Calibrating the projection factor for Galactic Cepheids

Abstract

Context. The projection factor (p), which converts the radial velocity to pulsational velocity, is an important parameter in the Baade-Wesselink (BW) type analysis and distance scale work. The p-factor is either adopted as a constant or linearly depending on the logarithmic of pulsating periods. Aims. The aim of this work is to calibrate the p-factor if a Cepheid has both the BW distance and an independent distance measurement, and examine the p-factor for δ Cephei -the prototype of classical Cepheids. Methods. We calibrated the p-factor for several Galactic Cepheids that have both the latest BW distances and independent distances either from Hipparcos parallaxes or main-sequence fitting distances to Cepheid-hosted stellar clusters. Results. Based on 25 Cepheids, the calibrated p-factor relation is consistent with latest p-factor relation in literature. The calibrated p-factor relation also indicates that this relation may not be linear and may exhibit an intrinsic scatter. We also examined the discrepancy of empirical p-factors for δ Cephei, and found that the reasons for this discrepancy include the disagreement of angular diameters, the treatment of radial velocity data, and the phase interval adopted during the fitting procedure. Finally, we investigated the impact of the input p-factor in two BW methodologies for δ Cephei, and found that different p-factors can be adopted in these BW methodologies and yet result in the same angular diameters.

Wesenheit function for Galactic Cepheids: Application to the projection factors

“…The p factor given in Storm et al (2011), or that calibrated here, does not agree with the empirical determination by Mérand et al (2005). Ngeow et al (2012) further investigated this problem and found that the derived angular diameters using the infrared surface-brightness (IRSB) method of Storm et al (2011) and the angular diameters empirically determined using interferometric techniques (Mérand et al 2005) do not agree (see fig. 4 in Ngeow et al 2012) angular diameters are proportional to the p factor, as shown by Eq.…”

“…The curves are constructed using Eq. (2.1) by simultaneously fitting the angular diameters and p factor (for more details, see Ngeow et al 2012). The fitted p factor is given in upper left-hand corner; it is still not consistent with the value by Mérand et al (2005), who determined p = 1.27. methods (such as Hipparcos parallaxes, BW-based distances, and distances from MS fitting), and can potentially be verified using Gaia's parallaxes in the near future.…”

“…Ngeow et al (2012) further investigated this problem and found that the derived angular diameters using the infrared surface-brightness (IRSB) method of Storm et al (2011) and the angular diameters empirically determined using interferometric techniques (Mérand et al 2005) do not agree (see fig. 4 in Ngeow et al 2012) angular diameters are proportional to the p factor, as shown by Eq. (2.1)-at the same distance and using the same radial velocity curve-disagreement of angular diameters naturally leads to a corresponding disagreement in the p factors.…”

“…(2.1)-at the same distance and using the same radial velocity curve-disagreement of angular diameters naturally leads to a corresponding disagreement in the p factors. Ngeow et al (2012) postulate two possibilities to explain the disagreement in angular diameters:…”

“…In addition, the metallicity dependence of the PL relation is still being debated. An alternative option is to use the Wesenheit function to derive distances to Galactic Cepheids (Opolski 1983;Ngeow 2012), when other independent methods cannot be applied.…”