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No signature of ejecta interaction with a stellarcompanion in three type Ia supernovaeRob P. Olling1, Richard Mushotzky1, Edward J. Shaya1, Armin Rest2, Peter M. Garnavich3, Brad E. Tucker4,5, Daniel Kasen5,6,Steve Margheim7 & Alexei V. Filippenko5

Type Ia supernovae are thought to be the result of a thermonuclearrunaway in carbon/oxygen white dwarfs, but it is uncertainwhether the explosion is triggered by accretion from a non-degen-erate companion star or by a merger with another white dwarf.Observations of a supernova immediately following the explosionprovide unique information on the distribution of ejected mater-ial1 and the progenitor system. Models predict2 that the interactionof supernova ejecta with a companion star or circumstellar debrislead to a sudden brightening lasting from hours to days. Here wepresent data for three supernovae that are likely to be type Iaobserved during the Kepler mission3 with a time resolution of 30minutes. We find no signatures of the supernova ejecta interactingwith nearby companions. The lack of observable interaction sig-natures is consistent with the idea that these three supernovaeresulted from the merger of binary white dwarfs or other compactstars such as helium stars.

Barring extraordinary luck, the continuous monitoring of manygalaxies is required to observe supernovae immediately after ignition.Our Kepler programme monitored 400 galaxies for two to three years,discovering five supernovae near explosion. Previously only a handfulof type Ia supernovae (SN 2009ig4, SN 2010jn5, SN 2011fe6,7, SN2012cg8, SN 2013dy9, and SN 2014J10) have been observed duringthe first few days after the explosion. The second Sloan Digital SkySurvey (SDSS-II) contains one of the largest samples of early type Ia

supernova lightcurves11, but that survey had an average cadenceexceeding four days. No clear companion interaction signature wasfound in the SDSS-II Supernova Survey12, thus ruling out red giants orlarger companions. Similar null results were found in analyses of 87supernovae from the Supernova Legacy Survey (SNLS) survey13, 61supernovae from the Lick Observatory Supernova Search (LOSS) sur-vey14, and a set of about 700 lightcurves from various sources15.

Before our Kepler observations, the earliest supernova observationswere for SN 2013dy (discovered an estimated 2.4 h post-explosion)9

and SN 2011fe (11 h post-explosion)7. The determination of the explo-sion time (actually, the time of first light), however, depends stronglyupon the model used to fit the lightcurve9. Our analysis of the Keplersupernovae suggests that to determine (in a model-independent way)the explosion time directly to an accuracy of better than 7 h, high-quality data taken at very high cadence are needed.

Analysis of the Kepler data is complicated by a variety of systematiceffects on long timescales. Because our procedure co-adds many morepixels centred on a target than the Kepler project3,16 pipeline, weaccount for more light from the source and our results are less sensitiveto various systematic effects such as centroid motion or variations inthe point-spread function. We also implemented methods that elim-inate diffuse background emission in the Kepler data, greatly improv-ing the long-term photometric stability. After correcting for theseeffects, the lightcurves show variance consistent with Poisson statistics.

Table 1 | Properties of galaxies with supernovae discovered with Kepler1 Kepler supernova ID KSN 2012a KSN 2011b KSN 2011c2 Kepler ID 8957091 3111451 78892293 Right ascension (J2000) 19 h 33 min 30.10 s 19 h 20 min 37.50 s 19 h 24 min 46.10 s4 Declination (J2000) 45u 159 0199 38u 159 0899 43u 409 51995 Kepler magnitude 17.61 15.93 16.876 Redshift 0.086 0.052 0.1447 Extinction (mag) 0.42 0.40 0.378 Supernova magnitude at peak 19.25 18.01 20.619 Supernova absolute magnitude at peak 219.14 219.07 217.7310 D(MLCS2k2) 0.66 6 0.11 0.18 6 0.06 0.84 6 0.2611 C 3 1,000 5.98 6 2.02 2.21 6 0.08 0.71 6 0.6412 a 2.12 6 0.14 2.44 6 0.15 2.58 6 0.3313 tfirst light (days) 215.70, 20.29, 10.30 218.11, 20.40, 10.30 220.0, 22.1, 11.514 t50%,before (days) 27.65 6 0.01 28.59 6 0.02 27.91 6 0.0315 tmax (MJD 6 0.5) 56176.666 6 0.02 55846.320 6 0.01 55928.414 6 0.0216 t50%,after (days) 12.46 6 0.01 14.08 6 0.07 10.26 6 0.0117 Red-giant companion, percentage of

angles excluded100, 100,100 100, 100, 100 72, 66, 61

18 Percentage of angles excluded for a six-solar-mass companion

94, 90, 86 100, 100, 98 0, 0, 0

19 Percentage of angles excluded for a two-solar-mass companion

77, 68, 61 94, 89, 84 0, 0, 0

The followingproperties are listed in the rows: (1) identifier; (2) number in the Kepler Input Catalog26; (3) and (4) sky coordinates; (5) the Kepler magnitude of the galaxy; (6) galaxy redshift; (7) V-band Galactic dustextinction; (8) peak Kepler magnitude of the supernova; (9) absolute magnitude of the supernova, corrected for extinction and assuming typical cosmological parameters: H0 5 72 km s21 Mpc21, VL 5 0.73,Vmatter 5 0.27; (10) D in the MLCS2k2 fit; (11), (12) and (13) the slope, exponent, and time of first detected light in the power-law fit, and the lower and upper 1s bounds; (14), (15) and (16) the time of 50% lightlevel before maximum, time of maximum, and the time of 50% level after maximum (the systematic error for tmax is about half a day); (17) the percentage of excluded viewing angles for red-giant companions (atthe 68%, 95% and 99.7% confidence levels); (18) and (19) as in (17), but for a six-solar-mass and a two-solar-mass main-sequence companion. All listed times are with respect to maximum light, in rest-frame

1Astronomy Department, University of Maryland, College Park, Maryland 20742-2421, USA. 2Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, Maryland 21218, USA. 3Department ofPhysics, University ofNotreDame, NotreDame, Indiana46556,USA. 4Mt StromloObservatory, The AustralianNationalUniversity, via CotterRoad,Weston Creek, AustralianCapital Territory 2611,Australia.5Department of Astronomy, University of California, Berkeley, California 94720-3411, USA. 6Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA. 7GeminiObservatory, Southern Operations Center, c/o AURA, Casilla 603, La Serena, Chile.

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We discovered the supernovae in the Kepler data by searching forvariability resembling supernova lightcurves. Spectra of the host gal-axies obtained subsequently with the Gemini and Keck telescopesindicate that all of our supernovae occurred in red passive galaxieswith redshifts of about 0.1 (see Table 1).

The high quality of the Kepler data (Fig. 1) can be seen by comparingthe lightcurves of Kepler supernova KSN 2011b and SN 2011fe7,17,which has one of the best ground-based early supernova lightcurves.The Kepler photometry of KSN 2011b is comparable to that of SN2011fe in depth, but with a significantly better cadence and overallphotometric stability.

We compared the Kepler transients to supernova lightcurve tem-plates using the PSNID code18, finding that KSN 2011b and KSN 2012aare clearly type Ia supernovae. The classification of KSN 2011c is moreuncertain, with a PSNID 54% probability of being type Ia and a 46%probability of being type Ibc (a core-collapse supernova). However,since the massive-star progenitor of a type Ibc supernova is veryunlikely to occur in an elliptical host galaxy, we classify KSN 2011cas a faint type Ia supernova. The three supernova lightcurves are alsowell fitted around their peaks by the type Ia supernova fitting programMLCS2k219 (Fig. 2), supporting the type Ia supernova identification.

KSN 2012a and KSN 2011b both show a secondary ‘bump’ in thepost-maximum lightcurve, a characteristic feature of normal type Iasupernovae observed at red wavelengths. KSN 2011c has the features ofunderluminous events: it lacks a clear second bump, rapidly declines,and is underluminous. KSN 2012a is moderately underluminous,while KSN 2011b is close to normal. Our type Ia supernovae aresystematically offset from the brightness distribution typicallyobserved for type Ia supernovae20 (Fig. 2e); however, our Kepler galaxyselection was biased towards red, passive galaxies, which preferentiallyhost dimmer supernovae21.

Simple analytic radiative-transfer models1,22 with power-law ejectaprofiles predict that the early luminosity L can be described by a powerlaw in time t as follows: L / ta, where a 5 1.522, depending on the

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Figure 1 | Ground-based and Kepler lightcurves compared. The lightcurve ofKSN 2011b was obtained by Kepler with a 30-min cadence (black) and binnedat 12 h (red). The green lines indicate the range of best-fit type Ia supernovalightcurve templates (using the MLCS2k219 analysis, modified to apply theKepler wavelength sensitivity function). A secondary peak in the lightcurve,characteristic of type Ia supernovae, is apparent in KSN 2011b. Open circlesshow the lightcurve of the well-observed, nearby SN 2011fe7,17, which has beenshifted in magnitude and time to match the peak of KSN 2011b. SN 2011fe hada lightcurve width near the average for type Ia supernovae, whereas the KSN2011b lightcurve is narrower. KJD measures time, in days, since 1 January of theyear that the Kepler mission was launched (2009), with KJD 5 MJD – 54832.5.

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(blue), with m the distance modulus in magnitudes.e, The distribution of the width parameter D versusredshift. The parameter D measures lightcurveshape and is anticorrelated with peak luminosity.The Kepler supernovae are biased towards large Dbecause the Kepler galaxies have lower star-formation rates, which preferentially host dimmersupernovae21. All error bars are 1s errors.

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ejecta structure. In detailed numerical models that use more complexejecta structures, the early lightcurve need not follow a single powerlaw. Previous studies11,23 of sparsely sampled lightcurves of numerousobserved type Ia supernovae found an early rise consistent with apower law with a < 2. However, the early lightcurves of SN 2013dy9

and SN 2014J10 are not well fitted by a single power law. Indeed,theoretical models predict that the shape of early type Ia supernovalightcurves is sensitive to the density and velocity structure of thesupernova ejecta as well as the radial distribution of radioactive 56Ni(ref. 1).

Figure 3 presents the Kepler early lightcurves, along with the best-fitpower-law function L(t) 5 C(t 2 t0)a, where t0 is the time of first lightand C is a constant, and where L is normalized by the peak supernovaluminosity. We find that the data are all well fitted by a single power

law up to the point that L(t) reaches 40% of the peak, beyond which thelightcurve turns over. The indices are a 5 2.12 6 0.14, 2.44 6 0.14, and2.58 6 0.33 for KSN 2012a, KSN 2011b and KSN 2011c, respectively.The errors include the correlations between the fitted parameters (seeMethods and Extended Data Fig. 1). The weighted average index of2.3 6 0.09 differs from the value a < 2 found in some previous studiesof supernovae observed at much lower cadence11,23 (but see SN 2013dy9

and SN 2014J10 for additional diversity in early behaviour). The Keplersupernovae thus provide new constraints on theoretical models thatlink the lightcurve rise to the properties of the supernova ejecta and theexplosion mechanism.

The shape of the early lightcurve can also be affected by emissionresulting from the collision of the supernova ejecta with circumstellarmatter or a companion star. Theoretical models2 find that the excessoptical/ultraviolet emission due to the collision shock causes a devi-ation from a simple power-law rise. The luminosity of the shock emis-sion is directly proportional to the radius of the companion star

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Figure 3 | The rise of the lightcurves. a, c, and e show the raw data (1symbols), along with the data binned to half-day resolution (blue points anderrors) and the best power-law fit (red line). The data are well fitted by a powerlaw up to the time that the lightcurve reaches 40% of its peak value, or 7.2 days,8.5 days, and 11.7 days for KSN 2012a, KSN 2011b, and KSN 2011c,respectively. The binned residuals (data minus fit) are shown in b, d, and f asgreen points with error bars. The time of first light and the 61s uncertainty areshown as the vertical lines. In units of the peak supernova brightness, theunbinned errors are about 0.022, 0.012 and 0.120 for KSN 2012a, KSN 2011band KSN 2011c, respectively. All error bars are 1s errors.

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Figure 4 | Predicted maximum photometric signatures due to companions.a–c display the residuals of the power-law fit to the lightcurves (black points)and the average amount of shock emission predicted when the companion iseither a red giant (red lines), or a six-solar-mass star (cyan) or a two-solar-massmain-sequence star (blue). The dashed red line shows the brightest possiblered-giant shock contribution at the 68% confidence level. We simulateobserving from different viewing angles by scaling the shock luminosity, anddetermining the probability that such a model can be excluded. d–f show thepercentage of viewing angles that can be excluded at a given confidence level.All error bars are 1s errors.

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(assumed to be in Roche-lobe overflow) and is dependent on orienta-tion, being brightest when the observer’s viewing angle is aligned withthe region of shocked ejecta. The lightcurves of SN 2011fe and SN2013dy show no signs of a shock interaction. Pre-explosion images24

of SN 2011fe taken with the Hubble Space Telescope exclude a red-giant or subgiant25 companion larger than about four solar masses.

In Fig. 4a, c and e, we examine the residuals of the power-law fits ofthe Kepler supernovae and find no systematic trends indicative ofshock emission. For comparison, we overplot predictions2 of the shockemission for three models assuming companions with orbital separa-tions of 2 3 1013 cm (typical for a red giant), 2 3 1012 cm (typical of amain-sequence star of six solar masses) and 5 3 1011 cm (a two-solar-mass star). The residuals of KSN 2012a and KSN 2011b are inconsist-ent with a red-giant companion viewed from any viewing angle. Thereis also no indication of a main-sequence star for most viewing angles.The fractions of viewing angles excluded for the six-solar-mass andtwo-solar-mass models are, respectively, 94% and 77% for KSN 2012aand 100% and 94% for KSN 2011b, at the 68% confidence level. KSN2011c is less constraining, given the lower signal-to-noise ratio.

Our discovery of three type Ia supernovae with Kepler hasopened a new window on the progenitor system and explosionphysics. K2, the follow up to the Kepler mission, is primarily usedto search for exoplanets. We use K2 to monitor up to severalthousand galaxies, which are being simultaneously observed byground-based photometric and spectroscopic programmes, makingit highly likely that many more supernovae will be detected in the earlystages of the explosion and allowing early and detailed follow-upobservations.

Online Content Methods, along with any additional Extended Data display itemsandSourceData, are available in the online version of the paper; references uniqueto these sections appear only in the online paper.

Received 16 January; accepted 23 March 2015.

1. Piro, A. L. & Nakar, E. What can we learn from the rising light curves of radioactivelypowered supernovae. Astrophys. J. 769, 67–79 (2013).

2. Kasen, D. Seeing the collision of a supernova with its companion star. Astrophys. J.708, 1025–1031 (2010).

3. Haas, M. et al. Kepler science operations. Astrophys. J. 713, L115–L119 (2010).4. Foley, R. J. et al. Very early ultraviolet and optical observations of the SN Ia

supernova 2009ig. Astrophys. J. 744, 38 (2012).5. Hachinger, S. et al. The UV/optical spectra of the SN Ia supernova SN 2010jn: a

bright supernova with outer layers rich in iron-group elements. Mon. Not. R. Astron.Soc. 429, 2228–2248 (2013).

6. Nugent, P. et al. Young SN Ia supernova PTF11kly in M101. Astron. Telegr. 3581, 1(2011).

7. Nugent, P. E. et al. Supernova SN 2011fe from an exploding carbon-oxygen whitedwarf star. Nature 480, 344–347 (2011).

8. Silverman, J. M. et al. The very young SN Ia supernova 2012cg: discovery andearly-time follow-up observations. Astrophys. J. 756, L7–L12 (2012).

9. Zheng, W. et al. The very young SN Ia supernova 2013dy: discovery, and strongcarbon absorption in early-time spectra. Astrophys. J. 778, L15–L20 (2013).

10. Zheng, W. et al. Estimating the first-light time of the type Ia supernova 2014J inM82. Astrophys. J. 783, L24–L28 (2014).

11. Hayden, B. T. et al. The rise and fall of SN Ia supernova light curves in the SDSS-IIsupernova survey. Astrophys. J. 712, 350–366 (2010).

12. Hayden, B. et al. Single or double degenerate progenitors? searching for shockemission in the SDSS-II type Ia supernovae. Astrophys. J. 722, 1691–1698 (2010).

13. Bianco, F. B. et al. Constraining SN Ia supernovae progenitors from three years ofsupernova legacy survey data. Astrophys. J. 741, 20–31 (2011).

14. Ganeshalingam, M., Li, W. & Filippenko, A. V. The rise-time distribution of nearbytype Ia supernovae. Mon. Not. R. Astron. Soc. 416, 2607–2622 (2011).

15. Tucker, B. E. UV properties of type Ia supernova and their host galaxies. Astrophys.Space Sci. 335, 223–230 (2011).

16. Jenkins, J. J. et al. Initial characteristics of Kepler long cadence data for detectingtransiting planets. Astrophys. J. 713, L120–L125 (2010).

17. Munari,U.et al.BVRI lightcurves of supernovaeSN2011fe inM101, SN2012aw inM95, and SN 2012cg in NGC 4424. New Astron. 20, 30–37 (2013).

18. Sako, M. et al. Photometric type Ia supernova candidates from the three-yearSDSS-II SN survey data. Astrophys. J. 738, 162–177 (2011).

19. Jha, S., Riess, A. G. & Kirshner, R. P. Improved distances to type Ia supernovae withmulticolor light-curve shapes: MLCS2k2. Astrophys. J. 659, 122 (2007).

20. Kessler, R. et al. First-year Sloan Digital Sky Survey-II supernova results: Hubblediagram and cosmological parameters. Astrophys. J. 185 (Suppl.), 32–84 (2009).

21. Gallagher, J. S.et al.Supernovae inearly-typegalaxies:directly connectingage andmetallicity with type Ia luminosity. Astrophys. J. 685, 752 (2008).

22. Arnett, W. D. Type I supernovae. I—Analytic solutions for the early part of the lightcurve. Astrophys. J. 253, 785–797 (1982).

23. Conley, A. et al. The rise time of type Ia supernovae from the Supernova LegacySurvey. Astron. J. 132, 1707–1713 (2006).

24. Li, W. et al. Exclusion of a luminous red giant as a companion star to the progenitorof supernova SN 2011fe. Nature 480, 348–350 (2011).

25. Bloom, J. S. et al. A compact degenerate primary-star progenitor of SN 2011fe.Astrophys. J. 744, L17–L21 (2012).

26. Brown, T. et al. Kepler Input Catalog: photometric calibration and stellarclassification. Astron. J. 142, 112–130 (2011).

Supplementary Information is available in the online version of the paper.

Acknowledgements Wethank M.Still, M. Fanelli, and S.Gezari for useful conversations,M. Graham, P. Kelly, K. Clubb, and O. Fox for assistance with the observations andreductions of the host-galaxy spectra, D. Scolnic for help with PSNID, and F. Bianco forsending us time series of the companion shock models integrated over the Keplerbandpass. D. Thilker kindly provided the SDSS magnitudes for the supernova hostgalaxies. R.P.O. and E.J.S. were, in a small part, supported by Kepler GO3 and GO4grantsNNX12AC95GandNNX13AC27G.P.M.G.waspartly supportedbyKeplergrantsNNX12AC89G and NNX11AG95G. A.V.F. and B.E.T. were supported by NSF grantAST-1211916, the TABASGO Foundation, and the Christopher R. Redlich Fund. Someof the data presented herein were obtained from the Mikulski Archive for SpaceTelescopes (MAST). STScI is operated by the Association of Universities for Research inAstronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HSTdata is provided by the NASA Office of Space Science via grant NNX13AC07G and byother grants and contracts. This paper includes data collected by the Kepler mission.Funding for the Kepler mission is provided by the NASA Science Mission directorate.This work is based in part on observations obtained at the Gemini Observatory(program IDs GN-2013A-Q-4 and GS-2013A-Q-115) which is operated by theAssociation of Universities for Research in Astronomy, Inc., under a cooperativeagreement with the NSF on behalf of the Gemini partnership: the National ScienceFoundation (United States), the National Research Council (Canada), CONICYT (Chile),the Australian Research Council (Australia), Ministerio da Ciencia, Tecnologia eInovaçao (Brazil) and Ministerio de Ciencia, Tecnologıa e Innovacion Productiva(Argentina). Some of the data presented herein were obtained at the W. M. KeckObservatory,which isoperatedasascientificpartnershipamong theCalifornia Instituteof Technology, the University of California, and NASA; the Observatory was madepossible by the generous financial support of the W. M. Keck Foundation.

Author Contributions R.P.O., R.M., and E.J.S.developed the ideaof looking for variabilityin galaxies using Kepler data. R.P.O. selected the target galaxies and created thepipeline to analyse the Kepler data, and developed and implemented most of theinnovations in data reduction. The analysis by R.P.O. and E.J.S. of Kepler’s Full FrameImages (not discussed here) convinced us that long-term stability for Kepler data wasachievable. E.J.S. has also confirmed the reduction results using independenttechniques. P.M.G. modified the MLCS2k2 program to fit Kepler light curves. A.R. usedPSNID to classify the supernova. D.K. computed the companion shock models. B.E.T.coordinated, with S.M. and A.V.F., the spectroscopic observations of the host galaxiesand measured the redshifts. All authors contributed to the analysis and interpretationof the Kepler supernova lightcurves, as well as the text of this Letter.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. The authors declare no competing financial interests.Readers are welcome to comment on the online version of the paper. Correspondenceand requests for materials should be addressed to R.P.O. (olling@astro.umd.edu).

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METHODSPhotometric calibration. The Kepler Mission3,16 provided nearly continuousobservations of many galaxies, resulting in a few supernova lightcurves that spanfrom months before to months after the supernova event at a 30-min cadence. OurKepler guest observer projects, GO20058, GO30032, and GO40057, monitoredabout 400 galaxies at 30-min cadence to look for brightness variations in theirnuclei indicative of an active galactic nucleus and to search for supernovae. Targetswere selected from the 2MASS extended source catalogue27. Typically, we obtained8 3 8 pixel cutout regions centred on each galaxy for two to three years.

On a timescale of minutes to hours, Kepler provides photometric precision of afew parts in a million for bright sources3,16. On longer timescales, various system-atic effects considerably reduce the precision of the standard Kepler products. Wehave developed a specialized analysis which obtains uncertainties of a few parts inten thousand on timescales from hours to years, at 17th magnitude.

The Kepler Archive Manual28 describes where the data are stored and how thePresearch Data Conditioning (PDC) Maximum A Posteriori (MAP) lightcurveproduction procedure significantly reduces sensitivity variations on timescalesexceeding a few days. However, PDC-MAP fails for objects having large intrinsic,astrophysical variations like supernovae. Below we describe our data-reductionprocedures that reduce instrumental variations on long timescales while preserv-ing real astrophysical signals. Our data-reduction method is based on the smallcutout images that Kepler obtains. These so-called target (TARG) pixel imageshave undergone standard astronomical calibration, including background sub-traction and flagging of cosmic-ray events or otherwise bad data28. The TARGfiles contain the background-subtracted images, as well as the subtracted back-ground itself (FLUX_BKG). Kepler’s simple aperture photometry (SAP) light-curves are extracted from these TARG images where only the light in certainpixels is added together. For the SAP, the choice of pixels, chosen to optimizethe signal-to-noise ratio at short timescales, is based on the source brightness andthe shape of the point-spread function.

The Kepler data processing is organized in three-month chunks labelled quar-ters Q0 to Q17. About once per month, the spacecraft goes through a pointingmanoeuvre to downlink the data to Earth. We virtually eliminate the large spikes inthe SAP lightcurves after repointing manoeuvres by using larger apertures. We usethree different apertures to measure the lightcurves. The first aperture type (‘535’)uses a 5 3 5 pixel box centred on our galaxies. For the second type of aperture(‘WEI’), we identify which pixels contain most of the light from the galaxy but arenot contaminated badly by neighbouring sources, and we assign a high weight topixels near the source centre and lower weights to pixels further out, decreasing tozero near strong confusing sources. Pixels without contributions from sources aregiven intermediate weight but are separately identified as background pixels. Wethen create a curve of growth with the cumulative flux as a function of pixel weight.If an error has been made in determining the background level, the upper part ofthe curve of growth will tilt upward or downward. Confusing sources will addtheir own growth curve. This procedure generally produces nonvarying light-curves for most of our galaxies, as expected. The WEI apertures typically contain30 to 40 pixels.

Our third aperture type (‘WAL’) uses the ensemble of the WEI apertures fromall quarters to design an aperture with the same number of pixels in all quarters.Lightcurves produced with these apertures also yield flat lightcurves for the major-ity of our galaxies. Close inspection of results for our ,400 galaxies indicates that itis not possible to decide which of the 535, WEI, or WAL lightcurves is best, so wedecided to combine all three apertures and use the variance amongst them as anindicator of the systematic uncertainties.

Another issue is that the lightcurves do not match up at the boundaries ofquarters. A new quarter brings a new orientation of the Kepler spacecraft andthus a different charge-coupled device (CCD). This has two effects: (1) even forwell-calibrated CCDs, there are sensitivity variations of a few per cent betweenpixels, and (2) an aperture in the next quarter could have a different size and becentred differently with respect to the source centre. Consequently, the aperturescapture a different fraction of the total light of the source. Both effects indicate thatthe quarters need to be ‘stitched together’ by using a multiplicative factor.Specifically, we fitted a polynomial to the last few days of the previous quarterand the first few days of the next quarter, thereby determining a multiplicativefactor. Our objects could be quiet or rapidly changing at a quarter boundary; there-fore, we used time windows of 4222 days and polynomial fits up to fifth order, andused the combination of parameters that had the smallest residuals. This procedureworks well but is imperfect, perhaps because of background-subtraction errors; thesecould be removed in future analyses with an additive stitching factor.

The remaining photometric trends strongly correlate with the backgroundlevels as extracted from the ‘FLUX_BKG’ in the target pixel files. This suggeststhat the background levels are not optimally determined by the Kepler pipeline.Based on the weights determined for the ‘WEI’ aperture above, we identify a

number of pixels in each cutout as ‘background pixels’, and we use those pixelsto construct our own estimate of the background level. We think that these ‘back-grounds’ are most probably caused by zodiacal emission from dust in the SolarSystem, and not by faint galaxies or stars. We used the model from the COBE/DIRBE team to predict the zodiacal emission29 at a wavelength of 1.25 mm towardsthe Kepler field, as seen from Kepler. There is a remarkable correspondencebetween the scaled COBE/DIRBE model and the background levels from theKepler data, justifying the removal of structure in our lightcurves that followsthe zodiacal emission. However, the long-term variation in our lightcurves doesnot exactly follow the zodiacal emission. Finally, the zodiacal emission may exhibitvariations that do not follow the model, possibly as a result of interactions betweenthe zodiacal dust and coronal mass ejections, the solar wind, or the intersection ofold comet dust trails with Kepler’s line of sight. In fact, brightening of the back-ground lasting days to weeks has been observed.

The trends in counts of our ,400 galaxies vary in roughly the same fashion,exhibiting four significant sinusoidal components with almost identical periodsand phases. The periods of these components are about one, half, a third, and aquarter of a Kepler year. Coefficients for these four sinusoids were determined forthe quiet periods of each supernova lightcurve and the sinusoids were subtractedfrom the entire time series.

We use three different versions of the lightcurves and fit two different versionsof our four-component sinusoidal model to the long-term background variations.For each of our 535, WEI, and WAL apertures we thus have six ways to eliminatethe background effects. This leads to 18 different estimates of the actual, intrinsiclightcurve. As far as we can determine, none of these versions is superior to theothers, so we construct a median value and its root-mean-square (RMS) ‘error’ ofthe 18 different estimates of each observation, after clipping outliers. When wepresent binned data in the figures or the data tables, we use the median value oftypically 26 data points (corresponding to one-half day in the observed frame)where we also reject outliers and undefined values. The reported errors are theweighted RMS scatter of the data, divided by the square-root of the number of validdata points.

The three different versions of the lightcurves are (1) the raw lightcurve beingeither 535, WEI, or WAL; (2) the raw lightcurve minus a scaled version of theKepler Project’s background, where the scale factor is chosen so as to minimize theresiduals; and (3) the raw lightcurve minus a scaled version of our own background.The two different fits we perform on raw lightcurves 123 are: (1) a four-componentsinusoidal fit where the periods are set to the one, half, a third and a quarter-yearperiods but allowing for a few days variation in those periods, and (2) as above, butallowing the periods to change by 67%. In these fits, we also include a quadraticpolynomial to accommodate the longest trends, including sensitivity losses.

Inspection of a large number of galaxy lightcurves produced in this way indi-cates that the procedure works well: long-term trends are removed and residualsare around the 0.25% level. In some cases, however, larger errors still occur, mostlyat the boundaries between quarters. The lightcurves for the supernovae presentedhere extend well beyond the regions that we used in the main part of this Letter,and we do not see signs of problems there. Thus, we are confident that the light-curves presented here are free from systematic effects above the 0.25% level ontimescales of weeks to years. As a function of Kepler magnitude (Kp), we achieveerrors of 3.6 1 0.29 (Kp 2 18)4 millimagnitudes, on a timescale of half a day.However, small residual background variations may still be present on timescalesof days to weeks, and we take this into account via the background B term inequation (2) below.Lightcurve fitting. We parameterize the observed lightcurve L, normalized by itsmaximum, as the sum of the supernova part (LSN) and a small background term,L(t) 5 LSN(t) 1 B(t), with

LSN tð Þ~C t{t0ð Þa ð1Þ

and

B tð Þ~b0zb1 t{t0ð Þzb2 t{t0ð Þ2 ð2Þ

The background terms are fitted over the time range before the onset of the event,and the L(t) function is fitted where t $ t0, but with the parameters of the back-ground fixed. The time range used for fitting starts roughly 20 days (30 days forKSN 2011c) before the supernova explosion and lasts until the lightcurve reaches40% of the peak amplitude, that is, until t~ t(LSN ~ 0:4) . The maximum occurs att 5 tmax. These ranges have been empirically determined to ensure that (1) B(t)faithfully describes the region before the supernova and is not affected by anyvariations lasting less than about one week; and (2) the eventual turnover ofthe lightcurve does not affect the fitted power-law index. The fits to the early

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lightcurves are excellent, and the reduced-x2 values confirm that this model is agood match to the data.

Experimentation with synthetic lightcurves that represent well the overallsupernova lightcurve yield constant a values, as long as the time span used forfitting is less than about t(LSN ~ 0:4). When using longer time spans, the fitted a andt0 change systematically. This effect may explain why different authors have founddifferent a values9–11,23: different time spans yield different power-law indices.

The reported uncertainties on t0, a, and C are derived from Nmod 5 2 3 106

random realizations of the data, where we perturb each measurement by a randomvalue based on the photometric error of the measurement, and where we perturbthe initial estimates for the fitting function by the a posteriori 1s errors. Toincorporate the strong correlations between the fit parameters, we determinethe parameter uncertainties from the maximum extent of the error ellipses thatcontain 68% of all models. The error ellipses are determined from the ensemble ofthe two-dimensional distribution (contour plots) of all the fit results (ExtendedData Fig. 1). These maximal extents of the 68%-error ellipses are indicated by thehorizontal and vertical lines in Extended Data Fig. 1.

Each contour diagram in Extended Data Fig. 1 comprising parameters i and j is ameasure of the total number of fitted models that fall within pixel (k,l) withparameter values (vi,vj). The contours drawn are based on the cumulative distri-bution of the pixel values, starting from the largest value. For example, the 0%contour corresponds to the peak in the map, the 100% contour encloses all pixelsthat contain fit results, while the 25% contour contains all pixels whose sum equalsa quarter of the number of models. Each map then provides an estimate for theaverage values A and the lower (L) and upper (U) 1s error bounds. We computethe average of parameter i based on map (i, j) as:

Ai;i,j~ Sk,l vi|Nk,l½ $=Sk,l Nk,l½ $f g ð3Þ

and similarly for Aj;i,j, where the sum over k,l includes all pixels that contain 25% ofall fit results. The lower 1s bound of parameter i, Li;i,j, corresponds to the lowerprojection of the 68% contour onto the i axis, and likewise for the upper boundUi;i,j. The symmetric error, ei;i,j, equals (Ui;i,j 2 Li;i,j)/2. Since there are three fitparameters, each parameter i is determined from two contour maps, (i,n) and(i,m). The weighted average for parameter i is then:

Aih i~P

j~n,mwi;i,j|Ai;i,j

!=

Pj~n,m

wi;i,j

!ð4Þ

where the weight wi;i,j 5 (1/ei;i,j)2 and the weighted error on ÆAiæ is:

ei ~P

j~n,mwi;i,j

!%1=2

ð5Þ

These lower, average, and upper values are determined for 5,000 subsets of thetotal number of models, and averaged.

Extended Data Fig. 1 shows the confidence regions for the a–t0 and a–C corre-lations, for all two million fit results combined (the t0–C map looks similar). Allparameters are highly correlated, which leads to relatively large and somewhatasymmetric errors. The results are given in Table 1.

We have performed extensive simulations of this fitting process, on both syn-thetic and actual data, to arrive at this procedure. Details will be presented else-where; here we discuss a few highlights. Because the curvature of the x2 surface islow and riddled with local minima, our fitter (modified Levenberg–Marquardt)can easily get stuck in a local minimum. Consequently, the fitted values depend onthe initial guess for the fit parameters—that is, if the initial estimates are off, theresults will be biased. To avoid these problems, we determine robust initial estimates,and randomize the initial guess values by an amount that roughly corresponds to thea posteriori errors. The fit results for KSN 2011c may have additional systematicerrors of unknown magnitude owing to our quarter-stitching procedure.

Figure 3 and the fitted values listed in Table 1 indicate that the early lightcurvesof the Kepler supernovae are substantially different: the power-law indices differby 21%, the times to reach 40% of the maximum vary by 55%, and the C terms varyby a factor of 8.4. Thus, there are substantial different evolutions of the temper-ature, the opacity, the rate of expansion of the ejecta, and the internal distributionof radioactive elements1.Shockwave interaction with the companion. The absolute strength of the shockemission depends on the size of the companion and its distance from the explodingwhite dwarf2. Analysis of the model light curves indicates that the observable shockemission depends on two orthogonal parameters: (1) the normalized time depend-ence of the shock emission, CSE(t), which is rather similar between 0.5 day and 5.5days for models that contain either a red giant or a main-sequence companion(Fig. 4); and (2) the viewing angle h away from the shocked region. The observable

shock emission is then reasonably well approximated by cobs(t,h) 5 CSE(t) 3 S(h),where, to within the errors:

S hð Þ< 0:982| exp { h=99:7ð Þ2! "

z0:018 ð6Þ

with h in degrees, and where the minimum observed shock strength of 0.055occurs at h 5 180u.

To evaluate the maximum strength allowed by the data, we multiply the modelCSE(t) curves by a series of factors s and compute the resulting x2

s value andprobability Ps that the data are consistent with cobs(t,h). As an example, inFig. 4a, c and e we plot (red dashed line) the strongest shock model that isconsistent with the data, at 68% confidence.

Thus, each s value corresponds to a level of confidence Cs 5 (1 2 Ps) that amodel can be excluded by the data. Likewise, each s value also corresponds to aviewing angle h (through equation (6)). Finally, given the three-dimensional dis-tribution of viewing angles, the fraction of viewing angles that have strengthexceeding s 5 S(h) is f(S) 5 (1 2 cosh)/2. In Fig. 4b, d and e, we present f(S) asa function of Cs: the fraction of excluded viewing angles (too strong shocks) as afunction of the confidence level that a shock with that strength can be excluded bythe data.Lightcurve analysis. We analysed the lightcurves of the Kepler supernovae usingthe fitting program MLCS2k2 (ref. 19). In MLCS2k2 a set of templates hasbeen created from a large number of real type Ia supernova light curves, andK-corrections are calculated from a large sample of observed spectra. A Keplerbandpass was converted to the MLCS2k2 format and used to K-correct the Keplermagnitudes to the standard rest-frame R band. MLCS2k2 also fits the colour curvesto estimate reddening due to dust in the host galaxy. However, there is no colourinformation for the Kepler supernovae, so the extinction was fixed at zero.Kepler magnitudes of the host galaxies. Both the ‘SDSS’ and Kepler magnitudeslisted in the Kepler Input Catalog26 for these supernova host galaxies were based onthe photographic magnitudes from the USNO-B Catalog31, which were trans-formed to SDSS-like magnitudes for the Kepler Input Catalog26. Such pho-tographic magnitudes rely on the diameter of the ‘spots’ on the photographicplates, which are affected by the fact that these sources are extended.Accordingly, the Kepler magnitudes listed in the Kepler Input Catalog26 for ourgalaxies are much too bright. The Kepler magnitudes listed in Table 1 are com-puted using CCD-based SDSS magnitudes.Spectroscopy of the host galaxies. Spectra were taken of the host galaxies of ourthree type Ia supernovae. Spectra obtained at Gemini North used the GeminiMulti-Object Spectrograph, with the R400 grating and the 1.50 slit. At Keck, weused the Low Resolution Imaging Spectrometer30 with the 600/4000 grism and400/8500 grating for coverage of wavelengths 3,010–9,000 s. All data werereduced using standard IRAF32 tasks to remove instrument and sky signatures,and to extract one-dimensional spectra for analysis.

The host galaxy of KSN 2011b is a red, passive galaxy at redshift z 5 0.052. It hasa high [N II]/Ha ratio, indicative of a possibly active nucleus, and we detect [S II]emission and Ca II H and K absorption. KSN 2011c occurred in a red, passive galaxyat z 5 0.144; we see Ca II H and K, Mg II, Na I, and multiple Fe I and Fe II absorptionlines. KSN 2012a was also in a red, passive galaxy, at z 5 0.086. The spectrum showsmultiple absorption features (Ca II H&K, Mg II, Na I), and the 4,000 s break.Code availability. Except for the programs mentioned below, most code is writtenin IDL by R.P.O., but is not available for public consumption due to its manyundocumented intricacies, and the lack of funds to make it possible to publish thecode in a user-friendly form. PSNID and MLCS2k2 can be obtained at: http://www.sas.upenn.edu/,gladney/html-physics/psnid/psnidII/ and http://www.phy-sics.rutgers.edu/,saurabh/mlcs2k2/, respectively. The shock interaction modelswere taken from the previously published results of ref. 2, which were run with theradiation transport code SEDONA (http://adsabs.harvard.edu/abs/2006ApJ...651..366K), which is not currently available for open access.

Source data for figs 1–4 are provided in the Supplementary Information.

27. Jarrett, T. H. et al. 2MASS Extended Source Catalog: overview and algorithms.Astron. J. 119, 2498–2531 (2000).

28. Thompson, S. E. et al. Kepler Archive Manual http://archive.stsci.edu/kepler/manuals/archive_manual.pdf (5 June 2014).

29. Kelsall, T. et al. The COBE diffuse infrared background experiment search for thecosmic infrared background. II. Model of the interplanetary dust cloud. Astron. J.508, 44–73 (1998).

30. Oke, J. B. et al. The Keck low-resolution imaging spectrometer. Publ. Astron. Soc.Pacif. 107, 375–385 (1995).

31. Monet, D. et al. The USNO-B Catalog. Astron. J. 125, 984–993 (2003).32. Tody, D. Astronomical Data Analysis Software and Systems II (eds Hanisch, R. J.,

Brissenden, R. J. V. & Barnes, J.), Vol. 52 of Astronomical Society of the PacificConference Series, 173–183 (1993).

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Extended Data Figure 1 | Confidence regions of fitted parameters. Two-dimensional projections (contour maps) of the three-dimensional distributionof the fit parameters a, t0, and C. For Kepler supernovae 2012a, 2011b, and2011c, from top to bottom. a, c, and e show a versus t0, and b, d, and f displaya versus C. The contours, from inside to out, contain 25%, 50%, 68.3% (red),90%, 95.5% (blue), and 99.7% of all 2 3 106 Monte Carlo model-fit results. Thedashed red lines are the 61s limits of the projections. The vertical cyan linerepresents the fireball model22. Details of the fitting procedure are described inthe Methods section.

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