CfAIR2: NEAR-INFRARED LIGHT CURVES OF 94 TYPE Ia SUPERNOVAE

For optical SN Ia LCs, many sophisticated methods are used to reduced the scatter in distance estimates. These include ${\rm{\Delta }}{m}_{15}(B)$ (Phillips 1993; Hamuy et al. 1996; Phillips et al. 1999; Prieto et al. 2006), multicolor LC shape (Riess et al. 1996, 1998; Jha et al. 2006b, 2007), "stretch" (Perlmutter et al. 1997; Goldhaber et al. 2001), Bayesian Adapted Template Match (Tonry et al. 2003), color–magnitude intercept calibration (Wang et al. 2003), spectral adaptive template (Guy et al. 2005, 2007; Astier et al. 2006), empirical methods (e.g., SiFTO; Conley et al. 2008), and BayeSN, a novel hierarchical Bayesian method developed at the CfA (M09, M11).

Unlike optical SN Ia, which are standardizable candles after a great deal of effort, spectroscopically normal NIR SN Ia appear to be nearly standard candles at the ∼0.15–0.2 mag level or better, depending on the filter (Meikle 2000; Krisciunas et al. 2004a, 2005a, 2007; Folatelli et al. 2010; Burns et al. 2011; Phillips 2012; WV08; M09; M11). Overall, SN Ia are superior standard candles and distance indicators in the NIR compared to optical wavelengths, with a narrow distribution of peak ${{JHK}}_{s}$ magnitudes and ∼5–11 times less sensitivity to reddening than optical B-band data alone.

Following Meikle (2000), pioneering work by Krisciunas et al. (2004a) (hereafter K04a) demonstrated that SN Ia have a narrow luminosity range in ${{JHK}}_{s}$ at ${t}_{B\mathrm{max}}$ with smaller scatter than in B and V. Using 16 NIR SN Ia, K04a found no correlation between optical LC shape and intrinsic NIR luminosity. K04a measured ${{JHK}}_{s}$ absolute magnitude distributions with 1σ uncertainties of only σ_J = 0.14, σ_H = 0.18, and ${\sigma }_{{K}_{s}}=0.12$ mag. While K04a used a small, inhomogeneous, sample of 16 LCs, in WV08, we presented 1087 ${{JHK}}_{s}$ photometric observations of 21 objects (including 20 SN Ia and 1 SN Iax), the largest homogeneously observed low-z sample at the time. NIR data from WV08 and the literature strengthened the evidence that normal SN Ia are excellent NIR standard candles, especially in the H band, where absolute magnitudes have an intrinsic rms of 0.15–0.16 mag, without applying any reddening or LC shape corrections, comparable to the scatter in optical data corrected for both.

WV08 suggested that LC shape variation, especially in the J band, might provide additional information for correcting NIR LCs and improving distance determinations. In M09, we applied a novel hierarchical Bayesian framework and a model accounting for variations in the J-band LC shape to NIR SN Ia data, constraining the marginal scatter of the NIR peak absolute magnitudes to 0.17, 0.11, and 0.19 mag in ${{JHK}}_{s}$, respectively (see Figure 9 of M09). Folatelli et al. (2010) obtained similar dispersions of 0.12–0.16 mag in ${{YJHK}}_{s}$, after correcting for NIR LC shape. Using 13 well-sampled, low-extinction, normal NIR SN Ia LCs from the Carnegie Supernova Project (CSP), K12 find scatters in absolute magnitude of 0.12, 0.12, and 0.09 mag in YJH, respectively. K12 also confirm that NIR LC shape correlates with intrinsic NIR luminosity, finding evidence for a nonzero correlation between the peak absolute JH maxima and the decline rate parameter ${\rm{\Delta }}{m}_{15}$, with only marginal dependence in Y. For a set of 12 SN Ia with JH LCs, Barone-Nugent et al. (2012) find a very small JH-band scatter of only 0.116 and 0.085 mag, respectively, although their data set only includes 3–5 LC points for each of the 12 objects. Similarly, Weyant et al. (2014) use only 1–3 data points for each of 13 low-z NIR SN Ia to infer an H-band dispersion of 0.164 mag. Both Barone-Nugent et al. (2012) and Weyant et al. (2014) use auxiliary optical data to estimate ${t}_{B\mathrm{max}}$. All of these results suggest that NIR data will be crucial for maximizing the utility of SN Ia as cosmological distance indicators.

This paper is organized as follows. In Section 2, we discuss the current sample of nearby NIR SN Ia data including CfAIR2, describe the technical specifications of PAIRITEL, and outline our follow-up campaign. In Section 3 we describe the data reduction process, including mosaicked image creation, sky subtraction, host galaxy subtraction, and our photometry pipeline. In Section 4, we present tests of PAIRITEL photometry, emphasizing internal calibration with Two Micron All Sky Survey (2MASS) field star observations, tests for potential systematic errors, and external consistency checks for objects observed by both PAIRITEL and the CSP. Throughout Sections 2–4, we frequently reference F12, where many additional technical details can be found. In Section 5, we present the principal data products of this paper, which include ${{JHK}}_{s}$ LCs of 94 SN Ia and 4 SN Iax. Further analysis of this data will be presented elsewhere. PAIRITEL and CSP comparison is discussed further in Section 6. Conclusions and directions for future work are summarized in Section 7. Additional details are included in a mathematical appendix (also see Section 7 of F12).

Technological advances in infrared detector technology have recently made it possible to obtain high-quality NIR photometry for large numbers of SN Ia. Phillips (2012) provides an excellent recent review of the cosmological and astrophysical results derived from NIR SN Ia observations made over the past three decades. Early NIR observations of SN Ia were made by Kirshner et al. (1973), Elias et al. (1981, 1985), and Frogel et al. (1987) and were particularly challenging as a result of the limited technology of the time. In addition, the flux contrast between the host galaxy and the SN Ia is typically smaller in the NIR than at optical wavelengths, making high-S/N observations possible only for the brightest NIR objects with the detectors available in the 1970s and 1980s. While this situation has improved somewhat in the subsequent decades, NIR photometry is still significantly more challenging than at optical wavelengths. Elias et al. (1985) was the first to present an NIR Hubble diagram for six SN Ia. Although these six SN Ia LCs were not classified spectroscopically, Elias et al. (1985) was also the first to use what became the modern spectroscopic nomenclature of Type Ia instead of Type I to distinguish between SN Ia and SN Ib; SN Ib are now thought to be core-collapse SN of stars that have lost their outer hydrogen envelopes (see Modjaz et al. 2014 and references therein).

In the late 1990s and early 2000s, panoramic NIR arrays made it possible to obtain NIR photometry comparable in quantity and quality to optical photometry for nearby SN Ia. The first early-time NIR photometry with modern NIR detectors observed before ${t}_{B\mathrm{max}}$ was presented for SN 1998bu (Jha et al. 1999; Hernandez et al. 2000). Since the first peak in the ${{JHK}}_{s}$ band occurs ∼3–5 days before ${t}_{B\mathrm{max}}$, depending on the filter, SN Ia must generally be discovered by optical searches at least ∼5–8 days before ${t}_{B\mathrm{max}}$ in order to be observed before the NIR maximum (F12; see Section 2.4).

Pioneering early work was performed in the early 2000s in Chile at the Las Campanas Observatory (LCO) and the Cerro Tololo Inter-American Observatory, spearheaded by the work of Krisciunas et al. (2000, 2001, 2003, 2004b, 2004c). K04a presented the largest Hubble diagram of its kind to date with 16 SN Ia. Before WV08 published 21 PAIRITEL NIR LCs observed by the CfA at FLWO, a handful of other NIR observations, usually for individual or small numbers of SN Ia or SN Iax of particular interest, were presented (Cuadra et al. 2002; Di Paola et al. 2002; Candia et al. 2003; Valentini et al. 2003; Benetti et al. 2004; Garnavich et al. 2004; Sollerman et al. 2004; Krisciunas et al. 2005b; Elias-Rosa et al. 2006, 2008; Krisciunas et al. 2006, 2007; Phillips et al. 2006, 2007; Pastorello et al. 2007a, 2007b; Stanishev et al. 2007; Stritzinger & Sollerman 2007; Pignata et al. 2008; Taubenberger et al. 2008; Wang et al. 2008). The largest NIR SN Ia sample prior to CfAIR2 was obtained by the CSP (Freedman 2005; Hamuy et al. 2006) at LCO, including observations of 59 normal and 14 peculiar NIR SN Ia LCs (Schweizer et al. 2008; Contreras et al. 2010; Stritzinger et al. 2010, 2011; Taubenberger et al. 2011).¹⁸ Other SN Ia or SN Iax papers with published NIR data since WV08 include Krisciunas et al. (2009, 2011), Leloudas et al. (2009), Yamanaka et al. (2009), Barone-Nugent et al. (2012), Biscardi et al. (2012), Matheson et al. (2012), Taddia et al. (2012), Silverman et al. (2013), Amanullah (2014), Cartier et al. (2014), Foley et al. (2014b), Goobar et al. (2014), Stritzinger et al. (2014), Weyant et al. (2014), Marion et al. (2015), and Stritzinger et al. (2015). See Table 3 for a fairly comprehensive listing of SN Ia and SN Iax with NIR observations in the literature or presented in this paper.

Overall, while ∼1000 nearby SN Ia have been observed at optical wavelengths, prior to CfAIR2, only 147 total unique nearby objects have at least one NIR band of published Y ${{JHK}}_{s}$ data obtained with modern NIR detectors (from SN 1998bu onward). These include 121 normal SN Ia, 22 peculiar SN Ia, and 4 SN Iax . CfAIR2 adds 66 new unique objects, including 62 normal SN Ia. By this measure, CfAIR2 increases the world published NIR sample of total unique objects by 66/147 ≈ 45% and normal SN Ia by 62/121 ≈ 51%. Twelve additional CfAIR2 objects have new data that supersede previously published PAIRITEL LCs and no data published by other groups. If we include these, CfAIR2 adds 78 total objects and 73 normal SN Ia to the literature. By this measure, CfAIR2 increases the world published sample of NIR objects by 78/135 ≈ 58% and the sample of normal SN Ia by 72/110 ≈ 65%. See Table 3.

Out of 121 total SN Ia and SN Iax observed from 2005 to 2011 by PAIRITEL, 23 are not included in CfAIR2. CfAIR2 includes improved photometry for 20 of 21 objects from WV08. For SN 2005cf, our photometry pipeline failed to produce a galaxy-subtracted LC, so we include the WV08 LC for SN 2005cf in CfAIR2 and all applicable figures or tables. These 20 objects include additional observations not published in WV08, processed homogeneously using upgraded mosaic and photometry pipelines (see Section 3). Table 1 lists general properties of the 94 CfAIR2 SN Ia, and Table 2 lists these for the 4 CfAIR2 SN Iax.

Heliocentric galaxy redshifts are provided in Tables 1 and 2 and CMB frame redshifts are given in Table 9 to ease construction of future Hubble diagrams including NIR SN Ia data.¹⁹ We obtained recession velocities from identified host galaxies as listed in the NASA/IPAC Extragalactic Database (NED). In cases where NED did not return a host galaxy or the host galaxy had no reported NED redshift, we either obtained redshift estimates from our own CfA optical spectra (Matheson et al. 2008; Blondin et al. 2012) or found redshifts reported in the literature. Figure 1 shows a histogram of CfAIR2 heliocentric galaxy redshifts z_helio for 86 normal SN Ia with ${t}_{B\mathrm{max}}$ estimates accurate to within less than 10 days.

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From 2005 to 2011, we also obtained extensive PAIRITEL NIR observations of 25 SN Ib/c (Bianco et al. 2014) and 20 SN II (to be presented elsewhere). Table 4 references all previously published and in preparation papers using PAIRITEL SN data, including multiwavelength studies of individual objects (Tominaga et al. 2005; Kocevski et al. 2007; Foley et al. 2009; Modjaz et al. 2009; Wang et al. 2009; Drout et al. 2013; Sanders et al. 2013; Fransson et al. 2014; Marion et al. 2014; Margutti et al. 2014) and NIR/optical LC compilations for SN of all types (e.g., Modjaz 2007; WV08; F12; Bianco et al. 2014). The most recent of these papers (Sanders et al. 2013; Bianco et al. 2014; Fransson et al. 2014; Marion et al. 2014; Margutti et al. 2014) used the same mosaic and photometry pipelines also used to produce the CfAIR2 data for this paper (see Section 3). For completeness, we also include information on all other types of SN with published PAIRITEL observations for both current and older pipelines.

Dedicated in October 2004, PAIRITEL uses the 2MASS (Skrutskie et al. 2006) northern telescope together with the 2MASS southern camera. PAIRITEL is a fully automated robotic telescope with the sequence of observations controlled by an optimized queue-scheduling database (Bloom et al. 2006). Two dichroic mirrors allow simultaneous observing in ${{JHK}}_{s}$ (1.2, 1.6, and 2.2 μm, respectively; Cohen et al. 2003; Skrutskie et al. 2006) with three 256 × 256 pixel HgCdTe NICMOS3 arrays. Figure 1 of WV08 shows a composite ${{JHK}}_{s}$ mosaicked image of SN 2006D (see Section 3.1).

Since the observations are conducted with the instrument that defined the 2MASS ${{JHK}}_{s}$ system, we use the 2MASS point source catalog (Cutri et al. 2003) to establish photometric zero points. Typical 30-minute (1800 s) observations (including slew overhead) reach 10σ sensitivity limits of ∼18, 17.5, and 17 mag for point sources in ${{JHK}}_{s}$, respectively (F12). For fainter objects, 10σ point source sensitivities of 19.4, 18.5, and 18 mag are achievable with 1.5 hr (5400 s) of dithered imaging in ${{JHK}}_{s}$, respectively (F12). PAIRITEL thus observes significantly deeper than 2MASS, which used a 7.8 s total exposure time to achieve 10σ point source sensitivities of 15.8, 15.1, and 14.3 mag in ${{JHK}}_{s}$, respectively (Skrutskie et al. 2006; see Section 4).

Automation of PAIRITEL made it possible to study SN with unprecedented temporal coverage in the NIR, by responding quickly to new SN and revisiting targets frequently (Bloom et al. 2006; WV08; F12). CfAIR2 followed up SN discovered by optical searches at δ ≳ −30° with V ≲ 18 mag, with significant discovery contributions from both amateur and professional astronomers (see Tables 1 and 2). SN candidates with a favorable observation window and airmass <2.5 from Mount Hopkins were considered for the PAIRITEL observation queue. We observed SN of all types but placed highest priority on the brightest SN Ia discovered early or close to maximum brightness. SN candidates meeting these criteria were often added to the queue before spectroscopic typing to observe the early-time LC. Since many optically discovered SN of all types brighter than V < 18 mag are spectroscopically typed by our group at the CfA²⁰ or other groups within 1–3 days of discovery, we rarely spent more than a few observations on objects we later deactivated after typing. All CfA SNe are spectroscopically classified using the SuperNova IDentification code (SNID; Blondin & Tonry 2007).

From 2005 to 2011, ∼20–30 SN per year were discovered that were bright enough to observe with the PAIRITEL 1.3 m, with ∼3–6 available on any given night from Mount Hopkins. Since we only perform follow-up NIR observations and are not conducting an NIR search to discover SN with PAIRITEL, we suffer from all the heterogeneous sample selection effects and biases incurred by each of the independent discovery efforts. A full analysis of the completeness of our sample is beyond the scope of this work. Overall, with ∼30% of the time on a robotic telescope available for SN observations, effectively amounting to over 6 months on the sky, we observed over 2/3 of the candidate SN that met our follow-up criteria. We also observed galaxy template images (SNTEMP) for each SN to enable host subtraction (see Section 3.4).

All CfAIR2 images were processed into mosaics at the CfA using p3.6 implemented in Python version 2.6.²¹ F12 and references in Table 4 describe older mosaic pipelines. Klein & Bloom (2014) provide a more detailed description of p3.6 as used for PAIRITEL observations of RR Lyrae stars. Figures 3–5 show sample p3.6 J-band mosaics for all 98 CfAIR2 objects.

Including slew overhead for the entire dither pattern, typical exposure times range from 600 to 3600 s, yielding ∼50–150 raw images for mosaicking. Excluding slew overhead, effective exposure times are generally ∼40%–70% of the time on the sky, yielding typical actual exposure times of ∼250 to ∼2500 s. Raw images are obtained with standard double-correlated reads with the long-exposure (7.8 s) minus short-exposure (51 ms) frames in each filter treated as the "raw" frame input to p3.6. These raw 256 × 256 pixel images are of ∼7.8 s duration with a plate scale of 2'' pixel⁻¹ and an 853 × 853 field of view (FOV). To aid with reductions, the telescope is dithered after each set of three exposures with a step size <2' based on a randomized dither pattern covering a typical ∼12' × 12' FOV. The three raw images observed at each dither position are then added into "triplestacks" before mosaicking. The p3.6 pipeline processes all raw images by flat correction, dark current and sky subtraction, registration, and stacking to create final ${{JHK}}_{s}$ mosaics using SWarp (Bertin et al. 2002). Bad pixel masks are created dynamically, and flat fields—which are relatively stable—were created from archival images. Since the short-timescale seeing also remains roughly constant in the several seconds of slew time between dithered images, we did not find it necessary to convolve the raw images to the seeing of a raw reference image before mosaicking. The seeing over long time periods (several months) remains relatively constant at 077–085.²² The raw images are resampled from a raw image scale of 2'' pixel⁻¹ into final mosaics with 1'' pixel⁻¹ sampling with SWarp (Bertin et al. 2002). The typical FWHM in the final PAIRITEL mosaics is ∼25–30, consistent with the average image quality obtained by 2MASS (Skrutskie et al. 2006).

The desired telescope pointing center for all dithered images is set to the SN R.A. and decl. coordinates from the optical discovery images. Unfortunately, as a result of various software and/or mechanical issues—for example, problems with the R.A. drive—the PAIRITEL 1.3 m telescope pointing accuracy can vary by ∼1'–30' from night to night. Catastrophic pointing errors can result in the SN being absent in all of the raw images and missing in the ∼12' × 12' mosaic FOV. More often, nonfatal pointing errors result in the SN being absent or off-center in some, but not all, raw images. In p2.0 used for WV08, the mosaic center was constrained to be the SN coordinates and the mosaic size in pixels was fixed. This resulted in a significant fraction of failed or low-S/N mosaics using an insufficient number of raw images. For p3.0–p3.6, the constraint fixing the SN at the mosaic center was relaxed and the mosaic center was allowed to be the center of all imaging. This resulted in ∼15% more mosaic solutions than p2.0. Mosaics that failed processing at intermediate photpipe stages were excluded from the LC automatically. Some mosaics that succeeded to the end of photpipe were excluded based on visual inspection or by identifying outlier LC points during post-processing.

The PAIRITEL camera has no cold shutter, so dark current cannot be measured independently, and background frames include both sky and dark photons ("skark"). Fortunately, the thermal dark current counts across the raw frames are negligible in ${{JHK}}_{s}$ for the NICMOS3 arrays on timescales comparable to the individual, raw, 7.8 s exposures (Skrutskie et al. 2006). Furthermore, the dark current rate does not detectably vary across the 1.5 hr of the maximum dither pattern used in these observations. Background frames also include an electronic bias, characterized by shading in each of the four raw image quadrants, which produces no noise, and amplifier glow, which peaks at the corners of the quadrants, and which, like thermal dark current, does produce Poisson noise. These intrinsic detector and sky noise contributions get smeared out over the mosaic dither pattern, producing characteristic patterns in the skark mosaics and mosaic noise maps (see Figure 2).²³

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PAIRITEL SN observations did not include on-off pointings alternating between the source and a nearby sky field, so skark frames were created for each raw image in the mosaic by applying a pixel-by-pixel average through the stack of a time series of unregistered raw frames, after removing the highest and lowest pixel values in the stack. The stack used a time window of 5 minutes before and after each raw image. This approximation assumes that the sky is constant on timescales less than 10 minutes. For reference, typical dithered image sequences have effective exposure times of 10–30 minutes. Figure 2 shows that for J band, where the sky counts are small compared to the various sources of detector noise, the skark and noise mosaics are dominated by the cumulative effect of the intrinsic detector features over the entire dither pattern, including dark current, shading, and amplifier glow.²⁴ By contrast, the H- and K_s-band skark and noise mosaics in Figure 2 are dominated by sky counts and sky noise, respectively, which combine with the various detector imprints and spatiotemporal sky variation to produce the large-scale patterns smeared across the dither pattern.

Although the telescope is dithered (<2') after three exposures at the same dither position, for host galaxies with large angular size ≳2'–5' (in the 853 raw image FOV), host galaxy flux contamination introduces additional systematic uncertainty by biasing skark count estimates toward larger values, leading to oversubtraction of sky light in those pixels (F12). Still, the relatively large PAIRITEL 853 FOV combined with a dither step size comparable or greater than the ∼1'–2' angular size of typical galaxies at z ∼ 0.02 allows us to safely estimate the sky from the raw frames in most cases. This observing strategy also gives us more time on target compared to on-off pointing. While our approach can lead to systematic sky oversubtraction for SN and stars near larger galaxies, by testing the radial dependence of PAIRITEL photometry of 2MASS stars within 3' of the SN (and close to the host galaxy), we estimate this systematic error to be negligible compared to our photometric errors, biasing SN photometry fainter by ≲0.01 mag in JH and ≲0.02 in K_s (F12). By comparison, mean photometric errors for each of the highest-S/N LC points from the set of SN in CfAIR2 are ∼0.03, 0.05, and 0.12 mag in ${{JHK}}_{s}$, respectively (with larger mean statistical errors for all LC points of ∼0.09, 0.12, and 0.18 mag in ${{JHK}}_{s}$, respectively). We thus choose to ignore systematic errors from sky oversubtraction in this work.

Since three raw frames are taken at each dither position and co-added into triplestacks before mosaicking, p3.6 now also constructs "tripleskarks," by co-adding the three associated skark frames taken at each dither position. To remove the estimated background counts, p3.6 now subtracts the associated tripleskark from each triplestack before creating final mosaics and new skark and noise mosaics (see Figure 2). Since the estimated skark noise can vary by ∼10%–100% across individual skark mosaics, modeling the noise in each pixel provides more reliable differential noise estimates at the positions of all 2MASS stars and the SN, although our absolute noise estimate is still underestimated since the noise mosaics do not model all sources of uncertainty (see Section 7.1 of F12). To account for this, we also use 2MASS star photometry to empirically calculate inevitable noise underestimates and correct for them in SN photometry on subtracted or unsubtracted images (see F12; Section 4).

The PAIRITEL infrared camera is undersampled because the 2'' detector pixels are larger than the sub-arcsecond atmospheric seeing disk at FLWO. This means that we cannot fully sample the PSF of the detected image. To achieve some subpixel sampling, PAIRITEL implements a randomized dither pattern. While dithering can help recover some of the image information lost from undersampling, large pixels with dithered imaging cannot fully replace a fully sampled imaging system (Lauer 1999; Fruchter & Hook 2002; Rowe et al. 2011), and in practice, dithering does not always reliably produce the desired sub-pixel sampling. When we subtract host galaxy light, which requires PSF matching SN and SNTEMP mosaics, undersampling leads to uncertainty in photometry for individual subtractions that can underestimate or overestimate the flux at the SN position. We correct for this by averaging many subtractions and removing bad subtractions, when producing CfAIR2 LCs (see Sections 3.4–3.7).

We obtain SNTEMP images after the SN has faded below detection for the PAIRITEL infrared camera, typically ≳6–12 months after the last SN observation. We use SNTEMP images to subtract the underlying host galaxy light at the SN position for each SN image that meets our image quality standards (see Sections 3.5–3.6). To limit the effects of variable observational conditions and sensitivity to individual template observations of poor quality and to minimize the photometric uncertainty from individual subtractions, we try to obtain at least ${N}_{{\rm{T}}}=2$, and as many as ${N}_{{\rm{T}}}=11$ SNTEMP images that satisfy our image quality requirements (see Section 3.7). In practice, we obtained medians of ${N}_{{\rm{T}}}=4$, $4$, and $3$ usable SNTEMP images in ${{JHK}}_{s}$, respectively (Figure 6). In cases with only ${N}_{{\rm{T}}}=1$ SNTEMP image, galaxy-subtracted LCs are deemed acceptable only for bright, well-isolated SN that are consistent with the unsubtracted LCs (see Sections 3.5, 4.2.2).

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Forced DoPHOT photometry (Schechter et al. 1993) at a fixed position was performed on the unsubtracted SN images as an initial step for all PAIRITEL SN. Forced DoPHOT LCs on unsubtracted images provide an excellent approximation to the final galaxy-subtracted LCs for SN that were clearly separated from their host galaxy (F12). Approximately 30% of SN of all types observed by PAIRITEL are well isolated from the host galaxy and bright enough so that the measured galaxy flux at the SN position is ≲10% of the SN flux at peak brightness. We use 20 of these bright, well-isolated SN to perform internal consistency checks to test for errors incurred from host galaxy subtraction (see Section 4.2; F12).

We perform galaxy subtraction on all CfAIR2 objects to reduce the data with a homogeneous method.²⁵ We used subtraction-based photometry following Miknaitis et al. (2007). The SN flux in the difference images is measured with forced DoPHOT photometry at fixed pixel coordinates, determined by averaging SN centroids from J-band or CfA optical V-band difference images with photometric detections of the object that had an S/N > 5. SN centroids are typically accurate to within ≲02. Tests show no systematic LC bias for forced DoPHOT photometry as a result of SN astrometry errors if the SN centroid is accurate to within ≲05 (F12). The R.A. and decl. values in Tables 1 and 2 show best-fit SN centroid coordinates. These are typically more accurate than optical discovery coordinates from IAU/CBET notices, which may only be accurate to within ≲1''–2''. Forced DoPHOT photometry at this fixed position in the difference images employs the DoPHOT PSF calculated from standard stars in the unconvolved image. For the difference images the calibrated zero point from the template is used, with suitable correction for the convolution of the SNTEMP image as detailed by Miknaitis et al. (2007).

We use NNT, an alternative galaxy subtraction method for CfAIR2, which uses fewer individual subtractions than the NN2 method (Barris et al. 2005) used in WV08. With NNT, for each of the N_SN mosaicked SN images, we subtract each of the usable ${N}_{{\rm{T}}}$ SNTEMP images, yielding at most ${N}_{\mathrm{NNT}}={N}_{\mathrm{SN}}\times {N}_{{\rm{T}}}$ individual subtractions. NNT yields ${N}_{{\rm{T}}}$ realizations of the LC that can be combined into a final galaxy-subtracted LC with a night-by-night weighted flux average after robust 3σ rejection and manual checks to exclude individual bad subtractions.²⁶ SN or SNTEMP images that failed our image quality requirements were also excluded from NNT via automatic photpipe tests and manual checks, yielding fewer bad subtractions than the purely automated process used in WV08.

By obtaining $1\lesssim {N}_{{\rm{T}}}\leqslant 11$ usable SNTEMP images, including additional observations since WV08, most CfAIR2 SN Ia have ${N}_{{\rm{T}}}\gtrsim 4$ SNTEMP images suitable for galaxy subtraction (see Figure 6). NNT allowed us to exclude individual bad subtractions, average over variance across subtractions from different templates, and produce CfAIR2 SN Ia LCs with more accurate flux measurements compared to NN2 for WV08. We discuss the statistical and systematic uncertainty incurred from NNT host galaxy subtraction in Section 4.2. CfAIR2 NNT LCs also show better agreement with CSP photometry for the same objects compared to WV08 (see Section 4.3).²⁷

Since WV08, we have implemented several improvements to photpipe. Photpipe now takes p3.6 mosaics as input (see Section 3.1). To use SN that are not in the p3.6 mosaic center, photpipe uses larger-radius photometric catalogs and improved image masks (see F12). In WV08, our "skark" noise estimate was assumed to be constant throughout the mosaic (see Section 3.2). Figure 2 shows that this is a bad approximation. Instead, p3.6 noise mosaics are used by photpipe and fed as inputs to DoPHOT (Schechter et al. 1993), our point source photometry module, and HOTPANTS (Becker et al. 2004, 2007), our difference imaging module (see Section 3.4), leading to improved image subtraction. See F12 for details on the computational implementation of photpipe and p3.6.

As a result of improvements discussed throughout Section 3, CfAIR2 supersedes WV08 photometry for 20 out of 21 LCs (excluding SN 2005cf). CfAIR2 and WV08 photometry agree best for the brightest, well-isolated SN with little galaxy light at the SN position. Fainter SN that required significant host galaxy subtraction show the most disagreement between CfAIR2 and WV08 due mainly to the differences between NN2 and NNT (see Section 4.3.1 of F12). Problems with WV08 NN2 photometry are most evident in the set of nine WV08 SN also observed by the CSP, which are discussed in Section 4.3. The improved agreement between CfAIR2 and CSP (see Section 6) gives evidence that CfAIR2 photometry is superior to WV08.

Although individual LCs show differences between CfAIR2 and WV08 data, we do not expect the revised photometry to significantly affect the overall conclusions of WV08. Preliminary analysis, which will be presented elsewhere, will derive mean NIR LC templates and mean absolute magnitudes using only normal CfAIR2 SN Ia and compare these to mean templates derived using only 18 normal PAIRITEL SN Ia from WV08.

We organize Section 4.1 as follows. In Section 4.1.1, we present PAIRITEL mean photometric measurements and uncertainties for all 2MASS stars for 118 out of 121 SN Ia and SN Iax fields observed from 2005 to 2011. In Section 4.1.2, we test whether DoPHOT is correctly estimating photometric uncertainties for PAIRITEL point sources. In Section 4.1.3, we assess whether PAIRITEL DoPHOT photometry globally agrees with 2MASS star photometry. Overall, Sections 4.1.2 and 4.1.3 test the precision and accuracy of DoPHOT photometry on unsubtracted PAIRITEL images. We find no significant systematic differences with 2MASS.

4.1.1. PAIRITEL Photometry of 2MASS Standard Stars

For 121 PAIRITEL SN fields observed from 2005 to 2011, including 23 objects not in CfAIR2, we performed DoPHOT photometry on all 2MASS stars to measure the photometric zero point for each image. In a typical 12' × 12' p3.6 mosaic FOV, there were between 6 and 92 2MASS stars in each filter (see Figures 3–5). While the exact coverage for a mosaic during a given night varies (see Section 3.1), the majority of the 2MASS stars are covered by each observation of a given SN field. Fewer 2MASS stars are detected by DoPHOT as wavelength increases from J to H to K_s. For all SN Ia or SN Iax fields with at least five mosaic images, the mean number of 2MASS stars was 39, 38, and 34 in ${{JHK}}_{s}$, respectively (see Table 4.1 of F12).

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We interpret the error on the weighted mean of the PAIRITEL photometric measurements to be the uncertainty in the measurement of the mean PAIRITEL magnitude for that 2MASS star (see Sections 4.1.2 and 7.3 of F12 for mathematical details). Table 5 presents weighted mean PAIRITEL photometric measurements and uncertainties for all 2MASS stars in 118 SN fields observed by PAIRITEL. A global comparison of PAIRITEL and 2MASS star measurements is presented in Sections 4.1.2 and 4.1.3.

Table 5.  PAIRITEL ${{JHK}}_{s}$ Photometry of 2MASS Standard Stars in SN Ia Fields

SNa	Starb	α(2000)c	δ(2000)c	NJ	${m}_{J}^{\mathrm{PTL}}$	${\sigma }_{{m}_{J}}^{\mathrm{PTL}}$ d	${m}_{J}^{2{\rm{M}}}$	${\sigma }_{{m}_{J}^{2{\rm{M}}}}$	NHd	${m}_{H}^{\mathrm{PTL}}$	${\sigma }_{{m}_{H}}^{\mathrm{PTL}}$	${m}_{H}^{2{\rm{M}}}$	${\sigma }_{{m}_{H}^{2{\rm{M}}}}$	NKd	${m}_{K}^{\mathrm{PTL}}$	${\sigma }_{{m}_{K}}^{\mathrm{PTL}}$	${m}_{K}^{2{\rm{M}}}$	${\sigma }_{{m}_{K}^{2{\rm{M}}}}$
					(mag)e	(mag)f	(mag)g	(mag)g		(mag)e	(mag)f	(mag)g	(mag)g		(mag)e	(mag)f	(mag)g	(mag)g
SN 2005ak	01	14:40:18.45	+03:30:55.44	34	16.549	0.007	16.504	0.159	35	15.940	0.009	16.024	0.183	30	15.675	0.012	15.251	0.173
SN 2005ak	02	14:40:18.56	+03:34:12.76	34	15.918	0.006	15.858	0.097	33	15.230	0.008	15.230	0.105	33	15.024	0.010	15.075	0.148
SN 2005ak	03	14:40:19.41	+03:30:22.95	34	15.112	0.006	15.118	0.056	35	14.768	0.007	14.822	0.085	33	14.686	0.008	14.814	0.112
SN 2005ak	04	14:40:20.77	+03:27:36.99	34	16.404	0.006	16.430	0.150	35	15.793	0.009	16.057	0.219	34	15.549	0.012	15.326	0.197
SN 2005ak	05	14:40:20.94	+03:33:41.82	33	15.013	0.006	15.071	0.049	34	14.408	0.007	14.511	0.071	34	14.301	0.007	14.285	0.074
SN 2005ak	06	14:40:22.26	+03:31:18.61	33	17.032	0.007	16.521	0.147	33	16.386	0.010	16.101	0.215	29	16.153	0.014	15.598	0.255
SN 2005ak	07	14:40:22.58	+03:32:56.39	35	15.637	0.006	15.665	0.066	35	15.001	0.007	15.133	0.089	34	14.765	0.008	14.946	0.148
SN 2005ak	08	14:40:26.00	+03:31:41.52	34	13.255	0.005	13.233	0.024	35	12.617	0.006	12.608	0.030	35	12.406	0.007	12.404	0.032
SN 2005ak	09	14:40:26.55	+03:30:58.65	34	14.780	0.006	14.762	0.037	35	14.212	0.007	14.121	0.035	35	13.967	0.007	14.003	0.071
SN 2005ak	10	14:40:29.45	+03:32:34.68	35	16.402	0.006	16.596	0.163	35	15.757	0.008	15.736	0.152	32	15.571	0.011	15.228	0.173
SN 2005ak	11	14:40:29.89	+03:28:05.44	33	14.455	0.006	14.444	0.038	34	14.160	0.006	14.114	0.035	33	14.055	0.007	14.095	0.072
SN 2005ak	12	14:40:30.02	+03:30:15.93	34	15.424	0.005	15.319	0.072	33	14.958	0.007	15.021	0.090	35	14.793	0.008	14.624	0.123
SN 2005ak	13	14:40:31.33	+03:28:33.93	24	15.472	0.010	15.589	0.082	28	14.814	0.011	15.169	0.100	31	14.488	0.010	14.898	0.150
SN 2005ak	14	14:40:31.52	+03:32:31.31	36	14.373	0.005	14.367	0.036	36	14.171	0.007	14.212	0.042	36	14.145	0.007	14.277	0.086
SN 2005ak	15	14:40:31.74	+03:29:10.30	35	15.420	0.006	15.304	0.056	34	14.804	0.007	14.823	0.070	35	14.574	0.008	14.704	0.116
SN 2005ak	16	14:40:32.31	+03:31:13.54	34	16.087	0.006	15.902	0.090	36	15.501	0.008	15.476	0.132	⋯	⋯	⋯	⋯	⋯
SN 2005ak	17	14:40:32.43	+03:33:34.39	28	14.766	0.010	14.756	0.056	26	14.069	0.012	14.143	0.085	29	13.836	0.011	13.802	0.070

Notes.

^aTables like the above sample are provided online for 118 out of 121 SN Ia and SN Iax fields observed with PAIRITEL from 2005 to 2011 (SN 2005ak-SN 2011df), including 23 SN Ia without CfAIR2 photometry (e.g., SN 2005ak above). Tables include weighted mean PAIRITEL photometry and uncertainties for all 2MASS stars in each SN Ia field. Three SN Ia are not included in Table 5 as a result of unresolved software errors: SN 2008fv, SN 2008hs (in CfAIR2), and SN 2011ay (not in CfAIR2). ^bSuperscripts $\mathrm{PTL}$ and $2{\rm{M}}$ denote PAIRITEL and 2MASS, respectively. Missing data are denoted by .... ^cR.A. (α) and decl. (δ) for Epoch 2000 in sexagesimal coordinates. ^dN_X is the number of PAIRITEL SN images in band X = J, H, K with this standard star used to measure ${m}_{X}^{\mathrm{PTL}}$ and ${\sigma }_{{m}_{X}}^{\mathrm{PTL}}$. ^ePAIRITEL apparent brightness in magnitudes ${m}_{X}^{\mathrm{PTL}}$ is computed as the weighted mean PAIRITEL magnitude over all N_X SN images with that 2MASS star. ^fPAIRITEL magnitude uncertainty ${\sigma }_{{m}_{X}}^{\mathrm{PTL}}$ is computed as the error on the weighted mean of the N_X measurements, each of which has already been corrected for DoPHOT uncertainty estimates as described in Section 4.1.2 and F12. (See Section 7.3 of F12.) ^gThe 2MASS magnitudes ${m}_{X}^{2{\rm{M}}}$ and uncertainties ${\sigma }_{{m}_{X}}^{2{\rm{M}}}$ for each star are from the 2MASS point source catalog (Cutri et al. 2003).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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4.1.2. Photometric Precision

4.1.3. Photometric Accuracy

In Section 4.2, we discuss internal consistency tests to assess other potential statistical and systematic errors with the photometry. In Sections 4.2.1–4.2.3, we evaluate our most important systematic and statistical uncertainty from the NNT host galaxy subtraction process, both for bright, well-isolated objects and for objects superposed on the nucleus or spiral arms of host galaxies. See Section 4 of F12 for discussions of systematic errors from sky subtraction and astrometric errors in the best-fit SN centroid position.

4.2.1. Galaxy Subtraction: Statistical and Systematic Errors

When subtracting SN and SNTEMP images observed under different seeing conditions, undersampling of the PAIRITEL NIR camera introduces uncertainties into both the estimates of the PSF and convolution kernel solution when attempting to transform the SN or SNTEMP image to the PSF of the other. This leads to flux being added or subtracted from photometry on individual subtractions. While NNT attempts to correct for this by averaging over many subtractions, there is always remaining uncertainty as a result of undersampling (see Section 3).

For an individual night of photometry, we conservatively estimate the statistical uncertainty from NNT, ${\sigma }_{\mathrm{NNT}}$, as the error-weighted standard deviation of the input flux measurements, weighted by the corrected DoPHOT flux uncertainties for each of the ${N}_{{\rm{T}}}$ subtractions (for details see Section 3 and the Appendix). For cases where only ${N}_{{\rm{T}}}=1$ or 2 subtractions survive both the pipeline's cuts and any manual rejection, NNT flux estimates can be biased high or low and either the weighted standard deviation cannot be computed or it is not a reliable estimate of the statistical uncertainty. To ensure accurate photometric uncertainties for these cases—at the expense of reduced photometric precision—we adopt a conservative systematic error floor of 0.25 and 0.175 mag for ${N}_{{\rm{T}}}=1$ and ${N}_{{\rm{T}}}=2$, respectively. Final galaxy-subtracted uncertainties $\tilde{{\sigma }_{\mathrm{NNT}}}$ are computed as in Table 6, which includes a final S/N cut of >3. Thus, when a given LC point has an uncertainty larger than its neighbors, either only one or two good subtractions were used or the scatter among the surviving three-plus subtractions was large.

Table 6.  Computing NNT Errors

${N}_{{\rm{T}}}$	$\tilde{{\sigma }_{\mathrm{NNT}}}$ mag Error	S/N	Note
1	$\mathrm{max}(0.25\;\mathrm{mag},{\sigma }_{\mathrm{NNT}})$	3 < S/N < ∼4.2	a
2	$\mathrm{max}(0.175\;\mathrm{mag},{\sigma }_{\mathrm{NNT}})$	3 < S/N < ∼5.5
3+	${\sigma }_{\mathrm{NNT}}$	3 < S/N	b

Notes.

^aIf ${N}_{{\rm{T}}}=1$, ${\sigma }_{\mathrm{NNT}}=\tilde{{\sigma }_{\mathrm{do}}}$, the corrected DoPHOT error for a single subtraction. ^bAn S/N >1 cut is used before NNT averaging. An S/N > 3 cut is placed on the final NNT LC points.

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In Sections 4.2.2 and 4.2.3, both for bright, well-isolated objects and SN superposed on the host galaxy, NNT produces no net systematic bias given ${N}_{{\rm{T}}}$ ≳ 3–4 usable host galaxy templates. For fainter objects, SN superposed on the host galaxy nucleus, or SN with insufficient high-quality SNTEMP images, the additional uncertainty from host galaxy subtraction can yield many LC points that are excluded based on S/N cuts, outlier rejection, or final quality checks, sometimes yielding LCs of insufficient quality for publication or cosmological analysis.

4.2.2. Galaxy Subtraction for Bright, Well-Isolated Objects

4.2.3. Galaxy Subtraction for Superposed SN

4.2.4. NNT versus Forced DoPHOT Errors

NNT can lead to larger reported errors (${\sigma }_{\mathrm{NNT}}$) compared to corrected DoPHOT point source photometry without galaxy subtraction ($\tilde{{\sigma }_{\mathrm{do}}}$) for cases with ${N}_{{\rm{T}}}$ ≲ 2–3, owing primarily to our imposed systematic error floor for these cases (see Table 6). However, for cases with ${N}_{{\rm{T}}}$ ≳ 3–4 templates, ${\sigma }_{\mathrm{NNT}}\lesssim \tilde{{\sigma }_{\mathrm{do}}}$ and NNT performs as well as or better than DoPHOT without host subtraction as a result of the effective division by $\sim \sqrt{{N}_{{\rm{T}}}}$ inside the error-weighted standard deviation used to compute ${\sigma }_{\mathrm{NNT}}$ (see the Appendix). Figure 7 shows median magnitude uncertainties for both the highest-S/N LC points for each SN and all LC points for both forced DoPHOT and NNT photometry. The spikes in the NNT error distributions are artifacts of our systematic error floor chosen for cases with ${N}_{{\rm{T}}}$ = 1–2 SNTEMP images.

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Comparing PAIRITEL CfAIR2 NNT LCs with published CSP photometry for the same SN Ia provides an important external consistency check. Although CfA and CSP observatories with NIR detectors are in the northern and southern hemispheres, respectively, an overlapping subset of 18 CfAIR2 objects in the declination range −24.94410 < δ < 25.70778 were observed in ${{JHK}}_{s}$ by both groups (see Table 7 and Figures 10–12).²⁹ Similar to Tables 1 and 2 of this paper, Table 1 of Contreras et al. (2010, hereafter C10) and Table 1 of Stritzinger et al. (2011, hereafter S11) present general properties of 35 and 50 SN Ia observed by the CSP, respectively. Some CSP SN Ia had only optical observations and no NIR data.³⁰ The 18 CSP NIR objects independently observed by PAIRITEL include 14 normal SN Ia, 1 peculiar, fast-decining object, 2 overluminous, slowly declining objects, and 1 SN Iax . Of these, 9 had data published in WV08 and 9 are new to CfAIR2. See Table 7.

Table 7.  18 NIR SN Ia Observed by PAIRITEL and CSP

SNa	Typeb	${\rm{\Delta }}J$ (mag)c	${\rm{\Delta }}H$ (mag)c	${\rm{\Delta }}{K}_{s}$ (mag)c	Agree?d	CSP
						Refse
SN 2005el	Ia	0.032 ± 0.026	0.042 ± 0.018	0.078 ± 0.024	234	(1)
SN 2005eq	Ia	−0.010 ± 0.030	−0.003 ± 0.024	−0.034 ± 0.030	112	(1)
SN 2005hk	Iax	−0.031 ± 0.027	−0.012 ± 0.028	0.050 ± 0.048	212	(3)
SN 2005iq	Ia	−0.025 ± 0.029	0.080 ± 0.060	−0.077 ± 0.045	122	(1)
SN 2005ke	Iap	−0.001 ± 0.014	−0.001 ± 0.014	0.010 ± 0.020	111	(1)
SN 2005na	Ia	−0.059 ± 0.030	−0.000 ± 0.023	⋯	21	(1)
SN 2006D	Ia	0.003 ± 0.011	−0.006 ± 0.014	0.000 ± 0.010	111	(1)
SN 2006X	Ia	0.009 ± 0.018	0.006 ± 0.011	−0.007 ± 0.010	111	(1)
SN 2006ax	Ia	−0.026 ± 0.014	0.003 ± 0.005	0.007 ± 0.018	211	(1)
SN 2007S	Ia	0.029 ± 0.023	0.015 ± 0.020	0.006 ± 0.024	211	(2)
SN 2007ca	Ia	0.004 ± 0.012	0.036 ± 0.025	⋯	12	(2)
SN 2007if	Iap	0.058 ± 0.033	0.053 ± 0.038	⋯	22	(2)
SN 2007le	Ia	0.015 ± 0.013	0.006 ± 0.008	⋯	21	(2)
SN 2007nq	Ia	0.004 ± 0.020	0.000 ± 0.054	⋯	11	(2)
SN 2007sr	Ia	0.022 ± 0.017	0.017 ± 0.012	⋯	22	(4)
SN 2008C	Ia	−0.004 ± 0.018	−0.001 ± 0.018	⋯	11	(2)
SN 2008hv	Ia	0.024 ± 0.024	0.011 ± 0.020	⋯	21	(2)
SN 2009dc	Iap	−0.004 ± 0.019	−0.006 ± 0.015	−0.002 ± 0.019	111	(5)

Notes.

^aAll SN LCs use NNT galaxy subtraction (see Section 3.7). The horizontal line in the middle of the table divides the nine PAIRITEL SN with CfAIR2 data that supersede WV08 data (top: SN 2005el-SN 2006ax) from the nine SN with PAIRITEL data new to this work (bottom: SN 2007S-SN 2009dc). ^bIa: spectroscopically normal. Iap: peculiar, underluminous (SN 2005ke), peculiar overluminous (SN 2007if, SN 2009dc). Iax: 02cx-like (SN 2005hk). ^cWeighted mean CSP–CfAIR2 residuals and 1σ errors, estimated by the error-weighted standard deviation of the residuals divided by 3. K_s-band data not available for some CSP SN Ia. ^dDo CSP–CfAIR2 weighted mean residuals agree within 1, 2, or 3σ for ${{JHK}}_{s}$, respectively? For example, 132 would mean the NIR LCs agree in J within 1σ, H within 3σ, and K_s within 2σ. All 18 LCs in JH and all 8 in K_s agree within at least 3σ by this metric (except for SN 2005el, K_s, which agrees at 4σ). ^eCSP References: (1) Contreras et al. (2010), (2) Stritzinger et al. (2011), (3) Phillips et al. (2007), (4) Schweizer et al. (2008), (5) Taubenberger et al. (2011).

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4.3.1. CSP–PAIRITEL Offsets and Color Terms

4.3.2. Zero-point Offsets from 2MASS Star Photometry

C10 used CSP photometric measurements of 984 J- and H-band 2MASS stars in their SN fields, finding these mean zero point offsets between the CSP Swope 1.0 m natural system and the 2MASS J and H filters:

$$\begin{eqnarray}{J}_{\mathrm{CSP}}-{J}_{2{\rm{M}}} & = & 0.010\pm 0.003\;\mathrm{mag},\\ {H}_{\mathrm{CSP}}-{H}_{2{\rm{M}}} & = & 0.043\pm 0.003\;\mathrm{mag}.\end{eqnarray} \tag{ 1 }$$

C10 did not derive zero-point offsets in K_s because they had only 41 CSP 2MASS star observations in K_s.

For 19 objects observed by both PAIRITEL and CSP (including SN 2006is, which is not in CfAIR2), we obtained CSP standard-star photometry for the local sequences for 16 objects from the literature (C10; S11; Taubenberger et al. 2011) and three additional objects from the CSP (M. Stritzinger 2012–2013;, private communication; see Section 4.33 of F12). In these 19 SN fields, we used 269, 264, and 24 2MASS stars observed by both PAIRITEL and CSP in ${{JHK}}_{s}$, respectively, limited to the color range $0.2\lt {(J-H)}_{\mathrm{CSP}}\lt 0.7$ mag also used by C10. We compute CSP−PAIRITEL residuals for each 2MASS star in ${{JHK}}_{s}$ and interpret the weighted mean residuals and the error on the weighted mean as our estimate of the zero-point offset and uncertainty between the CSP natural system (JH Swope, K_s du Pont) and the PAIRITEL/2MASS ${{JHK}}_{s}$ system. Although column 6 of Table 5 reports uncertainties on the weighted mean PAIRITEL magnitudes of 2MASS stars as the error on the weighted mean, we follow the method reported by the CSP here and instead use the rms to estimate our local sequence uncertainties (C10; S11), which yield larger, more conservative error estimates.

Using the rms error for PAIRITEL measurements of 2MASS stars, we find zero-point offsets of

$$\begin{eqnarray}{J}_{\mathrm{CSP}}-{J}_{\mathrm{PTL}} & = & 0.018\pm 0.002\;\mathrm{mag},\\ {H}_{\mathrm{CSP}}-{H}_{\mathrm{PTL}} & = & 0.038\pm 0.003\;\mathrm{mag},\\ {{K}_{s}}_{\mathrm{CSP}}-{{K}_{s}}_{\mathrm{PTL}} & = & 0.077\pm 0.011\;\mathrm{mag}.\end{eqnarray} \tag{ 2 }$$

The ${{JHK}}_{s}$ CSP–PAIRITEL zero-point offsets from Equation (2) are also shown in Figure 8 and agree with those from C10 in Equation (1) to within 2σ in J and 1σ in H. While C10 used ∼3–4 times as many 2MASS stars, Equation (1) technically estimates the offsets between CSP and 2MASS, not the offsets between CSP and PAIRITEL given by Equation (2). Since we are most interested in the latter, and since we do not consider the slight differences between Equations (1) and (2) to be significant, we simply use our own offsets from Equation (2) as needed. We do not consider the zero-point offset for K_s in Equation (2) to be reliable, since it is based on only 24 2MASS stars measured by both groups.

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4.3.3. CSP–PAIRITEL Color Terms

Considering only 2MASS stars in the color range $0.2\lt {(J-H)}_{\mathrm{CSP}}\lt 0.7$ mag, C10 obtained the following linear fits for the JH bands:

$$\begin{eqnarray}{J}_{\mathrm{CSP}}-{J}_{2{\rm{M}}} & = & (-0.045\pm 0.008)\times {(J-H)}_{\mathrm{CSP}},\\ & & +(0.035\pm 0.067)\;\mathrm{mag},\\ {H}_{\mathrm{CSP}}-{H}_{2{\rm{M}}} & = & (0.005\pm 0.006)\times {(J-H)}_{\mathrm{CSP}}\\ & & +(0.038\pm 0.080)\;\mathrm{mag}.\end{eqnarray} \tag{ 3 }$$

C10 thus find some evidence for a small color term slope in J, a negligible color term in H, and do not attempt to derive any color terms involving K_s.

Following C10, we test for linear color terms between CSP and PAIRITEL filters using 263 2MASS stars with both J- and H-band data. We use the Carpenter (2001) color terms for K_s.³¹ We find the following JH linear color term fits using the rms error for the PAIRITEL uncertainties of 2MASS stars (also see Figure 9):

$$\begin{eqnarray}{J}_{\mathrm{CSP}}-{J}_{\mathrm{PTL}} & = & (-0.014\pm 0.017)\times {(J-H)}_{\mathrm{CSP}}\\ & & +(0.025\pm 0.009)\;\mathrm{mag},\\ {H}_{\mathrm{CSP}}-{H}_{\mathrm{PTL}} & = & (0.042\pm 0.022)\times {(J-H)}_{\mathrm{CSP}}\\ & & +(0.020\pm 0.011)\;\mathrm{mag}.\end{eqnarray} \tag{ 4 }$$

Linear color term fits yield ${\chi }_{\nu }^{2}\lt 1$, indicating that while the fits are good, the errors are slightly overestimated by using the rms. For all panels in Figure 9, the probability that a correct model would give the observed ${\chi }_{\nu }^{2}$ is ∼1. JH color term fits from Equation (4) and from C10 in Equation (3) agree in the slopes at 2σ and the intercepts at 1σ. Both fits also yield the same signs for the slopes and indicate at most small JH color terms.

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Again, although the C10 fits used ∼3–4 times as many 2MASS stars, we consider the color terms from either Equation (3) or (4) to be equally reliable. For SN LCs with sufficient sampling to compute reliable colors, applying either set of color terms produced comparable results, since both color terms are small. In summary, either set of color terms (or no color terms) are reasonable choices to approximately put CSP data on the PAIRITEL/2MASS system. Still, to compare CSP and CfAIR2 data on the same footing, for the analysis in Section 4.4, we apply our own JH color terms from Equation (4) and K_s color terms from Carpenter (2001) as needed.

Because CfAIR2 and CSP observations were generally performed at slightly different phases, it is usually not possible to compute direct LC data differences. We thus require a smooth model fit to interpolate from to compute residuals, which we apply to all 18 overlap objects.³² The purpose of these model fits is not to estimate LC shape parameters, but merely to provide a baseline with which to compute residuals. Figures 10–12 overplot all 18 example CfAIR2 and CSP SN Ia LCs for comparison. Applying either set of color terms from Section 4.3.3 (or no color terms) had a negligible effect on the CSP LCs, model fits, and weighted mean residuals for the CSP-CfAIR2 data in Table 7.

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For all CfAIR2 and color-term-corrected CSP LC points at similar phases, the scatter in the residuals arises from both statistical photometric uncertainties and systematic uncertainties as a result of imperfect model fits, which can dominate, especially at late times. For individual SN Ia, we compute the weighted mean of the residuals about the joint model fit in the phase range [−10, 60] days where the model fit is generally valid. To include systematic uncertainty from the joint model fit, we conservatively estimated the 1σ uncertainty on the weighted mean CSP–CfAIR2 residual as the error-weighted standard deviation of the residuals, which we then divided by a factor of 3 to avoid overestimating the uncertainty. We then compute whether the mean CSP–CfAIR2 residuals are consistent with zero to within 1, 2 or 3σ in the selected phase range. We find that nearly all CfAIR2 and color-term-corrected CSP SN Ia LCs (18 JH and 8 K_s LCs) are consistent to within 3σ by this metric.³³ See Figures 10–12 and Table 7.

While this method is useful to compare entire LCs, we note that some CSP and CfAIR2 LCs in specific bands do show significant ∼0.1–0.4 mag deviations for individual data points at similar phases or ranges of data points over smaller phase ranges, beyond what can be explained from poor model fits alone. For example, these discrepancies were noted: SN 2005iq, H, <0 days; SN 2005na, H, 20–40 days; SN 2007if, JH, 20–30 days; SN 2008hv, J, >40 days; SN 2006D, H, >40 days; SN 2005el, JH, >40 days; SN 2007 sr, H, 10–20 days. Nevertheless, many of these differences come from ∼1–2, individual outlier CfAIR2 data points, and most of the LCs show broad agreement by the above metric across a broad range of phases. See Figures 10–12.

We can also test whether CfAIR2 and CSP are consistent for the entire overlap sample, rather than just individual objects. Figure 13 shows aggregated residuals in the phase range [−15,100] days after applying color terms from Equation (4) to the CSP data. Using 433, 390, and 218 CfAIR2 LC points, and 275, 257, and 42 CSP LC points, each in ${{JHK}}_{s}$, respectively, we find that the global weighted mean of the aggregated residuals is consistent with zero in each case (see Figure 13). Applying color terms from C10 (or no color terms) did not affect the results. We conclude that both for individual LCs and for the global aggregated sample, PAIRITEL CfAIR2 photometry and CSP photometry show satisfactory overall agreement.

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