JWST Observations Reject Unrecognized Crowding of Cepheid Photometry as an Explanation for the Hubble Tension at 8σ Confidence

In the past decade, an intriguing and persistent discrepancy referred to as the "Hubble tension" ⁷ has been apparent at high significance (>5σ) between the Hubble constant (H₀) directly measured from redshifts and distances, which are independent of cosmological models, and the same parameter derived from the ΛCDM model calibrated in the early Universe (for a recent review, see Verde et al. 2023).

The most significant disparity arises from the strongest constraints. These come from measurements of 42 local Type Ia supernovae (SNe Ia) calibrated by Cepheid variables, yielding H₀ = 73.0 ± 1.0 km s ⁻¹ Mpc (SH0ES Collaboration; Riess et al. 2022, hereafter R22), compared to the analysis of Planck observations of the cosmic microwave background (Planck Collaboration et al. 2020), predicting H₀ = 67.4 ± 0.5 km s ⁻¹ Mpc ⁻¹ in conjunction with ΛCDM. Cepheids are the preferred primary distance indicators in these studies due to the Leavitt law (P–L relation; Leavitt 1912), their extraordinary luminosity (M_H ∼ − 7 mag at a period of 30 days), intrinsic precision (approximately 3% in distance per star), reliable identification based on periodicity and light-curve shape (Hertzsprung 1926), and comprehensive understanding (since Eddington 1917). They also serve as the best-calibrated distance indicators accessible in the largest volume of SN Ia hosts (D ∼ 50 Mpc), thanks to the consistent use of a single stable instrument, Hubble Space Telescope (HST) WFC3 UVIS+IR, by the SH0ES team in measurements within SN hosts and in several independent geometric anchors: the megamaser host NGC 4258 (Reid et al. 2019), the Milky Way (through parallaxes, now including Gaia EDR3; Gaia Collaboration et al. 2021), and the Magellanic Clouds (via detached eclipsing binaries; Pietrzyński et al. 2019). Near-infrared (NIR) observations are crucial to mitigating the impact of dust, a challenge faced by many cosmic probes. Yet, the modest NIR resolution of HST, ∼01, has limited the inherent precision of individual Cepheid measurements due to the effects of crowding in nearby galaxies. As noted by Freedman et al. (2019), "[p]ossibly the most significant challenge for Cepheid measurements beyond 20 Mpc is crowding and blending from redder (RGB and AGB) disk stars, particularly for near-infrared H-band measurements [...]."

The James Webb Space Telescope (JWST) provides new capabilities to scrutinize and refine the strongest observational evidence contributing to the tension. Specifically, the significantly greater resolution of JWST over HST has greatly reduced—in practical terms, almost eliminated—the main source of noise in NIR photometry of Cepheid variables observed in the hosts of nearby SNe Ia. The resolution of JWST provides the ability to cleanly separate these vital standard candles from surrounding photometric "chaff." This study extends the scope of JWST measurements of Cepheids along the distance ladder, building upon measurements in one SN Ia host (NGC 5584) and the distance scale anchor NGC 4258 (Riess et al. 2023, hereafter R23). Here we present a greatly expanded sample of such measurements that doubles its distance range to span the full range of distances of nearby SN calibrators (the second rung of the distance ladder) and triples the Cepheid sample size, while raising the number of SN hosts studied from one to five and the number of SN Ia calibrated from one to eight. In Section 2 we present the observations, in Section 3 their analysis, and in Section 4 we discuss their interpretation.

The targets of this program, GO-1685, were selected at those richest in Cepheids and SN Ia from the SH0ES host sample of 37. The first two to execute, NGC 4258 and NGC 5584, were presented in R23 and the four presented here executed after, in mid 2023. The observational parameters of our JWST NIRCam imaging campaigns for four SN Ia hosts (NGC 1448, NGC 1559, NGC 5468, and NGC 5643) are provided in Table 1 and shown in Figure 1 (see R23 for the same information for NGC 4258 and NGC 5584). As in R23, the four new hosts were imaged with three filters (F090W, F150W, and F277W, centered at 0.9, 1.5, and 2.8 μm, respectively; see Figure 2 in R23 for filter curves) in two epochs separated by 15–16 days, with one short wavelength module of the NIRCam instrument covering the host and the other placed on a far halo field as shown in Figure 1. The epoch separation was selected by the JWST schedulers subject to the requirements of a 15–30 days spacing and an orientation difference within 5°. For the closer two hosts, NGC 1448 and NGC 5643, we swapped the A and B modules on the host on consecutive visits and thus doubled the spatial coverage of the far halo field on opposite sides.

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We analyzed the wave front history of JWST over the time span of the observations from the telescope monitoring data, 2023 June–August, as shown in Figure 2 to determine the photometric stability of our data set. There was a moderately large tilt of mirror segment C5 detected on July 16 (not present on July 14) that was corrected July 22 and we had no observations between these two dates. The wave front modeling indicates no large changes at the time of the observations and that variations in encircled energy at small radii (similar to point-spread function, PSF, photometry) would be <0.005 mag (less at longer wavelengths). Based on this we judged the epochs to be photometrically consistent and proceeded with our measurements. We note the impact to photometry due to changes in the shape of the PSF between epochs is further negated by the determinations of aperture corrections from stars within each frame.

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We used the STScI NIRCam reduction pipeline, version 1.12.0, to calibrate the data frames. There has been only one significant update to the reference files since those used in R23, 1125.pmap and 1126.pmap, which included zero-point updates for each sensor chip assembly and flat field improvements. The present work uses this update (and we have remeasured NGC 4258 and NGC 5584 from R23). As a result of these updates, the mean photometry of sources became brighter by ∼0.03 mag in F090W and ∼0.01 mag in F150W, where the latter band was used for our baseline distance measurements. Much of this change cancels when comparing Cepheids between NGC 4258 and NGC 5584. Updates after 1126.pmap through 2023 December do not affect NIRCam photometry.

We performed photometry on the images using the DOLPHOT package (Dolphin 2000, 2016) and its NIRCam module (Weisz et al. 2023; D.R. Weisz et al. 2024, in preparation), with the same procedures described in R23 with the same cuts on the crowding, sharpness, object type, signal-to-noise ratio, and error flags as reported by DOLPHOT ⁸ (see also Warfield et al. 2023). The only relevant changes since R23 are the version of the instrumental reference files provided by STScI stated above. We measured photometry with DOLPHOT with the same, recommended parameters on all of our images. The PSF fitting procedure is automated and performs the photometry of all frame stars simultaneously and blind to which are Cepheids, thus it is completely unsupervised, removing any human intervention from the Cepheid measurement procedure. The Cepheids were identified by astrometrically matching the JWST photometry catalogs to the Cepheid lists identified by the SH0ES team from multiepoch, optical HST imaging (Yuan et al. 2022b; Riess et al. 2022). The matching tolerance was set to 0.7 NIRCam short wavelength pixels in distance (002) but matches were generally within 001 of the expected position. This is the same result as seen in R23.

Among the 36 images we obtained for this program (three filters in two epochs for six hosts), only one suffered an issue. This was for the first epoch in F090W for NGC 5468 where the number of samples "up the ramp" during accumulation (four) resulted in incomplete cosmic-ray removal in the individual cal files (dithers). This produced some scattered artifacts in that single image. Although these artifacts are rare enough to have little impact on the PSF-fitting region of the Cepheids, they impacted the measurement of the aperture correction for this image due their presence in source-subtracted sky annuli (which extend to greater radii and thus cover more area than the PSF-fitting region). To solve this problem, we determined the appropriate aperture correction for this image and in each chip by comparing the nonvariable stars between this epoch and epoch 2 with F090W (which had more samples and no issues). The result from comparing the nonvariable stars between these two epochs produced an aperture correction consistent in value with the set of aperture corrections seen for other images.

As in R23, we imposed additional quality requirements on specific photometric parameters to ensure our sample contains reliable Cepheid magnitudes that yield robust distance measurements. The most important of these is based on the value of χ² (the quality of the scene modeling) reported by DOLPHOT, which we generally require to be better (lower) than 1.4 per degree of freedom; we allow a modest rise in this limit, up to 1.7, as a linear function of log period, since long-period Cepheids are very bright and their lower shot noise will reveal more imperfections in the PSF model. This cut excluded a median of ∼7% of sources among the set of hosts due to subpar scene modeling. The full Cepheid sample forms a tight locus when comparing log period to χ², such that the poor fits are readily apparent as a tail in the χ² distribution toward high values. The nature of poor χ² objects is that they are either confused even at JWST resolution or, more likely, include a resolved source such as a cluster or background galaxy, which is not well modeled with a set of PSFs by DOLPHOT. We also employ the same color cut as R23, 0.3 < F090W−F150W < 1.15 (equivalent to 0.5 < V−I < 1.7, a broad range for Cepheids) which excludes ∼5% of sources. Nearly all of these are redder than the cut and are either highly reddened or strongly blended with a red star. Not surprisingly, this red boundary corresponds to the blue edge of the highly populated red giant branch (RGB)/asymptotic giant branch (AGB) (see Figure 3) so the odds of a direct blend or misidentification will rise rapidly near this limit with hundreds to thousands of red stars at similar brightness for every Cepheid. The exception to the above is NGC 5643, the only host with moderate Milky Way foreground extinction (E(V−I) = 0.21 mag versus <0.05 mag for all others), shifting all apparent colors redward including the RGB/AGB branch and leading us to shift the accepted color range accordingly. The values of χ² for Cepheids in this host are also slightly higher than the other hosts leading us to relax the χ² limit by 0.3, resulting in the exclusion of a similar fraction as the other hosts.

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In Figure 3 we show the position of the Cepheids within the color–magnitude diagrams for the field stars in each host. In Figure 4 we show cutouts for two representative Cepheids with P ∼ 40 days from each of six host in three HST and three JWST filters. Inspection of the JWST F150W stamps shows a qualitative change relative to HST F160W thanks to the higher angular resolution. The background is effectively resolved, with the brightness fluctuations in the HST images transformed to reveal individual stars and spatially constant backgrounds.

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2.1. Artificial Stars

The Cepheids we report on were discovered between 5 and 20 yr ago by the SH0ES team using ∼12 epochs of optical imaging from HST, providing a measurement of their periods, amplitudes, and photometry in WFC3 F555W, F814W, and F160W (Hoffmann et al. 2016; Riess et al. 2022). However, the typical period uncertainty is ∼2% (Yuan et al. 2021), so knowledge of their phases elapses after just a few of years, and certainly by the time of our JWST observations. In order to recover their phases, we analyzed the change in the Cepheid magnitudes between the two epochs following the methods given in R23; we show an example of the relation between the change in magnitude and phase for the Cepheids in one of our hosts, NGC 5643, in Figure 5. The phase uncertainty for individual Cepheids is a function of the difference in phase (determined by the Cepheid period) for the two epochs. We note that the difference photometry between two epochs has less noise than the sum of the two epochs because some of the sources of error, such as the crowding term, are correlated between the two epochs. The determination of phase (discussed in R23) also provides a magnitude uncertainty that takes into account the quality of the phase constraint.

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The phase-corrected photometry is provided in Table 2 and includes the combined error terms (from artificial stars, shot noise, empirical determination of the phase, and intrinsic width of the instability strip). We show monochromatic P–L relations for each measured filter in Figure 6.

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3.1. Reddening-corrected Period–Magnitude Relation

3.2. Baseline Results

In Table 3 we provide the fits to the Cepheid P–L relations in each host for the baseline system with the NIR measurements from JWST versus HST (SH0ES). We fit a common formulation,

$$\begin{eqnarray}&&{zp}={m}_{H}^{W}-{b}_{W}\,(\mathrm{log}\,P-1)-{Z}_{W}[{\rm{O}}/{\rm{H}}],\end{eqnarray} \tag{ 1 }$$

where the zero-point or intercept, ${zp}={\mu }_{0}+{M}_{H,1}^{W}$, where μ₀ is the distance modulus and ${M}_{H,1}^{W}$ is the absolute magnitude of a Cepheid with $\mathrm{log}\,P=1$. The term Z_W is the Cepheid metallicity dependence in this system (−0.21 mag dex⁻¹; Breuval et al. 2022; Riess et al. 2022) and we provide the product of this times the difference from solar metallicity, [O/H], in Table 3 for each host. Because the Cepheids have near-solar metallicity, with measured [O/H] ∼ 0, these metallicity corrections are very small; their typical value is ∼0.01–0.02 mag. We include them for consistency when comparing with previous results from HST. We also include a variant where we set the metallicity term to zero and with double the nominal term.

Table 3. Baseline HST and JWST Cepheid P–L Fits

			JWST+HST NIR						HST NIR (SH0ES)						JWST-HST
Host	Metal	Slope	N	zp	σ	SD	μ	σc	N	ZP	σ	SD	μ	σc	Δ	σ
n4258	−0.018	−3.25	107	26.739	0.017	0.160	⋯	⋯	442	26.739	0.017	0.442	⋯	⋯	⋯	⋯
n5584	−0.022	−3.25	214	29.178	0.011	0.170	31.838	0.020	185	29.168	0.032	0.449	31.828	0.037	0.010	0.042
n5643	0.029	−3.25	270	27.861	0.011	0.166	30.520	0.020	251	27.859	0.028	0.424	30.518	0.033	0.002	0.039
n1559	0.003	−3.25	158	28.712	0.015	0.191	31.371	0.023	110	28.813	0.041	0.471	31.473	0.045	−0.102	0.050
n5468	−0.020	−3.25	112	30.316	0.019	0.227	32.975	0.026	93	30.398	0.049	0.463	33.058	0.052	−0.083	0.058
n1448	−0.022	−3.25	76	28.630	0.017	0.168	31.289	0.024	72	28.577	0.029	0.348	31.236	0.034	0.053	0.042

Note. R22 Table 6 μ_N5584 = 31.772 ± 0.052 based on three anchors and P > 18 days; here we use only one anchor, NGC 4258, and P > 15 days to allow a direct comparison. To allow a direct comparison with JWST+HST NIR, we applied a transformation of F150W–F160W = 0.033+0.036(F555W–F814W-1) which adds 0.03–0.04 for most hosts, and corrected here for CRNL by the subtraction of 0.035 mag for all hosts, the two corrections canceling to <0.01 mag with no impact on distance.

^a Error does not include geometric distance uncertainty for NGC 4258 of ± 0.032.

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We determine the intercepts within the JWST+HST NIR magnitude-system P–L relations from the weighted mean after applying an iterative 3σ clip (set by Chauvenet's criterion), which removes ∼3% of sources (∼30 Cepheids out of ∼1000, a comparable fraction to past studies such as R22). We note that the empirical rejection is applied to the full Cepheid sample discovered in the optical, so this is lieu of that imposed by the HST NIR data in R22. Because our uncertainties are well determined and nonuniform we apply rejection as an individual Cepheid contribution to the P–L, χ² > 3². We also provide results with no rejection. Table 4 provides summary results for the full sample including the mean P–L dispersion. The small dispersion for the JWST relations makes the small number of outliers quite evident, as on average they are ∼5σ off the P–L.

Table 4. Results

Sample	Comment	P–L	σ-	Cepheids	SD	${\chi }_{\nu }^{2}$	JWST	σ
		Slope	Clip				−HST
JWST+HST NIR	Baseline	−3.25	3	938	0.178	1.0	−0.011	0.032
JWST+HST NIR	σ-clip	−3.25	no	966	0.218	1.7	0.017	0.031
JWST+HST NIR	no min P or σ-clip	−3.25	no	1005	0.222	1.7	0.015	0.031
JWST+HST NIR	P > 15 days	−3.25	3	870	0.181	1.1 a	−0.020	0.043
JWST+HST NIR	shallower slope	−3.20	3	938	0.179	1.1	−0.010	0.032
JWST+HST NIR	steeper slope	−3.30	3	937	0.179	1.1	−0.008	0.032
JWST+HST NIR	no metallicity cor.	−3.25	3	937	0.178	1.0	−0.005	0.032
JWST+HST NIR	double metal cor.	−3.25	3	939	0.179	1.0	−0.016	0.032
JWST+HST NIR	and in SH0ES F160W	−3.25	3	611	0.172	1.1 a	0.014	0.035
JWST+HST NIR	no phase correction	−3.25	3	941	0.191	1.0 a	−0.007	0.033
JWST+HST NIR	least JWST crowding half	−3.25	3	487	0.165	1.1 a	−0.023	0.035
JWST+HST NIR	highest JWST crowding half	−3.25	3	451	0.201	0.9 a	−0.006	0.040
JWST+HST NIR	first epoch only	−3.25	3	821	0.224	1.0 a	−0.007	0.036
JWST NIR	F090W,F150W	−3.25	3	929	0.177	1.0	−0.012	0.032
JWST MIR	F090W,F150W,F277W	−3.25	3	864	0.197	1.0	−0.030	0.033

Note.

^a These variants affect the errors as well as magnitudes or sample so ${\chi }_{\nu }^{2}$ is not directly comparable.

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The fits are remarkably tighter than those measured with HST as seen in Figure 7, an expectable (but still impressive!) direct consequence of the improved telescope resolution (see R23; their Figure 1 for sources of noise in P–L relations). We see a consistent reduction in dispersion by a factor of 2.5 to a mean of ≤0.18 mag, with the three closest at 0.16–0.17 mag. Only NGC 5468 has a dispersion > 0.2 mag, a consequence of its 1.5 mag greater distance and relatively shorter exposure time. We determine distances to the SN hosts by using the geometric distance determination of NGC 4258 (Reid et al. 2019) μ_0,N4258 = 29.397 mag and the intercept difference between the SN hosts and NGC 4258, i.e.,

$$\begin{eqnarray}&&{\mu }_{0,\mathrm{SN}}={{zp}}^{\mathrm{SN}}-{{zp}}^{N4258}+{\mu }_{\mathrm{0,4258}},\end{eqnarray} \tag{ 2 }$$

fit from the P–L relations. The measured distances from the baseline systems are given in Table 3 with differences between HST and JWST, also plotted in Figure 8. The baseline mean difference, JWST−HST, seen in Table 4, is −0.011 ± 0.032 mag. ⁹ This uncertainty receives nearly equal contributions from three terms of size ∼0.02 mag: the intercepts of NGC 4258 measured with HST and with JWST, and the mean of the SN host period-luminosity relations. The latter term comes mostly from the HST intercept uncertainties, which are 3 times the size of the JWST means. The similarity of the NGC 4258 P–L error terms results from the combinations of smaller dispersion for JWST (0.16 versus 0.44 mag) balanced by the smaller JWST sample (N = 107 versus N = 442; more fields observed with HST), which may be remedied in the future with more JWST pointings for NGC 4258.

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Regressing all JWST crowding corrections versus the residuals from their best-fit P–L relations (see Figure 9), we find no interdependence between these quantities. The best-fit value of 0.06 ± 0.13 mag (residual) / mag (crowding) implies that at the mean crowding of the JWST sample (∼0.07 mag) the mean P–L bias is 0.004 ± 0.008 mag. This determination provides a useful estimate of the level of error that would apply when comparing this Cepheid photometry to that of Cepheids in the closest hosts, such as the Milky Way and the LMC, where crowding is absent.

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We can attempt to gain additional leverage in the JWST versus HST comparison by factoring in the distances of the hosts. For this purpose it is useful to devise a hypothetical model in which unrecognized crowding in Cepheid photometry measured with HST resolution grows linearly with distance (modulus) beyond the calibration from NGC 4258 to cause the Hubble tension, i.e., a size of $5\mathrm{log}(73/67.5)=0.17$ mag at the mean distance modulus of the SH0ES Cepheid sample (μ₀ = 31.7 mag), equivalent to ∼0.07 mag of bias per magnitude of distance modulus. This model is shown in Figure 8. We can reject this model at 8.2σ with the highest leverage from the farthest host, NGC 5468 (μ₀ = 33.0), which shows no evidence of such an effect. Indeed, the evidence we see against crowding as the source of the tension is now greater than the evidence of the tension itself. As is, we see no evidence of a growing difference between HST and JWST with distance as would be required for such a model.

3.3. Baseline Variants

The sample of observations of ∼1000 Cepheids with JWST in five hosts of eight SNe Ia and in NGC 4258 provides very strong evidence that NIR HST Cepheid photometry is accurate, albeit noisier than from JWST. While this may not be surprising since past observations used artificial stars to correct for crowding, the search for an explanation of the Hubble tension merits a broad array of investigations including independent checks on Cepheid photometry.

Although the sample of Cepheids remeasured with JWST and presented here represents nearly a third of the full SH0ES sample, we refrain from providing a value of H₀ determined exclusively from the JWST data because the sample size of calibrated SN Ia and independent geometric anchors is substantially inferior to what is available in R22. The true value of the JWST data provided here is to provide a high-fidelity test of the HST Cepheid measurements.

Additional JWST observations of some Cepheids in the SH0ES host sample are available from other Cycle 1 programs. These observations are more difficult to compare directly with HST observations because of the respective program design; however, they appear broadly consistent with the conclusions found here and in R23. Yuan et al. (2022a) presented a comparison of Cepheids in NGC 1365 from program GO-2107 (PI Lee) with NIRCam F200W. They obtained a similar result as the current program, albeit with lower significance, partly because the observations were not ideal for this purpose due to the very different wavelength than HST F160W and limited depth. We analyzed the first set of observations by program GO-1995 (PI Freedman), the only nonproprietary set at the time of writing, of the SH0ES host NGC 7250 observed in F115W and F444W and discussed in Freedman & Madore (2023). NGC 7250 is one of the smallest hosts in the sample in terms of physical size and has the lowest mass and the HST-based analysis by Riess et al. (2022) includes only 21 Cepheids, about 8 times less than the average host in this work. Consequently, the comparison between HST and JWST for NGC 7250 is limited in precision by the±0.13 mag error from the HST intercept. The comparison is further limited by the lack of more than one epoch to determine phase corrections for JWST and the large difference between JWST and HST filters (λ_eff = 1.15 versus 1.53 μm) necessitating a larger photometric transformation of ∼0.4−0.5 mag, which at present can only be obtained from model spectral energy distributions (SEDs). Nevertheless, a comparison of the JWST and transformed HST observations of NGC 7250, presented in the Appendix, are consistent at the ∼1.1σ level, with JWST brighter than HST (the direction of decreasing the distance to the host and increasing H₀).

4.1. Outlook

We are indebted to all of those who spent years and even decades bringing JWST to fruition. This research made use of the NASA Astrophysics Data System. We thank Martha Boyer, Yukei Murakami, and Siyang Li for helpful conversations related to this work. We thank our PC Alison Vick. We thank an anonymous referee for improving the draft. Please contact us if you have any questions or if something does not make sense.

Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations analyzed can be accessed via doi:10.17909/17eb-qz46.

We acknowledge support from JWST GO-1685. R.I.A. is funded by the SNSF via an Eccellenza Professorial Fellowship PCEFP2_194638 and acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant Agreement No. 947660). This research was supported by the Munich Institute for Astro-, Particle and BioPhysics (MIAPbP), which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy—EXC-2094—390783311.

We retrieved the JWST NIRCam observations of NGC 7250 from program 1995 (PI Freedman) from the MAST archive, calibration version 1130.pmap. We found the Cepheid observations in F444W (4.4 μm) to be of poor resolution due to the broad PSF and poor contrast between the Cepheids and red giants so we did not analyze them. Cepheids from the sample from Hoffmann et al. (2016) and Riess et al. (2022) were well detected in F115W and we measured their photometry with DOLPHOT following the same steps discussed above. Unfortunately a second useful color from JWST was not available to apply a similar color quality cut as employed here and only a single epoch was obtained so we could not measure phase corrections. Also, the JWST filter F115W (λ_eff = 1.15 μm) is quite different than the HST filter F160W (λ_eff = 1.53 μm) with no overlap, so unlike our comparisons with JWST F150W presented above, quantifying the difference requires a rather large, SED model-dependent (and hence uncertain) color transformation between the filters, equivalent to inferring the J − H colors of a Cepheid from these models. We used the Padova isochrone SED models to provide a synthetic relation between colors, F160W=F115W +0.41 ± 0.05 + 0.49(F555W−F814W −1) for Cepheid like SEDs, i.e., typical Cepheids with F555W−F814W∼1 must be offset by ∼0.4–0.5 ± 0.05 mag to compare between the telescopes. We identified 27 Cepheids in F115W from the optical sample of 40 (with minimum completeness LogP >1.25) from Hoffmann et al. (2016) using the same procedure as in Section 3. We used a 2.5σ clip (appropriate for this small sample size of N ≤ 40 by Chauvenet's criterion) for both the JWST and HST samples as shown in Figure 10. The clip rejected 2 of the 27 in the JWST set and 1 of the 21 Cepheids in NGC 7250 provided in Riess et al. 2022, ID = 65093 with P = 82.1 days. The 25 that remained for JWST have a dispersion of 0.29 mag (see Figure 10). Given the small Cepheid sample size, larger P–L dispersion, and large filter difference, we can only conclude the P–L relations are broadly consistent (JWST brighter than HST by 1.1σ) and that the JWST dispersion is a factor of ∼2 smaller than HST. A more conservative period completeness limit (see Hoffmann et al. 2016) of Log P >1.4 yields an ever closer match with the remaining JWST sample fainter by 0.3σ but leaves a very small comparison sample of 11 and 16 Cepheids for HST and JWST, respectively. The mean crowding for this irregular, star-bursting Sdm type host is substantially higher due of its compact nature, ∼2 times that of the large spiral hosts studied here and comprising most of the R22 sample. We also considered a "least crowded" sample selection, following Freedman & Madore (2023) who sought to reduce scatter by visual selection of the least crowded Cepheids according to the JWST images. As we did in Section 3 for the data from our program, a less crowded sample was selected as those with a DOLPHOT "crowd" parameter that was below the full sample median, 0.135. The reduced sample of 13 Cepheids have a mean crowding of 0.07 mag (comparable to the mean of the six hosts studied here without a crowding cut, estimated for the same 1.15 μm wavelength to be ∼0.05 mag) have a reduced scatter of 0.18 mag and the same intercept as the full sample within ∼0.02 mag. This sample is very small so that minor differences in its composition may produce large, stochastic variations. However, we are skeptical that there is any real gain to be made by subselecting less crowded Cepheids because their lower scatter is already reflected in their smaller uncertainties (measured with artificial stars) and their greater weight. In Table 4, this same selection also yielded a similar result, lowering the dispersion while yielding a difference in mean intercept of 0.01 mag, and given the also larger and independent samples, 40 times larger, the significance of this test is substantially stronger.

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