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To properly quantify the possible residual systematic errors affecting the classical Cepheid distance scale, a detailed theoretical scenario is recommended. By extending the set of nonlinear, convective pulsation models published for Z = 0.02 to Z = 0.004, Z = 0.008, and Z = 0.03, we provide a detailed homogeneous, nonlinear model grid taking into account simultaneous variations of the mass–luminosity relation, the efficiency of superadiabatic convection, and the chemical composition. The dependence of the inferred period–radius, period–mass–radius, and period–mass–luminosity–temperature relations on the input parameters is discussed for both the fundamental and first overtone modes. The trend of the instability strip getting redder as the metallicity increases is confirmed for the additional mass–luminosity assumptions and mixing length values. From the obtained multifilter light curves, we derive the mean magnitudes and colors, and in turn the period–luminosity–color and period–Wesenheit relations, for each assumed chemical composition, mass–luminosity relation, and efficiency of superadiabatic convection. Application to a well-studied sample of Cepheids in the Large Magellanic Cloud allows us to constrain the dependence of the inferred distance modulus on the assumed mass–luminosity relation, and the inclusion of the metallicity term in the derivation of the period–Wesenheit relations allows us, for each assumed mass–luminosity relation, to predict the metallicity dependence of the Cepheid distance scale. The obtained metal-dependent, period–Wesenheit relations are compared with recent results in the literature and applied to a sample of Gaia Early Data Release 3 Galactic Cepheids with known metal abundances to derive individual parallaxes. The comparison of these predictions with Gaia results is finally discussed.

Milky Way Cepheid variables with accurate Hubble Space Telescope photometry have been established as standards for primary calibration of the cosmic distance ladder to achieve a percent-level determination of the Hubble constant (H 0). These 75 Cepheid standards are the fundamental sample for investigation of possible residual systematics in the local H 0 determination due to metallicity effects on their period–luminosity relations. We obtained new high-resolution (R ∼ 81,000), high-signal-to-noise (S/N ∼ 50–150) multiepoch spectra of 42 out of 75 Cepheid standards using the ESPaDOnS instrument at the 3.6 m Canada–France–Hawaii Telescope. Our spectroscopic metallicity measurements are in good agreement with the literature values with systematic differences up to 0.1 dex due to different metallicity scales. We homogenized and updated the spectroscopic metallicities of all 75 Milky Way Cepheid standards and derived their multiwavelength (GVIJHK s ) period–luminosity–metallicity and period–Wesenheit–metallicity relations using the latest Gaia parallaxes. The metallicity coefficients of these empirically calibrated relations exhibit large uncertainties due to low statistics and a narrow metallicity range (Δ[Fe/H] = 0.6 dex). These metallicity coefficients are up to 3 times better constrained if we include Cepheids in the Large Magellanic Cloud and range between −0.21 ± 0.07 and −0.43 ± 0.06 mag dex−1. The updated spectroscopic metallicities of these Milky Way Cepheid standards were used in the Cepheid–supernovae distance ladder formalism to determine H 0 = 72.9 ± 1.0 km s−1 Mpc−1, suggesting little variation (∼0.1 km s−1 Mpc−1) in the local H 0 measurements due to different Cepheid metallicity scales.

Owing to its accurate distance measured from water-maser motions, NGC 4258 is one of the most important anchors for calibrating the Cepheid period–luminosity relations (PLRs). We expand on previous efforts and carry out a new Cepheid search in this system using the Hubble Space Telescope. We discover and measure a sample of 669 Cepheids in four new and two archival NGC 4258 fields, doubling the number of known Cepheids in this galaxy and obtaining an absolute calibration of their optical PLRs. We determine a Wesenheit (W VI HST) PLR of −2.574(±0.034)−3.294(±0.042)logP , consistent with an independent Large Magellanic Cloud (LMC) calibration at the level of 0.032 ± 0.044 mag in its zero-point, after accounting for a metallicity dependence of −0.20 ± 0.05 mag dex−1. Our determination of the PLR slope also agrees with the LMC-based value within their uncertainties. We attempt to characterize the metallicity effect of Cepheid PLRs using only the NGC 4258 sample, but a relatively narrow span of abundances limits our sensitivity and yields a W VI HST zero-point dependence of −0.07 ± 0.21 mag dex−1. The Cepheid measurements presented in this study have been used as part of the data to derive the Hubble constant in a companion paper by the SH0ES team.

It is beneficial to calibrate the period–Wesenheit–metallicity relation (PWZR) of Delta Cephei stars (DCEPs), i.e., classical Cepheids, using accurate parallaxes of associated open clusters (OCs) from Gaia data release 3 (DR3). To this aim, we obtain a total of 43 OC–DCEPs (including 33 fundamental mode, 9 first overtone mode, and 1 multimode DCEPs) and calibrate the PWZR as WG=(−3.356±0.033)(logP−1)+(−5.947±0.025) + (−0.285 ± 0.064)[Fe/H]. The concurrently obtained residual parallax offset in OCs, zp = −4 ± 5 μas, demonstrates the adequacy of the parallax corrections within the magnitude range of OC member stars. By comparing the field DCEPs’ DR3 parallaxes with their photometric parallaxes derived by our PWZR, we estimated the residual parallax offset in field DCEPs as zp = −15 ± 3 μas. Using our PWZR, we estimate the distance modulus of the Large Magellanic Cloud to be 18.482 ± 0.040 mag, which aligns well with the most accurate published value obtained through geometric methods.

Using an updated and significantly augmented sample of Cepheid and tip of the red giant branch (TRGB) distances to 28 nearby spiral and irregular galaxies, covering a wide range of metallicities, we have searched for evidence of a correlation of the zero-point of the Cepheid period–luminosity relation with H ii region (gas-phase) metallicities. Our analysis, for the 21 galaxies closer than 12.5 Mpc, results in the following conclusions: (1) The zero-points of the Cepheid and TRGB distance scales are in remarkably good agreement, with the mean offset in the zero-points of the most nearby distance-selected sample being close to zero, Δμ o (Cepheid—TRGB) = −0.026 ± 0.015 mag (for an I-band TRGB zero-point of M I = −4.05 mag); however, for the more distant sample, there is a larger offset between the two distance scales, amounting to −0.073 ± 0.057 mag 〈Δμ o 〉 (Cepheids—TRGB) = −0.026 ± 0.015 mag, for an I-band TRGB zero-point of M I = −4.05 mag. (2) The individual differences, about that mean, have a measured scatter of ±0.068 mag. (3) We find no statistically significant evidence for a metallicity dependence in the Cepheid distance scale using the reddening-free W(V, VI) period–luminosity relation: Δμ o (Cepheid − TRGB) = − 0.022( ± 0.015) × ([O/H] − 8.50) − 0.003(±0.007).

The number of known periodic variable stars has increased rapidly in recent years. As an all-sky transit survey, the Transiting Exoplanet Survey Satellite (TESS) plays an important role in detecting low-amplitude variable stars. Using 2 minute cadence data from the first 67 sectors of TESS, we find 72,505 periodic variable stars. We used 19 parameters including period, physical parameters, and light-curve (LC) parameters to classify periodic variable stars into 12 subtypes using the random forest method. Pulsating variable stars and eclipsing binaries are distinguished mainly by period, LC parameters, and physical parameters. Classical Cepheids, Type-II Cepheids, rotational variable stars, eruptive variable stars of the UV Ceti type, and young stellar objects are distinguished mainly by period and physical parameters. Compared to previously published catalogs, 63,106 periodic variable stars (87.0%) are newly classified, including 13 Cepheids, 27 RR Lyrae stars,​​​​​​ ~4600 δ Scuti variable stars, ~1600 eclipsing binaries, ~34,000 rotational variable stars, and about 23,000 other types of variable star. The purity of eclipsing binaries and pulsation variable stars ranges from 94.2% to 99.4% when compared to the variable star catalogs of Gaia Data Release 3 and Zwicky Transient Facility Data Release 2. The purity of rotational variable stars is relatively low at 83.3%. The increasing number of variables stars is helpful to investigate the structure of the Milky Way, stellar physics, and chromospheric activity.

Classical Cepheids (DCEPs) serve as fundamental standard candles for measuring cosmic distances and investigating the structure and evolution of the Milky Way disk. However, accurate distance estimation faces challenges due to severe extinction, particularly toward the Galactic center. Although the Gaia Wesenheit magnitude reduces extinction effects, its reliance on a constant optical extinction law introduces significant uncertainties in regions of heavy obscuration. Infrared period–luminosity relations, combined with 3D extinction maps, offer an alternative, but these maps become unreliable beyond approximately 5 kpc. In this work, we calibrate the period–luminosity–metallicity (PLZ) relations for DCEPs across three near-infrared bands (J, H, KS) and four mid-infrared bands (W1, W2, [3.6], and [4.5]). This includes the first calibration of the W1 and W2 bands. To correct for extinction, we employ the infrared multi-passband optimal distance method and the BP–RP method, which complement and validate each other. These homogeneous PLZ relations, combined with reliable extinction corrections, yield the most accurate Galactic DCEP distances to date, covering 3452 DCEPs with an average relative distance error of 3.1%.

Cepheids are fundamental distance indicators, playing a crucial role not only in the cosmic distance ladder but also in mapping the structure, kinematics, and extinction properties of the Milky Way. Using high-precision photometry and parallaxes from Gaia Data Release 3, we identify a significant anticorrelation between the G-band extinction coefficient and reddening for Galactic Cepheids, quantified as RG = 1.918 ± 0.060 − (0.106 ± 0.022) E(GBP − GRP). We propose that this anticorrelation arises from the combination of the nonlinear effects inherent to the broad Gaia bands and the RV variations caused by the diverse interstellar medium. Adopting a fixed RG would not only lead to an overestimation of the metallicity dependence of Cepheid luminosities but also systematically underestimate the distances to highly reddened Cepheids. Moreover, the strong reddening dependence of RG makes the Wesenheit function based on it unsuitable for highly reddened Cepheids, since the definition of Wesenheit magnitudes requires a fixed extinction coefficient. In contrast, infrared-based distances, being less affected by nonlinear effects and insensitive to RV, provide the most reliable Cepheid distances at present. This work emphasizes the importance of accurately determining RV for Galactic Cepheids and accounting for nonlinear effects in distance measurements, particularly in the optical bands.

This is the second of two papers exploring the effects of metallicity on the multiwavelength properties of Cepheids in terms of their multiwavelength period–luminosity (PL) relations, impacting their use as extragalactic distance indicators and underpinning one of the most popular paths to estimating the expansion rate of the Universe, H0. In Paper I, we presented five tests for the influence of metallicity on galactic and extragalactic Cepheid PL relations, spanning nearly 2 dex in metallicity and inspecting PL relations from the optical (BVI), through the near-infrared (JHK), and into the mid-infrared (at 3.4 and 4.5 μm). And in no case were any statistically significant results forthcoming. Here we interrogate published spectral energy distributions constructed from theoretical (static) stellar atmospheres, covering the surface gravity and temperature ranges attributed to classical (supergiant, F and K spectral type) Cepheid variables, and explore the differential effects of changing the atmospheric metallicity, down by 2 dex from solar (a factor of 100 below the average Milky Way value) and then up from solar by 0.5 dex (i.e., a factor of 3× above the Milky Way value). The theoretical models clearly show that metallicity systematically impacts each of the bandpasses differentially: the level of this effect is largest in the ultraviolet (where line blanketing is most intense), reversing sign in the optical (due to flux redistribution from the UV), and then asymptotically falling back to zero from the red to the far-infrared. The discovered effects of metallicity are systematic, but they are small, and as such, they do not contradict the findings of Paper I, but they do explain why the problem has been so hard to resolve given the low level of precision of the photometry for all but the very nearest and apparently brightest Cepheids. The most interesting (and useful) result of this investigation is that from a close examination of the models, we have discovered infrared regions in Cepheid spectral energy distributions that allow for the simultaneous correction for extinction and metallicity differences by the judicious combination of only two filters: one in the near-infrared and one in the mid-infrared, the former centered at 1.2 μm and the other centered at 3.6 μm. Even more exciting and promising is the fact that both of these bands can be simultaneously observed in single exposures using the dual-channel imager, NIRCam on JWST.

We report the discovery of the classical Cepheid OGLE-GD-CEP-1884 (= GDS_J1535467-555656) with the longest pulsation period known in our Galaxy. The period of 78.14 days is nearly 10 days longer than that of the previous record-holding Cepheid, S Vulpeculae, and thus, OGLE-GD-CEP-1884 can be categorized as the first ultra-long-period Cepheid in the Milky Way. This star is present in the ASAS-SN and Gaia DR3 catalogs of variable stars, but it has been classified as a long-period variable in those catalogs. Based on more than 10 yr of the photometric monitoring of this star carried out by the OGLE project in the I and V bands and a radial velocity curve from the Gaia Focused Product Release, we unequivocally demonstrate that this object is a fundamental-mode classical Cepheid. By employing the mid-infrared period–luminosity relation, we determine the distance to OGLE-GD-CEP-1884 (4.47 ± 0.34 kpc) and place it on the Milky Way map, along with about 2400 other classical Cepheids. We also discuss the potential of finding additional ultra-long-period Cepheids in our Galaxy.