arXiv:1312.3342v2 [astro-ph.HE] 20 May 2014

Persistent C II Absorption in the Normal Type Ia Supernova
2002fk∗Régis Cartier1,2 , Mario Hamuy2,1 , Giuliano Pignata3,1 , Francisco Förster4,1 , Paula Zelaya1,5 ,Gaston Folatelli6 , Mark M. Phillips7 , Nidia Morrell7 , Kevin Krisciunas8 , Nicholas
B. Suntzeff8 , Alejandro Clocchiatti5,1 , Paolo Coppi9 , Carlos Contreras7 , Miguel Roth7 ,Kathleen Koviak10 , José Maza2 , Luis González2 , Sergio González7 and Leonor Huerta2
ABSTRACT
We present well-sampled UBV RIJHK photometry of SN 2002fk starting 12 days
before maximum light through 122 days after peak brightness, along with a seriesof 15 optical spectra from -4 to +95 days since maximum. Our observations show
the presence of C II lines in the early-time spectra of SN 2002fk, expanding at
11,000 km s−1 and persisting until 8 days past maximum light with a velocity of∼9,000 km s−1 . SN 2002fk is characterized by a small velocity gradient of v̇Si II =26 km s−1 day−1 , possibly caused by an off-center explosion with the ignition
region oriented towards the observer. The connection between viewing angle of an
off-center explosion and the presence of C II in the early time spectrum suggests
1

Millennium Institute of Astrophysics, Casilla 36-D, Santiago, Chile2

Departamento de Astronomı́a, Universidad de Chile, Casilla 36-D, Santiago, Chile

3

Departamento Ciencias Fisicas, Universidad Andres Bello, Av. República 252, Santiago, Chile

4

Center for Mathematical Modelling, Universidad de Chile, Avenida Blanco Encalada 2120, Piso 7, Santiago, Chile
5

Departamento de Astronomı́a y Astrofı́sica, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
6

Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan
7

Carnegie Institution of Washington, Las Campanas Observatory, Colina el Pino s/n, Casilla 601, Chile

8

Department of Physics and Astronomy, Texas A&M University, 4242 TAMU, College Station, TX 77843,
USA
9

Department of Astronomy, Yale University, New Haven, CT 06520-8101

10

Carnegie Institution of Washington, 813 Santa Barbara Street, Pasadena, CA 911901, USA*

This paper includes data gathered with the 6.5 m Magellan telescopes at Las Campanas Observatory,
Chile

–2–
that the observation of C II could be also due to a viewing angle effect. Adopting
the Cepheid distance to NGC 1309 we provide the first H0 value based on nearIR measurements of a Type Ia supernova between 63.0±0.8 (± 2.8 systematic)
and 66.7±1.0 (± 3.5 systematic) km s−1 Mpc−1 , depending on the absolutemagnitude/decline rate relationship adopted. It appears that the near-IR yields
somewhat lower (6-9%) H0 values than the optical. It is essential to further
examine this issue by (1) expanding the sample of high-quality near-IR light
curves of SNe in the Hubble flow, and (2) increasing the number of nearby SNewith near-IR SN light curves and precise Cepheid distances, which affords thepromise to deliver a more precise determination of H0 .
Subject headings: supernovae: general - supernovae: individual: SN 2002fk cosmological parameters - cosmology: observations

1.

INTRODUCTION

Type Ia supernovae (SNe) have proven to be extremely useful as extragalactic distance indicators in the optical (Hamuy et al. 2006; Hicken et al. 2009; Folatelli et al. 2010)
thanks to the relation between peak luminosity and decline rate (Phillips 1993), which allows the standardization of their luminosities, and in the near infrared (Wood-Vasey et al.
2008; Krisciunas et al. 2004b,c) where they behave almost as standard candles (Kattner et al.
2012). Photometric observations of SNe Ia have delivered Hubble diagrams with unrivaled
low dispersions (0.15 mag), which permits one to determine precise values for fundamental
cosmological parameters such as the Hubble constant and the deceleration parameter. It was
this technique that led in 1998 to the surprising discovery that the Universe is in a state ofaccelerated expansion caused by a mysterious dark energy that comprises 70% of the energy
content of the Universe (Riess et al. 1998; Perlmutter et al. 1999). Measuring the equationof state parameter of the dark energy and its evolution with time constitutes one of the mostimportant astrophysical challenges today.
Since the discovery of the accelerated expansion, extensive surveys and follow-up programs have increased the number of SNe Ia by more than an order of magnitude. Furthermore, the quality of the follow–up observations (light curves, early–time optical spectra, nearinfrared (near-IR) spectra, nebular spectroscopy, polarization) has significantly increased. As
a consequence of the increase in the statistical samples available and the degree of details
observed, several indications of diversity have emerged within the family of SNe Ia thatmanifest in differences in several observables, most notably, early time velocity gradients(Benetti et al. 2004), the presence of unburned material, late-time nebular velocity shifts

–3–(Maeda et al. 2010a,c), line polarization (Leonard et al. 2005; Wang & Wheeler 2008), highvelocity components of spectral lines (Kasen et al. 2003; Thomas et al. 2004; Gerardy et al.
2004; Mazzali et al 2005), and interstellar line strengths (Sternberg et al. 2011; Foley et al.
2012d; Förster et al. 2012; Phillips et al. 2013). At this point the use of SNe Ia for thedetermination of cosmological parameters and the equation of state of the dark energy isdominated by systematics (see e.g. Kessler et al. 2009; Conley et al. 2011). Among themost important sources of systematics are the extinction by dust in the SN host galaxies(Folatelli et al. 2010, and references therein) and our lack of understanding of the explosion
mechanisms and the progenitor system (see e.g. Hillebrandt & Niemeyer 2000; Röpke et al.
2012; Maoz et al. 2014).
SNe Ia are believed to result from the nuclear burning of a C+O white dwarf (WD).
Given that carbon is not produced in the explosion, it provides unique evidence of the originalcomposition of the star before explosion. For this reason the amount and distribution of theunburned carbon material is fundamental to understand the burning process of the star.
Until recently only a handful of normal SNe Ia have shown carbon. Thanks to large surveys
that have discovered and followed–up SNe Ia from very early phases, carbon has been foundin nearly 30% of the SNe before maximum light (Parrent et al. 2011; Thomas et al. 2011b;
Folatelli et al. 2012; Silverman & Filippenko 2012b), and even more frequently within theclass of very luminous and low expansion velocities objects thought to be the result of asuper–Chandrasekhar–mass WD (Howell et al. 2006; Thomas et al. 2007; Yamanaka et al.
2009; Scalzo et al. 2010; Silverman et al. 2010).
Additional multi-wavelength and multi-epoch observations of SNe Ia will be required
to establish a scenario connecting the observed diversity among SNe Ia. Here we present
a contribution to this subject through extensive optical and near-IR observations for thenormal Type Ia SN 2002fk obtained in the course of the “Carnegie Type II Supernova
Survey” (CATS, hereafter) (Hamuy et al. 2009). While our optical data are complementary
to the photometry published by the Lick Observatory Supernova Search (LOSS, Riess et al.
2009b; Ganeshalingam et al. 2010), and by the Center for Astrophysics (CfA) Supernova
Program (CfA3 sample, Hicken et al. 2009), our near-IR data provide one of the earliest
near-IR light curves for a Type Ia SN. The exceptional coverage of the maximum both in the
optical and the near-IR light curves together with the Cepheid distance recently measured by
Riess et al. (2011a, 2009a), makes SN 2002fk one of the most suitable SNe Ia for calibrationof the Hubble constant. The completeness of the light curves also affords the opportunity totest independent methods for the determination of the host galaxy reddening using a mixtureof B −V and V-near–IR colors. In addition, we present 15 optical spectra obtained from −4
to +95 days since maximum in the B-band, which are complemented by spectra obtained by
the CfA Supernova Program (Blondin et al. 2012) and the Berkeley Supernova Ia Program

–4–(BSNIP, Silverman et al. 2012a). The spectra provide clear evidence for unburned carbon.
SN 2002fk is a very well observed SNe Ia showing carbon lines in pre-maximum spectra
and the only one where such lines persist several days past peak brightness. Thus, theseobservations provide important clues to our understanding of the explosion mechanisms fornormal SNe Ia.
This paper is organized as follows: in section 2 we describe the photometric and spectroscopic observations and data reductions; in section 3 we present the photometric data
and the determination of reddening caused by dust; in section 4 we show the spectroscopic
evolution of SN 2002fk; in section 5 we calculate the Hubble constant using the photometry
presented here complemented by LOSS and CfA3 photometry, and the distance to NGC 1309
(Riess et al. 2011a); we discuss our results and present our conclusions in section 6. In
an upcoming paper (Zelaya et al. 2014) we will present spectropolarimetric observations of
SN 2002fk.

2.

OBSERVATIONS AND DATA REDUCTION

SN 2002fk was discovered independently by Kushida, R. (2002) and by Wang & Qiu(2002) at V ≃ 15.0 mag on 2002 September 17.7. The supernova was located at α=03:22:05.71
and δ=-15:24:03.2 (J2000), 3.6′′ south and 12.6′′ west of the host galaxy NGC 1309 (seeFigure 1). NGC 1309 is an SA(s)bc galaxy with a heliocentric recession velocity of 2,136
km s−1 obtained from neutral hydrogen line measurements (Koribalski et al. 2004). Ayani & Yamaoka(2002) classified SN 2002fk as a Type Ia from an optical spectrum obtained on 2002 September 20.

2.1.

Instrumental Settings

The optical imaging of SN 2002fk was obtained with UBVRI Johnson-Kron-Cousins
filters using the Swope 1 m telescope, the Wide Field Re-imaging CCD Camera (WFCCD)
on the 2.5 m du Pont telescope, and the Low-Dispersion Survey Spectrograph (LDSS-2) on
the 6.5 m f/11 Magellan Clay telescope, all at Las Campanas Observatory (LCO). A few
additional optical images were obtained with the 0.9 m and 1.5 m telescopes at Cerro Tololo
Inter-American Observatory (CTIO). For galaxy subtraction, we used images obtained with
the Direct CCD Camera on the 2.5 m du Pont telescope. Additional observations with thePanchromatic Robotic Optical Monitoring and Polarimetry Telescope (PROMPT) at CTIO
were obtained for the single purpose of calibrating a photometric sequence of local standards

–5–around SN 2002fk.
IR images of SN 2002fk were obtained with JHKs filters with the Swope telescope IR
Camera (C40IRC) and the Wide Field IR Camera (WIRC) on the du Pont telescope. In
Table 1 we summarize the instruments used for the optical and IR imaging.
Optical spectroscopy of SN 2002fk was obtained with five instruments: LDSS-2 and the
B&C Spectrograph on the LCO Baade telescope, the WFCCD and Modular Spectrographon the LCO du Pont telescope, and FORS1-PMOS on the ESO (European Southern Observatory) Very Large Telescope located on Cerro Paranal. In Table 2 we summarize theinstruments used for the spectroscopic follow-up and their main characteristics. More details
about these instruments are given by Hamuy et al. (2009).

2.2.

Optical Photometry Reduction

We reduced the optical images using a custom IRAF11 script package, as described by
Hamuy et al. (2009). We processed the raw images through bias subtraction and flat fielding.
As long as sky flats were available, we corrected small gradients in dome flat illumination(∼ 1%). To reduce any possible galaxy contamination in our photometry we subtracted thehost galaxy from our SN images using high quality template images obtained with the Direct
CCD Camera on the du Pont telescope after the SN had vanished on 2005 February 13. This
instrument delivers a typical point-spread-function (PSF) of 0.7′′ (full width at half-maximum
intensity), thus providing templates with better image quality than any of the SN+galaxy
images. To secure high quality image subtractions, we employed the same UBV (RI)KC
filter set of the Swope telescope (which was used on the majority of our optical observations;see Table 5). Differential PSF photometry was made on the galaxy-subtracted images using
the sequence of local standards (Figure 1), calibrated against Landolt (1992) photometricstandards observed during several photometric nights. Systematic errors introduced by using
template images taken with the du Pont telescope are considered in Appendix A.
The Landolt stars were employed to derive the following photometric transformations
from instrumental to standard magnitudes,
U = u + ctu (u − b) + zpu
11(1)

IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National
Science Foundation.

–6–
B = b + ctb (b − v) + zpb(2)

V = v + ctv (v − i) + zpv(3)

R = r + ctr (v − r) + zpr(4)

I = i + cti (v − i) + zpi(5)

In these equations UBV RI (left-hand side) are the published magnitudes in the standard
system Landolt (1992), ubvri (right-hand side) correspond to the natural system magnitudes,
ctj to the color term, and zpj to the zero-point for filter j(j = u, b, v, r, i)12.
These transformations were then applied to 11 pre-selected stars in the field of the SN inorder to establish a sequence of local standards, which is presented in Table 3. In Appendix
B we perform a detailed analysis of our photometric calibration and a comparison with thatobtained by LOSS (Ganeshalingam et al. 2010) and CfA3 (Hicken et al. 2009).
Having established the photometric calibration of the SN 2002fk field, we carried out
differential photometry between the SN and the local standards. For all five optical cameras
we employed average color terms determined on multiple nights (listed in Table 4), solving
only for the photometric zero-points. The resulting UBV RI magnitudes covering 130 daysof evolution of SN 2002fk are summarized in Table 5.

2.3.

Near-IR Photometry Reduction

The vast majority (21/24) of the near-IR photometric observations were obtained with
WIRC on the du Pont telescope. WIRC has four different detectors. Usually only two of
the detectors were used to observe. The observing strategy consisted in taking five dithered
images of the object with detector 1, while detector 2 was used to take sky images. Thenthe detectors were switched, i.e. the SN was observed on detector 2 while detector 1 wasused to take sky images. The observations were reduced following standard procedures witha slighty modified version of the Carnegie Supernova Project (CSP) WIRC pipeline (written
in IRAF, Hamuy et al. 2006; Contreras et al. 2010). We had to modify the pipeline to workwithout dark and bias because these calibrations were not taken during the observations of
SN 2002fk. The pipeline first masks detectable sources in the sky frames and then combinesthem to create a final sky frame for each detector. Then the pipeline subtracts the final sky
image from the science images to get a bias/dark/sky subtracted science frame. In order to
12

In the case of the LDSS-2 instrument which does not have an I filter, we used (b − v) instead of (v − i)in equation 3.

–7–
correct for pixel–to–pixel gain variations we divide science images by a flat field constructedfrom the subtraction of a flat-off from a flat-on image and normalize the result. For nights
where flats were not taken we used the best calibration images from the two closest nights.
In addition to this, the pipeline masks cosmetic defects and saturated objects and combines
the dithered frames from each detector to deliver a final science image per detector.
Classic-Cam on the 6.5 m Baade telescope was used on three nights to obtain nearIR images. Since all calibrations (dark, bias, flat) were taken with this instrument, we
performed the standard data reduction. First we subtracted the bias and the dark from all
frames. Then we created a flat field for each night subtracting the flat–off from the flat–on
image and normalized the result. Finally, we corrected pixel–to–pixel variations dividing all
science images by the flat fields.
We obtained galaxy subtraction templates, using the WIRC/du Pont configuration,
on 2003 November 2 and 11 after the SN had vanished. We perfomed differential PSF
photometry of the SN in the WIRC galaxy–subtracted images with respect to four near-IR
local sequence stars around SN 2002fk. We calibrated these four local standards stars withrespect to Persson et al. (1998) standards using aperture photometry. The Persson standard
star images were taken close in time and airmass to the SN field, so it was not necessary tocorrect for atmospheric extinction. Photometry of the local sequence was obtained in four
photometric nigths with WIRC. In Table 6 we present our JHKs photometry for the local
sequence along with the 2MASS magnitudes for comparison. Within the uncertainties our
photometry is in good agreement with the 2MASS values. This is an encouraging result
considering that the Persson et al. (1998) system is not identical to the 2MASS photometricsystem (Skrutskie et al. 2006).
In the small field-of-view of Classic-Cam only star c5 was observed along with the SN.
This precluded us from subtracting the galaxy templates and performing PSF photometry,so we ended up measuring aperture photometry of the SN with respect to c5 alone. Table 7
presents the resulting JHKS photometry for SN 2002fk which covers 115 days of its evolution
since discovery.

2.4.

Spectroscopy

A total of 15 spectra of SN 2002fk were obtained, as summarized in Table 2. We
obtained five spectra with the 6.5 m Magellan Baade telescope using LDSS-2. For theseobservations, a 300 line mm−1 grism blazed at 5000 Å was employed, covering from 3600
to 9000 Å with a resolution of 14 Å. Three spectra were observed with the Baade telescope

–8–
using the B&C Spectrograph. This instrument uses a SITe 1752 × 572 pixel CCD with 300
line mm−1 grating blazed at 5000 Å. The wavelength range obtained was 3200 to 9200 Å witha resolution of 7 Å. Three times we used the du Pont telescope with the WFCCD instrument
in its spectroscopic long-slit mode. A 400 line mm−1 blue grism was employed, covering the
wavelength range from 3800 to 9200 Å with a resolution of 8 Å. We also obtained one
spectrum with the Las Campanas Modular Spectrograph on the du Pont telescope, coveringfrom 3790 to 7270 Å with a resolution of 7 Å. With all four instruments (WFCCD, LDSS2, B&C, and Modular Spectrograph) we observed the SN and the standard stars with theslit aligned along the parallactic angle (Filippenko 1982) to reduce the effects of atmosphericdispersion. Additional information about the instruments and observing modes are presented
in Hamuy et al. (2009).
Three of our spectra of SN 2002fk were obtained in polarimetric mode with the FORS1
instrument on the ESO VLT UT3 telescope on 2002 October 1st, 5th, and 14th. For eachof the three epochs observed, four exposures were taken with the retarder plate at position
angles of 0, 22.5, 45 and 67.5 degrees. The exposure times were 720 sec on October 1st, 720
sec on October 5th, and 600 sec on October 14th. Grism GRIS 300V was used with no orderseparation filter. This provides a dispersion of 2.59 Å pix−1 , and the resulting wavelength
range 3300–8500 Å. The spectral resolution with a 1′′ slit was 12.25 Å, which we measured
using the [OI] 5577 sky emission line. Additional observations of a flux standard, EG21, were
performed at position angle 0 degrees to calibrate the flux level. We followed a standard
data reduction procedure using IRAF. A single intensity spectrum was obtained for eachepoch, combining the four angle spectra with two beams each, in the following way:P

speci
specerri2
Ftot = P 1
specerri2(6)

with i=0, 22, 45 and 67, where speci is the sum of the two beams corresponding to ordinary and extraordinary rays, at each angle, and specerri is the quadratic sum of the errors
per beam for each of the four angles. Here we present the intensity spectra alone, andwe postpone the spectropolarimetric reduction details and results for an upcoming paper(Zelaya et al. 2014).
Despite having observed the SN along the parallactic angle, we checked the spectrophotometric quality of our spectra by convolving them with the standard BV (RI)KC bandpasses
described by Bessell (1990) and computing synthetic magnitudes. In general, this comparison shows very good agreement within 0.01-0.03 mag between the observed and syntheticcolors, thus demonstrating the excellent quality of our spectra. Having checked the relative
spectrophotometry we proceeded to apply a low–order wavelength dependent correction to–9–make all of our spectra fully consistent with the photometry.
Optical spectra of SN 2002fk were recently published by the CfA Program (Blondin et al.
2012) and the Berkeley Supernova Ia Program (BSNIP, Silverman et al. 2012a). CfA obtained 23 spectra covering from −3 to +120 days since maximum in B and BSNIP obtained
five spectra from +8 to +150 days after B maximum. In Figure 2 we compare our spectra(blue) taken with the CfA (green) and the BSNIP (orange) spectra observed within one dayfrom ours. As can be seen, the agreement is excellent, with only very small differences withthe first two CfA spectra. All of these data will be used subsequently in our study.

3.

LIGHT CURVES OF SN 2002fk
3.1.

Optical Light Curves

Optical photometry of SN 2002fk has been previously published by LOSS (Riess et al.
2009b; Ganeshalingam et al. 2010) and by the CfA Supernova Program (CfA3 sample,
Hicken et al. 2009). These data have good sampling, most notably the LOSS observations
that begin 11.8 days before B-band maximum. These datasets are a valuable complement toour optical photometry. However, since we have detected systematic differences between the
CATS, LOSS, and CfA3 photometric calibrations it has proven necessary to apply offsets
to the LOSS and CfA3 photometry in order to bring all measurements to the same CATS
photometric system, as described in Appendix B. In doing so, we added in quadrature to
the LOSS and CfA3 uncertainties those from the photometric offsets. Adding these offsets(summarized in Table 8) decrease significantly the differences in the R- and I–band SN
magnitudes among the three datasets (as illustrated in Figure 3 for the I–band), but has no
noticeable effects in the B- and V –bands.
Figure 4 presents the UBV RI light curves of SN 2002fk, including CATS (filled circles)
and the LOSS (open circles) and CfA3 data (open squares) after applying the corresponding
photometric offsets. A polynomial fit to the B-band light curve around maximum brightness
yields Bmax = 13.30 ± 0.03 mag on JD 2, 452, 547.8 ± 0.5 and a decline rate parameter∆m15 = 1.02 ±0.04 which is close to the fiducial value adopted by Phillips et al. (1999)
and Folatelli et al. (2010) for SNe Ia. Polynomial fits to the other lightcurves yield Umax =12.69 ± 0.07 mag on JD 2, 452, 546.0 ± 1.5, Vmax = 13.37 ± 0.03 mag on JD 2, 452, 548.5 ± 0.5,
Rmax = 13.36 ± 0.03 mag on JD 2, 452, 549.2 ± 0.5, and Imax = 13.57 ± 0.03 mag on JD
2, 452, 545.8 ± 0.5. V and R peak roughly one day after B, whilst U and I peak two days
before B. This is consistent with the typical behavior of SNe Ia. Bright Type Ia SNe
usually show a secondary maximum in R and I, and in the near-IR bands. A polynomial

– 10 –
fit to the secondary peaks yields R2nd max = 14.14 ± 0.03 on JD 2, 452, 568.3 ± 0.5 andI2nd max = 14.08 ± 0.03 on JD 2, 452, 575.4 ± 0.5. Errors in peak magnitudes include theuncertainty due to differences in filter transmissions (S-corrections; see Appendix C).
A small bump ∼ 0.15 mag is present in the I-band light curve of SN 2002fk located∼ 20 days past maximum and ∼ 7.5 days before the secondary maximum. This is seen in
Figure 3 which shows the individual I-band data points and the residuals from a polynomial
fit. The left panels correspond to the original CATS, LOSS, and CfA3 data, while the rightpanels correspond to the same data after applying the photometric offsets. Although thebump in question is supported by three photometric points (two from CATS and one from
CfA3), each one with a 3-7 σ significance, we cannot rule out the possibility that it is an
artifact due to the combination of photometry taken with different filters and detectors.
In Figure 5 we compare the BV RI light-curves of SN 2002fk and other SNe with similar∆m15. Despite their similar decline rates, we notice small yet real departures from a commom photometric behavior, namely: 1) a dispersion in the rise branch, where SN 2002bo,
SN 2002dj, and SN 2005cf show faster rise times, in agreement to what was found by
Pignata et al. (2008) and Ganeshalingam et al. (2011) where high-velocity gradient objects(as defined by Benetti et al. 2005) generally show shorter rise times; 2) the small bump∼ 0.15 mag in the I–band light curve of SN 2002fk that peaks 20 days past maximum in B;3) small differences in the time and amplitude of the secondary peaks in R and I (see also
Krisciunas et al. 2001; Folatelli et al. 2010; Burns et al. 2011).

3.2.

Near-IR Light Curves

Figure 6 shows our optical and near-IR light curves of SN 2002fk. Our near-IR observations begin 12 days before B-maximum, among the earliest JHK photometry everobtained for a SN Ia, and extend through 102 days past maximum which is exceptional
for a SN Ia (Krisciunas et al. 2004b; Wood-Vasey et al. 2008; Folatelli et al. 2010). The
photometric coverage is remarkably good before and close to peak brightness, through thenear-IR minimum, and at late times. The second near-IR peak, on the other hand, is not
so well sampled. Polynomial fits to the IR light curves around maximum brightness yield
Jmax = 13.76 ± 0.02 on JD 2, 452, 544.3 ± 0.5, Hmax = 13.98 ± 0.02 on JD 2, 452, 543.5 ± 0.5,
and Kmax = 13.76 ± 0.02 on JD 2, 452, 544.2 ± 0.5.
In Figure 7 we compare the IJHK-band light curves of SN 2002fk, SN 2001el (Krisciunas et al.
2003), SN 2002dj (Pignata et al. 2008), SN 2005cf (Wang et al. 2009), and SN 2006dd(Stritzinger et al. 2010) normalized to peak magnitudes in each band. These are well-studied

– 11 –
SNe with very complete optical and near-IR light curves and with similar ∆m15 values. We
also show in dotted-dashed lines the templates from Krisciunas et al. (2004b) and in dashedlines the templates from Wood-Vasey et al. (2008). In all bands SN 2002fk has a faster rise
to peak than both templates. After maximum it is evident that SN 2002fk has a more pronounced minimum in all IJHK bands compared with the other SNe and a deeper minimum
than the Wood-Vasey et al. (2008) and Krisciunas et al. (2004b) templates. Although thesecondary peak was not covered by our observations in JHK, the observations suggest a welldefined secondary maximum, clearly distinguishable from the first peak and from the minimum between the peaks. The differences in the light curves become much smaller aroundthe secondary peak, after which all five SNe show good agreement in their decline rates.
Kasen (2006) showed that the near–IR secondary maximum is related to the ionization
evolution of the iron group elements, in particular to the transition of the iron/cobalt gas fromdouble to singly ionized. In his scenario the mixing of 56 Ni outward increases the velocity
extent of the iron core. This hastens the ocurrence of the near–IR secondary maximum.
In SN 2002fk the secondary peak does not occur earlier than in the remaining SNe, so alarge mixing of 56 Ni is unlikely. Higher metallicity progenitors should produce a higher
fraction of stable iron group material (Timmes et al 2003). Kasen (2006) showed that alarge amount of iron group material would cause the recombination wave to reach the iron–rich layers relatively earlier, thus producing an earlier secondary maximum. Given thatin SN 2002fk the secondary peak was not observed to occur earlier, greater than normal
progenitor metallicity is also unlikely. In his models, Kasen (2006) presented evidence thata higher contrast between the peaks and the minima is expected in hotter SNe (i.e. thosewith relatively greater 56 Ni mass) because the transition wave from double to single ionizediron takes a longer time to reach the iron core. Perhaps then, the deep minimum observedin SN 2002fk is produced by a higher than normal ejecta temperature, and the I-band bump
∼20 days past maximum could be due to asymmetries in the distribution of iron groupelements.

3.3.

Reddening Determination

Given the early and complete optical and near-IR light curves of SN 2002fk we can estimate the amount of dust reddening (Galactic + host galaxy) using different colors, assuming
the standard Galactic extinction law of Cardelli et al. (1989).
Firstly, we estimate the reddening towards SN 2002fk from its late-time (B − V ) colors
using the standard Lira–Phillips relation (Lira 1996; Phillips et al. 1999), which yields E(B −V )Lira = 0.066 ± 0.019. The slope of SN 2002fk is in good agreement with the Lira relation

– 12 –
within the dispersion. Secondly, we use the near maximum optical colors versus decline
rate relations (Phillips et al. 1999), which yields E(B − V )Bmax −Vmax = 0.009 ± 0.044 andE(B − V )Vmax −Imax = 0.082 ± 0.038. Thirdly, we estimate the reddening using the V − nearIR colors by minimizing χ2 between the observed V − H and V − K colors with respect tothe Krisciunas et al. (2004b) zero-reddening templates. From these fits we obtain E(B −V )V −H = 0.014 ± 0.037 and E(B − V )V −K = 0.075 ± 0.036. Within the uncertainties theseresults are consistent with the optical methods.
In table 9 we summarize our results. The weighted mean of the reddening using these
five different methods is E(B − V ) = 0.057 with a dispersion of 0.036 mag. This value isclose to the measured Galactic reddening towards SN 2002fk, namely E(B − V ) = 0.035
mag (Schlafly & Finkbeiner 2011), which implies that the host galaxy reddening was low.
As shown by Phillips et al. (2013), the equivalent width of Na I D is not a reliable indicatorof host dust extinction in SNe Ia. According to these authors, only the absence of detectable
NaI D absorption in a high signal-to-noise ratio spectrum can be used to infer low dust
extinction. The fact that we detect a weak (0.018 Å) Na I D absorption in our highest
signal-to-noise spectra at the redshift of the host galaxy is consistent with the small dust
reddening inferred from the SN colors.

3.4.

Optical Colors

Figure 8 shows dust corrected color curves of well observed “normal” SNe Ia withsimilar ∆m15 to SN 2002fk. We dereddened the color curves using the recalibrated Galactic extinction maps of Schlegel et al. (1998) presented by Schlafly & Finkbeiner (2011) andthe host galaxy reddening derived from the Lira–Phillips relation (Lira 1996; Phillips et al.
1999). In all cases we transformed reddening into extinction at different filters using thestandard Galactic extinction law of Cardelli et al. (1989) with RV = 3.1, with the warningthat the use of RV = 3.1 can introduce systematic offsets for heavily reddened SNe likeSN 2002bo (Phillips et al. 2013), with the effect being largest in V − I. In red are shown
SN 1990N (Lira et al. 1998), SN 1994D (Patat et al. 1996), SN 1998aq (Riess et al. 2005),
SN 2003du (Stanishev et al. 2007) which are LVG SNe.13 In magenta we show SN 2001el(Krisciunas et al. 2003) and SN 2005cf (Wang et al. 2009) both of which are LVG with strong
high velocity Ca II lines near maximum light. Finally in blue are SN 2002dj (Pignata et al.
13

Benetti et al. (2005) separated SNe Ia into three groups: high-velocity gradient (HVG) objects, consistingof SNe with v̇Si II & 70 km s−1 day−1 and ∆m15 . 1.5 mag, low-velocity gradient (LVG) objects, consistingof SNe with v̇Si II . 70 km s−1 day−1 and ∆m15 . 1.5, and FAINT objects with ∆m15 & 1.5.

– 13 –
2008), SN 2002bo (Benetti et al. 2004), and SN 2009ig (Foley et al. 2012a) which are HVG
SNe.
In the upper left panel of Figure 8 we show the U − B color curves. Overall, we seean evident dispersion amounting to several tenths of a magnitude, despite all SNe having
been corrected for dust reddening. We see a progression in color before and near maximum,
where the LVG SNe display the bluest colors, the LVG SNe with strong high-velocity (HV)Ca II lines have intermediate colors, and the HVG SNe are the reddest. What is more
remarkable is the difference in shape between the two most complete U − B color curves.
While SN 1998aq grows steadily redder in U − B during the first 30 days, SN 2005cf shows
a dramatic blueing at early epochs followed by an upturn seven days before maximum. The
evolution of SN 2002fk is similar to SN 1994D, evolving with a linear trend from very blue
U − B colors at pre-maximum epochs to redder colors at about 30 days past maximum. It
is important to note at this point, that even though the dispersion in U − B colors can besignificantly affected by systematic errors in dust reddening corrections, the differences inshape cannot be accounted by this effect. Although filter transmission variations can reacha few tenths of a magnitude in the U-band, the differences observed at early epochs reacheven one magnitude, so we believe they are real and not a result of filter mismatches or sky
transmission.
The upper right panel of Figure 8 shows the B − V colors. Overall, the color evolutionof SN 2002fk is that of a normal Type Ia. The four SNe with the earliest observations(SN 1994D, SN 2002bo, SN 2005cf, SN 2003du, and SN 2009ig) all show clear evidence for
un upturn around 5 days before maximum that indicates an evolution from red to blue atthe very early epochs. Even though the sample is small, this seems to be a generic featureof SNe Ia. This behavior was already noted by Hamuy et al. (1991) in SN 1981D, basedon early-time observations obtained with photographic plates (see their Fig. 5). Promptly
after maximum all SNe grow redder for a period of ∼30 days, after which they all grow bluer
which corresponds to the linear tail of the optical light curves. As a reference we show withsolid line the Lira law (in cyan). Within the uncertainties it appears that all SNe share acommon slope at these epochs, but we observe small systematic offsets of ∼0.08 mag forsome individual objects. Considering that the use of different instrumental bandpasses canintroduce systematic errors ∼0.05 mag at these epochs (Stritzinger et al. 2002), it appears
that there are some small yet significant intrinsic color differences among SNe Ia during thephase corresponding to the Lira law.
The V − R colors are shown in the lower left panel of Figure 8. The evolution of
SN 2002fk has a normal shape compared to the other SNe. However, we see an intrinsic
scatter at the level of 0.4 mag among the different objects, with SN 2002fk and SN 1998aq

– 14 –
being among the reddest objects. SN 2005cf and SN 2001el, which are LVG objects withstrong HV Ca II lines, are in the middle of the distribution, while the HVG objects areamong the bluest objects. Note that this is the opposite trend that we observe in U − B.
This apparent gradient in V − R color is specially noticeable 10 days before B maximum. At
later times this gradient still seems to be present, but there is more scatter in the photometry.
In the lower right of Figure 8 we show the V − I color curves. We see evidence for adivergent behaviour at the very earliest epochs. We can separate the SNe in two groups
before maximum; the SN 2002fk-like SNe (LVG SNe without strong Ca II before maximum)
showing a steady evolution from red to blue; the SN 2005cf-like group (LVG SNe withstrong Ca II lines); and the HVG SNe, that show a downturn at day ∼-7. At about tendays before maximum, the former are nearly 0.3 mag redder then the latter. An interestingcase is SN 2009ig which belongs to the HVG group (Foley et al. 2012a) and is slightly redderthan SN 2005cf, but at ∼-15 days shows redder colors than the remaining SN 2005cf-likeobjects. The early-time dichotomy observed in V − I is reminiscent of what happens in
U − B. Interestingly, both the U and I bands share the presence of Ca II lines, namely the
Ca II H&K lines at 3951 Å and the Ca IR triplet at 8579 Å. However, as demostrated by
Cartier et al. (2011) the strength of the Ca II lines cannot completely explain the dichotomy
observed in U − B and V − I. About 10 days past B maximum all SNe grow redder through40 days after peak. Later on, all SNe grow bluer. Although the slope is similar we observe
significant offsets that exceed the potential systematic errors due to the use of different
instrumental bandpasses (Stritzinger et al. 2002).

3.5.

V − near-IR Colors

Figure 9 shows the dereddened V − near-IR colors of SN 2002fk. For comparison
we show the V − near-IR color curves of SN 2001el (Krisciunas et al. 2003), SN 2002dj(Pignata et al. 2008), SN 2003du (Stanishev et al. 2007), SN 2005cf (Wang et al. 2009), andSN 2006dd (Stritzinger et al. 2010). These are well studied SNe with similar ∆m15 , early,
and complete near-IR light curves. As in Section 3.4, we corrected the colors making use of
the Galactic extinction maps of Schlafly & Finkbeiner (2011), the Lira–Phillips relation toestimate host galaxy reddening, and the Cardelli et al. (1989) extinction law to transformfrom color excess to extinction in specific bandpasses. We caution the reader that our choiceof RV = 3.1 may introduce significant offsets in the V –near-IR colors of heavily reddened
objects with a lower value of RV .
We show in Figure 9 the V − near-IR templates of Krisciunas et al. (2004b). In dotteddashed lines are shown the loci for slow decliners while dashed lines correspond to the loci– 15 –of mid-range decliners. In the top panel we show the V − J colors. SN 2002fk declines fromblue to red at a similar rate as the locus of slow decliners, but is offset by ∼0.2 mag to redder
colors. At early epochs SN 2002fk is similar to SN 2002dj, SN 2003du, and SN 2006dd. Afterten days since maximum SN 2002fk is similar to SN 2001el, and SN 2005cf.
The middle panel of Figure 9 shows the V −H color curves. Here SN 2002fk fits the locusof the mid-range decliners at early epochs but after ten days SN 2002fk is ∼0.2 mag bluer
than the template. At early times SN 2002fk has similar colors to SN 2002dj, SN 2003du,SN 2005cf, and SN 2006dd. SN 2002dj and SN 2006dd resemble the mid-range decliners
template. After 10 days since maximum, the evolution of SN 2002fk continues to be similar
to SN 2005cf.
The V − K color curve is shown in the botton panel of Figure 9. SN 2002fk matches
the template quite well, although at early epochs it is slighty redder than the locus of the
mid-range decliners. SN 2002dj is very similar to SN 2002fk, whereas SN 2001el, SN 2003du,and SN 2005cf show colors that better fit the locus of the slow decliners.

4.

OPTICAL SPECTRA

Figure 10 shows 15 optical spectra of SN 2002fk that span from four days before B
maximum to 95 days past peak. Near maximum, SN 2002fk shows the characteristic Si II
λ6355 absorption, Ca II H&K lines, the Ca II near-IR triplet, the W-shaped S II lines,
and Si III λ4560. Nugent et al. (1995) found a correlation between peak luminosity andR(Si II), the ratio of the intensities of Si II λ5972 to Si II λ6355 lines near maximum, whichis interpreted as a temperature effect. For SN 2002fk we measure R(Si II) = 0.189 ± 0.002,
corresponding to a bright SN with a hot ejecta (see section 5, Nugent et al. 1995). Further
evidence that SN 2002fk was hotter than normal can be drawn from the blue B −V colors,and from the Si III λ4560 and λ5740 absorption lines before maximum, which are usuallypresent in the early spectra of bright SNe.
A relatively weak yet evident absorption is present at ∼ 6400 Å, which we identify as
C II λ6580. This line was previously identified by Blondin et al. (2012) in a spectrum taken−3.34 days since maximum. Support for this identification comes from two additional linesat ∼ 4600 Å and ∼ 7000 Å which can also be attributed to C II. Remarkably, the C II λ6580
feature persists until several days past maximum, which is unprecedented in normal SNe Ia(see Parrent et al. 2011; Thomas et al. 2011b; Folatelli et al. 2012; Silverman & Filippenko
2012b). Otherwise, the post-maximum evolution of SN 2002fk is consistent with that of a
Branch-normal Type Ia SNe (see section 4.1 below).

– 16 –
4.1.

Temporal Evolution of the Spectra

In Figure 11 we compare the spectra of SN 2002fk with three well-observed SNe withsimilar ∆m15: SN 1998aq (Branch et al. 2003), SN 2003du (Stanishev et al. 2007), andSN 2005cf (Wang et al. 2009; Bufano et al. 2009), the prototypical Branch-normal SN 1994D(Patat et al. 1996), and the super–Chandra candidate SN 2006gz (Hicken et al. 2007). We
choose -4, 0, +25 and +95 days after maximum light as comparison epochs. All the spectra
are in the host galaxy rest-frame and were reddening corrected as described in Section 3.4.
In the top-left of Figure 11 we show the spectra of SN 2002fk at ∼ −4 days. The
spectrum is characterized by lines of singly ionized intermediate-mass elements (Si, S, Mg,
and Ca), higher-ionized lines of Si III, C II, and a strong absorption at ∼ 3750 Å that
could correspond either to high-velocity Ca II H&K, Si II λ3858, or a blend of both (seeSection 4.4). At this epoch the spectrum of SN 2002fk is similar to SN 2003du with both SNeshowing strong Si III absorption lines. Also the super–Chandra candidate SN 2006gz shows
prominent Si III lines. Like SN 2002fk, SN 2006gz also shows strong C II λ6580 absorption,
which is broader than the ones in SN 2002fk. If the HV Ca II lines are present in SN 2002fk,
they are slightly stronger than the ones observed in SN 1994D, but not as remarkable as the
HV Ca II lines present in SN 2005cf at this epoch.
In the top-right panel of Figure 11 we show the spectrum of SN 2002fk near maximum
light. At this epoch SN 2002fk and SN 1998aq share similar spectral shape and featuresand both SNe show Si III lines comparable to the lines present in SN 2006gz. Additionally,
SN 2002fk shows normal Ca II, and maybe weak HV Ca II lines. In contrast SN 2005cf
shows strong HV Ca II lines. Remarkably, SN 2002fk still shows clear C II λ6580 and λ7234
absorption lines.
In the bottom-left of Figure 11 we show the spectrum of SN 2002fk at ≃ +25 days sincemaximum. This epoch corresponds to the beginning of the transition from the photosphericto the nebular phase and the spectra are becoming dominated by absorption of iron–peakelements (Fe II, Co II, Cr II, etc). The similarity of all the spectra at this epoch is impressive.
However, it is interesting to mention that the Na I absorption in SN 2002fk is slightly stronger
than in the others. In the bottom-right of Figure 11 we show the spectrum of SN 2002fk andother SNe at ≃ +95 days since maximum. At this epoch the transition from photospheric
to nebular phase is almost complete, and all the spectra are very similar showing forbidden
emission lines of iron elements (i.e. [Fe III], [Co III]). SN 2002fk is particularly similar to
SN 1998aq, and still has a slightly stronger Na I absorption line.

– 17 –
4.2.

Photospheric Expansion Velocity

In Figure 12 we show the photospheric expansion velocity of SN 2002fk measured fromthe minimum of the Si II λ6355 line, and a comparison with other SNe Ia. The Si II λ6355 lineis thought to trace the position of the photosphere (Benetti et al. 2005). In red we plot three
HVG SNe: SN 2002bo (Benetti et al. 2004), SN 2002dj (Pignata et al. 2008) and SN 2009ig(Foley et al. 2012a; Marion et al. 2013). In blue we show the five best observed LVG SNe:
SN 1990N (Leibundgut et al. 1991), SN 1994D (Patat et al. 1996), SN 1998aq (Branch et al.
2003), SN 2003du (Stanishev et al. 2007) and SN 2005cf (Wang et al. 2009). For SN 2002fk
we measure a velocity gradient of v̇ = 26.3 km s−1 day−1 between −4 and +14 days sincemaximum, which falls in the low end of the distribution of SNe Ia (Benetti et al. 2005). We
also measure the velocity ten days after maximum v10 ∼ 9,400 km s−1 . Compared to the
Benetti et al. (2005) sample, SN 2002fk falls 3σ below the mean (<v10 >∼10,300 km s−1 ±300 km s−1 ). From v̇ and v10 we unambiguously classify SN 2002fk as a LVG SN. Note thatin the sample of near-IR spectra of SNe Ia presented by Marion et al. (2003), SN 2002fk also
stands out for its anomalously low velocity measured from the Mg II λ 10910 absorption.
In the inset of Figure 12 we show velocities measured from other prominent lines inthe spectrum. Compared to Si II λ6355, the Si III λ4560, S II λ5635, and Si III λ5740
lines show lower velocities and higher velocity gradients, implying that they form below andrecede faster into the SN ejecta. We observe that Ca II H&K possibly has two components(see Section 4.4 for a detailed discussion). The main photospheric absorption is located atv ∼ 11,150 km s−1 and shows a flat evolution compared to Si II λ6355. It is possible thata detached high–velocity Ca II component is observed four days before maximum with v ∼16,700 km s−1 , and could be observed on day +5 with v ∼ 15,700 km s−1 (see Figure 10).
This is similar to the velocity evolution of the Ca II lines in HVG SNe.
Before maximum light the minimum of the C II λ6580 absorption line is formed at higher
velocites than Si II λ6355 (i.e. at larger radii in the SN ejecta), but near maximum light andthereafter the C II absorption minimum is measured deeper in the ejecta than Si II. Thismeans that there is a significant amount of unburned C II at the same position, in velocity
space, where the intermediate mass elements (IME) are located. The absorption minimumof C II λ6580 goes deeper in the ejecta with time, which could be due to emission comingfrom the red side of the Si II λ6355 line (see Folatelli et al. 2012). Although the velocity
estimation from the minimum of the C II lines has larger associated uncertainties owing to
the weakness of the lines, the fact that both the C II λ6580 and λ7234 lines have similar
velocities suggests that our measurements are correct. Previous studies of Parrent et al.
(2011) and Folatelli et al. (2012) have shown that the C II λ6580 line is found at higher
velocities than the Si II λ6355 line, and the velocity gradient of these two lines is roughly

– 18 –
the same (i.e. they are parallel in velocity versus time since maximum), which is different
from what we observe in SN 2002fk.

4.3.

Presence of Unburned Material

Nearly 30% of all SNe Ia show evidence of C II λ6580 before maximum (Parrent et al.
2011; Thomas et al. 2011b; Folatelli et al. 2012; Silverman & Filippenko 2012b). In the middle panels of Figures 13 and 14 we present a series of spectra of SN 2002fk from −3.96 to+7.70 days since B–band maximum. The x–axis shows the expansion velocity measured
with respect to C II λ6580. The presence of C II is confirmed by the simultaneous detectionof C II λ6580 and λ7234 lines at the same expansion velocities (∼ 10,000 km s−1 ). The
detection of both lines at several epochs, together with a possible detection of C II λ4745 in
our first two epochs with a similar velocity, gives us confidence in identifying these features
as C II.
Both C II λ6580 and λ7234 become weaker and shift to the red with time. Our latest
detection of C II λ7234 is at +4.50 days past B maximum while the C II λ6580 absorption
is detectable even at +8.07 days. Notably, this is the latest detection of C II in a normal SN
Ia and, as discussed in Section 4.2, it is clear indication of the presence of unburned material
mixed with IME’s if a homologous expansion of the ejecta is assumed.

4.4.

Spectral Modeling

We used SYN++ (Thomas et al. 2011a), an updated version of SYNOW (Fisher et al.
1997) written in C++, to model the spectra. We modeled our data, CfA, and BSNIP spectrafrom −3.96 to +7.70 days since maximum.
In SYN++, one computes a spectrum by specifying the location and optical depth fora given set of ions. The input parameters for SYN++ are the photospheric velocity, theoptical depth, the e-folding length of the opacity profile, the maximum and minimum cut–off velocity for each ion, and the Boltzmann excitation temperature for parameterizing line
strengths.
Recently Foley (2013) presented convincing evidence, though not definitive, that theabsorption on the blue side of the H&K Ca II line could be produced by Si II λ3858,
challenging the traditional interpretation that this absorption is caused by a HV Ca II line.
Here we attempt to test both hypotheses. To do this we fit a SYN++ model to all the
spectra from −3.96 to +7.70 days since B–band maximum. In Figure 15 we present some– 19 –
examples of our models which overall provide good fits to the observed spectra. We began ourmodeling by fitting only the photospheric lines, especially Si II and Ca II. The characteristic
blackbody temperature (Tphot ) in our models was ∼ 12, 800 K, and we set the excitation
temperature (Texc ) of most of the ions at 500 K below Tphot . For the high ionizaton lines
like Si III and Fe III we set Texc to be the same as Tphot . Then, in order to get a good fit to
the absorption on the blue side of the H&K line without appealing to a HV Ca II line, we
had to modify Texc for Si II to ∼ 7000 K. We note that small variations around this value
can change dramatically the strength of Si II λ3858 but not the strength of Si II λ6355.
Alternatively, we also modeled this feature by adding a HV Ca II component with Texc set
equal to the rest of the ions without modifying the rest of the parameters. Both approaches
produce equally good models (see Figures 13, 14, and 15).
The Foley (2013) approach requires fewer parameters and reproduces the observations
equally well. Remarkably, the velocity and optical depth of Si II λ6355 proved quite insensitive to Texc . However, the low Texc required to fit the Si II λ3858 line seems slighty
odd for a relatively bright SN with low R(Si II) (i.e. hot ejecta) and high ionization lines
like Si III and Fe III. Additionally, there is strong evidence that supports the presence of
HV Ca II in “normal” SNe Ia (Kasen et al. 2003; Gerardy et al. 2004; Mazzali et al 2005;
Stanishev et al. 2007; Tanaka et al. 2008; Childress et al. 2014). These features are clearlyobserved at very early phases (∼ −7 days) in both Ca II H&K and the Ca II IR–triplet,but near maximum they are not always easy to identify (Mazzali et al 2005). We conclude
that, while both Si II λ3858 and HV Ca II produce equally good fits to the data within the
SYN++ framework, more realistic radiative transfer models will be necessary to distinguishwhich line is responsible for the absorption on the blue side of the H&K line.
As can be seen in Figures 13 and 14, the red side of the Si II λ6355 profile is not properly
fit by Si II alone (shown in red). To obtain a better fit we added a C II HV component(shown in green). In the case of our spectra, which are not corrected for telluric absorption,
this feature on the red side of the Si II profile could be due to the lack of such corrections.
However, the CfA spectra obtained on days -3.34 and -1.36, which do include corrections
for telluric lines, are best modelled with a HV C II component. Interestingly, the HV C II
is at nearly the same velocity of the HV Ca II (∼ 16,000 km s−1 ). The presence of a HV
C II was previously suggested by Fisher et al. (1997), and is not completely unexpected
since unburned carbon material should be present in the outer layers of SNe Ia. We flag thepresence of HV C II as possible but not as certain.

– 20 –
5.

DETERMINATION OF THE HUBBLE CONSTANT USING THE
CEPHEID DISTANCE TO NGC 1309

With the relative Cepheid distance between NGC 1309 and NGC 4258 of Riess et al.
(2011a) (µN GC 1309 −µN GC 4258 = 3.276±0.05), the maser distance to NGC 4258 of Humphreys et al.
(2013) (µN GC 4258 = 29.40 ± 0.06), the peak brightness and reddening of SN 2002fk derived
in Section 3.3, it is straightforward to calculate the Hubble constant (H0 ) via the formula
1.1
1.1
H0 = 100.2(Mmax +25−α) , where Mmax
is the absolute magnitude of SN 2002fk corrected for
reddening and ∆m15, and α is the corresponding zero point of the Hubble diagram. In
the optical (BV I), we adopt the decline rate versus luminosity (∆m15/Mmax ) relations andzero points from Phillips et al. (1999), who employ the same prescription that we use here
for luminosity and reddening corrections. In the near-IR (JHK) we adopt ∆m15/Mmax
relations and zero points derived from two independent analysis of nearly the same near-IR
CSP observations, one by Folatelli et al. (2010) and the other by Kattner et al. (2012).
In Table 10 we summarize all the adopted parameters and the resulting values forH0 . The statistical uncertainty in H0 was computed from a Monte Carlo simulation. Our
code computes 10, 000 simulated values of H0 assuming a Gaussian distribution in peakmagnitude, reddening, ∆m15, the slope of the ∆m15/Mmax relationship, and the zero pointof the Hubble diagram. The systematic error includes 0.08 mag in distance modulus to NGC
1309, 0.03 mag in the photometric zero point, and the intrinsic dispersion in the ∆m15/Mmax
relationship from Phillips et al. (1999), Folatelli et al. (2010), and Kattner et al. (2012).
As can be seen in Table 10, the H0 values that we derive from the optical bands (BV I)
are very consistent with each other, allowing us to combine them into an BV I average of
H0 (BV I) = 69.6±2.1 (±5.0 systematic) km s−1 Mpc−1 , where the systematic error includes
0.08 mag in distance modulus to NGC 1309, 0.03 mag in the photometric zero point, and the
intrinsic dispersion in the ∆m15/Mmax relationship including the variance in each band andband-to-band covariances. Our value is 0.8 σ lower than the one published by Riess et al.
(2011a), H0 = 73.8 ± 2.4 km s−1 Mpc−1 , from eight SNe Ia with precise Cepheid distances.
This is due to the fact that SN 2002fk lies in the bright side of their luminosity distribution.
In fact, using the values listed in Table 3 of Riess et al. (2011a) and their Eq. (4), we find
H0 = 68.5 km s−1 Mpc−1 for this same SN, in very good agreement with our determination.
Thus, using SN 2002fk alone to determine H0 is expected to yield a lower value than the fit
to all eight SNe in their sample.
Table 10 shows that our near-IR estimate of H0 is sensitive to the adopted calibration:using Kattner et al. (2012), we obtain H0 (JH) = 66.7±1.0 (±3.5 systematic) km s−1 Mpc−1 ,whereas if we employ Folatelli et al. (2010) we get H0 (JHK) = 63.0 ± 0.8 (±2.8 systematic)
km s−1 Mpc−1 . This discrepancy is mainly due to the different zero points obtained from– 21 –
their analysis, 0.17 and 0.07 mag in J and H, respectively (see Table 10), which arise
from the different techniques employed to measure peak magnitudes. While Kattner et al.
(2012) directly measured peak magnitudes based on a cubic-spline interpolation to sevenexquisitely observed SNe with observations starting before maximum, Folatelli et al. (2010)
included peak magnitudes extrapolated from a template light curve fit. As mentioned by
Kattner et al. (2012) the large diversity in early time near-IR light curve shapes can lead tosignificant errors when fitting template light curves to derive peak brightnesses.
Despite the differences in H0 caused by the near-IR calibration adopted, it appears thatthe near-IR yields somewhat lower (6-9%) H0 values than the optical. How significant is thisdifference? Given that the systematic error for this particular SN is almost fully correlatedband to band (owing to the same Cepheid distance and the fact that the intrinsic dispersion
of SNe Ia is correlated band to band), the significance can be estimated from the statisticaluncertainty alone, which yields 1.2 and 2.9 σ for Kattner et al. (2012) and Folatelli et al.
(2010), respectively. It will be essential to further examine this issue by expanding thesample of near-IR SN light curves with good sampling near maximum, which should lead toa more robust determination of the zero point of the Hubble diagram and the ∆m15/Mmax
relationship. Such effort should be rewarded with a significantly more precise determinationof H0 : as can be seen in Table 10, the near-IR yields smaller statistical uncertainties due toa smaller sensitivity to extinction, decline rate correction, and higher precision in the zero
point of the Hubble diagram. As opposed to the optical bands where the zero point is subject
to inaccuracies caused by the heterogeneity in the various photometric systems employed,
our near-IR zero point is based in a single homogeneous Carnegie photometric dataset, anessential ingredient in lowering the statistical uncertainty in H0 .
An independent value of H0 = 69.77+2.07−2.07 was obtained by Sullivan et al. (2011) bycombining the SNLS3 data with the full WMAP7 power spectrum and the Sloan Digital Sky
Survey luminous red galaxy power spectrum (DR7). Similarly, Mehta et al. (2012) obtained
H0 = 69.8 ± 1.2 by fitting a ΛCDM model to the DR7 and WMAP7 data. Studies ofgalaxy clustering from the SDSS–III Data Release 8 (DR8) yield H0 = 70.5 ± 1.6 (Ho et al.
2012). More recently, the first results based on the Planck satellite measurements of the
CMB temperature and lensing-potential power spectra find a low value of H0 = 67.3 ± 1.2(Ade et al. 2014). All these experiments reveal some tension with the H0 = 73.8 ± 2.4 value
obtained by Riess et al. (2011a). Our analysis provides the first determination of H0 fromnear-IR SNe Ia data, and suggests that the near-IR could help to alleviate this tension.

– 22 –
6.

DISCUSSION AND CONCLUSIONSWe present early and complete optical (BV RI) and near-IR (JHK) light-curves of
SN 2002fk starting 12 days before maximum light through 122 days past maximum, alongwith a series of 15 optical spectra from -4 to +95 days since maximum. Our study reveals
the following distinguishing properties of SN 2002fk:• Low decline rate (∆m15=1.02) of the B lightcurve, consistent with a higher than
average peak luminosity (MB =-19.49).
• Negligible host galaxy reddening as inferred from the observed colors.
• Slightly bluer than average B − V color near maximum.
• Presence of Si II 6355 with a relatively low (9,500 km s−1 ) expansion velocity near
maximum, and a small velocity gradient, v̇Si II = 26 km s−1 day−1 .
• Blue U − B and a red V − I early-time color, expected for LVG SNe Ia (Cartier et al.
2011).
• Presence of C II lines in the early-time spectra expanding at 11,000 km s−1 persisting
until 8 days past maximum light with a velocity ∼9,000 km s−1 , and possible HV component
with 16,000 km s−1 .
• Possible presence of a HV Ca II H&K component in the early-time spectra expandingat ∼ 16, 000 km s−1 and persisting until ∼ 8 days past maximum, with similar velocity of a
possible HV C II component (an alternative explanation for the HV Ca II is Si II λ3858; see
Foley 2013).
In the off-center explosion models of Maeda et al. (2010c), SNe Ia with low Si II velocity
gradients are those with the ignition region oriented towards the observer. Therefore, we
expect a negative (blueshifted) velocity shifts of the [Fe II] λ7155 and [Ni II] λ7378 nebular lines (Vneb). Silverman et al. (2013) have recently shown that this is indeed the casefor SN 2002fk (Vneb = −2060 km s−1 ), lending support to the Maeda et al. (2010c) models, the Cartier et al. (2011) relations (see their Fig. 2), and Förster et al. (2012) work.
Parrent et al. (2011) and Folatelli et al. (2012) have noted that SNe showing C II in theirspectra are grouped preferentially in the bottom of the Si II expansion velocity distribution.
Our observations of SN 2002fk are consistent with such findings. The connection between
viewing angle of an off-center explosion and the presence of C II in the early time spectrum
suggests that the observation of C II could be also due to a viewing angle effect. A possible
explanation could be that when the ignition region is directed towards us, the burning front
leaves some pockets of unburned material in the direction of the observer. Our observations

– 23 –
indicate also that SN 2002fk is quite luminous and somewhat bluer than normal, which mightalso be a signature of an ignition region oriented towards the observer.
The possible presence of a HV Ca II component in the early-time spectra expanding at∼ 16, 000 km s−1 persisting until ∼ 8 days past maximum, at a similar velocity of a possible
detection of a HV C II component, suggests that these HV features may arise from density
enhanced regions containing a mixture of Ca II and C II.
Our photometry shows good agreement with the optical magnitudes published by Riess et al.
(2009b), except in the I-band where we find an offset of 0.07 mag. We do not have an explanation for this worrisome discrepancy except that LOSS employed an I filter with anextended red tail compared to the standard bandpass.
Adopting the Cepheid distance to NGC 1309 recently measured by Riess et al. (2011a)and Humphreys et al. (2013), we derive optical and near-IR absolute magnitudes for SN 2002fk.
Using the BV I absolute magnitude/decline rate calibration of Phillips et al. (1999) we solve
for the Hubble constant, obtaining a consistent value of H0 = 69.6 ± 2.1 (± 5.0 systematic),
which is 0.8 σ lower than the one published by Riess et al. (2011a), H0 = 73.8 ± 2.4 fromeight SNe Ia with precise Cepheid distances. This is due to the fact that SN 2002fk lies on
the bright side of their luminosity distribution.
We proceed in a similar manner for the JHK absolute magnitudes to derive the firstH0 value based on near-IR measurements of a SN Ia. As opposed to the optical method that
relies on many different photometric calibrations containing significant systematic differences(as shown in Appendix B), the near-IR has the great advantage that it is founded on a homogeneous Carnegie photometric dataset including (1) the Persson standards (Persson et al.
2002), (2) the CSP Hubble diagram (Folatelli et al. 2010; Kattner et al. 2012), and (3) the
calibrating CATS SN 2002fk. Our near-IR H0 values rely on two CSP different absolutemagnitude/decline rate relationships. Using the Kattner et al. (2012) relation, we obtain
H0 (JH) = 66.7 ± 1.0 (±3.5 systematic) km s−1 Mpc−1 , whereas employing Folatelli et al.
(2010) we get H0 (JHK) = 63.0 ± 0.8 (±2.8 systematic) km s−1 Mpc−1 . This discrepancy
is mainly due to the different zero points obtained from their analysis, 0.17 and 0.07 mag in
J and H, respectively, which arise from the different techniques employed to measure peakmagnitudes. More importantly, it appears that the near-IR yields somewhat lower (6-9%)
H0 values than the optical, with a significance of 1.2 and 2.9 σ depending on the near-IR
calibration adopted. It is essential to further examine this issue by (1) expanding the sampleof high-quality near-IR light curves of SNe in the Hubble flow, and (2) increasing the numberof nearby SNe with near-IR SN light curves and precise Cepheid distances, which affords thepromise to deliver a more precise determination of H0 .

– 24 –We thank the anonymous referee for comments that helped to improve our work. R.C.
acknowledges support by CONICYT through “Programa Nacional de Becas de Postgrado”
grant D-2108082, and by the Yale-Chile fellowship in astrophysics. R.C., G.P., M.H., P.Z.,
F.F., J.M., A.C. acknowledge support provided by the “Millennium Center for Supernova
Science” through grant P10-064-F and the “Millennium Institute of Astrophysics (MAS)”through grant IC120009 of the “Programa Iniciativa Cientı́fica Milenio del Ministerio de
Economı́a, Fomento y Turismo de Chile”. F.F., and G.P. acknowledge support from FONDECYT through grants 3110042, and 11090421. The authors acknowledge Rolling C. Thomas
for his support with syn++, and Ryan Foley for kindly providing spectra of SN 2009ig. We
also thank Santiago González-Gaitán and Adam Riess for their useful input and feedback.
The research presented in this article made use of SUSPECT 14 Online Supernova Spectrum Archive.
APPENDICESA.

CROSS-CAMERA SUBTRACTIONS

Since our template images in UBV RI were acquired with a different instrument thanthe ones used for the SN imaging (see Table 1), there is a potential systematic error caused byour cross-camera subtractions. To assess this error we performed the following intrepid test:
we subtracted the V template from the B SN images, the B template from the V SN images,
the V template from the R SN images, and the R template from the I SN images. Then wemeasured instrumental magnitudes with a 3 arcsec aperture both in the crossed subtracted
images and those performed with the same filter. The magnitude differences yielded by thistest amounted to 0.001-0.003 mag. Given that these cross subtractions involve wavelength
differences ∼1,000 Å between templates and SN images, the actual error caused by using
templates that differ by ∼10 Å in central wavelenghts (as in our case) from the SN images canbe ignored. In the near-IR this potential uncertainty does not exist because the templates
images were obtained with the same instrument employed for the SN.

B.

LOCAL STANDARDS & PHOTOMETRIC ZERO POINTSGiven that there are other sources of optical photometry available in the literature for
SN 2002fk, it is necessary to verify the compatibility of the individual photometric cali14

See http://suspect.nhn.ou.edu/∼suspect/– 25 –
brations before attempting to merge the photometry. Initially we started this exercise bycomparing the magnitudes of the four local standard stars in common (stars 5, 6, 7, 8)
between us (LCO/Swope) and LOSS. To our surprise we discovered very good agreement
in BVR but a significant systematic offset ∼0.07 mag in the I-band. When we noticed thisdiscrepancy, we proceeded to obtain additional measurements of the local standards with
the CTIO/0.9-m telescope (two nights) and the CTIO/PROMPT telescopes (two nights)
under photometric conditions. Given that we found very good agreement (≤0.015 mag) in
BV RI among all three calibrations and a reasonable (∼0.06 mag) consistency in the Uband between LCO/Swope and CTIO/0.9–m (no U measurements could be obtained with
CTIO/PROMPT) we decided to combine all of our UBV RI values into the single CATS
calibration, which is presented in Table 3.
Our internal consistency can be seen in detail in Table 8 which summarizes the differences in each filter between the magnitudes of the local standard stars measured with ourthree instruments (LCO/Swope, CTIO/0.9-m, CTIO/PROMPT) and our average CATS
calibration. We find excellent agreement in BV RI (≤0.015 mag). This is remarkableconsidering that the CTIO/PROMPT data were reduced with a completely independent
pipeline by one of us (GP). In the U-band the ∼0.06 mag difference between LCO/Swopeand CTIO/0.9–m (no U measurements could be obtained with CTIO/PROMPT) is not
surprising given that U–band photometry is generally difficult to calibrate as a result offilter mismatches or differences in the sky transmission (i.e. effective bandpass), and large
systematic differences are common.
Having demonstrated our own internal consistency (with the above mentioned caveat inU) we return to the issue of comparing our photometry with the external measurements of
the local standards obtained by LOSS (Riess et al. 2009b; Ganeshalingam et al. 2010) andCfA3 (Hicken et al. 2009). This comparison is presented in Table 8 which gives magnitudedifferences between the local standard stars measured by CATS, LOSS, and CfA3. Overall
we found good agreement between LOSS and CATS (≤0.02 mag), with the notable exceptionof the I-band where the LOSS magnitudes are systematically brighter by ∼ 0.07 mag. We
do not have an explanation for this worrisome discrepancy except that LOSS employed on
the Nickel telescope an I filter with an extended red tail compared to the standard bandpass[see Fig. 1 in Ganeshalingam et al. (2010)]. Perhaps this is also the cause of the systematicdifferences ∼0.1 mag in the I–band between LOSS and CfA2 (Jha et al. 2006) reported
by Ganeshalingam et al. (2010) for some SNe. When we compare CATS and CfA3, we findbetter agreement in I (CfA3 is between CATS and LOSS). However, what is more concerningis that CfA3 is consistently brighter than CATS by ∼ 0.03 − 0.04 mag in all UBV RI filters.
While LOSS is halfway between CATS and CfA3 in B, LOSS is much closer to CATS than
CfA3 in V and R. We cannot claim which one is correct, but the advantage of the CATS

– 26 –
calibration is that it was obtained with three different cameras, two independent pipelines,
and two reducers.
Based on this analysis, we adopt a systematic uncertainty of 0.03 mag for our photometric zero points. Unfortunately, we cannot apply this approach to the near-IR because
the 2MASS magnitudes are not sufficiently precise. Hence, we adopt the same uncertaintyof 0.03 mag.

C.

S-CORRECTIONS

SN magnitudes obtained with different instruments can potentally lead to significant
systematic errors due to the non-stellar nature of the SN spectrum. These effects, a.k.a.
S-terms, were computed by Stritzinger et al. (2002) for the normal Type Ia SN 1999ee. As
shown in their Fig. 4, the S-corrections change with time as the SN spectrum evolves.
The systematic errors for the CTIO/0.9-m camera are generally small in BV RI, from 0.01
mag near maximum to 0.04 mag at late times (∼60 days past maximum), suggesting that
this instrument provides a good match to the standard system (Bessell 1990), while for the
YALO instrument the systematic errors are larger (∼0.05-0.08 mag) owing to significant
instrumental departures from the standard bandpasses. In order to quantify this effect in
SN 2002fk, we took advantage of the fact that the object was measured with seven different
instruments allowing us to calculate magnitude differences among all of them after removing
the systematic differences caused by the photometric zero-points. This empirical approach
showed that the S-terms amount to 0.02 mag at maximum light and 0.03 mag at later epochs(40-80 days after peak), allowing us to to attach a systematic error to our BV RI photometry.
Its is encouraging that this empirical approach yields similar values to those computed by
Stritzinger et al. (2002) for the CTIO/0.9-m camera. Likewise, in the near-IR we estimate
the systematic errors caused by the S-terms to be 0.02 mag at maximum, from a comparisonof the SN magnitudes measured with Baade/Classic-Cam and du Pont/WIRC. We cannot
apply this technique at later times in the near-IR since SN 2002fk was observed with a single
instrument, but we can safely adopt the 0.03 uncertainty measured in the optical. Most
likely, this is an upper limit to the systematic errors in the near-IR, considering that the
instrument detector and filters used with WIRC and Classic-Cam were essentially the sameas those employed by Persson et al. (1998) in the establishment of the standard system.

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Table 1. Photometric Observations of SN 2002fk.
Telescope

Instrument

Detector

Plate Scale(arcsec pixel−1 )Filters

LCO
LCO
LCO
LCO
CTIO
CTIO
CTIO

Swope
du Pont
du Pont
Baade
0.9m
1.5m
PROMPT

CCD
WFCCD
CCD
LDSS-2a
CCD
CCD
CCDb

SITe 2048×3150
Tek 2048×2048
Tek 2048×2048
SITe 2048×2048
2048×2048
2048×2048
Alta U47 E2V 1024×1024

0.435
0.774
0.259
0.380
0.396
0.440
0.600

UBV (RI)KCBV (I)KCUBV (RI)KCBV (R)KCUBV (RI)KCBV (RI)KCBV (RI)KCLCO
LCO

du Pont
Baade

WIRCc
Classic-Cam

HAWAII-1 1024×1024
NICMOS3 256×256

0.196
0.094

JS HKS
JS HKSaAllington-Smith et al. (1994)b

Pignata et al. (2011)c

Persson et al. (2002)– 32 –

Observatory

– 33 –

Table 2. Spectroscopic Observations of SN 2002fk.
Date(UT)

JD
Phase-2,400,000 (days)

2002 Sep 26
2002 Sep 28
2002 Sep 30
2002 Oct 01
2002 Oct 05
2002 Oct 08
2002 Oct 14
2002 Oct 14
2002 Oct 25
2002 Oct 29
2002 Nov 11
2002 Nov 12
2002 Nov 28
2002 Dec 02
2003 Jan 0352543.84
52545.89
52547.89
52548.31
52552.32
52555.87
52561.36
52561.83
52573.15
52576.87
52589.82
52590.83
52606.75
52610.70
52642.73

-3.96
-1.91
0.09
0.50
4.50
8.07
13.54
14.03
25.35
29.07
42.02
43.03
58.95
62.90
94.93

Instrument/
Telescope

Wavelength
Range (Å)

Resolution(Å)

Exposure(s)

LDSS-2/Baade
LDSS-2/Baade
WFCCD/du Pont
FORS1-PMOS/VLTFORS1-PMOS/VLTWFCCD/du Pont
FORS1-PMOS/VLTLDSS-2/Baade
LDSS-2/Baade
LDSS-2/BaadeB&C Spec./BaadeB&C Spec./BaadeB&C Spec./Baade
WFCCD/du Pont
Mod. Spec./du Pont

3600 - 9000
3600 - 9000
3800 - 9200
3330 - 8500
3330 - 8500
3800 - 9200
3330 - 8500
3600 - 9000
3600 - 9000
3600 - 9000
3200 - 9200
3200 - 9200
3200 - 9200
3800 - 9200
3790 - 7270

14
14
8
12
12
8
12
14
14
14
7
7
7
8
7

120
200
200
2880
2880
200
2400
60
120
90
300
200
200
450
450

Table 3. UBRV I Photometric Sequence Around SN 2002fk.
U

N

B

N

V

N

R

N

I

N

c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11

13.604(0.018)
14.337(0.020)
13.248(0.013)
14.313(0.014)
16.197(0.009)
16.419(0.010)
16.209(0.011)
17.519(0.018)
···
···
···

4
4
4
4
6
6
6
6
4
4
4

13.424(0.016)
13.386(0.016)
13.278(0.025)
14.230(0.019)
16.330(0.013)
16.437(0.013)
16.276(0.008)
17.555(0.013)
19.083(0.028)
16.329(0.016)
15.221(0.016)

4
4
4
4
8
8
8
8
4
4
4

12.705(0.014)
12.346(0.014)
12.718(0.014)
13.620(0.013)
15.771(0.006)
15.820(0.006)
15.759(0.005)
16.948(0.008)
17.842(0.021)
15.780(0.014)
14.669(0.014)

4
4
4
4
8
8
8
8
4
4
4

12.322(0.015)
11.752(0.015)
12.366(0.016)
13.281(0.008)
15.424(0.007)
15.447(0.006)
15.429(0.010)
16.595(0.007)
17.069(0.010)
15.425(0.015)
14.310(0.015)

4
4
4
4
8
8
8
8
4
4
4

11.951(0.014)
11.279(0.014)
12.065(0.014)
12.961(0.008)
15.077(0.005)
15.080(0.006)
15.102(0.006)
16.237(0.008)
16.425(0.007)
15.122(0.010)
14.013(0.010)

4
4
4
4
8
8
8
8
4
4
4

LOSSa CfA3bname name
4
2
1
3
-

4
5
6
3
-

– 34 –

Star

Note. — Errors given in parenthesis, are 1σ statistical uncertainties. For each star we indicate N, the number ofphotometric nights used to calibrate them.
aGaneshalingam et al. (2010)b

Hicken et al. (2009)– 35 –

Table 4. Color Terms for the five Optical Cameras
Telescope

U

B

V

R

I

Swope/CCD+0.177 +0.053 -0.054 +0.021 +0.052
du Pont/WFCCD···+0.125 -0.045···+0.010Clay/LDDS-2···+0.132 +0.046······
CTIO 0.9-m/CCD +0.126 -0.086 +0.011 +0.004 +0.007
CTIO 1.5-m/CCD +0.139 -0.080 +0.030 +0.016 +0.017

Note. — Color terms are defined in equations 1-5.

Table 5. UBV RI Photometry of SN 2002fk.
JD-2,400,000

U

B

V

R

2002 Sep 21
2002 Sep 26
2002 Sep 30
2002 Oct 01
2002 Oct 08
2002 Oct 14
2002 Oct 20
2002 Oct 21
2002 Oct 24
2002 Oct 25
2002 Oct 29
2002 Oct 30
2002 Oct 08
2002 Nov 07
2002 Nov 08
2002 Nov 12
2002 Nov 18
2002 Dec 02
2002 Dec 04
2002 Dec 07
2003 Jan 07
2003 Jan 3152538.852543.952547.952548.952555.952561.852567.852568.8
52571.952572.852572.952576.952577.952585.8
52586.952590.852596.752610.7
52612.8
52615.7
52646.7
52670.6

13.523(0.013)······
12.792(0.018)······
15.044(0.010)
15.195(0.024)
15.544(0.017)
15.631(0.018)
···
···
···
16.388(0.018)···
16.531(0.020)
16.668(0.019)···
17.045(0.023)
17.043(0.018)
17.803(0.024)···

14.128(0.016)
13.443(0.012)
13.319(0.047)
13.287(0.016)
13.675(0.076)
14.261(0.017)
14.883(0.011)
15.014(0.011)
15.294(0.014)
15.394(0.016)···
15.782(0.018)
15.825(0.017)
16.238(0.016)
16.277(0.016)
16.396(0.016)
16.546(0.016)
16.819(0.062)
16.830(0.016)
16.848(0.016)
17.324(0.016)
17.762(0.014)

14.234(0.014)
13.515(0.014)
13.358(0.019)
13.350(0.014)
13.623(0.085)
13.904(0.014)
14.239(0.010)
14.355(0.023)
14.409(0.015)
14.500(0.014)
14.511(0.014)
14.714(0.010)
14.778(0.019)
15.229(0.014)
15.256(0.014)
15.440(0.014)
15.640(0.014)
16.075(0.033)
16.091(0.014)
16.128(0.014)
16.907(0.010)
17.397(0.015)

14.149(0.015)······
13.335(0.011)······
14.133(0.011)
14.139(0.013)
14.196(0.015)
14.205(0.015)···
14.376(0.014)···
14.888(0.015)
14.939(0.015)
15.129(0.015)
15.358(0.015)···
15.922(0.015)
15.981(0.015)
16.954(0.015)
17.633(0.015)

I

Telescope

14.119(0.010)
Swope
···
Baade
13.609(0.051)
du Pont
13.595(0.014)
Swope
14.003(0.074)
du Pont···
Baade
14.181(0.010)
Swope
14.218(0.023)
Swope
14.198(0.015) CTIO 0.9-m
14.121(0.014)
Swope
···
Baade
···
Baade
14.123(0.017)
du Pont
14.539(0.015)
Swope
14.570(0.019)
Swope
14.840(0.014)
Swope
15.161(0.014)
Swope
15.785(0.019)
du Pont
15.887(0.014)
Swope
16.000(0.014)
Swope
17.184(0.014)
Swope
18.069(0.027) CTIO 1.5-m– 36 –

Date(UT)Table 5—Continued
Date(UT)

JD-2,400,000 U

B

V

R

I

TelescopeNote. — Errors given in parenthesis, are 1σ statisticaluncertainties.

– 37 –

– 38 –

Table 6. JHKs Photometric Sequence Around SN 2002fk.
Star
c5
c8
c12
c13

J

J2M ASSH

H2M ASSKs

K2M ASS

14.599(0.014) 14.582(0.028) 14.259(0.008) 14.272(0.055) 14.148(0.009) 14.173(0.067)
15.764(0.020) 15.712(0.062) 15.439(0.009) 15.564(0.101) 15.299(0.024) 15.408(0.179)
16.093(0.011) 16.083(0.080) 15.439(0.009) 15.312(0.094) 15.190(0.019) 15.100(0.137)
18.224(0.064)···
17.628(0.077)
···
···
···

Note. — Errors given in parenthesis, are 1σ statistical uncertainties.

– 39 –

Table 7. JHKs Photometry of SN 2002fk.
Date(UT)

JD-2,400,000

J

H

Ks

Telescope2002 Sep 18
2002 Sep 19
2002 Sep 20
2002 Sep 21
2002 Sep 22
2002 Sep 23
2002 Sep 24
2002 Sep 24
2002 Sep 25
2002 Sep 27
2002 Sep 29
2002 Oct 14
2002 Oct 15
2002 Oct 20
2002 Oct 23
2002 Oct 24
2002 Nov 12
2002 Nov 14
2002 Nov 19
2002 Nov 22
2002 Dec 09
2002 Dec 11
2002 Dec 23
2003 Jan 1152535.752536.7
52537.852538.7
52539.752540.7
52541.7
52541.7
52542.752544.752546.6
52560.7
52562.7
52567.852570.6
52571.852590.852593.8
52597.552600.6
52617.5
52619.7
52631.6
52650.6

15.162(0.011)
14.798(0.011)
14.540(0.011)
14.324(0.011)
14.132(0.011)
14.000(0.011)
13.860(0.016)
13.879(0.011)
13.801(0.015)
13.764(0.015)
13.847(0.011)
15.623(0.011)
15.647(0.011)
15.549(0.011)
15.497(0.018)
15.377(0.011)
15.854(0.011)
16.073(0.011)
16.367(0.011)
16.549(0.013)
17.713(0.039)
17.798(0.030)
18.534(0.042)
19.434(0.103)

15.200(0.011)
14.859(0.011)
14.605(0.011)
14.405(0.011)
14.234(0.015)
14.133(0.011)
14.044(0.016)
14.036(0.011)
13.975(0.011)
13.981(0.011)
14.113(0.011)
14.590(0.011)
14.549(0.011)
14.332(0.011)···
14.175(0.011)
14.905(0.011)
15.030(0.011)
15.248(0.011)
15.367(0.014)
16.112(0.015)
16.185(0.011)
16.797(0.017)
17.597(0.027)

15.107(0.011)
14.797(0.011)
14.532(0.015)
14.323(0.011)
14.103(0.015)
13.997(0.011)
13.863(0.017)
13.926(0.011)
13.766(0.019)
13.741(0.017)
13.859(0.011)
14.264(0.011)
14.262(0.011)
14.152(0.011)···
14.083(0.011)
14.922(0.011)
15.063(0.011)
15.249(0.011)
15.350(0.030)
16.010(0.027)
16.070(0.027)
16.549(0.033)
17.039(0.056)

du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
Baade
du Pont
Baade
Baade
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont
du Pont

Note. — Errors given in parenthesis, are 1σ statistical uncertainties.

Table 8. Mean Differences among different photometric systems and our Averagea values

LCO/Swope − Averagea
CT IO/0.9m − Averagea
CT IO/P ROMP T − Averagea
LOSS b − Averagea
Cf A3c − Averagea
Cf A3c − LOSS b

∆U

∆B

∆V

∆R

∆I

0.025 ± 0.008−0.038 ± 0.012······−0.025 ± 0.026···

0.009 ± 0.004−0.006 ± 0.008−0.006 ± 0.028−0.020 ± 0.016−0.038 ± 0.022−0.017 ± 0.016

0.006 ± 0.006−0.009 ± 0.006−0.003 ± 0.010−0.001 ± 0.024−0.031 ± 0.004−0.026 ± 0.020

0.006 ± 0.004−0.004 ± 0.006−0.008 ± 0.012
0.004 ± 0.026−0.033 ± 0.004−0.037 ± 0.022

0.006 ± 0.002−0.007 ± 0.008−0.008 ± 0.008−0.070 ± 0.016−0.044 ± 0.008
0.022 ± 0.022

aCATS calibration (average of LCO/Swope, CTIO/0.9m, and CTIO/PROMPT measurements)b

LOSS calibration from Riess et al. (2009b); Ganeshalingam et al. (2010)c

CfA3 calibration from Hicken et al. (2009)– 40 –

Note. — Quoted uncertanties are weighted standard deviations

– 41 –

Table 9. SN 2002fk total (Galactic + host galaxy) reddening from different methods.
Method(B − V )T ail
Bmax − Vmax
Vmax − Imax
(V − H)(V − K)
Mean

E(B − V )Reference

0.066 ± 0.019
Phillips et al. (1999)
0.009 ± 0.044
Phillips et al. (1999)
0.082 ± 0.038
Phillips et al. (1999)
0.014 ± 0.037 Krisciunas et al. (2004b)
0.075 ± 0.036 Krisciunas et al. (2004b)
0.057 ± 0.036

Table 10. Hubble constant using different filter calibrations.
mmax aMmax b

1.1 c
Mmax

B
V
I
J
H
J
H
K

13.07(0.15)
13.19(0.11)
13.47(0.07)
13.71(0.04)
13.95(0.03)
13.71(0.04)
13.95(0.03)
13.74(0.03)-19.49(0.17)-19.37(0.14)-19.09(0.11)-18.85(0.09)-18.61(0.08)-18.85(0.09)-18.61(0.08)-18.82(0.08)-19.43(0.17)-19.32(0.15)-19.06(0.08)-18.83(0.09)-18.57(0.09)-18.80(0.09)-18.59(0.09)-18.76(0.09)

αd

σSN e

-3.671(0.043) 0.11
-3.615(0.037) 0.09
-3.236(0.035) 0.13
-2.893(0.003) 0.125-2.733(0.009) 0.053-2.727(0.01) 0.12
-2.667(0.02) 0.16
-2.717(0.03) 0.10aMagnitude at maximum of SN 2002fk corrected for reddening (Galactic + host).

b

Peak absolute magnitude of SN 2002fk corrected for reddening (Galactic + host).

cf

Systematicg
Error

Referenceh

70.5+5.4−5.0
72.4+4.5−4.1
68.3+2.8−2.7+1.4
65.1−1.3
68.0+1.4−1.2+1.3
60.8−1.3
65.4+1.2−1.2+1.6
61.9−1.5

4.5
4.1
4.9
4.5
3.2
4.1
5.5
5.4

Phillips et al. (1999)
Phillips et al. (1999)
Phillips et al. (1999)
Kattner et al. (2012)
Kattner et al. (2012)
Folatelli et al. (2010)
Folatelli et al. (2010)
Folatelli et al. (2010)

Peak absolute magnitude of SN 2002fk corrected for reddening (Galactic + host) and ∆m15.

d
e

H0 f
(km s−1 Mpc−1 )– 42 –

FilterZero point of the Hubble diagram.

Intrinsic dispersion in the decline rate versus luminosity relationship.

Statistical error includes uncertainties in apparent peak magnitude, reddening, correction for ∆m15, and zero point of the Hubble diagram.

g

Systematic error in H0 in units of km s−1 Mpc−1 includes 0.08 mag in distance modulus to NGC 1309, 0.03 mag in the photometric zero point, andthe intrinsic dispersion in the decline rate versus luminosity relationship.
h1.1
Reference for the ∆m15/Mmax relation, intrinsic dispersion in Mmax
, and the zero point of the Hubble diagram.

– 43 –

19:00.0

C2

C3

C1

-15:20:00.0

C7

Declination

21:00.0

C6

22:00.0C8C5C12 C13

23:00.0

C4
24:00.0

C9

SN

25:00.0

26:00.0

25.0

20.0

15.0

10.0

05.0

3:22:00.0

21:55.0

Right ascension

Fig. 1.— Field of SN 2002fk observed with the Swope telescope. North is up and east isto the left. SN 2002fk is marked with an arrow and eleven stars of the local standard stars
used to derive differential photometry are labeled.

– 44 –

-3.34
-3.96
-1.36
-1.91
+4.62

F ) + constant

+4.50
+7.60
+8.07
+7.70
+30.52+29.07+42.56Log(+43.03+41.70+64.47+62.90+72.88+95.35+94.93

3000

4000

5000

6000

7000

8000

Observed Wavelength (

A)

9000

10000

11000

Fig. 2.— Comparison between our spectra (blue), the CfA (green, Blondin et al. 2012), andthe BSNIP (orange, Silverman et al. 2012a) spectra taken at similar epochs. The phase isindicated on the right for each spectrum.

– 45 –

13.5
mag

14.0
14.5
15.0

Residuals

15.5
0.15
0.10
0.05
0.00
0.05
0.10
0.15







10 0
10 20 30
Time Since B Maximum (Days)

10 0
10 20 30
Time Since B Maximum (Days)

Fig. 3.— Upper left. I-band light curve of SN 2002fk (red=CATS, blue=LOSS, green=CfA3)
before applying the photometric offset found in the calibration of the local standards. Bottom
left. Magnitude residuals from the polynomial fit (blue line). Upper right. I-band light curveof SN 2002fk after applying the photometric offset caused by systematic differences in thelocal standards, along with a polynomial fit (blue line). Bottom left. Magnitude residuals
from the polynomial fit.

– 46 –

Fig. 4.— Optical light curves of SN 2002fk. Filled circles are our observations, open circles correspond to LOSS measurements, and open squares to CfA3 data. Photometry of
LOSS and CfA3 were shifted by the offsets given in Table 8 to bring them into our CATS
photometric system (as discussed in Appendix B).

– 47 –

0

2

4

6
-20

0

20

40

60

Fig. 5.— BV RI light curves of SN 1990N, SN 1998aq, SN 2001el, SN 2002bo, SN 2002dj,
SN 2002fk, SN 2003du, and SN 2005cf, (Lira et al. 1998; Riess et al. 2005; Krisciunas et al.
2003; Benetti et al. 2004; Pignata et al. 2008; Stanishev et al. 2007; Wang et al. 2009) selected for their similar decline rates, normalized to peak brightness. ∆m15 is given inparenthesis for each SN.

– 48 –

Fig. 6.— Our optical and Near-IR photometry of SN 2002fk. In JHK bands open symbols
are data obtained with Classic-Cam, whilst filled symbols correspond to WIRC observations.

– 49 –SN 2001el (1.15)
SN 2002dj (1.13)
SN 2002fk (1.02)
SN 2005cf (1.00)
SN 2006dd (1.12)

Fig. 7.— IJHK light curves of SN 2001el (cyan), SN 2002dj (blue), SN 2002fk (black),
SN 2005cf (magenta), and SN 2006dd (red), selected for their similar decline rates, normalized to peak brightness. We chose to compare the templates of Krisciunas et al. (2004b)(dotted-dashed line) and Wood-Vasey et al. (2008) (dashed line). ∆m15 is given in parenthesis for each SN.

– 50 –

-20

0

20

40

60

80

Time Since B Maximum (Days)

-20

0

20

40

60

80

Time Since B Maximum (Days)

Fig. 8.— Optical colors of SN 2002fk (in black). For comparison, in red are shown the
LVG SN 1990N, SN 1994D, SN 1998aq, and SN 2003du. In magenta are shown the LVG
SN 2001el and SN 2005cf with strong HV Ca II near maximum, and in blue the HVG
SN 2002bo, SN 2002dj and SN 2009ig.

– 51 –

Fig. 9.— V − near-IR colors of SN 2002fk and the well sampled SNe Ia of similar ∆m15:
SN 2001el, SN 2002dj, SN 2003du, SN 2005cf and SN 2006dd. Dashed line are V − near-IR
loci for mid-range decliners and dotted-dashed line are V − near-IR loci for slow decliners(Krisciunas et al. 2004b).

– 52 –

Fig. 10.— Optical spectral evolution of SN 2002fk. The spectra have been corrected for theredshift of the host galaxy (2,137 km s−1 ) and have been shifted vertically for clarity. The
labels on the right mark the days since B-band maximum.

– 53 –

4000

6000

8000

10000

4000

6000

8000

10000

Fig. 11.— Spectrum of SN 2002fk at -4, 0, +25 and +95 days after B maximum. We plot forcomparison SN 1994D, SN 1998aq, SN 2003du, SN 2006gz, and SN 2005cf at similar epochs.

– 54 –SN 1990N
SN 1994D
SN 1998aq
SN 2002bo
SN 2002dj
SN 2002fk
SN 2003duSN 2005cf
SN 2009ig

HV Ca II (H&K)
Ca II (H&K)

Fig. 12.— Time evolution of the photospheric expansion velocity derived from Si II λ6355.
Red simbols correspond to HVG SNe and blue simbols to LVG SNe. Black dots correspondto SN 2002fk, the black asterisc is the velocity of Si II λ16 910 obtained by Marion et al.
(2003) from a near-IR spectrum taken 12 days before maximum. In the inset we show thetime evolution of other optical lines in SN 2002fk.

– 55 –

H&K Ca II-3.96

Si II/C II

Ca II IR-Triplet

C II 6580
C II 7234

-1.96

-3.96

-3.34
-1.91

F ) + constant

-3.34

-1.91
+0.09



Log(

-1.36

-1.91

+0.50

-1.36

+0.50

+0.09

20

10

0

10

20 10 0 10 20 30
Expansion Velocity [103 km s 1 ]






20



10



0

10

Fig. 13.— SYN++ models of the SN 2002fk spectra. Data are shown in black. Leftpanel: The blue–dashed lines correspond to models of H&K Ca II lines using Texc of Si II∼ 12, 500 K, which is close to Tphot , with no HV Ca II component. In red we show models
using Texc of Si II ∼ 7, 000 K, and in green we show models using Texc of Si II ∼ 12, 500 K,
which is close to Tphot , and including a HV Ca II component. The x–axis is the expansion
velocity measured with respect to the H&K Ca II line. Middle panel: in red we show models
using Texc of Si II ∼ 7, 000 K. In green we show models using Texc of Si II ∼ 12, 500 K,
which is close to Tphot , and including a HV C II component to get a better fit to the redside of the Si II line. The x–axis is the velocity measured with respect to C II λ6580. Rightpanel: as in the left panel but for the Ca II IR–triplet. The x–axis is the expansion velocity
measured with respect to the Ca II triplet. The phase of each spectrum is on the right sideof each panel.

– 56 –

H&K Ca II

Si II/C II

Ca II IR-Triplet

C II 6580
C II 7234

Log(F ) + constant

+0.50

+0.50

+0.50
+4.50

+2.65

+2.65



+4.50

+7.70

+4.50
+7.70
+7.70



20



10

0

10

20 10 0 10 20 30
Expansion Velocity [103 km s 1 ]




20



10



0

10

Fig. 14.— SYN++ models of the SN 2002fk spectra. In all three panels we show the samemodels as in Figure 13 but for later phases. The phase of each spectrum is on the right sideof each panel.

– 57 –

Log(F ) + constant

-3.96
-1.36
+0.50
+2.65
+4.50

4000

5000
6000
7000
Rest-Frame Wavelength [A]8000

Fig. 15.— SYN++ models of the observed spectra of SN 2002fk spectra, shown in black.
The blue–dashed lines correspond to models using Texc of Si II ∼ 12, 500 K with no HVcomponents. In red we show models using Texc of Si II ∼ 7, 000 K with no HV components,
and in green we show models using Texc of Si II ∼ 12, 500 K, and including HV components
of Ca II, and C II. These are the same models of Figure 13, now showing the full spectral
range for representative phases. The phase of each spectrum is on the right side.