Comparing Tip of the Red Giant Branch Distance Scales: An Independent Reduction of the Carnegie-Chicago Hubble Program and the Value of the Hubble Constant

There is a growing tension in cosmology regarding the value of the Hubble Constant (H₀). The traditional "late-universe" approach in measuring H₀ involves the usage of Cepheid variables to determine distances to nearby type Ia supernova host galaxies all at z ≪ 1. The Cepheid distances are used to calibrate type Ia supernova luminosities, that are then applied to SN Ia out into the far-field to measure H₀. The most recent results of this analysis provide a precise value of H₀ = 73.0 ± 1.0 km s⁻¹ Mpc⁻¹ (Riess et al. 2021). On the other hand, the Planck satellite has collected high-resolution data of the cosmic microwave background (CMB). From their data, the Planck team has determined a present value for the Hubble Constant of 67.27 ± 0.60 km s⁻¹ Mpc⁻¹ (Planck Collaboration et al. 2020). This latter result is typically referred to as the "early-universe" approach following the naming convention for methods making use of the pre-recombination form of ΛCDM. The differences in these two methods is nearly a 5σ tension for H₀ at the present day, a fact that has sparked intense discussion about the new physics that would be required in the ΛCDM model to consolidate these two approaches. This issue is not just apparent in these two studies either; work by over a dozen separate groups with a wide variety of early and late-universe techniques show similar discrepancies between the two approaches at varying but persistent levels (as recently summarized by Di Valentino et al. 2021).

The tip of the red giant branch (TRGB) offers an an alternative tool to Cepheids in the otherwise most-popular rendition of the "traditional" distance ladder (Geometric Calibrator ⇒ Cepheids/TRGB ⇒ Type Ia Supernovae). While the TRGB method has become more popular recently due to its role in measuring the Hubble Constant, it has a long history of use and development (Lee et al. 1993; Méndez et al. 2002; Rizzi et al. 2007; Madore et al. 2009). Many groups now routinely use the TRGB as a method of determining distances to nearby galaxies, as it is possible to determine an accurate (∼5%) distance to galaxies within 10 Mpc with a single orbit of HST time (Anand et al. 2019; Hargis et al. 2020; Bennet et al. 2022), with farther distances coming into reach with additional observing time (McQuinn et al. 2017; Danieli et al. 2020; Anand et al. 2021a; Shen et al. 2021).

The physical basis for the use of the TRGB as a standard candle lies in the fact that low-mass stars (<2M_⊙) ascend the red giant branch due to the growth of degenerate helium cores until the cores become hot enough, at ∼10⁸ K, to ignite helium. At this instance (known as the helium flash), the star will rearrange its internal structure and present itself on the horizontal branch where it is dimmer by about four magnitudes. The key point is that the maximum core mass is almost constant at this event due to a close coupling between core mass and temperature, resulting in the standard candle bolometric luminosity nature of stars at the TRGB. In detail, there are age/mass and metallicity dependencies. More massive stars reach the TRGB at younger ages. Our concern will generally be with red giant branch populations older than 4 Gyr and masses below 1.4 M_⊙. The more important metallicity dependence largely results from the effects of line-blanketing in the atmospheres of these red giants that causes the release of energy from the star to shift to longer wavelengths with increasing metallicity. The luminosity dependence on metallicity within a specific spectral window is weakest at about the I-band, where consequently the technique is generally applied, but can become quite substantial at bluer or redder wavelengths.

Serenelli et al. (2017) have reviewed the theoretical framework of the evolution of low-mass stars in the red giant branch phase of their lives. As they express, either theoretical models can inform our expectations regarding TRGB luminosities or observations of the TRGB can provide discrimination between models. Currently the agreement between alternate models and with observations in both absolute luminosities and wavelength dependencies is at the level of ∼0.1 mag. Serenelli et al. (2017) consider that a dominant uncertainty with the models lies with bolometric corrections. Overall, the theoretical models provide confidence in the premise of the TRGB as a tool for measuring distances but the absolute scaling requires an empirical grounding. For detailed reviews of the method, see Salaris & Cassisi (2005), Beaton et al. (2018), and Anand et al. (2021b).

Tully et al. (2013, 2016) used both Cepheid and TRGB distances to set the scale of distances in the Cosmicflows compendium, leading to H₀ estimates of 74–76 km s⁻¹ Mpc⁻¹. Jang & Lee 2017a measured the TRGB in the hosts of SNe Ia with archival HST data (most from programs targeting Cepheids) and measured H₀ = 73.7 ± 2.0 (stat) ±1.9 (sys) for eight SNe (including two highly reddened SNe Ia, SN 1989B and 1998bu). Recently, the Carnegie-Chicago Hubble Program (CCHP, Beaton et al. 2016; Freedman et al. 2019) targeted eight additional hosts and re-observed three. In a series of papers (Jang et al. 2018; Hatt et al. 2018a, 2018b; Hoyt et al. 2019; Beaton et al. 2019; Hoyt et al. 2021), the CCHP team has presented a set of distances to type Ia supernovae hosts from which they ultimately derive their preferred value for H₀ = 69.8 ± 0.6 (stat) ±1.6 (sys) km s⁻¹ Mpc⁻¹ (Freedman 2021).

In this paper, we provide an independent analysis of the CCHP data with the well-tested methodology used as part of the Cosmicflows program (Tully et al. 2008, 2013, 2016) and the related Extragalactic Distance Database (EDD, Tully et al. 2009; Jacobs et al. 2009; Anand et al. 2021b). Our methodology differs from that used by the CCHP, as we use distinct photometry packages, TRGB measurement techniques, and calibrations for the absolute magnitude of the TRGB. These differences allow us to provide a measurement of the TRGB that is as independent as possible, given that we use the same underlying data.

There has been considerable recent discussion about the absolute calibration of the TRGB (see Table 3 in Blakeslee et al. 2021 and Section 7.2 in Anand et al. 2021b). A key ingredient, and one employed by both CCHP and Jang & Lee (2017a) is a TRGB measurement to the maser host galaxy NGC 4258. Here we consider new HST data in two new fields taken in the halo of NGC 4258, the first in this galaxy to be obtained with the same ACS F606W and F814W filters and state of the electronics that have been used to observe the TRGB in the SN Ia hosts. Our calibration is applied to both the Pantheon (Scolnic et al. 2018) and Carnegie Supernova Project/CCHP (Hamuy et al. 2006; Krisciunas et al. 2017) samples of Type Ia supernovae, and we determine values of the Hubble Constant from each.

An aim of the Cosmicflows team is to independently measure a TRGB distance to every galaxy that has the requisite HST observations, and to provide this information in an accessible, transparent, and uniform manner through the Extragalactic Distance Database CMDs/TRGB catalog. ⁵ To facilitate independent analyses, EDD provides the photometry on which the measurement is based for each host. Many of these observations have been initiated by the Cosmicflows team itself in order to investigate a variety of topics relating to stellar populations, the constituents of nearby galaxy groups, and large-scale structure. TRGB distances are an important component within the Cosmicflows compilation assembled to study cosmic expansion and deviations from uniform expansion. As of the writing of this paper, the CMDs/TRGB catalog has TRGB distances available for nearly 500 nearby galaxies.

While the details of our methodology have been described in several previous papers (Makarov et al. 2006; Rizzi et al. 2007; Jacobs et al. 2009; Wu et al. 2014; Anand et al. 2021b), an overview is warranted to provide a general sense of our method. To emphasize the distinctness of our pipeline from the one used by the CCHP team, we highlight three key points:

• 1.  
  We perform PSF photometry and artificial star experiments with DOLPHOT (Dolphin 2000, 2016). DOLPHOT is well tested and has been used by many groups and projects, including the Panchromatic Hubble Andromeda Treasury (PHAT) survey (Dalcanton et al. 2012; Williams et al. 2014). This software is distinct from the DAOPHOT/ALLFRAME program (Stetson 1987) used by the CCHP group in their main analysis. There is good general agreement between photometry obtained via these two separate packages, although there is the potential for small, systematic offsets in the final photometry at the 0%–3% level (Dalcanton et al. 2009; Monelli et al. 2010; Williams et al. 2014; Jang et al. 2021). We touch upon possible systematics further in Section 3. For this work, we use the recommended parameters presented in the DOLPHOT user's manual. ⁶
• 2.  
  Quantifying the position and uncertainty of the TRGB in real data is non-trivial due to the presence of overlapping AGB stars, a finite width of the TRGB, and photometric noise (see Figure 2 for an example). The CCHP group measures the location of the TRGB by using an edge-detection algorithm. They first smooth the luminosity function over a selected range of color and magnitude to a chosen smoothing scale and apply a weighted Sobel filter of a specified kernel size and shape to the result. From the output of the edge detection, they identify the midpoint of the dominant peak as the tip of the red giant branch. Our current methodology was first established by Makarov et al. (2006) (with influence from Méndez et al. 2002), where they model the luminosity function of asymptotic giant branch (AGB) and red giant branch (RGB) stars as a broken power law, with the break denoting the location of the TRGB. Specifically, the theoretical stellar luminosity function is given the form

  

  where a and c are the power law slopes for stars dimmer (RGB stars) and brighter (AGB stars) than m_TRGB, and b indicates the RGB jump. The artificial star experiments performed within DOLPHOT are used to quantify the levels of error, bias, and completeness present in the measured photometry, and these are all explicitly taken into account when modeling the observed luminosity function of AGB and RGB stars. Further work by Wu et al. (2014) present further refinements to improve on speed. The underlying methodology mentioned here has formed the basis for a large amount of work on the TRGB done by several groups (e.g., Jacobs et al. 2011; Karachentsev et al. 2014; McQuinn et al. 2017; Makarova et al. 2018; Crnojević et al. 2019, among many others). Full details of our methodology are available within Makarov et al. (2006); Wu et al. (2014), and Anand et al. (2021b), the latter of which provides a decadal update on the features (e.g., color images) of the CMDs/TRGB catalog first presented by Jacobs et al. (2009).
• 3.  
  Unlike the CCHP who use a singular value for M_TRGB, we standardize the TRGB measurement to a fiducial color following Rizzi et al. (2007) to include a color term to account for the modest metallicity dependence of the location of the TRGB in the F814W filter. While the CCHP use the bluest red giant branch stars for their analysis of each galaxy, these stars do not necessarily have the same color distribution from galaxy to galaxy. The zero–point of the Rizzi et al. (2007) calibration used in the EDD database was set via horizontal branch measurements in five nearby dwarf spheroidal galaxies, ultimately linked to trigonometric observations (Carretta et al. 2000). This calibration is entirely independent from the calibration in the LMC used by the CCHP, and is given by, for the F606W and F814W filters:

  

  where A_F814W is the adopted foreground extinction and is the median color of the TRGB, after correcting for reddening. In any event, in this paper, we will use the maser distance to NGC 4258 to calibrate the TRGB and reference both the CCHP and our measurements to this common zero-point peg.

Though not intentionally (as the established procedures for the CMDs/TRGB catalog go back over a decade), we find that our data reduction and analysis techniques provide for TRGB distance measurements that are as independent from the CCHP team as we think is possible, given the underlying imaging is the same.

We retrieved the individual *.flc HST images from the Mikulski Archive for Space Telescopes (MAST ⁷ ). These images are already corrected for issues that can arise due to charge transfer inefficiencies present with the HST cameras. For purposes of alignment within DOLPHOT, we create drizzled (*.drc) images using DrizzlePac (Avila et al. 2015). We stress that we do not use the drizzled images for photometry, as the resampling done to create these drizzled images can affect the accuracy of the final measurements. The photometry is performed directly on the individual *.flc exposures (and subsequently combined by DOLPHOT), with the drizzled image serving as the basis for object detection as well as a coordinate reference frame. ⁸ A summary of the observations used in this paper is shown in Table 1.

Table 1. Data Summary

Galaxy	Prop. ID	Prop. PI	Blue Filter	Exposure (V)	Exposure (I)	S/N (V)	S/N (I)	# Stars
M66	13691	W. Freedman	F606W	2420 s	4754 s	2	5	16,322	0.982
M96	13691	W. Freedman	F606W	2410 s	7204 s	2	5	8948	0.979
M101	13691	W. Freedman	F606W	3650 s	3489 s	5	5	8653	0.969
NGC 1309	10497	A. Riess	F555W	57,600 s	24,000 s	2	4	15,864	⋯
NGC 1316	13691	W. Freedman	F606W	14,676 s	24,396 s	2	5	8,812	0.905
NGC 1365	13691	W. Freedman	F606W	14,676 s	24,396 s	2	5	9,921	0.911
NGC 1404	15642	W. Freedman	F606W	37,628 s	39,946 s	5	5	5,724	0.713
NGC 1448	13691	W. Freedman	F606W	8551 s	18,253 s	2	5	5,913	0.830
NGC 3021	10497	A. Riess	F555W	57,600 s	24,000 s	2	4	6,732	⋯
NGC 3370	9351	A. Riess	F555W	57,600 s	24,000 s	2	4	20,682	⋯
NGC 4038/9	10580	I. Saviane	F606W	10,870 s	8,136 s	5	5	40,038	⋯
NGC 4258	16198	A. Riess	F606W	1059 s	1132 s	2	4	23,410	0.983
NGC 4424	13691	W. Freedman	F606W	3574 s	10,962 s	2	5	15,992	0.812
NGC 4526	13691	W. Freedman	F606W	3574 s	10,962 s	2	5	22,854	0.849
NGC 4536	13691	W. Freedman	F606W	3536 s	10,923 s	2	5	13,869	0.840
NGC 5584	11570	A. Riess	F555W*	45,540 s	14,400 s	2	4	13,097	⋯
NGC 5643	15642	W. Freedman	F606W	10,286 s	10,526 s	2	4	13,192	0.955

Note. Table describing the observations used for the comparison within this paper. The individual columns are (1) name of the galaxy, where clicking on the link will open a new browser tab with the respective CMDs/TRGB catalog page, (2) HST proposal ID for the underlying data, (3) proposal PI, (4) the bluer filter used to construct the color–magnitude diagram, (5) exposure time in the bluer filter, (6) exposure time in F814W, (7) adopted S/N cutoff in the bluer filter, (8) adopted S/N cutoff in F814W, (9) the number of stars in each galaxy's photometry catalog, and (10) where available, the completeness in F814W at the magnitude of the TRGB. In the table header, we use "V" and "I" to denote the approximate HST flight filter system counterparts (F555W/F606W and F814W). The "*" symbol in the "Blue Filter" column denotes that this observation (of NGC 5584) was taken with WFC3/UVIS instead of the preferred ACS/WFC combination.

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Once the combined photometry and artificial stars are complete, we apply quality cuts to both using a modified version of the criteria presented in McQuinn et al. (2017). Namely, we select for stars that meet the following criteria:

• 1.  
  Object type ≤2
• 2.  
  Error flag = 0 in both bands
• 3.  
  (Crowd_F555W/F606W + Crowd_F814W) < 0.8
• 4.  
  

To describe these selections, we briefly summarize the information presented in the DOLPHOT user's manual. Object types of 1 or 2 select for only "good" or "faint" stars, respectively, and stars with an error flag = 0 includes only stars which were determined to have been well-recovered. The sharpness criteria (zero for a perfect star) allows us to exclude cosmic rays (large positive sharpness values) and background galaxies or blends of stars (large negative sharpness values). Lastly, use of the crowding parameter allows us to remove stars which lie in highly crowded environments. The only metric we vary from galaxy to galaxy is the adopted signal-to-noise (S/N) cutoff, as the relative depth of the imaging varies for each target. We provide the final signal-to-noise selections used for each target in Table 1.

We note that we reduced this data set as independently as possible from the CCHP team. Our database has hosted the present TRGB distance to NGC 4038/9 since 2010. For the remainder of the targets under consideration, we performed reductions and TRGB analyses as data became publically available from their respective programs on the HST archives (and as time allowed), and subsequently made the results publicly available on EDD. As a consequence, distances to several of the CCHP selected galaxies (M66, M96, M101, NGC 4038/9, and NGC 5643) were first available within our catalog, whereas the rest were first published by the CCHP team.

Additionally, an important note about the photometric uncertainties determined throughout this work (and many others in the literature)− they are very likely to be underestimates, and in a way which is difficult, if not impossible to quantify with the present data set. Besides differences in choices of PSF fitting software and their respective suite of options, extensive work by the ANGST and PHAT collaborations (Dalcanton et al. 2009, 2012; Williams et al. 2014) have uncovered systematic offsets (∼0.02−0.05 mag) in PSF magnitude measurements of identical stars in different locations on HST's detectors. These systematic offsets are not only dependent on position, but also magnitude. The source of these systematic offsets likely lie in some combination of the adopted CTE-corrections, flat-fielding methods, and PSF libraries used. While the ACS and WFC3 instrument teams are continuously improving their methods (e.g., Hoffmann & Avila 2017; Anderson & Ryon 2018; Anderson 2018), some fraction of these issues likely persist. Without the wealth of data that these previous large surveys have covered, we are simply unable to quantify the analogous uncertainties in our data. Instead, we advise the reader to keep this additional, currently unquantified source of uncertainty (∼0%–3% in distance) in mind.

3.1. CCHP Sample Quality

3.2. Archival Sample Quality

While we find that the new data set obtained by the CCHP team is well-suited for measuring the TRGB, the same cannot be said for the set of older, archival data used in their analysis. Most of this data (with the exception of NGC 4038/9) was obtained to detect brighter Cepheids, and the observing programs targeted the disks and thus their fields of view include only a small fraction of the halos of these galaxies.

Take for comparison the CMD of NGC 1316 shown in the left panel of Figure 1, which we will find to lie at a distance of 19.1 Mpc. The data for this galaxy was obtained by the CCHP (GO-13691, PI W. Freedman). In F814W (the filter used for measuring m_TRGB), the total exposure time is 24,396 s. The "bluer" filter for this observation, which is used to isolate the red giant branch from younger stellar populations, is the preferred F606W. F555W can be used to construct a CMD and measure the TRGB but F606W is preferred because (1) the lesser infrared sensitivity of F555W causes the redward clip on the CMD to impinge substantially on the red giant branch, and (2) F606W is a significantly wider filter than F555W, ⁹ allowing more flux to reach the detector (there is an increase in depth of 0.7 mag for equal exposure times).

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Now give attention to the archival sample: NGC 1309, NGC 3021, and NGC 3370 all have 24,000 s of observations in F814W, essentially the same as NGC 1316. The right panel of Figure 1 shows the CMDs for each of these galaxies, trimmed to exclude regions that lie within the crowded and dusty disks (seen in the inset imaging). In displaying these main CMDs, we use the same quality cuts as described earlier, and adopt the least stringent S/N selections as we do for any other galaxy in this study (S/N = 2 in F555W, and S/N = 4 in F814W). Our photometry for these targets reach a similar depth as it does for NGC 1316 (F814W ∼ 29 mag). The expected values of m_TRGB are nearly 1 magnitude fainter for these galaxies than is the case with NGC 1316. A crude estimate of the exposure times required to reach the same S/N ratio at m_TRGB is 2.5² ∼ 6×. A second set of data is also plotted, in a dimmer gray color. For this sample, we lowered the S/N cut in F814W to 2.5, removed the crowding cuts, and weakened the (relatively stringent) sharpness cuts to ≤ ∣0.3∣ in both bands (the base recommendation from the DOLPHOT manual).

Beyond the limitation in depth, these observations have additional shortcomings. The placement of these archival fields in the disks (originally targeted for Cepheids) increases the potential of errors from crowding. Additionally, the bluer filter used for this set of data is F555W, instead of the preferred F606W, which causes part of the RGB to be "pushed" off the right edge of the observed CMD beyond the credible detection limit. While partially mitigated by the increased exposure time in F555W relative to F814W, the observations are targeting the disks of these galaxies, which are inherently more metal-rich (and hence redder and fainter in F555W). And while observations for a fourth supernova host (NGC 5584) are taken with what seemingly should be sufficient depth, the data for this target were taken with WFC3/UVIS instead of the standard ACS/WFC. The overall system throughput for WFC3 is decreased by nearly a factor of two in F814W (see Figure 2 in Deustua & Mack 2018). In addition, the disk of NGC 5584 covers most of the smaller WFC3/UVIS field, leaving only ∼15% of the field useful for detecting halo stars.

As noted earlier, one exception to the above issues involves the Antennae galaxies (NGC 4038/9). The archival observations for this target (GO-10580, PI I. Saviane) exhibit a confluence of preferred qualities. Namely, the camera and filters (ACS/WFC with F606W+F814W) are optimal for a measurement of the TRGB, and the field placement is in a less crowded region of the galaxy (away from the merging disks and on an outer tidal tail). This circumstance is not an accident, as these archival observations were taken with the primary goal of measuring the distance to the Antennae via the TRGB (Saviane et al. 2008; Schweizer et al. 2008).

In this section, we focus on a comparison between the CCHP and EDD TRGB results derived from the same underlying data. Afterwards, we provide a measurement of the TRGB in the megamaser host NGC 4258 based on new HST data obtained at two positions in the halo of the galaxy. These combined results allow a comparison of our two TRGB distance scales.

All our photometry and TRGB distance information, as well as footprints, CMDs, and color images are publicly available within the CMDs/TRGB catalog on EDD (hyperlinks to each galaxy's page can be found in the first column of Table 1). A complete description of the contents of the catalog is provided by Anand et al. (2021b). We also provide our determination of the observed magnitude of the TRGB for each galaxy (m_TRGB), as well as the measured median colors at the tip in Table 2. Additionally, we provide footprints, plots of stars used for developing our CMDs, the CMDs themselves (along with TRGB measurements), and luminosity functions for our reductions of the CCHP targeted galaxies in Appendix (see Figures A1, A2, A3, and A4).

Table 2. Values Used to Determine H₀

Host	mTRGB	Color0	AF814W	μTRGB,cal	SN	mB Pan
M66	26.32 ± 0.03	1.58 ± 0.04	0.050	30.22 ± 0.05	1989B	10.98 ± 0.12	11.16 ± 0.07
M96	26.30 ± 0.02	1.62 ± 0.06	0.038	30.20 ± 0.05	1998bu	11.00 ± 0.12	11.01 ± 0.06
M101	25.08 ± 0.03	1.27 ± 0.03	0.013	29.08 ± 0.05	2011fe	9.83 ± 0.10	9.82 ± 0.03
N1316	27.42 ± 0.05	1.47 ± 0.07	0.033	31.36 ± 0.07	1980N	11.98 ± 0.10	12.08 ± 0.06
N1316	27.42 ± 0.05	1.47 ± 0.07	0.033	31.36 ± 0.07	1981D	11.61 ± 0.23	11.99 ± 0.17
N1316	27.42 ± 0.05	1.47 ± 0.07	0.033	31.36 ± 0.07	2006dd	11.92 ± 0.08	12.38 ± 0.03
N1365	27.43 ± 0.03	1.28 ± 0.04	0.031	31.41 ± 0.05	2012fr	11.93 ± 0.13	12.09 ± 0.03
N1404	27.31 ± 0.06	1.35 ± 0.03	0.017	31.29 ± 0.07	2007on	12.46 ± 0.19	12.39 ± 0.07
N1404	27.31 ± 0.06	1.35 ± 0.03	0.017	31.29 ± 0.07	2011iv	11.98 ± 0.15	12.03 ± 0.06
N1448	27.35 ± 0.04	1.29 ± 0.03	0.021	31.33 ± 0.06	2001el	12.18 ± 0.09	12.30 ± 0.04
N4038	27.72 ± 0.13	1.14 ± 0.07	0.071	31.68 ± 0.14	2007 sr	12.30 ± 0.10	12.30 ± 0.15
N4258	25.43 ± 0.03	1.32 ± 0.04	0.025	⋯	⋯	⋯	⋯
N4424	27.05 ± 0.05	1.38 ± 0.02	0.031	31.00 ± 0.07	2012cg	11.62 ± 0.12	11.72 ± 0.06
N4526	27.03 ± 0.02	1.36 ± 0.03	0.035	30.99 ± 0.05	1994D	11.51 ± 0.17	11.76 ± 0.04
N4536	27.03 ± 0.12	1.27 ± 0.04	0.028	31.01 ± 0.13	1981B	11.60 ± 0.09	11.64 ± 0.04
N5643	26.70 ± 0.03	1.30 ± 0.03	0.278	30.42 ± 0.07	2013aa	11.27 ± 0.14	11.31 ± 0.09
N5643	26.70 ± 0.03	1.30 ± 0.03	0.278	30.42 ± 0.07	2017cbv	11.20 ± 0.14	11.30 ± 0.09

Note. Table providing the data used to measure the value of H₀ using our TRGB determinations and both the Pantheon and Carnegie Supernova Project (CSP) sample of supernovae. The individual columns are (1) host galaxy, (2) the measurement of m_TRGB in F814W, (3) the reddening corrected median F606W-F814W color of the measured TRGB, (4) adopted extinction for F814W, (5) the distance modulus to each galaxy, after rescaling the Rizzi et al. (2007) zero-point with our new TRGB measurement in NGC 4258, (6) name of the individual type Ia supernova, (7) standardized peak magnitude of the supernova provided by the Pantheon supernova sample, and (8) standardized peak magnitude of the supernova provided by the CSP sample. Note that the error as given in column (8) does not include an intrinsic error, and so we add 0.10 mag in quadrature during the process of determining H₀.

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4.1. CCHP Sample Results

We are able to reliably detect the TRGB for the sample of 11 galaxies with new data obtained by the CCHP group from GO-13691 and GO-15642 (PI. W. Freedman). An example color–magnitude diagram from our reduction of this data set is shown in Figure 2, with information on the remaining galaxies shown in Appendix (Figures A1–A4). The left panel shows the CMD and TRGB determination for NGC 1448, for which we derive a distance of D = 18.8 ± 0.8 Mpc. The observed luminosity function, best-fit model luminosity function, and results of a first-derivative edge detection (displayed for visual comparison) are shown in the top-right panel. The bottom-right panel shows a small portion of the drizzled F814W image used as the reference frame, with stellar detections that pass the DOLPHOT quality cuts encircled in green. The region shown is close to the top of the detector, where crowding is most significant, yet the stellar detections are still cleanly separated. Portions of the very top of the chip had been manually excluded from our analysis due to visible star formation, which had been measured via the presence of large amounts of blue, upper main sequence stars (see Figure A2 for a look at the full detector).

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4.2. Archival Sample Results

4.3. NGC 4258

NGC 4258 has a very precisely known distance of D = 7.568 ± 0.082 (stat) ±0.076 (sys) Mpc obtained from observations of its water megamaser (Reid et al. 2019). The previous CMDs/TRGB catalog distance determination for NGC 4258 was 7.65 ± 0.12 Mpc based on a TRGB measurement of m_TRGB = 25.43 ± 0.03 at a median color of F555W-F814W = 2.12 ± 0.04. This determination was derived from the outer regions (∼25%) of the field shown in dashed yellow of Figure 3 (GO-9477, PI. B. Madore).

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As part of a Cycle 28 HST program (GO-16198) designed to increase the sample of Cepheids in NGC 4258, A. Riess and collaborators obtained two fields of parallel ACS F606W and F814W imaging in the halo of NGC 4258. The footprints for these two ACS fields are shown in red in the top panel of Figure 3, where the background image is a composite color (gri) image created from Sloan Digital Sky Survey imaging (York et al. 2000).

While great effort has been put into measuring the magnitude of the TRGB in this galaxy (Macri et al. 2006; Rizzi et al. 2007; Mager et al. 2008; Jang et al. 2021), our new observations have two key benefits over all previous fields used in literature measurements. First, the bluer filter for these new fields is the preferred F606W instead of F555W. All the other TRGB measurements presented in this paper use F606W as the bluer filter, which allows for a more accurate comparison. Second, these are the first fields taken in the halo of NGC 4258 after the 2009 May mission (STS-125) that serviced the electronics and replaced the power supply on ACS and with the same or similar state of charge transfer efficiency degradation. There is a 10–15 year gap between 2003 and 2005 when the ACS observations of NGC 4258 used to calibrate TRGB by Jang et al. (2021) were obtained and those in the 2015–2020 time period of the SN host observations and the new NGC 4258 data. In this span, a TRGB star in the halo of NGC 4258 is estimated to suffer a change of 0.1 mag due to degrading CTE. While this is largely corrected by pixel-based CTE rectification in the pipeline, the correction is a model that is imperfect and it is likely some fixed fraction of the correction persists as an error in H₀ that is best reduced by using data for NGC 4258 and the SN Ia hosts for which the electronics are in a more similar state.

Our initial TRGB measurement was m_TRGB = 25.444 ± 0.031, from a combination of both of our new ACS fields. However, as shown by the recent careful analysis of Jang et al. (2021), it is possible for contamination from the outer disk of the galaxy to introduce small systematic deviations in the measured magnitude of the TRGB. It is not clear that our distinct methodology would suffer from these same issues, however we opt to be conservative in our analysis. To avoid any contamination from the outer disk of NGC 4258, we further restrict the selection of stars used for the final measurement by removing any stars that lie within D₂₅, which corresponds to a semimajor axis SMA (semimajor axis) >10'. This radius (shown as the dashed blue line in the top panel of Figure 3) is defined at a level of 25 in the B band, as reported by de Vaucouleurs et al. (1991). The isophotal radius of the sources in our two fields as seen in Figure 3 thus range between 10' and 16' SMA, similar to the range of radii used by Jang et al. (2021). This selection is also at a greater isophotal radius than the GO-9477 field (though similar to the region used for the previous CMDs/TRGB catalog analysis of this archival field).

Using this radius to trim our sample reduces the number of stars in the final CMD from 23,410 to 16,169. The removed stars are shown in the bottom-left panel of Figure 3. Our final result is shown in the bottom-middle panel of Figure 3, where we find m_TRGB = 25.427 ± 0.025 at a median color of F606W − F814W = 1.33 ± 0.04. The bottom-right panel shows the luminosity function and our best-fit result. The results of a first-derivative edge detection are also shown for comparison and match well with our modeled break. Our final result is fainter than the recent measurement of m_TRGB = 25.372 ± 0.014 by Jang et al. (2021) by 0.055 ± 0.028 mag, though the results are consistent at a level of 1.9σ given the mutual statistical uncertainties added in quadrature. As discussed in Section 3, the significance of this disagreement is likely an overestimate, as there are various small-scale systematics which are not easily brought out with such limited data sets. Our new measurement is nearly the same as the previous EDD determination from the outer 25% of the GO-9477 field (m_TRGB = 25.43 ± 0.03).

We can now compare TRGB distances to NGC 4258. In our case (EDD), = m_TRGB − A_F814W − M_TRGB = 25.427 −0.025 + 4.044 = 29.446 ± 0.079 mag. In the case of CCHP, mag, where the adopted foreground extinction A_F814W is the same and the value of M_TRGB is adopted from Hoyt (2021). The corresponding distances are Mpc and Mpc.

4.4. EDD and CCHP Comparison

Our independent TRGB measurements of stars in Cepheid hosts and NGC 4258 can be compared with those measured by the CCHP team. A comparison of the values of m_TRGB,0 with uncertainties ¹⁰ can be seen in the left-hand panel of Figure 4. The mean difference between our two sets of measured values is Δm_TRGB,0 (EDD-CCHP) = 0.042 ± 0.012 mag with a scatter of ±0.038 mag.

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However, we note that each team measures the tip in a different color range, so this comparison is not on equal terms. The CCHP tip is that of the bluest available RGB stars while the EDD methodology includes a broader and redder color range than those used by the CCHP. Since the F814W TRGB is observed to decrease in brightness at redder colors (with increasing metallicity), we would anticipate that the EDD TRGB measurements of higher metallicity populations would tend to be systematically fainter, which is in line with what is found. Ultimately, the translation of apparent TRGB magnitudes to distance moduli depend on the separate CCHP and EDD absolute magnitude calibrations and accounting for foreground obscuration.

In anticipation of assessing the Hubble constant, let us factor out zero-point calibrations by comparing CCHP and EDD distances normalized to their respective distance estimates to the maser host NGC 4258. To derive values from the CCHP, we begin by taking the most recent CCHP determinations of μ_TRGB (Freedman et al. 2019; Hoyt et al. 2021) with an adjustment to the new zero–point of = −4.045 (Hoyt 2021). We then subtract the CCHP distance modulus of NGC 4258 (μ = 29.392) from each of these values to obtain distance moduli that are relative to NGC 4258. Because the same TRGB absolute magnitude is assumed for the SN hosts and NGC 4258, its value is nullified in the difference between distance moduli.

For the same galaxies, we obtain the TRGB distance moduli as reported in EDD, which include the zero–point and color calibration of Rizzi et al. (2007). From each, we subtract our new TRGB distance modulus for NGC 4258 (μ = 29.446) to obtain a set of distance moduli that are also relative to NGC 4258. The comparison between the CCHP and EDD values are shown in the right panel of Figure 4. The mean offset between the relative distance scales is Δμ (EDD-CCHP) = −0.028 ± 0.035 mag, or ∼1.5% in distance, with a scatter of ±0.052 mag. The error on Δμ (±0.035 mag) is the quadrature summation of errors in each of the EDD and CCHP NGC 4258 tip values and the uncertainty in the differential between EDD and CCHP values of the tip absolute magnitude. It is important to note that this −0.028 mag difference is weighted by galaxy, and not by SN as is necessary for the determination of the Hubble constant.

An unmentioned detail is that the observed TRGB magnitudes must be corrected for foreground extinction. We, in common with the CCHP team, assume foreground extinction values given by Schlafly & Finkbeiner (2011). The one exception is that of NGC 5643. The galaxy NGC 5643 is located at the relatively low galactic latitude of b = 15° where the dust maps, which have relatively coarse resolution, give uncertain attenuation estimates. To determine E(B–V) for NGC 5643, we use the displacement of the zero-age main sequence (ZAMS) to measure the absolute foreground reddening of the galaxy (see the example shown for ALFAZOAJ1952+1428 in Rizzi et al. 2017). Using this method, we find a value of E(B–V) = 0.161, slightly higher than the value of E(B–V) = 0.149 from Schlafly & Finkbeiner (2011). For the purposes of producing Figure 4 and the values and discussion presented in this subsection, we have adopted the Schlafly & Finkbeiner (2011) value to ensure an even comparison. For the purposes of determining H₀ (in the next section), we adopt our new value of E(B–V) = 0.161 ± 0.024 mag.

To recap, the left side of Figure 4 compares the CCHP and EDD apparent, extinction-corrected observed magnitudes of the TRGB (m_TRGB,0) for all the galaxies under discussion (including NGC 4258). We find that the EDD values are ∼2% fainter. Because each group measures the tip over a different color range (with EDD probing redder), we expect a systematic offset in the observed direction that originates solely from the different color ranges used to measure the TRGB. The right-hand side of Figure 4 shows the comparison between our two distance measures relative to NGC 4258 (−0.028 mag), and is the more relevant comparison for the purpose of setting the extragalactic distance scale, and hence the value of H₀. Recently, Hoyt (2021) presented a similar figure to the right side of our Figure 4 in Figure 13 of that paper. An offset of 0.001 mag was found, smaller than the value we present here. Two differences are to be noted. The first is that we include our distance to NGC 1404, which was determined recently. The second is our new TRGB measurement for NGC 4258, which forms the basis of the zero-point scaling for the entire diagram. Broadly speaking, there is concordance that our two distance measures are in excellent agreement and that the TRGB is a reliable and efficient method of determining distances to nearby galaxies.

With our independently determined TRGB distances to the CCHP sample of galaxies, along with a new and consistent calibration of the TRGB enabled by the new observations in NGC 4258, we can derive the value of the Hubble Constant. Our procedure is relatively straightforward, as we are not reassessing the SN Ia portion of the distance ladder. Rather, we are reusing the two mostly widely used standardized SN Ia samples. These are the Pantheon (Scolnic et al. 2018) and Carnegie Supernova Project (CSP, Hamuy et al. 2006; Krisciunas et al. 2017) samples of supernovae. Each of the two is assessed separately, and the relevant parameters are provided in Table 2.

We make use of the following Equation from Riess et al. (2016):

where a_b is the intercept of the SN Ia Hubble diagram (translated to z = 0) and is the standardized absolute luminosity of a type Ia supernovae (at the fiducial point of a specific methodology for standardizing SN Ia light curves, e.g., Scolnic et al. (2018) or Burns et al. (2018). may be calibrated from our TRGB distances in SN Ia hosts.

We obtain an initial value of μ_TRGB for each galaxy by following Equation (2), the zero–point and color calibration from Rizzi et al. (2007). We then rescale these distances based on our new measurement of the TRGB in NGC 4258. In other words, we take the values of μ_TRGB for each galaxy and adjust these distance moduli by the difference in our measured value of μ_TRGB for NGC 4258 based on the Rizzi et al. (2007) calibration (μ = 29.446) and the known value based on the megamaser distance (μ = 29.397, Reid et al. 2019). We refer to these newly calibrated set of distance moduli as , where for each galaxy:

To obtain , we take the weighted average of the individual values of for each supernova. These are found by = m_B − μ_TRGB,cal, where m_B is the standardized peak magnitude of each type Ia supernovae in the sample. The weights used in this procedure are the errors in the measured TRGB distances added in quadrature with the errors in m_B . With the value of in hand, we adopt the value of a_b measured from supernovae in the Hubble flow and corrected to z = 0 (with q₀ = −0.55 and j₀ = 1 as in Riess et al. 2016 and Freedman et al. 2019). For the Pantheon sample (with SN peak magnitudes m_B ^Pan), we use a_b = 0.71435 ± 0.001 which was derived from 746 SNe Ia at 0.023 < z < 0.15 in the expanded Pantheon sample that pass standard quality cuts ¹¹ (Scolnic et al. 2018; Brout et al. 2022). While the CCHP program did not explicitly provide the equivalent a_b CSP value in Freedman et al. (2019), we are able to derive a_b = 0.690 ± 0.002 from their values of H₀ = 69.8 km s⁻¹ Mpc⁻¹ and using Equation (3).

Along with the measurement of H₀, equally important is the error budget associated with our final reported values. To provide the final quoted uncertainty associated with our result, we add in quadrature the following terms: (1) the mean error in (which accounts for the errors from the individual TRGB (including an assumed 15% uncertainty in the extinction) and supernova measurements), (2) the error in the NGC 4258 TRGB measurement, (3) the error in the NGC 4258 megamaser distance, and (4) the error in 5a_b . These individual contributions are also summarized in Table 3.

Following the above prescription, from the Pantheon sample we find a value of = −19.31 ± 0.04 and H₀ =71.5 ± 1.8 km s⁻¹ Mpc⁻¹. Using the CSP sample, we find = −19.18 ± 0.03 and the same value of H₀ = 71.5 ± 1.8 km s⁻¹ Mpc⁻¹, implying good agreement between the values of H₀ derived from the two supernova samples. We note that it is not meaningful to compare the values of and a_b between the two SN Ia light curve standardization methods because each depends on fiducial terms (i.e., which SN Ia light curve shape and point along its light curve serves as the reference). This difference cancels in Equation (3) and the determination of H₀. We also calculated H₀ accounting for the covariance of multiple SNe Ia in the same host using the same TRGB distance (i.e., 3 in NGC 1316, 2 in NGC 1404, and 2 in NGC 5643) and found it made little difference–the net effect was raising the Pantheon value by ∼0.1 km s⁻¹ Mpc⁻¹ and lowering the CCHP value by the same. We retain the simpler calculation for its accessibility.

Our preferred value of H₀ (71.5 ± 1.8 km s⁻¹ Mpc⁻¹) is somewhat larger than the value of H₀ = 69.8 ± 0.6 (stat) ± 1.6 (sys) km s⁻¹ Mpc⁻¹ found by Freedman (2021) due to differences that are summarized in Table 4. We provide these differences in magnitudes which are more directly traceable to the observations and correspond to units of , where a difference of 0.03 mag corresponds to a difference of ∼1 km s⁻¹ Mpc⁻¹. Broken down explicitly, these differences are:

• 1.  
  There is a −0.028 mag difference (EDD−CCHP) between our two distance scales, when compared relative to the maser host NGC 4258 (weighted by galaxy). There are multiple factors which contribute to this (albeit small) difference. Our measurement of the TRGB in NGC 4258 is slightly further (0.055 mag) than the average difference between our two sets of measurements of m_TRGB for the sample as a whole (0.042 mag). When weighted by the SNe, this difference is −0.02 mag for Freedman (2021) or −0.03 mag for Freedman et al. (2019). Another difference is the assumed color structure of the TRGB. The CCHP assume a slope of zero for their chosen color ranges, while we assume the slope found by Rizzi et al. (2007). Because the TRGB sample brackets the color of NGC 4258, the net effect of the color term is an additional 0.01 mag in H₀. A shallower or steeper color term would produce a fraction of this 0.01 mag difference.
• 2.  
  We remove four galaxies (NGC 1309, NGC 3021, NGC 3370, and NGC 5584) for which we are not able to determine reliable TRGB distances (see Section 4.2 for details). Comparing the error-weighted mean of the calibrated SN luminosities in Freedman et al. (2019) and Freedman (2021) with and without these four, there is no change to M_B (or H₀) however, the error increases by 10%.
• 3.  
  Line 4 in Table 4 provides differences in H₀ related to the host NGC 5643. NGC 5643 hosted two SNe Ia, 2017cbv and 2013aa which were not included in Freedman et al. (2019) (raising H₀ by 0.01 mag here), but were included in Freedman (2021) (no additional difference). If we use the foreground extinction estimate, A_I , from Schlafly & Finkbeiner (2011) for NGC 5643, which is 0.02 mag lower than our own as done by F21 our value of H₀ would decrease by 0.07 km s⁻¹ Mpc⁻¹.Line 3 in Table 4 provides differences related to the host NGC 1404. NGC 1404 hosted SN 2007on and 2011iv; both used in the CCHP result from Freedman et al. (2019) and Freedman et al. (2020). These SNe Ia are fast decliners or "transitional" SNe (S_BV = −0.6) and after standardization they differ from each other by 0.4 mag. SN 2007on is ∼0.2 mag fainter than the mean M_B of 18 SNe Ia and conversely SN 2011iv is ∼0.2 mag brighter (Freedman et al. 2019), yet both are consistent with the mean at ∼2σ. Freedman (2021) now excludes SN 2007on on the grounds that "it appears significantly underluminous." SN 2007on does not appear to be an outlier in our analyses using Chauvenet's criterion. It is fainter than the mean supernova M_B by 2.0σ for the CSP SN analysis and by 1.9σ for the Pantheon SN analysis, with one other SN more discrepant and in the other direction (SN 1981D). ¹² For consistency, we would need to exclude both SNe in this host, all transitional SNe in the calibrator and Hubble flow set, and all SNe from either analysis that are this discrepant. The alternative is to exclude none, which is what we have done. Retaining 2007on raises H₀ by 0.01 mag relative to Freedman (2021). If we remove 2007on from our sample as done by F21 our value of H₀ would decrease by ∼0.5 km s⁻¹ Mpc⁻¹.

To directly compare the effects of sample selection versus TRGB measurements themselves, we can choose to hew as close as possible to the choices made by the CCHP. Namely, if we remove SN 2007on from our sample (however see point 3 above) and revert our extinction measurement for NGC 5643 to those obtained from the dust maps, we find H₀ = 70.84 km s⁻¹ Mpc⁻¹ using the CSP sample of supernovae, as opposed to our primary measurement of H₀ = 71.5 ± 1.8 km s⁻¹ Mpc⁻¹. We can also compare our final values with the result derived from Cepheids and NGC 4258 in Reid et al. (2019), namely H₀ = 72.0 ± 1.9 km s⁻¹ Mpc⁻¹. The relative difference is 0.5 ± 2.0 km s⁻¹ Mpc⁻¹ (excluding the maser distance uncertainty in common to both). We can separate the terms in the error budget in Table 3 that are independent from this Cepheid-SN Ia measurement. These include the tip measurement for NGC 4258 and 10 of the 16 SNe Ia that were not included in the SH0ES analyses. The TRGB-SN Ia error independent of the Cepheid-SN Ia ladder using NGC 4258 is 0.035 mag or 1.1 km s⁻¹ Mpc⁻¹, thus showing good agreement between the TRGB and Cepheid routes. We also note that a detailed analysis of the covariance between calibrator and Hubble flow SNe Ia by Dhawan et al. (2020) not included here shows such covariance may raise H₀ by 0.5 km s⁻¹ Mpc⁻¹ in the Pantheon SN analysis (see their Table 2). This effect has not yet been measured for SNe Ia in TRGB hosts nor is this information available for the CSP SN analysis.

In this paper, we present a new determination of the Hubble Constant using TRGB distances as calibrators for type Ia supernovae. We use the same underlying data as Freedman et al. (2019) and Freedman (2021), except we remove the four most distant hosts (NGC 1309, NGC 3021, NGC 3370, and NGC 5584) as we find the data to be insufficient to derive a robust measurement of the TRGB. We also include two hosts (NGC 1404 and NGC 5643, with a total of four SNe Ia) from Hoyt et al. 2021 and Freedman (2021). Combining these results with a new measurement of the TRGB in the maser host NGC 4258 based on new HST observations and the Pantheon or CSP sample of supernovae, we find a value of the Hubble Constant of H₀ = 71.5 ± 1.8 km s⁻¹ Mpc⁻¹ (for both supernova samples). This value is ∼2% larger than the CCHP value of H₀ = 69.8 ± 0.8 ± 1.7 km s⁻¹ Mpc⁻¹ found by Freedman et al. (2019). Our determination of H₀ from the EDD TRGB lies near the midpoint between the value from the CCHP TRGB and the most recent SH0ES Cepheid-based result of 73.0 km s⁻¹ Mpc⁻¹ (Riess et al. 2021). The situation can be seen summarized in Figure 5, where ultimately, both our and the CCHP's determination of the Hubble Constant from the TRGB-SNIa ladder fall in between those of Planck and the Cepheids. Key sources of uncertainty in the TRGB distance ladder remain, including the zero–point and color calibrations for the absolute magnitude of the TRGB, as well as the restricted number of TRGB calibrators for type Ia supernovae.

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In the coming months, we anticipate another important measurement of the Hubble Constant, this time from Cosmicflows-4 (R. B. Tully et al. 2022, in preparation). Cosmicflows is a program that collects tens of thousands of redshift-independent distances to galaxies, placed on a common distance scale. Cosmicflows-4 will provide ∼50,000 galaxy distances, and includes TRGB distances from the CMDs/TRGB catalog as a key calibrator of methods that extend to greater distance (e.g., the Tully-Fisher relation, type Ia supernovae, etc.).

In the coming years, the sample of galaxies with TRGB distances and type Ia supernova will continue to expand. Part of this increase is due to additional programs with HST, but the truly substantial increase will happen with JWST. With HST, we have shown that reliable TRGB distances can be measured out to ∼20 Mpc. With JWST, this limit will at least double, providing a substantial increase in volume and thus the number of calibrators. Additionally, JWST will allow for the TRGB calibration of a substantial number of galaxies whose distances can also be measured via surface-brightness fluctuations (Blakeslee et al. 2021), providing a truly independent measure of H₀ from the current Cepheid+Type Ia supernova distance ladder.

This research is supported by an award from the Space Telescope Science Institute in support of program SNAP-15922. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. G.A. thanks Zach Claytor and Ryan Dungee for useful discussions. A.R. thanks Dan Scolnic and Dillon Brout for useful discussions about SN light curve fitting. We thank the anonymous referee for useful comments which improved the quality of our manuscript.

Facility: HST: ACS/WFC & WFC3/UVIS. -

Software: DOLPHOT (Dolphin 2000, 2016), DrizzlePac (Avila et al. 2015).

Here we provide a complete figure set for the CCHP targeted galaxies, including footprint images (Figure A1), spatial selections of stars used for our TRGB measurements (Figure A2), resulting color-magnitude diagrams (Figure A3), and luminosity function fits (Figure A4).

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