts at late phases.The number of HVG SNe is ∼ % of the total number of HVG and LVG SNe. To explainthis, the angle to the observer at which an SN changes its appearance from an LVG to an HVGis ∼ − ◦ , measured relative to the direction between the centre and the initial sparks.The velocity shift of , km s − in the distribution of the deflagration ashes, as derived for thenormal SN Ia 2003hv through a detailed spectral analysis , corresponds to v neb ∼ km s − ifviewed from this transition angle. The configuration then predicts that all LVG SNe should show − , < v neb < km s − , while all HVG SNe should be in the range < v neb < , km s − . These ranges are shown as arrows in Fig. 2, and provide a good match to the observations.Figure 4a shows an example of a hydrodynamic model in which the thermonuclear sparkswere ignited off-centre in a Chandrasekhar-mass WD (an alternative way of introducing globalasymmetries is double detonations in sub-Chandrasekhar-mass WDs ). Although this model hasnot been fine-tuned to reproduce the present finding, it does have the required generic features. Thedensity distribution is shallow and extends to high velocity in the direction opposite to the initialsparks (Fig. 4b). Initially, the photosphere is at high velocity if viewed from this direction, as theregion at the outer, highest velocities is still opaque. Later on, the photosphere recedes inwardsfaster in this opposite direction, owing to the shallower density gradient. As a result, the SN lookslike an LVG if viewed from the offset direction, but like an HVG SN from the opposite direction(Fig. 4c), as in our proposed picture (Fig. 3).Our finding provides not only strong support for the asymmetric explosion as a generic fea-5ure, but also constraints on the still-debated deflagration-to-detonation transition. In this particularsimulation, the change in appearance (as an HVG or an LVG SN) takes place rather abruptly aroundthe viewing direction of ∼ ◦ . Owing to the offset ignition, the deflagration flame propagatesasymmetrically and forms an off-centre, shell-like region of high density deflagration ash. The det-onation is ignited at an offset following the deflagration, but tries to expand almost isotropically.However, the angle between ◦ and ◦ is covered by the deflagration ash, into which the strongdetonation wave (fueled by the unburned material near the centre of the WD) cannot penetrate. Onthe other hand, in the − ◦ direction, the detonation can expand freely, creating a shallowdensity distribution. The ‘abrupt’ change in appearance, as inferred by the observational data, istherefore a direct consequence of the offset models, controlled by the distribution of the deflagra-tion ash. The ‘opening angle’ of the transition is on the other hand dependent on the details ofthe explosion. To accurately model this according to our finding ( ∼ − ◦ for the typicaltransition angle), either a smaller offset of the initial deflagration sparks or an earlier deflagration-to-detonation transition would be necessary. Such changes are also required to produce the typicalvelocity shift of ∼ , km s − in the distribution of the deflagration ash.Our proposed model unifies into a single scheme recent advances in both theoretical andobservational studies of SNe Ia - and it does not conflict with other results produced by spectraltomography , or polarization measurements (SI § Ni. They might in fact show somewhat different light curve evolution if viewed from the samedirection (relative to the offset between the centre and the initial sparks), but the light curves look6he same to an observer as ∆ m ( B ) can change with viewing direction (SI § Ni productionand in the viewing angles. Our finding regarding the explosion mechanism will lead to quantitativeevaluation on the contribution of this random effect to the observed scatter in the SN Ia luminositiesbeyond the one-parameter description , as compared to other systematic effects, such as the stellarenvironment .1. Phillips, M. M., et al., The Reddening-Free Decline Rate Versus Luminosity Relationship forType Ia Supernovae, Astron. J., , 1766-1776 (1999)2. Permutter, S., et al., Measurements of Ω and Λ from 42 High-Redshift Supernovae, Astrophys.J., , 565-586 (1999)3. Riess, A., et al., Observational Evidence from Supernovae for an Accelerating Universe and aCosmological Constant, Astron. J., , 1009-1038 (1998)4. Kuhlen, M., Woosley, S. E., & Glatzmaier, G. A., Carbon Ignition in Type Ia Supernovae. II.A Three-dimensional Numerical Model, Astrophys. J., , 407-416 (2006)5. Kasen, D., R¨opke, F. K., & Woosley, S. E., The Diversity of Type Ia Supernovae from BrokenSymmetries, Nature, , 869-872 (2009)6. Maeda, K., et al., Nucleosynthesis in Two-Dimensional Delayed Detonation Models of TypeIa Supernova Explosions, Astrophys. J., , 624-638 (2010)7. R¨opke, F. K., Woosley, S. E., & Hillebrandt, W., Off-Center Ignition in Type Ia Supernovae.I. Initial Evolution and Implications for Delayed Detonation, Astrophys. J., , 1344-1356(2007)8. Jordan, G. C., et al., Three-Dimensional Simulations of the Deflagration Phase of the Gravi-tationally Confined Detonation Model of Type Ia Supernovae, Astrophys. J., , 1448-1457(2008)9. Branch, D., Drucker, W., & Jeffery, D. J., Differences among Expansion Velocities of Type IaSupernovae, Astrophys. J., , L117-L118 (1988)10. Benetti, S., et al., The Diversity of Type Ia Supernovae: Evidence for Systematics?, Astrophys.J., , 1011-1016 (2005)11. Khokhlov, A. M., Delayed Detonation Model for Type Ia Supernovae, Astron. Astrophys. ,114-128 (1991)12. Iwamoto, K., et al., Nucleosynthesis in Chandrasekhar Mass Models for Type Ia Supernovaeand Constraints on Progenitor Systems and Burning-Front Propagation, Astrophys. J. Suppl. , 439-462 (1999)13. Nomoto, K., Thielemann, F.-K., & Yokoi, K., Accreting White Dwarf Models of Type I Su-pernovae. III - Carbon Deflagration Supernovae, Astrophys. J., , 644-658 (1984)14. Woosley, S. E., & Weaver, T. A., The Physics of Supernova Explosions, Ann. Rev. Astron.Astrophys., , 205-253 (1986) 85. H¨oflich, P., et al., Maximum Brightness and Postmaximum Decline of Light Curves of Type IaSupernovae: A Comparison of Theory and Observations, Astrophys. J., , L81-L84 (1996)16. Mazzali, P. A., R¨opke, F. K., Benetti, S., & Hillebrandt, W., A Common Explosion Mechanismfor Type Ia Supernovae, Science, , 825-828 (2007)17. Benetti, S., et al., Supernova 2002bo: Inadequacy of The Single Parameter Description, Mon.Not. R. Astron. Soc., , 261-278 (2004)18. Branch, D., Fisher, A., & Nugent, P., On The Relative Frequencies of Spectroscopically Nor-mal and Peculiar Type Ia Supernovae, Astron. J., , 2383-2391 (1993)19. Maeda, K., et al., Nebular Spectra and Explosion Asymmetry of Type Ia Supernovae, Astro-phys. J., , 1703-1715 (2010)20. Fink, M., R¨opke, F. K., Hillebrandt, W., Seitenzahl, I. R., Sim, S. A., & Kromer, M., Double-Detonation Sub-Chandrasekhar Supernovae: Can Minimum Helium Shell Masses DetonateThe Core?, Astron. Astrophys., , 53-62 (2010)21. Stehle, M., Mazzali, P.A., Benetti, S., & Hillebrandt, W., Abundance Stratification in Type IaSupernovae - I. The Case for SN 2002bo, Mon. Not. R. Astron. Soc., , 1231-1243 (2005)22. Wang, L., Baade, D., & Patat, F., Spectropolarimetric Diagnostics of Thermonuclear Super-nova Explosions, Science, , 212-214 (2007)23. Neill, J. D., et al., The Local Hosts of Type Ia Supernovae, Astrophys. J., , 1449-1465(2009) 94. Jha, S., et al., The Type Ia Supernova 1998bu in M96 and The Hubble Constant, Astrophys. J.Suppl., , 73-97 (1999)25. Cappellaro, E., et al., Detection of a Light Echo from SN 1998bu, Astrophys. J., , L215-L218 (2001)26. Filippenko, A. V., et al., The Subluminous, Spectroscopically Peculiar Type Ia Supernova1991bg in The Elliptical Galaxy NGC 4374, Astron. J., , 1543-1556 (1992)27. Turatto, M., et al., The Properties of The Peculiar Type Ia Supernova 1991bg. I. Analysis andDiscussion of Two Years of Observations, Mon. Not. R. Astron. Sco., , 1-17 (1996)28. Morrell, N., Folatelli, G., & Stritzinger, M., Supernova 2007on In NGC 1404, CBET, (2007)29. Altavilla, G., et al., The Early Spectral Evolution of SN 2004dt, Astron. Astrophys., ,585-595 (2007)30. Wang, X., et al., Improved Distances to Type Ia Supernovae with Two Spectroscopic Sub-classes, Astrophys. J., , L139-L143 (2009) Acknowledgements
The authors thank Wolfgang Hillebrandt for discussions. This study is partly basedon observations obtained at the Gemini Observatory, Chile (GS-2009B-Q-8, GS-2008B-Q-32/40/46), theMagellan Telescopes, Chile, and by ESO Telescopes at the La Silla or Paranal Observatories under pro-gramme 080.A-0516. This research made use of the
SUSPECT archive, at the Department of Physics andAstronomy, University of Oklahoma. This work was supported by World Premier International Research enter Initiative (WPI Initiative), MEXT, Japan. K. M. was supported by JSPS Grant-in-Aid for young sci-entists. S.B. acknowledges partial support from ASI contracts ‘COFIS’. M.S. was supported by the NationalScience Foundation. F.K.R. was supported through the Emmy Noether Program of the German ResearchFoundation and by the Cluster of Excellence ‘Origin and Structure of the Universe’. G.F. and M.H. acknowl-edge support from Iniciativa Cientifica Milenio and CONICYT programs FONDECYT/FONDAP/BASAL.J.S. is a Royal Swedish Academy of Sciences Research Fellow supported by the Knut and Alice Wallen-berg Foundation. S.T. acknowledges support by the Transregional Collaborative Research Centre under theprogramme ‘The Dark Universe’. The Dark Cosmology Centre is funded by the Danish National ResearchFoundation. Author Contributions
S.B. and K.M. found the relation between the velocity gradient and the nebular ve-locity, initiated and organized the project. K.M. wrote the manuscript with the assistance of M.S., J.S., G.F.,and S.T. S.B. is responsible for the late-phase spectrum of SNe 1997bp. M.S., G.F., and M.H are responsiblefor acquisition and reduction of SNe 2007on, 2007sr, and 2009ab. F.K.R. and K.M. are responsible for theexplosion simulation. All the authors contributed to discussions.
Competing Interests
The authors declare that they have no competing financial interests.
Correspondence
Correspondence and requests for materials should be addressed to K.M. (email:[email protected]). igure 1
Comparison between HVG SN Ia 2002bo and LVG SN Ia 1998bu.
Thedecline-rate parameter ∆ m ( B ) is . and . mag for SNe 2002bo and 1998bu, re-spectively. a. The B -band light curves , . The magnitudes for SN 1998bu have beenartificially shifted in the y -direction for presentation. b. Si II λ , (in days with respect to B -band maximum). SN 2002bo had initially a larger absorptionvelocity than SN 1998bu, but later its velocity approached that of SN 1998bu. The velocityevolved quicker and the velocity gradient ( ˙ v Si ) is larger for SN 2002bo than for SN 1998bu. c. [Fe II] λ and [Ni II] λ in late-time spectra , . The horizontal axis denotes theline velocity measured from the rest wavelength of [Ni II] λ λ λ v neb ) ( v neb < km s − , i.e., the blue-shift, if thematerial is moving toward us). These are the strongest lines among those emitted fromthe deflagration ash according to the previous analysis of late-time emission lines . In-deed, there are stronger lines which do not show Doppler shifts, e.g., [Fe III] λ (see also SI §
1) and arethus not useful in the present study. igure 2 Relations between the features in early- and late-phases. a.
Early-phasevelocity gradient ( ˙ v Si : vertical axis) as compared to late-phase emission-line shift velocity( v neb : horizontal axis) for 20 SNe Ia. The errors are for σ in fitting the velocity evolutionfor ˙ v Si , while for v neb the errors are from differences in measurement between differentemission lines (see Sup § − (black open circles). SN 2004dt (orange square) is an HVG SNaccording to the value of ˙ v Si , but displayed peculiarities in the late-time spectrum (SI § (SI § ˙ v Si is exceptionally large s compared to other HVG SNe. These suggest that SN 2004dt is an outlier and theorigin of its large ˙ v Si is probably different from that of other SNe Ia. The two arrowson top indicate the regions where HVG and LVG SNe are expected, based on a simplekinematic interpretation (see main text). b. Number distribution of 20 SNe as a functionof ˙ v Si . White and orange areas are for faint SNe and SN 2004dt. The remaining SNeare marked depending on whether they show a blue-shift ( v neb < km s − : blue area) orred-shift ( v neb > km s − : red area) in their late-time spectra. c. Number distribution of20 SNe as a function of v neb . igure 3 A schematic picture of the structure of SN Ia ejecta.
This configurationsimultaneously explains the relative fractions of HVG and LVG SNe Ia, and the relationbetween ˙ v Si and v neb . It is also consistent with the diversity in v neb (ref. 19). The ashesof the initial deflagration sparks are shifted with respect to the center of the SN ejecta by ∼ , km s − (yellow: Although expressed by a spherical region for presentation, it maywell have an amorphous shape owing to the hydrodynamic instability in the deflagrationflame ). This region is rich in stable Ni with a small amount of radioactive Ni, and emits[Fe II] λ λ (SI § λ he deflagration ashes (cyan). Although the detonation can produce Ni which decaysinto Fe, it has been argued that these regions (blue and cyan) are not main contribu-tors to [Fe II] λ λ (SI § ∼ − ◦ . This angle is derived from therelative numbers of HVG and LVG SNe (see main text); the fraction of HVG SNe to thetotal number of HVG and LVG SNe ∼ % (ref. 10), as was also supported by a largersample with more than 100 SNe (using the observed trend that the HVG SNe showhigher velocities than LVG objects at early times). igure 4 Expectations from a hydrodynamic explosion model. a.
Cross section of thedensity distribution of an offset ignition model (similar to a model in ref. 5). It is shown t 10 seconds after the ignition, when the homologous expansion is already reached. Inthis model, the deflagration sparks were ignited offset, within an opening angle of 45 ◦ and between − km from the centre of a WD whose radius is ∼ , km. Thedeflagration products are distributed in the high-density offset shell, which covers − ◦ in this particular model. This resulting velocity shift is ∼ , km s − in this model,which is larger than the observational requirement ( ∼ , km s − ). b. Radial densitydistribution of the same model for several directions (where the angle is measured fromthe direction of the offset sparks). The magenta lines show the density distribution for theangle in − ◦ , roughly corresponding to the putative directions for which a SN lookslike an HVG SN inferred from the observational data (Fig. 3). Also shown is the densitydistribution multiplied by the mass fraction of Intermediate mass elements, which gives arough distribution of Si, for two directions ( − ◦ and − ◦ ). It is seen that thedistribution of Si roughly follows the density distribution. c. Model photospheric velocityevolution for several directions (lines) as compared to the observed Si II λ (filled and open symbols for HVG and LVG SNe, respectively; the phasein days with respect to B -band maximum). The position of the photosphere is estimatedby integrating the optical depth with a constant opacity along each direction. Using the Sidistribution for the velocity estimate provides a similar result. upplementary Information Supplementary Table 1 summarizes the data of the SNe used in the present study. Thevalues of the velocity gradients ( ˙ v Si ) are obtained from the literature when available. Theyare mostly drawn from a previous compilation (see Supplementary Tab. 1 for the sourcesof the observations), with values for additional SNe obtained from the references listedin Supplementary Table 1. For SN 1998aq, we have measured ˙ v Si from the publishedspectra .The line-of-sight velocity of the deflagration ash is derived as follows. Late-timespectra of SNe Ia show various forbidden lines from Fe-peak elements. These lines canbe divided into two groups. The first group requires intense heating from radioactive Ni → Co → Fe decays and low material density (e.g., [Fe III] λ λ λ , the former lines areargued to be preferentially emitted from the detonation ash (because it is at relatively lowdensity with a large amount of Ni), while the latter lines are formed in the deflagration ash(because it is at high density with a small amount of Ni). These two groups of lines showmutually different properties in observations, strengthening the interpretation that they areemitted from different regions: The ‘deflagration ash’-lines show the diversity in Doppler hift (not only in [Fe II] λ λ , ), while the ‘detonation ash’-lines showvirtually no Doppler shifts. This property led to the conclusion that the deflagration ash ison average located offset, while the detonation ash is distributed roughly spherically .For v neb (the line-of-sight velocity of the deflagration ash), we have therefore mea-sured the wavelength shift in [Ni II] λ λ v neb as themean value of them (see Supplementary Tab. 1 for the source of the observational data).The error bars are taken to be the difference in the measurements for the two lines. Inall SNe except for SN 2004dt, the difference in these two measurements is at most km s − . For SNe Ia in which either of [Fe II] λ λ v neb only from the other single line, with a conservative error of km s − . For SNe 2007on, 2007sr, and 2009ab, we have measured ˙ v Si and v neb from ourown spectra taken at the Gemini South, the Magellan, and the ESO (La Silla, Paranal)telescopes. The late-time spectrum of SNe 1997bp has also been obtained by us andused to measure v neb . The 20 SNe in Supplementary Table 1 are all the objects we havefound for which both ˙ v Si and v neb are reliably available to date. Also shown in the table arethe light-curve decline-rate parameters ∆ m ( B ) .Supplementary Table 1 also lists the epoch (after B -band maximum) of the late-timespectra from which v neb is measured. For most of the SNe Ia, it is at least 200 daysafter B -band maximum, and thus errors caused by the blending of additional lines to thisfeature (e.g., permitted lines emitted at relatively early phases) in measuring v neb can be voided. The features at ∼ , − , ˚A, which we interpret to be dominated by [FeII] λ λ ∼ > − days after B -band maximum .It has been shown that normal SNe Ia (which constitute ∼ > % of the whole SN Iapopulation), faint 1991-bg like SNe Ia , and bright 1991T-like SNe Ia , show differ-ent properties in ˙ v Si10 . Normal SNe Ia show a diversity in ˙ v Si , which is apparently not correlated with ∆ m ( B ) . Faint 1991bg-like SNe Ia, which are characterized by a rapidfading (i.e., large ∆ m ( B ) ), always show large ˙ v Si . Bright 1991T-like SNe Ia with small ∆ m ( B ) always show small ˙ v Si . In deriving v neb , we have noticed that the identification of[Fe II] λ λ λ . Bright1991T-like SNe Ia tend to show a broad single peak, possibly indicating that [Fe II] λ λ ∆ m ( B ) description, which is a problem only in normal SNe Ia.For normal SNe Ia, we categorize HVG SNe and LVG SNe according to ˙ v Si , with the ivision line at km s − day − . According to its ˙ v Si , SN 2004dt is an HVG. However,its peculiar observational features suggest that it is an outlier, and the origins of its highvelocity gradient and the negative v neb are likely different than the one for other HVGs(see Fig. 2 caption). One of the peculiar features of SN 2004dt appears in its late-timespectra. Supplementary Fig. 1 shows a late-time spectrum of SN 2004dt compared tothe prototypical faint SN 1991bg and to the normal HVG SN 2007sr. The spectrum ofSN 2004dt provides a good match to that of the faint SN 1991bg. Both the intensity andthe width of the lines at ∼ , − , ˚A are similar for these two SNe. In normalHVG SN 2007sr, the features at , − , ˚A are much fainter than for SNe 2004dt and1991bg. This indicates that in the case of SN 2004dt the feature is probably contaminatedby other lines, most likely [Ca II] λλ v neb than the other SNe Ia). In addition, the strongest lines at late phases, i.e., the[Fe III] blend at ∼ , ˚A and the [Fe II] and [Fe III] blend at ∼ , ˚A have similar ratiosin SN 2004dt and 1991bg; these ratios have been noticed to be peculiar . The normalHVG SN 2007sr has broader lines, and different line ratios. These similarities betweenthe ‘normal’ SN 2004dt and the faint SN 1991bg at late phases, which have not beennoticed previously, suggest that these explosions might be closely related to one another.SN 2004dt may represent a new class of SNe Ia which have SN 1991bg-like features inthe late-time spectrum, but are more energetic and brighter. upplementary Table 1: Supernovae SampleSN ∆ m ( B ) ˙ v Si v neb Epoch Class , References(km s − day − ) (km s − ) (day)1986G . ± .
07 64 ± − ±
257 HVG/Faint 1, 31, 321990N . ± .
05 41 ± − ±
280 LVG 1, 10, 33, 341994D . ± .
05 39 ± − ±
306 LVG 1, 34, 351997bp . ± . ± ±
300 HVG 10, 361998aq . ± .
05 35 ± − ±
241 LVG 37, 381998bu . ± .
05 10 ± − ±
329 LVG 1, 10, 24, 25, 392000cx . ± .
04 2 ± − ±
147 LVG/peculiar 40-432001el . ± .
04 31 ± ±
398 LVG 44-462002bo . ± .
06 110 ± ±
368 HVG 17, 212002dj . ± .
05 86 ± ±
275 HVG 472002er . ± .
03 92 ± ±
216 HVG 48, 492003du . ± .
05 31 ± − ±
377 LVG 50, 512003hv . ± .
02 41 ± − ±
320 LVG 522004dt . ± .
05 160 ± − ±
152 HVG/peculiar 292004eo . ± .
04 45 ± ±
228 LVG 53, 542005cf . ± .
03 35 ± ±
267 LVG 55-582006X . ± .
05 123 ±
10 1280 ±
277 HVG 592007on . ± .
01 85 ± ±
356 HVG/Faint This work2007sr . ± .
02 80 ±
15 1910 ±
256 HVG 602009ab . ± .
02 36 ± − ±
278 LVG This work Other Observational Constraints
In abundance ‘tomography’ , , − , a temporal sequence of spectra of individual SNe Iaare used to infer the distribution of different elements through the SN ejecta, assuming thedensity structure of a spherically symmetric explosion model . From this type of analysis,it has been indicated that the abundance distribution is generally a function of ∆ m ( B ) .The difference between the HVG and LVG SNe, not related to ∆ m ( B ) , is mainly on theextent of the Si-rich layer and on the photospheric velocity , which are explained by ourproposed scenario (main text).On the other hand, the spatial extent of the Ni-rich region does not seem to bedependent on whether it is a HVG or a LVG SN . This could provide a constraint onthe ejecta asymmetry. In the offset explosion model, the spatial extent of the Ni region,as well as the density structure at the outer edge of that region, are not sensitive to thedirection, despite the initially large asymmetry in the ignition . This stems from the natureof the propagation of the detonation wave as described in the main text; unlike the defla-gration flame, the detonation tries to expand isotropically, producing roughly sphericallydistributed Ni. This region is not sensitively affected by the existence of the deflagrationashes, which is essential in determining the structure of Si-rich region. As a result, thespatial extent of the Ni-rich region is mainly controlled by the different amounts of Niproduced in the explosion, and the viewing angle dependence could add some diversityat most as a secondary effect ; this is consistent with the observational indications . he asymmetric distribution of the outermost layer may imprint its signature in po-larization measurements, which may be linked to the velocity gradient . The polariza-tion of the Si II line is correlated with ∆ m ( B ) , but only for LVG SNe (SupplementaryFig. 2). HVG SNe generally show larger polarization than LVG SNe , but they clearlydo not follow this trend. A global one-sided asymmetry as in the present interpretationwould produce relatively low continuum polarization and relatively high line polarization atSi II λ . In our proposed scenario the global asymmetry is of smaller degree than inan extremely asymmetric model producing Si II polarization of ∼ % , thus this is likelynot a major contributor to the observed polarization. Alternatively, it has been suggested,based on the correlation between the Si II polarization and ∆ m ( B ) , that the observedSi II polarization could be a measure of the thickness of the outer layer above the Ni-richregion, in which the local inhomogeneity, e.g., a few relatively dense blobs, is assumed tobe a source of polarization. In this interpretation, the large Si II polarization in HVG SNecould be a consequence of an extended outer layer in the direction opposite to the initialsparks. Viewing-Angle Effect on the Light Curve
It has been suggested that if the ejecta are asymmetric, ∆ m ( B ) is dependent on thedirection to the observer . Supplementary Fig. 3 shows the comparison between ∆ m ( B ) and v neb for SNe Ia.In the same figure, the possible effect of the viewing angle on the light curve shape,and the implication on the scatter in the luminosity calibration beyond the one-parameterdescription, are schematically illustrated. For example, the LVG SN 1998bu and the HVGSN 2002bo had similar ∆ m ( B ) values, and this could be interpreted as follows.These two SNe would indeed have intrinsically different amounts of M ( Ni) andaccordingly different luminosity. Because of different M ( Ni), ∆ m ( B ) would be differentif viewed from the same direction. Assuming that (1) ∆ m ( B ) would be smaller andthe luminosity is thus larger for LVG SN 1998bu than for HVG SN 2002bo, for a putativeobserver at the same direction, and that (2) ∆ m ( B ) appears larger for an observercloser to the offset direction, as a viewing angle effect. Then, these two SNe wouldshow similar ∆ m ( B ) as observed, despite the intrinsic difference in luminosity, since theviewing direction is closer to the offset direction for SN 1998bu.This effect would produce a scatter in the luminosity of SNe Ia, around the standardluminosity determined by M ( Ni). Pairs of SNe with similar ∆ m ( B ) , as a result ofthe viewing angle originating from SNe with different amounts of M ( Ni), are naturally xpected if we observe a large number of SNe Ia (Sup. Fig. 3) for the following tworeasons: (1) SNe Ia do indeed show large variations in M ( Ni), and (2) the viewingangles should display large variations.A question for this interpretation is whether any indication of such an effect is seenin the data. Supplementary Fig. 3 shows that there is no clear (but perhaps a marginal)correlation between ∆ m ( B ) and v neb . According to the prediction of the viewing-angleeffect on ∆ m ( B ) for models similar to the one shown in the main text, the observed ∆ m ( B ) could vary by ∼ . mag depending on the direction to the observer (schemat-ically shown in Sup. Fig. 3). This is smaller than the intrinsic variation in ∆ m ( B ) fordifferent M ( Ni), and thus such an effect is difficult to notice in Supplementary Fig. 3,as is consistent with the low correlation in the present data. Any marginal correlation be-tween ∆ m ( B ) and v neb may already hint that such an effect is indeed there, but a largernumber of SNe Ia is necessary to test this possibility with statistical significance. Supplementary Figure 1
Spectrum of SN 2004dt at 120 days after B -band maximum, compared to those ofthe faint SN 1991bg and of the normal HVG SN 2007sr at similar epochs. Supplementary Figure 2
Si II λ , , .The dashed line shows a linear fit to the data excluding SN 2004dt . The colors of thesymbols are the same as in Fig. 2 of the main text. Supplementary Figure 3
The decline-rate parameter ∆ m ( B ) versus the late-time emission-line velocity shift.The three dashed lines schematically illustrate the expected viewing angle effect on thedecline-rate parameter, which would produce a ∼ . mag difference in the observed ∆ m ( B ) for an observer in the offset direction as opposed to the opposite direction .The lines correspond to three hypothesized explosion configurations which are mutuallydifferent in M ( Ni) and therefore in the intrinsic luminosity.
1. Phillips, M. M., et al., The Type Ia Supernova 1986G in NGC 5128 - Optical Photom-etry and Spectra, Pub. Astron. Soc. Pac., , 592-605 (1987)32. Cristiani, S., et al., The SN 1986 G in Centaurus A, Astron. Astrophys., , 63-70(1992)33. Leibundgut, B., et al., Premaximum Observations of the Type Ia SN 1990N, Astro-phys. J., , L23-L26 (1991)34. G ´omez, G., L ´opez, R., S ´anchez, F., The Canaris Type Ia Supernovae Archive (I),Astron. J., , 2094-2109 (1996)35. Patat, F., et al., The Type Ia Supernova 1994D in NGC 4526: The Early Phases, Mon.Not. R. Astron. Soc., , 111-124 (1996)36. Altavilla, G., et al., Cepheid Calibration of Type Ia Supernovae and The Hubble Con-stant, Mon. Not. R. Astron. Soc., , 1344-1352 (2004)37. Riess, A. G., et al., The Rise Time of Nearby Type Ia Supernovae, Astron. J., ,2675-2688 (1999)38. Branch, D., et al., Optical Spectra of The Type Ia Supernova 1998aq, Astron. J., ,1489-1498 (2003)39. Hernandez, M., et al., An Early-Time Infrared and Optical Study of The Type Ia Su-pernova 1998bu in M96, Mon. Not. R. Astron. Soc., , 223-234 (2000)40. Li, W., et al., The Unique Type Ia Supernova 2000cx in NGC 524, Pub. Astron. Soc.Pac., , 1178-1204 (2001)41. Patat, F., et al., Upper Limit for Circumstellar Gas around The Type Ia SN 2000cx, stron. Astrophys., , 931-936 (2007)42. Candia, P., et al., Optical and Infrared Photometry of the Unusual Type Ia Supernova2000cx, Pub. Astron. Soc. Pac., , 277-294 (2003)43. Sollerman, J., et al., The Late-Time Light Curve of The Type Ia Supernova 2000cx,Astron. Astrophys., , 555-568 (2004)44. Krisciunas, K., et al., Optical and Infrared Photometry of the Nearby Type Ia Super-nova 2001el, Astron. J., , 166-180 (2003)45. Wang, L., et al., Spectropolarimetry of SN 2001el in NGC 1448: Asphericity of aNormal Type Ia Supernova, Astrophys. J., , 1110-1128 (2003)46. Mattila, S., et al., Early and Late Time VLT Spectroscopy of SN 2001el - ProgenitorConstraints for a Type Ia Supernova, Astron. Astrophys., , 649-662 (2005)47. Pignata, G., et al., Optical and Infrared Observations of SN 2002dj: Some PossibleCommon Properties of Fast-Expanding Type Ia Supernovae, Mon. Not. R. Astron. Soc., , 971-990 (2008)48. Pignata, G., et al., Photometric Observations of The Type Ia SN 2002er in UGC10743, Mon. Not. R. Astron. Soc., , 178-190 (2004)49. Kotak, R., et al., Spectroscopy of The Type Ia Supernova SN 2002er: Days -11 to+215, Astron. Astrophys., , 1021-1031 (2005)50. Anupama, G. C., Sahu, D. K., Jose, J., Type Ia Supernova SN 2003du: Optical Ob-servations, Astron. Astrophys., , 667-676 (2005)51. Stanishev, V., et al., SN 2003du: 480 days in The Life of a Normal Type Ia Supernova, stron. Astrophys., , 645-661 (2007)52. Leloudas, G., et al., The Normal Type Ia SN 2003hv out to Very Late Phases, Astron.Astrophys., , 265-279 (2009)53. Pastorello, A., ESC and KAIT Observations of The Transitional Type Ia SN 2004eo,Mon. Not. R. Astron. Soc., , 1531-1552 (2007)54. Hachinger, S., Mazzali, P.A., & Benetti, S., Exploring the Spectroscopic Diversity ofType Ia Supernovae, Mon. Not. R. Astron. Soc., , 299-318 (2006)55. Pastorello, A., et al., ESC Observations of SN 2005cf - I. Photometric Evolution of aNormal Type Ia Supernova, Mon. Not. R. Astron. Soc., , 1301-1316 (2007)56. Wang, X., et al., The Golden Standard Type Ia Supernova 2005cf: Observations fromThe Ultraviolet to The Near-Infrared Wavebands, Astrophys. J., , 380-408 (2009)57. Leonard, D. C., Constraining the Type Ia Supernova Progenitor: The Search for Hy-drogen in Nebular Spectra, AIP Conference Proceedings, , 311-315 (2007)58. Garavini, G., et al., ESC Observations of SN 2005cf. II. Optical Spectroscopy andThe High-Velocity Features, Astron. Astrophys., , 527-535 (2007)59. Wang, X. et al., Optical and Near-Infrared Observations of the Highly Reddened,Rapidly Expanding Type Ia Supernova SN 2006X in M100, Astrophys. J., , 626-643(2008)60. Schweizer, F., et al., A New Distance to the Antennae Galaxies (NGC 4038/39) Basedon The Type Ia Supernova 2007sr, Astron. J., , 1482-1489 (2008)61. Motohara, K., et al., The Asymmetric Explosion of Type Ia Supernovae as Seen from ear-Infrared Observations, Astrophys. J., , L101-L104 (2006)62. Gerardy, C.L., et al., Signatures of Delayed Detonation, Asymmetry, and ElectronCapture in the Mid-Infrared Spectra of Supernovae 2003hv and 2005df, Astrophys. J., , 995-1012 (2007)63. Filippenko, A.V., et al., The peculiar Type Ia SN 1991T - Detonation of a white dwarf?,Astrophys. J., , L15-L18 (1992)64. Phillips, M. M., et al., SN 1991T - Further evidence of the heterogeneous nature oftype Ia supernovae, Astron. J., , 1632-1637 (1992)65. Pakmor, R., et al., Sub-Luminous Type Ia Supernovae from The Mergers of Equal-Mass White Dwarfs with Mass ∼ . M ⊙ , Nature, , 61-64 (2010)66. Tanaka, M., et al., The Outermost Ejecta of Type Ia Supernovae, Astrophys. J., ,448-460 (2008)67. Mazzali, P.A., Sauer, D.N., Pastorello, A., Benetti, S., & Hillebrandt, W., AbundanceStratification in Type Ia Supernovae - II. The Rapidly Declining, Spectroscopically NormalSN 2004eo, Mon. Not. R. Astron. Soc., , 1897-1906 (2008)68. Hachinger, S., Mazzali, P. A., Taubenberger, S., Pakmor, R., & Hillebrandt, W., Spec-tral Analysis of The 91bg-like Type Ia SN 2005bl: Low Luminosity, Low Velocities, Incom-plete Burning, Mon. Not. R. Astron. Soc., , 1238-1254 (2009)69. Patat, F., Baade, D., H ¨oflich, P., Maund, J. R., Wang, L., Wheeler, J. C., VLT Spec-tropolarimetry of The Fast Expanding Type Ia SN 2006X, Astron. Astrophys., , 229-246(2009)
0. Leonard, D.C., Li, W., Filippenko, A.V., Foley, R.J., & Chornock, R., Evidence forSpectropolarimetric Diversity in Type Ia Supernovae, Astrophys. J., , 450-475 (2005)71. Chornock, R., & Filippenko, A.V., Deviation from Axisymmetry Revealed by Line Po-larization in the Normal Type Ia Supernova 2004S, Astron. J., , 2227-2237 (2008)72. Kasen, D., & Plewa, T., Detonating Failed Deflagration Model of Thermonuclear Su-pernovae. II. Comparison to Observations, Astrophys. J., , 459-471 (2007), 459-471 (2007)