Observational calibration of the projection factor of Cepheids

Abstract

The projection factor (p-factor) is an essential component of the classical Baade-Wesselink (BW) technique, which is commonly used to determine the distances to pulsating stars. It is a multiplicative parameter used to convert radial velocities into pulsational velocities. As the BW distances are linearly proportional to the p-factor, its accurate calibration for Cepheids is of critical importance for the reliability of their distance scale. We focus on the observational determination of the p-factor of the long-period Cepheid RS Pup (P = 41.5 days). This star is particularly important as this is one of the brightest Cepheids in the Galaxy and an analog of the Cepheids used to determine extragalactic distances. An accurate distance of 1910 ± 80 pc (±4.2%) has recently been determined for RS Pup using the light echoes propagating in its circumstellar nebula. We combine this distance with new VLTI/PIONIER interferometric angular diameters, photometry, and radial velocities to derive the p-factor of RS Pup using the code Spectro-Photo-Interferometry of Pulsating Stars (SPIPS). We obtain p = 1.250 ± 0.064 (±5.1%), defined for cross-correlation radial velocities. Together with measurements from the literature, the p-factor of RS Pup confirms the good agreement of a constant p = 1.293 ± 0.039 (±3.0%) model with the observations. We conclude that the p-factor of Cepheids is constant or mildly variable over a broad range of periods (3.7 to 41.5 days).

Observational calibration of the projection factor of Cepheids

“…Combining with MW results from Kervella et al (2017), Breitfelder et al (2016 and Mérand et al (2015), we confirm a linear relation of the p-factor with the pulsation period, consistent with the last results of Nardetto et al (2009). This relation shows a decreasing p-factor with the period.…”

“…The resulting redundancy in the observables ensures a high level of robustness. We already proved the efficiency of SPIPS for type I and II Galactic Cepheids (Kervella et al 2017;Breitfelder et al 2016Breitfelder et al , 2015.…”

“…But these phases correspond to the minimum of the diameter, so ignoring them probably provides a biased estimate of the projection factor. Breitfelder et al (2016) apply the SPIPS method (with B, V, J, H, and K photometric bands) to the same sample of nine Cepheids and instead found a constant Galactic p-factor, later confirmed by Kervella et al (2017) who found p = 1.29±0.04. However, their sample is smaller (only 11 stars).…”

“…Benedict et al (2007) obtained a set of ten parallax measurements to Galactic Cepheids using the Fine Guidance Sensor of the Hubble Space Telescopes, however, the average precision is ∼ 8 %. These measurements were used in our previous SPIPS analysis (Kervella et al 2017;Breitfelder et al 2016) to determine their p-factor. The accuracy of the first data release of Gaia-TGAS (Lindegren et al 2016) is too low to provide an accurate calibration.…”

The atmosphere, the p-factor and the bright visible circumstellar environment of the prototype of classical Cepheids δ Cep

“…Thus, if the distance is known, the p-factor can be derived. This has been done for several Cepheids already ( [8,9]), but with Gaia parallaxes, it should be possible to derive the projection factor of about 300 Cepheids with a 3% precision. In this context, the p-factor decomposition into three subconcepts proposed by [10] will be useful in order to interpret the Gaia p-factors (Sect.…”