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The Hubble Tension, a >5 sigma discrepancy between direct and indirect measurements of the Hubble constant (H0), has persisted for a decade and motivated intense scrutiny of the paths used to infer H0. Comparing independently-derived distances for a set of galaxies with different standard candles, such as the tip of the red giant branch (TRGB) and Cepheid variables, can test for systematics in the middle rung of the distance ladder. The I band is the preferred filter for measuring the TRGB due to constancy with color, a result of low sensitivity to population differences in age and metallicity supported by stellar models. We use James Webb Space Telescope (JWST) observations with the maser host NGC 4258 as our geometric anchor to measure I-band (F090W vs F090W-F150W) TRGB distances to 8 hosts of 10 Type Ia supernovae (SNe Ia) within 28 Mpc: NGC 1448, NGC 1559, NGC 2525, NGC 3370, NGC 3447, NGC 5584, NGC 5643, and NGC 5861. We compare these with Hubble Space Telescope (HST) Cepheid-based relative distance moduli for the same galaxies and anchor. We find no evidence of a difference between their weighted means, 0.01 +/- 0.04 (stat) +/- 0.04 (sys) mag. We produce fourteen variants of the TRGB analysis, altering the smoothing level and color range used to measure the tips to explore their impact. For some hosts, this changes the identification of the strongest peak, but this causes little change to the sample mean difference producing a full range of 0.01 to 0.03 mag, all consistent at 1 sigma with no difference. The result matches past comparisons of I-band TRGB and Cepheids when both use HST. SNe and anchor samples observed with JWST are too small to yield a measure of H0 that is competitive with the HST sample of 42 SNe Ia and 4 anchors; however, they already provide a vital systematic crosscheck to HST measurements of the distance ladder.

We present phase-corrected photometric measurements of 88 Cepheid variables in the core of the Small Magellanic Cloud (SMC), the first sample obtained with the Hubble Space Telescope's (HST) Wide Field Camera 3, in the same homogeneous photometric system as past measurements of all Cepheids on the SH0ES distance ladder. We limit the sample to the inner core and model the geometry to reduce errors in prior studies due to the nontrivial depth of this cloud. Without crowding present in ground-based studies, we obtain an unprecedentedly low dispersion of 0.102 mag for a period-luminosity (P-L) relation in the SMC, approaching the width of the Cepheid instability strip. The new geometric distance to 15 late-type detached eclipsing binaries in the SMC offers a rare opportunity to improve the foundation of the distance ladder, increasing the number of calibrating galaxies from three to four. With the SMC as the only anchor, we find H\\(_0\\!=\\!74.1 \\pm 2.1\\) km/s/Mpc. Combining these four geometric distances with our HST photometry of SMC Cepheids, we obtain H\\(_0\\!=\\!73.17 \\pm 0.86\\) km/s/Mpc. By including the SMC in the distance ladder, we also double the range where the metallicity ([Fe/H]) dependence of the Cepheid P-L relation can be calibrated, and we find \\(\\gamma = -0.234 \\pm 0.052\\) mag/dex. Our local measurement of H\\(_0\\) based on Cepheids and Type Ia supernovae shows a 5.8\\(\\sigma\\) tension with the value inferred from the cosmic microwave background assuming a Lambda cold dark matter (\\(\\Lambda\\)CDM) cosmology, reinforcing the possibility of physics beyond \\(\\Lambda\\)CDM.

The Cepheid period-luminosity (PL) relation (or Leavitt law) has served as the first rung of the most widely used extragalactic distance ladder and is central to the determination of the local value of the Hubble constant (\\(H_0\\)). We investigate the influence of metallicity on Cepheid brightness, a term that significantly improves the overall fit of the distance ladder, to better define its wavelength dependence. To this aim, we compare the PL relations obtained for three Cepheid samples having distinct chemical composition (in the Milky Way and Magellanic Clouds) and focusing on the use of improved and recent data while covering a metallicity range of about 1 dex. We estimate the metallicity effect (hereafter \\(\\gamma\\)) in 15 filters from mid-IR to optical wavelengths, including five Wesenheit indices, and we derive a significant metallicity term in all filters, in agreement with recent empirical studies and models, in the sense of metal-rich Cepheids being brighter than metal-poor ones. We describe the contribution of various systematic effects in the determination of the \\(\\gamma\\) term. We find no evidence of \\(\\gamma\\) changing over the wavelength range \\(0.5-4.5 \\, \\rm \\mu m\\), indicating that the main influence of metallicity on Cepheids is in their luminosity rather than color. Finally, we identify factors that sharpen the empirical constraints on the metallicity term over past studies, including corrections for the depth of the Magellanic Clouds, better-calibrated Cepheid photometry, improved Milky Way extinction estimates, and revised and expanded metallicity measurements in the LMC.

As primary anchors of the distance scale, Cepheid stars play a crucial role in our understanding of the distance scale of the Universe because of their period-luminosity relation. Determining precise and consistent parameters (radius, temperature, color excess, and projection factor) of Cepheid pulsating stars is therefore very important. With the high-precision parallaxes delivered by the early third Gaia data release, we aim to derive various parameters of Cepheid stars in order to calibrate the period-luminosity and period-radius relations and to investigate the relation of period to p-factor. We applied an implementation of the parallax-of-pulsation method through the algorithm called Spectro-Photo-Interferometry of Pulsating Stars, which combines all types of available data for a variable star in a global modeling of its pulsation. We present the SPIPS modeling of a sample of 63 Galactic Cepheids. Adopting Gaia EDR3 parallaxes as an input associated with the best available dataset, we derive consistent values of parameters for these stars such as the radius, multiband apparent magnitudes, effective temperatures, color excesses, period changes, Fourier parameters, and the projection factor. We then derive new calibrations of the period-luminosity and period-radius relations. After investigating the dependences of the p-factor on the parameters of the stars, we find a high dispersion of its values and no evidence of its correlation with the period or with any other parameters. Statistically, the p-factor has an average value of p=1.26\\(\\pm\\)0.07, but with an unsatisfactory agreement. In absence of any clear correlation between the p-factor and other quantities, the best agreement is obtained under the assumption that the p-factor can take any value in a band with a width of 0.15. This result highlights the need for a further examination of the physics behind the p-factor.

We present a low-dispersion period-luminosity relation (PL) based on 154 Cepheids in Messier 33 (M33) with Hubble Space Telescope (HST) photometry from the PHATTER survey. Using high-quality ground-based light curves, we recover Cepheid phases and amplitudes for multi-epoch HST data and we perform template fitting to derive intensity-averaged mean magnitudes. HST observations in the SH0ES near-infrared Wesenheit system significantly reduce the effect of crowding relative to ground-based data, as seen in the final PL scatter of \\(\\sigma\\) = 0.11 mag. We adopt the absolute calibration of the PL based on HST observations in the Large Magellanic Cloud (LMC) and a distance derived using late-type detached eclipsing binaries to obtain a distance modulus for M33 of \\(\\mu\\) = 24.622 \\(\\pm\\) 0.030 mag (d = 840 \\(\\pm\\) 11 kpc), a best-to-date precision of 1.3%. We find very good agreement with past Cepheid-based measurements. Several TRGB estimates bracket our result while disagreeing with each other. Finally, we show that the flux contribution from star clusters hosting Cepheids in M33 does not impact the distance measurement and we find only 3.7% of the sample is located in (or nearby) young clusters. M33 offers one of the best sites for the cross-calibration of many primary distance indicators. Thus, a precise independent geometric determination of its distance would provide a valuable new anchor to measure the Hubble constant.

The Cepheid Period-Luminosity (PL) relation is the key tool for measuring astronomical distances and for establishing the extragalactic distance scale. In particular, the local value of the Hubble constant (\\(H_0\\)) strongly depends on Cepheid distance measurements. The recent Gaia Data Releases and other parallax measurements from the Hubble Space Telescope (HST) already enabled to improve the accuracy of the slope (\\(\\alpha\\)) and intercept (\\(\\beta\\)) of the PL relation. However, the dependence of this law on metallicity is still largely debated. In this paper, we combine three samples of Cepheids in the Milky Way (MW), the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) in order to derive the metallicity term (hereafter \\(\\gamma\\)) of the PL relation. The recent publication of extremely precise LMC and SMC distances based on late-type detached eclipsing binary systems (DEBs) provides a solid anchor for the Magellanic Clouds. In the MW, we adopt Cepheid parallaxes from the early third Gaia Data Release. We derive the metallicity effect in \\(V\\), \\(I\\), \\(J\\), \\(H\\), \\(K_S\\), \\(W_{VI}\\) and \\(W_{JK}\\). In the \\(K_S\\) band we report a metallicity effect of \\(-0.221 \\pm 0.051\\) mag/dex, the negative sign meaning that more metal-rich Cepheids are intrinsically brighter than their more metal-poor counterparts of the same pulsation period.