tokens: in the analysis for Figs 8 and 9 where we looked specifically for differences in the PL relations derived from known metal-rich and metal-poor stars. Figure 11. Distance moduli for the 20 RRLs in our DZ sample as a function of [Fe/H] (spectroscopic metallicities from C05 ). The solid grey line is the distance modulus ±2σ (dashed lines) estimated using as a reference the PL relation derived by Neeley et al. ( 2017 ) and only the RRab stars in the D4 sample. Metal-poor sources are magenta squares and metal-rich are green triangles. RRab and RRc stars are encircled by blue squares and red circles, respectively. The RRLs marked with a cross are the rejected stars. The least-squares fit (black line) has been calculated in four different cases: considering the whole sample (case A, top left panel), removing the ‘closest’ star (in terms of distance from us; top right panel, case B), removing the ‘most distant’ star (case C, bottom left panel), and excluding both (case D, bottom right panel). In every case, the slope (d μ /d[Fe/H]) is consistent with zero within 1σ (see the text and Table 8 for details). Table 8. d μ /d[Fe/H] derived from the DZ sample. 5 SUMMARY AND CONCLUSION As part of the SMHASH program, using IRAC- Spitzer data we have determined a new distance modulus of the Sculptor dSph using RRLs located in the inner region of the galaxy. We obtained time-series photometry for 49 RRLs, (36 RRab and 13 RRc) at 3.6 μm. Seven stars were discarded from the initial sample mainly due to photometric contamination effects. Adopting periods from Kaluzny et al. ( 1995 ) and Clementini et al. ( 2005 ), we built light curves for the remaining 42 highest quality stars, delineating their mid-IR pulsation properties. In order to investigate the photometric properties of the sample, and to choose the highest quality subsample of stars, we created four data sets (D1, D2, D3, and D4) by removing various problematical stars (see Section 3 for details). PL relations were derived for each RRab-only and RRab+RRc ( fundamentalized ) data set, and were found to be in reasonable agreement (i.e. within 1σ) with the empirical relations published in Madore et al. ( 2013 ) and Neeley et al. ( 2015 ), as well as the revised relations from Neeley et al. ( 2017 ) and the recent PL relations derived by Muraveva et al. ( 2018b ) (Table 4 ). We adopt for Sculptor the distance modulus derived from the D4 sample, as this has the cleanest RRL selection and the best-fitting slopes are the closest to the published empirical relations that we have considered as a reference in this work. We are aware that mid-IR studies of the RRL PL are increasing (Madore et al. 2013 ; Dambis et al. 2014 ; Klein et al. 2014 ; Neeley et al. 2015 , 2017 ; Muraveva et al. 2018b ), but choose the Madore et al. ( 2013 ), Neeley et al. ( 2015 ), Neeley et al. ( 2017 ), and Muraveva et al. ( 2018b ) PLs as fiducial as they are built using the sample of RRL calibrators whose trigonometric parallaxes were
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