THE CARNEGIE-CHICAGO HUBBLE PROGRAM. I. AN INDEPENDENT APPROACH TO THE EXTRAGALACTIC DISTANCE SCALE USING ONLY POPULATION II DISTANCE INDICATORS^*

We turn now to a discussion of the uncertainties in both the distance ladder and CMB methods for determining H₀. A longstanding "first rung" for the distance ladder is the Large Magellanic Cloud (LMC). The distance to the LMC is, in itself, a source of active research (see, for instance, the summary of de Grijs et al. 2014), and its suitability as the "anchor" for the distance ladder is much debated (see, for instance, Efstathiou 2014). The LMC is a low-metallicity, dwarf irregular galaxy, unlike the spiral galaxies with higher metallicity and higher luminosity that are common hosts to SNe Ia. The potential for metallicity effects between their Cepheid populations is therefore a concern. The proximity of the LMC to the Sun permits the application of numerous independent distance measurement techniques, however, including those with uncertainties much easier to control than those of the Cepheids. Of note is the work of Pietrzyński et al. (2013), in which a set of eight late-type double-eclipsing binaries in the LMC were used to obtain a (largely geometric) 2.2% estimate of the distance to the LMC. On the other hand, the proximity of the LMC also means that its three-dimensional structure and line-of-sight depth are both of larger concern than in most extragalactic applications, and extra attention must be given to membership in specific structural components for a given distance tracer (for further discussion, see Clementini et al. 2003; Clementini 2011; Moretti et al. 2014). Replacement of the LMC with the megamaser-host NGC 4258 as the anchor point for the distance ladder provides an independent zero-point calibration, but does not fully settle the issue of the zero-point, given that, effectively, only one data set exists (with multiple distinct distance measurements, including Herrnstein et al. 1999; Humphreys et al. 2013; Riess et al. 2016, among others), for which the systematic errors are difficult to ascertain.

The advantages of the Leavitt law (or the Cepheid period–luminosity (PL) relation¹³ ) are well known. (a) Cepheids are intrinsically high-luminosity supergiants. (b) In the infrared, especially, their PL relations have small intrinsic dispersion (∼0.1 mag) for the I band and redder wavelengths. (c) They are found in all star-forming galaxies (spiral and irregular). Lastly, (d) their variability is sufficiently stable over a human lifetime that they can be repeatedly observed with different instruments operating at different wavelengths and thereby be tested for any number of systematic effects. Transient objects (like SNe Ia) are much more problematic in the latter regard. There are remaining challenges for the Cepheid distance ladder, however, such as (a) the need for a robust determination of the metallicity dependence of the Leavitt law, particularly at optical wavelengths (e.g., Romaniello et al. 2005, 2008, among others); (b) the need for additional trigonometric parallaxes to lay a more robust geometric calibration of the zero-point of the Leavitt law (see a prospectus for variable stars in the final Gaia sample in Eyer 2000); (c) contending with crowding at intermediate and large distances, especially by redder stellar populations that increase in relative brightness moving from the optical to the near- and MIR; and finally, (d) potential unknown changes in the reddening law as a function of metallicity and/or environment. Some of these concerns were largely minimized by moving into the MIR (e.g., the Carnegie Hubble Program; Freedman & Madore 2011; Freedman et al. 2012b, see our Figure 1), but tension between the Cepheid distance ladder and other techniques has remained.

Only about 800 Cepheids are known in the Galaxy, most of which are located in the solar neighborhood. Gaia is expected to observe up to 9000 classical Cepheids across the Galaxy to a limiting apparent magnitude G ∼ 20 mag (Eyer 2000; Turon et al. 2012) and measure their parallax to better than σ_π/π = 10%, on average, and to better than 1% for those located within 1–2 kpc (Turon et al. 2012). Beyond the Galaxy, Gaia will measure the parallaxes for at least 1000 of the brightest LMC Cepheids with σ_π/π ∼ 50%–100%, providing a probe of the Leavitt law at lower mean metallicity. In addition to the parallaxes, Gaia obtains metallicity estimates from R = 11,500 spectroscopy with the Radial Velocity Spectrometer for all stars brighter than V ∼ 16 mag and permits study of star-by-star metallicity effects. The bulk of the Cepheids observed by Gaia are also accessible for independent high-resolution abundance studies from the ground (e.g., Luck & Lambert 2011, among others). In combination, such data sets will allow direct study of the various dependencies of the Leavitt law and permit improvement in the calibration of the Cepheid distance ladder in the future.

There are also challenges in estimating H₀ from measurements of anisotropies in the CMB. The microwave background data from which these measurements are derived are highly complex and require highly precise Galactic foreground removal as well as multiwavelength dust modeling: there is still debate regarding the effects on the resulting parameter fits (for instance, see discussion in Spergel et al. 2015). The power spectrum of CMB fluctuations derived from such maps is then modeled using six primary parameters that, hereto, have provided an excellent fit to existing data sets. However, in addition to the priors imposed on the parameters in the specific fitting procedure employed, there exist strong degeneracies in the derived cosmological parameters, and these covariant degeneracies are strongly coupled to H₀ (see discussion of such effects in Planck Collaboration et al. 2014). Moreover, comprehensive reanalysis by independent teams and detailed comparisons with complementary data sets (often at different frequencies or spatial resolutions) can produce significantly differing results (for instance see Addison et al. 2015), suggesting that there is still more to learn about methodology (both data and analysis) before the results can be interpreted at high confidence. Moreover, some authors have argued that, with the numerous complementary data sets available, the inclusion of additional parameters in the standard modeling is now feasible and perhaps, more appropriate (Di Valentino et al. 2015, 2016).

Trigonometric parallaxes have been obtained for five Galactic RRL using the HST Fine Guidance Sensor (HST+FGS; Benedict et al. 2011). The Hipparcos measurements for RR Lyrae were at its measurement limit; with the exception of RR Lyr (σ_π/π ∼ 18%), the over 100 RR Lyrae in Hipparcos have parallax uncertainties greater than 30% (with over 100 stars in the sample; see Clementini 2016). Practical constraints limited the application of HST+FGS  to only the most nearby RR Lyrae. As such, trigonometric parallaxes were obtained for only five stars, of which four were type RRab (SU Dra, RR Lyr, UV Oct, and XZ Cyg) and one type RRc (RZ Cep). The properties of these five stars are given in Table 3.

Table 3.  Properties of RR Lyrae Variables in the CCHP Galactic Calibration Sample

Target	Type	$\mathrm{log}({P}_{F})$	[Fe/H]a	$\langle V\rangle$ a	$\langle {\boldsymbol{H}}\rangle$ b	AVc	AHd	πa	μ
SU Dra	RRab	−0.180	−1.80 ± 0.20	9.78	8.69 ± 0.03	0.03	0.01	1.42 ± 0.16	9.28 ± 0.24
RR Lyr	RRab	−0.247	−1.41 ± 0.13	7.76	6.61 ± 0.01	0.13	0.02	3.77 ± 0.13	7.11 ± 0.07
UV Oct	RRab	−0.266	−1.74 ± 0.11	9.50	8.30 ± 0.02	0.28	0.05	1.71 ± 0.10	8.84 ± 0.13
XZ Cyg	RRab	−0.331	−1.44 ± 0.20	9.68	8.79 ± 0.04	0.30	0.05	1.67 ± 0.17	8.89 ± 0.22
RZ Cep	RRc	−0.384e	−1.77 ± 0.20	9.47	8.06 ± 0.05	0.75	0.13	2.54 ± 0.19	7.98 ± 0.16

Notes.

^aFrom Benedict et al. (2011). ^bDerived from single 2MASS phase points following the technique described in Section 3.1.3. ^cFrom Feast et al. (2008). ^dAssuming A_H/A_V = 0.178. ^e $\mathrm{log}({P}_{F})=\mathrm{log}({P}_{{FO}})+0.127$.

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3.1.1. Uncertainty in the PL zero-point

In Figure 2, we combine the Benedict et al. (2011) trigonometric parallaxes with NIR photometry from 2MASS (Skrutskie et al. 2006) and MIR photometry from the CRRP to demonstrate the NIR (J, H, K_s) and MIR (Spitzer 3.6 and 4.5 μm) PLs. The five stars give sparse sampling in $\mathrm{log}({P}_{F})$ ¹⁴ , and it is not feasible to determine the slope directly from the parallax sample. Thus, we adopt the PL slopes measured in M4 by (Braga et al. 2015, their Table 2) for the J (−1.739 ± 0.109), H (−2.408 ± 0.082), and K_s (−2.326 ± 0.074) and by (Neeley et al. 2015, their Table 3) for 3.6 μm (−2.332 ± 0.106) and 4.5 μm (−2.336 ± 0.105).

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The adopted PL is overplotted in Figure 2 for each passband. We estimate the impact on our measurements from the uncertainty on the slope by performing a Monte Carlo simulation by varying the slope within its uncertainties and find a modulation of the resulting zero-point on the order of 0.002 mag or smaller for all bands. Because we define the zero-point of the PL relation at the midpoint of our $\mathrm{log}(P)$ distribution (here, $\mathrm{log}({P}_{F})$ = −0.30), the effect of the slope uncertainty on the zero-point is effectively eliminated. Moreover, we test the full range of metallicity slopes in (see Muraveva et al. 2015 (see their Table 3 for a summary) and find no significant impact on the zero-point (defined at the midpoint of [Fe/H] = −1.58 dex) for metallicity terms between 0.235 and 0.03 mag dex⁻¹. We suspect that the lack of an effect of the metallicity is due to the lack of a large metallicity span in the HST  calibrators and that they are relatively clustered (see our Table 3). Thus, we neglect the metallicity term for this demonstration because the range of values for the effect in the literature is great, empirical studies are mainly limited to the K_s band at this time, and because we see no strong impact for our current RRL calibration sample (the individual uncertainties are much larger than the differential metallicity effect).

As shown in Figure 2, the variance about the PL for all passbands is approximately σ_λ ∼ 0.11, although the mean uncertainty on the distance moduli is $\langle {\sigma }_{\mu }\rangle =0.15$ mag (seven times larger than the mean apparent magnitude uncertainty of $\langle {\sigma }_{H}\rangle =0.03$ mag; Table 3). As anticipated by the dominance of the parallax uncertainty to the total uncertainty in the absolute magnitude, the residuals for each band are highly correlated. Indeed, for RRc variables, the only independent measurement of the absolute magnitude by Kollmeier et al. (2013) is in 2.5σ tension with the Benedict et al. (2011) value for RZ Cep. This highlights the critical need for accurate and precise absolute magnitude measurements for RRL.

We compute the χ² statistic compared to the PL for each of our passbands, finding χ² = 0.39, 0.40, 0.42, 0.38, and 0.36 for the J, H, K_s, [3.6], and [4.5], respectively. For the purposes of the following discussion we use ${\chi }_{H}^{2}=0.40$ or the reduced chi-squared metric of ${\chi }_{H}^{2}{\nu }^{-1}=0.1$ (where ν is the number of degrees of freedom), which is representative of results for all bands. For χ² ν⁻¹ < 1, the implications are that (i) the model is incorrect, (ii) the uncertainties follow a non-Gaussian distribution, (iii) the uncertainties are improperly assigned (i.e., Bevington & Robinson 2003, chapter 11), or (iv) the intrinsic variance of a sample has not been accounted for (i.e., Bedregal et al. 2006, their Section 3.1). We can evaluate each of these possibilities.

For the first option, our adopted PL is supported by several studies of the PL for globular clusters (Braga et al. 2015; Neeley et al. 2015 being the most recent), and thus our model is representative of the behavior of NIR and MIR RR Lyrae. We did neglect metallicity, but accounting for this would only reduce the measured variance and, using the maximal estimate for the metallicity component (Bono et al. 2001), in the K band, we obtain an effect of 0.07 mag, which, when removed, only lowers the measured variance to 0.08 mag. For the second option regarding the nature of the uncertainties, discussions involving the uncertainty for the reference frame in (Benedict et al. 2011, their Figure 4) imply that the final uncertainties are, indeed, Gaussian in nature using their procedure. For the third possibility, we use the analysis of Benedict et al. (2002, their Figure 7), in which the results for the early HST+FGS parallax program were compared to Hipparcos, from which the authors conclude that it is likely that the uncertainties for the HST+FGS parallaxes are overestimated by a factor of ∼1.5. Comparing Benedict et al. (2002) to Benedict et al. (2011), we find no significant change of procedure that would have altered the conclusion reached by this comparison.

For the fourth possibility, we undertake a series of Monte Carlo simulations, described in detail in a forthcoming publication focused on the zero-points, to understand the interplay between the intrinsic dispersion about the PL and the parallax uncertainties in a statistical sense. These simulations use a well-measured PL as a fiducial by which to compare the parallax uncertainties. Even with the intrinsic variance of the PL included, the resulting variance of the fits is still statistically inconsistent with the input uncertainties (i.e., ${\chi }_{H}^{2}{\nu }^{-1}$ < 1). If the parallax errors are scaled by 50%, our simulations produce final variances consistent with those measured in Figure 2 with ${\chi }_{H}^{2}{\nu }^{-1}\sim 1$. Thus, comparison of the HST+FGS parallaxes to two independent fiducial measurements, Hipparcos and the well-established NIR PL, indicate that the uncertainties are overestimated by ∼50%.

Our assessment is consistent with prior works that employed the HST+FGS parallax program for distance scale applications using both Cepheids and RR Lyrae (for instance, Freedman et al. 2012b; Braga et al. 2015; Muraveva et al. 2015; Neeley et al. 2015; Clementini 2016, among others). For the purpose of forecasting an error budget for the CCHP, we scale the dispersion, σ = 0.11 mag, about the PL shown in Figure 2 by 50%, to project that σ = 0.05 mag is statistically consistent with current data. While these statistical arguments are compelling, they are not conclusive. Owing to the release of initial parallaxes for objects common to Hipparcos in the near future (see Michalik et al. 2015), a more exhaustive exploration of the zero-point for the NIR+MIR PL (and perhaps a better understanding of the Benedict et al. uncertainties) will be feasible at a later stage of our program.

3.1.2. HST Observations of Galactic RR Lyrae

3.1.3. RR Lyrae Light Curve Fitting for Predictive Templates

To estimate the mean magnitudes of our Galactic RRL calibrators directly from the $F160W$ observations, we employ a technique that uses well-sampled optical light curves to generate a template suitable for longer wavelength data. Instead of using Fourier fits modeled to high-cadence NIR observations for select stars (i.e., as in Jones et al. 1996), we will use high-cadence observations in multiple optical bands to derive NIR and MIR light curve templates for each individual star from its own optical light curve. This technique has the advantage of capturing the specific color-structure of an individual RR Lyrae's light curve.

Our template technique was first developed for Cepheids by Freedman (1988) and Freedman & Madore (2010a), and requires high-cadence optical (B, V, I) time-series data. We have initiated an observational survey to obtain such data and derive templates for individual stars that will be fully described in a series of forthcoming publications (the optical data, not including the new HST observations, in A. Monson et al. 2016, in preparation and the template technique in R. Beaton et al. 2016, in preparation). To demonstrate the technique and its role in the CCHP, we present data from our optical campaign for RR Gem of RRab type in Figure 3.

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The optical light curves for RR Gem are given in Figure 3(a) for the B, V, and I broadband filters. These optical luminosity variations are sensitive to two physical effects that change due to the pulsations: (i) temperature and (ii) radius. The temperature variability can thus be isolated using the optical color as a proxy for temperature. The optical color curves for RR Gem are given in Figure 3(b) for ${(B-V)}_{0}$, ${(V-I)}_{0}$, and ${(B-I)}_{0}$.

With the temperature effect constrained by color curves, it is then possible to remove it from the optical light curves and thereby isolate the component that is due to radial variations. The residual curves after a scaled subtraction of the color curves, called the F magnitude by Freedman & Madore (2010a), are given in Figure 3(c) for each of the color curves in Figure 3(b). These F curves predict the shapes of the NIR and MIR light curves, modulo scale factors (see discussion in Freedman & Madore 2010a). Figure 3(d) compares the NIR and MIR light curves predicted from the F magnitude to K_s and J photometry from Liu & Janes (1989) and MIR photometry from the CRRP, which show very good overall agreement.

We can compute the shift between our template light curve in a given photometric band and the single-phase point to adjust the photometric zero-point of our template, as is demonstrated for the 2MASS photometry of RR Gem in Figure 3(d). With the zero-point shift, the template can then be used to determine the appropriate mean intensity in a given band. Thus, from a single-phase point for the CCHP in the $F160W$ filter, we can determine reliable mean magnitudes. Example preliminary measurements from our HST SNAP proposal (PID 13472; Freedman 2013) in $F160W$ are also plotted in Figure 3(d) for RR Gem and show overall agreement with the ground-based H curve (we note that RR Gem had only few of the complications of the significantly brighter HST  RRL calibrators and was chosen as a demonstration object for this reason).

The application of this method requires knowledge of the ephemeris of an RRL (time of maximum light, period, and any period-change related terms) to high precision. Our optical campaign is sufficiently well sampled that when tied into literature observations, we are able to test and revise the ephemerides for our RRL calibrator stars and be relatively confident in our phasing (A. Monson et al. 2016, in preparation). The uncertainty in the mean magnitude is a function of phase (ϕ) and will be discussed in R. Beaton et al. (2016, in preparation). The mean H magnitudes and uncertainties for the RRL calibrators in Table 3 and used in Figure 2 were determined from a single 2MASS observation from this technique.

Our key concern at this state of the CCHP is the precision to which we can measure the distance to our Local Group targets (see Table 4, bottom section). Our Local Group targets span a range of [Fe/H] from −1.68 dex (Sculptor) to −0.44 dex (M32), with a mean and median metallicity of −1.3 dex and −1.5 dex, respectively (values based on the M_V–[Fe/H] relationship for the RRL in our pointings are given in Table 4, unless otherwise noted). Thus, our Local Group sample is relatively well matched to the mean metallicity of our five RRL calibrators (median_[Fe/H] = −1.58 dex). Our distance precision is limited by sources of scatter that are either observational (i.e., measurement) or astrophysical in nature. For the former, typical effects are photometric accuracy, repeatability, and crowding, which generally can be identified and controlled for an individual data set. For the latter, there are numerous physical factors that add scatter to the PL, including but not limited to (i) chemical abundances, (ii) the evolutionary state, and (iii) changes in period (e.g., Smith 1995; Cacciari 2013).

Table 4.  Summary of New Observations Obtained for the RRL Stage of the CCHP

Target	Class	$\langle [\mathrm{Fe}/{\rm{H}}]\rangle$ a	Supplementary Imaging	$F160W\,({N}_{\mathrm{obs}})$	NRRL	RR Lyrae Discovery
RR Lyrae zero-point—
RR Lyr	Galactic RRab	−1.41 ± 0.13	TMMT	2 Random	⋯	⋯
RZ Cep	Galactic RRc	−1.77 ± 0.20	TMMT	2 Random	⋯	⋯
UV Oct	Galactic RRab	−1.47 ± 0.11	TMMT	2 Random	⋯	⋯
XZ Cyg	Galactic RRab	−1.44 ± 0.20	TMMT	2 Random	⋯	⋯
SU Dra	Galactic RRab	−1.80 ± 0.20	TMMT	2 Random	⋯	⋯
Metallicity Effects—
ω Centauri	Cluster	−2.5 to −1.1	Magellan+FourStar	2 Random	34	Sollima et al. (2008)b
TRGB zero-point—
Sculptor	dSph	−1.68c	Magellan+FourStar	2 Random	52	Kaluzny et al. (1995)d
Fornax	dSph	−0.99c	Magellan+FourStar	2 Random	105	Bersier & Wood (2002)
						Mackey & Gilmore (2003)
IC 1613	IB(s)m	−1.60c	⋯	12 Phased	67	Bernard et al. (2010)
M32	compact E2	−0.44	⋯	12 Phased	305	Fiorentino et al. (2012)
M31	SAB(s)b	−1.50	⋯	12 Phased	256	Sarajedini et al. (2009)
M33	SA(s)cd	−1.48	⋯	12 Phased	69	Sarajedini et al. (2006)

Notes.

^aGalactic RRL metallicities are from Benedict et al. (2011) and Local Group metallicities from Column 7, unless otherwise noted. ^bThe most recent compilation of ω Centauri RR Lyrae is Navarrete et al. (2015). ^cMean stellar metallicity for RGB stars with medium-resolution spectroscopy from the compilation of McConnachie (2012) for Sculptor and Fornax and from detailed main sequence fitting for IC 1613. ^dThe most recent compilation of Sculptor RR Lyrae is Martínez-Vázquez et al. (2015).

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Diagnosis of such astrophysical complications requires independent data sets or specialized statistical methods to be properly taken into account (see discussion in Sandage et al. 2015, their Appendix B). Unfortunately, for our Local Group targets such independent measurements are prohibitively expensive for all of the six objects; the mean magnitude of an RR Lyrae at M31 distance is V ∼ 25.5 mag, which is out of reach for current high-resolution spectroscopy and requires HST or imaging on an >8 m facility for high-quality temporal monitoring. Thus, to understand the role of these astrophysical effects on the precision of our Population II distance scale, we can only account for them in a statistical fashion. With comparison of the scatter about a local well-characterized "ideal" PL to a local well-characterized analog to our Local Group RR Lyrae targets, it is possible to make such a measurement.

To assess the scatter about the PL for our NIR data, we compare the H PL for the LMC star cluster Reticulum to that of the star cluster ω Centauri. Reticulum is a cluster (i) of low central concentration (Walker 1992), (ii) of mono-abundance ([Fe/H] = −1.57 ± 0.03; Grocholski et al. 2006), (iii) with an apparent single stellar population (Mackey & Gilmore 2004), (iv) that is located $\sim 11^\circ$ from the LMC center (Walker 1992), and (v) has low apparent foreground and background contamination (Mackey & Gilmore 2004). In contrast, ω Centauri is one of the most massive and metal-rich star clusters with a wide metallicity spread for its RR Lyrae (−2.5 < [Fe/H] < −1.1; Rey et al. 2000; Sollima et al. 2008) and a rather complex horizontal branch morphology (for discussion see Gratton et al. 1986). Moreover, while we have "recent" NIR light curves that can be used to correct for shifts in period for individual stars in Reticulum (a detailed description of how this is done in application to our Galactic RRL calibrators will be given in A. Monson et al. 2016, in preparation), we did not make such changes in ω Centauri. The median [Fe/H] for Reticulum and ω Centauri are well matched to the median of our Local Group sample. Moreover, the total range of metallicity in ω Centauri is also comparable to the total range of our Local Group sample, although it is more metal-poor overall (see Table 4). Thus, a comparison of the PL scatter between these two systems provides a meaningful estimate of the added uncertainty that is due to astrophysical scatter in the RRL populations we anticipate for our Local Group sample.

Figure 4(a) compares the H PL for Reticulum and ω Centauri using image data collected with the FourStar camera on the Baade 6.5 m telescope at Las Campanas Observatory (Persson et al. 2013) and mean magnitudes determined from GLOESS fitting (see discussion in Persson et al. 2004). The data for both clusters are overall of the same quality (i.e., despite the larger distance to Reticulum, the same signal-to-noise ratio is reached). As in Section 3.1.1, we adopt an H period slope from Braga et al. (2015) for the fundamental period (P_F). The study of Sollima et al. (2006) for 16 star clusters found no significant difference in the slopes for clusters spanning a range of nearly 2 dex in [Fe/H]—a very similar span as for ω Centauri (see Table 4). Since the goal of this demonstration is to study the scatter and not the zero-point itself, we neglect a correction for the mean metallicity for either system because it only modulates the absolute magnitude of the zero-point (Marconi et al. 2015; Muraveva et al. 2015). We limit the ω Centauri sample to those stars outside of the ω Centauri half-light radius (Trager et al. 1995, i.e., r < 5')¹⁵ to avoid complications from crowding in its very dense inner regions. We are left with a sample of 81 stars in ω Centauri and 26 stars in Reticulum.

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We determine residuals about the PL as the difference between the magnitude of a given source and its magnitude were it on the PL relation (i.e., vertical from the PL in Figure 4(a)). A normalized marginal distribution for the residuals is shown in Figure 4(b) for Reticulum and in Figure 4(c) for ω Centauri. From a comparison of Figures 4(b) and (c) it is clear that the residuals for ω Centauri show a much larger overall variance than those of Reticulum. For Reticulum, we measure a scatter of σ_tot = 0.04 mag with a median H magnitude uncertainty of σ_meas = 0.02 mag, and for ω Centauri, we measure σ_tot = 0.07 mag with a median H magnitude error of σ_meas = 0.02 mag. We now use these variances to isolate the component in ω Centauri from astrophysical effects. We note that this approach to estimating the effect requires no assumption of the underlying distribution for the residuals from any one source.

Based on the evidence summarized previously, it is not unreasonable to assume that Reticulum represents a system for which the astrophysical sources of scatter (metallicity, evolution, and period shift) are minimal. For Reticulum, the total variance, ${\sigma }_{\mathrm{tot}}^{2}$, is the quadrature sum of the variance that is due to measurement uncertainties (σ_meas) and the intrinsic width of the PL (σ_int). Thus, we can derive an upper limit on the intrinsic variance as

$$\begin{eqnarray}&&{\sigma }_{\mathrm{int}}\lt \sqrt{{\sigma }_{\mathrm{tot}}^{2}-{\sigma }_{\mathrm{meas}}^{2}},\end{eqnarray} \tag{ 1 }$$

from which we estimate that the intrinsic width of the PL is σ_int < 0.03 mag.

The total variance ω Centauri must include an additional term for astrophysical effects (${\sigma }_{\mathrm{astro}}$). We can similarly determine an upper limit on the added variance that is due to the combination of these astrophysical effects as

$$\begin{eqnarray}&&{\sigma }_{\mathrm{astro}}\lt \sqrt{{\sigma }_{\mathrm{tot}}^{2}-{\sigma }_{\mathrm{meas}}^{2}-{\sigma }_{\mathrm{int}}^{2}},\end{eqnarray} \tag{ 2 }$$

from which we estimate that the additional scatter in ω Centauri from astrophysical effects is σ_astro < 0.06 mag, using our estimate of σ_int from Reticulum.

In application to our Local Group RRL sample, we proceed to adopt an uncertainty due to astrophysical effects of σ_astro < 0.06 mag in the H band based on our comparisons to ω Centauri. We will probe this effect directly in the $F160W$ magnitudes by observing a subset of ω Centauri RRL and combining these single-phase observations with our FourStar H templates to derive mean magnitudes (see Table 4). A more in-depth look at these effects requires a larger sample of individual spectroscopic metallicities common to our NIR data set and one that fully samples the multiple stellar populations in ω Centauri.

Assuming the intrinsic dispersion for a multiabundance population is best matched to that of the total scatter in ω Centauri, we adopt σ_astro = 0.06 mag from ω Centauri for the intrinsic scatter term in our preliminary uncertainty estimate for the Local Group RRL pointings. This term will be evaluated on a case-by-case basis for each of our RRL pointings in the H₀ error budget at the conclusion of our program. This is then coupled with the uncertainty of our zero-point discussion for H (σ_fit = 0.05 mag), and we project a total uncertainty on the determination of a given distance using the PL of σ_total = 0.079 mag. Converting into the error on the mean (σ_total/$\sqrt{(}5)$), we find an uncertainty on the mean of 0.036 mag, or 1.7% in distance. Adopting instead the scatter from a mono-abundance population from Reticulum of ${\sigma }_{H}=0.04$ mag, we project an uncertainty on the mean of 0.030 or 1.4% in distance. At this stage in our program, in advance of the anticipated results from Gaia, we select the conservative 1.7% zero-point uncertainty for the RR Lyrae $F160W$ PL zero-point for our preliminary error budget.

Currently, the only technique capable of measuring geometric distances outside of the Local Group is using H₂O megamasers that are found in the accretion disks around central black holes. If seen approximately edge-on and tracked over time, the individual maser sources can be used to trace the dynamics within the accretion disk, and, under the assumption of Keplerian motion, constrain the line-of-sight distance to the host galaxy using geometry.

NGC 4258 is the only galaxy near enough to be used as a TRGB calibrator. It has a geometric distance derived from the kinematics of its circumnuclear maser disk (Humphreys et al. 2013). Modeling of the accretion disk using the detailed kinematical data produces a line-of-sight distance of d_{NGC 4258} = 7.60 ± 0.17 (random) ± 0.15 (systematic) Mpc or μ_{NGC 4258} = 29.40 ± 0.05 (random) ± 0.04 (systematic) mag.

Mager et al. (2008) measured TRGB stars in the halo of this same galaxy using HST + ACS observations (Madore 2002, PID 9477), specifically designed to target its Population II rich stellar halo. Figure 5(a) demonstrates the location of the HST + ACS field, and Figure 5(b) presents the exquisite red giant branch with a highly resolved TRGB. We note that the metallicity dependence of the TRGB, which is projected into a color dependence in the CMD, has been calibrated out of Figure 5(b) following the procedure discussed in Mager et al. (2008) and more formally presented in Madore et al. (2009). The results of applying an edge-detection algorithm to the luminosity function is shown Figure 5(c) and determines the TRGB at I = 25.24 ± 0.04 (Mager et al. 2008).

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Combining the maser distance with the TRGB estimate, we obtain an absolute magnitude for the M_I^TRGB = −4.16 ± 0.06 (random) ± 0.04 (systematic) mag. This value is broadly consistent with other calibrations of the TRGB, M_I^TRGB = −4.04 ± 0.12 mag for [Fe/H] = −1.52 (Bellazzini et al. 2001, 2004), which is the relation used by Mager et al. (2008) to calibrate the dependence of the TRGB on metallicity, but is slightly offset. We note that the initial maser distance at the time of the Mager et al. (2008) from Herrnstein et al. (1999) was entirely consistent with both the TRGB and Cepheid based distances.

Within the context of the CCHP, we use these existing observations to provide a direct calibration of the TRGB, beyond those shown in Table 5. More specifically, we are reanalyzing these archival data to ensure identical image processing techniques and photometry are employed. We plan to calibrate the TRGB in the native $F814W$ HST-ACS flight magnitude system to eliminate uncertainties imposed by filter conversions.

Table 5.  Summary of New Observations Obtained for the TRGB Stage of the CCHP

Target	Classa	Supplementary Imaging	Rgal	Cepheid Distance?	Notes
TRGB zero-point
Sculptor	dSph	Magellan+IMACS	33 (0.08 kpc)	N	⋯
Fornax	dSph	Magellan+IMACS	62 (0.25 kpc)	N	⋯
IC 1613	IB(s)m	Magellan+IMACS	102 (2.17 kpc)	Y	⋯
M32	compact E2	⋯	29 (0.64 kpc)	N	⋯
M31	SAB(s)b	⋯	204 (4.62 kpc)	Y	⋯
M33	dSpr	⋯	159 (4.08 kpc)	Y	⋯
SNe Ia zero-point
M101	SAB(rs)cd	⋯	116 (23.1 kpc)	Y	SNe Ia: 2011fe
M66	SAB(S)b	⋯	40 (11.5 kpc)	Y	SNe Ia: 1989B
M96	SAB(rs)ab	⋯	42 (13.2 kpc)	Y	SNe Ia: 1998bu
NGC 4536	SAB(rs)bc	⋯	30 (13.4 kpc)	Y	SNe Ia: 1981B
NGC 4526	SAB0(s),edge-on	⋯	32 (14.2 kpc)	N	SNe Ia: 1994D
NGC 4424	SAB(s)	⋯	23 (10.3 kpc)	N	SNe Ia: 2012cg
NGC 1448	SAcd, edge-on	⋯	26 (13.3 kpc)	N	SNe Ia: 2001el
NGC 1365	SB(s)b	⋯	36 (19.1 kpc)	Y	SNe Ia: 2012fr
NGC 1316	SAB(0) pec	⋯	92 (53.6 kpc)	N	SNe Ia: 1980D, 1981D,
					2006dd, 2006 mr

Note.

^aFrom the NASA Extragalactic Database.

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Using the RR Lyrae PL discussed in the previous section, we can determine precise distances to Local Group galaxies. Each of these Local Group galaxies has a stellar halo rich in resolved Population II RGB stars, and we can thereby place the TRGB absolute magnitude firmly onto the RRL geometric distance scale.

We have selected galaxies in the Local Group that have known and well-characterized RRL (i.e., with light curves sufficient to identify the pulsation mode and to determine the period). To avoid effects from multiple populations, line-of-sight depth, and differential extinction, among others, we explicitly opt to exclude the LMC or the inner regions of other nearby star-forming galaxies that are not seen face-on. Imposing these requirements yields six nearby galaxies: M31, M32, IC 1613, M33, Sculptor, and Fornax, which have the prerequisite discovery data with HST+ACS (published in the literature; specifics are given in Table 4). Owing to the galactic demographics of the Local Group, five of our six calibrators are dwarf galaxies, but given that these systems are the primary building blocks of the galactic halos we will probe in the SNe Ia hosts, the stellar content of these dwarf galaxies is likely representative of these larger galaxies.

4.2.1. New HST Observations

As discussed in Section 3.3, we have used the HST+WFC3–IR channel with the $F160W$ filter for our studies of the RR Lyrae. As in the CHP-I for Cepheids (for example light curves see Scowcroft et al. 2011; Monson et al. 2012), we obtain 12 phase points that are used with our template fitting techniques (Section 3.1.3) to determine the phase-weighted mean magnitudes. This combination of these two techniques can produce mean magnitudes at the 2% level for individual stars (see detailed discussions in Madore & Freedman 2005; Scowcroft et al. 2011). Example data from our pointing in IC 1613 are given in Figure 6, where Figure 6(a) shows the pointing map (the HST+WFC3–IR pointing has a smaller FOV), and example light curves in $F475W$ (blue), $F814W$ (red), and $F160W$ (black) for RRab and RRc variables in IC 1613 are shown in Figures 6(b) and (c), respectively. The data presented in Figures 6(b) and (c) will be presented in full by in D. Hatt et al. (2016, in preparation) and include a comparison to published works using other methods in addition to our first estimate of the $F160W$ TRGB zero-point. Figure 6 demonstrates that we have sufficient light curve sampling to determine mean magnitudes to high precision.

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The RRL observations for each of the six galaxies are effectively identical, with the exception of Fornax and Sculptor (to be discussed below), and are summarized in Table 4. Fields were chosen to have about 100 RR Lyrae that were previously characterized in at least two optical photometric bands. We anticipate that some fraction of the objects in each field will be blended or crowded due to both the change in resolution from their detection in HST + ACS at $0\buildrel{\prime\prime}\over{.} 05$ pixel⁻¹ to HST + WFC3–IR at $0\buildrel{\prime\prime}\over{.} 135$ pixel⁻¹ and to the increase in the relative brightness of the AGB populations at this wavelength. To cover the majority of the original HST + ACS field, two HST + WFC3–IR fields are required per single HST + ACS field, and we optimized the placement of these fields to maximize the total number of RR Lyrae. We also intentionally placed some overlap between the two fields to test for systematic effects.

The RRL observations for ω Centauri, Fornax, and Sculptor are designed to obtain closely spaced phase points during a single HST orbit in $F160W$. For both Fornax and Sculptor, parallel ACS observations for the purpose of the TRGB are also obtained, as is discussed in Section 4.2.2 (exposures in ω Centauri were too frequent to permit parallel observations due to data transmission rates). The RRL observations will be combined with literature optical light curves (see Figure 4), and the self-template technique of Section 3.1.3 is applied to determine mean magnitudes.

For the TRGB observations, the Local Group targets can be split into two categories: those of low surface brightness and those of high surface brightness. For the low surface brightness galaxies, a single ACS field does not have sufficient sampling of the TRGB, and the photometry for these objects has been supplemented with ground-based observations (Section 4.2.2). For the high surface brightness galaxies, the ACS field does have sufficient statistics to measure the TRGB directly, as we now describe. The TRGB data for the Local Group objects are obtained with ACS in parallel mode to the RRL data previously described.

We constrained the roll angle of the HST observations such that the ACS field occurs at larger object-centric radii, both safely within their halos and at sufficiently low stellar density to avoid significant crowding. For clarity, we include an example Local Group pointing in Figure 6(a) for IC 1613 to demonstrate the coupled observations and their relationship to the archival HST imaging. We are also using imaging data from the archived HST RRL discovery programs (as noted in Table 4) to measure directly the TRGB magnitude in these fields to improve statistics and check for slight differences, if any, in crowding and metallicity between the fields.

4.2.2. Supplementary Wide Field Observations

The TRGB method has been widely applied and extensively tested by many groups. Most recently, Rizzi et al. (2007) reduced and analyzed in a uniform manner HST V and I data. Rizzi et al. (2007) find that the mean statistical uncertainty in an individual distance estimate using the TRGB is only 0.05 mag or 2.5% in distance. The geometric distance to the maser host galaxy NGC 4258 has also been measured to an accuracy of 2% in distance, and its TRGB magnitude has also been measured to 2%. Our new seven independent (Local Group and NGC 4258) estimates of the TRGB absolute magnitude will result in an error on the mean of 0.05/$\sqrt{7}$ = 0.019 mag. For the purposes of understanding our CCHP error budget, we project an error of 0.9% for this stage of the Population II distance ladder.

SNe Ia are the de facto standard candles for determining distances at cosmologically significant scales. SNe Ia, however, are not trivial objects to characterize. Once discovered in transient surveys or by serendipity, the transient event must be typed with spectroscopy, followed with time series and multiband photometry for up to ∼30 days to identify maximum light from which the proper decline rate correction is determined, and a long-baseline photometry is required to determine a precise host galaxy template from which the internal component of reddening can be estimated (see Hamuy et al. 2006, for a good description of the required data for SNe Ia characterization). The need for such studies to be undertaken with as few systematics as possible has inspired several large-scale SNe Ia surveys, including the CSP (see Freedman et al. 2009; Folatelli et al. 2010; Burns et al. 2014, for descriptions of the process).

The internal scatter (i.e., the precision) of SNe Ia luminosities is found to be ∼0.16 mag (e.g., Folatelli et al. 2010). SNe Ia are intrinsically rare events, and it is even more unusual to have one occur sufficiently close to the Milky Way that the distance to its host galaxy can be independently measured. In the last quarter century there have been only 19 SNe Ia found and measured (using modern, linear detectors) in spiral galaxies that are close enough for their distances to be determined independently by Cepheids.¹⁶

Beyond the limited sample size, there are other concerns with respect to the SNe Ia. In particular, there is evidence (e.g., Sullivan et al. 2010; Rigault et al. 2015, among others) that the absolute magnitudes of SNe Ia depend on whether they are hosted by lower mass (spiral and/or irregular) or high-mass (elliptical and/or lenticular) galaxies. The Cepheid distance scale is only applicable to SNe Ia whose hosts contain significant young (20–400 Myr) populations, predominantly spiral galaxies. Thus, a Cepheid-based calibration of the SNe Ia absolute magnitude is subject to any population effects within the SNe Ia sample (regardless of whether systematic or random in nature). Our Population II route will immediately bring SNe Ia hosted by non-spiral systems into the calibration sample and provides a direct test of such population differences. Additionally, the use of Population II distance indicators permits use of SNe Ia in host galaxies where the Cepheid population is not suitable because of crowding or large extinction, as occurs commonly for edge-on galaxies.

Regardless of Hubble type, galaxy luminosity, and inclination, hundreds of TRGB stars populate the dust-free, low-metallicity, low-crowding stellar halos. Nine SNe Ia have been found in such galaxies in the past quarter century; all but one of them had good-quality (non-photographic) light curves. The TRGB is not without pitfalls, however, the most important of which is the need to choose pointings appropriate for the method to reliably produce measurements of the quality required here.

Before discussing the calibration of the TRGB further, there are several challenges of the TRGB as a distance indicator that are worth consideration in the development of a Population II distance scale. Two important examples of applying the TRGB method inappropriately are M101 and NGC 4038/39. As we will discuss in application to these two case studies, there are clear reasons, either in the observational data or in the edge-detection itself, that drive the dispersion in published distance estimates.

There are four published TRGB distance estimates to M101 in the literature: they range from 29.05 ± 0.06 (random) ±0.12 (systematic) mag (Shappee & Stanek 2011), to 29.42 ± 0.04 (random) ±0.10 (systematic) mag (Sakai et al. 2004), to 29.34 ± 0.08 (random) ±0.02 (systematic) mag (Rizzi et al. 2007), and then most recently a value of 29.30 ± 0.01 (random) ±0.12 (systematic) mag (Lee & Jang 2012) based on the weighted mean of nine individual fields. These studies present a wide range of moduli, spanning almost 0.4 mag (in contrast, the Cepheid-based distances span a range of 0.7 mag, see the compilation in Lee & Jang 2012). Not only do the cited distances span a wide range, but this sample demonstrates the broad range of uncertainties quoted (both random and systematic) by various studies.

As it stands, this is an unacceptable outcome for ultimately calibrating the SN Ia. Unfortunately, the fields used to determine the TRGB distances were based on the same data used to study the Cepheids. Owing to their initial purpose, all of those fields are well into the disk of M101 and are therefore very crowded at the significantly fainter magnitude level of the TRGB. Moreover, they are heavily contaminated by brighter intermediate-age AGB and post-AGB stars that confuse and bias any attempt(s) to identify a pure sample of TRGB stars in the optical bands.

This latter problem and its negative consequences are not new. Saviane et al. (2004, 2008), using data deep into the star-forming regions of NGC 4038/39 and contaminated by a brighter and dominant population of AGB stars, measured the distance moduli to be μ = 30.7 ± 0.25 (random) ± 0.14 (systematic) mag and μ = 30.62 ± 0.09 (random) ±0.14 (systematic) mag, respectively. This was soon rectified by Schweizer et al. (2008), who measured the TRGB at μ = 31.51 ± 0.12 (random) ± 0.12 (systematic) mag. This measurement pushed the host galaxy out to 20.0 Mpc, nearly a 50% increase over the distance of 13 Mpc suggested by the initial studies. More recently, Jang & Lee (2015) have independently confirmed the result of Schweizer et al. (2008). Again, high-quality distances can be determined if proper care is taken to either avoid the high stellar density disk or to systematically exclude crowded regions from the TRGB fit.

Further confirmation of the importance of carefully selecting TRGB halo fields comes from the complementary studies of Caldwell (2006) and Durrell et al. (2007), each of which used HST+ACS to measure TRGB distances to individual Virgo cluster dwarf galaxies, and in Caldwell (2006), to intra-cluster stellar populations. These observations were designed with the TRGB in mind and targeted regions of low stellar density with limited contamination from young and intermediate-age populations. A mean distance modulus of μ = 31.05 ± 0.05 mag or d = 16.1 ± 0.4 Mpc was obtained for the nine fields (seven dwarfs and two intermediate regions). Individual distance moduli have quoted uncertainties of ∼0.10 mag and span a range of 0.3 mag. We note, however, that identical methods and data-collection strategies were used in these works, and confirmation by an independent team (as was the case for M101 and NGC 4038/39) is required to verify these measurements. Nevertheless, as was shown for NGC 4258 in Figure 5 and as has been demonstrated in the literature for M66 and M96 (Lee & Jang 2013), M74 (Jang & Lee 2014), and NGC 5584 (Jang & Lee 2015), in addition to these previously described objects, halos provide excellent environs for application of the TRGB as a distance indicator.

In the cases where the TRGB is measured using imaging of appropriate galactic locales, i.e., those in which the old metal-poor population dominates, and in which careful consideration is given to how to measure the discontinuity, the TRGB proves to be of comparable precision as other distance indicators at these faint magnitudes.

In our sample, there are 9 galaxies that have hosted 12 well-observed SNe Ia (Table 5), with the most distant object, NGC 1316, hosting 4 SNe Ia. Our observing strategy for these galaxies was based on the study of Caldwell (2006), who measured the TRGB for the equally distant Virgo cluster dwarfs with ACS to a precision of 0.1 mag. However, we adopt the much higher throughput filter $F606W$, as opposed to $F555W$ as used by Caldwell (2006), to increase observing efficiency. The HST observations (Table 5) were designed to yield a 10σ detection at the TRGB in the $F814W$ filter and, since the color will only be used to remove contaminants, a ∼3σ detection in $F606W$ for stars at the anticipated TRGB in each galaxy. Preliminary reductions of one of our more distant objects, NGC 1365, to be presented by I. Jang et al. (2016, in preparation), suggests this goal for the signal-to-noise ratio is being met.

The field choice for our HST imaging was governed by the following general strategy. First, we avoided extended disks and other obvious young or tidal structures. Second, we attempted to target preferentially along the minor axis to minimize the likely contamination from low surface-brightness thick-disk structure. Lastly, we straddled the WISE W1 25–26 mag arcsec⁻² isophote, and if applicable, the GALEX Near-UV 27–28 mag arcsec⁻² isophote (using custom builds of the public raw data). This resulted in a sample that ranges in galacto-centric distances from ∼10 kpc in NGC 4424 (one of the least luminous galaxies) to ∼60 kpc in NGC 1316 (having prominent shell features and being one of the most massive galaxies). The total anticipated RGB source density was confirmed using published data from Mager et al. (2008) for NGC 4258 and from Lee & Jang (2013) for M66 and M96, as well as providing verification of our signal-to-noise ratio estimates.

Using the metallicity profile of Gilbert et al. (2014) for the resolved stellar halo of M31 (between R_proj ∼ 10 and 165 kpc) as a proxy for our galaxies, we can expect an M31-analog galaxy to have median stellar metallicities between ∼−0.5 dex and ∼−1.0 dex over this radius range (see Figure 11 of Gilbert et al. 2014). The dispersion of the median metallicity is ∼0.5 dex at any given location (see Figure 9 of Gilbert et al. 2014). Thus, the range of metallicities we expect in our SNe Ia hosts is representative of the range of [Fe/H] spanned by our Local Group and Galactic targets (Table 4). Thus, our TRGB ZP determination relative to the RRL will include variations over this metallicity range.

A great benefit of the metallicity dependence of the TRGB is that, unlike the dependence for RRL and Cepheids, the effect of metallicity is encoded into the color of the RGB star, and the most metal-poor stars—those that dominate in our halos—are brighter than the metal-rich stars. Thus, adding additional metal-rich stellar populations will "blur" the tip detection preferentially to fainter magnitudes. The total impact on our TRGB measurements will depend on the star formation history of a given pointing, and we can use our M31, M33, and M32 TRGB data to study these effects empirically within the context of our program. For the purposes of this discussion, we assume an equal distribution of stars over our color range. The impact of metallicity on the TRGB detection has been studied by Rizzi et al. (2007), Mager et al. (2008), and Madore et al. (2009, among others), and these studies consistently find a TRGB slope of ∼0.2 mag color⁻¹ for both the ground-based Johnson filters and the HST flight magnitude system. Using the published TRGB results of Lee & Jang (2013), we can expect a well populated TRGB over a 0.5 mag color range in $F606W-F814W$, which implies a uniform change in the TRGB magnitude of ∼0.1 mag in $F814W$ (using the TRGB slope in the flight magnitude system from Rizzi et al. 2007). Converting the uniform change into an effective dispersion, we predict a blurring over this color range of ${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}$ = 0.028 mag.

Taking considerations from the previous sections to heart, as part of our program, we plan to reanalyze the Lee & Jang (2013) pointings for M96 and M66 (GO-10433), as well as extensive archival fields (taken as parallel pointings) available for NGC 4258 and M101 that reach a similar signal-to-noise ratio as our primary program. This will provide independent checks on our methods (i.e., in comparison to previous work) and also direct empirical tests for AGB-contamination, crowding, and metallicity effects as a function of galacto-centric radius for these objects.

For our final measurement of H₀ from this distance ladder, individual fitting errors, derived independently for each galaxy and including constraints on the effects of metallicity (color), crowding, and completeness, will be used (a first exploration of this will be presented for NGC 1365 by I. Jang et al. 2016, in preparation). For the goals of this work, we make an estimate of the uncertainty for the CCHP error budget by adopting twice the TRGB fitting uncertainty from Rizzi et al. (2007) (σ = 0.10 mag) to account for increased errors in the I-band photometry at the tip for our more distant sample of SNe Ia hosts, a value that is consistent with the uncertainties quoted by Caldwell (2006) for the Virgo cluster. We adopt a TRGB blurring of σ_[Fe/H] = 0.028 mag, which is negligible when added in quadrature to our anticipated TRGB fitting uncertainty. To our total TRGB uncertainty, we then add in quadrature the 0.12 mag intrinsic scatter in the SNe Ia absolute magnitudes (with the term for large-scale flows removed, see Folatelli et al. 2010) and obtain a projected uncertainty for our calibrating sample of ±0.157 mag per source. For the pure Population II calibration using twelve TRGB-calibrated SNe Ia, we obtain a systematic error on the mean of 0.157/$\sqrt{12}$ = 0.046 mag or 2.1% in distance. Thus, we project a 2.1% uncertainty for this stage of the distance ladder.

We now summarize the uncertainties for each of the steps in our current Population II distance ladder, as given in the black notation in the top fork of Figure 8. The CCHP has a geometric foundation calibrated by five Galactic RR Lyrae with HST+FGS  parallaxes (Section 3), which calibrate the zero-point of the RRL $F160W$ PL relation to 1.7% (first box in top fork of Figure 8). The megamaser distance to NGC 4258 and RRL in six Local Group galaxies provide seven independent calibrations of the zero-point for the TRGB (Section 4) to 0.9% accuracy (second box in top fork of Figure 8). The TRGB is then used to set the zero-point for the local SNe Ia sample, here in a set of 9 host galaxies with a total of 12 individual SNe Ia (Section 5), resulting in a precision of 2.1% (middle box of Figure 8). The CCHP can then tie into the current sample of over 200 (and growing) well-observed SNe Ia well into the Hubble flow (Section 6) with a precision of 0.5% (second box from right in Figure 8). Combining in quadrature each of the four systematic uncertainties in the Population II route to the Hubble constant, we conclude that a net uncertainty of 2.9% is achievable with this program (rightmost box for the top fork of Figure 8).

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An ancillary benefit of CCHP is the ability to compare this distance ladder to that from the Cepheids. As indicated in Table 5, five galaxies in our SNe Ia sample and three in our Local Group sample also have distances via the Leavitt Law and, often, measured by multiple independent teams (see summary in Freedman & Madore 2010b; Freedman et al. 2012b). Thus, we can look for effects that are due to crowding, reddening, and metallicity in the Cepheid distances by comparing their results with those from this program (see discussion in Section 1.1). Moreover, we gain additional leverage on the calibration of the SNe Ia zero-point by combining host galaxies with distances determined from both Population I and Population II distance indicators, although this is a process that requires extreme care as it combines measurements with very different systematic uncertainties. Thus, we anticipate that the greatest gain from the existence of two independent distance ladders is the ability to test individually stages of either distance ladder with a careful and systematic approach. In the near future, however, there are significant opportunities to improve stages of these two distance ladders (although we focus in the following discussion on the Population II route described here).

As summarized in Clementini (2016, and references therein), Gaia is expected to observe over 100,000 Galactic RRL, a sample increase of several orders of magnitude compared to the 186 observed by Hipparcos. According to Gaia's post-commissioning performance estimates (see Table 1 in de Bruijne et al. 2014), all RRL with $\langle V\rangle$ < 12.1 mag will have the parallax measured to better than ∼10 μas, whereas individual accuracies will range between 17 and 140 μas for RRL in Galactic globular clusters with typical $\langle {V}_{{HB}}\rangle$ between 14 and 18 mag. This implies that in a few years there will be more than an order of magnitude more RRL PL zero-point calibrators. Moreover, owing to improvements in period coverage and metallicity spanned by this larger sample, it may even be feasible to calibrate all terms in the PL–metallicity relation directly from the calibrators.

According to the current plan¹⁷ , with the first Gaia release having occured in September 2016, parallaxes with submilliarcsecond accuracy for the stars in common between the Tycho-2 Catalog and Gaia will be available soon. This initial catalog will be based on the Tycho-Gaia Astrometric Solution (TGAS; see Michalik et al. 2015) that will compare positions between the Gaia first release and the Tycho-2 catalog. Folding the Gaia trigonometric parallaxes into our Population II distance scale, however, requires additional observations.

In anticipation of the parallaxes being obtained by Gaia, we are obtaining high-quality B, V, I optical light curves of the quality demonstrated for RR Gem in Figures 3(a) and (b) for 55 Galactic RRL with the Three-hundred Millimeter Magellan Telescope (TMMT; A. Monson et al. 2016, in preparation). A completed HST Cycle 21 SNAP program to obtain $F160W$ magnitudes includes 25 additional Galactic RRL calibrators (PID 13472 Freedman 2013) for a total sample of 30 such stars when combined with the CCHP presented in Section 3.1.1. These same 55 stars were also included in the CRRP (Freedman et al. 2012a, V. Scowcroft et al. 2016, in preparation) and have light curves in the MIR similar to that of RR Gem in Figure 3(d). When the trigonometric parallaxes become available, these additional Galactic calibrators can be seamlessly folded into the framework described in Section 3 to set the RRL foundation for the CCHP.

Beyond the gains for the Galactic calibrators, Gaia will also provide distances to better than 1% for about 77 Galactic globular clusters (49% of the known clusters and all clusters within 16 kpc; Cacciari 2013). Thus, Gaia will directly probe the RRL population within ω Centauri and other clusters within ∼16 kpc of the Sun. When coupled with chemical abundances derived from high-resolution spectroscopy, the larger sample of RRL within Gaia has the potential to resolve concerns over how metallicity affects the PL, both for the slope and zero-point (i.e., discussions in Section 3.2), which will further reduce the uncertainty associated with the use of RRL.

The order-of-magnitude increase in parallax calibrators and the more than an order-of-magnitude decrease in mean parallax error could drop the uncertainty on the RRL zero-point from 1.7% to 0.5% in distance (0.079/$\sqrt{55}$ = 0.011 mag; indicated by red text in the leftmost box in upper fork of Figure 8; note that we have adopted the zero-point fitting uncertainty from Section 3.1.1 as an upper limit). Propagating this change through to the measurement of H₀ reduces the total predicted uncertainty on H₀ from 2.9% to 2.4% (indicated by red text in the rightmost box in the upper fork of Figure 8).

As previously discussed, the current systematic error on the absolute TRGB magnitude is 0.12 mag or 6% in distance (Rizzi et al. 2007) and thus going directly to the TRGB at present is not an improvement from our current two-step process using the RRL (black notations in the forks of Figure 8). Moreover, using the current TRGB calibration results in a 6.3% measure of H₀ that is not currently competitive with our current path (∼3.0% measure of H₀). Ultimately, if we wish to calibrate the TRGB directly to better than 1%, we must construct a distance ladder that relies only on the TRGB technique from our local environment that is then applied directly to the SNe Ia calibrators.

Tabur et al. (2009) have combined Hipparcos (Perryman et al. 1997) and photometry from the 2-Micron All Sky Survey (2MASS Skrutskie et al. 2006) to calibrate the magnitude of the TRGB in the NIR (K_s). An optical all-sky catalog with comparable photometric precision does not yet exist. Following the example of Tabur et al. (2009), we are producing high-quality optical photometry for as many tip stars as are accessible from Las Campanas Observatory. More than 1000 of the Tabur et al. (2009) tip stars (determined from Hipparcos) are accessible by the TMMT, and we are pursuing B, V, I photometry for these stars (with multiple epochs to test for variable AGB contaminants at the tip).

The current CCHP TMMT sample contains over 1000 stars, and the resulting TMMT I-band magnitudes (part way through the survey) have mean photometric error of σ_I ∼ 0.04 mag (with removal of stars showing variability). Unfortunately, the current Hipparcos parallaxes have a mean σ_π/π = 30%, and the average M_I is only accurate to ${\sigma }_{{M}_{I}}\sim 0.9$ mag or 45% in distance. Conservatively assuming ∼50 bona fide tip stars, this results in an uncertainty of 0.128 mag (5.9% in distance), which offers no improvement on prior isochrone-based TRGB calibrations (Section 4).

The median magnitude of our TRGB sample is I = 5.34 (the average is $\langle I\rangle$ = 7.4), which also falls well within the highest precision Gaia sample (σ_π <  7 μas for 3 < G < 12.1 mag; see de Bruijne et al. 2014, for end of mission values). Assuming the fractional error of the trigonometric parallaxes (π) is reduced tenfold for our sources (a conservative projection), the mean σ_π/π = 3%. Using our mean I magnitude error (σ_I = 0.04) and a conservative estimate of 50 stars at the tip, Gaia produces a 0.5% calibration of the TRGB magnitude. Gaia will sample many more tip stars than Hipparcos and with corresponding optical photometry can be added to our calibration sample (e.g., Mignard 2003, 2005). Moreover, the associated spectroscopic data products (R = 11,500) from Gaia for stars brighter than G ∼ 16 will permit a high-precision empirical calibration of the metallicity dependence that is fully empirical and relies on metallicities derived from a homogeneous analysis (i.e., not using isochrones as in previous calibrations by Mager et al. 2008; Madore et al. 2009).

Using projections for a Gaia calibration of the TRGB, we estimate that a 2.6% measure of H₀ is feasible (rightmost box of the bottom fork of Figure 8). The Gaia branch of the bottom fork of Figure 8 represents a route to H₀ where the floor set by the uncertainty on the SNe Ia zero-point is reached. Upon the completion of the work described here, the number of SNe Ia calibrators (i.e., those near enough for independent distance determination) becomes the single limiting factor in the "local" measure of H₀.

Even anticipating the significant gains for the distance ladder provided by the Gaia parallaxes, the total H₀ error budget is driven by the relatively small number of local SNe Ia calibrators (see blue points in Figure 7). More importantly, this step affects not just our Population II route, but also those using Cepheids (e.g., SH₀ES and CHP; Riess et al. 2011; Freedman et al. 2012b). As discussed by Freedman & Madore (2010b), the small number of SNe Ia calibrators is a function of several factors: (i) nature's rate of SNe Ia production, (ii) the ability of the astronomical community to detect transient objects, and (iii) the properties of the host galaxy that make the SNe Ia an ideal calibrator. While we have no control over the rate of SNe Ia, the CCHP Population II distance ladder now permits using SNe Ia that are found in early-type and in edge-on late-type host galaxies, which would previously have been precluded from the calibrator sample owing to limitations of distance measurements with Cepheids. Detectability of SNe Ia can only be improved with the increased number and efficiency of transient surveys, for example, the dual-hemisphere ASAS-SN (e.g., Shappee et al. 2014) and the full-sky multiepoch monitoring provided by the Gaia satellite (with alerts predicted to total over 6000 transient objects over its five-year lifetime), which permit a vastly more complete sample of nearby bright SNe Ia to be discovered.

These discoveries can only be capitalized upon for the distance ladder under specific circumstances, which are that the host galaxy is amenable to the non-trivial SNe Ia follow-up described in Section 5 and within the volume probed by independent distance measures. There are two factors setting volume: (i) collecting area (aperture), and (ii) resolution. For HST, this volume (set by practical concerns) is ∼35 Mpc for Cepheids, ∼20 Mpc for the optical TRGB, and ∼1 Mpc for the optical/NIR RR Lyrae—all of which require large numbers of orbits (>10 orbits, with the non-variable TRGB being the most overall observationally efficient). With a sevenfold increase in collecting area and a fourfold increase in resolution, the James Webb Space Telescope will greatly extend the volume within SNe Ia host galaxies that have independently determined distances. Proposed 30 m class optical telescopes equipped with adaptive optics, such as the Giant Magellan Telescope, the Thirty-Meter Telescope, and the European Extremely Large Telescope will be able to surpass HST resolution in the NIR and will boast at minimum a 150-fold increase in collecting area over HST, although these gains will be modulated by atmospheric conditions. The combination of an increased observational effort from transient surveys, the new large-aperture and high-resolution facilities, and the ability to follow-up SNe Ia from nearly any host galaxy using our Population II techniques, demonstrates that the technology and infrastructure are available to increase the number of SNe Ia calibrators.

The fiducial precision required to place high-level constraints on the CMB modeling from these "local" techniques is to measure H₀ to 1% (see discussions in Planck Collaboration et al. 2014). When we use the minimal Population II ladder that is schematically visualized in the bottom fork of Figure 8 with a Gaia-calibrated TRGB and no other changes to the method, reaching 1% in H₀ would require a SNe Ia zero-point calibrated to 0.7% and would require ∼100 SNe Ia calibrators. With 50 SNe Ia calibrators, the SNe Ia zero-point is calibrated to 1.5% and H₀ measured to 1.7%; with 25 SNe Ia calibrators, the zero-point is calibrated to 0.9% and H₀ to 1.3%. We estimate that the anticipated number of nearby SNe Ia is severely limited by Poisson noise (and the relatively short operational lifetimes of all-sky transient programs—1–2 years; Holoien et al. 2016), but a "handful" (two to five) can be anticipated on an annual basis (Gal-Yam et al. 2013).¹⁸ Thus, it may be feasible in the next two decades to reach a ∼1% measure of H₀ from the Population II distance ladder.