Cepheid Distance Scale Research Articles

The Cepheid Distance Scale: A Novel Method for Obtaining Mean Magnitudes from Single-epoch Observations

We present a novel technique for mapping single-phase observations of Cepheids in any given band into their time-averaged values, using strong priors on the known interrelations of the multiwavelength widths of Cepheid period–luminosity (PL) relations, combined with the physical ordering of individual Cepheids within and across the instability strip, as a function of temperature (or radius). The method is empirically calibrated and tested using high-precision published multiwavelength observations of Cepheids in the LMC. The example, given herein, takes a single-epoch B-band PL relation and transforms those random-phase observations to within ±0.05–0.06 mag of their time-averaged values. For high-precision single-phase data points, this method can transform single-phase magnitudes into mean magnitudes (without additional observations), bringing the statistical error budget for the PL relation at that wavelength down to the systematic floor. This technique is of particular importance for use with space-based facilities (e.g., Hubble Space Telescope or JWST) where limits on the availability of telescope time preclude dense phase coverage, often resulting in only single-epoch observations being available.

Systematics in the Cepheid and TRGB Distance Scales: Metallicity Sensitivity of the Wesenheit Leavitt Law

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).

An Updated Metal-dependent Theoretical Scenario for Classical Cepheids

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.

Current Challenges in Cepheid Distance Calibrations Using Gaia Early Data Release 3

Abstract Using parallaxes from Gaia Early Data Release 3 (EDR3), we determine multi-wavelength BVI c , JHK s , and [3.6] and [4.5] micron absolute magnitudes for 37 nearby Milky Way Cepheids, covering the period range between 5 and 60 days. We apply these period–luminosity relations to Cepheids in the Large and Small Magellanic Clouds and find that the derived distances are significantly discrepant with the geometric distances according to detached eclipsing binaries (DEBs). We explore several potential causes of these issues, including reddening, metallicity, and the existence of an additional zero-point offset, but none provide a sufficient reconciliation with both DEB distances. We conclude that the combination of the systematic uncertainties on the EDR3 parallaxes with the uncertainties on the effect of metallicity on the Cepheid distance scale leads to a systematic error floor of approximately 3%. We therefore find that the EDR3 data are not sufficiently accurate in the regime of these bright Cepheids to determine extragalactic distances precise to the 1% level at this time, in agreement with a number of contemporary studies.

The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch*

Abstract We present a new and independent determination of the local value of the Hubble constant based on a calibration of the tip of the red giant branch (TRGB) applied to Type Ia supernovae (SNe Ia). We find a value of H 0 = 69.8 ± 0.8 (±1.1% stat) ± 1.7 (±2.4% sys) km s−1 Mpc−1. The TRGB method is both precise and accurate and is parallel to but independent of the Cepheid distance scale. Our value sits midway in the range defined by the current Hubble tension. It agrees at the 1.2σ level with that of the Planck Collaboration et al. estimate and at the 1.7σ level with the Hubble Space Telescope (HST) SHoES measurement of H 0 based on the Cepheid distance scale. The TRGB distances have been measured using deep HST Advanced Camera for Surveys imaging of galaxy halos. The zero-point of the TRGB calibration is set with a distance modulus to the Large Magellanic Cloud of 18.477 ± 0.004 (stat) ± 0.020 (sys) mag, based on measurement of 20 late-type detached eclipsing binary stars, combined with an HST parallax calibration of a 3.6 μm Cepheid Leavitt law based on Spitzer observations. We anchor the TRGB distances to galaxies that extend our measurement into the Hubble flow using the recently completed Carnegie Supernova Project I ( CSP-I ) sample containing about 100 well-observed SNe Ia . There are several advantages of halo TRGB distance measurements relative to Cepheid variables; these include low halo reddening, minimal effects of crowding or blending of the photometry, only a shallow (calibrated) sensitivity to metallicity in the I band, and no need for multiple epochs of observations or concerns of different slopes with period. In addition, the host masses of our TRGB host-galaxy sample are higher, on average, than those of the Cepheid sample, better matching the range of host-galaxy masses in the CSP-I distant sample and reducing potential systematic effects in the SNe Ia measurements.

On Cepheid Distance Scale Bias Due to Stellar Companions and Cluster Populations

Abstract State-of-the-art photometric measurements of extragalactic Cepheids account for the mean additional light due to chance superposition of Cepheids on crowded backgrounds through the use of artificial star measurements. However, light from stars physically associated with Cepheids may bias relative distance measurements if the changing spatial resolution along the distance ladder significantly alters the amount of associated blending. We have identified two regimes where this phenomenon may occur: Cepheids in wide binaries and in open clusters. We estimate stellar association bias using the photometric passbands and reddening-free Wesenheit magnitudes used to set up the distance scale. For wide binaries, we rely on Geneva stellar evolution models in conjunction with detailed statistics on intermediate-mass binary stars. For the impact of cluster stars, we have compiled information on the clustered Cepheid fraction and measured the typical cluster contribution in M31 via deep Hubble Space Telescope imaging provided by the Panchromatic Hubble Andromeda Treasury project. We find that the dominant effect on the distance scale comes from Cepheids in clusters, even though cluster Cepheids are a relatively rare phenomenon. Wide binaries have a negligible effect of 0.004% on H 0 for long-period Cepheids observed in the near-infrared or when considering Wesenheit magnitudes. We estimate that blending due to cluster populations has previously resulted in a 0.23% overestimate of H 0. Correcting for this bias, we obtain , which remains in 3.3σ tension with the Planck value. We conclude that stellar association bias does not constitute a limit for measuring H 0 with an accuracy of 1%.

Optical interferometry and Gaia parallaxes for a robust calibration of the Cepheid distance scale

AbstractWe present the modeling tool we developed to incorporate multi-technique observations of Cepheids in a single pulsation model: the Spectro-Photo-Interferometry of Pulsating Stars (SPIPS). The combination of angular diameters from optical interferometry, radial velocities and photometry with the coming Gaia DR2 parallaxes of nearby Galactic Cepheids will soon enable us to calibrate the projection factor of the classical Parallax-of-Pulsation method. This will extend its applicability to Cepheids too distant for accurate Gaia parallax measurements, and allow us to precisely calibrate the Leavitt law's zero point. As an example application, we present the SPIPS model of the long-period Cepheid RS Pup that provides a measurement of its projection factor, using the independent distance estimated from its light echoes.

Toward a renewed Galactic Cepheid distance scale from Gaia and optical interferometry

Through an innovative combination of multiple observing techniques and mod- eling, we are assembling a comprehensive understanding of the pulsation and close environment of Cepheids. We developed the SPIPS modeling tool that combines all observables (radial velocimetry, photometry, angular diameters from interferometry) to derive the relevant physical parameters of the star (effective temperature, infrared ex- cess, reddening,...) and the ratio of the distance and the projection factor d/p. We present the application of SPIPS to the long-period Cepheid RS Pup, for which we derive p = 1.25 +/- 0.06. The addition of this massive Cepheid consolidates the existing sample of p-factor measurements towards long-period pulsators. This allows us to conclude that p is constant or mildly variable around p = 1.29 +/- 0.04 (+/-3%) as a function of the pulsation period. The forthcoming Gaia DR2 will provide a considerable improvement in quantity and accuracy of the trigonometric parallaxes of Cepheids. From this sample, the SPIPS modeling tool will enable a robust calibration of the Cepheid distance scale.

THE CARNEGIE-CHICAGO HUBBLE PROGRAM. I. AN INDEPENDENT APPROACH TO THE EXTRAGALACTIC DISTANCE SCALE USING ONLY POPULATION II DISTANCE INDICATORS*

ABSTRACT We present an overview of the Carnegie-Chicago Hubble Program, an ongoing program to obtain a 3% measurement of the Hubble constant (H 0) using alternative methods to the traditional Cepheid distance scale. We aim to establish a completely independent route to H 0 using RR Lyrae variables, the tip of the red giant branch (TRGB), and Type Ia supernovae (SNe Ia). This alternative distance ladder can be applied to galaxies of any Hubble type, of any inclination, and, using old stars in low-density environments, is robust to the degenerate effects of metallicity and interstellar extinction. Given the relatively small number of SNe Ia host galaxies with independently measured distances, these properties provide a great systematic advantage in the measurement of H 0 via the distance ladder. Initially, the accuracy of our value of H 0 will be set by the five Galactic RR Lyrae calibrators with Hubble Space Telescope Fine-Guidance Sensor parallaxes. With Gaia, both the RR Lyrae zero-point and TRGB method will be independently calibrated, the former with at least an order of magnitude more calibrators and the latter directly through parallax measurement of tip red giants. As the first end-to-end “distance ladder” completely independent of both Cepheid variables and the Large Magellanic Cloud, this path to H 0 will allow for the high-precision comparison at each rung of the traditional distance ladder that is necessary to understand tensions between this and other routes to H 0.

The long-period Galactic Cepheid RS Puppis

As one of the most luminous Cepheids in the Milky Way, the 41.5-day RS Puppis is an analog of the long-period Cepheids used to measure extragalactic distances. An accurate distance to this star would therefore help anchor the zero-point of the bright end of the period-luminosity relation. But, at a distance of about 2 kpc, RS Pup is too far away for measuring a direct trigonometric parallax with a precision of a few percentage points with existing instrumentation. RS Pup is unique by being surrounded by a reflection nebula whose brightness varies as pulses of light from the Cepheid propagate outward. We present new polarimetric imaging of the nebula obtained with HST/ACS. The derived map of the degree of linear polarization pL allows us to reconstruct the three-dimensional structure of the dust distribution. To retrieve the scattering angle from the pL value, we consider two different polarization models, one based on a Milky Way dust mixture and one assuming Rayleigh scattering. Considering the derived dust distribution in the nebula, we adjust a model of the phase lag of the photometric variations over selected nebular features to retrieve the distance of RS Pup. We obtain a distance of 1910 ± 80 pc (4.2%), corresponding to a parallax of π = 0.524 ± 0.022 mas. The agreement between the two polarization models that we considered is good, but the final uncertainty is dominated by systematics in the adopted model parameters. The distance we obtain is consistent with existing measurements from the literature, but light echoes provide a distance estimate that is not subject to the same systematic uncertainties as other estimators (e.g., the Baade-Wesselink technique). RS Pup therefore provides an important fiducial for calibrating the systematic uncertainties of the long-period Cepheid distance scale.

TOWARD A NEW GEOMETRIC DISTANCE TO THE ACTIVE GALAXY NGC 4258. III. FINAL RESULTS AND THE HUBBLE CONSTANT

We report a new geometric maser distance estimate to the active galaxy NGC 4258. The data for the new model are maser line-of-sight velocities and sky positions from 18 epochs of Very Long Baseline Interferometry observations, and line-of-sight accelerations measured from a 10-year monitoring program of the 22 GHz maser emission of NGC 4258. The new model includes both disk warping and confocal elliptical maser orbits with differential precession. The distance to NGC 4258 is 7.60 +/- 0.17 +/- 0.15 Mpc, a 3% uncertainty including formal fitting and systematic terms. The resulting Hubble Constant, based on the use of the Cepheid Variables in NGC 4258 to recalibrate the Cepheid distance scale (Riess et al. 2011), is H_0 = 72.0 +/- 3.0 km/s/Mpc.

The distance to NGC 1316 (Fornax A): yet another curious case

The distance of NGC1316, the brightest galaxy in Fornax, is an interesting test for the cosmological distance scale. First, because Fornax is the 2nd largest cluster of galaxies at <~25 Mpc after Virgo and, in contrast to Virgo, has a small line-of-sight depth; and second, because NGC1316 is the galaxy with the largest number of detected SNeIa, giving the opportunity to test the consistency of SNeIa distances internally and against other indicators. We measure SBF mags in NGC1316 from ground and space-based imaging data, providing a homogeneous set of measurements over a wide wavelength interval. The SBF, coupled with empirical and theoretical calibrations, are used to estimate the distance to the galaxy. We present the first B-band SBF measurements of NGC1316 and use them together with the optical and near-IR SBF data to analyze the properties of field stars. Our distance modulus m-M=31.59 +-0.05(stat) +-0.14(sys), when placed in a consistent Cepheid distance scale, agrees with the results from other indicators. However, our result is ~17% larger than the most recent estimate based on SNeIa. Possible explanations for this disagreement are the uncertainties on internal extinction, or calibration issues. Concerning the stellar population analysis, we confirm earlier results from other indicators: the field stars in NGC1316 are dominated by a solar metallicity, intermediate age component. A substantial mismatch exists between B-band SBF models and data, a behavior that can be accounted for by an enhanced percentage of hot horizontal branch stars. Our study of the SBF distance to NGC1316, and the comparison with distances from other indicators, raises some concern about the homogeneity between the calibrations of different indicators. If not properly placed in the same reference scale, significant differences can occur, with dramatic impact on the cosmological distance ladder.

The Classical Cepheid Distance scale in the NIR bands

The Period-Luminosity (PL) relation of classical Cepheids is one of the most popular standard candle, being the first rung of the cosmic distance ladder. We discuss both theoretical and empirical features of the PL, Period-Luminosity-Color (PLC) and Period-Wesenheit (PW) relations using the largest optical (V,I; OGLEIII) and near-infrared (NIR, J,H,Ks; IRSF/SIRIUS) data sets ever collected for classical Cepheids in the Magellanic Clouds (MCs). The MCs are indeed a fundamental benchmark to calibrate the cosmic distance scale. We found that the PW relations are linear over the entire period range and show a very low dispersion. Moreover, their slopes appear independent of the metallicity since they attain similar values in the MCs and in the Galaxy. This indicates that Cepheids in NIR bands obey to universal PW relations.

CARNEGIE HUBBLE PROGRAM: A MID-INFRARED CALIBRATION OF THE HUBBLE CONSTANT

Using a mid-infrared calibration of the Cepheid distance scale based on recent observations at 3.6 um with the Spitzer Space Telescope, we have obtained a new, high-accuracy calibration of the Hubble constant. We have established the mid-IR zero point of the Leavitt Law (the Cepheid Period-Luminosity relation) using time-averaged 3.6 um data for ten high-metallicity, Milky Way Cepheids having independently-measured trigonometric parallaxes. We have adopted the slope of the PL relation using time-averaged 3.6 um data for 80 long-period Large Magellanic Cloud (LMC) Cepheids falling in the period range 0.8 < log(P) < 1.8. We find a new reddening-corrected distance to the LMC of 18.477 +/- 0.033 (systematic) mag. We re-examine the systematic uncertainties in H0, also taking into account new data over the past decade. In combination with the new Spitzer calibration, the systematic uncertainty in H0 over that obtained by the Hubble Space Telescope (HST) Key Project has decreased by over a factor of three. Applying the Spitzer calibration to the Key Project sample, we find a value of H0 = 74.3 with a systematic uncertainty of +/-2.1 (systematic) km/s/Mpc, corresponding to a 2.8% systematic uncertainty in the Hubble constant. This result, in combination with WMAP7 measurements of the cosmic microwave background anisotropies and assuming a flat universe, yields a value of the equation of state for dark energy, w0 = -1.09 +/- 0.10. Alternatively, relaxing the constraints on flatness and the numbers of relativistic species, and combining our results with those of WMAP7, Type Ia supernovae and baryon acoustic oscillations yields w0 = -1.08 +/- 0.10 and a value of N_eff = 4.13 +/- 0.67, mildly consistent with the existence of a fourth neutrino species.

Circumstellar envelopes of Cepheids: a possible bias affecting the distance scale?

AbstractCircumstellar envelopes (CSEs) have been detected around many Cepheids, first based on long-baseline interferometry, and now also using other observing techniques. These envelopes are particularly interesting for two reasons: their presence could impact the Cepheid distance scale, and they may be valuable tracers of stellar mass loss. Here we focus on their potential impact on the calibration of the Cepheid distance scale. We consider the photometric contribution of the envelopes in the visible, near-, and thermal-infrared domains. We conclude that the impact of CSEs on the apparent luminosities of Cepheids is negligible at visible wavelengths and generally weak (&lt;5%) in the near-infrared (λ ≈ 2 μm). In the thermal-infrared domain (λ ≈ 8 μm), the flux contribution of the CSEs differs depending on the pulsation period: it is relatively weak (&lt;15%) for stars with periods shorter than P ≈ 10 days, but can reach ≈ 30% for long-period Cepheids. We specifically discuss the long-period Galactic Cepheid RS Puppis, which exhibits a very large circumstellar, dusty envelope, and we conclude that this is not a representative case. Overall, the contribution of CSEs to the usual period–luminosity relations (from the visible to the K band) is mostly negligible. They could affect calibrations at longer wavelengths, although the presence of envelopes may have been partially taken into account in the existing empirical calibrations.

The Carnegie Hubble Program: From parallaxes to the Tully–Fisher relation

AbstractThe Carnegie Hubble Program (CHP) is a Warm Spitzer program with the aim of reducing the uncertainty in the Hubble constant to below 3%. The program is calibrated using Galactic Cepheids with precise parallax distances from the Hubble Space Telescope (HST), combined with a large sample of Cepheids in the Large Magellanic Cloud. We extend the Cepheid distance scale to the Local Group and beyond, into the regime probed by the Tully–Fisher relation. The entire program—from Galactic Cepheids to the most distant galaxies—uses the Spitzer/IRAC instrument. Completing the entire program with a single instrument on a single telescope virtually eliminates instrumental effects, whilst moving to the mid-infrared drastically reduces the reddening and metallicity effects that trouble the optical Cepheid distance scale. Our first measurement of the Hubble constant, using only two CHP galaxies tied into the HST Key Project results has produced a measurement of H0 = 74.3 ± 2.1 (systematic) km s−1 Mpc−1, which corresponds to a systematic uncertainty of 2.8%.

Cepheid distances from the Baade–Wesselink method

AbstractRecent progress on Baade–Wesselink (BW)-type techniques to determine the distances to classical Cepheids is reviewed. Particular emphasis is placed on the near-infrared surface-brightness (IRSB) version of the BW method. Its most recent calibration is described and shown to be capable of yielding individual Cepheid distances accurate to 6%, including systematic uncertainties. Cepheid distances from the IRSB method are compared to those determined from open cluster zero-age main-sequence fitting for Cepheids located in Galactic open clusters, yielding excellent agreement between the IRSB and cluster Cepheid distance scales. Results for the Cepheid period–luminosity (PL) relation in near-infrared and optical bands based on IRSB distances and the question of the universality of the Cepheid PL relation are discussed. Results from other implementations of the BW method are compared to the IRSB distance scale and possible reasons for discrepancies are identified.

Cosmic distances from surface brightness fluctuations

AbstractHigh spatial-resolution measurements of surface brightness fluctuations (SBFs) with the Hubble Space Telescope (HST) provide the most precise distances available to early-type galaxies beyond the Local Group. The observable SBF magnitude in a given bandpass is a basic property of any stellar system, corresponding to a ratio of the first and second moments of the stellar luminosity function. Calibration of the method has presented challenges, but we now have an excellent empirical determination of how the SBF observable varies with galaxy color in broad bandpasses at the red end of the optical spectrum, and we are working towards a similar calibration for HST's Wide-Field Camera 3 in the near-infrared wavelength range, where the SBF magnitudes are considerably brighter. From HST Advanced Camera for Surveys data, we have determined the relative distances of the Virgo and Fornax clusters to within a precision of 2%, and resolved their internal structures. More recent measurements allow us to tie the Coma cluster, the standard of comparison for distant cluster studies, to the same precise distance scale. The SBF method can be calibrated in an absolute sense either empirically using Cepheids or theoretically based on stellar population models. The agreement between model and empirical zero points provides an independent confirmation of the Cepheid distance scale.

Surface brightness fluctuations as primary and secondary distance indicators

The surface brightness fluctuations (SBF) method measures the variance in a galaxy's light distribution arising from fluctuations in the numbers and luminosities of individual stars per resolution element. Once calibrated for stellar population effects, SBF measurements with HST provide distances to early-type galaxies with unrivaled precision. Optical SBF data from HST for the Virgo and Fornax clusters give the relative distances of these nearby fiducial clusters with 2% precision and constrain their internal structures. Observations in hand will allow us to tie the Coma cluster, the standard of comparison for distant cluster studies, into the same precise relative distance scale. The SBF method can be calibrated in an absolute sense either empirically from Cepheids or theoretically from stellar population models. The agreement between the model and empirical zero points has improved dramatically, providing an independent confirmation of the Cepheid distance scale. SBF is still brighter in the near-IR, and an ongoing program to calibrate the method for the F110W and F160W passbands of the WFC3 IR channel will enable accurate distance derivation whenever a large early-type galaxy or bulge is observed in these passbands at distances reaching well out into the Hubble flow.

THE CARNEGIE HUBBLE PROGRAM: THE LEAVITT LAW AT 3.6 μm AND 4.5 μm IN THE LARGE MAGELLANIC CLOUD

The Carnegie Hubble Program (CHP) is designed to improve the extragalactic distance scale using data from the post-cryogenic era of Spitzer. The ultimate goal is a determination of the Hubble constant to an accuracy of 2%. This paper is the first in a series on the Cepheid population of the Large Magellanic Cloud, and focusses on the period-luminosity relations (Leavitt laws) that will be used, in conjunction with observations of Milky Way Cepheids, to set the slope and zero--point of the Cepheid distance scale in the mid-infrared. To this end, we have obtained uniformly-sampled light curves for 85 LMC Cepheids, having periods between 6 and 140 days. Period-luminosity and period-color relations are presented in the 3.6 \mu m and 4.5\mu m bands. We demonstrate that the 3.6 \mu m band is a superb distance indicator. The cyclical variation of the [3.6]-[4.5] color has been measured for the first time. We attribute the amplitude and phase of the color curves to the dissociation and recombination of CO molecules in the Cepheid's atmosphere. The CO affects only the 4.5 \mu m flux making it a potential metallicity indicator.