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We focus on empirically measure the p-factor of a homogeneous sample of 29 LMC and 10 SMC Cepheids for which an accurate average LMC/SMC distance were estimated from eclipsing binary systems. We used the SPIPS algorithm, which is an implementation of the BW method. As opposed to other conventional use, SPIPS combines all observables, i.e. radial velocities, multi-band photometry and interferometry into a consistent physical modeling to estimate the parameters of the stars. The large number and their redundancy insure its robustness and improves the statistical precision. We successfully estimated the p-factor of several MC Cepheids. Combined with our previous Galactic results, we find the following P-p relation: -0.08(log P-1.18)+1.24. We find no evidence of a metallicity dependent p-factor. We also derive a new calibration of the P-R relation, logR=0.684(log P-0.517)+1.489, with an intrinsic dispersion of 0.020. We detect an IR excess for all stars at 3.6 and 4.5um, which might be the signature of circumstellar dust. We measure a mean offset of $Delta m_{3.6}=0.057$mag and $Delta m_{4.5}=0.065$mag. We provide a new P-p relation based on a multi-wavelengths fit, and can be used for the distance scale calibration from the BW method. The dispersion is due to the MCs width we took into account because individual Cepheids distances are unknown. The new P-R relation has a small intrinsic dispersion, i.e. 4.5% in radius. Such precision will allow us to accurately apply the BW method to nearby galaxies. Finally, the IR excesses we detect raise again the issue on using mid-IR wavelengths to derive P-L relation and calibrate the $H_0$. These IR excesses might be the signature of circumstellar dust, and are never taken into account when applying the BW method at those wavelengths. Our measured offsets may give an average bias of 2.8% on the distances derived through mid-IR P-L relations.
The projection factor (p-factor) is an essential component of the classical Baade-Wesselink (BW) technique, that is commonly used to determine the distances to pulsating stars. It is a multiplicative parameter used to convert radial velocities into p
The distance to pulsating stars is classically estimated using the parallax-of-pulsation (PoP) method, which combines spectroscopic radial velocity measurements and angular diameter estimates to derive the distance of the star. An important applicati
The distances of pulsating stars, in particular Cepheids, are commonly measured using the parallax of pulsation technique. The differe
The projection factor p is the key quantity used in the Baade-Wesselink (BW) method for distance determination; it converts radial velocities into pulsation velocities. Several methods are used to determine p, such as geometrical and hydrodynamical m
Classical Cepheids (DCEPs) are the most important primary indicators for the extragalactic distance scale. Establishing the dependence on metallicity of their period--luminosity and period--Wesenheit (PL/PW) relations has deep consequences on the est