Type Ia Supernovae are Excellent Standard Candles in the Near-Infrared

TL;DR

This study demonstrates that Type Ia supernovae observed in the near-infrared serve as highly precise standard candles, offering a promising method to improve cosmic distance measurements and constrain dark energy.

Contribution

We develop a hierarchical Bayesian model for constructing NIR light curve templates and show that NIR observations yield smaller distance uncertainties than optical methods.

Findings

NIR-only Hubble diagram RMS of 0.117 mag using GP method.

NIR light curves at maximum light provide smaller distance RMS than optical methods.

NIR observations reduce systematic errors in measuring the universe's expansion.

Abstract

We analyze a set of 89 Type Ia supernovae (SN Ia) that have both optical and near-infrared (NIR) photometry to derive distances and construct low redshift ($z < 0.04$) Hubble diagrams. We construct mean light curve (LC) templates using a hierarchical Bayesian model. We explore both Gaussian process (GP) and template methods for fitting the LCs and estimating distances, while including peculiar velocity and photometric uncertainties. For the 56 SN Ia with both optical and NIR observations near maximum light, the GP method yields a NIR-only Hubble-diagram with a RMS of $0.117 \pm 0.014$ mag when referenced to the NIR maxima. For each NIR band, a comparable GP method RMS is obtained when referencing to NIR-max or B-max. Using NIR LC templates referenced to B-max yields a larger RMS value of $0.138 \pm 0.014$ mag. Fitting the corresponding optical data using standard LC fitters that use LC shape and color corrections yields larger RMS values of $0.179 \pm 0.018$ mag with SALT2 and $0.174 \pm 0.021$ mag with SNooPy. Applying our GP method to subsets of SN Ia NIR LCs at NIR maximum light, even without corrections for LC shape, color, or host-galaxy dust reddening, provides smaller RMS in the inferred distances, at the $\sim 2.3 - 4.1\sigma$ level, than standard optical methods that do correct for those effects. Our ongoing RAISIN program on the Hubble Space Telescope will exploit this promising infrared approach to limit systematic errors when measuring the expansion history of the universe to constrain dark energy.

Tables

Table 1. Table 1: Data cuts

Cuts	# SN Ia after cuts
Initial sample	177
	138
	122
	122
	111
Remove duplicates	100
Normal spectrum	95
$\ge$ 3 LC points	89
Reduction of the initial sample based on data cuts

Table 2. Table 2: SN Ia Light Curve Parameters

SN name	$z_{\left(\mathrm{helio}\right)}^a$	$z_{\mathrm{CMB}}^b$	${\sigma }_{\mathrm{pec}}^c$	LC Data	$t_{B\max }^e$	$\Delta m_{15}{\left(B\right)}^f$	$E{\left(B-V\right)}_{\mathrm{host}}^g$	$E{\left(B-V\right)}_{\mathrm{MW}}^h$
			(mag)	Sourced	(MJD days)	(mag)	(mag)	(mag)

Table 3. Table 6: Mean Y ​ J ​ H ​ K s 𝑌 𝐽 𝐻 subscript 𝐾 𝑠 YJHK_{s} absolute magnitudes at t B ​ max subscript 𝑡 𝐵 max t_{B{\rm max}} or t NIR subscript 𝑡 NIR t_{\rm NIR} max.

Band	$N_{\mathrm{SN}}$	$⟨M⟩$	Std. deviation
		(mag)	(mag)
Template method
$Y$	44	$-18.12$	$0.15$
$J$	87	$-18.34$	$0.17$
$H$	81	$-18.18$	$0.17$
$K_s$	32	$-18.35$	$0.21$
Gaussian-process method at NIR max
$Y$	29	$-18.39$	$0.11$
$J$	52	$-18.52$	$0.14$
$H$	44	$-18.30$	$0.11$
$K_s$	14	$-18.37$	$0.18$
Gaussian-process method at $B$ max
$Y$	29	$-18.16$	$0.12$
$J$	52	$-18.34$	$0.15$
$H$	44	$-18.19$	$0.12$
$K_s$	14	$-18.28$	$0.17$

Table 4. Table 7: Hubble Residual Intrinsic Scatter, σ int subscript 𝜎 int \sigma_{\rm int} , and RMS.

Band	Method	$N_{\mathrm{SN}}$	${\sigma }_{\mathrm{int}}$ [mag]	${\sigma }_{\mathrm{int}}$ [mag]	wRMS [mag]	RMS [mag]
			(${\sigma }_{\mathrm{pec}}=150$ km/s)	(${\sigma }_{\mathrm{pec}}=250$ km/s)	(${\sigma }_{\mathrm{pec}}=150$ km/s)
Optical $BVR$	SALT2	56	$0.133\pm 0.022$	$0.107\pm 0.025$	$0.174\pm 0.020$	$0.179\pm 0.018$
Optical $BVR$	SNooPy	56	$0.128\pm 0.018$	$0.111\pm 0.020$	$0.159\pm 0.019$	$0.174\pm 0.021$
any $YJH{K}_s$	Template	56	$0.112\pm 0.016$	$0.096\pm 0.019$	$0.140\pm 0.016$	$0.138\pm 0.014$
any $YJH{K}_s$	GP (NIR max)	56	$0.047\pm 0.018$	$0.000\pm {0.000}^{\ast }$	$0.100\pm 0.013$	$0.117\pm 0.014$
any $YJH{K}_s$	GP ($B$ max)	56	$0.066\pm 0.016$	$0.044\pm 0.023$	$0.106\pm 0.010$	$0.115\pm 0.011$

Table 5. Table 15: Values of the GP hyperparameters

band	$l$	${\sigma }_K$
$Y$	7.90	0.70
$J$	7.02	0.95
$H$	9.81	0.75
$K_s$	8.19	0.55

Equations

$$\mu_{\rm eff}=5\log_{10}\Big{(}\frac{H_{0}^{\prime}}{H_{0}}\Big{)}+\mu^{\prime}$$

$$v_{\mathrm{eff}}=c{z}_{\mathrm{eff}}$$

$$\sigma_{v_{\rm eff}}=c\ \sigma_{z_{\rm eff}}=c\ z_{\rm eff}\Big{(}\frac{\ln 10}{5}\sigma_{\mu_{\rm eff}}\Big{)}$$

$$M_s(t)=m_s(t)-{\mu }_{\Lambda \mathrm{CDM}}(z_s)-K_{OQ}^s-A_O^s,$$

$$\mu_{\Lambda{\rm CDM}}(z_{s})=5\log_{10}\Bigg{[}\frac{d_{L}(z_{s})}{1\text{Mpc}}\Bigg{]}+25$$

$$d_{L}(z)=\Big{(}\frac{c}{H_{0}}\Big{)}(1+z)\int_{0}^{z}\frac{dz}{E(z)}$$

$${\sigma }_M^2={\sigma }_m^2+{\sigma }_{{\mu }_{\mathrm{pec}}}^2+{\sigma }_A^2+{\sigma }_{\mathrm{Kcorr}}^2,$$

$${\sigma }_{{\mu }_{\mathrm{pec}},s}^2(z_s)={\left(\frac{5}{z_s\ln (10)}\right)}^2\left[{\left(\frac{{\sigma }_{\mathrm{pec}}}{c}\right)}^2+{\sigma }_{z,s}^2\right].$$

$$\mathbf{L}\equiv {\mathcal{M}}^{\ast }-{\mathcal{M}}_{0}1$$

$${\mu }_s^{\mathrm{L}}\sim \mathcal{N}({\eta }_s,{\sigma }_{\eta ,s}^2)$$

$$p\left(\{{\eta }_s\}|\theta ,{\sigma }_{\theta }^2\right)=\prod _{s=1}^{N_{\mathrm{T}}^{\ast }}\mathcal{N}\left({\eta }_s|\theta ,{\sigma }_{\theta }^2\right)$$

$$\Delta m_s(t)\equiv m_s(t)-\theta (t)-m_{0,s}$$

$$\Delta {\mathbf{m}}_s\equiv \left(\begin{array}{c}\Delta m_s(t_1)\\ \Delta m_s(t_2)\\ ⋮\\ \Delta m_s(t_n)\end{array}\right).$$

$$-2\ln \mathcal{L}(m_{0,s})=\Delta {\mathbf{m}}_s^{\top }\cdot {\mathbf{C}}^{-1}\cdot \Delta {\mathbf{m}}_s+\mathrm{constant},$$

$$C_{ij}\equiv$$

$$=$$

$${\hat{\sigma }}_{m,s}^2(t_i){\delta }_{ij},$$

$$\hat{m}_{0,s}=\left[\sum^{n}_{i,j}(C^{-1})_{ij}\right]^{-1}\times\\ \sum^{n}_{i}\left[\Bigl{(}m_{s}(t_{i})-\theta(t_{i})\Bigr{)}\sum^{n}_{j}(C^{-1})_{ij}\right],$$

$${\hat{\sigma }}_{\mathrm{fit},s}={\left[\sum _{i,j}^n(C^{-1}{)}_{ij}\right]}^{-1/2},$$

$${\hat{\mu }}_s={\hat{m}}_{0,s}-⟨M_0⟩.$$

$${\hat{\sigma }}_{\mu ,s}^2={\hat{\sigma }}_{\mathrm{fit},s}^2+{\hat{\sigma }}_{\mathrm{int}}^2.$$

$$\Delta {\mu }_s\equiv {\hat{\mu }}_s-{\mu }_{\Lambda \mathrm{CDM}}(z_s).$$

$${\sigma }_{\Delta ,s}^2={\hat{\sigma }}_{\mathrm{fit},s}^2+{\hat{\sigma }}_{\mathrm{int}}^2+{\sigma }_{{\mu }_{\mathrm{pec}},s}^2.$$

$${\hat{\mu }}_s={\hat{m}}_{\max ,s}-⟨M_{\max }⟩$$

$$\delta {\mathbf{\mu }}_s\equiv \left(\begin{array}{c}{\hat{\mu }}_s^Y-{\mu }_s\\ {\hat{\mu }}_s^J-{\mu }_s\\ {\hat{\mu }}_s^H-{\mu }_s\\ {\hat{\mu }}_s^K-{\mu }_s\end{array}\right).$$

$$-2\ln \mathcal{L}({\mu }_s)=\delta {\mathbf{\mu }}_s^{\top }\cdot C_{\mu }^{-1}\cdot \delta {\mathbf{\mu }}_s+\mathrm{constant},$$

$${\hat{\mu }}_s=\sum _b{w}_b{\hat{\mu }}_s^b$$

$$w_b=\left[\sum _{b^{\prime }}(C^{-1}{)}_{b{b}^{\prime }}\right]\times {\left[\sum _{b^{\prime },b^{\prime \prime }}(C^{-1}{)}_{b^{\prime }{b}^{\prime \prime }}\right]}^{-1}.$$

$${\hat{\sigma }}_{\mathrm{fit},s}=\sqrt{\sum _b{w}_b^2{\hat{\sigma }}_{s,b}^2}$$

$${\mu }_s=m_{B,s}-M_B+\alpha x_{1,s}-\beta c_s,$$

$${\sigma }_{\mu ,s}^2={\sigma }_{\mathrm{fit},s}^2+{\sigma }_{\mathrm{int}}^2.$$

Full text

distance scale – supernovae: cosmology, general, infrared observations, optical observations, photometry

††journal: ApJ

1 Introduction

The increasing sample of high quality, low-redshift (low-$z$), near-infrared (NIR) light curves (LCs) of Type Ia supernovae (SN Ia) provides an opportunity to further investigate their utility as cosmological standard candles. Optical samples of SN Ia are large enough now that systematic uncertainties are major limitation to accurate cosmological constraints. Infrared observations of SN Ia can help in that essential way because supernovae are more nearly standard candles in the NIR and the effects of dust are diminished. This paper explores ways to use NIR observations of SN Ia to measure distances. This investigation is for a low-$z$ sample, but we are working to extend this technique to cosmologically-interesting distances with the Hubble Space Telescope (HST).

Before NIR photometry became practical for large samples of SN Ia, photometry and spectroscopy of SN Ia at optical wavelengths enabled the unexpected 1998 discovery of cosmic acceleration (Riess et al. 1998; Schmidt et al. 1998; Perlmutter et al. 1999). Since then, a suite of independent cosmological methods has confirmed the SN Ia results (see Frieman et al. 2008; Weinberg et al. 2013 for reviews). The prevailing view is that the mechanism behind cosmic acceleration is some form of dark energy. The constraints on cosmological parameters from the SN Ia Pantheon sample (Scolnic et al. 2018) combined with the Planck 2015/2018 Cosmic Microwave Background data (Planck Collaboration et al. 2016b, 2018), as well as Baryon Acoustic Oscillations (Alam et al. 2017) and local Hubble constant measurements (Riess et al. 2016, 2018c, 2018b, 2018a) are consistent with this view. Among the major cosmological techniques, SN Ia provide precise measurements of extragalactic distances and the most direct evidence for cosmic acceleration (see Goobar & Leibundgut 2011; Kirshner 2013; Goobar 2015; Davis & Parkinson 2016; Riess et al. 2018c for reviews).

Optical SN Ia LCs are known to be excellent standardizable candles that exploit correlations between intrinsic luminosity and LC shape and color (Phillips 1993; Phillips et al. 1999; Hamuy et al. 1996; Riess et al. 1996, 1998; Perlmutter et al. 1997; Goldhaber et al. 2001; Tonry et al. 2003; Wang et al. 2003; Prieto et al. 2006; Jha et al. 2006, 2007; Astier et al. 2006; Takanashi et al. 2008; Conley et al. 2008; Mandel et al. 2009; Guy et al. 2005, 2007, 2010; Mandel et al. 2011, 2017). Recent work has demonstrated that SN Ia in the NIR are more nearly standard candles, even before correction for LC shape or host galaxy dust reddening (e.g. Krisciunas et al. 2004a; Wood-Vasey et al. 2008; Mandel et al. 2009; Krisciunas et al. 2009; Friedman 2012; Kattner et al. 2012). NIR LCs are $\sim$5–11 times less sensitive to dust extinction than optical $B$-band data (Cardelli et al. 1989). When constructing SN Ia Hubble diagrams using NIR data, the distance errors produced by extinction are small: ignoring dust would be fatal for optical studies, but nearly not as serious for NIR studies like Wood-Vasey et al. 2008 or the present work. An improved approach would use optical and infrared data simultaneously to determine the extinction (Mandel et al. 2011).

Optical-only samples yield typical Hubble diagram intrinsic scatter of $\sigma_{\rm int}\sim 0.12$ mag and a RMS of 0.141 mag after applying light-curve shape, host-galaxy dust, and host-galaxy mass corrections, assuming a peculiar-velocity uncertainty of 250 km s*-1* (e.g. Scolnic et al. 2018). For simplicity, we adopt a conservative peculiar-velocity uncertainty for the host galaxies in our sample of 150 km s*-1*. If the typical redshifts in the sample were large enough, this would be of no consequence, but for our nearby sample, the inferred intrinsic scatter of the supernova luminosities depends on the value we choose. As a result, though we have confidence when comparing the RMS and intrinsic scatter for various subsamples containing the same SN with both optical and infrared data, the real value of the scatter should be determined from observations that are securely in the Hubble flow beyond 10,000 km s*-1*.

When including a peculiar-velocity uncertainty of 150 km s*-1*, our best method yields intrinsic scatters as small as $\sim 0.03$-$0.11$ mag, depending on the NIR filter subset, and a RMS of $\sim 0.087\pm 0.013$ mag for the best NIR $YJH$-band subset, confirming and strengthening previous results for NIR methods (Meikle 2000; Krisciunas et al. 2004a, 2005, 2007; Folatelli et al. 2010; Burns et al. 2011; Wood-Vasey et al. 2008; Mandel et al. 2009, 2011; Kattner et al. 2012; Dhawan et al. 2015). Assuming a larger peculiar-velocity uncertainty, such as 250 km s*-1*, makes our estimated intrinsic scatter even smaller. In addition, our best NIR method using any of the $YJHK_{s}$ bands yields an RMS of only $0.117\pm 0.014$ mag, compared to $0.179\pm 0.018$ mag and $0.174\pm 0.021$ mag for SALT2 and SNooPy fits to optical $BVR$ data for the same 56 SN Ia, respectively. While using LC shape, color, and host galaxy dust corrections would likely lead to improvements, the simpler approaches in this paper are still remarkably effective.

Overall, a substantial body of evidence indicates that rest-frame LCs of SN Ia in NIR are both better standard candles than at optical wavelengths and less sensitive to the confounding effects of dust. When NIR data are combined with $UBVRI$ photometry, this yields accurate and precise distance estimates (Krisciunas et al. 2004b, 2007; Wood-Vasey et al. 2008; Folatelli et al. 2010; Burns et al. 2011; Friedman 2012; Phillips 2012; Kattner et al. 2012; Burns et al. 2014; Mandel et al. 2009, 2011, 2014, 2017).

This is significant for supernova cosmology because, along with photometric-calibration uncertainties (Scolnic et al. 2015; Foley et al. 2018), uncertain dust extinction estimates and the intrinsic variability of SN Ia colors present challenging and important systematic problems for dark energy measurements (Wang et al. 2006; Jha et al. 2007; Wood-Vasey et al. 2007; Hicken et al. 2009a; Kessler et al. 2009; Guy et al. 2007, 2010; Conley et al. 2007, 2011; Komatsu et al. 2011; Campbell et al. 2013; Rest et al. 2013; Scolnic et al. 2013; Narayan 2013; Betoule et al. 2014; Rest et al. 2014; Mosher et al. 2014; Scolnic et al. 2014b, a, 2015; Narayan et al. 2016; Scolnic et al. 2017; Mandel et al. 2017; Foley et al. 2018; Scolnic et al. 2018; Brout et al. 2018a; Kessler et al. 2018). Combining optical and NIR LCs promises to reduce these systematic distance uncertainties (Folatelli et al. 2010; Burns et al. 2011; Kattner et al. 2012; Mandel et al. 2011, 2014).

This work is organized as follows. In §2, we review previous results with SN Ia in NIR, detail our analysis selection criteria, and discuss host galaxy redshifts. In §3, we outline our Gaussian process (GP) procedure to fit LCs and our hierarchical Bayesian model to construct mean $YJHK_{s}$ LC templates. In §4, we use these templates and GP fits to individual LCs to construct Hubble diagrams in each NIR band, as well as a combined $YJHK_{s}$ NIR Hubble diagram. We compare this to optical $BVR$ Hubble diagrams for the very same set of 56 supernovae that use the SALT2 and SNooPy LC fitters. We end with §5 by documenting how, even without correcting for LC shape or dust, SN Ia in the NIR using our GP fits at NIR maximum are better standard candles than optical SN Ia observations corrected for these effects. Mathematical details of the Gaussian process, the hierarchical Bayesian model, and the method for determining the intrinsic scatter are presented in the Appendices.

2 SN Ia in NIR as Standard Candles

Pioneering studies by Meikle (2000) and Krisciunas et al. (2004a) demonstrated that SN Ia have smaller luminosity variation in the NIR $JHK_{s}$ bands than in the optical $BV$ bands at the time of $B$-band maximum light ($t_{\rm Bmax}$). Krisciunas et al. (2004a) found that optical LC shape and intrinsic NIR luminosity were uncorrelated in a sample of 16 SN Ia, while measuring a NIR absolute magnitude scatter of $\sigma_{J}=0.14$, $\sigma_{H}=0.18$, and $\sigma_{K_{s}}=0.12$ mag. Following this, Wood-Vasey et al. (2008) used a homogeneously-observed sample of 18 spectroscopically-normal SN Ia in the $JHK_{s}$ bands, with intrinsic root-mean-square (RMS) absolute magnitudes of $0.15$ mag in the $H$-band, without applying any reddening or LC shape corrections. By combining these 18 objects with 23 SN Ia from the literature, the sample in Wood-Vasey et al. (2008) yielded an $H$-band RMS of $0.16$ mag, strengthening the evidence that normal SN Ia are excellent NIR standard candles. In the present work, we show that SN Ia in NIR yield a narrow distribution of $YJHK_{s}$ peak magnitudes with RMS Hubble Diagram scatter as small as $0.087\pm 0.013$ mag for the combined $YJH$ bands and as large as $0.179\pm 0.029$ mag for the $K_{s}$ band, consistent with previous results.

Following Wood-Vasey et al. 2008, Mandel et al. 2009 developed a new hierarchical Bayesian model (BayeSN) and a template model to account for $J$-band LC shape variation to the existing SN Ia in NIR sample, finding a marginal scatter in the peak absolute magnitudes of $0.17$, $0.11$, and $0.19$ mag, in $JHK_{s}$, respectively, while finding that $J$-band LC shape does correlate with NIR intrinsic luminosity. Subsequent work by Folatelli et al. 2010 applied a different LC shape correction method, but found scatters of $0.12$–$0.16$ mag in $YJHK_{s}$, consistent with the results of Mandel et al. (2009).

Additional work by Kattner et al. (2012) found an absolute magnitude scatter of $0.12$, $0.12$, and $0.09$ mag in $YJH$, respectively, by analyzing a subset of 13 well-sampled normal NIR SN Ia LCs with relatively little host galaxy dust extinction. Kattner et al. 2012 also showed evidence for a correlation between the $JH$-band absolute magnitudes at $t_{\rm Bmax}$ and, $\Delta m_{15}(B)$, the light-curve decline rate parameter in $B$-band after 15 days of $t_{\rm Bmax}$ (Phillips 1993), with no evidence for strong correlation in the $Y$-band. This is also consistent with the results of Mandel et al. 2009, who found that $J$-band LC shape and luminosity are correlated.

Using a small data set of 12 SN Ia $JH$-band LCs, each with only $3$-$5$ data points, Barone-Nugent et al. 2012, 2013 find a scatter of $0.116$ mag and $0.085$ mag in the $J$ and $H$-bands, respectively. In the first data release of the SweetSpot survey, Weyant et al. 2014 present a similarly small sample of 13 low-$z$ SN Ia, each with $1$-$3$ LC points, finding an $H$-band scatter of $0.164$ mag. This was followed by a second SweetSpot data release, which included a total of 33 SN Ia with 168 $JHK_{s}$ observations in the redshift range $0.02<z<0.09$, well into the smooth Hubble flow, but which did not yet include NIR Hubble diagrams (Weyant et al. 2018).

By analyzing 45 NIR LCs with data near NIR-maximum, Stanishev et al. 2018 find an intrinsic Hubble diagram scatter of $\sim 0.10$ mag, after accounting for potential new correlations between light curve shape, color excess, and $J-H$ color at NIR-max. Stanishev et al. 2018 also present single-epoch $JH$ photometry for 16 new SN Ia with $z>0.037$. The Carnegie Supernova Project (CSP) final data release (CSP-I; Krisciunas et al. 2017), was recently analyzed in Burns et al. (2018), which found peculiar velocity corrected Hubble diagram dispersions of $\sim 0.08-0.15$ mag, depending on the subset of the 120 SN Ia they considered. Additional CSP-II photometric data, to be published in 2019, was recently described in Phillips et al. 2019. Hsiao et al. (2019) present an overview of the NIR SN Ia spectroscopy obtained by the CSP and the Center for Astrophysics (CfA) Supernova Group.

While the current sample of optical SN Ia LCs exceeds 1000 (Scolnic et al. 2018), and will be increased by orders of magnitude by ongoing and future surveys including the Dark Energy Survey (DES; DES Collaboration et al. 2018a, b; Brout et al. 2018b; D’Andrea et al. 2018), the Zwicky Transient Facility (ZTF; Smith et al. 2014), and the Large Synoptic Survey Telescope (LSST; Ivezic et al. 2008; Zhan & Tyson 2017), the number of normal SN Ia with published NIR LCs is still less than $250$. Nevertheless, the NIR sample has the potential to improve systematics compared to optical-only SN Ia cosmology samples, which are already systematics limited (Scolnic et al. 2018).

Overall, the growing sample of photometric data suggests that NIR observations of SN Ia present a promising path to standardize SN Ia for distance estimates (Dhawan et al. 2015; Shariff et al. 2016; Burns et al. 2018; Stanishev et al. 2018), Hubble constant estimates (Cartier et al. 2014; Efstathiou 2014; Riess et al. 2016; Cardona et al. 2017; Dhawan et al. 2018; Burns et al. 2018), and eventually, cosmological parameter estimates, when the nearby and high-$z$ samples are combined as in the HST RAISIN program (RAISIN: *Tracers of cosmic expansion with SN IA in the *IR, PI. R. Kirshner, HST GO-13046, GO-14216).

2.1 Nearby SN Ia in NIR Sample and Data Cuts

This work analyzes a suitable subset including 89 objects from the current sample of low-redshift photometric data for SN Ia NIR $YJHK_{s}$-band LCs including data releases 1 and 2 from the Carnegie Supernova Project (Schweizer et al. 2008; Contreras et al. 2010; Stritzinger et al. 2010, 2011; Taddia et al. 2012), now superseded by CSP data release 3 (Krisciunas et al. 2017), the CfA (Wood-Vasey et al. 2008; Friedman 2012; Friedman et al. 2015), and other groups (e.g. Krisciunas et al. 2000, 2004b, 2004c, 2005, 2007). We limit our analysis to spectroscopically normal SN Ia from Table 3 of Friedman et al. 2015, plus the definitive version of the CSP-I DR3 sample of low-$z$ SN Ia (Krisciunas et al. 2017), and other groups. Additional CSP-II photometric data, to be published in 2019, was recently described in Phillips et al. 2019 and will be analyzed in future work. We apply the following data cuts to analyze a subset of 89 SN Ia with NIR data. Table 1 shows how the initial sample of 177 SN Ia decreases after applying the different cuts, and Table 2.1 lists the general properties of the remaining 89 SN Ia. We determine $\Delta m_{15}(B)$ and $E(B-V)_{\rm host}$ with SNooPy.

• •

Optical light curve shape parameter $0.8<\Delta m_{15}(B)<1.6$, to consider normal SN Ia only (Hicken et al. 2009b). Objects must have accompanying $B$-band optical data to measure $\Delta m_{15}(B)$.

• •

Host galaxy reddening: $-0.15<E(B-V)_{\rm host}<0.4$. This cut is inspired by the standard SALT2 cut in color, $-0.3<c<0.3$, in optical-only analysis (Betoule et al. 2014; Scolnic et al. 2018) but with a less stringent cut considering that SN Ia in the NIR are less sensitive to dust.

• •

One advantage of the relative NIR insensitivity to dust reddening is that it also allows us to set a large threshold for Milky Way color excess: $E(B-V)_{\rm MW}<1$ mag, to exclude highly reddened SN Ia. All 177 SN Ia in the sample passed this cut. SN2006lf with $E(B-V)_{\rm MW}=0.8135$ mag has the largest color excess in the initial sample.

• •

Redshift range: $z<0.04$. The maximum redshift cut limits the effects of Malmquist bias. Section 2.2 describes corrections to deal with SN Ia at $z<0.01$, that suffer from peculiar velocity bias.

• •

Duplicates: For a given supernova observed by multiple surveys, we use the CSP data (Krisciunas et al. 2017), which typically has smaller photometric uncertainties than the CfA PAIRITEL data (Friedman et al. 2015).

• •

We include only spectroscopically normal SN Ia as identified by the Supernova Identification Code (SNID) Blondin & Tonry (2007).

• •

At least 3 photometric points in a given band for each SN Ia LC. A large fraction of the NIR data from Barone-Nugent et al. (2012), Stanishev et al. (2018), and the SweetSPOT survey with WIYN (Weyant et al. 2014, 2018) did not meet this criterion, so we chose not to analyze these data in this work.