LMC Cepheids Research Articles

Geometric perspective for explaining Hubble tension: theoretical and observational aspects

The Universe expansion rate has two different but very precise values ( and km s−1Mpc−1) that are not compatible. This problem, known as a Hubble tension, adds to other cosmological questions such as the origin of dark energy and the flatness problem. In turn, alternative models have attempted to explain similar phenomena but without dark energy. The aim of this work was to explain the Hubble tension by using a geometrical interpretation of observational viewpoints in embedded manifolds. Our technique consists of a set of parametric projections of radially inhomogeneous metrics, linking indistinguishable behaviours of accelerated flat and non-accelerated closed universes. A dark-energy-like phenomenon emerges from the distortion of matter-independent hyperconical metrics. To contrast our model, numerical solutions of dark energy/matter densities and Hubble parameter were obtained and compared to the standard model fitted to the Pantheon Supernovae Ia sample and in contrast to the SH0ES LMC Cepheid findings. Finally, Hubble tension is modelled by the different extrinsic/intrinsic viewpoints of the manifold. Compared to the Planck Legacy’s 2018 release of km s−1Mpc−1, we found ΛCDM-dependent (intrinsic) ranges between 66.38 and 68.87 km s−1Mpc−1, which were theoretically derived by setting local compatibility of metrics. The ΛCDM-independent extrinsic viewpoint resulted in a Hubble parameter between 73 and 74 km s−1Mpc−1 (compared to km s−1Mpc−1 of SH0ES). Datasets of 1048 Pantheon Type Ia supernovae () and 34 cosmic chronometers combined with 7 radial baryon acoustic oscillation size-based samples () were used to constraint the model. According to this geometrical perspective, dark parameters (energy and matter) could partially or totally be considered ‘apparent physical quantities’, a consequence of the stereographic projection of the extrinsic curvature.

Peeping into recent star-formation history of Magellanic Clouds

Here, we study the distribution of Fundamental-mode Cepheids in the Magellanic Cloud as a function of their positions and ages using the data from the OGLE~IV survey. Age of the Cepheids are determined through well known period - age relations for the LMC and SMC Cepheids which are used to understand the star formation scenario in the Magellanic Cloud. The age distributions of the Cepheids in LMC and SMC show peak around $155^{+45}_{-35}$ Myr and $224^{+51}_{-42}$ Myr, respectively. This indicates that a major star formation event took place in the Magellanic Cloud at about 200\,Myr ago. It is believed that this event might have been triggered by a close encounter between the two components of the Magellanic Cloud or due to a possible tidal interaction between the Magellanic Cloud and Milky Way galaxy during one of its pericentric passages round the Milky Way. Cepheids are found to be asymmetrically distributed in both the LMC and SMC. A high-density clumpy structure is found to be located towards eastern side of the LMC and south-west direction of the SMC from their respective galactic centres.

Metallicity estimations of MW, SMC, and LMC classical Cepheids from the shape of the V- and I-band light curves

Context. Estimating the metallicity of classical Cepheids is of prime importance for studying metallicity effects on stellar evolution and the chemical evolution of galaxies, as well as on the period–luminosity relation used on the extragalactic distance scale. Aims. Our first aim is to establish new empirical relations for estimating the iron content of classical Cepheids for short and long periods based on Fourier parameters from the V- and I-band light curves. We go on to apply these relations to Cepheids from data on the Milky Way (MW) as well as the Small and Large Magellanic Clouds (SMC and LMC) from the literature. Methods. We retrieved the metallicities of 586 fundamental-mode Cepheids from spectroscopic determinations in the literature and we found well-sampled light curves for 545 of them in different V-band catalogs. We then described the shape of these light curves by applying a Fourier decomposition and we fit the empirical relations between the Fourier parameters and the spectroscopic metallicities individually, for short-period (2.5 < P < 6.3 days) and long-period Cepheids (12 < P < 40 days). We verified the accuracy of these relations by applying them to V-band light curves of Cepheids from the Small and Large Magellanic Clouds and comparing these derived metallicities to literature values. We calibrated new interrelations of Fourier parameters to convert these empirical relations into the I band. We then used these I-band relations to derive the metallicity of fundamental-mode Cepheids from OGLE-IV for MW, SMC, and LMC (486, 695, and 1697 stars, respectively). Finally, we mapped the metallicity distribution in these galaxies for the purpose of investigating potential applications in galactic archeology. Results. For short-period Cepheids, our best fit is given for a relation based on explicit amplitude terms A1 and A2 of the first and second harmonic, respectively. In the V and I bands, these empirical relations are found with an intrinsic scatter (rms) of 0.12 dex. This relation performs well for estimations of [Fe/H] between about −0.5 and 0.1 dex, but it remains uncertain outside this range because of the lack of a spectroscopic metallicity required for the calibration. For long-period Cepheids, we found a metallicity dependence on the Fourier parameters A1, ϕ21, and R41. We found an intrinsic scatter of 0.25 dex when using this relation. The empirical relations in the V and I bands allow us to derive the mean metallicity of a sample of MW, SMC, and LMC Cepheids that is in agreement with literature values within 1σ. We also show that these relations are precise enough to reconstruct the radial metallicity gradients within the MW from OGLE data. Conclusions. The empirical relations in the V and I bands that are calibrated in this work for short- and long-period Cepheids provide a useful new tool for estimating the metallicity of Cepheids that are not accessible via spectroscopy. The calibration can be improved with further high-resolution spectroscopic observations of metal-poor Cepheids and homogeneous photometries in the V and I bands.

The iron and oxygen content of LMC Classical Cepheids and its implications for the extragalactic distance scale and Hubble constant

Classical Cepheids are primary distance indicators and a crucial stepping stone to determining the present-day Hubble constant Ho to the precision and accuracy required to constrain apparent deviations from the LCDM Concordance Cosmological Model. We have measured the iron and oxygen abundances of of 89 Cepheids in the LMC, one of the anchors of the local Distance Scale, quadrupling the prior sample and including 68 of the 70 Cepheids used to constrain Ho by the SH0ES program. The goal is to constrain the extent to which the Cepheid luminosity is influenced by their chemical composition, an important contributor to the uncertainty on the determination of the Ho itself and a critical factor in the internal consistency of the distance ladder. We have derived stellar parameters and abundances from a self-consistent spectroscopic analysis based on Equivalent Width of absorption lines. The [Fe/H] distribution of LMC Cepheids is a single Gaussian with a mean of -0.4079+-0.003 dex (0.1 dex systematic uncertainty) and sigma 0.076+-0.003 dex. The latter is fully compatible with the measurement error and supports the low dispersion of 0.069 mag seen in the NIR HST LMC period-luminosity relation. The uniformity of the abundance has the important consequence that the LMC Cepheids alone cannot provide any meaningful constraint on the dependence of the Cepheid Period-Luminosity relation on chemical composition at any wavelength. This revises a prior claim based on a small sample of 22 LMC Cepheids that there was little dependence (or uncertainty) between composition and NIR luminosity, a conclusion which would produce a conflict between anchors of the distance ladder with different mean abundance. The chemical homogeneity of the LMC Cepheid population makes it an ideal environment to calibrate the metallicity dependence between the more metal poor SMC and metal rich Milky Way and NGC4258.

Cepheids with Giant Companions. I. Revealing a Numerous Population of Double-lined Binary Cepheids* †

Abstract Masses of classical Cepheids of 3–11 M ⊙ are predicted by theory but those measured clump between 3.6–5 M ⊙. As a result, their mass–luminosity relation is poorly constrained, impeding our understanding of basic stellar physics and the Leavitt Law. All Cepheid masses come from the analysis of 11 binary systems, including only five that are double lined and well suited for accurate dynamical mass determination. We present a project to analyze a new, numerous group of Cepheids in double-lined binary (SB2) systems to provide mass determinations in a wide mass interval and study their evolution. We analyze a sample of 41 candidate binary LMC Cepheids spread along the P–L relation, which are likely accompanied by luminous red giants, and present indirect and direct indicators of their binarity. In a spectroscopic study of a subsample of 18 brightest candidates, for 16 we detected lines of two components in the spectra, already quadrupling the number of Cepheids in SB2 systems. Observations of the whole sample may thus lead to quadrupling all the Cepheid mass estimates available now. For the majority of our candidates, erratic intrinsic period changes dominate over the light-travel-time effect due to binarity. However, the latter may explain the periodic phase modulation for four Cepheids. Our project paves the way for future accurate dynamical mass determinations of Cepheids in the LMC, Milky Way, and other galaxies, which will potentially increase the number of known Cepheid masses even 10-fold, hugely improving our knowledge about these important stars.

Reconciling Hubble constant discrepancy from holographic dark energy

Holographic dark energy (HDE) describes the vacuum energy in a cosmic IR region whose total energy saturates the limit of avoiding the collapse into a black hole. HDE predicts that the dark energy equation of the state transiting from greater than the $-1$ regime to less than $-1$, accelerating the Universe slower at the early stage and faster at the late stage. We propose the HDE as a new {\it physical} resolution to the Hubble constant discrepancy between the cosmic microwave background (CMB) and local measurements. With Planck CMB and galaxy baryon acoustic oscillation (BAO) data, we fit the HDE prediction of the Hubble constant as $H_0^{}\!=\, 71.54\pm1.78\,\mathrm{km\,s^{-1} Mpc^{-1}}$, consistent with local $H_0^{}$ measurements by LMC Cepheid Standards (R19) at $1.4\sigma$ level. Combining Planck+BAO+R19, we find the HDE parameter $c=0.51\pm0.02$ and $H_0^{}\! = 73.12\pm 1.14\,\mathrm{km \,s^{-1} Mpc^{-1}}$, which fits cosmological data at all redshifts. Future CMB and large-scale structure surveys will further test the holographic scenario.

The effect of metallicity on Cepheid period-luminosity relations from a Baade-Wesselink analysis of Cepheids in the Milky Way and Magellanic Clouds

Context. The extragalactic distance scale builds on the Cepheid period-luminosity (PL) relation. Decades of work have not yet convincingly established the sensitivity of the PL relation to metallicity. This currently prevents a determination of the Hubble constant accurate to 1% from the classical Cepheid-SN Ia method. Aims. In this paper we carry out a strictly differential comparison of the absolute PL relations obeyed by classical Cepheids in the Milky Way (MW), LMC, and SMC galaxies. Taking advantage of the substantial metallicity difference among the Cepheid populations in these three galaxies, we want to establish a possible systematic trend of the PL relation absolute zero point as a function of metallicity, and to determine the size of such an effect in the optical and near-infrared photometric bands. Methods. We used a IRSB Baade-Wesselink-type method to determine individual distances to the Cepheids in our samples in the MW, LMC, and SMC. For our analysis, we used a greatly enhanced sample of Cepheids in the SMC (31 stars) compared to the small sample (5 stars) available in our previous work. We used the distances to determine absolute Cepheid PL relations in the optical and near-infrared bands in each of the three galaxies. Results. Our distance analysis of 31 SMC Cepheids with periods of 4–69 days yields tight PL relations in all studied bands, with slopes consistent with the corresponding LMC and MW relations. Adopting the very accurately determined LMC slopes for the optical and near-infrared bands, we determine the zero point offsets between the corresponding absolute PL relations in the three galaxies. Conclusions. We find that in all bands the metal-poor SMC Cepheids are intrinsically fainter than their more metal-rich counterparts in the LMC and MW. In the K band the metallicity effect is −0.23 ± 0.06 mag dex−1, while in the V, (V − I) Wesenheit index it is slightly stronger, −0.34 ± 0.06 mag dex−1. We find suggestive evidence that the metallicity sensitivity of the PL relation might be nonlinear, being small in the range between solar and LMC Cepheid metallicity, and becoming steeper towards the lower-metallicity regime.

A Precision Determination of the Effect of Metallicity on Cepheid Absolute Magnitudes in VIJHK Bands from Magellanic Cloud Cepheids

Abstract Using high-quality observed period–luminosity (P–L) relations in both Magellanic Clouds in the VIJHK s bands and optical and near-infrared Wesenheit indices, we determine the effect of metallicity on Cepheid P–L relations by comparing the relative distance between the LMC and SMC as determined from the Cepheids to the difference in distance between the Clouds that has been derived with very high accuracy from late-type eclipsing binary systems. Within an uncertainty of 3%, which is dominated by the uncertainty on the mean difference in metallicity between the Cepheid populations in the LMC and SMC, we find metallicity effects smaller than 2% in all bands and in the Wesenheit indices, consistent with a zero metallicity effect. This result is valid for the metallicity range from −0.35 dex to −0.75 dex corresponding to the mean [Fe/H] values for classical Cepheids in the LMC and SMC, respectively. Yet most Cepheids in galaxies beyond the Local Group and located in the less crowded outer regions of these galaxies do fall into this metallicity regime, making our result important for applications to determine the distances to spiral galaxies well beyond the Local Group. Our result supports previous findings that indicated a very small metallicity effect on the near-infrared absolute magnitudes of classical Cepheids, and resolves the dispute about the size and sign of the metallicity effect in the optical spectral range. It also resolves one of the most pressing problems in the quest toward a measurement of the Hubble constant with an accuracy of 1% from the Cepheid–supernova Ia method.

How stable are our standard candles? Time-resolved analysis of amplitude and period changes in OGLE-III LMC Cepheids

AbstractWe revisit a group of OGLE-III Cepheids that exhibit nearby double peaks in their periodograms using a technique of statistics called kernel modelling. We investigate the phenomenology of these Cepheids (termed twin-peak Cepheids in this paper) in more detail by comparing a sample of 29 LMC Cepheids that exhibit twin frequency peaks with 24 other Cepheids that do not. Using the kernel technique, we investigate light curve variability as a function of time, revealing both frequency and amplitude modulations. We present the preliminary results of our study in progress, which suggests a complex interplay between the two types of modulations and their detectability via twin peaks in the periodogram. The study reveals the potential of the kernel technique to help theory and modelling with detailed data analyses, capable of tracing fine time-dependent variations of the phenomenology of pulsations for objects of surveys or observation campaigns producing sufficiently dense time sampling.

Evolution and pulsation period change in the Large Magellanic Cloud Cepheids

Theoretical estimates of the pulsation period change rates in LMC Cepheids are obtained from consistent calculation of stellar evolution and nonlinear stellar pulsation for stars with initial chemical composition X = 0.7, Z = 0.008, initial masses 5M ⊙ ≤ M ZAMS ≤ 9M ⊙ and pulsation periods ranged from 2.2 to 29 day. The Cepheid hydrodynamical models correspond to the evolutionary stage of thermonuclear core helium burning. During evolution across the instability strip in the HR diagram the pulsation period Π of Cepheids is the quadratic function of the evolution time for the both fundamental mode and first overtone. Cepheids with initial masses M ZAMS ≥ 7M ⊙ pulsate in the fundamental mode and the period change rate \(\dot \Pi\) varies nearly by a factor of two for both crossings of the instability strip. In the period-period change rate diagram the values of Π and \(\dot \Pi\) concentrate within the strips, their slope and half-width depending on both the direction of the movement in the HR-diagram and the pulsation mode. For oscillations in the fundamental mode the half-widths of the strip are \(\delta log\dot \Pi = 0.35\) and \(\delta log\dot \Pi = 0.2\) for the first and the secon crossings of the instability strip, respectively. Results of computations are comparedwith observations of nearly 700 LMC Cepheids. Within existing observational uncertainties of \(\dot \Pi\) the theoretical dependences of the period change rate on the pulsation period are in a good agreement with observations.

Radii of LMC and SMC Cepheids

AbstractWe collected long sets of precise radial velocity observations of radial velocities for 8 SMC and 14 LMC Cepheids. Based on these series of radial velocity measurements and on multicolor photoelectric observations, we calculated radii of the program extragalactic Cepheids using a modification of Balona's method. Our main goal was to determine the long‐period branch of the period‐radius diagram and reveal a dependence on metallicity. We derived the following period‐radius relation: log R = 1.06(±0.03)+0.74(±0.02) log P. We did not find any significant difference between the period‐radius relation of extragalactic Cepheids and that of fundamental‐mode galactic Cepheids. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A GLOBAL PHYSICAL MODEL FOR CEPHEIDS

We perform a global fit to ~5,000 radial velocity and ~177,000 magnitude measurements in 29 photometric bands covering 0.3 to 8.0 microns distributed among 287 Galactic, LMC, and SMC Cepheids with P > 10 days. We assume that the Cepheid light curves and radial velocities are fully characterized by distance, reddening, and time-dependent radius and temperature variations. We construct phase curves of radius and temperature for periods between 10 and 100 days, which yield light curve templates for all our photometric bands and can be easily generalized to any additional band. With only 4 to 6 parameters per Cepheid, depending on the existence of velocity data and the amount of freedom in the distance, the models have typical rms light and velocity curve residuals of 0.05 mag and 3.5 km/s. The model derives the mean Cepheid spectral energy distribution and its derivative with respect to temperature, which deviate from a black body in agreement with metal-line and molecular opacity effects. We determine a mean reddening law towards the Cepheids in our sample, which is not consistent with standard assumptions in either the optical or near-IR. Based on stellar atmosphere models we predict the biases in distance, reddening, and temperature determinations due to the metallicity and we quantify the metallicity signature expected for our fit residuals. The observed residuals as a function of wavelength show clear differences between the individual galaxies, which are compatible with these predictions. In particular, we find that metal-poor Cepheids appear hotter. Finally, we provide a framework for optimally selecting filters that yield the smallest overall errors in Cepheid parameter determination, or filter combinations for suppressing or enhancing the metallicity effects on distance determinations. We make our templates publicly available.

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.

The Baade-Wesselinkp-factor applicable to LMC Cepheids

Context. Recent observations of LMC Cepheids bring new constraints on the slope of the period-projection factor relation (hereafter Pp relation) that is currently used in the Baade-Wesselink (hereafter BW) method of distance determination. The discrepancy between observations and theoretical analysis is particularly significant for short period Cepheids Aims. We investigate three physical effects that might possibly explain this discrepancy: (1) the spectroscopic S/N that is systematically lower for LMC Cepheids (around 10) compared to Galactic ones (up to 300), (2) the impact of the metallicity on the dynamical structure of LMC Cepheids, and (3) the combination of infrared photometry/interferometry with optical spectroscopy. Methods. To study the S/N we use a very simple toy model of Cepheids. The impact of metallicity on the projection factor is based on the hydrodynamical model of delta Cep already described in previous studies. This model is also used to derive the position of the optical versus infrared photospheric layers. Results. We find no significant effect of S/N, metallicity, and optical-versus-infrared observations on the Pp relation. Conclusions. The Pp relation of Cepheids in the LMC does not differ from the Galactic relation. This allows its universal application to determine distances to extragalactic Cepheids via BW analysis.

Period-colour and amplitude-colour relations in classical Cepheid variables - VI. New challenges for pulsation models

We present multiphase Period-Color/Amplitude-Color/Period-Luminosity relations using OGLE III and Galactic Cepheid data and compare with state of the art theoretical pulsation models. Using this new way to compare models and observations, we find convincing evidence that both Period-Color and Period-Luminosity Relations as a function of phase are dynamic and highly nonlinear at certain pulsation phases. We extend this to a multiphase Wesenheit function and find the same result. Hence our results cannot be due to reddening errors. We present statistical tests and the urls of movies depicting the Period-Color/Period Luminosity and Wesenheit relations as a function of phase for the LMC OGLE III Cepheid data: these tests and movies clearly demonstrate nonlinearity as a function of phase and offer a new window toward a deeper understanding of stellar pulsation. When comparing with models, we find that the models also predict this nonlinearity in both Period-Color and Period-Luminosity planes. The models with (Z=0.004, Y=0.25) fare better in mimicking the LMC Cepheid relations, particularly at longer periods, though the models predict systematically higher amplitudes than the observations.

TESTING MASS LOSS IN LARGE MAGELLANIC CLOUD CEPHEIDS USING INFRARED AND OPTICAL OBSERVATIONS. II. PREDICTIONS AND TESTS OF THE OGLE-III FUNDAMENTAL-MODE CEPHEIDS

In this article, we test the hypothesis that Cepheids have infrared excesses due to mass loss. We fit a model using the mass-loss rate and the stellar radius as free parameters to optical observations from the OGLE-III survey and infrared observations from the 2MASS and SAGE data sets. The sample of Cepheids have predicted minimum mass-loss rates ranging from zero to $10^{-8}M_\odot$ $yr^{-1}$, where the rates depend on the chosen dust properties. We use the predicted radii to compute the Period-Radius relation for LMC Cepheids, and to estimate the uncertainty caused by the presence of infrared excess for determining angular diameters with the infrared surface brightness technique. Finally, we calculate the linear and non-linear Period-Luminosity (P-L) relations for the LMC Cepheids at VIJHK + IRAC wavelengths and we find that the P-L relations are consistent with being non-linear at infrared wavelengths, contrary to previous results.

Characteristics of the Galaxy according to Cepheids

Classical and Type II Cepheids are used to reinvestigate specific properties of the Galaxy. A new Type II reddening-free Cepheid distance parameterization is formulated from LMC Cepheids (OGLE), with uncertainties typically no larger than 5-15%. A distance to the Galactic centre of R0=7.8+-0.6 kpc is derived from the median distance to Type II Cepheids in the bulge (OGLE), R0=7.7+-0.7 kpc from a distance to the near side of the bulge combined with an estimated bulge radius of 1.3+-0.3 kpc derived from planetary nebulae. The distance of the Sun from the Galactic plane inferred from classical Cepheid variables is Zsun=26+-3 pc, a result dependent on the sample's distance and direction because of the complicating effects of Gould's Belt and warping in the Galactic disk. Classical Cepheids and young open clusters delineate consistent and obvious spiral features, although their characteristics do not match conventional pictures of the Galaxy's spiral pattern. The Sagittarius-Carina arm is confirmed as a major spiral arm that appears to originate from a different Galactic region than suggested previously. Furthermore, a major feature is observed to emanate from Cygnus-Vulpecula and may continue locally near the Sun. Significant concerns related to the effects of metallicity on the VI-based reddening-free Cepheid distance relations used here are allayed by demonstrating that the computed distances to the Galactic centre, and to several globular clusters (M54, NGC 6441, M15, and M5) and galaxies (NGC 5128 and NGC 3198) which likely host Type II Cepheids: agree with literature results to within the uncertainties.

Blazhko Effect in Double Mode Cepheids

Systematic survey for multiperiodicity in the LMC Cepheids (Moskalik, Kolaczkowski & Mizerski 2004, 2006) has led to discovery of several new forms of pulsational behaviour. One of them is periodic amplitude and phase modulation observed in many first/second overtone (FO/SO) double mode Cepheids. In the current paper we present detailed discussion of this newly discovered phenomenon, based on a combined OGLE+MACHO sample of double mode pulsators.

The detailed forms of the LMC Cepheid PL and PLC relations

Possible deviations from linearity of the Large Magellanic Cloud Cepheid period‐luminosity (PL) and period‐luminosity‐colour (PLC) relations are investigated. Two data sets are studied, respectively from the Optical Gravitational Lensing Experiment (OGLE) and MACHO projects. A non-parametric test, based on linear regression residuals, suggests that neither PL relation is linear. If colour dependence is allowed for, then the MACHO PL relation is found to deviate more significantly from the linear, while the OGLE PL relation is consistent with linearity. These findings are confirmed by fitting ‘Generalized Additive Models’ (non-parametric regression functions) to the two data sets. Colour dependence is shown to be non-linear in both data sets, distinctly so in the case of the MACHO Cepheids. It is also shown that there is interaction between the period and the colour functions in the MACHO

Erratum: "Hubble Space TelescopeFine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: Period-Luminosity Relations" ([URL ADDRESS="/cgi-bin/resolve?2007AJ....133.1810B" STATUS="OKAY"]AJ, 133, 1810 [2007][/URL

(abridged) We present new absolute trigonometric parallaxes and relative proper motions for nine Galactic Cepheid variable stars: l Car, zeta Gem, beta Dor, W Sgr, X Sgr, Y Sgr, FF Aql, T Vul, and RT Aur. We obtain these results with astrometric data from Fine Guidance Sensor 1r, a white-light interferometer on Hubble Space Telescope. We find absolute parallaxes with an average sigma_pi/pi = 8%. Two stars (FF Aql and W Sgr) required the inclusion of binary astrometric perturbations, providing Cepheid mass estimates. With these parallaxes we compute absolute magnitudes in V, I, K, and Wesenheit W_{VI} bandpasses corrected for interstellar extinction and Lutz-Kelker-Hanson bias. Adding our previous absolute magnitude determination for delta Cep, we construct Period-Luminosity relations for ten Galactic Cepheids. We compare our new Period-Luminosity relations with those adopted by several recent investigations, including the Freedman and Sandage H_0 projects. Adopting our Period-Luminosity relationship would tend to increase the Sandage H_$ value, but leave the Freedman H_0 unchanged. Comparing our Galactic Cepheid PLR with those derived from LMC Cepheids, we find the slopes for K and W_{VI} identical in the two galaxies within their respective errors. Our data lead to a W_{VI} distance modulus for the Large Magellanic Cloud, m-M = 18.50\pm0.03, uncorrected for any metallicity effects. Applying recently derived metalllcity corrections yields a corrected LMC distance modulus of (m-M)_0=18.40\pm0.05. Comparing our Period-Luminosity relationship to solar-metallicity Cepheids in NGC 4258 results in a distance modulus, 29.28 \pm 0.08, which agrees with that derived from maser studies.