A 2.4% DETERMINATION OF THE LOCAL VALUE OF THE HUBBLE CONSTANT^*

Considerable progress in the local determination of H₀ has been made in the last 25 years, assisted by observations of water masers, strong-lensing systems, supernovae (SNe), the Cepheid period–luminosity (P–L) relation (also known as the Leavitt law; Leavitt & Pickering 1912), and other sources used independently or in concert to construct distance ladders (see Freedman & Madore 2010; Livio & Riess 2013, for recent reviews).

A leading approach utilizes Hubble Space Telescope (HST) observations of Cepheids in the hosts of recent, nearby SNe Ia to link geometric distance measurements to other SNe Ia in the expanding universe. The SN Ia HST Calibration Program (Sandage et al. 2006) and the HST Key Project (Freedman et al. 2001) both made use of HST observations with WFPC2 to resolve Cepheids in SN Ia hosts. However, the useful range of that camera for measuring Cepheids, ≲25 Mpc, placed severe limits on the number and choice of SNe Ia that could be used to calibrate their luminosity (e.g., SNe 1937C, 1960F, 1974G). A dominant systematic uncertainty resulted from the unreliability of those nearby SNe Ia which were photographically observed, highly reddened, spectroscopically abnormal, or discovered after peak brightness. Only two objects (SNe 1990N and 1981B) used by Freedman et al. (2001, 2012) and four by Sandage et al. (2006) (the above plus SN 1994ae and SN 1998aq) were free from these shortcomings, leaving a very small set of reliable calibrators relative to the many hundreds of similarly reliable SNe Ia observed in the Hubble flow. The resulting ladders were further limited by the need to calibrate WFPC2 at low flux levels to the ground-based systems used to measure Cepheids in a single anchor, the Large Magellanic Cloud (LMC). The use of LMC Cepheids introduces additional systematic uncertainties because of their shorter mean period (${\rm{\Delta }}\langle \mathrm{log}\,P\rangle$ ≈ 0.7 dex) and lower metallicity (${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})$ = −0.25 dex, Romaniello et al. 2008) than those found with HST in the large spiral galaxies that host nearby SNe Ia. Despite careful work, the estimates of H₀ by the two teams (each with 10% uncertainty) differed by 20%, owing in part to the aforementioned systematic errors.

More recently, the SH0ES (SNe, H₀, for the Equation of State of dark energy) team used a number of advancements to refine this approach to determining H₀. Upgrades to the instrumentation of HST doubled its useful range for resolving Cepheids (leading to an eight-fold improvement in volume and in the expected number of useful SN Ia hosts), first with the Advanced Camera for Surveys (ACS; Riess et al. 2005, 2009b) and later with the Wide Field Camera 3 (WFC3; Riess et al. 2011, hereafter R11) owing to the greater area, higher sensitivity, and smaller pixels of these cameras. WFC3 has other superior features for Cepheid reconnaissance, including a white-light filter (F350LP) that more than doubles the speed for discovering Cepheids and measuring their periods relative to the traditional F555W filter, and a 5 arcmin² near-infrared (NIR) detector that can be used to reduce the impact of differential extinction and metallicity differences across the Cepheid sample. A precise geometric distance to NGC 4258 measured to 3% using water masers (Humphreys et al. 2013, hereafter H13) has provided a new anchor galaxy whose Cepheids can be observed with the same instrument and filters as those in SN Ia hosts to effectively cancel the effect of photometric zeropoint uncertainties in this step along the distance ladder. Tied to the Hubble diagram of 240 SNe Ia (now >300 SNe Ia; Scolnic et al. 2015; Scolnic & Kessler 2016), the new ladder was used to initially determine H₀ with a total uncertainty of 4.7% (Riess et al. 2009a, hereafter R09). R11 subsequently improved this measurement to 3.3% by increasing to 8 the number of Cepheid distances to reliable SN Ia hosts, and formally including HST/FGS trigonometric parallaxes of 10 Milky Way (MW) Cepheids with distance D < 0.5 kpc and individual precision of 8% (Benedict et al. 2007). The evolution of the error budget in these measurements is shown in Figure 1.

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Here we present a broad set of improvements to the SH0ES team distance ladder including new NIR HST observations of Cepheids in 11 SN Ia hosts (bringing the total to 19), a refined computation of the distance to NGC 4258 from maser data, additional Cepheid parallax measurements, larger Cepheid samples in the anchor galaxies, and additional SNe Ia to constrain the Hubble flow. We present the new Cepheid data in Section 2 and in S. L. Hoffmann et al. (2016, in preparation; hereafter H16). Other improvements are described throughout Section 3, and a consideration of analysis variants and systematic uncertainties is given in Section 4. We end with a discussion in Section 5.

The procedure for identifying Cepheids from time-series optical data (see Table 1 and Figure 2) has been described extensively (Saha et al. 1996; Stetson 1996; Riess et al. 2005; Macri et al. 2006); details of the procedures followed for this sample are presented by H16, utilize the DAO suite of software tools for crowded-field PSF photometry, and are similar to those used previously by the SH0ES team. The complete sample of Cepheids discovered or reanalyzed by H16 in these galaxies (NGC 4258 and the 19 SN Ia hosts) at optical wavelengths contains 2062 variables above the periods for completeness across the instability strip (with limits estimated using the HST exposure-time calculators and empirical tests as described in that publication). There are 1566 such Cepheids in the 19 SN Ia hosts within the smaller WFC3-IR fields alone. The positions of the Cepheids within each target galaxy are shown in Figure 3. For hosts in which we used F350LP to identify Cepheid light curves, additional photometry was obtained over a few epochs in F555W and F814W. These data were phase-corrected to mean-light values using empirical relations based on light curves in both F555W and F350LP from Cepheids in NGC 5584. Figure 4 shows composite Cepheid light curves in F350LP/F555W for each galaxy. Despite limited sampling of the individual light curves, the composites clearly display the characteristic "saw-toothed" light curves of Population I fundamental-mode Cepheids, with a rise twice as fast as the decline and similar mean amplitudes across all hosts.

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For every host, optical data in F555W and F814W from WFC3 were uniformly calibrated using the latest reference files from STScI and aperture corrections derived from isolated stars in deep images to provide uniform flux measurements for all Cepheids. In a few cases, F555W and F814W data from ACS and WFC3 were used in concert with their well-defined cross-calibration to obtain photometry with a higher signal-to-noise ratio (S/N). The cross-calibration between these two cameras has been stable to <0.01 mag over their respective lifetimes.

As in R11, we calculated the positions of Cepheids in the WFC3 F160W images using a geometric transformation derived from the optical images using bright and isolated stars, with resulting mean position uncertainties for the variables <0.03 pix. We used the same scene-modeling approach to F160W NIR photometry developed in R09 and R11. The procedure is to build a model of the Cepheid and sources in its vicinity using the superposition of point-spread functions (PSFs). The position of the Cepheid is fixed at its predicted location to avoid measurement bias. We model and subtract a single PSF at that location and then produce a list of all unresolved sources within 50 pixels. A scene model is constructed with three parameters per source (x, y, and flux), one for the Cepheid (flux) and a local sky level in the absence of blending; the best-fit parameters are determined simultaneously using a Levenberg–Marquardt-based algorithm. Example NIR scene models for each of the 19 SN Ia hosts are shown in Figure 5.

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Care must be taken when measuring photometry of visible stellar sources in crowded regions as source blending can alter the statistics of the Cepheid background (Stetson 1987). Typically the mean flux of pixels in an annulus around the Cepheid is subtracted from the measured flux at the position of the Cepheid to produce unbiased photometry of the Cepheid. This mean background or sky would include unresolved sources and diffuse background. However, we can improve the precision of Cepheid photometry by correctly attributing some flux to the other sources in the scene, especially those visibly overlapping with the Cepheid. The consequence of differentiating the mean sky into individual source contributions plus a lower constant sky level is that the new sky level will underestimate the true mix of unresolved sources and diffuse background superimposed with the Cepheid flux (in sparse regions without blending, the original and new sky levels would approach the same value). This effect may usefully be called the sky bias or the photometric difference due to blending and is statistically easily rectified. To retrieve the unbiased Cepheid photometry from the result of the scene model we could either recalculate the Cepheid photometry using the original mean sky or correct the overestimate of Cepheid flux based on the measured photometry of artificial stars added to the scenes. The advantage of the artificial star approach is that the same analysis also produces an empirical error estimate and can provide an estimate of outlier frequency.

Following this approach, we measure the mean difference between input and recovered photometry of artificial Cepheids added to the local scenes in the F160W images and fit with the same algorithms. As in R09 and R11, we added and fitted 100 artificial stars, placed one at a time, at random positions within 5 arcsec of (but not coincident with) each Cepheid to measure and account for this difference. To avoid a bias in this procedure, we initially estimate the input flux for the artificial stars from the Cepheid period and an assumed P–L relation (iteratively determined), measure the difference caused by blending, refine the P–L relation, and iterate until convergence. Additionally, we use the offset in the predicted and measured location of the Cepheid, a visible consequence of blending, to select similarly affected artificial stars to customize the difference measurements for each Cepheid. The median difference for the Cepheids in all SN hosts hosts observed with HST is 0.18 mag, mostly due to red-giant blends, and it approaches zero for Cepheids in lower-density regions such as the outskirts of hosts. The Cepheid photometry presented in this paper already accounts for the sky bias. We also estimate the uncertainty in the Cepheid flux from the dispersion of the measured artificial-star photometry around the 2.7σ-clipped mean. The NIR Cepheid P–L relations for all hosts and anchors are shown in Figure 6.

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Likewise, in the optical images, we used as many as 200 measurements of randomly placed stars in the vicinity of each Cepheid in F555W and F814W images to measure and account for the photometric difference due to the process of estimating the sky in the presence of blending. Only 10 stars at a time were added to each simulated image to avoid increasing the stellar density. These tests show that similarly to the NIR measurements, uncertainty in the Cepheid background is the leading source of scatter in the observed P–L relations of the SN hosts. The mean dispersions at F555W and F814W, with values for each host listed in Table 2 in columns 6 and 7, are 0.19 and 0.17 mag, respectively. All SN hosts and NGC 4258 display some difference in their optical magnitudes due to blending, with mean values of 0.05 and 0.06 mag (bright) in F555W and F814W, respectively. The most crowded case (ΔV = 0.32 and ΔI = 0.26 mag) is NGC 4424, a galaxy whose Cepheids are located in a circumnuclear starburst region with prominent dust lanes. We tabulate the mean photometric differences due to blending for each host in Table 2, columns 2 and 3. However, the effect of blending largely cancels when determining the color F555W–F814W used to measure Cepheid distances via Equation (1) since the blending is highly correlated across these bands. Indeed, the estimated change in color across all hosts given in Table 2, column 4 has a mean of only 0.005 mag (blue) and a host-to-host scatter of 0.01 mag, implying no statistically significant difference from the initial measurement and thus we have not applied these to the optical magnitudes in Table 4. Even the additional scatter in the ${m}_{H}^{W}$ P–L relation owing to blending in the optical color measurement is a relatively minor contribution of 0.07 mag. The small correction due to blending in the optical bands does need to be accounted for when using a conventional optical Wesenheit magnitude, ${m}_{I}^{W}$ = F814W–R_I (F555W–F814W), because (unlike the color) the cancellation in ${m}_{I}^{W}$ is not complete. We find a small mean difference for ${m}_{I}^{W}$ in our SN hosts of 0.025 mag (bright) with a host-to-host dispersion in this quantity of 0.03 mag. If uncorrected, this would lead to a 1% underestimate of distances and an overestimate of H₀ for studies that rely exclusively on ${m}_{I}^{W}$. The more symmetric effect of blending on ${m}_{I}^{W}$ than ${m}_{H}^{W}$ magnitudes results from the mixture of blue blends (which make ${m}_{I}^{W}$ faint) and red blends (which make ${m}_{I}^{W}$ bright). These results are consistent with those found from simulations by Ferrarese et al. (2000), who drew similar conclusions. We will make use of these results for ${m}_{I}^{W}$ in Section 4.2. Although the net effect of blending for ${m}_{I}^{W}$ is typically small, the uncertainty it produces is the dominant source of dispersion with a mean of 0.36 mag for the SN hosts, similar in impact and scatter to what was found for ${m}_{H}^{W}$.

Table 2.  Artificial Cepheid Tests in Optical Images

Host	ΔV	ΔI	Δct	${\rm{\Delta }}{m}_{I}^{W}$	σ(V)	σ(I)	σct	$\sigma ({m}_{I}^{W})$
	(mmag)				(mag)
M101	6	3	1	−2	0.09	0.09	0.03	0.16
N1015	41	40	1	27	0.13	0.13	0.06	0.31
N1309	105	63	12	−1	0.35	0.26	0.10	0.48
N1365	15	19	0	7	0.13	0.13	0.06	0.29
N1448	31	24	1	6	0.14	0.13	0.06	0.29
N2442	141	109	8	23	0.24	0.21	0.10	0.48
N3021	106	134	0	75	0.23	0.22	0.09	0.46
N3370	69	55	5	26	0.23	0.19	0.07	0.37
N3447	34	23	4	−1	0.14	0.12	0.06	0.29
N3972	79	68	7	25	0.18	0.17	0.07	0.38
N3982	82	69	0	22	0.22	0.19	0.09	0.44
N4038	38	28	2	12	0.19	0.15	0.07	0.34
N4258I	5	7	−1	10	0.20	0.23	0.05	0.36
N4258O	−2	1	0	0	0.08	0.07	0.02	0.10
N4424	318	262	−2	111	0.31	0.28	0.11	0.58
N4536	12	16	−1	10	0.11	0.10	0.05	0.24
N4639	56	85	−5	89	0.21	0.22	0.09	0.51
N5584	26	23	2	7	0.15	0.13	0.05	0.26
N5917	54	51	−2	32	0.20	0.19	0.08	0.42
N7250	152	91	13	−1	0.24	0.20	0.08	0.42
U9391	36	42	−3	38	0.15	0.15	0.06	0.34

Note. Δ = median magnitude or color offset derived from tests; σ = dispersion around Δ; V stands for F555W; I stands for F814W; ct = R × (V − I), with R = 0.39 for R_V = 3.3 and the Fitzpatrick (1999) extinction law; ${m}_{I}^{W}$ is defined in the text.

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Although we quantify and propagate the individual measurement uncertainty for each Cepheid, we conservatively discard the lowest-quality measurements. As in R11, scene models of Cepheids were considered to be useful if our software reported a fitted magnitude for the source with an uncertainty <0.7 mag, a set of model residual pixels with root-mean square (rms) lower than 3σ from the other Cepheid scenes, and a measured difference from the artificial star analyses of <1.5 mag. In addition, we used a broad (1.2 mag) allowed range of F814W–F160W colors centered around the median for each host, similar to the V − I color selection common to optical studies (see H16), to remove any Cepheids strongly blended with redder or bluer stars of comparable brightness. As simulations in Section 4.1 show, most of these result from red giants but also occasionally from blue supergiants.

1028 of the 1566 Cepheids present in the F160W images of the SN Ia hosts with periods above their respective completeness limits yielded a good quality photometric measurement within the allowed color range. Excessive blending in the vicinity of a Cepheid in lower-resolution and lower-contrast NIR images was the leading cause for the failure to derive a useful measurement for the others. The number of Cepheids available at each step in the measurement process is given in Table 3.

Table 3.  Properties of NIR P–L Relations

Galaxy	Number			$\langle P\rangle$	ΔT	$\langle {\sigma }_{{\rm{tot}}}\rangle$	σPL
	FOV	Meas.	Fit	(days)	(days)
LMC	⋯	785	775	6.6	⋯	0.09	0.08
MW	⋯	15	15	8.5	⋯	0.21	0.12
M31	⋯	375	372	11.5	0	0.15	0.15
M101	355	272	251	17.0	0	0.30	0.32
N1015	27	14	14	59.8	100	0.32	0.36
N1309	64	45	44	55.2	0	0.35	0.36
N1365	73	38	32	33.6	12	0.32	0.32
N1448	85	60	54	30.9	54	0.30	0.36
N2442	285	143	141	32.5	68	0.52	0.38
N3021	36	18	18	32.8	0	0.42	0.51
N3370	86	65	63	42.1	0	0.33	0.33
N3447	120	86	80	34.5	59	0.28	0.34
N3972	71	43	42	31.5	38	0.49	0.38
N3982	22	16	16	40.6	0	0.30	0.32
N4038	28	13	13	63.4	0	0.43	0.33
N4258	228	141	139	18.8	0	0.40	0.36
N4424	8	4	3	28.9	33	0.56	⋯
N4536	47	35	33	36.5	0	0.27	0.29
N4639	35	26	25	40.4	0	0.36	0.45
N5584	128	85	83	42.6	11	0.32	0.33
N5917	21	14	13	39.8	100	0.39	0.38
N7250	39	22	22	31.3	60	0.44	0.43
U9391	36	29	28	42.2	100	0.34	0.43
Total SN	1566	1028	975	32.5	⋯	⋯	⋯
Total All	⋯	2358	2286	⋯	⋯	⋯	⋯

Note. FOV: located within the WFC3/IR field of view. Meas.: good quality measurement within allowed color range and with period above completeness limit. Fit: after global outlier rejection, see Section 4.1. $\langle P\rangle$: median period of the final NIR sample used in this analysis; ΔT = time interval between first and last NIR epochs; $\langle {\sigma }_{{\rm{tot}}}\rangle$ = median value of σ_tot (uncertainties) for Cepheids in each host (see text for definition); σ_PL = apparent dispersion of NIR P–L relation after outlier rejection.

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We now quantify the statistical uncertainties that apply to Cepheid-based distance estimates. As described in the previous section, the largest source of measurement uncertainty for ${m}_{H}^{W}$ (defined in Equation (1)) arises from fluctuations in the NIR sky background due to variations in blending, and it is measured from artificial star tests; we refer to this as σ_sky. For SN Ia hosts at 20–40 Mpc and for NGC 4258, the mean σ_sky for Cepheids in the NIR images is 0.28 mag, but it may be higher or lower depending on the local stellar density. The next term which may contribute uncertainty in Equation (1) is σ_ct = Rσ(V − I). While blending does not change the mean measured optical colors (discussed in Section 2.1), it does add a small amount of dispersion. The artificial star tests in the optical data yield a mean value for σ_ct of 0.07 mag across all hosts, with values for each host given in Table 2, column 8). There is also an intrinsic dispersion, σ_int, resulting from the nonzero temperature width of the Cepheid instability strip. It can be determined empirically using nearby Cepheid samples which have negligible background errors. We find σ_int = 0.08 mag for ${m}_{H}^{W}$ (0.12 mag for ${m}_{I}^{W}$) using the LMC Cepheids from Macri et al. (2015) over a comparable period range (see Figure 6). This agrees well with expectations from the Geneva stellar models (R. I. Anderson et al. 2016, in preparation). We use this value as the intrinsic dispersion of mean ${m}_{H}^{W}$ magnitudes. The last contribution comes from our use of random- or limited-phase (rather than mean-phase) F160W magnitudes. Monte Carlo sampling of complete H-band light curves from Persson et al. (2004) shows that the use of a single random phase adds an error of σ_ph = 0.12 mag.¹³ The relevant fractional contribution of the random-phase uncertainty for a given Cepheid with period P depends on the temporal interval, ΔT, across NIR epochs, a fraction we approximate as f_ph = 1 − (ΔT/P) for ΔT < P and f_ph = 1 for ΔT > P; the values of ΔT are given in Table 3. The value of this fraction ranges from ∼1 (NIR observations at every optical epoch) to zero (a single NIR follow-up observation).

Thus, we assign a total statistical uncertainty arising from the quadrature sum of four terms: NIR photometric error, color error, intrinsic width, and random-phase:

$$\begin{eqnarray*}&&{\sigma }_{{\rm{tot}}}={({\sigma }_{{\rm{sky}}}^{2}+{\sigma }_{{\rm{ct}}}^{2}+{\sigma }_{{\rm{int}}}^{2}+{({f}_{{\rm{ph}}}{\sigma }_{{\rm{ph}}})}^{2})}^{\tfrac{1}{2}}.\end{eqnarray*}$$

We give the values of σ_tot for each Cepheid in Table 4. These have a median of 0.30 mag (mean of 0.32 mag) across all fields; mean values for each field range from 0.23 mag (NGC 3447) to 0.47 mag (NGC 4424). The mean for NGC 4258 is 0.39 mag. We also include in Table 4 an estimate of the metallicity at the position of each Cepheid based on metallicity gradients measured from optical spectra of H ii regions obtained with the Keck-I 10 m telescope and presented in H16.

We now make use of additional sources for the calibration of Cepheid luminosities, focusing on those which (i) are fundamentally geometric, (ii) have Cepheid photometry available in the V, I, and H bands, and (iii) offer precision comparable to that of NGC 4258, i.e., less than 5%. For convenience, the resulting values of H₀ are summarized in Table 6.

3.1.1. Milky Way Parallaxes

Trigonometric parallaxes to MW Cepheids offer one of the most direct sources of geometric calibration of the luminosity of these variables. As in R11, we use the compilation from van Leeuwen et al. (2007), who combined 10 Cepheid parallax measurements with HST/FGS from Benedict et al. (2007) with those measured at lower precision with Hipparcos, plus another three measured only with significance by Hipparcos. We exclude Polaris because it is an overtone pulsator whose "fundamentalized" period is an outlier among fundamental-mode Cepheids. In their analysis, Freedman et al. (2012) further reduced the parallax uncertainties provided by Benedict et al. (2007), attributing the lower-than-expected dispersion of the P–L relation of the 10 Cepheids from Benedict et al. (2007) as evidence for lower-than-reported measurements errors. However, we think it more likely that this lower scatter is caused by chance (with the odds against ∼2σ) than overestimated parallax uncertainty, as the latter is dominated by the propagation of astrometry errors which were stable and well-characterized through extensive calibration of the HST FGS. As the sample of parallax measurements expands, we expect that this issue will be resolved, and for now we retain the uncertainties as determined by Benedict et al. (2007).

We add to this sample two more Cepheids with parallaxes measured by Riess et al. (2014) and Casertano et al. (2015) using the WFC3 spatial scanning technique. These measurements have similar fractional distance precision as those obtained with FGS despite their factor of 10 greater distance and provide two of only four measured parallaxes for Cepheids with P > 10 days. The resulting parallax sample provides an independent anchor of our distance ladder with an error in their mean of 1.6%, though this effectively increases to 2.2% after the addition of a conservatively estimated σ_zp = 0.03 mag zeropoint uncertainty between the ground and HST photometric systems (but see discussion in Section 5).

We use the parallaxes and the H, V, and I-band photometry of the MW Cepheids by replacing Equation (2) for the Cepheids in SN hosts and in M31 with

$$\begin{eqnarray}&&{m}_{H,i,j}^{W}={\mu }_{0,i}+{M}_{H,1}^{W}+{b}_{W}\,\mathrm{log}\,{P}_{i,j}+{Z}_{W}\ {\rm{\Delta }}\mathrm{log}\,{{\rm{(O/H)}}}_{i,j},\end{eqnarray} \tag{ 6 }$$

where ${M}_{H,1}^{W}$ is the absolute ${m}_{H}^{W}$ magnitude for a Cepheid with P = 1 d, and simultaneously fitting the MW Cepheids with the relation

$$\begin{eqnarray}&&{M}_{H,i,j}^{W}={M}_{H,1}^{W}+{b}_{W}\ \mathrm{log}\,{P}_{i,j}+{Z}_{W}\ {\rm{\Delta }}\mathrm{log}\,{{\rm{(O/H)}}}_{i,j},\end{eqnarray} \tag{ 7 }$$

where ${M}_{H,i,j}^{W}={m}_{H,i,j}^{W}-{\mu }_{\pi }$ and μ_π is the distance modulus derived from parallaxes, including standard corrections for bias (often referred to as Lutz–Kelker bias) arising from the finite S/N of parallax measurements with an assumed uncertainty of 0.01 mag (Hanson 1979). The H, V, and I-band photometry, measured from the ground, are transformed to match the WFC3 F160W, F555W, and F814W as discussed in the next subsection. Equation (3) for the SNe Ia is replaced with

$$\begin{eqnarray}&&{m}_{x,i}^{0}={\mu }_{0,i}-{M}_{x}^{0}.\end{eqnarray} \tag{ 8 }$$

The determination of ${M}_{x}^{0}$ for SNe Ia together with the previous term a_x then determines H₀,

$$\begin{eqnarray}&&\mathrm{log}\,{H}_{0}=\displaystyle \frac{{M}_{x}^{0}+5{a}_{x}+25}{5}.\end{eqnarray} \tag{ 9 }$$

The statistical uncertainty in H₀ is now derived from the quadrature sum of the two independent terms in Equation (9), ${M}_{x}^{0}$ and 5a_x.

For ${m}_{H}^{W}$ Cepheid photometry not derived directly from HST WFC3, we assume a fully correlated uncertainty of 0.03 mag included as an additional, simultaneous constraint equation, 0 = Δzp ± σ_zp, to the global constraints with σ_zp = 0.03 mag. The free parameter, Δzp, which expresses the zeropoint difference between HST WFC3 and ground-based data, is now added to Equation (7) for all of the MW Cepheids. This is a convenience for tracking the correlation in the zeropoints between ground-based data and providing an estimate of its size. In future work we intend to eliminate Δzp and its uncertainty by replacing the ground-based photometry with measurements from HST WFC3 enabled by spatial scanning (Riess et al. 2014).

Using these 15 MW parallaxes as the only anchor, we find H₀ = 76.18 ± 2.17 km s⁻¹ Mpc⁻¹ (stat). In order to use the parallaxes together with the maser distance to NGC 4258, we recast the equations for the Cepheids in NGC 4258 in the form of Equation (7) with μ_0,N4258 in place of μ_π and the addition of the residual term Δμ_N4258 to these as a convenience for keeping track of the correlation among these Cepheids and the prior external constraint on the geometric distance of NGC 4258. We then add the simultaneous constraint equation 0 = Δμ_N4258 ± σ_μ0,N4258 with σ_μ0,N4258 = 0.0568 mag. Compared to the use of the maser-based distance in Section 3, σ_μ0,N4258 has moved from Equation (4) to the a priori constraint on Δμ_N4258. This combination gives H₀ = 74.04 ± 1.74 km s⁻¹ Mpc⁻¹ (stat), a 2.4% measurement that is consistent with the value from NGC 4258 to 1.2σ considering only the distance uncertainty in the geometric anchors.

3.1.2. LMC Detached Eclipsing Binaries

In R11 we also used photometry of Cepheids in the LMC and estimates of the distance to this galaxy based on detached eclipsing binaries (DEBs) to augment the set of calibrators of Cepheid luminosities. DEBs provide the means to measure geometric distances (Paczynski & Sasselov 1997) through the ability to determine the physical sizes of the member stars via their photometric light curves and radial velocities. The distance to the LMC has been measured with both early-type and late-type stars in DEBs. Guinan et al. (1998), Fitzpatrick et al. (2002), and Ribas et al. (2002) studied three B-type systems (HV 2274, HV 982, EROS 1044) which lie close to the bar of the LMC and therefore provide a good match to the Cepheid sample of Macri et al. (2015). In R11 we used an average distance modulus for these of 18.486 ± 0.065 mag.¹⁵ However, for early-type stars it is necessary to estimate their surface brightness via non-LTE (local thermodynamic equilibrium) model atmospheres, introducing an uncertainty that is difficult to quantify.

The approach using DEBs composed of late-type stars is more reliable and fully empirical because their surface brightness can be estimated from empirical relations between this quantity and color, using interferometric measurements of stellar angular sizes to derive surface brightnesses (Di Benedetto 2005). Pietrzyński et al. (2013) estimated the distance to the center of the LMC to 2% precision using 8 DEBs composed of late-type giants in a quiet evolutionary phase on the helium burning loop, located near the center of the galaxy and along its line of nodes. The individual measurements are internally consistent and yield μ_LMC = 18.493 ± 0.008 (stat) ± 0.047 (sys) mag, with the uncertainty dominated by the accuracy of the surface brightness versus color relation.

Recently, Macri et al. (2015) presented NIR photometry for LMC Cepheids discovered by the OGLE-III project (Soszynski et al. 2008), greatly expanding the sample size relative to that of Persson et al. (2004) from 92 to 785, although the number of Cepheids with P > 10 days increased more modestly from 39 to 110. Similarly to the M31 Cepheids, the LMC Cepheids provide greater precision for characterizing the P–L relations than those in the SN Ia hosts, and independently hint at a change in slope at P ≈ 10 days (Bhardwaj et al. 2016).

We transform the ground-based V, I and H-band Vega-system photometry of Macri et al. (2015) into the Vega-based HST/WFC3 photometric system in F555W, F814W and F160W, respectively, using the following equations:

$$\begin{eqnarray}&&{m}_{555}=V+0.034+0.11(V-I)\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{m}_{814}=I+0.02-0.018(V-I)\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{m}_{160}=H+0.16(J-H)\end{eqnarray} \tag{ 12 }$$

where the color terms were derived from synthetic stellar photometry for the two systems using SYNPHOT (Laidler et al. 2005). To determine any zeropoint offsets (aside from the potentially different definitions of Vega) for the optical bands we compared photometry of 97 stars in the LMC observed in V and I by OGLE-III and in WFC3/F555W and F814W as part of HST-GO program #13010 (P.I.: Bresolin). The latter was calibrated following the exact same procedures as H16, which uses the UVIS 2.0 WFC3 Vegamag zeropoints. The uncertainties of the zeropoints in the optical transformations were found to be only 4 mmag. The change in color, V − I is quite small, at 0.014 mag or a change (decrease) in H₀ of 0.3% for a value determined solely from an anchor with ground-based Cepheid photometry (LMC or MW). For H-band transformed to F160W, the net offset besides the aformentioned color term is zero after cancellation of an 0.02 mag offset measured between HST and 2MASS NIR photometry (Riess 2011) and the same in the reverse direction from the very small count-rate non-linearity of WFC3 at the brightness level of extragalactic Cepheids (Riess 2010). The mean metallicity of the LMC Cepheids is taken from their spectra by Romaniello et al. (2008) to be ${\rm{[O/H]}}=-0.25$ dex.

Using the late-type DEB distance to the LMC as the sole anchor and the Cepheid sample of Macri et al. (2015) for a set of constraints in the form of Equation (7) yields H₀ = 72.04 ±2.56 km s⁻¹ Mpc⁻¹ (stat). As in the prior section, these fits include free parameters Δμ_LMC and Δzp, with additional constraint 0 = Δμ_LMC ± σ_μ,LMC. The Appendix shows how the system of equations is arranged for this fit. The last few equations (see Appendix) express the independent constraints on the external distances (i.e., for NGC 4258 and the LMC) with uncertainties contained in the error matrix. Using the anchor combination of NGC 4258 and the LMC, the optimal set for TRGB calibration, gives H₀ = 71.62 ± 1.68 km s⁻¹ Mpc⁻¹ (stat).

Using all three anchors, the same set used by R11 and by Efstathiou (2014), results in H₀ = 73.24 ± 1.59 km s⁻¹ Mpc⁻¹ (stat), a 2.2% determination. The fitted parameters which would indicate consistency within the anchor sample are Δμ_N4258 = −0.043 mag, within the range of its 0.0568 mag prior, and Δμ_LMC = −0.042 mag, within range of its 0.0452 mag prior. The metallicity term for the NIR-based Wesenheit has the same sign but only about half the size as in the optical (Sakai et al. 2004) and is not well-detected with Z_W = −0.14 ± 0.06 mag dex⁻¹ including systematic uncertainties.

3.1.3. DEBs in M31

As discussed in Section 3, we make use of a sample of 375 Cepheids in M31 in order to help characterize the Cepheid P–L relations. In principle, we can also use M31 as an anchor in the determination of H₀ by taking advantage of the two DEB-based distance estimates to the galaxy (Ribas et al. 2005; Vilardell et al. 2010) which have a mean of μ₀ = 24.36 ± 0.08 mag.

Yet, there are several obstacles with the use of M31 as an anchor. The PHAT HST program (Dalcanton et al. 2012), which obtained the HST data, did not use the F555W filter, nor did it include time-series data, so we cannot use the same individual, mean-light F555W–F814W colors to deredden the Cepheids in F160W as for other SH0ES galaxies (or the individual mean V − I colors to deredden H-band data with a 0.03 mag uncertainty as for LMC and MW Cepheids as individual ground-based colors are too noisy). The best available color for measuring the individual reddenings of the M31 Cepheids is F110W–F160W so we must recalibrate these colors to match the reddening in the V − I data. Following Riess et al. (2012), we add a constant to these colors so that their mean measured F160W extinction is the same as derived from the mean V − I Cepheid colors in M31 based on data from the ground-based DIRECT program (Kaluzny 1998).¹⁶ The advantage of the latter approach is that it can account for differential reddening along the line of sight while providing a reddening correction which is consistent with that used for Cepheids in all other targets. We adopt an 0.02 mag systematic uncertainty, ${\sigma }_{{\rm{zp,opt}}}$, between the ground-based optical colors of Cepheids and those measured from space. With the same formalism used for the LMC but with M31 as the sole anchor we find H₀ = 74.50 ± 2.87 km s⁻¹ Mpc⁻¹ (stat), consistent with the value derived from the other three anchors.

On the other hand, as previously discussed, DEB distances for early-type stars (the only ones currently measured in M31) include significant inputs from non-LTE stellar model atmospheres with systematic uncertainties that are hard to assess. It is somewhat reassuring to note that in the LMC, where both types of DEBs have been measured, the difference in the distance moduli obtained from either type is only 0.01 ± 0.08 mag, a test with the same precision as the early-type DEB distance to M31. Future measurements of late-type DEBs or water masers in M31 (Darling 2011) would place M31 as an anchor on equal footing with the others.

To be conservative, we use as our primary determination of H₀ the result from the combination of NGC 4258 masers, MW parallaxes, and LMC late-type DEBs (the same set of anchors used by R11): H₀ = 73.24 ± 1.59 km s⁻¹ Mpc⁻¹ (stat). Note, however, the consistency of our primary result with the result using M31 alone. If M31 were included together with the other anchors, the resulting value of H₀ would be 73.46 ±1.53 km s⁻¹ Mpc⁻¹ (stat).

While the global model accounts for the covariance between all distances and model parameters, we can explore the internal agreement of the Cepheid and SN distance estimates by deriving approximate Cepheid-only distances for the 19 hosts. For each host, we remove only its SN distance from the global fit and derive its Cepheid distance, μ_0,i based on the remaining data. The result is a set of Cepheid distances to each host which are independent of their SN distances (although these distances are slightly correlated with each other and thus do not provide a substitute for the full analysis which accounts for such covariance). The results are listed in Table 5, column 5 as approximate Cepheid distances (i.e., ignoring the covariance) and Figure 9 shows the SN distances versus those from Cepheid optical and NIR magnitudes. Figure 10 shows an approximation to the full distance-ladder fit to provide a sense of the sampling using the previously described approximations. These approximations should be good to ∼0.01–0.02 mag. The resulting relation between the SN and Cepheid-based distances will be considered in the next section. The Cepheid-based distances for seven of the eight hosts used in R11 have a mean difference of 0.01 mag and a dispersion of 0.12 mag. The eighth host, N4038, shifted from −1.6σ to ± 1.7σ relative to the SN-inferred distances (Δμ = −0.37 mag, closer in this work). The shift primarily arises because we conservatively excluded a unique set of 10 variables from R11 with ultra-long periods (P > 100 days) due to very sparse phase coverage and the poorly constrained properties of the P-L relation for these intrinsically rare objects (Bird et al. 2009; Fiorentino et al. 2012).

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The Cepheid outlier fraction in Section 3 is ∼2% for all hosts (or ∼5% across all SN hosts), smaller than the 15%–20% in R11. This reduction in the outlier fraction results largely from the use of a color selection in F814W–F160W around the median color in each host to remove blends with unresolved sources of comparable luminosity and different color (e.g., red giants, blue supergiants, unresolved star clusters). This is a useful criterion as it is distance- and period-independent, insensitive to reddening, and anchored to the physical properties of Cepheids (i.e., stars with spectral types F–K). The well-characterized LMC Cepheids from Macri et al. (2015) have a mean I − H of 0.96 mag with a dispersion of just 0.10 mag, much smaller than the allowed 1.2 mag breadth which alone would exclude only stars hotter than early-F or cooler than late-K (i.e., colors which cannot result from Cepheids). Because measurement errors owing to blending are correlated across bands, the uncertainty in this color is smaller than either band and a factor of ∼6 smaller than the allowed range, so colors outside the range primarily result from color blends rather than noise. Doubling the breadth of the color cut decreased H₀ by 0.9 km s⁻¹ Mpc⁻¹ and removing a color cut altogether lowered H₀ by an additional 0.2 km s⁻¹ Mpc⁻¹, both shifts much smaller than the statistical uncertainty.

We further tested the use of our color cut by simulating the appearance of a distribution of Cepheids in a galaxy at D ≈ 30 Mpc using star catalogs of the LMC. Cepheids with low optical blending (hence identifiable by amplitude and allowed range in F555W–F814W; see H16 and Ferrarese et al. (2000)) but with significant NIR blending are most often blended with red giants. This shifts their colors redward in F814W–F160W to a degree, on average, that is proportional to their local surface brightness. While we account for this mean, blended sky level in our photometry, the "direct hits" by red or blue sources are removed by the color cut. However, blending may still occur with stars of a similar color, such as the (less common) yellow supergiants, or the sample may include a small number of objects erroneously identified as Cepheids. For these reasons we still identify and remove a small fraction of the sample (∼2%) as outliers from the P–L relations.

A number of reasonable approaches would likely suffice for identifying these outliers as demonstrated for the R11 sample (Efstathiou 2014; Becker et al. 2015; Kodric et al. 2015). R11 used a 2.5σ threshold to identify outliers from the individual H-band P–L relations for their primary H₀ analysis, while evaluating the impact of no outlier rejection to determine the sensitivity of H₀ to this step. Efstathiou (2014) used a similar threshold but applied to outliers of the final, global fit. Kodric et al. (2015) used a global rejection as well but recalculated the global fit after removing the single most deviant point until none remained above the threshold. Becker et al. (2015) applied a Bayesian characterization of outliers, attributing them to a second, contaminating distribution with uniform properties. However, the artificial-star tests and LMC analysis indicate that the outliers are well described by the tails of the blending distribution. For our primary fit we use a global rejection of 2.7σ, the threshold where the ${\chi }_{\nu }^{2}=0.95$ of our global fit matches that of a normal distribution with the same rejection applied. Following Kodric et al. (2015) we recalculated the global fit after removing the single most deviant point until none remain above the 2.7σ threshold. We also performed as variants a single-pass, global rejection and a rejection from individual P–L relations, both applied at the aforementioned threshold and a larger 3.5σ threshold, as well as no outlier rejection. The results of all these variants are presented in Table 8. These variants of outlier rejection changed H₀ by less than 0.6 km s⁻¹ Mpc⁻¹. Because the outlier fraction of 2% is quite small here and the Cepheid slope is better constrained relative to that of R11, we conclude that the outlier analysis does not warrant further consideration. The Cepheids in Table 4 are those that passed the best-fit, global 2.7σ outlier rejection.

We consider a number of variants related to the Cepheid reddening law. Besides the primary fits, which use a Fitzpatrick (1999) law with R_V = 3.3, we also use R_V = 2.5 and alternative formulations of the reddening law from Cardelli et al. (1989) and Nataf et al. (2015). We also explore variants related to a possible break in the Cepheid P–L relation near 10 days. Our primary fit allows for a break or discontinuity (while not requiring one) by providing two independent slope parameters: one for Cepheids at P > 10 days and one for P < 10 days. The allowance for a break only increases the uncertainty in H₀ by 0.01 km s⁻¹ Mpc⁻¹ which is negligible. We also evaluate changes in H₀ arising from a single-slope formulation for all periods, as well as from removing all Cepheids with P < 10 days, or removing those with P > 60 days as shown in Table 8. Interestingly, we see no evidence of a change in slope at P = 10 d in the ${M}_{H}^{W}$ P–L relation to a precision of 0.02 mag dex⁻¹ in the global fit to all Cepheids. Hints of an increasing (LMC) or decreasing (M31) slope with period are not confirmed in this broader analysis with many more hosts. We further included variants that ignored the possibility of a Cepheid metallicity dependence and another based on a T_e recalibration of nebular oxygen abundances (Bresolin 2011). We also included a variant foregoing the use of optical colors to correct for NIR reddening as it tends to be low. The results of all these variants are presented in Table 8.

Comparing the individual SN distances to the previously discussed approximate, independent Cepheid distances, we find none of the hosts to be an outlier. There is also no evidence (<1σ) for a trend between SN and Cepheid NIR distances over a 3.8 mag range in distance modulus (equivalent to a factor of 5.8 in distance). This suggests that Cepheids are not associated with significant unresolved luminosity overdensities across the range of 7–38 Mpc spanned by our sample of SN hosts and one of our anchors (NGC 4258). This agrees well with Senchyna et al. (2015), who used HST to determine that only ∼3% of Cepheids in M31 are in parsec-scale clusters. Further, only a small fraction of these would alter Cepheid photometry at the resolution available from the ground or the similar resolution of HST at the distance of the SN hosts.

Lastly, we test for a dependence of the measured Cepheid distance with the level of blending by comparing the six hosts with blending higher than the inner region of NGC 4258 to the remaining 13. The difference in the mean model residual distances of these two subsamples is 0.02 ± 0.07 mag, providing no evidence of such a dependence.

The SH0ES program was designed to identify Cepheids from optical images and to observe them in the NIR with F160W to reduce systematic uncertainties related to the reddening law, its free parameters, sensitivity to metallicity, and breaks in the P–L relation. However, some insights into these systematics may be garnered by replacing the NIR-based Wesenheit magnitude, ${m}_{H}^{W}$, with the optical version used in past studies (Freedman et al. 2001), ${m}_{I}^{W}=I-R(V-I)$, where R ≡ A_I/(A_V − A_I) and the value of R here is ∼4 times larger than in the NIR. The advantage of this change is the increase in the sample by a little over 600 Cepheids in HST hosts owing to the greater FOV of WFC3/UVIS. Of these additional Cepheids, 250 come from M101, 94 from NGC 4258, and the rest from the other SN hosts. In Table 8 we give results based on Cepheid measurements of ${m}_{I}^{W}$ instead of ${m}_{H}^{W}$ for the primary fit variant with all four anchors, the primary fit anchor set of NGC 4258, MW, and LMC, and for NGC 4258 as the sole anchor.

The fits for all Cepheids with ${m}_{I}^{W}$ data generally show a significantly steeper slope for P < 10 days than for P > 10 days, with our preferred variant giving a highly significant slope change of 0.22 ± 0.03 mag dex⁻¹. We also see strong evidence of a metallicity term with a value of −0.20 ± 0.05 mag dex⁻¹ for our preferred fit, also highly significant and consistent with the value from Sakai et al. (2004) of −0.24 ± 0.05 mag dex⁻¹. The constraint on the metallicity term is nearly unchanged when using NGC 4258 as the sole anchor, −0.19 ± 0.05 mag dex⁻¹, demonstrating that the metallicity constraint comes from the metallicity gradients and SN host-to-host distance variations and not from improving the consistency in the distance scale of different anchors.

The dispersion between the individual SN and Cepheid distances (see Figure 9 and the next subsection) is σ = 0.12 mag for ${m}_{I}^{W}$, somewhat smaller than σ = 0.15 mag from ${m}_{H}^{W}$. Some reduction may be expected because a larger number of Cepheids are available in the optical relative to the NIR. However, the SNe have a mean distance uncertainty of 0.12 mag and the sets of ${m}_{H}^{W}$ magnitudes in each host have a typical mean uncertainty of 0.06 mag, indicating that the dispersion between SN and Cepheid distances is already dominated by the SN error and leaving little room for improvement with additional Cepheids. The one exception is NGC 4424, where the paucity of variables with valid NIR measurements results in a Cepheid-dominated calibration error which is reduced by a third by adding Cepheids only available in the optical. Based on the good agreement between the relative SN and Cepheid distances and uncertainties, we conclude that the intrinsic SN dispersion of 0.1 mag from SALT-II is reasonable.

Using the three primary anchors and the optical Wesenheit P–L relation, we find H₀ = 71.56 ± 1.52 km s⁻¹ Mpc⁻¹ (stat), extremely similar to the NIR-based result and with a statistical error just 0.05 km s⁻¹ Mpc⁻¹ smaller. We determined the systematic error for the optical Wesenheit from the dispersion of its variants after eliminating those expected to perform especially poorly in the optical: no allowance for reddening, no metallicity term, and no lower-period cutoff. Even without these variants, the systematic error in the optical of 2.8% is still considerably worse than its NIR counterpart and is also larger than the statistical error. The reason is that changes to the treatment of reddening, metallicity, P–L relation breaks, and outlier rejection cause larger changes in H₀ for the optical Wesenheit magnitudes than for the NIR counterparts. This is a fairly uniform result, not driven by any one or two variants. For example, changing from the preferred Fitzpatrick (1999) reddening law to the alternative formulations by Cardelli et al. (1989) or Nataf et al. (2015) changes H₀ by 0.10 and 0.15 km s⁻¹ Mpc⁻¹ for ${m}_{H}^{W}$, respectively. These same variants change H₀ by −2.15 and 3.82 km s⁻¹ Mpc⁻¹ for the ${m}_{I}^{W}$ data. This increased sensitivity to the reddening law is a natural consequence of the larger value of R. Changing the two-slope P–L formulation to a single slope or restricting the period range to P > 10 or P < 60 days changes H₀ by −1.64, −1.24, and 1.79 km s⁻¹ Mpc⁻¹, respectively, for the optical formulation. These changes are generally smaller for the NIR Wesenheit at 0.03, −1.59, and −0.18 km s⁻¹ Mpc⁻¹, respectively. Finally, changing the outlier clipping from one-at-a-time to a single pass changes H₀ by 0.01 and −0.90 km s⁻¹ Mpc⁻¹ for the NIR and optical approaches, respectively.

Using the three primary anchors with the optical Wesenheit and now including systematic errors, we find H₀ = 71.56 ±2.49 km s⁻¹ Mpc⁻¹, equivalent to an uncertainty of 3.5%. This result is somewhat less precise than the 3.3% total error of R11, which used the NIR Wesenheit but only 8 SN-Cepheid hosts instead of the present 19. Until or unless additional studies can improve our understanding of Cepheid reddening, metallicity sensitivity, and the scale of P–L breaks at optical wavelengths, our analysis shows that improvements in the determination of H₀ via Cepheids must primarily rely on the inclusion of NIR observations.

Similar conclusions are reached when using only NGC 4258 as an anchor: H₀ = 72.04 ± 2.23 km s⁻¹ Mpc⁻¹ without systematic errors, so the statistical error is slightly better than the equivalent NIR result at 3.1%. However, the systematic error of 2.4% is considerably worse, leading to a combined value of H₀ = 72.04 ± 2.83 km s⁻¹ Mpc⁻¹. While the use of strictly optical Wesenheit magnitudes can be informative, our best results for H₀ with lowest systematics consistently come from using the NIR data in concert with optical observations.

The SALT-II SN light-curve fits, the composition of the Hubble-flow sample, and sources of SN photometry used to determine a_X in Equation (5) are described in Scolnic et al. (2015) and Scolnic & Kessler (2016). These take advantage of the "Supercal" procedure (Scolnic et al. 2015) which uses reference stars in the fields of the SNe and the homogeneous set of star photometry over 3π steradians from Pan-STARRS to remove small photometric inconsistencies between SN photometry obtained across multiple observatories and systems. As is common in recent analyses of SN Ia distances (e.g., Betoule et al. 2014), to determine a_X we use "quality cuts" to include only SN Ia light curves for which the SALT color parameter (c) is within ±0.3, the light-curve parameter (x₁) is within ±3.0 (error <1.5), the χ² of the light-curve fit is "good" (fitprob >0.001), the peak time of the light curve is constrained to better than 2 days, and the uncertainty in the corrected peak magnitude is <0.2 mag. All of the 19 calibrators pass these quality cuts as well. The SN redshifts are corrected for coherent (peculiar) flows based on density maps (Scolnic et al. 2014, 2015) which reduces correlated deviations from expansion caused by visible large-scale structure and empirical residuals determined from simulations (Scolnic & Kessler 2016). A residual velocity (peculiar) error of 250 km s⁻¹ is assumed. As a final step, we exclude SNe Ia which deviate from the form of Equation (5) by more than 3σ; this excludes 3% of the sample for the primary fit with 0.0233 < z < 0.15, leaving 217 SNe Ia (or 281 SNe Ia for variants with 0.01 < z < 0.15). These have a dispersion of 0.128 mag around Equation (5) with a mean error of 0.129 mag and a χ² per degree of freedom of 0.91, and yield a_B = 0.71273 ± 0.00176 for SALT-II (a_V = 0.7005 for MLCS2k2). As an alternative to the SALT-II light-curve fitter, we used the MLCS2k2 fitter (Jha et al. 2007) with a value of R_V = 2.5 for the SN host galaxy, the same as the primary fits of R11. The resulting value of H₀ is higher by 1.9 km s⁻¹ Mpc⁻¹ or 1.1σ of the total error as given in Table 8.

As in R11, we make use of several studies (Hicken et al. 2009b; Kelly et al. 2010; Lampeitl et al. 2010; Sullivan et al. 2010) which have shown the existence of a small step brighter for the corrected SN magnitude for hosts more massive than $\mathrm{log}{M}_{{\rm{stellar}}}\sim 10$. We use the same value of 0.06 mag used by Betoule et al. (2014) for the size of the mass step to account for this effect. The net effect on H₀ is a small decrease of 0.7% because of the modest difference in masses of the nearby hosts (mean $\mathrm{log}{M}_{{\rm{stellar}}}=9.8$) and of those that define the magnitude-redshift relation (Sullivan et al. 2010, mean $\mathrm{log}{M}_{{\rm{stellar}}}=10.5$). We include these corrections based on host-galaxy mass in our present determination of ${m}_{B,i}^{0}$ given in Table 5 and for a_x, correcting those with hosts above and below $\mathrm{log}{M}_{{\rm{stellar}}}\sim 10$ by 0.03 fainter and brighter, respectively.

An alternative host dependence on SN Ia distance has been proposed by Rigault et al. (2013, 2015) based on the local star formation rate (LSFR) measured at the site of the SN. The results from Rigault et al. (2015) suggested a ∼3σ correlation between SN distance residual and LSFR inferred from ultraviolet photometry measured with GALEX for a set of 82 SNe Ia from Hicken et al. (2009a), with somewhat higher significance for distances from MLCS2k2 and somewhat lower for SALT-II. Jones et al. (2015) repeated the LSFR analysis using a larger sample of SNe Ia which better matched the samples and light-curve quality selection used in the cosmological analyses of R11 and Betoule et al. (2014) as well as the more recent version of SALT II. Using 179 GALEX-imaged SN Ia hosts from the JLA SN sample (Betoule et al. 2014) and the Pan-STARRS sample (Scolnic et al. 2015), or 157 used by R11, the significance of a LSFR effect diminished to ≲1σ due to two differences from Rigault et al. (2015): (1) the increase in the sample statistics, and (2) use of the JLA or R11 quality criteria. Because we employ both the larger local SN sample as well as the quality cuts used by Jones et al. (2015), we include only the mass-based correction whose significance has remained in cosmological SN samples.

Nevertheless, if we were to assume the existence of a LSFR (despite the preceding lack of significance), we can select a Hubble-flow sample to match the LSF of the calibrator sample and thus nullify the possible impact on H₀. In the calibrator sample, 17 of 19 hosts (or 89%) are above the LSFR threshold adopted by Rigault et al. (2013, 2015), which is a larger fraction than the 50%–60% in the Hubble-flow sample (Jones et al. 2015). To determine an upper limit on a LSFR mismatch and thus H₀ across sets, we selected all Hubble-flow SNe significantly above the LSFR threshold (i.e., a purely LSFR sample), requiring these SNe Ia to have good GALEX detections. By changing the Hubble flow selection, only the term a_X is affected. For this all-LSFR sample, a_B is higher than for the primary fit by 0.00446 at z > 0.0233 and lower by 0.0010 at z > 0.01. Thus the Hubble constant from the primary fit increased by 0.8 or 0.2 km s⁻¹ Mpc⁻¹, respectively (see Table 8). Thus, even if a relation existed, we find that a LSFR in SN hosts would have no significant impact on the determination of H₀ here.

However, to address the possibility of host-galaxy dependence that arises from sample selection, we also recalculated the intercept of the Hubble-flow SNe (a_X) using only those found in spiral hosts. Because the 19 hosts selected for Cepheid observations were chosen on the basis of their appearance as spirals (as well as their proximity and modest inclination), this selection would be expected to match the two samples if global star formation or its history had an impact on the measured SN distance. Because the Hubble-flow sample is so much larger than the nearby sample, such a cut has a modest effect on the uncertainty in H₀. Doing so raised H₀ for the SALT-II fitter and lowered H₀ for MLCS2k2 each by ∼0.5 km s⁻¹ Mpc⁻¹. We note that the spiral-host sample has a mean LSFR of −2.21 dex, similar to the mean of the 19 calibrators at −2.23 dex and higher than the full Hubble-flow set of −2.58 dex.

We also changed the lower redshift cutoff of the Hubble diagram from z = 0.023 to z = 0.01, originally adopted to mitigate the impact of a possible local, coherent flow. This raised H₀ by 0.2 km s⁻¹ Mpc⁻¹ for the primary fit. Changing the deceleration parameter used to fit the SNe Ia at 0.0233 < z < 0.15 from q₀ = −0.55 (as expected for Ω_M = 0.3, Ω_Λ = 0.7) to −0.60 (Ω_M = 0.27, Ω_Λ = 0.73; or Ω_M = 0.3, Ω_DE = 0.7, w = −1.05) decreases H₀ by 0.2%. More generally, an uncertainty in Ω_M of 0.02 (Betoule et al. 2014) produces an uncertainty in q₀ of 0.03 resulting in an uncertainty in H₀ of 0.1%. As expected, the sensitivity of H₀ to knowledge of q₀ is very low as the mean SN redshift is only 0.07. As a further test, we reduced the upper range of redshifts used to measure the intercept from 0.15 to 0.07. This reduces the sample by nearly half, increases the uncertainty in the intercept by 40% and increases the intercept and H₀ by 0.7%. We do not use this more limited redshift range because it introduces the potential for larger peculiar flows and the sensitivity to knowledge of q₀ is already very low.

Two of the SNe in the calibrator sample (SN 1981B and SN 1990N) were measured before the Hubble-flow sample was acquired. Relative to the global fit, SN 1990N is faint by 0.15 ± 0.14 mag and SN 1981B is bright by 0.08 ± 0.14 mag, so this older digital photometry does not appear to bias the value of H₀ in a significant way.

A budget for the sources of uncertainty in the determination of H₀ is given in Table 7. These are necessarily marginalized approximations, as they do not show the (small) covariance between terms included in the full global fit.

Table 7.  H₀ Error Budget for Cepheid and SN Ia Distance Ladders^a

Term	Description	Prev.	R09	R11	This Work
		LMC	N4258	All 3	N4258	All 3
σanchor	Anchor distance,mean	5%	3%	1.3%	2.6%	1.3%
${\sigma }_{{\rm{anchor}}{\rm{PL}}}$ b	Mean of P–L in anchor	2.5%	1.5%	0.8%	1.2%	0.7%
${\sigma }_{{\rm{host}}{\rm{PL}}}/\sqrt{n}$	Mean of P–L values in SN Ia hosts	1.5%	1.5%	0.6%	0.4%	0.4%
${\sigma }_{{\rm{SN}}}/\sqrt{n}$	Mean of SN Ia calibrators	2.5%	2.5%	1.9%	1.2%	1.2%
${\sigma }_{m-z}$	SN Ia m − z relation	1%	0.5%	0.5%	0.4%	0.4%
Rσzp	Cepheid reddening &colors,anchor-to-hosts	4.5%	0.3%	1.4%	0%	0.3%
σZ	Cepheid metallicity,anchor-to-hosts	3%	1.1%	1.0%	0.0%	0.5%
${\sigma }_{{\rm{PL}}}$	P–L slope,Δ log P, anchor-to-hosts	4%	0.5%	0.6%	0.2%	0.5%
σWFPC2	WFPC2 CTE, long-short	3%	N/A	N/A	N/A	N/A
Subtotal, ${\sigma }_{{H}_{0}}$ c		10%	4.7%	2.9%	$3.3 \%$ d	2.2%
Analysis Systematics		N/A	1.3%	1.0%	1.2%	1.0%
Total, ${\sigma }_{{H}_{0}}$		10%	4.8%	3.3%	3.5%	2.4%

Notes.

^aDerived from diagonal elements of the covariance matrix propagated via the error matrices associated with Equations (1), (3), (7), and (8). ^bFor MW parallax, this term is already included with the term above. ^cFor R09, R11, and this work, calculated with covariance included. ^dOne anchor not included in R11 estimate of ${\sigma }_{{H}_{0}}$ to provide a crosscheck.

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Our systematic error is estimated based on the variations in H₀ resulting from the reasonable, alternative fits. These alternatives are, by their nature, difficult to formally include in the global fit. All of the discussed NIR variants, 207 in total including combinations of anchors, are listed in Table 8. As shown in Figure 11, the histogram for the primary-fit anchors (NGC 4258, MW, and LMC) is well fit by a Gaussian distribution with σ = 0.71 km s⁻¹ Mpc⁻¹, a systematic uncertainty that is a little less than half of the statistical error. None of the variants is a noteworthy outlier from this distribution. The complete error in H₀ using multiple anchors can be traced to the quadrature sum of three terms, the two independent terms in Equation (9) and the systematic error. The error in ${M}_{X}^{0}$ for any variant, derived from the global fit, is given in third column of Table 8 and the error in the intercept, a_X, was given in Section 3.

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Table 8.  Fits for H₀

${\chi }_{\mathrm{dof}}^{2}$	H0	Anc	Brk	Clp	σ	Opt	PL	R	RV	N	Z	γ	b	bl	SN	zm	${M}_{V}^{0}$	av	Gal
0.92	73.46 1.53	All	Y	1	2.7	Y	WH	F	3.3	2277	Z	−0.13 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
0.93	73.48 1.53	All	Y	G	2.7	Y	WH	F	3.3	2280	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
0.88	72.73 1.49	All	Y	I	2.7	Y	WH	F	3.3	2280	Z	−0.10 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.27	0.71273	A
1.28	73.68 1.79	All	Y	G	No	Y	WH	F	3.3	2345	Z	−0.10 0.08	−3.26 0.02	−3.24 0.02	S	0.02	−19.24	0.71273	A
1.10	73.67 1.66	All	Y	G	3.5	Y	WH	F	3.3	2321	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
1.09	73.64 1.66	All	Y	1	3.5	Y	WH	F	3.3	2320	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
0.92	72.69 1.52	All	Y	I	3.5	Y	WH	F	3.3	2320	Z	−0.09 0.07	−3.30 0.02	−3.22 0.02	S	0.02	−19.27	0.71273	A
1.11	73.21 1.66	All	Y	G	3.5	Y	WH	F	2.5	2322	Z	−0.14 0.07	−3.25 0.02	−3.24 0.02	S	0.02	−19.25	0.71273	A
0.92	74.04 1.54	All	Y	G	2.7	Y	WH	C	3.3	2278	Z	−0.11 0.07	−3.27 0.02	−3.27 0.02	S	0.02	−19.23	0.71273	A
0.94	73.14 1.54	All	Y	G	2.7	Y	WH	N	3.3	2278	Z	−0.11 0.07	−3.24 0.02	−3.24 0.02	S	0.02	−19.25	0.71273	A
0.93	73.49 1.52	All	N	G	2.7	Y	WH	F	3.3	2280	Z	−0.12 0.07	−3.25 0.01	⋯	S	0.02	−19.24	0.71273	A
1.12	72.19 1.72	All	10	G	2.7	Y	WH	F	3.3	1318	Z	−0.15 0.08	−3.26 0.03	⋯	S	0.02	−19.28	0.71273	A
0.91	73.32 1.51	All	60	G	2.7	Y	WH	F	3.3	2180	Z	−0.16 0.07	−3.25 0.01	⋯	S	0.02	−19.25	0.71273	A
1.06	75.55 1.67	All	Y	G	2.7	Y	H	F	3.3	2240	Z	−0.08 0.07	−3.07 0.02	−3.16 0.02	S	0.02	−19.18	0.71273	A
0.94	73.45 1.54	All	Y	G	2.7	Y	WH	F	3.3	2281	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
0.93	73.60 1.53	All	Y	G	2.7	Y	WH	F	3.3	2280	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.24	0.71347	A
0.93	75.08 1.65	All	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.06 0.07	−3.27 0.02	−3.25 0.02	M	0.02	−19.15	0.70326	A
0.94	74.66 1.55	All	Y	G	2.7	N	WH	F	3.3	2417	Z	−0.15 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.21	0.71273	A
0.93	73.85 1.58	All	Y	G	2.7	Y	WH	F	3.3	2280	B	−0.10 0.09	−3.25 0.02	−3.25 0.02	S	0.02	−19.23	0.71273	A
0.93	73.59 1.60	All	Y	G	2.7	Y	WH	F	3.3	2280	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.24	0.71340	S
0.93	74.57 1.70	All	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.06 0.07	−3.27 0.02	−3.25 0.02	M	0.02	−19.15	0.70031	S
0.93	73.76 1.66	All	Y	G	2.7	Y	WH	F	3.3	2280	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.24	0.71444	L
0.93	74.23 1.71	All	Y	G	2.7	Y	WH	F	3.3	2280	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.24	0.71719	L
0.92	73.24 1.59	NML	Y	1	2.7	Y	WH	F	3.3	2276	Z	−0.13 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.25	0.71273	A
0.93	73.25 1.60	NML	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.25	0.71273	A
0.88	72.67 1.56	NML	Y	I	2.7	Y	WH	F	3.3	2279	Z	−0.10 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.27	0.71273	A
1.28	73.49 1.87	NML	Y	G	No	Y	WH	F	3.3	2344	Z	−0.10 0.08	−3.26 0.02	−3.24 0.02	S	0.02	−19.24	0.71273	A
1.10	73.45 1.74	NML	Y	G	3.5	Y	WH	F	3.3	2320	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
1.09	73.42 1.73	NML	Y	1	3.5	Y	WH	F	3.3	2319	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.25	0.71273	A
0.92	72.62 1.59	NML	Y	I	3.5	Y	WH	F	3.3	2319	Z	−0.09 0.07	−3.30 0.02	−3.22 0.02	S	0.02	−19.27	0.71273	A
1.11	73.15 1.74	NML	Y	G	3.5	Y	WH	F	2.5	2321	Z	−0.14 0.07	−3.25 0.02	−3.24 0.02	S	0.02	−19.25	0.71273	A
0.92	73.33 1.59	NML	Y	G	2.7	Y	WH	C	3.3	2277	Z	−0.12 0.07	−3.27 0.02	−3.27 0.02	S	0.02	−19.25	0.71273	A
0.94	73.39 1.61	NML	Y	G	2.7	Y	WH	N	3.3	2277	Z	−0.11 0.07	−3.24 0.02	−3.24 0.02	S	0.02	−19.25	0.71273	A
0.93	73.26 1.59	NML	N	G	2.7	Y	WH	F	3.3	2279	Z	−0.12 0.07	−3.25 0.01	⋯	S	0.02	−19.25	0.71273	A
1.12	71.64 1.81	NML	10	G	2.7	Y	WH	F	3.3	1317	Z	−0.16 0.08	−3.26 0.03	⋯	S	0.02	−19.30	0.71273	A
0.91	73.06 1.58	NML	60	G	2.7	Y	WH	F	3.3	2179	Z	−0.17 0.07	−3.25 0.01	⋯	S	0.02	−19.26	0.71273	A
1.06	74.79 1.73	NML	Y	G	2.7	Y	H	F	3.3	2239	Z	−0.09 0.07	−3.06 0.02	−3.17 0.02	S	0.02	−19.21	0.71273	A
0.94	73.30 1.61	NML	Y	G	2.7	Y	WH	F	3.3	2280	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.25	0.71273	A
0.93	73.38 1.60	NML	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.25	0.71347	A
0.93	74.89 1.72	NML	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.06 0.07	−3.27 0.02	−3.25 0.02	M	0.02	−19.15	0.70326	A
0.94	74.39 1.62	NML	Y	G	2.7	N	WH	F	3.3	2416	Z	−0.15 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.22	0.71273	A
0.93	73.64 1.63	NML	Y	G	2.7	Y	WH	F	3.3	2279	B	−0.11 0.09	−3.25 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
0.93	73.37 1.66	NML	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.25	0.71340	S
0.93	74.39 1.76	NML	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.06 0.07	−3.27 0.02	−3.25 0.02	M	0.02	−19.15	0.70031	S
0.93	73.54 1.73	NML	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.25	0.71444	L
0.93	74.01 1.77	NML	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.12 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.25	0.71719	L
0.92	74.04 1.74	NM	Y	1	2.7	Y	WH	F	3.3	2275	Z	−0.16 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.23	0.71273	A
0.93	74.01 1.75	NM	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.23	0.71273	A
0.87	73.67 1.71	NM	Y	I	2.7	Y	WH	F	3.3	2278	Z	−0.13 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.24	0.71273	A
1.28	74.20 2.04	NM	Y	G	No	Y	WH	F	3.3	2343	Z	−0.12 0.08	−3.26 0.02	−3.24 0.02	S	0.02	−19.22	0.71273	A
1.10	74.30 1.90	NM	Y	G	3.5	Y	WH	F	3.3	2319	Z	−0.17 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.22	0.71273	A
1.09	74.27 1.89	NM	Y	1	3.5	Y	WH	F	3.3	2318	Z	−0.17 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.22	0.71273	A
0.92	73.57 1.75	NM	Y	I	3.5	Y	WH	F	3.3	2318	Z	−0.12 0.07	−3.30 0.02	−3.22 0.02	S	0.02	−19.24	0.71273	A
1.11	74.04 1.90	NM	Y	G	3.5	Y	WH	F	2.5	2320	Z	−0.17 0.08	−3.25 0.02	−3.24 0.02	S	0.02	−19.23	0.71273	A
0.92	74.03 1.74	NM	Y	G	2.7	Y	WH	C	3.3	2277	Z	−0.15 0.07	−3.28 0.02	−3.27 0.02	S	0.02	−19.23	0.71273	A
0.95	74.17 1.77	NM	Y	G	2.7	Y	WH	N	3.3	2278	Z	−0.14 0.07	−3.24 0.02	−3.24 0.02	S	0.02	−19.22	0.71273	A
0.93	74.03 1.73	NM	N	G	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.25 0.01	⋯	S	0.02	−19.23	0.71273	A
1.12	71.36 2.17	NM	10	G	2.7	Y	WH	F	3.3	1316	Z	−0.15 0.08	−3.26 0.03	⋯	S	0.02	−19.31	0.71273	A
0.91	73.98 1.73	NM	60	G	2.7	Y	WH	F	3.3	2179	Z	−0.22 0.08	−3.25 0.01	⋯	S	0.02	−19.23	0.71273	A
1.06	75.57 1.89	NM	Y	G	2.7	Y	H	F	3.3	2239	Z	−0.12 0.07	−3.07 0.02	−3.17 0.02	S	0.02	−19.18	0.71273	A
0.94	73.70 1.74	NM	Y	G	2.7	Y	WH	F	3.3	2279	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.24	0.71273	A
0.93	74.14 1.75	NM	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.23	0.71347	A
0.94	75.50 1.86	NM	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.10 0.07	−3.27 0.02	−3.25 0.02	M	0.02	−19.14	0.70326	A
0.93	75.27 1.77	NM	Y	G	2.7	N	WH	F	3.3	2415	Z	−0.19 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.19	0.71273	A
0.93	74.57 1.83	NM	Y	G	2.7	Y	WH	F	3.3	2278	B	−0.16 0.10	−3.25 0.02	−3.25 0.02	S	0.02	−19.21	0.71273	A
0.93	74.13 1.80	NM	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.23	0.71340	S
0.94	74.99 1.91	NM	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.10 0.07	−3.27 0.02	−3.25 0.02	M	0.02	−19.14	0.70031	S
0.93	74.31 1.86	NM	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.23	0.71444	L
0.93	74.78 1.91	NM	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.23	0.71719	L
0.92	71.62 1.68	NL	Y	1	2.7	Y	WH	F	3.3	2276	Z	−0.18 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.30	0.71273	A
0.93	71.86 1.70	NL	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.29	0.71273	A
0.87	71.60 1.66	NL	Y	I	2.7	Y	WH	F	3.3	2279	Z	−0.13 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.30	0.71273	A
1.28	72.14 1.98	NL	Y	G	No	Y	WH	F	3.3	2344	Z	−0.13 0.08	−3.25 0.02	−3.24 0.02	S	0.02	−19.28	0.71273	A
1.09	72.01 1.84	NL	Y	G	3.5	Y	WH	F	3.3	2320	Z	−0.18 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.29	0.71273	A
1.09	71.99 1.83	NL	Y	1	3.5	Y	WH	F	3.3	2319	Z	−0.18 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.29	0.71273	A
0.92	71.51 1.70	NL	Y	I	3.5	Y	WH	F	3.3	2319	Z	−0.12 0.07	−3.29 0.02	−3.22 0.02	S	0.02	−19.30	0.71273	A
1.10	71.77 1.84	NL	Y	G	3.5	Y	WH	F	2.5	2321	Z	−0.17 0.07	−3.24 0.02	−3.25 0.02	S	0.02	−19.29	0.71273	A
0.92	71.80 1.69	NL	Y	G	2.7	Y	WH	C	3.3	2278	Z	−0.18 0.07	−3.27 0.02	−3.27 0.02	S	0.02	−19.29	0.71273	A
0.94	71.86 1.71	NL	Y	G	2.7	Y	WH	N	3.3	2277	Z	−0.15 0.07	−3.24 0.02	−3.24 0.02	S	0.02	−19.29	0.71273	A
0.93	71.84 1.69	NL	N	G	2.7	Y	WH	F	3.3	2279	Z	−0.15 0.07	−3.25 0.01	⋯	S	0.02	−19.29	0.71273	A
1.13	71.21 1.86	NL	10	G	2.7	Y	WH	F	3.3	1319	Z	−0.19 0.08	−3.26 0.03	⋯	S	0.02	−19.31	0.71273	A
0.91	71.42 1.67	NL	60	G	2.7	Y	WH	F	3.3	2180	Z	−0.24 0.08	−3.25 0.01	⋯	S	0.02	−19.31	0.71273	A
1.06	73.32 1.83	NL	Y	G	2.7	Y	H	F	3.3	2240	Z	−0.13 0.07	−3.06 0.02	−3.17 0.02	S	0.02	−19.25	0.71273	A
0.93	72.25 1.70	NL	Y	G	2.7	Y	WH	F	3.3	2280	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.28	0.71273	A
0.93	71.98 1.70	NL	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.29	0.71347	A
0.93	73.53 1.81	NL	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.11 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.19	0.70326	A
0.93	72.78 1.71	NL	Y	G	2.7	N	WH	F	3.3	2417	Z	−0.21 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.26	0.71273	A
0.93	72.24 1.70	NL	Y	G	2.7	Y	WH	F	3.3	2279	B	−0.22 0.10	−3.25 0.02	−3.25 0.02	S	0.02	−19.28	0.71273	A
0.93	71.97 1.75	NL	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.29	0.71340	S
0.93	73.03 1.85	NL	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.11 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.19	0.70031	S
0.93	72.15 1.81	NL	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.29	0.71444	L
0.93	72.60 1.85	NL	Y	G	2.7	Y	WH	F	3.3	2279	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.29	0.71719	L
0.92	74.15 1.82	ML	Y	1	2.7	Y	WH	F	3.3	2275	Z	−0.14 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.22	0.71273	A
0.93	74.27 1.84	ML	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.22	0.71273	A
0.88	72.84 1.75	ML	Y	I	2.7	Y	WH	F	3.3	2278	Z	−0.10 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.26	0.71273	A
1.28	74.51 2.15	ML	Y	G	No	Y	WH	F	3.3	2343	Z	−0.10 0.08	−3.26 0.02	−3.24 0.02	S	0.02	−19.21	0.71273	A
1.10	74.43 1.99	ML	Y	G	3.5	Y	WH	F	3.3	2319	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.22	0.71273	A
1.09	74.40 1.99	ML	Y	1	3.5	Y	WH	F	3.3	2318	Z	−0.14 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.22	0.71273	A
0.92	72.92 1.80	ML	Y	I	3.5	Y	WH	F	3.3	2318	Z	−0.09 0.07	−3.30 0.02	−3.22 0.02	S	0.02	−19.26	0.71273	A
1.11	73.95 1.99	ML	Y	G	3.5	Y	WH	F	2.5	2320	Z	−0.14 0.07	−3.25 0.02	−3.24 0.02	S	0.02	−19.23	0.71273	A
0.92	74.45 1.83	ML	Y	G	2.7	Y	WH	C	3.3	2276	Z	−0.12 0.07	−3.27 0.02	−3.27 0.02	S	0.02	−19.22	0.71273	A
0.94	74.35 1.85	ML	Y	G	2.7	Y	WH	N	3.3	2275	Z	−0.11 0.07	−3.24 0.02	−3.24 0.02	S	0.02	−19.22	0.71273	A
0.93	74.28 1.82	ML	N	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.25 0.01	⋯	S	0.02	−19.22	0.71273	A
1.12	72.70 2.18	ML	10	G	2.7	Y	WH	F	3.3	1316	Z	−0.15 0.08	−3.26 0.03	⋯	S	0.02	−19.27	0.71273	A
0.90	74.29 1.81	ML	60	G	2.7	Y	WH	F	3.3	2176	Z	−0.14 0.07	−3.25 0.01	⋯	S	0.02	−19.22	0.71273	A
1.06	75.96 1.99	ML	Y	G	2.7	Y	H	F	3.3	2237	Z	−0.09 0.07	−3.06 0.02	−3.16 0.02	S	0.02	−19.17	0.71273	A
0.93	74.40 1.84	ML	Y	G	2.7	Y	WH	F	3.3	2279	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.22	0.71273	A
0.93	74.39 1.84	ML	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.22	0.71347	A
0.93	75.96 1.95	ML	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.06 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.12	0.70326	A
0.93	75.65 1.86	ML	Y	G	2.7	N	WH	F	3.3	2414	Z	−0.15 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.18	0.71273	A
0.93	74.94 1.89	ML	Y	G	2.7	Y	WH	F	3.3	2278	B	−0.13 0.09	−3.25 0.02	−3.25 0.02	S	0.02	−19.20	0.71273	A
0.93	74.38 1.89	ML	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.22	0.71340	S
0.93	75.44 1.99	ML	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.06 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.12	0.70031	S
0.93	74.56 1.95	ML	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.22	0.71444	L
0.93	75.03 1.99	ML	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.22	0.71719	L
1.04	72.25 2.38	N	Y	1	2.7	Y	WH	F	3.3	1485	Z	−0.16 0.08	−3.10 0.03	−3.46 0.05	S	0.02	−19.28	0.71273	A
1.05	72.52 2.39	N	Y	G	2.7	Y	WH	F	3.3	1486	Z	−0.14 0.08	−3.10 0.03	−3.45 0.05	S	0.02	−19.27	0.71273	A
0.89	73.31 2.43	N	Y	I	2.7	Y	WH	F	3.3	1486	Z	−0.14 0.07	−3.21 0.03	−3.40 0.05	S	0.02	−19.25	0.71273	A
1.48	72.78 2.56	N	Y	G	No	Y	WH	F	3.3	1540	Z	−0.13 0.09	−3.11 0.04	−3.46 0.06	S	0.02	−19.26	0.71273	A
1.26	72.93 2.48	N	Y	G	3.5	Y	WH	F	3.3	1522	Z	−0.17 0.08	−3.09 0.04	−3.47 0.06	S	0.02	−19.26	0.71273	A
1.25	72.97 2.48	N	Y	1	3.5	Y	WH	F	3.3	1520	Z	−0.18 0.08	−3.09 0.04	−3.47 0.06	S	0.02	−19.26	0.71273	A
0.96	73.12 2.44	N	Y	I	3.5	Y	WH	F	3.3	1520	Z	−0.13 0.08	−3.18 0.04	−3.42 0.05	S	0.02	−19.25	0.71273	A
1.26	73.03 2.49	N	Y	G	3.5	Y	WH	F	2.5	1522	Z	−0.18 0.08	−3.08 0.04	−3.47 0.06	S	0.02	−19.26	0.71273	A
1.06	72.20 2.38	N	Y	G	2.7	Y	WH	C	3.3	1486	Z	−0.14 0.08	−3.11 0.03	−3.44 0.06	S	0.02	−19.28	0.71273	A
1.04	72.61 2.39	N	Y	G	2.7	Y	WH	N	3.3	1485	Z	−0.14 0.08	−3.09 0.03	−3.45 0.05	S	0.02	−19.27	0.71273	A
1.06	71.57 2.35	N	N	G	2.7	Y	WH	F	3.3	1485	Z	−0.15 0.08	−3.23 0.02	⋯	S	0.02	−19.30	0.71273	A
1.12	70.99 2.39	N	10	G	2.7	Y	WH	F	3.3	1203	Z	−0.15 0.08	−3.11 0.04	⋯	S	0.02	−19.32	0.71273	A
1.04	71.09 2.35	N	60	G	2.7	Y	WH	F	3.3	1388	Z	−0.23 0.08	−3.25 0.03	⋯	S	0.02	−19.32	0.71273	A
1.11	74.35 2.45	N	Y	G	2.7	Y	H	F	3.3	1470	Z	−0.12 0.07	−2.90 0.03	−3.14 0.06	S	0.02	−19.22	0.71273	A
1.05	72.21 2.38	N	Y	G	2.7	Y	WH	F	3.3	1487	Z	⋯	−3.09 0.03	−3.45 0.05	S	0.02	−19.28	0.71273	A
1.05	72.64 2.39	N	Y	G	2.7	Y	WH	F	3.3	1486	Z	−0.14 0.08	−3.10 0.03	−3.45 0.05	S	0.01	−19.27	0.71347	A
1.06	74.16 2.50	N	Y	G	2.7	Y	WH	F	3.3	1487	Z	−0.10 0.08	−3.11 0.03	−3.44 0.06	M	0.02	−19.18	0.70326	A
1.05	72.90 2.39	N	Y	G	2.7	N	WH	F	3.3	1626	Z	−0.17 0.07	−3.05 0.03	−3.46 0.05	S	0.02	−19.26	0.71273	A
1.05	72.52 2.39	N	Y	G	2.7	Y	WH	F	3.3	1486	B	−0.20 0.11	−3.10 0.03	−3.45 0.05	S	0.02	−19.27	0.71273	A
1.05	72.63 2.43	N	Y	G	2.7	Y	WH	F	3.3	1486	Z	−0.14 0.08	−3.10 0.03	−3.45 0.05	S	0.02	−19.27	0.71340	S
1.06	73.66 2.53	N	Y	G	2.7	Y	WH	F	3.3	1487	Z	−0.10 0.08	−3.11 0.03	−3.44 0.06	M	0.02	−19.18	0.70031	S
1.05	72.80 2.48	N	Y	G	2.7	Y	WH	F	3.3	1486	Z	−0.14 0.08	−3.10 0.03	−3.45 0.05	S	0.01	−19.27	0.71444	L
1.05	73.26 2.52	N	Y	G	2.7	Y	WH	F	3.3	1486	Z	−0.14 0.08	−3.10 0.03	−3.45 0.05	S	0.02	−19.27	0.71719	L
0.92	76.18 2.17	M	Y	1	2.7	Y	WH	F	3.3	2274	Z	−0.18 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.17	0.71273	A
0.93	76.12 2.18	M	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.17	0.71273	A
0.87	74.58 2.08	M	Y	I	2.7	Y	WH	F	3.3	2277	Z	−0.14 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.21	0.71273	A
1.28	76.30 2.55	M	Y	G	No	Y	WH	F	3.3	2342	Z	−0.13 0.08	−3.26 0.02	−3.24 0.02	S	0.02	−19.16	0.71273	A
1.10	76.46 2.37	M	Y	G	3.5	Y	WH	F	3.3	2318	Z	−0.17 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.16	0.71273	A
1.09	76.40 2.36	M	Y	1	3.5	Y	WH	F	3.3	2317	Z	−0.17 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.16	0.71273	A
0.92	74.64 2.13	M	Y	I	3.5	Y	WH	F	3.3	2317	Z	−0.12 0.07	−3.29 0.02	−3.22 0.02	S	0.02	−19.21	0.71273	A
1.10	75.94 2.36	M	Y	G	3.5	Y	WH	F	2.5	2319	Z	−0.17 0.08	−3.25 0.02	−3.24 0.02	S	0.02	−19.17	0.71273	A
0.92	76.27 2.17	M	Y	G	2.7	Y	WH	C	3.3	2276	Z	−0.16 0.07	−3.27 0.02	−3.27 0.02	S	0.02	−19.16	0.71273	A
0.94	76.21 2.20	M	Y	G	2.7	Y	WH	N	3.3	2276	Z	−0.14 0.07	−3.23 0.02	−3.24 0.02	S	0.02	−19.16	0.71273	A
0.93	76.15 2.16	M	N	G	2.7	Y	WH	F	3.3	2277	Z	−0.15 0.07	−3.25 0.01	⋯	S	0.02	−19.17	0.71273	A
1.12	74.42 3.70	M	10	G	2.7	Y	WH	F	3.3	1315	Z	−0.16 0.08	−3.26 0.03	⋯	S	0.02	−19.22	0.71273	A
0.91	76.38 2.15	M	60	G	2.7	Y	WH	F	3.3	2176	Z	−0.23 0.08	−3.25 0.01	⋯	S	0.02	−19.16	0.71273	A
1.06	77.83 2.37	M	Y	G	2.7	Y	H	F	3.3	2238	Z	−0.12 0.07	−3.06 0.02	−3.17 0.02	S	0.02	−19.12	0.71273	A
0.93	75.64 2.16	M	Y	G	2.7	Y	WH	F	3.3	2278	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.18	0.71273	A
0.93	76.25 2.18	M	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.17	0.71347	A
0.94	77.64 2.29	M	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.10 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.08	0.70326	A
0.93	77.84 2.22	M	Y	G	2.7	N	WH	F	3.3	2413	Z	−0.20 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.12	0.71273	A
0.93	77.77 2.41	M	Y	G	2.7	Y	WH	F	3.3	2277	B	−0.23 0.10	−3.25 0.02	−3.25 0.02	S	0.02	−19.12	0.71273	A
0.93	76.24 2.22	M	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.17	0.71340	S
0.94	77.11 2.32	M	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.10 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.08	0.70031	S
0.93	76.42 2.28	M	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.17	0.71444	L
0.93	76.91 2.32	M	Y	G	2.7	Y	WH	F	3.3	2277	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.17	0.71719	L
0.92	72.04 2.56	L	Y	1	2.7	Y	WH	F	3.3	2275	Z	−0.18 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.29	0.71273	A
0.93	72.27 2.58	L	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.28	0.71273	A
0.87	70.97 2.49	L	Y	I	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.32	0.71273	A
1.28	72.58 2.88	L	Y	G	No	Y	WH	F	3.3	2343	Z	−0.13 0.08	−3.25 0.03	−3.24 0.02	S	0.02	−19.27	0.71273	A
1.09	72.30 2.72	L	Y	G	3.5	Y	WH	F	3.3	2319	Z	−0.18 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.28	0.71273	A
1.09	72.28 2.72	L	Y	1	3.5	Y	WH	F	3.3	2318	Z	−0.17 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.28	0.71273	A
0.92	71.09 2.53	L	Y	I	3.5	Y	WH	F	3.3	2318	Z	−0.12 0.07	−3.29 0.02	−3.23 0.02	S	0.02	−19.32	0.71273	A
1.10	71.82 2.71	L	Y	G	3.5	Y	WH	F	2.5	2320	Z	−0.17 0.08	−3.24 0.02	−3.25 0.02	S	0.02	−19.29	0.71273	A
0.91	72.34 2.57	L	Y	G	2.7	Y	WH	C	3.3	2276	Z	−0.17 0.07	−3.27 0.02	−3.27 0.02	S	0.02	−19.28	0.71273	A
0.94	72.31 2.59	L	Y	G	2.7	Y	WH	N	3.3	2276	Z	−0.14 0.07	−3.24 0.02	−3.24 0.02	S	0.02	−19.28	0.71273	A
0.93	72.25 2.57	L	N	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.01	⋯	S	0.02	−19.28	0.71273	A
1.12	72.20 2.75	L	10	G	2.7	Y	WH	F	3.3	1316	Z	−0.16 0.08	−3.26 0.03	⋯	S	0.02	−19.28	0.71273	A
0.91	71.74 2.54	L	60	G	2.7	Y	WH	F	3.3	2178	Z	−0.23 0.08	−3.25 0.01	⋯	S	0.02	−19.30	0.71273	A
1.06	73.82 2.74	L	Y	G	2.7	Y	H	F	3.3	2238	Z	−0.12 0.07	−3.06 0.02	−3.17 0.02	S	0.02	−19.23	0.71273	A
0.93	73.07 2.58	L	Y	G	2.7	Y	WH	F	3.3	2279	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.26	0.71273	A
0.93	72.39 2.58	L	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.28	0.71347	A
0.93	74.05 2.69	L	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.18	0.70326	A
0.93	73.43 2.61	L	Y	G	2.7	N	WH	F	3.3	2414	Z	−0.20 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.25	0.71273	A
0.93	72.93 2.57	L	Y	G	2.7	Y	WH	F	3.3	2278	B	−0.22 0.10	−3.25 0.02	−3.25 0.02	S	0.02	−19.26	0.71273	A
0.93	72.38 2.62	L	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.28	0.71340	S
0.93	73.55 2.71	L	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.11 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.18	0.70031	S
0.93	72.56 2.66	L	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.28	0.71444	L
0.93	73.02 2.70	L	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.28	0.71719	L
0.92	74.50 2.87	All	Y	1	2.7	Y	WH	F	3.3	2275	Z	−0.18 0.07	−3.26 0.02	−3.25 0.02	S	0.02	−19.21	0.71273	A
0.93	74.53 2.89	All	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.21	0.71273	A
0.87	73.00 2.75	All	Y	I	2.7	Y	WH	F	3.3	2278	Z	−0.14 0.07	−3.31 0.02	−3.22 0.02	S	0.02	−19.26	0.71273	A
1.28	74.53 3.39	All	Y	G	No	Y	WH	F	3.3	2343	Z	−0.13 0.08	−3.25 0.03	−3.24 0.02	S	0.02	−19.21	0.71273	A
1.09	74.69 3.14	All	Y	G	3.5	Y	WH	F	3.3	2319	Z	−0.17 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.21	0.71273	A
1.09	74.66 3.14	All	Y	1	3.5	Y	WH	F	3.3	2318	Z	−0.17 0.08	−3.25 0.02	−3.25 0.02	S	0.02	−19.21	0.71273	A
0.92	73.00 2.82	All	Y	I	3.5	Y	WH	F	3.3	2318	Z	−0.12 0.07	−3.29 0.02	−3.23 0.02	S	0.02	−19.26	0.71273	A
1.10	73.38 3.10	All	Y	G	3.5	Y	WH	F	2.5	2320	Z	−0.17 0.08	−3.24 0.02	−3.25 0.02	S	0.02	−19.25	0.71273	A
0.92	77.66 3.00	All	Y	G	2.7	Y	WH	C	3.3	2277	Z	−0.18 0.07	−3.27 0.02	−3.27 0.02	S	0.02	−19.12	0.71273	A
0.94	71.80 2.81	All	Y	G	2.7	Y	WH	N	3.3	2277	Z	−0.14 0.07	−3.23 0.02	−3.24 0.02	S	0.02	−19.29	0.71273	A
0.93	74.50 2.88	All	N	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.01	⋯	S	0.02	−19.21	0.71273	A
1.12	74.40 3.19	All	10	G	2.7	Y	WH	F	3.3	1316	Z	−0.16 0.08	−3.26 0.03	⋯	S	0.02	−19.22	0.71273	A
0.91	74.70 2.86	All	60	G	2.7	Y	WH	F	3.3	2178	Z	−0.23 0.08	−3.25 0.01	⋯	S	0.02	−19.21	0.71273	A
1.06	79.49 3.29	All	Y	G	2.7	Y	H	F	3.3	2239	Z	−0.12 0.07	−3.06 0.02	−3.17 0.02	S	0.02	−19.07	0.71273	A
0.93	74.04 2.87	All	Y	G	2.7	Y	WH	F	3.3	2279	Z	⋯	−3.26 0.02	−3.25 0.02	S	0.02	−19.23	0.71273	A
0.93	74.66 2.89	All	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.21	0.71347	A
0.93	75.97 3.00	All	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.10 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.12	0.70326	A
0.93	75.98 2.94	All	Y	G	2.7	N	WH	F	3.3	2413	Z	−0.19 0.07	−3.21 0.02	−3.26 0.02	S	0.02	−19.17	0.71273	A
0.93	76.11 3.09	All	Y	G	2.7	Y	WH	F	3.3	2278	B	−0.22 0.10	−3.25 0.02	−3.25 0.02	S	0.02	−19.17	0.71273	A
0.93	74.65 2.93	All	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.21	0.71340	S
0.93	75.46 3.02	All	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.10 0.07	−3.26 0.02	−3.25 0.02	M	0.02	−19.12	0.70031	S
0.93	74.83 2.97	All	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.01	−19.21	0.71444	L
0.93	75.30 3.01	All	Y	G	2.7	Y	WH	F	3.3	2278	Z	−0.15 0.07	−3.25 0.02	−3.25 0.02	S	0.02	−19.21	0.71719	L
0.91	71.96 1.47	All	Y	1	2.7	Y	WI	F	3.3	3138	Z	−0.20 0.05	−3.17 0.02	−3.40 0.02	S	0.02	−19.29	0.71273	A
0.91	71.74 1.54	NML	Y	1	2.7	Y	WI	F	3.3	3137	Z	−0.20 0.05	−3.17 0.02	−3.40 0.02	S	0.02	−19.30	0.71273	A
1.09	72.41 2.26	N	Y	1	2.7	Y	WI	F	3.3	2364	Z	−0.19 0.05	−3.08 0.03	−4.14 0.05	S	0.02	−19.28	0.71273	A

Note. H₀: error listed from fit for ${M}_{X}^{0}$ in Equation (9) or ${m}_{x,4258}^{0}$ in Equaiotn (4) only. Anc: Anchors used; N = N4258 Masers, M = MW Parallaxes, L = LMC DEBs, NML = primary fit using all three, All = NML+M31 DEBs. Brk: Break in P–L relation; Y = two-slope solution, N = single-slope solution, 10 = single slope restricted to P > 10 days, 60 = single slope restrcited to P < 60 days. Clp: Clipping procedure; G = global, I = individual, 1 = Global but removing single largest outlier at a time. σ: clipping threshold. Opt: optical completeness required, Y = Yes, N = No. PL: Form of P–L relation used; W_H: NIR Wesenheit; H NIR without extinction correction; W_I: Optical Wesenheit. R: reddening law; F99 = Fitzpatrick (1999), CCM = Cardelli et al. (1989), N = Nataf et al. (2015). R_V: Extinction-law parameter. N: Number of Cepheids fit. Z: Metallicity scale; Z = traditional R₂₃ method (Zaritsky et al. 1994), B = T_e method (Bresolin 2011). γ: change in Wesenheit mag per dex in $\mathrm{log}({\rm{O}}/{\rm{H}})$. b: slope of P–L for all P in no-break variants or for P > 10 days for two-slope variants. bl: slope of P–L for P < 10 days (when applicable). SN: light-curve fitter; S = SALT, M = MLCS2k2. z_m: minimum z used in SN Hubble diagram (0.02 stands for 0.0233). ${M}_{V}^{0}$: SN absolute magnitude (X stands for B or V depending on the SN fitter, see the text). a_X: intercept of SN Hubble diagram (X = B or V). Gal: SN host galaxy sample; A = All, S = Spiral, L = high LSF.

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