Cepheid limb darkening, angular diameter corrections, and projection factor from static spherical model stellar atmospheres

Abstract

Context. One challenge for measuring the Hubble constant using classical Cepheids is the calibration of the Leavitt law or periodluminosity relationship. The Baade-Wesselink method for distance determination to Cepheids relies on the ratio of the measured radial velocity and pulsation velocity, the so-called projection factor and the ability to measure the stellar angular diameters. Aims. We use spherically-symmetric model stellar atmospheres to explore the dependence of the p-factor and angular diameter corrections as a function of pulsation period. Methods. Intensity profiles are computed from a grid of plane-parallel and spherically-symmetric model stellar atmospheres using the SAtlas code. Projection factors and angular diameter corrections are determined from these intensity profiles and compared to previous results. Results. Our predicted geometric period-projection factor relation including previously published state-of-the-art hydrodynamical predictions is not with recent observational constraints. We suggest a number of potential resolutions to this discrepancy. The model atmosphere geometry also affects predictions for angular diameter corrections used to interpret interferometric observations, suggesting corrections used in the past underestimated Cepheid angular diameters by 3-5%. Conclusions. While spherically-symmetric hydrostatic model atmospheres cannot resolve differences between projection factors from theory and observations, they do help constrain underlying physics that must be included, including chromospheres and mass loss. The models also predict more physically-based limb-darkening corrections for interferometric observations.

Cepheid distances from the SpectroPhoto-Interferometry of Pulsating Stars (SPIPS)

“…, where B is the baseline and a = 1/r Ross. We note that our results notably depart from those of Neilson et al (2012) (defined as θ LD by Neilson et al 2012); and 2) our θ UD /θ Ross is a function of angular diameter and baseline. Overall, we found our values of θ UD /θ Ross to be higher than those published in Neilson et al (2012).…”

“…Overall, we found our values of θ UD /θ Ross to be higher than those published in Neilson et al (2012).…”

Calibrating the projection factor for Galactic Cepheids

“…That analysis assumed plane-parallel radiative transfer, but Neilson & Lester (2011) found that for stars with low gravity (log g ∼ 1−3), more realistic spherically symmetric model atmospheres predicted greater variations of limb darkening than those found by Marengo et al (2003). Neilson et al (2012) also showed that angular diameter corrections from plane-parallel model atmosphere lead to an approximately 2% underestimate of the angular diameter, which gives a ∼2% systematic underestimate of the p-factor. It is likely that the interferometric observations predict angular diameters that are smaller than predicted by the IRSB, which measured the angular diameter from the stellar flux and temperature-color relations.…”

“…Nevertheless, confirmation or refutation of nonlinearity of the p-factor relation has to wait for accurate parallax measurements from Gaia mission for Cepheids in S11 sample. Furthermore, based on spherically symmetric atmosphere models, Neilson et al (2012) found that the theoretical Pp relation is also nonlinear. Figure 2 also suggests a possible existence of intrinsic dispersion on the Pp relation, albeit large error bars, which could be caused by systematics in the BW or independent distances, or both.…”

Observational calibration of the projection factor of Cepheids

“…A calibration of the p-factor of the intrinsically brightest Cepheids is therefore highly desirable. Theoretical studies (e.g., Neilson et al 2012) indicate that the pfactor may vary with the period, but the dependence differs between authors (Nardetto et al 2014a;Storm et al 2011;Breitfelder et al 2016).…”