tokens: 0.04 and 0.03 mag for and distance modulus, with metallicities from Rey et al. , and 0.06 and 0.05 mag for the and values derived with the metallicities from Sollima et al. At the same time, results from previous studies (e.g., Cacciari Clementini 2003 ; Del Principe et al. 2006 ; Feast et al. 2008 ; Gran et al. 2015 ) suggest that distances derived on the basis of such relations can probably not yet be considered accurate to better than about mag. Thus, we adopt the latter value as a conservative estimate of the systematic error affecting the distance moduli provided in our study. Fig. 8 Fundamental (in purple circles) and first-overtone (in yellow triangles) SX Phe as classified by Olech et al. (2005) , based on their frequency spectrum. The dotted lines are the PL relations derived previously. As can be seen, there are some claimed first-overtone pulsators that also follow the relations defined by fundamental-mode pulsators. Table 4 Adopted distance moduli based on T2Cs and RRL stars. 4.2. Pulsational distance modulus from T2Cs and RRL stars Table 4 lists the weighted-average distance modulus values from T2Cs and RRL stars and sigma as the dispersion around the mean. The weights for each individual distance modulus values were defined as the inverse of the squared of the total error, including statistical and systematic errors (summed up in quadrature). As expected, the error is lower for the PL relations compared to , since the former have lower intrinsic dispersion, and is based on a more extensive dataset. Comparing both variability types, T2Cs lead to a less accurate distance modulus, probably because they are few in number, which increases the statistical error, and they have higher systematic errors since the effect of metallicity and pulsation mode separation in the derivation of the PL relations is not completely established. Considering the distance modulus values found using T2Cs stars as well as RRL stars, both in and , the weighted-average distance modulus to Cen was determined, leading to a final value of mag, where the error bar corresponds to the standard deviation of the mean. Given the discussion of systematic errors in the previous section, our final adopted distance modulus is mag, where the error bars correspond to the adopted statistic and systematic errors, respectively. Adding the errors in quadrature (as recommended, for instance, by Barlow et al. 2002 ), this corresponds to a heliocentric distance of kpc. Table 5 Distance modulus for Cen from the literature. Notes. (a) Most of the error estimates do not consider the contribution of systematic errors, which in the case of T2Cs and RRL stars can reach values of order 0.10 mag. (b) The listed error was determined considering the internal uncertainties of the mean distance modulus value, 0.02 mag, and the observational error, 0.1 mag, as described by McNamara (2000) . (c) Based on the -[Fe/H] relation from Bono et al. (2003) and mean magnitudes from Kaluzny et al.
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