No Arabic abstract
In a previous paper (Maoz et al. 1999), we reported a Hubble Space Telescope (HST) Cepheid distance to the galaxy NGC 4258 obtained using the calibrations and methods then standard for the Key Project on the Extragalactic Distance Scale. Here, we reevaluate the Cepheid distance using the revised Key Project procedures described in Freedman et al. (2001). These revisions alter the zero points and slopes of the Cepheid Period-Luminosity (P-L) relations derived at the Large Magellanic Cloud (LMC), the calibration of the HST WFPC2 camera, and the treatment of metallicity differences. We also provide herein full information on the Cepheids described in Maoz et al. 1999. Using the refined Key Project techniques and calibrations, we determine the distance modulus of NGC 4258 to be 29.47 +/- 0.09 mag (unique to this determination) +/- 0.15 mag (systematic uncertainties in Key Project distances), corresponding to a metric distance of 7.8 +/- 0.3 +/- 0.5 Mpc and 1.2 sigma from the maser distance of 7.2 +/- 0.5 Mpc. We also test the alternative Cepheid P-L relations of Feast (1999), which yield more discrepant results. Additionally, we place weak limits upon the distance to the LMC and upon the effect of metallicity in Cepheid distance determinations.
Distances measured using Cepheid variable stars have been essential for establishing the cosmological distance scale and the value of the Hubble constant. These stars have remained the primary extragalactic distance indicator since 1929 because of the small observed scatter in the relationship between their pulsation period and luminosity, their large numbers, which allow many independent measures of the distance to a galaxy, and the simplicity of the basic physics underlying their variability. Potential systematic uncertainties in the use of the LMC-calibrated Cepheid period-luminosity relation to determine distances using HST are estimated to be 8-10%. Here we describe the results of a search for Cepheids in the nearby galaxy NGC 4258, which has an independently determined geometric distance of 7.2 +/- 0.5 Mpc (Herrnstein et al. 1999). We obtain a Cepheid distance of 8.1 +/- 0.4 (excluding possible systematic errors affecting all HST Cepheid distances) Mpc; there is a 1.3 sigma difference between the two measurements. If the maser-based distance is adopted and other HST Cepheid distances are revised according to our results, the derived value of the Hubble constant would be increased by 12 +/- 9%, and the corresponding age of the Universe would decrease by the same factor.
In a recent paper describing HST observations of Cepheids in the spiral galaxy NGC 4258, Newman et al. (2001) report that the revised calibrations and methods for the Key Project on the Extragalactic Distance Scale yield that the true distance modulus of this galaxy is 29.40+-0.09 mag, corresponding to a metric distance of 7.6+-0.3 Mpc. This Cepheid distance, which holds for 18.50 mag as the true distance modulus of the LMC, is not significantly larger than 7.2+-0.5 Mpc, the value determined by Herrnstein et al. (1999) from purely geometric considerations on the orbital motions of water maser sources. However, if the metallicity difference D[O/H]~0.35 between NGC 4258 and LMC is taken into account, then the Key Project methods lead to a metallicity-corrected value of 29.47+-0.09 mag, with 18.50 mag for the LMC, namely to a Cepheid distance of 7.8+-0.3 Mpc, which is 1.2 sigma from the maser determination. In this paper we show that the metallicity correction on Cepheid distance determinations, as suggested by pulsation models, might provide the natural way of reaching a close agreement between Cepheid and maser distance to NGC 4258 for a wide variety of LMC distance determinations.
The fortuitous occurrence of a type II-Plateau (IIP) supernova, SN 2014bc, in a galaxy for which distance estimates from a number of primary distance indicators are available provides a means with which to cross-calibrate the standardised candle method (SCM) for type IIP SNe. By applying calibrations from the literature we find distance estimates in line with the most precise measurement to NGC 4258 based on the Keplerian motion of masers (7.6$pm$0.23,Mpc), albeit with significant scatter. We provide an alternative local SCM calibration by only considering type IIP SNe that have occurred in galaxies for which a Cepheid distance estimate is available. We find a considerable reduction in scatter ($sigma_I = 0.16$, mag.), but note that the current sample size is limited. Applying this calibration, we estimate a distance to NGC 4258 of $7.08pm0.86$ Mpc.
We develop and describe a Bayesian statistical analysis to solve the surface brightness equations for Cepheid distances and stellar properties. Our analysis provides a mathematically rigorous and objective solution to the problem, including immunity from Lutz-Kelker bias. We discuss the choice of priors, show the construction of the likelihood distribution, and give sampling algorithms in a Markov Chain Monte Carlo approach for efficiently and completely sampling the posterior probability distribution. Our analysis averages over the probabilities associated with several models rather than attempting to pick the `best model from several possible models. Using a sample of thirteen Cepheids we demonstrate the method. We discuss diagnostics of the analysis and the effects of the astrophysical choices going into the model. We show that we can objectively model the order of Fourier polynomial fits to the light and velocity data. By comparison with theoretical models of Bono et al. (2001) we find that EU Tau and SZ Tau are overtone pulsators, most likely without convective overshoot. The period-radius and period-luminosity relations we obtain are shown to be compatible with those in the recent literature.
The distance to NGC 7331 has been derived from Cepheid variables observed with HST/WFPC2, as part of the Extragalactic Distance Scale Key Project. Multi-epoch exposures in F555W (V) and F814W (I), with photometry derived independently from DoPHOT and DAOPHOT/ALLFRAME programs, were used to detect a total of 13 reliable Cepheids, with periods between 11 and 42 days. The relative distance moduli between NGC 7331 and the LMC, imply an extinction to NGC 7331 of A_V = 0.47+-0.15 mag, and an extinction-corrected distance modulus to NGC 7331 of 30.89+-0.14(random) mag, equivalent to a distance of 15.1 Mpc. There are additional systematic uncertainties in the distance modulus of +-0.12 mag due to the calibration of the Cepheid Period-Luminosity relation, and a systematic offset of +0.05+-0.04 mag if we applied the metallicity correction inferred from the M101 results of Kennicutt et al 1998.