Table 5: Derived projections factors for all stars computed from the decomposition presented in Eq. (2).
Name HD Pb $p_{{\rm o}}^{c}$ $f_{\rm grad}^{d}$ $f_{{\rm o-g}}^{e}$ pf
    [days]        
R TrA 135592 3.38925 $1.396_{\pm 0.010}$ $0.995_{\pm 0.009}$ $0.967_{\pm 0.005}$ $1.34_{\pm 0.03}$
S Cru 112044 4.68976 $1.392_{\pm 0.010}$ $0.996_{\pm 0.007}$ $0.966_{\pm 0.005}$ $1.34_{\pm 0.03}$
Y Sgr 168608 5.77338 $1.387_{\pm 0.010}$ $0.991_{\pm 0.005}$ $0.962_{\pm 0.005}$ $1.32_{\pm 0.02}$
$\beta$ Dor 37350 9.84262 $1.380_{\pm 0.010}$ $0.997_{\pm 0.004}$ $0.955_{\pm 0.005}$ $1.31_{\pm 0.02}$
$\zeta$ Gem 52973 10.14960 $1.380_{\pm 0.010}$ $0.994_{\pm 0.005}$ $0.953_{\pm 0.005}$ $1.31_{\pm 0.02}$
RZ Vel 73502 20.40020 $1.375_{\pm 0.010}$ $0.994_{\pm 0.004}$ $0.951_{\pm 0.005}$ $1.30_{\pm 0.02}$
$\ell $ Car 84810 35.55134 $1.366_{\pm 0.010}$ $0.989_{\pm 0.005}$ $0.944_{\pm 0.005}$ $1.27_{\pm 0.02}$
RS Pup 68860 41.51500 $1.360_{\pm 0.010}$ $0.995_{\pm 0.005}$ $0.943_{\pm 0.005}$ $1.28_{\pm 0.02}$
$\delta~Cep ^{a}$ 213306 5.419 $1.390_{\pm 0.010}$ $0.990_{\pm 0.005} $ $0.963_{\pm 0.005}$ $1.33_{\pm 0.02}$
$\ell~Car ^{a}$ 84810 35.60 $1.366_{\pm 0.010}$ $0.988_{\pm 0.005} $ $0.944_{\pm 0.005}$ $1.27_{\pm 0.02}$
a
$\delta $ Cep and $\ell $ Car are hydrodynamical models.

b
The corresponding Julian dates ( $T_{{\rm o}}$) can be found in Paper II.

c
$p_{{\rm o}}$ is derived from the linear limb-darkening laws of Claret et al. (2000) based on the static models of Kurucz (1992). We then apply a slight correction based on the $\delta $ Cep and $\ell $ Car hydrodynamical models: $p_{\rm o}[{\rm hydro}]=p_{\rm o}[{\rm geo}]-(0.0174 \log P -0.0022)$ to take the dynamical structure of the Cepheid's atmosphere into account.

d
$f_{{\rm grad}}$ is derived directly from observations using Eq (3). It is important to notice that the results indicated here correspond to the Fe I 4896.439 Å line. In the case of a modeled star, it is derived directly from the hydrodynamical model (see Sect. 4.3).

e
$f_{\rm o-g}$ is derived directly from the hydrodynamical models (see Sect. 4.4).

f
p-factors defined by $p=p_{{\rm o}} f_{{\rm grad}} f_{{\rm o-g}}$. $p_{{\rm o}}$ and $f_{\rm o-g}$ are derived from geometrical and hydrodynamical models respectively. $f_{{\rm grad}}$ is derived from observations.


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