Unsupervised clustering of Type II supernova light curves

0.83 MB·

by  Adam Rubin

Draft version February 8, 2016
PreprinttypesetusingLATEXstyleemulateapjv.01/23/15
UNSUPERVISED CLUSTERING OF TYPE II SUPERNOVA LIGHT CURVES
Adam Rubin and Avishay Gal-Yam
WeizmannInstituteofScience
Draft version February 8, 2016
ABSTRACT
As new facilities come online, the astronomical community will be provided with extremely large
datasets of well-sampled light curves (LCs) of transient objects. This motivates systematic studies
of the light curves of supernovae (SNe) of all types, including the early rising phase. We performed
6 unsupervised k-means clustering on a sample of 59 R-band Type II SN light curves and find that
1 our sample can be divided into three classes: slowly-rising (II-S), fast-rise/slow-decline (II-FS), and
0 fast-rise/fast-decline (II-FF). We also identify three outliers based on the algorithm. We find that
2 performing clustering on the first two components of a principal component analysis gives equivalent

b results to the analysis using the full LC morphologies. This may indicate that Type II LCs could
e possibly be reduced to two parameters. We present several important caveats to the technique, and
F find that the division into these classes is not fully robust and is sensitive to the uncertainty on the
time of first light. Moreover these classes have some overlap, and are defined in the R-band only. It
5
is currently unclear if they represent distinct physical classes, and more data is needed to study these

issues. However,ouranalysisshowsthattheoutliersareactuallycomposedofslowly-evolvingSNIIb,
]
E demonstrating the potential use of such methods. The slowly-evolving SNe IIb may arise from single
H massive progenitors.
.
h
p 1. INTRODUCTION been attempted—perhaps due to the sparse sampling of
- There is a controversy in the literature regarding the typical SN LCs.
o The Rubin et al. (2015) sample has the advantage of
division of SNe II into photometric sub-classes. The
r containing LCs with very well constrained times of first
t classical division into Type II-P and II-L events (Bar-
s light, allowing us to utilize the early-time LC behavior
bon et al. 1979) based on the post-peak light curve has
a
whichhaspreviouslybeenunaccessible. Hereweexplore
[ been supported by Arcavi et al. (2012) and Faran et al.
(2014a,b), but challenged by Anderson et al. (2014) and how the sample divides into classes, and explain this
2 Sanders et al. (2015). Until now, the focus has been on technique’s limitations and pitfalls when it is applied to
v SN LCs.
extracting characteristics from light curves (e.g. peak
6
magnitude, post-peak decline rate, plateau length), and
4 searching for separation into populations. However, it is 2. ANALYSIS
4
also known that some SNe have strikingly similar light We used the light curve sample presented in Ru-
1
curves,andthedeterminationofwhichcharacteristicsto bin et al. (2015), and added two SNe (iPTF13blq and
0
compare is not straightforward. iPTF14bas; Arcavi et al. 2016 in prep.) which were
.
2 New surveys such as the Zwicky Transient Facil- originally in that sample, but were removed for rea-
0 ity (ZTF; Bellm 2014) and the Large Synoptic Survey sons explained below and discussed in Section 6. We
6 (LSST; Ivezic et al. 2008) will provide the astronomi- smoothed the LCs using the algorithm described in Ru-
1
cal community with large datasets of well-sampled light bin et al. (2015). The Rubin et al. (2015) algorithm did
:
v curves (LCs). The rolling nature of these surveys will notfitiPTF14baswellaroundpeak,andwefoundthata
i providegoodcoverageofthepoorlystudiedearlyphases smoothingsplineperformedmuchbetter. Thesmoothed
X
of SNe. However, there is and will remain a permanent LCs of both iPTF13blq and iPTF14bas are presented in
r lack of resources for spectroscopic classification of the appendix Figure 1.
a
transients found. Therefore it is of utmost importance WeusedtheK-means++(Arthur&Vassilvitskii2007)
to develop tools for the study and classification of SN algorithm, implemented as kmeans in Matlab, to auto-
LCs based on their photometry alone. matically divide our light curves into classes. We inter-
Here we attempt to divide the sample of 57 LCs pre- polated our smoothed light curves to measure the mag-
sented in Rubin et al. (2015)—in addition to two SN nitude between rest frame days 1 and 30, with uniform
LCs which were originally included in that sample but spacing of 0.1 days. This is equivalent to treating the
subsequently removed—into classes of similar LC shape data set as 59 observations (the number of SNe in the
byusingtheunsupervisedclusteringalgorithmK-Means sample) of 291 highly correlated parameters (relative R-
on the LCs directly (as opposed to extracted parame- band magnitude at 291 times). Data from t < 1 days
ters). This algorithm is one of the simplest both con- was ignored because it contained information that was
ceptually and algorithmically. Unsupervised clustering interpolated between the last limit and the first detec-
on SN characteristics (using a different technique) has tion.
been previously used for Type Ia SNe by Benetti et al. K-means is an iterative algorithm that searches for
(2005). K-means has been used for many applications in proximity in multi-dimensional spaces. It is necessary
the past, however its use on SN light curves has not yet to specify the number of clusters beforehand. The algo-
2
rithm operates as follows:
Table 1
1. Randomly select a starting point for each cluster Meanandstandarddeviationofeachcluster. Thefull
tableisgivenintheonlinematerial.
in the multi-dimensional space.
II-FS II-FF II-S
2. Classifyallpointsaccordingtotheirclosestcluster.
Phase Mean σ Mean σ Mean σ
Days M−M
peak
1.0 0.68 0.22 0.68 0.28 1.54 0.40
3. Calculate a new centroid for each cluster based on ··· ··· ··· ··· ··· ··· ···
the classified points. 30.0 -0.01 0.07 0.31 0.11 0.20 0.18
centroid LCs and the standard deviations of each clus-
4. Repeat 2 and 3 until convergence. ter are shown in Figure 2 and given in the online ma-
terial (the structure of the table is given in Table 1).
Weusedthesimplestdistancemetric—sumofsquares— Histograms showing the cumulative distribution of peak
to determine proximity. On the one hand this is rea- magnitude,rise-time,and∆m 1 withineachclusterare
15
sonable because all of our observations are in magnitude shown in Figures 3, 4, and 5 respectively. Note that the
differences. Ontheotherhand,theriseismuchshorterin II-FSclusterdoesnotcomefromthesamepopulationas
duration than the decline/plateau. Therefore late time II-FF and II-S in both peak magnitude and decline rate
data can dominate the division. Limiting our analysis atthe95%significancelevelaccordingtoaKolmogorov-
until day 30 after first light gives similar weight to both Smirnov (KS) test. The II-S cluster does not come from
the rise and the decline of the LCs. There are various the same population as the II-FF and II-FS clusters in
techniques for determining the number of clusters, how- rise-time at the 95% significance level according to a KS
ever in real-world cases the correct number of clusters is test.
neithertrivialnotobjective. Wefoundthatdividingour
sample into four clusters gave an interesting subdivision
ofthedata. K-meanswasinitializedrandomly100times
to eliminate sensitivity to the arbitrary starting point of
the algorithm.
In order to visualize our results, we also performed
principal component analysis (PCA). PCA finds direc-
tions in multi-dimensional sample space (in descending
order) along which the variance is maximal. In other
words, it finds eigenvector LCs which give the highest
variance when the sample LCs are projected onto them.
Defining our m×n matrix of LCs (where m is the num-
berofSNeandnisthenumberofparameters)asK,and
our PCA eigenvectors as p(cid:126) , the principal components(cid:126)c
i i
are given by
(cid:126)c =K·p(cid:126) (1)
i i
Note that (cid:126)c is a vector of the ith components of all of
i
the LCs in the sample. Figure 1. Visualplotofthe clusters. Colorrepresentsthemag-
nitude(normalizedtothepeak). EachrowisaSN,wheretheSNe
have been ordered by cluster. The red line highlights the cluster
3. RESULTS
locations. Wecanclearlyseeaseparationintothreeclusters.
WefoundthatdividingourSNlightcurvesampleinto
four clusters provides an intriguing physical interpreta- The first four PCA eigenvectors are shown in Figure
tion. One cluster contained only two events (iPTF13blq 6. The first two components describe most (90%) of
and iPTF14bas) which we identify as outliers. After the the variance between light curves. They are a slow ris-
analysiswascompletedusingfourclusterswealsoidenti- ing, and fast rising fast declining light curve. Figure 7
fiedathirdoutlier(iPTF14ajq),whichwassubsequently shows that applying K-means clustering on the interpo-
alsoidentifiedbythealgorithmoncethenumberofclus- lated light curves is equivalent to performing clustering
ters was raised to five. We removed these three events ontheprojectionoftheLCsonthefirsttwoPCAeigen-
anddiscussthemseparatelyinSection6. Wefoundthat vectors. Moreover, we show that applying K-means di-
the remaining LCs were best divided into three clusters. rectly on the PCA projections divides our sample into
Acolorvisualizationofthelightcurvessortedbycluster identical clusters. Figure 8 shows that the algorithm is
ispresentedinFigure1. Therisetime,whichisuniquely not clustering based on rise-time and decline rate. Clus-
available for this sample, plays a major role. Two clus- tering based on the LC morphology is not equivalent to
ters which have fast rise times (II-F) are separated by clustering based on rise-time and decline rate.
their decline phase. One cluster has a fast rise and slow
decline (II-FS; similar to a II-P), while the other has a 4. CAVEATS
fast rise but fast decline (II-FF; similar to a II-L). The
remainingclusterisseparatedbyitsslowrise(II-S).The 1 Defined as the difference in magnitude between the peak and
II-FS, II-FF, and II-S clusters are of similar size. The 15daysafterthepeak.
3
0
0.5
k
pea 1
M
M - II-FS II-S
1.5
2
2.5
0 5 10 15 20 25 0 5 10 15 20 25 30
0
0.5
k
pea 1
M
M - II-FF
1.5
2
2.5
0 5 10 15 20 25
Days from explosion
Figure 2. K-means clusters found using R-band light curves sampled from day 1 to 30. The median rise-time of each cluster has been
marked with a vertical line. Type II-P SN 2005cs (Pastorello et al. 2009) is superimposed, and fits only the II-FS category. This is the
onlywell-studiedSNII-Pwithgoodsamplingoftherise.
1 1
0.9 0.9
0.8 0.8
n0.7 n0.7
o o
uti uti
e distrib00..56 e distrib00..56
v v
ulati0.4 ulati0.4
m m
u u
C0.3 C0.3
0.2 II-FF (14) 0.2 II-FF (14)
II-S (18) II-S (18)
0.1 II-FS (24) 0.1 II-FS (24)
Outliers Outliers
0 0
-19 -18.5 -18 -17.5 -17 -16.5 -16 -15.5 -15 -14.5 -14 0 5 10 15 20 25 30
Peak absolute R-band magnitude Rise time in days
Figure 3. Cumulativedistributionfunctionofthepeakabsolute Figure 4. Cumulative distribution function of the rise-time for
R-bandmagnitudeforeachoftheclusters. Thenumberofobjects eachoftheclusters. Thenumberofobjectsineachclusterisgiven
in each cluster are given in parenthesis. The II-FS cluster is en- in parenthesis. The II-S cluster is not consistent with having the
richedinlower-luminosityevents,anddoesnotcomefromthesame sameparentpopulationastheII-FFandII-FSclustersatthe95%
population as the II-FF and II-S clusters at the 95% significance significancelevel(basedonaKStest).
level(basedonaKStest).
Wedrawthereader’sattentiontothefollowingcaveats over the range [−∆t ,+∆t ] we found that 34 ob-
0 0
and issues we observed during this analysis. jectshadaprobabilityofchangingclusterlessthan
20%. This is extremely conservative, because for
• The clustering is sensitive to the determination of most events there are measurements during the
the time of explosion. Running 100 simulations rise, making a random uniform distribution an ex-
whereweshiftedeachlightcurverandomlyintime treme overestimation of the uncertainty. Figure 11
4
1 K-means on LCs
4
0.9 II-FF
II-S
0.8 3 II-FS
n0.7
utio ent 2
b0.6 n
ulative distri00..45 PCA compo 01
m d
u n
C0.3 o
c
e
S-1
0.2 II-FF (14)
II-S (18)
0.1 II-FS (24) -2
Outliers
0
0 0.1 0.2 0.3 0.4 0.5 0.6
-3
∆ M -2 0 2 4 6 8 10
15
First PCA component
Figure 5. Cumulativedistributionfunctionof∆m15 foreachof K-means on PCA components
the clusters. The number of objects in each cluster is given in 4
parenthesis. The II-FS cluster is not consistent with having the
II-FF
sameparentpopulationastheII-FFandII-Sclustersatthe95%
II-S
significancelevel(basedonaKStest). 3 II-FS
-0.15 nt 2
e
n
-0.1 po
m 1
o
c
-0.05 A
C
P 0
nits 0 ond
u c
y Se-1
r 0.05
a
r
bit
Ar 0.1 -2
0.15 p~1
-3
p~2 -2 0 2 4 6 8 10
0.2 p~3 First PCA component
p~4
Figure 7. First two PCA components colored by their cluster
0.25
association. Top: objectsassociatedbyapplyingK-meansdirectly
0 5 10 15 20 25 30
on the LCs. Bottom: objects associated by applying K-means on
Days from explosion thefirsttwoPCAcomponents. ThefullinterpolatedLCs(untilday
30)encodesimilarinformationasthefirsttwoPCAcomponents.
Percent ofVarianceexplained246000 • Wteremdinoenotthehanvuemaberorbuofstcolubsjteecrtsiv.e mWetericditdo ndoet-
find the Calin´ski & Harabasz (1974) test (which
0
1 (57%) 2 (36%) 3 (3%) 4 (2%) maximizes the inter-variance while minimizing the
Principal component
inner-variance)toberobust. Insomecasestheop-
timal number of clusters according to the test was
Figure 6. Top panel: the first four PCA eigenvectors. Bottom
56. An improved metric is clearly necessary.
panel: percentofthevarianceexplainedbyeachcomponent. The
firsttwocomponentsexplain90%oftheobservedvariance.
• We normalize the LCs by their peak luminosity.
shows the probability of each SN to change cluster This may be reasonable given our uncertainties re-
andFigure12showshowtheseprobabilitiesaredis- gardinghostgalaxyextinction,andourobjectiveof
tributed. Some objects are more sensitive to these finding SNe that have very similar LC shapes, but
shiftsthanothers. Despitewhatonemightexpect, verydifferentpeakluminosities. However, muchof
the probability to change cluster does not appear the physics is encoded in the peak luminosity, and
to be correlated with the uncertainty on the time with a larger sample it may be more meaningful
of explosion (see Figure 13). to explore clustering while taking peak luminosity
into account.
• An optimal way of weighting the full light curve
(including information beyond day 30) is still lack- • Our clustering is performed in R-band. It is well
ing. known that LC shapes can vary in different filters,
5
0.5 and R-band may not be the optimal filter in which
II-FF to perform such an analysis.
II-S
0.4 II-FS
5. DISCUSSION
0.3
Several recent works explore the morphology of large
samplesofTypeIIlightcurves. Arcavietal.(2012);An-
0.2 derson et al. (2014); Faran et al. (2014a,b) and Sanders
m15 et al. (2015) tried to assess whether II-P and II-L light
∆
0.1 curves actually form two disjoint classes, or are rather a
continuousclass. Theyallexaminedpost-maximummor-
phology. Arcavi et al. (2012) and Faran et al. (2014a,b)
0
foundthatII-PandII-LaredisjointinR-band,butmay
have suffered from small number statistics. Studies of
-0.1 largersamples(Andersonetal.2014;Sandersetal.2015)
ledtheirauthorstotheconclusionthatthedeclinerates,
-0.2 peak magnitudes, and plateau lengths are all continuous
2 4 6 8 10 12 14 16 18
properties, with no clear separation into disjoint popu-
Rise-time in days
lations. Anderson et al. (2014) was particularly careful
Figure 8. ∆m15 as a function of rise-time colored by cluster infittingthepostmaximumdeclinerateseparatelyfrom
association.
the plateau decline rate, and found these quantities to
be continuous in a sample of 116 V-band light curves.
-0.2
More recently Rubin et al. (2015) presented a sample of
0 57 very well sampled LCs and did not observe any clear
0.2 discontinuities in the LC properties including the rise-
time.
0.4
We have, for the first time, performed unsupervised
0.6 clustering on Type II light curves. Importantly, our
peak 0.8 methodtakesintoaccountthefullmorphologyuntilday
M 30, including rise time data. Our division into four SN
M - 1 light curve classes leads us to several conclusions. First,
whiletherapidlyrisingSNeappeartonaturallyseparate
1.2
into two populations, divided by their slow/fast declines
1.4
(II-FSandII-FF,whichresembleII-PandII-L)thelate-
1.6 time morphology of the slow rising events (II-S, Figure
II-FF
2) does not appear to be very different from the classic
1.8 II-S
II-FS II-P/II-L classes. Therefore the previous classes of II-P
andII-Lmayhavehadalargenumberofinterlopersfrom
0 5 10 15 20 25 30
thisslowrisingpopulation—perhapsthisisthesourceof
Days from explosion
the continuum behavior observed in the previous works
Figure 9. ThesampleLCscoloredbycluster.
mentioned. While there is some excess at longer rise-
times, our sample is consistent with originating from a
-0.2
single population.
Figure 9 overplots these three clusters, while Figure
0
10 overplots the three centroid clusters and their stan-
dard deviations. It is clear from the figure that the
0.2
fast-rise/slow-decline(II-FS,Figure2)andfast-rise/fast-
0.4 decline (II-FF, Figure 2) are disjoint at late times, but
the II-S class bridgesthe gap—possiblyinducing theob-
kaep 0.6 served continuum in previous works.
M
- M 0.8 taiEnxsalmowineirngluFmiignuorseit3yweveesnetes,thwahtiltehtehIeI-rFeSmcaliunsintegrcclouns--
tersarecomprisedofbrighterSNeonaverage(recallthat
1 the clustering does not take into account peak magni-
tude). This excess of faint objects is the slow/faint SN
1.2 II-P population (e.g. SN 2005cs and PTF10vdl). Using
II-FF
II-S a KS test we find that the II-FS cluster does not come
1.4 II-FS from the same population as the II-FF and II-S clusters
inpeakmagnitudeatthe95%significancelevel. Thefact
0 5 10 15 20 25 30
Days from explosion that the II-FS cluster differs in an observable other than
LC shape may indicate that there is a physical meaning
Figure 10. Plots of the cluster 1−σ limits. Notice that II-FF
andII-FSaredisjointatlatetimes,andthetwoareweaklydisjoint for the clusters found.
fromtheII-Satearlytimes. Theslow-risersbridgethegapatlate Our comparison to PCA is instructive. We found that
timebetweenII-FFandII-FS. using the full LC information is equivalent to using just
6
0.75
±∆t0
bility toe cluster 0.5 ±∆t0/2
ag
oban0.25
Prch
0
09cjq09ecm09fma10abyy10bgl10gva10gxi10jwr10mug10osr10pjg10qwz10rem10uls10umz10uqg10uqn10vdl10xtq11ajz11cwi11go11hsj11htj11iqb11izt11qax12bbm12bro12bvh12cod12efk12fip12fo12ftc12gnn12grj12hsx12krf13aaz13akg13bjx13bld13bsg13ccu13clj13cly13cnk13dkk13dkz13dla13dqy13dzb14abc14adz14aoi
Figure 11. Probability of each object to change cluster when LCs were shifted randomly in time between [−∆t0,+∆t0] and
[−∆t0/2,+∆t0/2].
18 is unclear if they represent distinct physical classes. We
have found some sensitivity to the determination of the
16 time of explosion. Moreover, the sensitivity does not ap-
peartobecorrelatedwiththeuncertaintyonthetimeof
14
explosion, making it unclear if higher cadence photome-
try would improve the results.
12
s
ct These clusters may be useful in photometric identifi-
e
obj10 cation of SNe, or the completion of gaps in photomet-
of ric coverage. Our discovery of a spectroscopically dis-
ber 8 tinctclassinanunsupervisedfashionencouragesfurther
m work. However the true test of these results will be the
u
N 6 application of the this analysis on an independent sam-
ple of similar size and quality. As photometric surveys
4 begin to supply the community with large data sets of
similarly sampled LCs, it will likely become necessary to
2
employ unsupervised techniques to identify and classify
transients.
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 6. OUTLIERS:TYPEIIbSNeFROMMASSIVE
Probability to change cluster
PROGENITORS
Figure 12. Histogramoftheprobabilitytochangeclusterwhen Examiningtheoutliersmoreclosely,wefoundthattwo
LCswereshiftedrandomlyintimebetween[−∆t0,+∆t0]. of them (iPTF13blq and iPTF14bas) have spectra that
are consistent with a IIb classification, although their
0.8
light curves are unusually slowly-rising. This was the
reason they were removed from the Rubin et al. (2015)
0.7
sample after performing the analysis presented in this
work. We present their spectra with similar IIb spec-
er0.6 tra superimposed in Appendix Figure 2. Only later did
st
u werealizethatiPTF14ajqisalsoanoutlier, andwecon-
e cl0.5 firmedthatthealgorithmidentifiesthisbyincreasingthe
g
n
a number of clusters to five, which clustered iPTF13blq
h
o c0.4 and iPTF14ajq together, leaving iPTF14bas as a cluster
y t alone. Returning to Rubin et al. (2015) we find that the
bilit0.3 spectrum of iPTF14ajq suffered heavy galaxy contami-
a
b nation. While it is conclusively a Type II SN, we cannot
o
Pr0.2 rule out a IIb classification based on the only available
spectrum. All three spectra are available on WISeREP
0.1 (Yaron & Gal-Yam 2012).
Type IIb (as well as Type Ib and Ib/c) originate from
0 strippedenvelopeprogenitors. Whilethestrippingmech-
0 0.5 1 1.5 2 2.5 3
∆t indays anism is the subject of some debate, the two main pos-
0
sibilities are stripping via binary interaction (Podsiad-
Figure 13. Probabilitytochangeclusterplottedagainsttheun-
lowski et al. 1992), and stripping due to episodic mass
certaintyonthetimeoffirstlight. Nocorrelationisapparent.
loss or to stellar winds. While the low ejecta masses and
two parameters, the projections of the LCs on the first high rates of SNe IIb (19-25% by volume; Li et al. 2011)
two principal components. This may have far reaching may point towards the binary interaction channel, it is
ramifications, and may indicate that Type II LCs of this expectedthatatleastsomeSNeIIbwillresultfromsingle
qualityareatwoparameterproblem. Includinglatetime massive stars that are stripped by winds. These are ex-
data,andthepeakmagnitudewilladdsomecomplexity. pected to produce a large ejecta mass, leading to a long-
Itisimportanttonotethattheclassesidentifiedinthis risingLC.SN2009jfisanexamplearelatedevent,where
work have some overlap, are limited to R-band, and it a massive star was almost completely stripped of its hy-
7
drogen envelope, leading to a Ib classification. Valenti We thank Y. Cao for reducing the spectrum of
etal.(2011)andSahuetal.(2011)foundthatSN2009jf iPTF13blq. We thank A. Tanay and B. Zackay for help-
wasmostlikelyaTypeIbSNoriginatingfromamassive ful discussions. A.G.Y. is supported by the EU/FP7
single-star progenitor with M (cid:38)20−30 M . via ERC grant no. 307260, the Quantum Universe I-
ZAMS (cid:12)
In Figure 14 we compare the outliers to SN 2009jf and CORE Program by the Israeli Committee for Planning
findthatthelightcurvesarestrikinglysimilar. Wespec- and Budgeting and the Israel Science Foundation (ISF);
ulate that iPTF14ajq is in fact a IIb and suggest that byMinervaandISFgrants;bytheWeizmann-UK“mak-
theseextremelyslowly-evolvingIIb’soriginatefrommas- ingconnections”program;andbyKimmelandARCHES
sive stripped envelope stars. They are also relatively lu- awards.
minous, two with absolute peak magnitudes less than -
17.5whileiPTF14ajqpeaksat-16.4,lendingfurthersup-
port that these are high-energy events originating from
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APPENDIX
8
13blq 14bas
550 3500
500
3000
450
400
2500
350
Flux [counts]223050000 Flux [counts]12500000
150 1000
100
500
50
0
0
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100
MJD - 56428.8087 MJD - 56786.2892
Figure 1. Smoothed LCs of iPTF13blq and iPTF14bas. iPTF13blq was smoothed with the algorithm of Rubin et al. (2015) while
iPTF14baswassmoothedwithasmoothingspline.
1.6 2
13blq
SN 1993J +13
1.4 1.8
1.2 1.6
y] y]
ar 1 ar1.4
bitr bitr
ar ar
x [0.8 x [1.2
u u
Fl Fl
0.6 1
0.4 0.8
14bas
SN 2006ep +44
0.2 0.6
4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000
Observed wavelength Observed wavelength
Figure 2. SNIDcomparisonofSNeiPTF13blq(left)andiPTF14bas(right)withIIbspectra.