H_{0} from a Refurbished Distance Ladder

A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3 1

Abstract

We use the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) to determine the Hubble constant from optical and infrared observations of over 600 Cepheid variables in the host galaxies of 8 recent Type Ia supernovae (SNe Ia), which provide the calibration for a magnitude-redshift relation based on 240 SNe Ia. Increased precision over past measurements of the Hubble constant comes from five improvements: (1) more than doubling the number of infrared observations of Cepheids in the nearby SN hosts; (2) increasing the sample size of ideal SN Ia calibrators from six to eight with the addition of SN 2007af and SN 2007sr; (3) increasing by 20% the number of Cepheids with infrared observations in the megamaser host NGC 4258; (4) reducing the difference in the mean metallicity of the Cepheid comparison samples between NGC 4258 and the SN hosts from to 0.05; and (5) calibrating all optical Cepheid colors with a single camera, WFC3, to remove cross-instrument zeropoint errors. The result is a reduction in the uncertainty in due to steps beyond the first rung of the distance ladder from 3.5% to 2.3%. The measurement of via the geometric distance to NGC 4258 is km s Mpc, a 4.1%  measurement including systematic uncertainties. Better precision independent of the distance to NGC 4258 comes from the use of two alternative Cepheid absolute calibrations: (1) 13 Milky Way Cepheids with trigonometric parallaxes measured with HST/FGS and Hipparcos, and (2) 92 Cepheids in the Large Magellanic Cloud, for which multiple accurate and precise eclipsing binary distances are available yielding km s Mpc, a 3.4%  uncertainty including systematics. Our best estimate uses all three calibrations but a larger uncertainty afforded from any two: km s Mpc including systematic errors, corresponding to a 3.3% uncertainty. The improved measurement of , when combined with the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year data, results in an improved constraint on the equation-of-state parameter of dark energy of . It also rules out the best fitting gigaparsec-scale void models, posited as an alternative to dark energy. The combined + WMAP results also have implications for the number of relativistic particle species in the early Universe, yielding , an excess for the value expected from the three known neutrino flavors, though not with high significance. The distance ladder used here for the determination of does not yet appear to be limited by systematic errors, suggesting that further improvements in precision approaching 1% may be feasible.

galaxies: distances and redshifts — cosmology: observations — cosmology: distance scale — supernovae: general

1 Introduction

Measurements of the expansion history, , from Type Ia supernovae (SNe Ia) provide crucial, empirical constraints to help guide the emerging cosmological model. While high-redshift SNe Ia reveal that the Universe is now accelerating (Riess et al., 1998; Perlmutter et al., 1999), nearby ones provide the most precise measurements of the present expansion rate, .

Recently, high-redshift measurements from the cosmic microwave background radiation (CMB), baryon acoustic oscillations (BAO), and SNe Ia have been used in concert with an assumed cosmological model to predict the value of (e.g., Komatsu et al., 2011). They are not, however, a substitute for its measurement in the local Universe. Such forecasts of from the high-redshift Universe also make specific assumptions about unsettled questions: the nature of dark energy, the global geometry of space, and the basic properties of neutrinos (number and mass). Instead, we can gain insights into these unknowns from a precise, local measurement of . The most precise measurements of have come from distance ladders which calibrate the luminosities of nearby SNe Ia through Hubble Space Telescope (HST) observations of Cepheids in their host galaxies (see Freedman & Madore 2010 for a review).

In the early Cycles of HST, the SN Ia HST Calibration Program (Sandage et al., 2006, hereafter SST) and the HST Key Project (Freedman et al., 2001, hereafter KP) each calibrated via Cepheids and SNe Ia using the Wide Field/Planetary Camera 2 (WFPC2) and the Large Magellanic Cloud (LMC) as the first rung on their distance ladder. Unfortunately, the LMC was not an ideal anchor for the cosmic ladder because its distance was constrained to only 5–10% (Gibson, 2000), its Cepheids (observed from the ground) are of shorter mean period ( d), and lower metallicity () than those of the spiral galaxies hosting nearby SNe Ia. These differences and uncertainties between ground-based and space-based photometric zeropoints introduced a 7% systematic error in the determinations of obtained by those teams (see §4). Additional uncertainty arose from the unreliability of the measurements from several of the SNe Ia selected by SST, which were photographically observed, highly reddened, atypical, or discovered after peak brightness. Only three SNe Ia (SNe 1990N, 1981B, and 1998aq) from the SST sample lacked these shortcomings, defining only a small set of nearby SNe suitable to calibrate . Despite careful work, the teams’ estimates of , each with an uncertainty of %, differed from each other’s by 20%, due to the aforementioned systematic errors. Additional progress required rebuilding the distance ladder to address these systematic errors.

The installation of the Advanced Camera for Surveys (ACS) extended the range of HST for observing Cepheids, reduced their crowding with finer pixel sampling, and increased their rate of discovery by doubling the field of view. In Cycle 11, members of our team began using ACS to measure Cepheids at optical wavelengths in the hosts of more modern SNe Ia (SN 1994ae by Riess et al. 2005; SN 1995al and SN 2002fk by Riess et al. 2009b) and in a more ideal anchor galaxy (NGC 4258 by Macri et al., 2006).

In HST Cycle 15, we began the “Supernovae and for the Equation of State” (SH0ES) project to measure to better than 5% precision by addressing the largest remaining sources of systematic error. The SH0ES program constructed a refurbished distance ladder from high-quality light curves of SNe Ia, a geometric distance to NGC 4258 determined through radio (very long baseline interferometry; VLBI) observations of megamasers, and Cepheid variables observed with HST in NGC 4258 and in the hosts of recent SNe Ia. The reduction in systematic errors came from additional observations of NGC 4258 and from our use of purely differential measurements of the fluxes of Cepheids with similar metallicities and periods throughout all galaxies in our sample. The latter rendered our distance scale insensitive to possible changes in Cepheid luminosities as a function of metallicity or to putative changes in the slope of the period-luminosity relations from galaxy to galaxy. We measured to 4.7% precision (Riess et al., 2009a, hereafter R09), a factor of two better than previous measurements with HST and WFPC2. An alternate analysis using the Benedict et al. (2007) parallax measurements of Milky Way Cepheids in lieu of the megamaser distance to NGC 4258 showed good agreement, with comparable 5.5% precision.

This result formed a triumvirate of constraints in the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year analysis (i.e., BAO + + WMAP-7yr) which were selected as the combination most insensitive to systematic errors with which to constrain the cosmological parameters (Komatsu et al., 2011). Together with the WMAP constraint on , this measurement of provides a constraint on the nature of dark energy, (R09 and Komatsu et al., 2011), which is comparable to but independent of the use of high-redshift SNe Ia. It also improves constraints on the properties of the elusive neutrinos, such as the sum of their masses and the number of species (Komatsu et al., 2011).

In HST Cycle 17 we used the newly installed Wide Field Camera 3 (WFC3) to increase the sample sizes of both the Cepheids and the SN Ia calibrators along the ladder used by SH0ES to determine . The near-infrared (IR) channel of WFC3 provides an order of magnitude improvement in efficiency for follow-up observations of Cepheids over the Near-Infrared Camera and Multi-Object Spectrograph (NICMOS), while the finer pixel scale of the visible channel (relative to ACS) is valuable for reducing the effects of crowding when searching for Cepheids. We present these new observations in §2, the redetermination of in §3, and an analysis of the error budget including systematics in §4. In §5, we address the use of this new measurement along with external datasets to constrain properties of dark energy and neutrinos.

2 WFC3 Observations of Cepheids in the SH0ES Program

The SH0ES program was developed to improve upon the calibration of the luminosity of SNe Ia in order to better measure the Hubble constant. To ensure a reliable calibration sample we selected SNe Ia having the following qualities: (1) modern photometric data (i.e., photoelectric or CCD), (2) observed before maximum brightness, (3) low reddening (implying mag), (4) spectroscopically normal, and (5) optical HST-based observations of Cepheids in its host galaxy. In addition to providing robust distance measures, these qualities are crucial for producing a calibration sample which is a good facsimile of the SN Ia sample they are used to calibrate — i.e., those defining the modern SN Ia magnitude-redshift relation at (e.g., Hicken et al., 2009a).

In HST Cycles 16 and 17, we used WFC3, ACS, and WFPC2 to discover Cepheids in two new SN Ia hosts: NGC 5584 (host of SN 2007af; Macri et al., 2011b) and NGC 4038/9 (“the Antennae,” host of SN 2007sr; Macri et al., 2011c) whose light curves were presented in Hicken et al. (2009a)12. We also employed the optical channel of WFC3 to reobserve all previous SN Ia hosts in the calibration sample and NGC 4258. This provided for the first time a calibration of all Cepheid optical and infrared photometry using the same zeropoints. In the case of some hosts, the additional epoch (obtained well after the prior ones) allowed us to discover previously unidentified, longer period ( d) variables. We also used these observations to search for additional Cepheids in the hosts which previously had the smallest numbers of Cepheids: NGC 3021, NGC 3982, NGC 4536, and NGC 4639 (Macri et al., 2011a). The new observations, together with those from Riess et al. (2009b), Saha et al. (1996, 1997, 2001), Gibson et al. (2000), Stetson & Gibson (2001), and Macri et al. (2006), provide the position, period, and phase of 730 Cepheids in 8 hosts with reliable SN Ia data as well as NGC 4258. The Cepheids in each host were typically imaged on 14 epochs in and 2–5 epochs with (except for NGC 4258, which has 12 epochs of data). An illustration of the entire dataset used to observe the Cepheids is shown in Figure 1. Having previously determined the positions, periods, and optical magnitudes of these Cepheids, it is highly advantageous to observe their near-IR magnitudes with a single photometric system in order to (1) reduce the differential extinction by a factor of five over visual bands, (2) reduce the possible dependence of Cepheid luminosities on chemical composition (Marconi et al., 2005), and (3) negate zeropoint errors. This was previously done with NICMOS on HST in Cycle 15 by R09 for a subset of these Cepheids.

The near-IR channel on WFC3 provides a tremendous gain over NICMOS for the study of extragalactic Cepheids. Photometry of comparable signal-to-noise ratio can be obtained in a quarter of the exposure time. More significant for Cepheid follow-up observations is the factor of 40 increase in area of WFC3-IR over NICMOS/Camera 2 (NIC2), the channel which offered the best compromise between area and uniform pixel sampling. The one advantage of NIC2 over WFC3-IR is better sampling of the point-spread function (PSF); the pixels of WFC3-IR undersample the HST PSF by a factor of 1.6 at 1.6 m. However, the finer sampling of NIC2 is largely offset by the numerous photometric anomalies unique to that camera, whose subsequent correction leads to correlated noise among neighboring pixels which reduces the independence of the NICMOS pixel sampling. In contrast, the detector of WFC3-IR is much better behaved and pixel sampling noise can be mitigated with dithering.

2.1 WFC3 Data Reduction

Each host galaxy was observed for 2–7 ks with individual exposures 400–700 s in length, using integer and half-pixel dithering between exposures to improve sampling of the PSF (see Table 1). The WFC3 images of the two new hosts, NGC 5584 and NGC 4038, are shown in Figures 2 and 3. Figure 4 shows an example of a host previously observed with NIC2 by R09 and with WFC3-IR in this study.

We developed an automated pipeline to calibrate the raw WFC3 frames. The first step was to pass the data through the STScI-supported calwf3 pipeline in the STSDAS suite of routines in PyRAF to remove the bias and dark current, reject cosmic rays through up-the-ramp sampling, and flat-field the data. A small correction to the standard flat-field frame was used to correct the WFC3 “blobs,” which are 10% depressions in flux covering % of the area due to spotting on the WFC3 Channel Select Mechanism (CSM). Next, we used multidrizzle to combine the exposures from each visit into a master image, resampling onto a finer pixel scale while correcting for the known geometric distortions in the camera. We utilized a final pixel scale of per pixel and an input-to-output fraction of 0.6.

We identified the positions of Cepheids in the WFC3-IR images by deriving geometric transformations from the images to those in , successively matching fainter sources to improve the registration. This procedure empirically determined the difference in plate scale between ACS-WFC, WFPC2, WFC3-UVIS, and WFC3-IR. We typically identified more than 100 sources in common, resulting in an uncertainty in the mean position of each Cepheid below 0.03 pixels ( milliarcsec).

We carried out the photometry of Cepheids using the algorithms developed by R09; they employ PSF fitting to model the crowded regions around Cepheids, fixing their positions to those derived from optical data and using artificial-star tests to determine photometric errors and crowding biases. As an example, we show in Figure 5 the HST optical image, near-IR image, model, and residuals for 8 typical Cepheids spanning a wide range of periods in the SN host NGC 5584. We used the same approach to determine zeropoints as in R09 from the Persson et al. (1998) standard star P330E.

Table 1: Hosts Observed with WFC3-IR by GO-11570
Host SN Ia Exp. time (s)
NGC 4536 SN 1981B 2564
NGC 4639 SN 1990N 5377
NGC 3982 SN 1998aq 4016
NGC 3370 SN 1994ae 4374
NGC 3021 SN 1995al 4424
NGC 1309 SN 2002fk 6988
NGC 4038/9 SN 2007sr 6794
NGC 5584 SN 2007af 4926
NGC 4258 ———— 2011
Data in GO-11577
Depth per pointing; galaxy covered in 16 pointing mosaic

Due to the low amplitudes of their near-IR light curves ( mag), Cepheid magnitudes determined at random phases provide nearly the same precision as mean fluxes for determining the intercept of their  relations (Madore & Freedman, 1991).13

Since we had previously observed with NIC2 many of the Cepheids now observed with WFC3-IR, we can directly compare their photometry on these two systems. Figure 6 shows the magnitude differences for the Cepheids utilized in the  relations in both R09 and in §2.2. The mean difference is  mag (in the sense that photometry with WFC3 is brighter), with no apparent dependence on Cepheid brightness. While the difference in photometry between instruments may include differences in system zeropoints, the subsequent determination of via Cepheids observed with a single instrument in the SN Ia hosts and in NGC 4258 will be independent of instrument zeropoints. Thus, for the determination of it is more relevant to calculate the change in magnitudes between Cepheids in NGC 4258 and the SN hosts between WFC3 and NIC2; the measurement of this change is  mag.

Table 2 contains relevant parameters for each Cepheid observed with WFC3 . The first 8 columns give the Cepheid’s host, position, identification number (from Macri et al. 2006, Riess et al. 2009b, Macri et al. 2011b, c, a), period, mean color, WFC3 magnitude, and the magnitude uncertainty. Column 9 contains the displacement of the flux centroid in the near-IR data relative to the optical Cepheid position, expressed in units of pixels (1 pixel ), a quantity used to refine the determination of the crowding bias. Column 10 gives the photometric crowding bias determined using the artificial-star tests for each Cepheid’s environment (see §2.3 of R09) and the displacement tabulated in the previous column; this correction has already been applied to the magnitudes listed in Column 7. Column 11 contains the root-mean square of the residual image, weighted by the inverse distance from the Cepheid position, useful for determining the quality of the crowded-scene fit. Column 12 contains the metallicity parameter, 12 + log [O/H] (Zaritsky et al., 1994) derived from the deprojected galactocentric radii of each Cepheid and the abundance gradient of its host.14 Column 13 contains a rejection flag used for the  relations.

2.2 Near-Infrared Cepheid Relations

The nine individual  relations measured with WFC3 and fit with a common slope are shown in Figure 7. Intercepts relative to NGC 4258 are given in Table 3 and compared in Figure 8 to the SN distances. While 636 Cepheids previously identified at optical wavelengths were measurable15 in the WFC3-IR images, % appeared as outliers in the IR  relations. This is not surprising, as we expect outliers to occur from (1) a complete blend with a bright, red source such as a red giant, (2) a poor model reconstruction of a crowded group when the Cepheid is a small component of the group’s flux, (3) objects misidentified as classical Cepheids in the optical (e.g., blended Type II Cepheids), and (4) Cepheids with the wrong period (aliasing or incomplete sampling of a single cycle). As expected, the outlier fraction is greater in WFC3 images than in NIC2 ones because the former contain a larger fraction of Cepheids from crowded regions (such as the nucleus) which yield more outliers and were intentionally avoided in the small, selective NIC2 pointings (see Figure 4).

As in R09, we eliminated outliers mag or (following Chauvenet’s criterion) from an initial fit of the  relations, refitted the relations and repeated these tests for outliers until convergence. This resulted in a reduction of the sample to 484 objects; the next section considers the effect of this rejection on the determination of and an alternative method for contending with outliers.

3 Measuring the Hubble Constant

The determination of the Hubble constant follows from the relations given in §3 of R09. To summarize, we perform a single, simultaneous fit to all Cepheid and SN Ia data to minimize the statistic and measure the parameters of the distance ladder. We express the jth Cepheid magnitude in the ith host as

(1)

where the “Wesenheit reddening-free” mean magnitude (Madore, 1982) is given as

(2)

and . The Cepheid parameters with subscripts are given in Table 2. For a Cardelli et al. (1989) reddening law, a Galactic-like value of , and the band corresponding to the WFC3 band, we have . In the next section we consider the sensitivity of to the value of .

We determine the values of the nuisance parameters and  — which define the relation between Cepheid period, metallicity, and luminosity — by minimizing the for the global fit to all Cepheid data. The reddening-free distances, , for the hosts relative to NGC 4258 are given by the fit parameters , while is the intercept of the  relation simultaneously fit to the Cepheids of NGC 4258.

The SN Ia magnitudes in the SH0ES hosts are simultaneously expressed as

(3)

where the value is the maximum-light apparent -band brightness of a SN Ia in the ith host at the time of -band peak corrected to the fiducial color and luminosity. This quantity is determined for each SN Ia from its multi-band light curves and a light-curve fitting algorithm, either from the MLCS2k2 (Jha et al., 2007) or the SALT-II (Guy et al., 2005) prescription (see §4.2 for further discussion).

A minor change from R09 is the inclusion of a recently identified, modest relationship between host-galaxy mass and the calibrated SN Ia magnitude. Several studies (Hicken et al., 2009b; Kelly et al., 2010; Lampeitl et al., 2010; Sullivan et al., 2010) have shown the existence of a correlation between the corrected SN magnitude and the mass of its host, with a value of 0.03 mag per dex in , in the sense that more massive (and metal rich) hosts produce more luminous SNe. This correlation has been independently detected using both low- and high-redshift samples of SNe Ia, as well as with multiple fitting algorithms. The effect on is quite small, a decrease of 0.75%, due to the modest difference in mean masses for the nearby hosts (Neill et al., 2009, mean log ) and for those that define the magnitude-redshift relation (Sullivan et al., 2010, mean log ). We include these corrections based on host-galaxy mass in our present determination of , given in Table 3, normalizing to a fiducial host mass of log as appropriate for the objects used to measure the Hubble flow.

Table 3: Distance Parameters
Host SN Ia Filters best
n4536 SN 1981B 15.147 0.145 1.567 (0.0404) 30.91 (0.07)
n4639 SN 1990N 16.040 0.111 2.383 (0.0630) 31.67 (0.08)
n3370 SN 1994ae 16.545 0.101 2.835 (0.0284) 32.13 (0.07)
n3982 SN 1998aq 15.953 0.091 2.475 (0.0460) 31.70 (0.08)
n3021 SN 1995al 16.699 0.113 3.138 (0.0870) 32.27 (0.08)
n1309 SN 2002fk 16.768 0.103 3.276 (0.0491) 32.59 (0.09)
n5584 SN 2007af 16.274 0.122 2.461 (0.0401) 31.72 (0.07)
n4038 SN 2007sr 15.901 0.137 2.396 (0.0567) 31.66 (0.08)
Weighted Mean —– —– —– 0.0417 —— (0.0133) —–
For MLCS2k2, 0.08 mag added in quadrature to fitting error.

The simultaneous fit to all Cepheid and SN Ia data via Equations (1) and (3) results in the determination of , which is the expected reddening-free, fiducial, peak magnitude of a SN Ia appearing in NGC 4258. Lastly, the Hubble constant is determined from

(4)

where is the independent, geometric distance estimate to NGC 4258 obtained through VLBI observations of water megamasers orbiting its central supermassive black hole (Herrnstein et al., 1999; Humphreys et al., 2005; Argon et al., 2007; Humphreys et al., 2008; Greenhill, 2009). The term is the intercept of the SN Ia magnitude-redshift relation, approximately but given for an arbitrary expansion history as

(5)

measured from the set of SN Ia () independent of any absolute (i.e., luminosity or distance) scale. As in R09, we determine from a Hubble diagram for 240 SNe Ia from Hicken et al. (2009a) using MLCS2k2 (Jha et al., 2007) or the SALT-II (Guy et al., 2005) prescription to determine . Limiting the sample to (to avoid the possibility of a local, coherent flow; is the redshift in the rest frame of the CMB) leaves 140 SNe Ia. (In the next section we consider a lower cut of .) Together with the present acceleration and prior deceleration (Riess et al., 2007), we find . Note that Ganeshalingam et al. (2010) recently published light curves of large sample of SNe Ia from the Lick Observatory Supernova Search, but there is a large overlap with those given by Hicken et al. (2009a). There are only 13 SNe Ia at not already included in our sample, and their inclusion would have a negligible impact on the uncertainty in , itself one of the smallest contributors to the error in .

The full statistical error in is the quadrature sum of the uncertainty in the three independent terms in Equation (4): , , and , where is the geometric distance estimate to NGC 4258 by Herrnstein et al. (1999), claimed by Greenhill (2009) to currently have a 3% uncertainty.

Hui & Greene (2006) point out that the peculiar velocities of SN Ia hosts and their correlations can produce an additional systematic error in the determination of the SN Ia relation used for cosmography. However, by making use of a map of the matter density field, it is possible to correct individual SN Ia redshifts for these peculiar flows (Riess et al., 1997). Neill et al. (2007) made use of the IRAS PSCz density field (Branchini et al., 1999) to determine the effect of the density field on the low-redshift SN Ia relation and its impact on the equation-of-state parameter of dark energy, (where is pressure and is energy density). Using their results for a light-to-matter bias parameter and the dipole from Pike & Hudson (2005) results in an increase of the mean velocity of the low-redshift sample and in the Hubble constant by 0.4% over the case of uncorrelated velocities at rest with respect to the CMB. We use a new estimate of this mean peculiar velocity for the Hicken et al. (2009a) SN sample which is a slightly larger value of 0.5%. We account for this and assume an uncertainty of 0.1% resulting from a error in the value of .

The result is km s Mpc, a 4.0%  measurement (top line, Table 4). It is instructive to deconstruct the individual sources of uncertainty to improve our insight into the measurement. In principle, the covariance between the data and parameters does not allow for an exact and independent allocation of propagated error for each term toward the determination of . However, in our case, the diagonal elements of the covariance matrices provide a very good approximation to the individual components of error. These are given in Table 5 and shown in Figure 9 for past and present determinations of .

A number of improvements since R09 are evident by comparing Columns 2 and 3 in Table 5 and as shown in Figure 9. The uncertainty in from all of the terms independent of the megamaser distance to NGC 4258 is 2.3%, 50% smaller than these same terms in R09, a result of the increased sample of Cepheids and SN calibrators. This term includes uncertainties due to the form of the  relation, Cepheid metallicity dependences, photometry bias, and zeropoints — all of which were important systematic uncertainties in past determinations of the Hubble constant (see Column 1, which contains the values from Freedman et al., 2001). In this analysis, as in R09, these uncertainties have been reduced by the collection of samples of Cepheids whose measures (i.e., metallicity, periods, and photometric systems) are a good match between NGC 4258 and the SN hosts. Here the contribution from an unknown dependence of Cepheid luminosity on metallicity has been furthered reduced by 40% owing to a better match between the metallicity of the Cepheid samples in NGC 4258 and the expanded SN host sample. In R09, the mean metallicity of the NGC 4258 Cepheid sample on the ZHK abundance scale was 12 + log [O/H] =8.91, nearly the same as the present mean of 8.90. However, the mean metallicity of the Cepheid sample in the SN hosts has risen from 8.81 to 8.85. Some of this change can be attributed to the inclusion of Cepheids closer to the nuclei of the hosts and some to the inclusion of two new hosts, NGC 5584 and NGC 4038/9, with higher-than-average metallicities. The reduction in the mean abundance difference between NGC 4258 and the SN Ia hosts from 0.077 to 0.045 dex results in a decrease of the error propagated into from 1.1% to 0.6%. A similar reduction is seen with the use of Milky Way Cepheids whose mean metallicity of 8.9 is closer to the mean of the new Cepheid sample in the SN hosts. We consider an alternative calibration of abundances from Bresolin (2011) in §4.1.

3.1 Buttressing the First Rung

In our present determination of , the 3% uncertainty in the distance to NGC 4258 claimed by Greenhill (2009) is now greater than all other sources combined (in quadrature). The next largest term, the uncertainty in mean magnitude of the eight nearby SNe Ia, is 1.9%. To significantly improve upon our determination of , we would need an independent calibration of the first rung of the distance ladder as good as or better than the megamaser-based measurement to NGC 4258 in terms of precision and reliability. Independent calibration of the first rung is also valuable as an alternative to NGC 4258, should future analyses reveal previously unidentified systematic errors affecting its distance measurement.

A powerful alternative has recently become available through high signal-to-noise ratio measurements of the trigonometric parallaxes of Milky Way Cepheids using the Fine Guidance Sensor (FGS) on HST. Benedict et al. (2007) reported parallax measurements for 10 Cepheids, with mean individual precision of 8% and an error in the mean of the sample of 2.5%. These were used in R09 as a test of the distance scale provided by NGC 4258, but the improvement in precision beyond the first rung in the previous section suggests greater value in their use to enhance the calibration of the first rung.

van Leeuwen et al. (2007) reanalyzed Hipparcos observations and determined independent parallax measurements for the same 10 Cepheids (albeit with half the precision of HST/FGS) and for 3 additional Cepheids (excluding Polaris which is an overtone pulsator and whose estimated fundamental period is an outlier among the Cepheids pulsing in the fundamental mode). The resulting sample can be considered an independent anchor with a mean, nominal uncertainty of just 1.7%. We use the combined parallaxes tabulated by van Leeuwen et al. (2007) and their -band photometry as an alternative to the Cepheid sample of NGC 4258 by replacing Equation (1) for the Cepheids in the hosts of SNe Ia with

(6)

where is the absolute Wesenheit magnitude for a Cepheid with  d, and simultaneously fitting the Milky Way Cepheids with the relation

(7)

Equation (3) for the SNe Ia is replaced with

(8)

The determination of for SNe Ia together with the previous term then determines the Hubble constant,

(9)

Since the near-IR magnitudes of these Milky Way Cepheids have not been directly measured with WFC3, the use of these variables requires an additional allowance for possible differences in their photometry. These may arise from differences in instrumental zeropoints, crowding, filter transmission functions, and detector well depth at which the sources are measured together with an uncertainty in detector linearity. Analysis of the absolute photometry from WFC3-IR (Kalirai et al., 2009) and the ground system (e.g., 2MASS; Skrutskie et al. 2006) claim absolute precision of 2%–3%. We therefore assume a systematic uncertainty in the relative magnitudes between HST WFC3 Cepheid photometry and the ground-based measurements of Milky Way Cepheids on the -band system of Persson et al. (1998) of 4%. This reduces the effective precision of the parallax distance scale from 1.7% to 2.6%. The ground-based photometry of these Milky Way Cepheids is tabulated by Groenewegen (1999) and R09. This systematic error is included in the global fit as an additional calibration equation with uncertainty given in the error correlation matrix.

When using the Milky Way Cepheids, we now include an external constraint on the slope of the near-IR  relation. No such constraint was necessary or even of significant value in the previous section because the Cepheid periods in NGC 4258 (mean log ) are so similar to those in the SN Ia host (mean log ). In contrast, the mean period of the Milky Way sample (mean log ) is substantially lower, giving an unconstrained slope of the  relation a greater and unrealistically large lever arm. Following analyses of optical and near-IR Cepheid data in the Milky Way (Fouqué et al., 2007) and the LMC (Persson et al., 2004; Udalski et al., 1999), we adopt a conservative constraint on the slope of the Wesenheit relation of  mag per dex in log .

Using the Milky Way Cepheids instead of NGC 4258 as the first rung of the distance ladder gives km s Mpc, in good agreement with (and even greater precision than) the NGC 4258-based value. However, an overall improvement in precision is realized by the simultaneous use of both the Milky Way parallaxes and the megamaser-based distance to NGC 4258, yielding km s Mpc, a remarkably small uncertainty of 3.0% .

Another opportunity to improve upon the first rung on the distance ladder comes from the sample of -band observations of Cepheids in the LMC by Persson et al. (2004). Recent studies of detached eclipsing binaries (DEBs) by different groups provide claims of a reliable and precise distance to the LMC. Guinan et al. (1998), Fitzpatrick et al. (2002), and Ribas et al. (2002) studied three B-type systems (HV2274, HV982, EROS1044) which lie close to the bar of the LMC and therefore provide a good match to the Cepheid sample of Persson et al. (2004). The error-weighted mean of these is kpc16. Pietrzyński et al. (2009) analyzed OGLE-051019.64-685812.3, an eclipsing binary system comprised of two giant G-type stars also located near the barycenter of the LMC, and found a distance of kpc. The average result, 49.8 kpc, provides a good estimate of the distance to the LMC17. Here we retain the larger of the two previous uncertainties to estimate the distance modulus as  mag, or an effective error of  mag when including the aforementioned 0.04 mag uncertainty between the ground-based and HST-based near-IR photometric systems. Using this distance to the LMC and the Cepheid sample of Persson et al. (2004) yields km s Mpc, as seen in Table 4.

Combining all three first rungs (Milky Way, Large Magellanic Cloud, and NGC 4258) provides the most precise measurement of : km s Mpc, a slightly smaller uncertainty of 2.9% . As expected, the use of all three anchors for the distance ladder instead of just one has the largest impact on the overall uncertainty, reducing the total contribution of the first rung to the error from 3.3% to 1.5%. However, a substantial penalty is paid for the mixing of ground-based and space-based photometric systems and the resultant uncertainties in Wesenheit or dereddened magnitudes, adding a 1.4% error to where for NGC 4258 alone none pertained. Modest increases in error also result from the larger difference in mean Cepheid metallicity (LMC) and period (LMC and Milky Way).

Past determinations of the absolute distance scale have had a checkered history, with revisions common. Thus, it may be prudent to rely on no more than any two of the three possible anchors of the distance scale in the determination of . The omission of NGC 4258, Milky Way parallaxes, or the LMC yields a precision in of 3.3%, 3.2%, and 3.0%, respectively. We thus adopt as our best determination km s Mpc, the measurement from all three sources of the distance scale, but with the larger error associated from only two independent origins of the distance scale.

Should future work revise the distance to any one of the absolute distance scale determinations, we provide the following recalibration: decreases by 0.25, 0.30, and 0.14 km s Mpc for each increase of 1% in the distance to either NGC 4258, the Milky Way parallax scale, or the distance to the LMC.

In the last column of Table 3 we also give the best estimate of the distance to each host from the global fit to all first rungs, Cepheid and SN data. These are useful to compare to alternative methods of measuring distances to these hosts or to place a sample of relative measures of SNe Ia distances onto an absolute scale. For example, there has been recent dissagreement on the distance modulus of the Antennae (NGC 4038/9); Saviane et al. (2008) claim a value of =30.62  mag based on the apparent tip of the red giant branch (TRGB), while Schweizer et al. (2008) obtain  mag from SN 2007sr and  mag from a different determination of the TRGB, in agreement with previous estimates by Whitmore et al. (1999) and Tonry et al. (2000) based on flow-field models. Our result of  mag (with the uncertainty based on the global fit) strongly favors the “long” distance to the Antennae.

Although we have been careful to propagate our statistical errors, as well as past sources of systematic error such as metallicity dependence, system zeropoint, and instrumental uncertainties, we now consider a broader range of systematic uncertainties relating to alternative approaches to the analysis of the data.

4 Analysis Systematics

In the preceding section we presented our preferred approach to analyzing the Cepheid and SN Ia data, incorporating uncertainties within the framework used to model the data. Here we follow the same approach used by R09 to quantify the systematic uncertainty in the determination of , by measuring the impact of a number of variants in the modeling of the Cepheid and SN Ia data.

In Table 4 we show 15 variants of the previously described analysis for every combination of choices of distance anchors (NGC 4258, Milky Way, or LMC), any two of the preceding or all three; these amount to a total of 105 combinations. Our primary analysis for any anchor choice is given in the first row (shown in bold) for which that choice initially appears. Column (1) gives the value of , Column (2) the number of Cepheids in the fit, Column (3) the value and total uncertainty in , and Column (4) whether the near-IR data for Cepheids with periods shorter than the completeness limit from the optical selection were included. Column (5) gives the SN Ia magnitude-redshift intercept parameter, Column (6) gives the determination of which is specific to the light-curve fitter employed, Column (7) the calibration system for the metal abundances Column (8) the value and uncertainty in the metallicity dependence, and Column (9) the value and uncertainty of the slope of the Cepheid  or relation. Column (10) gives the minimum SN Ia redshift used to define the relation, Column (11) encodes aspects of the SN fitting routine and assumptions therein addressed below, and Column (12) is the choice of anchors to set the distance scale. Column (13) gives the type of  relation employed, either Wesenheit () or -band only. Column (14) is the reddening law value used for the Cepheids. Column (15) lists the filters allowed for fitting the SN Ia light curves and column (16) gives the value of used to fit the SN light curves.

4.1 Cepheid Systematics

In the preceding analysis of the Cepheid data, differences in the determination of may result from the following variants in the primary analysis: (1) retention of Cepheids with periods below the optical incompleteness limit; (2) not allowing for a metallicity dependence; (3) changing the Cepheid reddening law from to ; (4) using only near-IR magnitudes without reddening corrections; (5) no rejection of outliers in the  relations; and (6) a change in the calibration of chemical abundances. Each of these changes was implemented as a variant of the primary analysis with results given in Table 4. The rationale for the primary analysis over each variant was discussed in detail in §4 of R09, with the exception of (6) which is discussed below.

Taken individually, these variants result in rising or declining by km s Mpc, which is less than half of the statistical uncertainty. A variant resulting in a larger change occurs when we do not reject Cepheids which are outliers on the  relation, raising by 1.3 km s Mpc. However, the value of also triples, with a total increase in of 6 per rejected outlier. As we expect outliers a priori to arise from blending or misidentification of Cepheids (type or period), resulting in residuals in excess of the typical uncertainty, we believe it is most sensible to reject them to minimize their impact on the global solution. The use of higher or lower thresholds for outlier rejection has even less impact than including all outliers. Lowering the outlier threshold to (and its accompanying residual magnitude) reduces by 0.1 km s Mpc. Raising the threshold to or reduces by 1.0 or 0.8 km s Mpc, respectively. Neglecting a reddening correction for the Cepheids also raises by 1.3 km s Mpc but we believe this correction is warranted.

As an alternative to rejecting outliers we also considered the approach of simultaneously modeling the distribution of Cepheids and the outliers. Following Kunz et al. (2007) we allowed for a nuisance population of sources along the  relation characterized by a broader distribution ( mag) and an intercept independent from that of classical Cepheids. The a posteri likelihood function for the intercepts of the Cepheid hosts was then compared to that derived from outlier rejection. The mean zeropoint of the SN hosts is greater by 0.013 0.012 mag. The mean uncertainty of the intercepts are a factor of 1.38 greater than those from outlier rejection but still small compared to the distance precision of each SN. The only difference of note (i.e., mag) was for the intercept of NGC 4536 which was greater by mag in the outlier modeling over the use of rejection.

The chemical abundance values for the Cepheids used in R09 and here were estimated from nebular lines in H ii regions of the Cepheid hosts using the R parameter and the transformation to an oxygen abundance following Zaritsky et al. (1994, hereafter ZKH). There are several alternative calibrations of the transformation from R to (e.g. McGaugh, 1991; Pilyugin & Thuan, 2005), but these primarily affect the absolute normalization of the metallicity scale and do not alter the relative host-to-host differences in abundance or the determination of . Recently, Bresolin (2011) has redetermined the abundance gradient of NGC 4258 by adopting the Pilyugin & Thuan (2005) calibration of R. This calibration yields abundances that are consistent with those determined directly by Bresolin (2011) in 4 H ii regions in the outer disk of NGC 4258, measuring the electron temperature () via the auroral line [O iii] 4363. Given this agreement, Bresolin (2011) suggests the adoption of a so-called “T scale” for the determination of absolute chemical abundances of extragalactic Cepheids.

The T recalibration of nebular oxygen abundances not only reduces the values of by 0.4 dex at the metal-rich end but also compresses the abundance scale by a factor of 0.69. Based on this scale and consistent atomic data, Bresolin (2011) finds a nebular oxygen abundance for the LMC of , moderately lower than the “canonical” value of 8.5 in the ZKH scale. On the T scale, the mean apparent metallicity of the SN Ia and maser hosts would be ; this is closer to the LMC Cepheids than to the Milky Way Cepheids and a departure from the ZKH scale. While the abundances of Milky Way Cepheids are not measured the same way (i.e., they are based on stellar absorption lines rather than on nearby ionized gas), they have been directly measured to be 0.3 dex higher than those of LMC Cepheids (Andrievsky et al., 2002; Romaniello et al., 2008). The resulting estimate of 8.66 for the MW Cepheids on the T scale would agree well with recent estimates of the solar oxygen abundance of 8.69 (Asplund et al., 2009) together with a small gradient in metallicity away from the solar neighborhood. This LMC to MW Cepheid abundance difference of 0.3 dex also agrees well with the T scale compression of the 0.4 dex difference on the ZKH scale for which the value for MW Cepheids was taken (here and in R09) to be 8.9.

We determined the effect on of a change from the ZKH scale to the T scale by transforming the values of 12+log using equation (3) of Bresolin (2011) and assigning values of 8.36 and 8.66 to LMC and MW Cepheids, respectively. As seen in Table 4, the value of increases by 0.4 km s Mpc when using all 3 calibrators and increases by less than 1.0 km s Mpc for any combination of 2 calibrators. The biggest change, an increase of 2.0 km s Mpc, occurs when only the MW is used to calibrate the first rung, a direct consequence of the increase of the metallicity difference between the SN Ia host and MW Cepheids on the T scale. In the presence of uncertainties concerning the appropriate values of Cepheid abundances, the determination of based on infrared observations of Cepheids should be significantly less sensitive to metallicity differences than optical Cepheid data (Marconi et al., 2005). Indeed, the metallicity correction empirically determined here, mag/dex (using all 3 calibrations) is less than half the value of mag/dex measured at optical wavelengths (Kennicutt et al., 1998; Sakai et al., 2004) and its absolute value is not significant. A better determination of the difference in metallicity between MW and extragalactic Cepheids may not occur until the launch of JWST.

4.2 SN Systematics

Here we consider the following variants in the analysis of the SN Ia data: (1) minimum range of SN Ia relation lowered from to , (2) discarding -band SN Ia light-curve data (fit 61), (3) SN Ia reddening parameter (fits 29, 28, and 20), (4) use of a SN Ia luminosity-color correction with no prior (i.e., as in the parameter of SALT II instead of an extinction parameter, , in MLCS2k2) (fit 26), (5) a host-galaxy extinction likelihood prior from galaxy simulations (fit 27), and (6) use of the SALT-II light-curve fitter (fit 42). The motivation for these variants is described in greater detail in R09.

As seen in Table 4, none of these variants taken individually alters the value of by more than km s Mpc from the preferred solution, less than half the statistical uncertainty. One of the more noteworthy variants is the use of the SALT-II light-curve fitter (Guy et al., 2005) in lieu of MLCS2k2, since the result of this change can be substantial for high-redshift data (Kessler et al., 2009). Observations of high-redshift SNe Ia typically have lower signal-to-noise ratios, and thus place greater reliance on fitters and on the assumptions they include (e.g., the relation between SN Ia color and distance). In contrast, the determination of is quite insensitive to the fitter; the use of SALT-II results in an increase in of 1 km s Mpc.

The dispersion of the 15 different determinations of is 0.7 or 0.8 km s Mpc for any selected pair of sources of the absolute distance scale. Adding this measure of analysis systematics to the previous yields km s Mpc, a 3.3%  uncertainty, our best determination.

Table 5: Error Budget for Cepheid and SN Ia Distance Ladders
Term Description Previous R09 Here Here
LMC N4258 N4258 All 3
Anchor distance 5% 3% 3% 1.3%
Mean of  in anchor 2.5% 1.5% 1.4% 0.7%
Mean of  values in SN hosts 1.5% 1.5% 0.6 % 0.6%
Mean of SN Ia calibrators 2.5% 2.5% 1.9% 1.9%
SN Ia relation 1% 0.5% 0.5% 0.5%
Cepheid reddening, zeropoints, anchor-to-hosts 4.5% 0.3% 0.0% 1.4%
Cepheid metallicity, anchor-to-hosts 3% 1.1% 0.6 % 1.0%
 slope, log , anchor-to-hosts 4% 0.5% 0.4% 0.6%
WFPC2 CTE, long-short 3% 0% 0% 0%
subtotal, 10% 4.7 % 4.0% 2.9%
Analysis Systematics NA 1.3% 1.0% 1.0%
Total, 10% 4.8 % 4.1% 3.1%
For Milky Way parallax, this term is already included with the term above.
  with Equations 1, 3, 7, and 8.
Derived from diagonal elements of the covariance matrix propagated via the error matrices associated

5 Dark Energy and Neutrinos

An independent and precise measurement of is an important complement to the determination of cosmological model parameters. Alternatively, it serves as a powerful test of model-constrained measurements at higher redshifts. It is beyond the scope of this paper to provide a complete analysis of the impact of the measurement of on the cosmological model from all extant data. We encourage others to do so. However, one such example using the present measurement of can be illustrative.

Making use of the simplest present hypothesis for the cosmological model (namely -cold-dark-matter without curvature, exotic neutrino physics, or specific early-Universe physics), and using the single most powerful cosmological data set (the 7-year WMAP results from Komatsu et al. 2011), results in a predicted value of km s Mpc. This value agrees well with our determination of km s Mpcat better than the combined 1 confidence level.

Alternatively, we can use the WMAP data together with the measured value of to constrain added complexity to the model. In Figure 10 we show the use of this data combination for constraining a redshift-independent dark energy equation-of-state parameter (), the number of relativistic species (e.g., neutrino number), and the sum of neutrino masses. The result for dark energy is , about 20% more precise than the same result derived from the determination of in R09. If we had perfect knowledge of the CMB, our overall 30% increase in the precision of would yield the same-sized improvement in the determination of . However, the fractional uncertainty in from the WMAP 7-year analysis is comparable to our measurement of ; thus, greater precision in may still be wrung from future higher-precision measurements of the CMB by WMAP or Planck.

The enhanced precision in measuring also provides a strong rebuff to recent attempts to explain accelerated expansion without dark energy but rather by our presence in the center of a massive void of gigaparsec scale. Already such models are hard to fathom as they require an exotic location for the observer, at the center of the void to within a part in a million (Blomqvist & Mörtsell, 2010) to avoid an excess dipole in the CMB. It is also not yet apparent if such a model is consistent with other observables of the CMB or the late-time integrated Sachs-Wolfe effect. However, using measurements of to constrain void models of the Lemaitre, Tolmon, and Bondi variety already predicts slower-than-observed local expansion with values of =60 (Nadathur & Sarkar, 2010) or 62 (Wiltshire, 2007) km s Mpc, more than 5 below our measurement.

Comparable improvements to cosmological constraints on relativistic species are also realized from R09, as shown in Figure 10. Most interesting may be the effective number of relativistic species, , which is nominally higher than the value of 3.046 expected from the three known neutrino species plus tau-neutrino heating from collisions (Mangano & Serpico, 2005). While this nominal excess of relativistic species has been noted previously (Reid et al., 2010; Komatsu et al., 2011; Dunkley et al., 2010, e.g.,), and even interpreted as a possible indication of the presence of a sterile neutrino (Hamann et al., 2010), we caution that the cosmological model provides other avenues for reducing the significance of this result including additional degrees of freedom for curvature, dark energy, primordial helium abundance, and neutrino masses. The 30% improvement in the present constraint on combined with improved high resolution CMB data (e.g., Dunkley et al. (2010)) and ultimately with Planck satellite CMB data should reduce the present uncertainty in by a factor of 3 which may provide a more definitive conclusion on the presence of excess radiation in the early Universe.

6 Discussion

Examination of the complete error budget for in the last two columns of Table 5 indicates additional approaches for improved precision in future measurements of . Expanding the sample of well-measured parallaxes to Milky Way Cepheids (especially those at log ) with the GAIA satellite could drive the precision of the first rung of the distance ladder well under 1%. However, as we have found with the “baker’s dozen” of present Milky Way parallaxes, much of this precision would be lost without better cross-calibration between the space and ground photometric systems used to measure Cepheids, near and far.

The largest remaining term comes from the quite limited sample of ideal SN Ia calibrators, just 8 objects. The occurrence of an ideal SN Ia in the small volume within which HST can measure Cepheids ( Mpc) is rare, on average only once every 2–3 yr. Given the recent proliferation of SN surveys and instances of multiple, independent discoveries, we are confident that all such SNe Ia within this volume are being found. Collecting more will require extending the range of Cepheid measurements — without introducing new systematics — and patience. The forthcoming James Webb Space Telescope (JWST) offers a promising route to extend Cepheid observations out to 50 Mpc and to redder wavelengths, where uncertainties due to possible variations in the extinction law and the dependence of Cepheid luminosities on metallicity are further reduced. This extension would increase the SN sample suitable for calibration by a factor of , reaching ideal SNe Ia observed over the past 20 yr. Based on a 5% distance precision per ideal SN, such a sample would enable a determination of to better than 1%. However, discovering these Cepheids may require imaging at optical wavelengths where the amplitude of the variations is significant, a requirement which will challenge the short-wavelength capabilities of JWST.

7 Summary and Conclusions

We have improved upon the precision of the measurement of from Riess et al. (2009a) by (1) more than doubling the sample of Cepheids observed in the near-IR in SN Ia host galaxies, (2) expanding the SN Ia sample from 6 to 8 with the addition of SN 2007af and SN 2007sr, (3) increasing the sample of Cepheids observed in NGC 4258 by 20%, (4) reducing the difference in metallicity for the observed sample of Cepheids between the calibrator and the SN hosts, and (5) calibrating all optical Cepheid colors with WFC3 to remove cross-instrument zeropoint errors. Further improvements to the precision and reliability of the measurement of come from the use of additional sources of calibration for the first rung, foremost of these are the trigonometric parallaxex of 13 Cepheids in the Milky Way.

Our primary analysis gives km s Mpc including systematic errors determined from varying assumptions and priors used in the analysis. The combination of this result alone with the WMAP 7-year constraints yields and improves constraints on a possible but still uncertain excess in relativistic species above the number of known neutrino flavors. The measured is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the Universe without dark energy. Given that statistical errors still dominate over systematic errors, future work is likely to further improve the precision of the determination of .


We are grateful to William Januszewski for his help in executing this program on HST. We are indebted to Mike Hudson for assisting with the peculiar-velocity calculations from the PSCz survey, to David Larson for contributions to the WMAP MCMC analysis, to Daniel Scolnic for donating some useful routines, and to Mark Huber for an analysis of pre-discovery observations of SN 2007sr. We thank Chris Kochanek and Kris Stanek for their support of GO-11570. Financial support for this work was provided by NASA through programs GO-11570 and GO-10802 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. A.V.F.’s supernova group at U. C. Berkeley is also supported by NSF grant AST–0607485 and by the TABASGO Foundation. L.M.M. acknowledges support from a Texas A&M University faculty startup fund. The metallicity measurements for NGC 5584 and NGC 4038/9 presented herein were obtained with the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA; the observatory was made possible by the generous financial support of the W. M. Keck Foundation.

Figure Captions

Figure 1: HST observations of the host galaxies used to measure . The data employed to observe Cepheids in 8 SN Ia hosts and NGC 4258 have been collected over 15 yr with 4 cameras over orbits of HST time. Two-month long campaigns in and were initially used to discover Cepheids from their light curves. Subsequent follow-up observations in enabled the discovery of Cepheids with  d. Near-IR follow-up data have been used to reduce the effects of host-galaxy extinction and sensitivity to metallicity.

Figure 2: HST images of NGC 5584. The positions of Cepheids with periods in the range  d,  d, and  d are indicated by red, blue, and green circles, respectively. A yellow circle indicates the position of the host galaxy’s SN Ia. The orientation is indicated by the compass rose whose vectors have lengths of 15. The black and white regions of the images show the WFC3 optical data and the color includes the WFC3-IR data.

Figure 3. As in Figure 2, for NGC 4038/4039.

Figure 4: HST WFC3- image of NGC 3370. Upper panel: The positions of Cepheids with periods in the range  d,  d, and  d are indicated by red, blue, and green circles, respectively. A yellow circle indicates the position of the host galaxy’s SN Ia. The orientation is indicated by the compass rose whose vectors have lengths of 15. The fields of view for the NIC2 follow-up fields from Riess et al. (2009a) are indicated. Lower Panel: close-up showing the field of NGC3370-blue as observed with WFC3-IR (left) and with 4.7 times more exposure time with NIC2 (right).

Figure 5: Example of scene modeling for the surrounding typical short, medium, and long-period Cepheids in one WFC3 field, NGC 5584. For each Cepheid, the stamp on the left shows the region around the Cepheid, the middle stamp shows the model of the stellar sources, and the right stamp is the residual of the image minus the model. The position of the Cepheid as determined from the optical data is indicated by the circle.

Figure 6: WFC3-IR versus NIC2 Cepheid photometry. Some of the apparent dispersion results from the random phases of the Cepheids observed with WFC3.

Figure 7: Near-IR Cepheid period-luminosity relations. For the 8 SN Ia hosts and the distance-scale anchor, NGC 4258, the Cepheid magnitudes are from the same instrument and filter combination, WFC3 . This uniformity allows for a significant reduction in systematic error when utilizing the difference in these relations along the distance ladder. The measured metallicity for all of the Cepheids is comparable to solar (log [O/H] ). A single slope has been fit to the relations and is shown as the solid line. 20% of the objects were outliers from the relations (open diamonds) and are flagged as such for the subsequent analysis. Filled points with asterisks indicate Cepheids whose periods are shorter than the incompleteness limit identified from their optical detection.

Figure 8: Relative distances from Cepheids and SNe Ia. The bottom abscissa shows the peak apparent visual magnitude of each SN Ia (red points) corrected for reddening and to the fiducial brightness (using the luminosity vs. light-curve shape relations), . The top abscissa includes the intercept of the –log  relation for SNe Ia, to provide SN Ia distance measures, , quantities which are independent of the choice of a fiducial SN Ia. The right-hand ordinate shows the relative distances between the hosts determined from the Cepheid Wesenheit relations. The left ordinate shows the same thing, with the addition of the independent geometric distance to NGC 4258 (blue point) based on its circumnuclear megamasers. The contribution of the nearby SN Ia and Cepheid data to can be expressed as a determination of , the theoretical mean of 8 fiducial SNe Ia in NGC 4258.

Figure 9: Uncertainties in the determination of the Hubble constant. Uncertainties are squared to show their contribution to the quadrature sum. These terms are given in Table 5.

Figure 10: Confidence regions in the plane of and the equation-of-state parameter of dark energy, and neutrino properties. The localization of the third acoustic peak in the WMAP 7-year data (Komatsu et al., 2011) produces a confidence region which is narrow but highly degenerate with the dark energy equation of state (upper panel). The improved measurement of , km s Mpc, from the SH0ES program is complementary to the WMAP constraint, resulting in a determination of assuming a constant . This result is comparable in precision to determinations of from baryon acoustic oscillations and high-redshift SNe Ia, but is independent of both. The inner regions are 68% confidence and the outer regions are 95% confidence. The modest tilt of the SH0ES measurement of 0.2% in for a change in of 0.1 shown as the dotted lines in the upper panel, results from the mild dependence of on , corresponding to the change in for changes from at the mean SN rdshift of . The measurement of is made at (i.e., ). Constraints on the mass and number of relativisitic species (e.g., neutrinos) are shown in the middle and lower panels, respectively.

Field Id P Offset Bias IM [O/H] Flag
(J2000) (J2000) (days) (mag) (mag) (mag) (pix) (mag)
n4536 188.590 2.16830 27185 13.00 0.97 24.91 0.31 1.64 0.13 2.16 8.54
n4536 188.604 2.18312 42353 13.07 0.73 26.29 0.74 3.32 0.37 4.30 8.97 rej
n4536 188.584 2.18070 50718 13.73 0.88 24.51 0.42 0.88 0.28 11.4 8.64
n4536 188.583 2.19700 72331 13.91 0.89 24.84 0.44 0.07 0.22 1.40 8.81
n4536 188.590 2.19545 65694 14.38 0.98 25.26 0.38 2.91 0.39 30.8 8.90
n4536 188.587 2.18864 58805 14.44 1.13 23.41 0.35 3.94 0.26 47.9 8.78 rej
n4536 188.586 2.18406 53703 14.53 0.72 25.38 0.47 0.63 0.27 14.9 8.72
n4536 188.592 2.20025 70938 14.62 0.64 25.81 0.58 2.39 0.30 17.4 8.94 rej
n4536 188.594 2.17693 40098 14.64 0.95 25.12 0.52 4.40 0.63 12.9 8.72
n4536 188.597 2.18489 48539 15.03 0.90 23.53 0.31 0.46 0.29 7.28 8.89 rej
n4536 188.590 2.19521 65695 15.16 1.03 24.49 0.41 1.45 0.26 19.3 8.89
n4536 188.584 2.19350 66974 15.65 1.13 23.43 0.44 0.85 0.56 71.9 8.79 rej
n4536 188.588 2.19589 67328 16.24 0.82 23.98 0.32 0.76 0.24 30.2 8.87
n4536 188.593 2.20097 71258 17.02 0.82 24.01 0.27 0.70 0.22 23.5 8.95
n4536 188.603 2.20339 68306 17.16 0.63 24.72 0.19 1.03 0.05 8.53 8.97
n4536 188.590 2.17853 45164 17.31 0.93 24.72 0.56 1.80 0.43 7.22 8.69
n4536 188.590 2.18273 50050 17.56 1.06 23.58 0.26 0.69 0.29 7.02 8.75 rej
n4536 188.592 2.19544 64661 17.65 0.94 24.29 0.30 4.48 0.19 15.0 8.92
n4536 188.585 2.17323 40923 18.16 1.06 23.95 0.24 0.38 0.01 18.9 8.53
n4536 188.578 2.19021 66029 18.39 0.67 24.72 0.24 1.40 0.13 8.38 8.67
n4536 188.573 2.19417 75137 18.67 0.90 24.45 0.22 0.40 0.05 8.95 8.63
n4536 188.589 2.17226 35584 18.89 0.60 25.24 0.36 1.13 0.16 0.90 8.58 rej
n4536 188.585 2.18952 60991 19.01 0.49 24.60 0.47 4.48 0.44 45.4 8.77
n4536 188.589 2.20092 74017 19.31 0.85 25.22 0.50 0.34 0.37 19.2 8.91 rej
n4536 188.589 2.17081 33174 19.47 0.67 24.58 0.25 0.95 0.13 9.05 8.55
n4536 188.587 2.17317 38963 19.60 1.04 24.38 0.26 0.69 0.11 2.62 8.57
n4536 188.590 2.17361 37037 19.65 0.85 24.37 0.25 2.89 0.21 16.2 8.62
n4536 188.576 2.18837 65214 19.69 0.75 24.13 0.23 0.18 0.11 14.9 8.61
n4536 188.598 2.19878 65080 19.98 0.76 24.76 0.25 0.70 0.16 20.3 9.01
n4536 188.576 2.19187 69821 20.41 0.92 24.43 0.21 0.69 0.06 20.9 8.65
n4536 188.590 2.19151 60845 21.26 0.75 23.93 0.29 0.83 0.14 13.6 8.86
n4536 188.596 2.17595 36586 21.29 0.95 25.16 0.61 3.13 0.48 8.65 8.74 rej
n4536 188.597 2.18182 45000 21.58 0.90 24.39 0.35 1.71 0.35 5.02 8.85
n4536 188.588 2.18875 58232 21.94 0.89 24.34 0.25 3.15 0.24 11.1 8.80
n4536 188.592 2.18304 49022 22.66 0.95 24.97 0.62 3.44 0.05 3.38 8.79
n4536 188.586 2.18894 60060 22.68 1.11 24.80 0.47 3.15 0.36 22.5 8.77
n4536 188.593 2.16838 25262 22.91 1.30 25.05 0.43 1.45 0.19 23.1 8.58 rej
n4536 188.583 2.18540 57215 23.21 0.91 24.48 0.34 1.05 0.12 16.9 8.68
n4536 188.585 2.19171 64002 24.31 1.20 23.77 0.31 4.71 0.25 52.0 8.79
n4536 188.599 2.20055 67162 24.43 0.96 24.02 0.18 0.50 0.07 13.2 9.00
n4536 188.587 2.18386 52964 28.05 1.17 23.18 0.24 0.94 0.08 50.9 8.73 rej
n4536 188.591 2.18233 49080 28.74 0.97 23.89 0.32 0.83 0.15 5.33 8.76
n4536 188.587 2.18716 56988 29.06 0.47 23.74 0.35 1.96 0.22 29.3 8.77
n4536 188.598 2.17839 39040 29.98 1.12 23.48 0.36 0.72 0.28 21.8 8.81
n4536 188.593 2.18398 49524 30.20 1.11 24.32 0.50 6.19 0.37 19.9 8.82
n4536 188.592 2.16953 28024 30.22 1.13 24.14 0.26 1.55 0.10 35.7 8.58
n4536 188.593 2.16817 24880 30.23 1.05 24.65 0.29 1.57 0.07 8.61 8.57 rej
n4536 188.598 2.18340 46407 31.32 1.00 23.55 0.21 1.05 0.12 9.07 8.89
n4536 188.591 2.17663 41282 32.94 0.97 23.21 0.26 0.50 0.18 3.49 8.69
n4536 188.583 2.19109 64465 35.16 0.90 22.90 0.24 0.56 0.16 4.45 8.75 rej
n4536 188.587 2.18693 56960 35.88 1.09 23.56 0.29 0.17 0.21 29.6 8.76
n4536 188.588 2.18631 55447 37.27 0.92 23.91 0.32 0.41 0.23 18.7 8.77
n4536 188.578 2.19303 70171 37.59 0.95 23.49 0.17 0.31 0.08 23.0 8.69
n4536 188.605 2.19774 59779 39.62 0.75 24.23 0.16 0.31 0.05 8.52 9.05 rej
n4536 188.590 2.20194 74682 42.66 1.04 23.10 0.19 0.07 0.12 11.2 8.92
n4536 188.587 2.17143 35530 42.93 1.06 24.10 0.19 1.15 0.06 9.11 8.54 rej
n4536 188.587 2.18828 58154 49.38 0.78 22.97 0.22 0.20 0.10 38.5 8.79
n4536 188.599 2.19737 62963 50.04 1.09 23.47 0.14 0.27 0.02 1.93 9.02
n4536 188.583 2.17335 42055 50.67 1.02 23.31 0.14 0.86 0.02 4.32 8.52
n4536 188.584 2.19363 66973 52.41 0.75 22.79 0.21 0.14 0.19 0.88 8.79
n4536 188.582 2.19568 71233 54.45 1.00 22.52 0.16 0.50 0.07 9.93 8.78 rej
n4536 188.583 2.17743 47585 54.53 0.97 22.68 0.12 0.34 0.03 13.8 8.57 rej
n4536 188.599 2.19942 65517 60.16 1.13 22.93 0.13 0.44 0.07 20.7 9.01
n4536 188.589 2.20044 73471 64.74 1.04 21.34 0.16 0.27 0.06 37.9 8.90 rej
n4536 188.588 2.19976 72937 66.23 0.94 23.10 0.20 0.61 0.09 21.9 8.89
n4536 188.600 2.18247 44078 111.9 0.90 22.61 0.13 0.56 0.04 9.95 8.90 rej
n4536 188.597 2.18476 48663 119.1 1.14 22.21 0.12 0.44 0.03 21.8 8.88
n4536 188.587 2.18864 58929 158.1 1.09 21.79 0.12 0.02 0.02 22.6 8.78
n4536 188.592 2.18447 51147 187.2 1.25 21.87 0.18 0.99 0.04 30.4 8.80 rej
n4639 190.731 13.2610 33734 21.69 0.86 24.58 0.30 0.30 0.15 0.26 8.88
n4639 190.726 13.2570 42674 21.82 0.86 25.51 0.73 2.38 0.43 23.0 9.14
n4639 190.725 13.2588 45895 21.89 0.95 24.51 0.43 5.73 0.42 8.56 9.13
n4639 190.705 13.2507 102787 22.38 1.00 25.18 0.32 2.48 0.11 17.7 8.77
n4639 190.715 13.2490 70860 24.25 1.05 24.68 0.59 5.88 0.44 19.3 8.97
n4639 190.721 13.2473 46993 24.90 1.10 24.71 0.48 1.09 0.42 19.5 8.98
n4639 190.724 13.2507 41122 25.80 0.92 23.87 0.35 5.19 0.69 49.5 9.10 rej
n4639 190.724 13.2492 39959 26.99 0.90 25.52 0.67 1.16 0.28 15.9 9.05 rej
n4639 190.721 13.2648 64316 27.14 0.93 23.82 0.60 0.37 0.41 1.85 9.03 rej
n4639 190.726 13.2481 34553 29.19 0.72 25.18 0.49 1.58 0.20 4.07 8.98
n4639 190.709 13.2699 107795 30.02 0.87 24.81 0.28 0.17 0.19 15.0 8.87
n4639 190.719 13.2680 78588 30.84 0.78 24.37 0.36 0.66 0.13 15.3 8.93
n4639 190.716 13.2761 97020 30.90 1.13 25.24 0.14 0.69 0.01 0.56 8.63 rej
n4639 190.733 13.2565 27312 33.04 0.82 24.21 0.20 0.75 0.06 9.54 8.88
n4639 190.710 13.2495 89925 33.44 0.75 24.93 0.26 0.41 0.14 2.61 8.87
n4639 190.724 13.2547 45055 35.00 0.87 23.75 0.43 2.88 0.46 53.5 9.19
n4639 190.723 13.2584 50944 35.16 0.97 24.17 0.61 1.86 0.43 20.9 9.20
n4639 190.726 13.2430 32876 36.41 1.04 23.83 0.32 2.73 -0.10 16.4 8.81
n4639 190.715 13.2566 81322 38.15 0.88 24.99 0.81 6.21 0.49 49.7 9.25
n4639 190.711 13.2523 87883 40.90 0.88 23.52 0.32 1.02 0.23 10.6 9.01
n4639 190.705 13.2679 114011 41.18 0.92 23.95 0.23 0.23 0.08 16.8 8.86
n4639 190.717 13.2535 65236 41.36 0.78 25.04 0.80 4.98 0.67 62.6 9.20 rej
n4639 190.733 13.2561 26954 43.75 0.94 23.88 0.20 1.98 0.09 17.4 8.88
n4639 190.715 13.2524 76749 45.67 1.06 24.23 0.67 3.35 0.45 26.6 9.10
n4639 190.704 13.2685 115343 48.34 1.15 24.44 0.24 0.11 0.15 10.9 8.84
n4639 190.718 13.2740 86917 48.91 1.03 23.98 0.11 0.18 -0.0 7.92 8.69
n4639 190.711 13.2558 91692 49.61 1.18 23.35 0.39 2.04 0.33 33.4 9.11
n4639 190.720 13.2466 47978 54.97 0.85 24.14 0.39 4.23 0.19 1.56 8.95
n4639 190.715 13.2556 80923 58.32 1.12 24.21 0.40 2.05 0.42 16.2 9.21
n4639 190.728 13.2564 36973 64.85 1.42 23.64 0.25 0.23 0.16 9.71 9.07
n4639 190.714 13.2650 91486 86.69 0.93 24.90 0.71 4.73 0.50 7.54 9.09 rej
n4639 190.714 13.2631 89399 105.3 0.85 23.12 0.35 1.09 0.36 49.8 9.15
n3370 161.759 17.2801 8807 23.72 1.05 25.78 0.45 3.95 0.58 7.55 8.92
n3370 161.776 17.2596 47494 24.43 1.22 24.42 0.45 0.44 0.16 20.3 8.77 rej
n3370 161.761 17.2605 23575 24.45 0.94 25.74 0.23 0.34 0.13 5.02 8.58
n3370 161.787 17.2600 53228 24.73 0.86 26.06 0.24 2.49 0.07 0.80 8.43 rej
n3370 161.768 17.2808 23818 26.33 1.04 25.20 0.53 1.01 0.66 7.35 8.94
n3370 161.761 17.2623 22838 26.38 1.00 25.16 0.31 0.94 0.07 0.09 8.66
n3370 161.770 17.2785 81239 26.42 0.67 24.69 0.59 1.69 0.93 60.9 8.95
n3370 161.775 17.2754 39583 26.87 0.95 24.50 0.61 1.52 0.75 9.54 8.84
n3370 161.782 17.2727 48470 27.35 1.07 25.61 0.27 0.38 0.17 7.90 8.55
n3370 161.756 17.2805 5744 27.74 1.06 25.33 0.49 1.50 0.54 8.07 8.83
n3370 161.780 17.2561 51334 28.79 0.98 26.88 0.62 0.56 0.26 0.44 8.61 rej
n3370 161.758 17.2889 4531 29.23 1.00 25.38 0.29 1.15 0.18 3.05 8.71
n3370 161.758 17.2803 62219 29.43 1.11 25.16 0.58 2.50 0.39 21.2 8.89
n3370 161.775 17.2574 46992 29.60 0.95 25.42 0.68 5.34 0.17 3.45 8.72
n3370 161.781 17.2572 51430 30.43 1.04 24.55 0.23 4.61 0.11 13.8 8.62
n3370 161.772 17.2840 27556 30.69 0.99 25.36 0.23 0.55 0.13 2.62 8.70
n3370 161.762 17.2696 19943 30.80 0.73 24.19 0.81 0.60 0.85 6.91 8.97 rej
n3370 161.762 17.2787 13380 31.74 0.85 23.71 0.79 0.54 1.29 12.5 9.05 rej
n3370 161.766 17.2858 15081 32.56 1.22 25.12 0.26 0.37 0.12 0.65 8.80
n3370 161.761 17.2686 18200 32.86 1.12 24.54 0.42 0.23 0.17 7.99 8.88
n3370 161.765 17.2670 26416 33.40 1.19 24.68 0.50 0.86 0.34 24.4 8.98
n3370 161.784 17.2609 52428 33.48 1.03 24.80 0.20 0.57 0.01 2.62 8.54
n3370 161.773 17.2814 31439 33.49 1.00 25.28 0.34 2.52 0.24 3.33 8.76
n3370 161.763 17.2752 17886 33.56 1.25 24.35 0.52 2.39 1.48 75.0 9.13
n3370 161.780 17.2642 49211 33.57 0.96 24.57 0.37 0.43 0.20 12.6 8.72
n3370 161.785 17.2658 52279 33.69 1.04 25.26 0.18 0.38 0.03 0.54 8.48
n3370 161.756 17.2835 4345 34.07 1.21 24.82 0.38 5.57 0.28 17.9 8.79
n3370 161.752 17.2858 1320 34.58 1.06 24.81 0.32 0.49 0.15 15.5 8.62
n3370 161.761 17.2697 17969 34.71 1.17 24.43 0.60 6.27 0.53 19.9 8.93
n3370 161.761 17.2807 10677 35.24 1.12 25.00 0.57 4.86 0.49 16.3 8.97
n3370 161.763 17.2724 19618 35.66 1.20 24.81 0.57 5.94 1.16 38.1 9.10
n3370 161.768 17.2810 22097 36.02 0.98 24.08 0.52 0.52 0.50 37.5 8.95
n3370 161.781 17.2610 50582 36.69 1.07 24.74 0.26 0.25 0.08 2.83 8.67
n3370 161.757 17.2839 59919 36.99 0.90 25.07 0.47 1.30 0.33 16.5 8.81
n3370 161.775 17.2624 45614 37.02 0.82 24.45 0.34 2.97 0.25 2.64 8.86
n3370 161.769 17.2864 21445 37.10 1.09 24.94 0.23 0.37 0.09 3.91 8.68
n3370 161.759 17.2654 16214 37.21 1.18 23.10 0.39 7.88 0.06 57.2 8.67 rej
n3370 161.773 17.2820 30965 37.28 0.95 24.90 0.27 2.20 0.20 6.33 8.74
n3370 161.763 17.2705 20306 37.28 0.76 24.52 0.68 5.55 1.02 36.9 9.02
n3370 161.768 17.2841 21506 38.54 0.76 24.41 0.34 1.84 0.09 12.5 8.80
n3370 161.773 17.2823 31251 39.29 0.92 24.80 0.26 0.14 0.13 3.78 8.72
n3370 161.776 17.2584 47492 39.41 1.14 24.68 0.32 0.86 0.09 8.32 8.75
n3370 161.769 17.2895 18990 40.01 0.80 24.66 0.12 0.33 0.00 1.33 8.56
n3370 161.768 17.2832 20732 41.55 1.17 23.98 0.37 1.52 0.19 28.9 8.86
n3370 161.761 17.2839 9431 43.10 0.84 24.52 0.36 2.43 0.40 24.9 8.89
n3370 161.758 17.2821 6440 43.94 1.18 24.63 0.45 0.69 0.29 3.14 8.86
n3370 161.772 17.2767 85483 44.57 1.14 23.90 0.59 4.94 0.39 42.2 8.93
n3370 161.765 17.2649 28504 44.97 0.82 24.18 0.31 0.80 0.23 21.9 8.90
n3370 161.760 17.2823 9014 45.10 1.12 25.24 0.34 4.86 0.22 11.8 8.91
n3370 161.777 17.2792 40168 45.40 1.02 23.73 0.15 0.73 0.06 15.5 8.64 rej
n3370 161.757 17.2831 5439 45.82 0.97 24.10 0.25 0.20 0.43 19.6 8.83
n3370 161.779 17.2685 46830 45.88 1.07 24.80 0.35 3.42 0.18 8.22 8.78
n3370 161.780 17.2752 46035 50.13 1.09 24.39 0.19 2.93 0.03 7.59 8.59
n3370 161.766 17.2683 28129 50.57 1.12 25.29 0.72 0.81 0.59 37.5 9.07 rej
n3370 161.757 17.2827 5361 50.60 0.89 24.42 0.33 0.41 0.33 9.09 8.82
n3370 161.770 17.2797 28534 51.15 0.97 24.72 0.41 4.19 0.23 25.9 8.91
n3370 161.778 17.2602 48903 51.68 1.07 24.40 0.25 0.28 0.11 7.61 8.74
n3370 161.764 17.2808 15864 52.41 1.02 23.68 0.51 0.87 0.24 21.1 9.01
n3370 161.755 17.2808 4367 52.72 1.23 25.34 0.39 0.60 0.17 1.26 8.78 rej
n3370 161.765 17.2873 13303 52.74 1.15 24.31 0.24 0.34 0.05 7.04 8.75
n3370 161.752 17.2841 1528 60.68 0.82 24.03 0.17 0.22 0.08 6.74 8.63
n3370 161.757 17.2819 5501 62.70 1.26 23.71 0.29 0.64 0.26 1.20 8.83
n3370 161.759 17.2847 6706 64.79 0.96 24.11 0.28 1.38 0.12 10.8 8.84
n3370 161.760 17.2868 7014 66.71 1.07 23.68 0.28 0.14 0.09 4.09 8.79
n3370 161.768 17.2667 33669 67.23 1.38 23.99 0.35 0.70 0.37 33.7 9.06
n3370 161.759 17.2789 9063 68.90 0.80 23.84 0.24 0.88 0.14 13.1 8.92
n3370 161.769 17.2831 22612 69.35 1.03 23.68 0.19 0.17 0.14 5.44 8.83
n3370 161.765 17.2642 29662 71.52 0.90 23.81 0.22 0.36 0.19 1.44 8.88
n3370 161.768 17.2812 22718 73.36 0.90 23.59 0.32 0.18 0.14 12.9 8.93
n3370 161.753 17.2861 1454 79.26 1.34 24.00 0.15 0.19 0.07 6.67 8.63
n3370 161.769 17.2677 33346 80.84 0.89 24.04 0.60 4.44 0.17 10.6 9.10
n3370 161.773 17.2814 33195 81.04 1.00 23.84 0.13 0.23 0.05 17.1 8.72
n3370 161.757 17.2854 4471 83.28 1.43 23.83 0.18 0.18 0.04 8.78 8.78
n3370 161.768 17.2812 22098 86.33 1.05 23.64 0.27 0.44 0.10 8.05 8.94
n3370 161.753 17.2785 3205 88.25 1.02 23.62 0.13 0.49 0.00 7.03 8.66
n3370 161.768 17.2697 31067 88.54 1.14 24.73 0.71 3.19 1.12 54.1 9.17 rej
n3370 161.778 17.2600 48741 96.48 0.97 23.75 0.13 0.03 0.05 7.22 8.75
n3370 161.761 17.2879 8038 96.82 1.09 23.35 0.12 0.37 0.02 1.43 8.76
n3370 161.762 17.2722 17501 98.72 1.07 23.79 0.41 3.27 0.17 39.4 9.02
n3982 179.109 55.1304 48062 20.84 0.62 25.24 0.56 3.88 1.42 44.0 9.04
n3982 179.117 55.1339 35102 21.38 0.90 24.67 0.46 0.63 0.80 7.47 8.98
n3982 179.133 55.1149 16746 21.46 1.05 25.16 0.35 3.08 0.12 2.83 8.64
n3982 179.126 55.1324 20027 22.73 1.00 25.58 0.52 3.25 0.92 11.6 8.97
n3982 179.130 55.1205 85628 23.58 0.92 24.60 0.48 2.07 0.65 16.8 8.92
n3982 179.113 55.1370 40688 23.69 0.86 25.24 0.51 2.80 0.29 5.17 8.78
n3982 179.113 55.1055 51886 24.55 1.10 25.05 0.18 0.70 0.01 1.59 8.36
n3982 179.097 55.1208 65962 24.58 0.86 26.43 0.59 0.82 0.19 6.04 8.70 rej
n3982 179.103 55.1296 57905 25.24 0.68 25.42 0.41 0.73 0.74 15.6 8.88
n3982 179.121 55.1314 86821 25.36 0.75 25.35 0.65 3.65 1.44 39.4 9.10
n3982 179.125 55.1333 21186 26.78 0.61 23.99 0.42 1.04 0.46 4.33 8.94 rej
n3982 179.109 55.1295 49777 27.33 0.79 25.66 0.89 4.69 1.25 51.2 9.05 rej
n3982 179.100 55.1102 65677 28.58 1.28 22.76 0.15 3.81 0.02 82.2 8.44 rej
n3982 179.121 55.1146 35316 29.03 1.20 24.77 0.45 4.48 0.62 16.4 8.84
n3982 179.085 55.1225 72633 32.52 1.13 25.68 0.28 0.68 0.00 2.96 8.32 rej
n3982 179.119 55.1138 39405 33.84 0.75 23.21 0.36 0.87 0.20 51.1 8.81 rej
n3982 179.139 55.1187 10406 34.20 1.25 24.80 0.16 0.41 0.03 1.79 8.57
n3982 179.129 55.1156 21055 37.34 1.22 24.48 0.24 1.12 0.11 13.2 8.76
n3982 179.131 55.1228 16117 37.99 1.12 24.37 0.36 1.49 0.26 17.3 8.93
n3982 179.137 55.1277 10837 38.47 1.10 24.19 0.26 0.47 0.07 20.9 8.77
n3982 179.094 55.1095 69280 38.68 1.19 24.39 0.12 0.34 0.02 3.78 8.28
n3982 179.128 55.1305 17690 39.19 1.09 25.51 0.58 2.32 0.56 37.2 8.98 rej
n3982 179.098 55.1200 82298 40.31 0.82 24.41 0.25 1.04 0.17 17.9 8.72
n3982 179.096 55.1132 67799 40.44 1.01 24.54 0.12 0.10 0.00 2.51 8.46
n3982 179.138 55.1253 10346 40.44 1.27 24.11 0.21 1.04 0.07 13.0 8.72
n3982 179.122 55.1177 32060 40.72 1.26 25.03 0.58 2.49 0.54 7.58 8.99
n3982 179.086 55.1217 72603 51.61 0.92 23.95 0.13 0.17 0.00 2.40 8.32
n3982 179.106 55.1278 89486 62.44 0.88 23.28 0.40 4.86 0.44 34.2 9.02
n3982 179.134 55.1305 12402 72.36 1.00 23.06 0.28 0.54 0.02 15.5 8.82
n3021 147.725 33.5550 71145 16.12 0.67 24.88 0.36 0.11 0.26 4.11 8.73 rej
n3021 147.731 33.5582 64603 16.28 1.27 26.28 0.75 7.71 1.24 26.2 9.01
n3021 147.749 33.5517 29320 18.68 0.73 25.66 0.69 3.30 1.29 27.9 8.90
n3021 147.750 33.5472 26176 19.47 0.73 25.56 0.39 0.47 0.33 1.11 8.67
n3021 147.737 33.5601 54363 20.45 1.13 26.89 0.76 4.88 0.61 6.35 8.80 rej
n3021 147.742 33.5490 42349 20.56 0.77 25.08 0.44 2.33 1.46 51.1 9.10
n3021 147.747 33.5566 35001 20.99 0.96 25.48 0.60 6.21 0.73 17.2 8.77
n3021 147.726 33.5558 70351 22.57 0.92 24.43 0.56 0.23 0.49 6.29 8.82 rej
n3021 147.721 33.5551 73805 22.90 0.77 25.61 0.20 0.47 -0.0 0.81 8.44
n3021 147.727 33.5561 69513 23.98 0.97 24.70 0.44 0.86 0.41 7.44 8.88
n3021 147.726 33.5600 70368 25.14 0.71 25.96 0.41 0.10 0.06 3.82 8.68
n3021 147.732 33.5488 60391 28.67 0.86 24.89 0.31 0.61 0.11 10.4 8.76
n3021 147.748 33.5503 31450 31.64 0.70 24.30 0.54 8.72 0.69 36.1 8.98
n3021 147.737 33.5593 54600 32.59 0.86 24.80 0.47 1.07 0.27 20.1 8.92
n3021 147.728 33.5475 66191 32.66 0.79 25.81 0.24 1.17 0.04 0.72 8.36 rej
n3021 147.734 33.5515 57991 35.43 0.67 24.93 0.62 2.19 0.49 1.85 9.18
n3021 147.728 33.5589 68742 36.73 0.96 25.10 0.29 0.11 0.19 13.8 8.83
n3021 147.746 33.5560 94290 37.11 1.11 25.10 0.73 4.34 0.86 16.0 8.93
n3021 147.732 33.5489 59774 39.19 0.92 24.56 0.32 1.26 0.27 6.17 8.79
n3021 147.748 33.5511 32262 44.79 1.26 24.24 0.55 3.30 0.57 19.2 9.02
n3021 147.747 33.5550 34624 48.27 1.00 23.98 0.59 0.94 0.38 34.1 8.93
n3021 147.739 33.5581 101986 56.24 1.20 24.70 0.53 5.76 0.70 21.8 9.03
n3021 147.751 33.5541 26664 58.58 0.76 24.33 0.26 0.69 0.05 3.17 8.67
n3021 147.745 33.5562 38746 74.77 0.81 23.18 0.52 2.32 0.27 31.4 8.96
n3021 147.733 33.5579 61619 81.02 1.14 24.06 0.38 0.28 0.36 7.11 9.10
n3021 147.747 33.5517 33806 108.3 0.87 23.76 0.49 2.64 0.39 49.6 9.08
n1309 50.5352 -15.4110 7989 39.41 0.89 24.55 0.26 0.38 0.05 5.12 8.85
n1309 50.5262 -15.4100 27980 39.92 1.07 25.06 0.60 3.55 0.52 17.2 8.93
n1309 50.5131 -15.4122 52975 40.52 0.76 25.57 0.17 0.18 0.03 1.80 8.56 rej
n1309 50.5339 -15.3869 7994 40.68 0.89 25.35 0.61 4.59 0.45 3.05 8.81
n1309 50.5416 -15.3965 1166 41.11 1.10 25.12 0.21 0.41 0.08 2.13 8.82
n1309 50.5241 -15.4028 76534 41.86 0.62 25.55 0.77 2.05 1.45 36.5 9.09
n1309 50.5282 -15.4087 22918 42.03 0.82 24.28 0.43 2.23 0.45 34.4 8.99 rej
n1309 50.5402 -15.3941 2032 42.53 0.72 24.45 0.24 0.22 0.05 5.20 8.85
n1309 50.5161 -15.3861 48747 42.68 0.85 24.96 0.16 0.51 0.03 2.93 8.63
n1309 50.5288 -15.3977 67393 42.74 0.85 25.01 0.67 1.40 1.08 42.6 9.23
n1309 50.5351 -15.3855 58298 43.52 0.77 24.87 0.21 0.88 0.05 7.39 8.75
n1309 50.5350 -15.4007 7331 44.58 0.52 24.73 0.81 4.11 0.98 59.2 9.08
n1309 50.5406 -15.3946 1732 45.00 0.72 24.73 0.21 0.03 0.07 10.2 8.84
n1309 50.5298 -15.4083 19368 45.25 0.79 26.25 0.67 2.51 0.38 0.21 9.00 rej
n1309 50.5162 -15.3983 49584 45.67 0.78 25.75 0.58 3.55 0.52 19.4 8.83 rej
n1309 50.5302 -15.3905 16143 46.74 1.00 25.05 0.37 0.70 0.37 14.6 8.97
n1309 50.5315 -15.4069 15346 46.85 0.81 24.18 0.54 0.79 0.31 32.2 9.04
n1309 50.5132 -15.4039 52566 47.41 0.53 24.70 0.38 5.01 0.16 1.76 8.70
n1309 50.5135 -15.3988 52170 47.99 0.96 24.89 0.35 0.11 0.24 14.6 8.73
n1309 50.5370 -15.4121 4882 48.91 0.75 25.24 0.19 0.31 0.00 6.58 8.78
n1309 50.5283 -15.4053 68817 49.93 0.53 25.11 0.57 5.29 0.78 26.6 9.11
n1309 50.5304 -15.3868 15318 51.45 0.76 24.71 0.18 0.41 0.05 1.49 8.84
n1309 50.5266 -15.4058 71911 51.99 0.76 24.90 0.69 1.98 0.72 24.1 9.07
n1309 50.5260 -15.4077 28132 52.24 1.02 25.43 0.65 8.51 0.50 1.50 9.00
n1309 50.5360 -15.4115 6581 58.98 0.79 24.61 0.20 0.09 0.07 2.35 8.82
n1309 50.5361 -15.4123 6542 59.12 0.90 24.49 0.21 0.22 0.04 9.43 8.79
n1309 50.5120 -15.3991 53187 59.75 0.57 24.85 0.29 2.70 0.11 10.1 8.68
n1309 50.5281 -15.4092 69494 60.17 0.92 24.34 0.33 2.48 0.26 19.7 8.97
n1309 50.5296 -15.4089 19918 64.94 0.81 24.96 0.36 0.27 0.22 4.42 8.98
n1309 50.5311 -15.4079 64757 65.02 1.09 24.02 0.37 0.18 0.18 8.58 9.01
n1309 50.5315 -15.3895 13102 66.34 0.82 24.73 0.26 0.18 0.19 8.57 8.93
n1309 50.5186 -15.3946 45088 71.40 0.78 24.44 0.56 5.02 0.32 30.0 8.88
n1309 50.5379 -15.4064 3836 73.27 0.87 24.27 0.17 0.61 0.07 11.0 8.90
n1309 50.5355 -15.4141 7702 73.76 0.86 24.12 0.22 0.11 0.02 6.18 8.74
n1309 50.5284 -15.4175 23616 82.13 0.90 24.34 0.12 0.10 0.01 5.35 8.67
n1309 50.5364 -15.4017 4908 97.89 0.96 23.99 0.27 0.25 0.08 14.9 9.02
n5584 215.612 -0.393170 835998 97.75 1.38 23.67 0.14 0.57 0.02 17.0 8.81 rej
n5584 215.609 -0.384550 625643 93.91 1.17 24.11 0.23 0.56 0.08 8.95 8.85 rej
n5584 215.601 -0.377940 414458 91.51 1.52 23.37 0.21 0.11 0.05 4.01 8.88
n5584 215.600 -0.374360 325718 88.51 1.14 23.18 0.18 1.13 0.06 40.0 8.80
n5584 215.604 -0.378170 449432 84.69 1.03 23.39 0.23 0.38 0.06 22.3 8.83
n5584 215.614 -0.387300 735368 81.35 1.09 23.15 0.16 0.20 0.05 0.75 8.74
n5584 215.597 -0.379210 395114 81.19 1.28 23.91 0.23 0.47 0.12 1.19 8.95
n5584 215.589 -0.372140 172880 79.48 1.23 23.18 0.16 0.13 0.07 0.33 8.73
n5584 215.594 -0.378680 354807 75.26 1.17 23.83 0.20 0.73 0.07 2.32 8.92
n5584 215.590 -0.373060 200686 74.80 1.34 23.62 0.20 1.11 0.08 29.2 8.76
n5584 215.598 -0.398630 801059 71.46 1.04 23.45 0.17 0.57 0.09 12.3 8.86
n5584 215.606 -0.393670 781327 68.17 0.97 24.62 0.38 1.10 0.20 2.26 8.96 rej
n5584 215.612 -0.402910 1 65.82 1.15 23.69 0.14 0.10 0.07 16.8 8.70
n5584 215.589 -0.379540 325206 64.08 1.20 24.02 0.19 0.31 0.08 4.51 8.87
n5584 215.595 -0.369590 185292 63.11 0.90 23.89 0.25 0.68 0.07 23.7 8.70
n5584 215.600 -0.393670 715226 60.54 1.10 24.25 0.34 2.88 0.16 31.7 9.01
n5584 215.608 -0.384140 607520 60.04 1.11 23.76 0.24 0.09 0.14 4.45 8.87
n5584 215.607 -0.392060 758598 58.78 1.20 25.00 0.43 0.73 0.21 18.2 8.95 rej
n5584 215.608 -0.384910 628911 57.83 1.03 23.94 0.29 1.55 0.24 19.0 8.87
n5584 215.616 -0.388220 770520 57.73 1.36 23.27 0.14 0.41 0.04 33.9 8.70 rej
n5584 215.587 -0.369790 111577 56.72 0.95 23.66 0.23 0.20 0.12 16.4 8.67
n5584 215.608 -0.394910 823580 56.17 1.36 23.68 0.23 0.55 0.06 3.63 8.91
n5584 215.606 -0.378690 473829 55.13 1.02 23.72 0.26 0.67 0.10 16.6 8.82
n5584 215.592 -0.395400 673309 53.56 1.21 23.49 0.20 0.20 0.13 21.8 8.84
n5584 215.596 -0.387210 549082 52.16 1.05 24.15 0.33 2.98 0.28 22.9 9.09
n5584 215.601 -0.382500 502797 51.92 1.17 23.65 0.24 2.47 0.17 12.1 9.00
n5584 215.603 -0.399250 858989 51.77 1.11 23.08 0.20 3.38 0.09 45.3 8.87 rej
n5584 215.616 -0.387860 766511 49.35 1.14 24.56 0.23 0.25 0.08 9.49 8.68
n5584 215.613 -0.389650 775000 47.94 1.50 23.97 0.27 0.52 0.15 1.14 8.77
n5584 215.606 -0.399040 891587 47.86 1.05 23.79 0.21 0.41 0.14 4.00 8.86
n5584 215.613 -0.402950 1 47.05 1.09 24.17 0.17 0.28 0.10 14.3 8.70
n5584 215.602 -0.380740 478350 46.75 1.36 24.41 0.29 0.94 0.16 4.59 8.94
n5584 215.605 -0.394330 781586 46.66 0.65 24.38 0.36 0.83 0.36 26.7 8.97
n5584 215.604 -0.378480 455911 46.10 1.15 25.36 0.54 5.50 0.27 8.08 8.84 rej
n5584 215.590 -0.377880 295981 45.66 0.93 24.23 0.21 0.02 0.11 7.26 8.85
n5584 215.600 -0.375400 347072 44.98 0.89 23.05 0.35 0.11 0.27 11.7 8.83 rej
n5584 215.589 -0.368510 97566 43.49 1.42 23.84 0.26 3.50 0.14 10.4 8.65
n5584 215.597 -0.379930 411135 43.46 1.01 24.20 0.38 0.56 0.25 19.5 8.97
n5584 215.610 -0.388250 715986 42.45 1.46 24.46 0.32 0.25 0.14 1.60 8.85
n5584 215.599 -0.377030 374736 41.52 1.07 24.12 0.44 1.19 0.36 30.4 8.88
n5584 215.594 -0.373010 238461 39.16 1.35 24.65 0.46 0.91 0.13 18.7 8.79
n5584 215.605 -0.383690 571414 39.16 1.07 24.04 0.31 0.50 0.28 6.99 8.93
n5584 215.604 -0.406030 1 39.01 1.07 23.91 0.31 0.30 0.21 11.7 8.70
n5584 215.603 -0.383460 545366 38.81 0.88 25.31 0.46 3.05 0.16 18.9 8.98 rej
n5584 215.614 -0.386790 727892 38.65 1.02 24.73 0.29 0.25 0.24 10.6 8.72
n5584 215.593 -0.383720 449157 38.49 0.94 24.72 0.55 4.63 0.43 26.4 9.00
n5584 215.597 -0.384860 513827 38.20 1.16 23.80 0.48 1.38 0.36 18.3 9.09
n5584 215.593 -0.391580 605531 38.07 1.10 24.79 0.41 3.28 0.20 10.1 8.94
n5584 215.612 -0.378940 550433 38.04 1.22 24.27 0.19 0.27 0.07 8.55 8.66
n5584 215.611 -0.402760 1 37.17 1.00 24.15 0.26 4.17 0.11 11.8 8.72
n5584 215.609 -0.383490 606041 36.88 0.86 23.84 0.32 5.17 0.24 14.1 8.83
n5584 215.599 -0.394940 738261 36.54 1.29 24.60 0.48 1.15 0.36 29.2 8.98
n5584 215.600 -0.377150 390652 36.48 0.86 24.25 0.49 7.21 0.22 34.2 8.86
n5584 215.597 -0.380400 421192 36.29 1.09 23.90 0.38 1.50 0.11 29.5 8.98
n5584 215.596 -0.372430 253461 36.27 1.36 24.54 0.60 3.98 0.54 10.8 8.77
n5584 215.594 -0.370740 200467 35.85 1.40 24.93 0.35 0.28 0.28 3.16 8.73
n5584 215.595 -0.370750 208725 35.13 0.98 24.76 0.44 3.60 0.31 24.5 8.73
n5584 215.598 -0.383300 493790 34.44 1.01 24.94 0.60 2.71 0.53 0.50 9.05
n5584 215.597 -0.372950 267902 33.47 0.84 25.99 0.65 5.00 0.62 8.74 8.78 rej
n5584 215.591 -0.394450 644384 33.11 0.89 25.58 0.69 1.96 0.23 12.7 8.83 rej
n5584 215.588 -0.375070 220248 31.36 1.05 24.49 0.28 0.13 0.09 2.92 8.77
n5584 215.614 -0.391150 811974 31.06 1.04 24.33 0.37 1.02 0.14 15.5 8.76
n5584 215.611 -0.398250 918325 30.50 0.95 24.61 0.31 1.04 0.14 11.6 8.81
n5584 215.594 -0.386960 521128 30.46 1.07 24.45 0.40 2.11 0.44 26.5 9.02
n5584 215.590 -0.386380 464626 30.31 1.21 24.64 0.36 0.68 0.28 14.9 8.90
n5584 215.609 -0.372140 378235 30.17 1.15 24.69 0.19 0.20 0.09 10.8 8.59
n5584 215.589 -0.384210 418643 30.10 1.09 23.99 0.30 0.43 0.32 23.1 8.90
n5584 215.600 -0.383340 511109 30.00 1.07 24.72 0.44 3.01 0.55 23.8 9.04
n5584 215.601 -0.380690 466137 29.60 1.19 24.53 0.55 1.11 0.26 9.32 8.96
n5584 215.609 -0.406810 1 29.51 1.20 23.91 0.21 0.52 -0.10 16.9 8.66 rej
n5584 215.600 -0.378480 412396 28.87 0.79 24.66 0.66 5.53 0.46 25.3 8.91
n5584 215.589 -0.374740 230093 28.36 1.36 24.49 0.37 5.96 0.29 21.7 8.79
n5584 215.596 -0.384910 504490 28.31 0.76 24.40 0.51 6.73 0.56 4.91 9.08
n5584 215.613 -0.397280 927325 27.86 1.34 24.68 0.29 0.03 0.23 7.12 8.76
n5584 215.601 -0.372440 298430 27.53 0.93 25.12 0.30 1.26 0.26 13.2 8.73
n5584 215.609 -0.383140 602554 26.71 1.06 24.19 0.46 0.80 0.34 19.4 8.82
n5584 215.605 -0.383200 563696 26.66 1.10 24.94 0.34 6.03 0.32 21.9 8.92
n5584 215.613 -0.386730 711358 26.64 0.98 25.59 0.39 0.43 0.02 8.44 8.77
n5584 215.611 -0.394850 852752 26.36 1.20 23.96 0.27 0.33 0.22 12.6 8.84 rej
n5584 215.595 -0.386440 519642 25.75 1.02 23.63 0.43 0.27 0.47 38.1 9.05 rej
n5584 215.613 -0.378740 550434 25.59 1.09 24.99 0.28 1.72 0.07 6.68 8.64
n5584 215.601 -0.394200 740028 25.57 0.97 24.66 0.63 1.80 0.38 12.4 9.00
n5584 215.598 -0.400160 825506 25.30 1.01 26.32 0.49 4.23 0.16 10.2 8.81 rej
n5584 215.610 -0.398360 912240 25.06 0.92 25.21 0.41 3.17 0.27 19.3 8.82
n5584 215.612 -0.396350 892554 25.02 1.32 24.48 0.38 0.49 0.20 3.84 8.81
n5584 215.588 -0.400160 729270 24.71 1.00 25.06 0.27 0.72 0.23 4.88 8.64
n5584 215.587 -0.368490 82928 24.28 0.85 25.13 0.43 1.00 0.09 8.70 8.64
n5584 215.583 -0.393870 552392 23.44 0.92 25.91 0.33 0.09 0.14 4.35 8.64 rej
n5584 215.582 -0.393560 534937 23.33 1.03 25.03 0.13 0.38 0.33 17.5 8.61
n5584 215.594 -0.388450 549585 22.92 0.89 24.82 0.47 2.86 0.65 30.6 9.01
n5584 215.612 -0.393990 853244 22.52 1.00 26.65 0.69 2.85 0.28 12.1 8.80 rej
n5584 215.598 -0.375010 321323 21.51 1.09 24.77 0.76 2.71 0.92 34.0 8.83
n5584 215.603 -0.395320 787283 21.07 0.97 24.90 0.50 2.39 0.54 17.9 8.97
n5584 215.598 -0.402950 889136 20.77 1.15 24.54 0.35 2.16 0.20 5.19 8.75
n5584 215.595 -0.373140 258671 20.28 1.00 25.50 0.43 4.15 0.81 24.6 8.79
n4038 180.478 -18.8573 2899 28.29 1.31 24.23 0.39 1.57 0.33 18.1 8.98
n4038 180.486 -18.8701 50618 30.05 1.09 25.62 0.61 5.42 1.02 41.0 9.00 rej
n4038 180.486 -18.8727 61212 30.06 1.18 23.69 0.55 0.81 0.61 33.5 8.97 rej
n4038 180.482 -18.8616 14127 32.61 0.94 24.77 0.50 4.32 0.74 33.9 9.05
n4038 180.457 -18.8744 66568 35.15 1.11 24.87 0.57 0.41 0.17 17.5 9.00
n4038 180.468 -18.8564 2098 36.06 1.10 24.64 0.45 3.47 0.32 31.4 8.95
n4038 180.463 -18.8704 52139 36.53 1.13 24.13 0.42 4.38 1.01 99.4 9.12
n4038 180.458 -18.8717 56965 37.87 1.01 23.26 0.57 2.09 0.58 103. 9.05 rej
n4038 180.466 -18.8612 12318 38.71 0.94 23.93 0.57 2.23 1.01 130. 9.06
n4038 180.455 -18.8718 57613 39.82 1.10 23.70 0.51 0.81 0.36 58.8 9.01
n4038 180.458 -18.8723 59401 40.07 1.40 24.34 0.43 1.42 0.67 9.46 9.04
n4038 180.458 -18.8728 61493 40.84 0.93 24.56 0.54 4.28 0.39 69.6 9.04
n4038 180.458 -18.8746 67110 41.07 0.92 24.66 0.48 1.23 0.37 9.32 9.01
n4038 180.467 -18.8844 87068 42.41 1.20 24.85 0.54 3.80 0.28 14.4 8.82
n4038 180.457 -18.8726 60844 42.91 1.04 23.83 0.54 6.32 0.47 49.5 9.03
n4038 180.471 -18.8783 75207 42.99 1.27 24.19 0.37 5.52 0.12 17.0 8.97
n4038 180.474 -18.8558 1757 43.98 1.26 23.81 0.27 0.81 0.21 26.7 8.95
n4038 180.457 -18.8680 40839 45.85 1.13 24.25 0.35 3.97 0.55 40.5 9.05
n4038 180.457 -18.8734 63839 46.16 1.12 24.09 0.39 1.30 0.34 33.4 9.02
n4038 180.484 -18.8781 74894 46.31 0.93 22.97 0.50 0.89 0.69 112. 8.89 rej
n4038 180.473 -18.8812 80094 46.73 1.48 23.27 0.47 0.76 0.33 38.8 8.89 rej
n4038 180.485 -18.8699 49858 50.34 1.00 24.36 0.49 1.67 0.77 27.3 9.02
n4038 180.475 -18.8849 88457 53.95 1.27 23.99 0.43 7.73 1.06 16.7 8.78
n4038 180.473 -18.8612 12435 54.50 0.81 23.95 0.52 1.63 0.80 95.6 9.09
n4038 180.458 -18.8728 61356 58.78 1.23 24.59 0.57 2.70 0.39 14.7 9.04 rej
n4038 180.481 -18.8825 82809 61.04 1.03 23.11 0.43 2.81 0.50 82.2 8.81
n4038 180.476 -18.8796 77376 61.36 1.40 23.70 0.62 2.16 0.79 0.20 8.91
n4038 180.485 -18.8731 62538 64.41 1.28 23.14 0.29 0.22 0.27 54.2 8.97
n4038 180.469 -18.8606 10441 66.68 1.23 24.70 0.63 3.52 0.83 73.5 9.06 rej
n4038 180.469 -18.8748 67639 72.93 1.28 23.53 0.38 0.51 0.26 6.33 9.07
n4038 180.487 -18.8749 67811 76.83 1.45 23.03 0.21 0.30 0.21 13.4 8.92
n4038 180.470 -18.8585 5006 102.9 1.13 23.42 0.45 4.17 0.31 67.8 9.02
n4038 180.475 -18.8622 16265 117.6 1.32 22.80 0.39 0.44 0.21 75.3 9.11
n4038 180.475 -18.8644 24649 118.8 1.00 22.71 0.35 1.08 0.39 76.3 9.16
n4038 180.477 -18.8599 8342 121.8 1.23 23.24 0.27 0.69 0.05 0.20 9.05
n4038 180.468 -18.8588 5625 133.9 1.27 22.29 0.31 1.30 0.13 134. 9.02
n4038 180.459 -18.8681 41146 162.1 0.84 22.60 0.21 0.20 0.15 54.4 9.07
n4038 180.470 -18.8757 69575 197.1 1.07 22.09 0.16 0.54 0.05 26.2 9.04
n4038 180.475 -18.8651 27608 203.3 0.89 22.30 0.30 0.75 0.10 8.49 9.17
n4258 184.713 47.3122 50193 93.23 0.82 21.20 0.15 0.37 0.05 55.7 8.95 rej
n4258 184.715 47.3114 42837 95.92 0.93 20.74 0.18 0.18 0.05 219. 8.96
n4258 184.728 47.3159 9633 69.46 1.18 20.60 0.23 0.10 0.10 259. 9.00
n4258 184.719 47.3101 31107 58.21 1.21 21.59 0.24 6.69 0.07 26.3 8.97
n4258 184.727 47.3178 15470 50.70 1.48 20.89 0.27 6.80 0.22 150. 8.99 rej
n4258 184.714 47.3127 47358 50.89 0.86 21.58 0.27 0.31 0.14 232. 8.96
n4258 184.720 47.3110 29058 40.54 0.95 21.59 0.33 9.81 0.30 279. 8.97
n4258 184.719 47.3121 34159 41.57 1.01 21.77 0.32 0.16 0.26 85.9 8.97
n4258 184.723 47.3121 19435 39.53 0.82 20.92 0.35 0.14 0.25 453. 8.99 rej
n4258 184.731 47.3206 8480 37.63 0.75 21.27 0.43 0.27 0.11 125. 8.98
n4258 184.712 47.3096 49279 36.12 0.94 21.70 0.27 1.66 0.16 216. 8.94
n4258 184.730 47.3200 8723 35.57 0.96 22.73 0.46 5.21 0.52 121. 8.99
n4258 184.724 47.3119 17423 34.57 1.27 22.24 0.40 1.63 0.38 29.3 8.99
n4258 184.724 47.3106 15103 34.36 1.14 23.36 0.61 2.91 0.50 134. 8.99 rej
n4258 184.720 47.3141 33434 34.48 0.78 20.86 0.32 0.38 0.41 196. 8.97 rej
n4258 184.722 47.3069 17369 34.93 1.00 21.59 0.37 5.77 0.10 95.5 8.97
n4258 184.715 47.3083 189390 34.41 0.95 22.09 0.29 1.26 0.22 62.6 8.95
n4258 184.722 47.3120 22927 33.99 1.04 21.58 0.29 0.72 0.47 214. 8.98
n4258 184.732 47.3184 3147 33.39 1.01 22.50 0.41 1.99 0.37 232. 8.99
n4258 184.719 47.3150 36217 31.10 1.25 23.29 0.53 6.28 0.34 12.3 8.97 rej
n4258 184.717 47.3114 36357 29.48 0.86 22.50 0.41 0.56 0.49 8.14 8.96
n4258 184.720 47.3056 21518 30.95 0.46 21.53 0.34 4.57 0.30 99.9 8.96
n4258 184.725 47.3111 14316 29.63 1.14 22.45 0.44 4.71 0.62 37.4 8.99
n4258 184.715 47.3113 44839 24.95 1.10 22.42 0.47 2.88 0.64 56.5 8.95
n4258 184.720 47.3132 30136 26.07 1.21 22.47 0.47 3.19 0.64 178. 8.98
n4258 184.714 47.3117 46945 25.12 0.90 22.09 0.49 4.13 0.37 122. 8.95
n4258 184.724 47.3169 24960 25.49 1.06 22.19 0.38 2.44 0.56 100. 8.99
n4258 184.711 47.3124 56661 23.83 0.68 23.31 0.42 2.64 0.34 10.8 8.94
n4258 184.731 47.3212 9241 27.25 0.72 22.26 0.50 3.18 0.53 280. 8.98
n4258 184.720 47.3132 31615 23.98 1.32 22.20 0.50 0.34 0.71 95.0 8.97
n4258 184.715 47.3111 43119 23.81 0.85 21.87 0.38 1.92 0.40 63.7 8.96 rej
n4258 184.729 47.3175 8361 23.79 1.22 22.32 0.44 0.67 0.69 172. 8.99
n4258 184.728 47.3197 17151 22.35 1.65 22.23 0.35 0.50 0.57 137. 8.99
n4258 184.724 47.3162 23741 22.68 1.43 22.98 0.56 2.51 0.51 152. 8.99
n4258 184.726 47.3146 14643 22.04 1.92 23.66 0.44 2.01 0.92 19.8 8.99 rej
n4258 184.727 47.3176 17357 22.45 1.21 22.11 0.36 1.62 0.60 177. 8.99
n4258 184.719 47.3141 34408 22.42 0.85 22.11 0.55 2.65 0.68 273. 8.97
n4258 184.728 47.3164 12898 22.82 0.94 23.19 0.56 8.13 0.78 270. 8.99
n4258 184.726 47.3134 14775 21.61 0.72 22.44 0.39 0.69 1.11 113. 8.99
n4258 184.731 47.3164 1824 20.10 0.94 22.96 0.45 0.81 0.77 59.1 9.00
n4258 184.729 47.3169 8052 20.76 0.90 22.05 0.53 2.71 0.81 178. 9.00 rej
n4258 184.728 47.3133 6616 16.99 0.93 23.16 0.49 3.34 1.17 239. 9.00
n4258 184.719 47.3189 40434 16.43 1.22 22.66 0.48 1.17 0.82 85.4 8.98
n4258 184.716 47.3109 38988 17.53 0.85 23.34 0.67 3.80 1.00 270. 8.96
n4258 184.728 47.3173 158057 16.68 1.22 23.95 0.62 1.11 0.98 80.0 8.99 rej
n4258 184.728 47.3223 19414 16.38 0.90 23.27 0.44 2.88 0.68 145. 8.98
n4258 184.714 47.3134 49332 16.00 0.71 23.33 0.49 2.24 0.80 104. 8.96
n4258 184.728 47.3161 11066 15.91 1.21 23.70 0.55 6.82 1.15 113. 9.00
n4258 184.711 47.3149 60978 15.21 1.17 24.55 0.67 1.67 0.80 146. 8.95 rej
n4258 184.723 47.3192 29222 14.58 0.96 22.86 0.60 7.09 0.75 320. 8.98
n4258 184.727 47.3176 16299 12.28 1.28 24.49 0.72 3.35 1.30 183. 8.99 rej
n4258 184.712 47.3097 51416 11.09 0.77 23.45 0.56 2.45 1.07 122. 8.94
n4258 184.711 47.3118 57246 10.90 0.89 23.47 0.45 0.13 1.09 80.5 8.94
n4258 184.728 47.3228 20566 10.36 1.04 22.52 0.56 0.88 1.10 9.65 8.98 rej
n4258 184.725 47.3206 25811 10.30 0.89 23.62 0.61 2.54 1.25 167. 8.98
n4258 184.726 47.3218 25760 9.979 0.92 24.38 0.54 1.95 1.46 122. 8.98
n4258 184.709 47.3142 64217 10.06 0.99 23.40 0.51 3.27 0.95 120. 8.94
n4258 184.703 47.3262 89807 98.42 1.26 21.11 0.11 0.20 0.03 114. 8.93 rej
n4258 184.705 47.3209 80885 65.23 1.13 20.75 0.15 5.40 0.04 251. 8.93 rej
n4258 184.737 47.3354 10849 51.51 1.34 21.63 0.29 0.28 0.20 98.1 8.92
n4258 184.719 47.3489 77289 46.39 1.53 21.69 0.18 0.63 0.11 14.7 8.90
n4258 184.739 47.3340 1625 45.43 1.03 21.19 0.29 0.49 0.16 95.5 8.92
n4258 184.743 47.3424 2686 44.05 1.06 21.78 0.31 0.22 0.10 85.2 8.88
n4258 184.706 47.3209 77610 42.82 1.00 21.58 0.23 0.22 0.16 211. 8.94
n4258 184.731 47.3383 32759 42.31 0.94 21.78 0.23 0.68 0.31 188. 8.92
n4258 184.739 47.3324 475 41.88 0.97 21.80 0.34 0.87 0.17 75.1 8.93
n4258 184.713 47.3226 62769 33.02 0.77 21.80 0.25 0.67 0.18 192. 8.96
n4258 184.708 47.3456 97135 31.78 1.20 22.85 0.28 1.22 0.10 27.5 8.92
n4258 184.709 47.3512 99756 29.05 1.04 22.82 0.27 0.64 0.21 147. 8.90
n4258 184.696 47.3331 106960 28.26 0.97 22.81 0.27 0.72 0.13 27.6 8.92
n4258 184.703 47.3195 83857 28.13 0.76 21.51 0.30 1.48 0.19 141. 8.93 rej
n4258 184.724 47.3262 37683 26.18 1.41 22.82 0.31 0.56 0.48 119. 8.97
n4258 184.701 47.3380 103070 24.86 1.12 22.91 0.45 4.15 0.21 53.7 8.92
n4258 184.733 47.3425 33002 22.48 0.75 23.72 0.56 4.53 0.44 182. 8.90 rej
n4258 184.698 47.3334 104131 22.89 0.87 22.34 0.25 2.90 0.20 41.5 8.92
n4258 184.699 47.3369 105183 23.00 1.11 22.50 0.26 0.81 0.22 36.2 8.92
n4258 184.734 47.3390 24365 22.38 0.92 22.83 0.59 3.91 0.52 165. 8.91
n4258 184.712 47.3515 95003 20.57 1.20 23.15 0.29 4.42 0.36 74.8 8.90
n4258 184.703 47.3314 93585 18.19 0.97 22.98 0.41 1.94 0.42 14.2 8.93
n4258 184.706 47.3457 99411 17.02 0.98 24.05 0.50 2.02 0.35 9.51 8.92 rej
n4258 184.709 47.3242 75254 16.52 0.98 22.85 0.39 2.94 0.38 15.6 8.95
n4258 184.710 47.3475 94632 16.03 1.14 22.22 0.44 0.89 0.39 141. 8.91 rej
n4258 184.727 47.3452 54398 15.73 1.06 22.74 0.53 0.50 0.81 109. 8.91
n4258 184.691 47.3461 122858 14.28 0.78 23.08 0.33 1.10 0.25 40.1 8.90
n4258 184.701 47.3507 111064 14.59 0.98 22.51 0.33 0.92 0.35 42.7 8.90 rej
n4258 184.736 47.3575 43585 14.80 0.94 23.36 0.31 0.60 0.09 72.1 8.84
n4258 184.703 47.3257 90355 14.50 0.92 23.57 0.49 3.05 0.24 44.1 8.93
n4258 184.710 47.3538 99783 14.31 0.80 23.19 0.67 1.77 0.65 110. 8.89
n4258 184.725 47.3447 58469 13.08 1.03 24.42 0.84 2.55 0.88 256. 8.91 rej
n4258 184.714 47.3221 59576 12.65 1.10 23.91 0.61 3.81 0.72 55.4 8.96
n4258 184.700 47.3341 102255 12.25 1.04 24.59 99.0 0.44 0.52 33.9 8.92 rej
n4258 184.705 47.3291 89618 12.47 1.01 23.37 0.38 0.41 0.55 77.1 8.94
n4258 184.709 47.3244 74725 11.99 0.80 23.19 0.43 5.67 0.67 71.2 8.95
n4258 184.687 47.3467 126765 11.64 1.02 24.97 0.56 4.73 0.28 11.2 8.89 rej
n4258 184.708 47.3500 100093 12.02 0.72 22.65 0.58 6.25 0.46 232. 8.91 rej
n4258 184.738 47.3365 7952 11.92 0.90 23.46 0.53 3.27 1.04 142. 8.91
n4258 184.701 47.3493 110213 11.60 1.19 23.15 0.46 0.47 0.53 98.1 8.90
n4258 184.709 47.3329 84547 11.30 0.81 23.52 0.36 1.47 0.79 86.2 8.94
n4258 184.698 47.3422 109630 10.93 0.82 23.91 0.49 1.97 0.66 83.9 8.91
n4258 184.711 47.3499 95403 11.58 1.03 24.27 0.62 4.36 0.61 47.7 8.91
n4258 184.703 47.3279 91129 11.16 1.00 23.50 0.35 0.41 0.55 25.8 8.93
n4258 184.705 47.3318 91209 10.80 0.88 23.60 0.48 0.76 0.67 2.96 8.94
n4258 184.709 47.3423 91907 10.51 1.20 22.71 0.42 0.55 0.73 46.0 8.93 rej
n4258 184.710 47.3483 94562 10.20 1.03 23.90 0.41 3.58 0.91 74.4 8.91
n4258 184.706 47.3414 97498 9.987 0.98 24.22 0.62 3.80 0.73 64.6 8.93
n4258 184.706 47.3497 104039 9.770 1.17 23.20 0.56 2.20 0.63 37.5 8.91
n4258 184.858 47.2018 10401 5.297 0.75 24.97 0.67 2.73 1.45 18.7 8.70
n4258 184.871 47.2067 5387 6.487 0.71 22.65 0.56 0.28 1.15 245. 8.68 rej
n4258 184.853 47.1854 9483 6.803 0.75 25.14 0.72 4.32 1.10 62.8 8.69 rej
n4258 184.850 47.1925 11990 8.024 0.65 23.83 0.65 5.28 0.83 87.0 8.71
n4258 184.872 47.1820 2134 8.137 0.72 24.73 0.60 4.98 1.25 27.2 8.66
n4258 184.852 47.2056 13262 8.288 0.92 24.61 0.64 2.60 0.75 95.3 8.72
n4258 184.859 47.2006 9786 8.920 0.72 24.23 0.59 2.09 0.87 91.6 8.70
n4258 184.703 47.3161 81614 20.31 1.01 21.94 0.30 0.18 0.29 118. 8.92 rej
n4258 184.705 47.3086 67208 18.29 1.09 22.49 0.37 1.34 0.28 106. 8.92
n4258 184.690 47.3326 116159 21.87 0.89 22.79 0.30 1.40 0.12 42.4 8.90
n4258 184.649 47.3196 143829 18.28 1.25 23.13 0.13 0.10 0.03 17.5 8.73
n4258 184.687 47.3347 121078 18.42 0.97 22.94 0.31 0.69 0.19 106. 8.89
n4258 184.668 47.3360 138294 15.81 0.93 22.95 0.20 0.18 0.12 5.28 8.83
n4258 184.692 47.3224 106997 15.29 0.84 23.29 0.39 0.88 0.25 59.7 8.89
n4258 184.653 47.3302 144134 15.61 0.89 23.34 0.16 0.05 0.05 43.4 8.77
n4258 184.691 47.3215 107947 14.67 1.03 23.60 0.30 0.41 0.32 2.21 8.89
n4258 184.689 47.3355 118961 12.82 1.26 22.30 0.26 0.31 0.31 34.2 8.89 rej
n4258 184.695 47.3162 95987 11.26 1.28 24.91 0.73 4.07 0.34 39.3 8.89 rej
n4258 184.655 47.3223 141685 10.99 0.83 23.72 0.21 2.46 0.11 12.7 8.76
n4258 184.651 47.3319 145186 10.69 0.88 23.36 0.23 0.27 0.10 3.72 8.77
n4258 184.827 47.1922 26262 5.007 0.77 23.86 0.28 3.54 0.46 88.0 8.73 rej
n4258 184.807 47.1879 40543 5.372 0.80 25.43 0.73 2.02 0.39 21.4 8.72 rej
n4258 184.812 47.1725 31191 5.834 0.70 22.71 0.34 0.10 0.17 73.3 8.67 rej
n4258 184.823 47.1940 29843 5.864 0.72 24.13 0.40 5.54 0.48 53.3 8.73
n4258 184.837 47.1950 20639 6.735 1.03 24.57 0.53 0.69 0.63 1.61 8.73
n4258 184.830 47.1966 25502 7.538 0.92 23.72 0.54 1.52 0.45 76.9 8.73
n4258 184.833 47.1973 24134 8.937 0.87 24.87 0.52 2.54 0.33 19.7 8.73 rej
n4258 184.839 47.1708 12705 9.942 0.84 24.37 0.59 5.65 0.38 25.4 8.67
n4258 184.836 47.1743 14709 10.97 0.84 22.58 0.26 0.44 0.17 44.1 8.68 rej
n4258 184.839 47.1948 19312 13.55 0.82 23.98 0.47 5.13 0.20 88.2 8.72
n4258 184.835 47.1738 15276 16.43 0.87 22.34 0.20 3.56 0.17 61.6 8.68 rej
n4258 184.699 47.3561 118782 25.56 0.89 22.43 0.22 0.63 0.17 42.2 8.89
n4258 184.698 47.3593 121312 17.85 1.02 24.78 0.32 0.47 0.16 3.48 8.88 rej
n4258 184.699 47.3550 117710 14.30 0.83 24.32 0.49 1.46 0.30 48.9 8.89 rej
n4258 184.714 47.3568 95711 10.94 1.12 23.80 0.61 1.20 0.40 33.5 8.88
n4258 184.849 47.2111 17005 5.739 0.92 24.97 0.57 5.57 0.94 41.4 8.73
n4258 184.842 47.2190 23710 5.920 0.77 25.75 0.31 2.81 1.21 33.1 8.75 rej
n4258 184.856 47.2120 12774 6.189 0.68 22.91 0.51 0.16 0.79 68.0 8.71 rej
n4258 184.728 47.3634 999999 92.00 1.00 20.50 0.10 0.38 0.02 256. 8.84 rej
n4258 184.811 47.2035 42010 8.961 0.95 24.41 0.32 1.28 0.17 20.0 8.76
n4258 184.795 47.2022 28881 86.15 1.80 19.94 0.10 0.34 0.00 50.4 8.75 rej
n4258 184.800 47.2073 28076 31.17 1.06 22.51 0.11 0.31 0.00 27.3 8.77
n4258 184.800 47.2062 27963 21.26 1.27 22.76 0.15 0.00 0.06 18.4 8.77
n4258 184.800 47.2073 220887 31.29 1.26 22.52 0.12 0.31 0.01 27.3 8.77
n4258 184.800 47.2062 220789 21.29 1.04 22.73 0.14 0.00 0.03 18.4 8.77
n4258 184.842 47.2107 21853 6.063 0.96 25.86 0.35 2.93 0.17 15.7 8.74 rej
n4258 184.852 47.2138 15227 7.140 0.95 23.78 0.32 1.41 0.13 42.3 8.72
n4258 184.840 47.2134 24025 9.253 0.84 22.82 0.25 1.03 0.05 15.9 8.75 rej
n4258 184.836 47.2201 28606 53.88 1.03 23.34 0.10 0.09 0.01 7.13 8.76 rej
n4258 184.836 47.2201 19756 48.79 1.22 21.85 0.10 0.00 0.00 9.52 8.76
n4258 184.845 47.2127 16719 109.3 1.25 21.02 0.10 0.00 0.00 51.8 8.74 rej
n4258 184.858 47.2297 8073 32.29 1.30 22.20 0.10 0.00 0.00 5.61 8.71
n4258 184.857 47.2298 307758 32.40 1.02 22.20 0.10 0.00 -0.0 5.61 8.71
n4258 184.658 47.3445 144755 12.05 1.16 23.06 0.20 0.46 0.13 45.5 8.81
n4258 184.827 47.2018 29163 6.739 0.80 24.48 0.57 2.86 0.38 42.1 8.75
n4258 184.819 47.1987 34729 14.92 1.12 23.12 0.50 6.29 0.00 108. 8.75
n4258 184.696 47.3103 89375 12.38 0.92 22.79 0.45 1.66 0.42 78.8 8.89
n4258 184.697 47.3108 246695 11.20 0.91 22.97 0.40 1.17 0.49 152. 8.89
n4258 184.833 47.2491 312665 39.09 0.80 23.10 0.11 0.47 0.01 15.1 8.78 rej
Table 2: WFC3-IR Cepheids
# P b Fit Scale PLW C SNe SN
0.65 448 74.80(3.02) Y 0.697 -19.12 zkh -0.25(0.10) -3.02(0.06) 0.023 37 4258 3.1 UBVRI 2.5
0.65 448 75.62(3.05) Y 0.702 -19.12 zkh -0.25(0.10) -3.02(0.06) 0.010 37 4258 3.1 UBVRI 2.5
0.64 497 76.03(3.02) N 0.697 -19.09 zkh -0.25(0.09) -2.99(0.06) 0.023 37 4258 3.1 UBVRI 2.5
0.61 448 76.52(3.05) Y 0.697 -19.07 zkh -0.29(0.10) -2.91(0.06) 0.023 37 4258 3.1 UBVRI 2.5
0.66 448 73.85(2.96) Y 0.697 -19.15 zkh —— -3.06(0.06) 0.023 37 4258 3.1 UBVRI 2.5
0.65 448 74.45(3.05) Y 0.700 -19.15 zkh -0.27(0.10) -3.02(0.06) 0.023 61 4258 3.1 BVRI 2.5
1.87 570 76.16(3.83) Y 0.697 -19.08 zkh -0.27(0.15) -2.89(0.09) 0.023 37 4258 3.1 UBVRI 2.5
0.65 448 74.52(3.04) Y 0.701 -19.15 zkh -0.24(0.10) -3.02(0.06) 0.023 20 4258 3.1 UBVRI 3.1
0.64 448 75.12(3.02) Y 0.697 -19.11 zkh -0.26(0.10) -3.00(0.06) 0.023 37 4258 2.5 UBVRI 2.5
0.65 448 74.83(3.00) Y 0.690 -19.09 zkh -0.26(0.10) -3.02(0.06) 0.023 28 4258 3.1 UBVRI 2.0
0.66 448 75.00(2.99) Y 0.684 -19.06 zkh -0.27(0.10) -3.02(0.06) 0.023 29 4258 3.1 UBVRI 1.5
0.64 448 73.42(3.04) Y 0.691 -19.13 zkh -0.22(0.10) -3.03(0.06) 0.023 26 4258 3.1 UBVRI 2.5
0.64 448 74.71(3.11) Y 0.699 -19.14 zkh -0.25(0.10) -3.02(0.06) 0.023 27 4258 3.1 UBVRI 3.1
0.65 497 75.92(2.99) N —- —- zkh -0.25(0.09) -3.00(0.06) 0.023 42 4258 3.1 UBVRI —-
0.64 497 76.25(2.99) N —- —- zkh -0.25(0.09) -2.97(0.06) 0.023 42 4258 2.5 UBVRI —-
0.65 448 74.80(3.02) Y 0.697 -19.12 T -0.37(0.15) -3.02(0.06) 0.023 37 4258 3.1 UBVRI 2.5
0.76 514 75.66(2.61) Y 0.697 -19.10 zkh -0.20(0.11) -3.19(0.03) 0.023 37 MW 3.1 UBVRI 2.5
0.76 514 76.49(2.63) Y 0.702 -19.10 zkh -0.20(0.11) -3.19(0.03) 0.010 37 MW 3.1 UBVRI 2.5
0.75 563 76.70(2.58) N 0.697 -19.07 zkh -0.17(0.10) -3.18(0.03) 0.023 37 MW 3.1 UBVRI 2.5
0.88 553 75.98(2.73) Y 0.697 -19.09 zkh -0.24(0.12) -3.08(0.02) 0.023 37 MW 3.1 UBVRI 2.5
0.77 514 74.92(2.55) Y 0.697 -19.12 zkh —— -3.20(0.03) 0.023 37 MW 3.1 UBVRI 2.5
0.76 514 75.29(2.65) Y 0.700 -19.13 zkh -0.21(0.11) -3.19(0.03) 0.023 61 MW 3.1 BVRI 2.5
1.86 636 77.58(4.07) Y 0.697 -19.04 zkh -0.19(0.15) -3.14(0.04) 0.023 37 MW 3.1 UBVRI 2.5
0.76 514 75.38(2.64) Y 0.701 -19.13 zkh -0.19(0.11) -3.19(0.03) 0.023 20 MW 3.1 UBVRI 3.1
0.75 514 76.10(2.60) Y 0.697 -19.09 zkh -0.20(0.11) -3.17(0.03) 0.023 37 MW 2.5 UBVRI 2.5
0.77 514 75.70(2.58) Y 0.690 -19.06 zkh -0.20(0.11) -3.19(0.03) 0.023 28 MW 3.1 UBVRI 2.0
0.77 514 75.88(2.56) Y 0.684 -19.03 zkh -0.21(0.11) -3.19(0.03) 0.023 29 MW 3.1 UBVRI 1.5
0.76 514 74.29(2.66) Y 0.691 -19.11 zkh -0.16(0.11) -3.19(0.03) 0.023 26 MW 3.1 UBVRI 2.5
0.76 514 75.56(2.72) Y 0.699 -19.11 zkh -0.20(0.11) -3.19(0.03) 0.023 27 MW 3.1 UBVRI 3.1
0.76 563 76.62(2.53) N —- —- zkh -0.17(0.10) -3.18(0.03) 0.023 42 MW 3.1 UBVRI —-
0.75 563 77.05(2.52) N —- —- zkh -0.18(0.10) -3.16(0.03) 0.023 42 MW 2.5 UBVRI —-
0.76 514 77.72(3.15) Y 0.697 -19.04 T -0.29(0.16) -3.19(0.03) 0.023 37 MW 3.1 UBVRI 2.5
0.75 514 71.31(3.84) Y 0.697 -19.23 zkh -0.20(0.11) -3.19(0.03) 0.023 37 LMC 3.1 UBVRI 2.5
0.75 514 72.09(3.88) Y 0.702 -19.23 zkh -0.20(0.11) -3.19(0.03) 0.010 37 LMC 3.1 UBVRI 2.5
0.73 563 72.46(3.82) N 0.697 -19.19 zkh -0.18(0.10) -3.18(0.03) 0.023 37 LMC 3.1 UBVRI 2.5
0.86 553 69.68(3.91) Y 0.697 -19.28 zkh -0.24(0.11) -3.08(0.02) 0.023 37 LMC 3.1 UBVRI 2.5
0.75 514 73.34(3.76) Y 0.697 -19.17 zkh —— -3.19(0.03) 0.023 37 LMC 3.1 UBVRI 2.5
0.75 514 70.76(3.85) Y 0.700 -19.26 zkh -0.21(0.11) -3.19(0.03) 0.023 61 LMC 3.1 BVRI 2.5
1.84 636 72.70(5.31) Y 0.697 -19.18 zkh -0.19(0.15) -3.14(0.04) 0.023 37 LMC 3.1 UBVRI 2.5
0.75 514 71.13(3.85) Y 0.701 -19.25 zkh -0.19(0.11) -3.19(0.03) 0.023 20 LMC 3.1 UBVRI 3.1
0.74 514 71.37(3.83) Y 0.697 -19.22 zkh -0.21(0.11) -3.17(0.03) 0.023 37 LMC 2.5 UBVRI 2.5
0.75 514 71.24(3.82) Y 0.690 -19.20 zkh -0.21(0.11) -3.19(0.03) 0.023 28 LMC 3.1 UBVRI 2.0
0.76 514 71.26(3.82) Y 0.684 -19.17 zkh -0.22(0.11) -3.19(0.03) 0.023 29 LMC 3.1 UBVRI 1.5
0.74 514 70.48(3.86) Y 0.691 -19.22 zkh -0.16(0.11) -3.19(0.03) 0.023 26 LMC 3.1 UBVRI 2.5
0.74 514 71.23(3.90) Y 0.699 -19.24 zkh -0.20(0.11) -3.19(0.03) 0.023 27 LMC 3.1 UBVRI 3.1
0.74 563 72.44(3.80) N —- —- zkh -0.17(0.10) -3.18(0.03) 0.023 42 LMC 3.1 UBVRI —-
0.73 563 72.51(3.79) N —- —- zkh -0.18(0.10) -3.16(0.03) 0.023 42 LMC 2.5 UBVRI —-
0.75 514 73.22(3.75) Y 0.697 -19.17 T -0.29(0.16) -3.19(0.03) 0.023 37 LMC 3.1 UBVRI 2.5
0.76 514 74.53(2.25) Y 0.697 -19.13 zkh -0.19(0.11) -3.20(0.03) 0.023 37 4258+MW 3.1 UBVRI 2.5
0.76 514 75.34(2.26) Y 0.702 -19.13 zkh -0.19(0.11) -3.20(0.03) 0.010 37 4258+MW 3.1 UBVRI 2.5
0.75 563 75.61(2.23) N 0.697 -19.10 zkh -0.17(0.10) -3.19(0.02) 0.023 37 4258+MW 3.1 UBVRI 2.5
0.88 553 75.48(2.39) Y 0.697 -19.10 zkh -0.24(0.12) -3.08(0.02) 0.023 37 4258+MW 3.1 UBVRI 2.5
0.77 514 73.90(2.20) Y 0.697 -19.15 zkh —— -3.20(0.03) 0.023 37 4258+MW 3.1 UBVRI 2.5
0.76 514 74.15(2.30) Y 0.700 -19.16 zkh -0.21(0.11) -3.20(0.03) 0.023 61 4258+MW 3.1 BVRI 2.5
1.86 636 75.90(3.44) Y 0.697 -19.09 zkh -0.18(0.15) -3.15(0.04) 0.023 37 4258+MW 3.1 UBVRI 2.5
0.76 514 74.25(2.28) Y 0.701 -19.16 zkh -0.19(0.11) -3.20(0.03) 0.023 20 4258+MW 3.1 UBVRI 3.1
0.75 514 74.92(2.24) Y 0.697 -19.12 zkh -0.20(0.11) -3.18(0.03) 0.023 37 4258+MW 2.5 UBVRI 2.5
0.77 514 74.56(2.21) Y 0.690 -19.10 zkh -0.20(0.11) -3.20(0.03) 0.023 28 4258+MW 3.1 UBVRI 2.0
0.77 514 74.72(2.19) Y 0.684 -19.06 zkh -0.21(0.11) -3.20(0.03) 0.023 29 4258+MW 3.1 UBVRI 1.5
0.76 514 73.19(2.32) Y 0.691 -19.14 zkh -0.16(0.11) -3.20(0.03) 0.023 26 4258+MW 3.1 UBVRI 2.5
0.76 514 74.43(2.38) Y 0.699 -19.15 zkh -0.19(0.11) -3.20(0.03) 0.023 27 4258+MW 3.1 UBVRI 3.1
0.76 563 75.55(2.16) N —- —- zkh -0.17(0.10) -3.19(0.02) 0.023 42 4258+MW 3.1 UBVRI —-
0.75 563 75.93(2.15) N —- —- zkh -0.17(0.10) -3.17(0.02) 0.023 42 4258+MW 2.5 UBVRI —-
0.77 514 75.06(2.45) Y 0.697 -19.12 T -0.18(0.14) -3.20(0.03) 0.023 37 4258+MW 3.1 UBVRI 2.5
0.75 514 72.34(2.28) Y 0.697 -19.20 zkh -0.17(0.10) -3.19(0.03) 0.023 37 4258+LMC 3.1 UBVRI 2.5
0.75 514 73.13(2.30) Y 0.702 -19.20 zkh -0.17(0.10) -3.19(0.03) 0.010 37 4258+LMC 3.1 UBVRI 2.5
0.73 563 73.45(2.26) N 0.697 -19.16 zkh -0.16(0.09) -3.18(0.03) 0.023 37 4258+LMC 3.1 UBVRI 2.5
0.87 553 72.64(2.44) Y 0.697 -19.19 zkh -0.17(0.10) -3.08(0.02) 0.023 37 4258+LMC