The Carnegie Chicago Hubble Program X: Tip of the Red Giant Branch Distances to NGC 5643 and NGC 1404

Observations were taken with the Advanced Camera for Surveys (ACS) Wide Field Camera (WFC) on board the HST. Four orbits were dedicated to the stellar halo of NGC 5643 in each of the F814W and F606W bandpasses. For NGC 1404, 17 ACS/WFC orbits in each of the F814W and F606W bands were aimed slightly northwest of, but still including, the elliptical galaxy's nucleus. The observations are summarized in Table 1.

In the left column of Figure 1, we show the HST/ACS imaging footprints in red, overlaid on ground-based false-color images that contain each target. For NGC 5643 we show a Digitized Sky Surveys (DSS) ¹¹ blue/red/far-red image, and for NGC 1404 we show a gri image made from Fornax Deep Survey (FDS; Venhola et al. 2018) imaging. ¹² The right column of images in Figure 1 are pseudo-RGB (F606W, (F606W+F814W)/2, F814W) representations of the HST/ACS imaging.

Zoom In Zoom Out Reset image size

In the RGB images of NGC 5643 shown in Figure 1 a large number of blue foreground stars can be seen, a result of its position at a galactic latitude b = +15°. We can identify disk, bar, and spiral arm structures in this late-type spiral galaxy, in addition to a well-defined transition from disk-dominated to halo-dominated components. A portion of the disk is still evident in the southeast corner of the ACS imaging. In Section 3.2, we will describe our procedure for determining the extent to which the disk must be masked in order to measure predominantly halo RGB stars. Additionally, there is a faint blue glow visible in the northwest corner of the ACS imaging that we suspect is due to scattered light in the optics or diffuse glow from a galactic substructure (see Section 3.2 for why we do not think it is a structure belonging to NGC 5643).

The gri image that contains NGC 1404 (V = 10.00 ± 0.13 mag) also reveals $10^{\prime}$ to the northwest the giant elliptical NGC 1399, the central bright galaxy of the Fornax cluster ¹³ with V = 9.59 ± 0.10 mag (Gil de Paz et al. 2007). In designing the observing program, we needed to take into account the halo of NGC 1399, which Iodice et al. (2016) showed extends as far as $33^{\prime}$ (∼180 kpc), as well as the V = 8.09 mag star HD 22862 located $3^{\prime}$ southeast of NGC 1404 (not pictured). So we aimed HST at the northwest quadrant of the main body of NGC 1404 and not in its outskirts, as would have otherwise been ideal for a TRGB measurement. As a result, unresolved light from the nucleus of NGC 1404 dominates in the innermost chip (Chip 2). The pseudo-color representation of the HST imaging shown in the bottom-right panel of Figure 1 also reveals a diffuse, red light extending from the major axis of the galaxy nucleus. This nebulous light in the ACS imaging is most prominent where seen bridging the chip gap, but also can be seen in the northwest corner. These artifacts are elongated along the same axis as the nucleus and are much redder than the unsaturated light from the galaxy, providing evidence that they are optical artifacts produced by the saturated nucleus of NGC 1404, and not astrophysical structures.

Additionally, HST could not acquire guide stars for a portion of its visit to this field, which led to a small positional offset between the observations taken in each bandpass. In the bottom-right panel of Figure 1, the effect can be identified by the unaligned chip gaps of two different colors. Despite this, we found no evidence of complications (e.g., blurring of the PSF) within each exposure.

Here, we briefly summarize the CCHP photometry pipeline, and we refer the reader to Beaton et al. (2019) for a detailed description. We performed point-spread function (PSF) photometry on the HST images with an automated DAOPHOT/ALLFRAME (Stetson 1987, 1994) pipeline that utilizes TinyTim theoretical PSFs (Krist et al. 2011). Aperture corrections to a 10 pixel (0.5'') radius were computed and applied to each frame individually. The CCHP pipeline computes aperture corrections on a frame-by-frame basis. This is intended to improve the accuracy of our final averaged photometry by better tracking variations in the focus over time.

The initial photometry catalogs contained a total of 107,009 sources in the NGC 5643 imaging, with 63,448 and 181,566 sources detected in Chip 1 and Chip 2 of the NGC 1404 imaging. To clean the catalogs, we make cuts on morphology parameters returned by DAOPHOT: the magnitude error, χ, and Sharp. To do this, the automated pipeline fit exponential curves to the distributions of these parameters as a function of both F606W and F814W magnitude, and clipped those sources that lie outside of the envelopes of these exponential distributions. See Figure 2 of Beaton et al. (2019) for an example in M101. The cleaning process left 49,104 sources in the NGC 5643 catalog, as well as 48,143 and 131,116 sources in the NGC 1404 Chip 1 and Chip 2 catalogs. Importantly, the photometry cleaning process had no measurable effect on the final TRGB distance determined here. This is expected because the cleaning process predominantly targets sources near the limiting magnitude of the photometry. However, because parts of our analysis depend on the photometry of these stars fainter than the TRGB magnitude (see Section 3.2), we choose to adopt the cleaned catalogs going forward.

We also required that a source be detected in a minimum of six (75%) and 17 (50%) frames in the NGC 5643 and NGC 1404 imaging, respectively. This requirement left 40,031, 48,060, and 130,934 in the NGC 5643, NGC 1404-C1, and NGC 1404-C2 photometry, respectively. We note that we varied the fraction of frames in which a source must be detected between 30% and 88%, and observed no change to our final TRGB distances.

Finally, we made a conservative cut on the sky background determined locally to each detected source, which we use to mask extended and saturated sources that survived our source morphology cuts. We did not apply this sky background cut to the Chip 2 photometry because unresolved light from the nucleus dominates in that chip, leading to background counts that span three orders of magnitude, from the saturation limit of the chip to a few dozens of analog-to-digital units. If we were to apply the same sky cut that was made on the Chip 1 catalog, only 27,374 sources (20%) would remain in the Chip 2 photometry. This final cut left 38,888 and 45,843 sources in the NGC 5643 and NGC 1404-C1 catalogs, respectively, while the NGC 1404-C2 catalog retained its 130,934 sources.

Due to the low galactic latitude of NGC 5643, there were plenty of bright, isolated stars from which the automated pipeline could determine an aperture correction, determined there to better than 0.01 mag. In NGC 1404 on the other hand, the algorithm to select for candidate aperture correction stars was significantly contaminated by barely resolved GCs. We manually excluded these GCs from our standard star sample by inverting a color–magnitude selection (described in Appendix A). This reduced our sample of aperture correction stars for Chip 1 from 20 to two/four, depending on bandpass. In the Chip 2 photometry, we were unable to identify any isolated, bright stars suitable for determining PSF-to-aperture corrections, which is due to the high source density observed in this chip. So we instead choose to apply the Chip 1 aperture corrections to the Chip 2 photometry. Aperture corrections for the two ACS chips should be close to (though not exactly) equal, and we expect this to be the most reliable way to calibrate the Chip 2 photometry. Note that we do not use the Chip 2 photometry at all in our determination of the TRGB distance to NGC 1404. In Table 2, we present the mean and standard deviations of the aperture corrections determined for each chip, band, and target.

We then calibrate the photometry to the ST VEGAMAG system by applying encircled energy corrections to an infinite aperture (presented in Bohlin 2016) and infinite aperture photometric zero-points provided by STScI. ¹⁴

In Figure 2 we present cleaned F606W and F814W CMDs of photometry for NGC 5643 and NGC 1404, where we have separated the latter by chip, with the corresponding labels N1404-C1 and N1404-C2.

Zoom In Zoom Out Reset image size

For NGC 5643, the CMDs indicate that young, blue stars (F606W−F814W ≃ 0.2 mag), as well as red supergiants (F606W−F814W ≃ 1.0 mag), are present in the imaging. In Section 3.2, we confirm that these sources, typically classified as belonging to young stellar populations, are associated with the disk feature visible in the southeast corner of the HST imaging.

In the N1404-C2 CMD, thousands of sources can be seen forming a vertical plume centered around (F606W−F814W) ≃ 1.5 mag that extends several magnitudes above the TRGB magnitude we would expect based on the distance to the Fornax cluster (F814W ∼ 27.5 mag). Because this feature is not present in the Chip 1 photometry at all, has an average color equal to a typical RGB star, and appears as a disjoint population, we conclude that these sources are likely source blends of fainter RGB stars.

Additionally, we identify ∼250 GC candidates, selected by their photometric colors (F606W−F814W) ≃ 1.00 mag and F606W magnitudes. They can be seen forming a narrow vertical sequence extending from F814W = 24–20 mag, beyond the boundaries of the N1404-C1 and N1404-C2 panels in Figure 2. Appendix A, we present details of the color–magnitude selection and photometry for these GC candidates.

Also in Appendix A, we present photometry of sources belonging to FCC B1281 (marked in Figure 1) and measure a TRGB distance to this dwarf satellite. The distance we measured agrees well with our TRGB distance to NGC 1404, which provides a sanity check on the precision of our distance measurement, and confirms the membership of FCC B1281 to NGC 1404.

In Hatt et al. (2017) we introduced a method of standardizing the representation of the RGB LF for the purposes of detecting the TRGB. We first constructed the LF with a bin size of 0.01 mag, which is much smaller than the typical photometric error (∼0.10 mag) of a TRGB star in our data. We then smoothed the LF by fitting a second order polynomial about each bin's center. The fit domain included the entirety of the data set (i.e., a non-truncated window), and each data point in the fit was weighted by a Gaussian centered on each interpolated bin, or GLOESS (Gaussian-windowed LOcal regrESSion method, GLOESS, Persson et al. 2004). The width of the Gaussian weighting window was then set equal to the typical photometric error of a single source at the magnitude of the expected TRGB, and then optimized using artificial star simulations. Assuming that the TRGB feature is a step function in the limit of infinite signal to noise, this choice is expected to minimally distort the location of the TRGB edge, while sufficiently suppressing higher frequency noise.

Next, to measure the location of the TRGB magnitude we pass a Sobel {−1, 0, +1} difference filter over the smoothed LF. Each point δ_i (m_i ) in the resultant discrete first derivative is then multiplied by a Poisson weighting scheme $({N}_{i+1}-{N}_{i-1})/\sqrt{(}{N}_{i-1}+{N}_{i+1})$ associated with the corresponding bin in the LF. The resulting TRGB response function is displayed in the rightmost column of Figure 3.

Zoom In Zoom Out Reset image size

In this paper we make one minor change to the CCHP edge detection methodology. We use a simple Gaussian kernel to smooth the LF instead of the GLOESS interpolation method described above. Because the LFs for both galaxies are well populated (with no gaps), we observed no difference between a simple kernel smoother versus using the GLOESS interpolation scheme; both gave identical results when detecting the TRGB edge.

In the left column of Figure 3, we show the results of the TRGB edge detection for the full, cleaned catalogs. The LF for NGC 5643 contains many AGB stars, and the edge response for NGC 1404 is broad with a long tail to brighter magnitudes. We suspect this tail in the edge response is due to crowded RGB stars migrating above the true TRGB, which are producing false edges in the LF. In Section 3.2, we will show that both TRGB detections can be improved by selecting for stars in the outer regions of each image set. In the right column, we show the TRGB detections for those sources contained in the outer region selections.

In order to accurately measure a TRGB distance, we must classify and isolate old, metal-poor stellar populations in the HST photometry. To do this, we invoke an analysis similar to that presented in Hoyt et al. (2019) and Mager & Hoyt (2020), in which a running cut on galactocentric radius was used to probe the effects of source location (relative to the host galaxy) on measurement of the TRGB. Here, we expand on that methodology by parameterizing the spatial dimension by semimajor axis (SMA) of an elliptical profile adopted for each galaxy, as opposed to galactocentric radius. We then divide the photometry into regions with boundaries that are defined in such a way as to produce equal signal strength in each region's TRGB edge.

The bounds of each elliptical region are iteratively optimized such that the quantity ${N}_{\mathrm{RGB}}-{N}_{\mathrm{AGB}}=\mathrm{const}.$, where N_RGB and N_AGB are defined as the number of sources with (F606W−F814W) > 1.00 mag, and that lie within 1 mag fainter and brighter, respectively, of a single adopted value for the TRGB magnitude. We expect the difference between N_RGB and N_AGB to approximate to first order the observed signal in the TRGB edge, since contaminant AGB stars that lie under the RGB will linearly decrease the contrast of the true TRGB discontinuity. We do not redetermine within each spatial bin the TRGB magnitude used to define this calculation. That is because the unbiased TRGB magnitude should be a constant across all regions. Instead, in order to refine the determination of these quantities, we complete the following analysis twice, and use the results from the first iteration to update our estimate of the true TRGB magnitude in each galaxy. The figures discussed in this section were generated using the results of the second iteration.

In Figure 4, we show the results of the region determination algorithm, where a subset of the annular ellipses are plotted over a stellar source density map for each galaxy. In each panel, the large black dot marks the centroid of the elliptical profile adopted.

Zoom In Zoom Out Reset image size

For each region, we compute the following statistics: N_RGB, N_AGB, (V–I)_RGB, sky _avg, and N arcsec⁻². Again, N_RGB is defined as the number of stars measured to have colors (F606W−F814W) > 1.00 mag and which lie within 1 mag fainter than the adopted TRGB magnitude. Conversely, N_AGB has the same color constraint with an oppositely signed magnitude constraint. (V−I)_RGB is defined as the average color of the same sources that contribute to N_RGB (where V and I are used synonymously with F606W and F814W). The 〈 sky 〉 is the average local sky counts (in analog-to-digital units) returned by DAOPHOT for all stars contained in each region, where the values have been zeroed to the modal sky value in each chip. In Figure 5, we plot all of these quantities as a function of the average SMA of each bin.

Zoom In Zoom Out Reset image size

Then, in Figure 6 we simultaneously plot the edge response (the rightmost curves plotted in each tri-panel of Figure 3) for all spatial bins at once. The x-axis is the newly added spatial dimension (the mean SMA of each region), the y-axis is F814W magnitude, and the color map represents the power in the edge response function (corresponding to the x-axis in the rightmost panels of Figure 3). The response function within each spatial bin is first normalized, then rescaled such that the maximum value across all bins is unity.

Zoom In Zoom Out Reset image size

Finally, in the right column of Figure 3 we present our finalized TRGB detections for both galaxies. The halo CMDs contain no young, blue stars, the LFs are well populated, and the edge responses become unambiguous and single peaked. Now, we separately describe for each galaxy the details and results of the spatial analysis.

NGC 5643

NGC 1404

Because our edge detection determination of the TRGB is nonparametric, we turn to simulations of the photometry and edge detection procedure in order to estimate the uncertainties in our TRGB measurements. This procedure was introduced in Hatt et al. (2017) and we summarize it here. We build up a library of ∼1 million artificial stars, which are drawn from an LF with AGB slope 0.1 dex/mag, and RGB slope 0.3 dex/mag. At one time, we randomly sample 4000 artificial stars from the model LF and inject them self-consistently into all exposures in a data set. We then proceed to photometer these injected-source images following the same photometric routines described previously. The injection procedure is then repeated 120 times for each chip, until photometry of at least half a million artificial sources have been tabulated. The input and output (before and after applying photometry quality cuts) artificial star luminosity functions (ASLFs) are shown in the upper-left panels in Figure 7.

Zoom In Zoom Out Reset image size

The photometry quality cuts (discussed in Section 2.3) are then applied, and the output ASLF is downsampled to reflect as closely as possible the number of stars on either side of the TRGB discontinuity observed in the real data. Thirty of these downsampled ASLFs, and the resulting edge detector response functions are shown in the upper-right panel of Figure 7. This downsampled edge detection procedure is then repeated for 10,000 realizations, to ensure convergence in the simulations, defined to occur when the values of the scatter σ₈₁₄ and the offset Δm₈₁₄ reach stable values, as shown in the middle-left panels of Figure 7.

The final values of these parameters are then adopted as the statistical and systematic errors on our edge detection measurement. The distribution of all 10,000 simulated TRGB measurements, as well as the final adopted uncertainties, are shown in the middle-right panel of Figure 7. Additionally, because this process injects sources directly into the images, this evaluation of the uncertainties explores all of the following: crowding biases, biases due to incompleteness, and convolution of the photometric error distribution with the LF.

In the bottom panel of Figure 7, we plot σ₈₁₄ and Δm₈₁₄ as a function of the smoothing kernel width. Circled is the smoothing size adopted for the final TRGB detection. The smoothing size for NGC 5643 was chosen to minimize the cumulative error curve. The smoothing scale adopted for NGC 1404 was chosen to avoid merging the dominant peak observed with adjacent secondary peaks.

In addition to the edge detection uncertainties determined from the artificial star experiments, we also add to the systematic error budget three terms associated with our photometric calibration: (i) the dispersion observed in the frame-to-frame PSF-to-aperture corrections (see Table 2 for values), (ii) a 0.02 mag term for the uncertainty in the ACS encircled energy (EE) corrections to an infinite aperture, and (iii) a 0.02 mag term for the uncertainty in the ACS photometric zero-point. The quadature sum of these three calibration errors and the edge detection systematic error combine to give the σ_sys column in Table 3.

Table 3. TRGB Magnitudes, Foreground Reddenings, and True Distances to NGC 5643 and NGC 1404

Galaxy	${m}_{814}^{\mathrm{TRGB}}$	σstat	σsys a	A814	${\sigma }_{{A}_{814}}$	${\left(m-M\right)}_{0}$ b	σstat	σsys a	D	σstat	σsys
	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(Mpc)	(Mpc)	(Mpc)
NGC 5643	26.68	0.02	0.04	0.26	0.04	30.48	0.03	0.07	12.5	0.2	0.4
NGC 1404	27.32	0.03	0.04	0.02	0.01	31.36	0.04	0.05	18.7	0.3	0.5

Note.

^a Includes uncertainties in PSF-to-aperture corrections, encircled energy corrections to an infinite aperture, and the uncertainty in the STScI infinite aperture zero-point. ^b ${M}_{814}^{\mathrm{TRGB}}=-4.054\pm 0.022\,(\mathrm{stat})\pm 0.039\,(\mathrm{sys})$ mag (Freedman et al. 2020).

Download table as:  ASCIITypeset image

In this section, we first consider the effects of a color cut on our observed TRGB magnitudes before determining the true TRGB distances to NGC 5643 and NGC 1404 via correction for foreground reddening and application of the CCHP calibration of the TRGB luminosity.

We tested the effects of a color selection on our measured TRGB magnitudes. This selection, also considered in previous CCHP papers, is defined by slopes −4.00 mag/mag, and bounded by 0.90 < (F606W−F814W) < 2.00 mag at the magnitude of the TRGB. Additionally, we perturbed the data quality cuts described in Section 2 and found the effects of both on the detected TRGB magnitude to be negligible (<0.01 mag).

The apparent TRGB magnitudes ${m}_{814}^{\mathrm{TRGB}}$ are corrected for foreground reddening using the Schlafly & Finkbeiner (2011) recalibration of the Schlegel et al. (1998) dust maps and their preferred normalization of a Fitzpatrick (1999) reddening law with R_V = 3.1. Next, we apply the CCHP calibration of the TRGB absolute magnitude M₈₁₄ = −4.054 ± 0.022(stat) ± 0.039(sys) (Freedman et al. 2020) to the de-reddened TRGB magnitude to determine the true distance to each galaxy.

For NGC 5643, this results in an extinction in the F814W band A₈₁₄ = 0.257 ± 0.035 mag, corresponding to E(B−V) = 0.15 ± 0.02 mag, where we have conservatively rounded up to the nearest hundredth of a magnitude the 10% (0.015 mag) uncertainty suggested by Schlafly & Finkbeiner (2011) for observations made near the galactic plane. Applying the CCHP calibration, we find for NGC 5643 a true distance modulus, μ₀ = 30.48 ± 0.03(stat) ± 0.07(sys)

For NGC 1404, we again correct for the foreground reddening measured by maps presented in Schlegel et al. (1998) and recalibrated by Schlafly & Finkbeiner (2011). However, since NGC 1404 does not lie near the galactic plane, we cannot adopt the 10% uncertainty suggested by Schlafly & Finkbeiner (2011). Instead, we conservatively adopt half the measured reddening as the error on the measurement, i.e., E(B−V) = 0.01 ± 0.005 mag, or A₈₁₄ = 0.018 ± 0.009 mag. Finally, with the Freedman et al. (2020) zero-point, we find for NGC 1404 a true distance modulus, μ₀ = 31.36 ± 0.04(stat) ± 0.05(sys).

The above measurements and uncertainties are summarized in Table 3.

Eight distances have previously been measured to NGC 5643, according to the compilation on NED (https://ned.ipac.caltech.edu/). All were determined using the Tully–Fisher relation, with a mean equal to 30.25 mag and standard deviation 0.44 mag. Note that the low inclination of NGC 5643 will significantly limit the accuracy of any Tully–Fisher distance measurement. ¹⁶

More recently, however, a number of distances have been published to SN 2017cbv, the most recent of the two SNe hosted by this galaxy. Sand et al. (2018) determined a distance μ = 30.45 ± 0.09 mag assuming an H₀ = 72 km s⁻¹ Mpc⁻¹. (Burns et al. 2020, hereafter B20) tested three different light-curve fitters on their CSP photometry of SN 2013aa and SN 2017cbv, finding a range of values between 30.62 mag and 30.39 mag. Note that the two extremal values are from one light-curve fitter (SALT2) and that the other four distances exhibited a full range of only 0.10 mag. Wang et al. (2020) considered three different methods of determining the distance to SN 2017cbv (all assuming an H₀ = 72 km s⁻¹ Mpc⁻¹): (1) NIR calibrations, (2) SNooPy (Burns et al. 2011, 2018) light-curve fits, and (3) color–magnitude information in the tail of the Ia light curve. First, from considering many different NIR luminosity–width relations they found distances ranging from 30.11–30.41 mag. From the SNooPy fits to their optical and NIR photometry, they found 30.46 ± 0.08 mag, which is in perfect agreement with the SNooPy fit made to independent CSP photometry. From their late-time color–magnitude fit, they determined 30.58 ± 0.05 mag.

For our purposes, however, we want to know if the SNe Ia in NGC 5643 are consistent with the Paper VIII results. Since that paper used CSP SNe to measure the Hubble constant, we will consider for the rest of this section the B20 SNooPy distances to 2013aa and 2017cbv. B20 found ${\mu }_{2013\mathrm{aa}}^{72}=30.47\pm 0.08$ mag and ${\mu }_{2017\mathrm{cbv}}^{72}=30.46\pm 0.08$ mag where the superscript denotes the adopted H₀ value of 72 km s⁻¹ Mpc⁻¹in their light-curve fitter. However, a direct comparison between our TRGB distance and the B20 distances to NGC 5643 would implicitly fold in the assumption of an H₀ value that does not agree with that found in Paper VIII. To avoid this unlike comparison, we will rescale the B20 distances so that they are instead calibrated by the existing CCHP TRGB-based H₀. We describe this process in more detail in Appendix B.

This results in the CCHP-anchored SN distances mag and ${\mu }_{2017\mathrm{cbv}}^{69.6}=30.53\pm 0.09$ mag, which can be directly compared with the TRGB distance measured here, μ_TRGB = 30.48 ± 0.03(stat) ± 0.07(sys) mag. The agreement between the TRGB and SN distances indicates that the TRGB distance to, and SNe hosted by, NGC 5643 are consistent with the results presented in Paper VIII.

For NGC 1404, we consider the 52 distances aggregated by NED coming from nine different distance indicators (not including those classified as Tully–Fisher). To the sample of literature distances we add a recent PNLF distance from Spriggs et al. (2020), who used data from the Fornax 3D survey (Sarzi et al. 2018) to determine a modern PNLF distance to NGC 1404 equal to μ = 31.42 ± 0.1 mag, which is in very good agreement with the TRGB distance determined here. In Figure 9, we plot Gaussian-kernel-smoothed distributions for those methods with distances that exhibited standard deviations less than 0.3 mag: GCLF, PNLF, SBF, and SN Ia (see Section 1 for a full list of references). For comparison, we plot a Gaussian representation of the TRGB distance determined here. The modes of the distance distributions range from 31.2 mag (PNLF) to 31.6 mag (SBF), but are still largely in agreement, with our TRGB distance landing in the middle. This is consistent with the findings in Hatt et al. (2018b), who saw an identical distribution of distances measured to NGC 1316. Note that Figure 9 presents a broad view of the literature and is intended solely to provide a contextual summary, rather than a rigorous meta-analysis. For example, in the case of the PNLF distance, the recent Spriggs et al. (2020) result should probably be taken as the sole preferred PNLF distance, being at least 20 years more modern than the other four PNLF measurements included in Figure 9.

Zoom In Zoom Out Reset image size

Thus, to get a better understanding for where our TRGB measurement stands, we compute the relative line of sight (for the remainder of this section the term distance refers to a line-of-sight distance, unless otherwise specified) distances Δμ = μ¹⁴⁰⁴ − μ¹³¹⁶ between NGC 1316 and NGC 1404, as determined with the TRGB (this study and Paper VIII), SN Ia (B20), and SBF (Blakeslee et al. 2009, hereafter B09) methods. Both galaxies are massive ellipticals located in the Fornax cluster, with comparable masses and multiple SNe Ia to compare. The use of these similar galaxies, should, to some degree, cancel out systematic uncertainties associated with each method of distance measurement. Further reducing the contribution of systematic uncertainties, each set of distances we have chosen to use were determined homogeneously in the same study.

The resulting relative distances are Δμ_TRGB = −0.104 ± 0.060 mag, Δμ_SBF = −0.081 ± 0.097 mag, Δμ_07on = 0.309 ± 0.059 mag, and Δμ_11iv = −0.101 ± 0.063 mag (see Section C for a detailed description of the calculations). For this comparison, we have averaged the consistent line-of-sight distances to the four SNe Ia hosted by NGC 1316, but considered separately each of the SNe Ia in NGC 1404 (2007on and 2011iv) because they are ∼0.4 mag discrepant. In Figure 10, we plot these relative distance values as arrows, and the corresponding absolute distances used to calculate them as black squares (NGC 1404) and black triangles (NGC 1316). From comparing the direction and size of the relative distances, it is clear that SN 2007on is significantly underluminous (see Section C for a discussion on this), while SN 2011iv gives a relative distance in very good agreement with the SBF and TRGB relative distances.

Zoom In Zoom Out Reset image size

Converting the TRGB-based relative line-of-sight distance Δμ_TRGB to physical units, we have ΔD_TRGB = −0.92 ± 0.54 Mpc. If we also include the on-sky separation of the two galaxies, we determine a three-dimensional separation ${\rm{\Delta }}{r}_{\mathrm{TRGB}}=\left|{\vec{r}}_{1404}-{\vec{r}}_{1316}\right|={1.50}_{-0.39}^{+0.25}$ Mpc. Combining our TRGB-only constraint with the two other consistent relative distance determinations, we compute ${\rm{\Delta }}{r}_{\mathrm{All}}={1.48}_{-0.25}^{+0.18}$ Mpc, providing a powerful constraint on the 3D alignment of these two galaxies within the Fornax cluster.

Based on the consistency seen in the relative SBF and TRGB distances, our high-precision TRGB distances to these two giant elliptical galaxies should also provide a useful zero-point calibration for the red edge of the SBF method. We find a combined (NGC 1404 and NGC 1316) offset between our TRGB distances and the B09 (again chosen here for their internal consistency) SBF distances equal to μ_TRGB−μ_SBF = −0.156 ± 0.067 mag, where we have used the total (stat.+sys.) uncertainties quoted for the TRGB and SBF distances.

Because they share similar RGB-dominated stellar populations, the integrated light from GCs occupies a narrow strip in photometric color. As a result, GC candidates can be classified with a simple color–magnitude selection. We found that the expected morphology of the GC sequence (Forbes et al. 1998) was best observed in a F606W versus F606W−F814W CMD. We combined the N1404-C1 and N1404-C2 CMDs shown in Figure 2 and made the following cuts 0.40 < (F606W−F814W) < 1.40 and 20.0 < F606W < 25.5. The results of the selection are shown in Figure 11.

Zoom In Zoom Out Reset image size

Conceivably, the TRGB distance we measured to NGC 1404 could be compared to a distance measured from the GCLF presented here. That comparison could provide a useful evaluation on how the GCLF performs as a distance indicator.

There is a clear resolved dwarf galaxy in the outer region of our HST imaging of NGC 1404. To the best of our knowledge, Ferguson (1989) first documented this object in their FCC and gave it the identifier FCC B1281. It was included there as part of the "possible members and likely background galaxies" subcatalog. Then, Hilker et al. (1999) definitively classified this object as a likely dwarf member in their Catalog of Galaxies of Fornax (CGF), giving it the identifier CGF 1-44. Most recently, Venhola et al. (2018) observed this dwarf in their FDS, naming it FDS11_DWARF186 within their own catalog of member galaxies.

It is an interesting question to ask whether we can measure a TRGB distance to this resolved dwarf galaxy, both to determine whether FCC B1281 is bound to NGC 1404 and to provide a check on our TRGB distance measured to NGC 1404. To do this, we must first construct a CMD of the dwarf's stellar population by selecting sources that are sufficiently close-in to the dwarf's center—to minimize contributions from NGC 1404—while also avoiding source blends in its crowded inner regions. To that end, we used the sky value returned by DAOPHOT to construct a surface brightness profile of the galaxy (see bottom-left panel of Figure 12). Within that profile, we defined three regions inner, outer, and field for local sky values sky > 3, 0 < sky < 3, sky < −2.5. As before, the sky counts here have been zeroed to the modal value across the entire chip. The results of these selections are (de)projected onto the sky in the right-hand panel of Figure 12. There, the inner and outer boundaries are marked by green and white ellipses, respectively, while field sources are individually identified with red circles.

Zoom In Zoom Out Reset image size

In Figure 13, we present TRGB detection plots for each region. In each plot we demonstrate the effects of a narrow color selection with slope = −4 mag/mag and 0.80 < (F606W−F814W) < 1.55 mag at F814W = 27.3 mag. As gray points we plot the sources belonging to the field region and in red are those sources that were excluded by the color–magnitude selection. This narrow color cut was determined from the inner region's CMD, which should preferentially select for RGB stars that belong to FCC B1281 and not NGC 1404. Indeed, the effectiveness of the color selection is confirmed by the decreasing number of sources contained within it for each progressively more extended region, with 93%, 84%, and 58% for the inner, outer, and field, respectively. This can be considered a very coarse-grain implementation of filter matching the morphology of the inner CMD to that of the other two regions.

Zoom In Zoom Out Reset image size

In Figure 13, we see that the inner region's stellar population is dominated by bright sources and the edge response peaks near F814W = 27 mag. We suspect this brighter tip could be due to a combination of crowding effects and potentially an increase in the AGB-to-RGB ratio in this inner region, causing the edge detector to trigger off of a false tip. For that reason, we do not consider this region further.

In the outer CMD, there are an increased number of contaminant sources from NGC 1404 visible, but this region is still dominated by the same population associated with the inner region (as indicated by the color selection). The edge response is unambiguous and single peaked, landing at F814W = 27.30 mag.

The field (NGC 1404) CMD definitively shows that the inner and outer regions contain a stellar population that is distinct from NGC 1404 because the locus of the field TRGB lies outside of the color selection. This has a dramatic effect on the edge detection, where the kernel can be seen triggering off of the depleted, blue edge of the TRGB stars, leading to a faint edge detection at F814W = 27.43 mag. Reassuringly, without the color selection (i.e., inclusion of the red points) we measured a strongly peaked TRGB magnitude at F814W = 27.32 mag, which exactly agrees with the value we determined from the full NGC 1404 catalog.

The fact that the color selection degraded the quality of the field region's edge detection, but sharpened the edge measured in the outer region, provides further evidence that the stellar populations measured in these two regions are distinct. As a result, we can conclude that the TRGB magnitude determined to the outer region ${m}_{814}^{\mathrm{TRGB}}=27.30$ mag is indeed an independent distance measured via RGB stars belonging to FCC B1281, and not NGC 1404. Based on the findings of Madore & Freedman (1995) on the determination of a TRGB magnitude in numbers-limited samples, we attribute a systematic error σ_sys ∼ 0.1 mag to our TRGB distance to FCC B1281.

We have determined a direct TRGB distance to FCC B1281 that is within 0.02 mag of our measured distance to NGC 1404. Considering the on-sky proximity (<30 kpc) of FCC B1281 to the center of NGC 1404 and their identical TRGB distances, we conclude that this dwarf satellite is very likely bound to NGC 1404. At the same time, the agreement in line-of-sight distances demonstrates the self-consistency of our TRGB distance measured to NGC 1404.