## Appendix B: Spectral synthesis examples for sulfur

Figure B.1 shows the comparison between observed spectra and the best-fit synthetic models for a sample of four stars, acquired with different spectrographs, in the sulfur line region at 6757 Å. Specifically, the HARPS spectrum (R~115 000) is for the star $\zeta$ Gem (T$_{eff}$ = 5617 K, log g = 1.2 dex, [Fe/H] = 0.02 dex, $v_t$ = 3.4 km s$^{-1}$, A(S) = 7.13 ± 0.03 dex); the FEROS spectrum (R~48 000) is for T Vel (T$_{eff}$ = 5721 K, log g = 1.6 dex, [Fe/H] = -0.06 dex, $v_t$ = 3.3 km s$^{-1}$, A(S) = 7.02 ± 0.05 dex); the UVES spectrum (R~40 000) is for XX Sgr (T$_{eff}$ = 6259 K, log g = 1.3 dex, [Fe/H] = -0.06 dex, $v_t$ = 2.9 km s$^{-1}$, A(S) = 7.05 ± 0.05 dex); and the STELLA spectrum (R~55 000) is for the star VZ Cyg (T$_{eff}$ = 6169 K, log g = 1.3 dex, [Fe/H] = -0.02 dex, $v_t$ = 2.9 km s$^{-1}$, A(S) = 7.03 ± 0.04 dex).

<figure><img src="image_13.png" /></figure>

**Fig. B.1.** Examples of spectral synthesis for the S I line at 6757 Å. The observed (HARPS, FEROS, UVES, and STELLA) and best-fit synthetic spectra are plotted as black points and magenta solid lines, respectively. The line of interest is marked as the green area.

<figure><img src="image_14.png" /></figure>

**Fig. C.1.** Comparison with literature of the atmospheric parameters and abundances estimated in the current work. The panels show the differences as a function of the effective temperature for stars in common in the current study (TS) and data from Luck et al. (2011, L11) and Trentin et al. (2023, T23).

## Appendix C: Comparison with stars in common

Figure C.1 shows a comparison of the atmospheric parameters and the O and S abundances for Cepheids in common in our sample and the literature (Luck et al. 2011; Trentin et al. 2023). The differences are close to zero within the errors for most of the comparisons. The surface gravity and the microturbulent velocity are systematically higher in Luck et al. (2011), which might be due to differences in the line lists used. Sulfur abundances are systematically overabundant in both literature works compared to our estimates. Again, the line list differences likely play an important role. Our measurements are based on one single line of sulfur, whereas those authors used additional S lines in their estimates.
## Appendix B: Spectral synthesis examples for sulfur

Figure B.1 shows the comparison between observed spectra and the best-fit synthetic models for a sample of four stars, acquired with different spectrographs, in the sulfur line region at 6757 Å. Specifically, the HARPS spectrum (R~115 000) is for the star $\zeta$ Gem ($T_{\text{eff}}$ = 5617 K, $\log g$ = 1.2 dex, [Fe/H] = 0.02 dex, $v_t$ = 3.4 km s$^{-1}$, A(S) = 7.13 ± 0.03 dex); the FEROS spectrum (R~48 000) is for T Vel ($T_{\text{eff}}$ = 5721 K, $\log g$ = 1.6 dex, [Fe/H] = -0.06 dex, $v_t$ = 3.3 km s$^{-1}$, A(S) = 7.02 ± 0.05 dex); the UVES spectrum (R~40 000) is for XX Sgr ($T_{\text{eff}}$ = 6259 K, $\log g$ = 1.3 dex, [Fe/H] = -0.06 dex, $v_t$ = 2.9 km s$^{-1}$, A(S) = 7.05 ± 0.05 dex); and the STELLA spectrum (R~55 000) is for the star VZ Cyg ($T_{\text{eff}}$ = 6169 K, $\log g$ = 1.3 dex, [Fe/H] = -0.02 dex, $v_t$ = 2.9 km s$^{-1}$, A(S) = 7.03 ± 0.04 dex).

<figure><img src="image_12.png" /><figcaption>**Fig. B.1.** Examples of spectral synthesis for the S I line at 6757 Å. The observed (HARPS, FEROS, UVES, and STELLA) and best-fit synthetic spectra are plotted as black points and magenta solid lines, respectively. The line of interest is marked as the green area.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. C.1.** Comparison with literature of the atmospheric parameters and abundances estimated in the current work. The panels show the differences as a function of the effective temperature for stars in common in the current study (TS) and data from Luck et al. (2011, L11) and Trentin et al. (2023, T23).</figcaption></figure>

## Appendix C: Comparison with stars in common

Figure C.1 shows a comparison of the atmospheric parameters and the O and S abundances for Cepheids in common in our sample and the literature (Luck et al. 2011; Trentin et al. 2023). The differences are close to zero within the errors for most of the comparisons. The surface gravity and the microturbulent velocity are systematically higher in Luck et al. (2011), which might be due to differences in the line lists used. Sulfur abundances are systematically overabundant in both literature works compared to our estimates. Again, the line list differences likely play an important role. Our measurements are based on one single line of sulfur, whereas those authors used additional S lines in their estimates.
## Appendix D: Abundances in the pulsation cycle

Figure D.1 shows the O and S abundances plotted as a function of the pulsation phase for the 20 calibrating CCs provided by da Silva et al. (2022). This is a selection of Cepheids from our sample for which high-resolution spectra cover either the entire cycle or a significant portion of the pulsation cycle.

The phases ($\phi$) in the pulsation cycle were calculated by using the following equation and the ephemerides that we previously published in da Silva et al. (2022):

$$ \phi = \begin{cases} x - \text{int}(x) - 1 & \text{if } x - \text{int}(x) > 0 \\ x - \text{int}(x) + 1 & \text{if } x - \text{int}(x) < 0 \\ x - \text{int}(x) & \text{otherwise} \end{cases} $$

$$ x = \frac{\text{MJD} - (T_0 - 2400\,000) + 0.5}{P}, \qquad (\text{D.1}) $$

where MJD is the modified Julian date from their Table 4, while $T_0$ (as defined in that paper) and the pulsation period ($P$) are from their Table 5. For Cepheids for which more than one value of $T_0$ was available, we adopted the first one (ephemeris source = 0). We note that a shift was applied to the phases of VY Sgr (-0.05), RZ Vel (+0.03), and WZ Sgr (-0.03) for the reasons mentioned in the notes to Table 5. Finally, we mention that the oxygen abundance for the variable Y Oph was not included in our current study. Although the S/N of the spectra available for this variable is quite high (from ~70 to more than 180), there are several emission features close to the oxygen line at 6300.3 Å. This means that the position of the continuum could not be assessed accurately. This oxygen line is relatively weak, which makes the abundance measurements very sensible to the continuum definition. The observed features might be related to airglow emission lines (see Noll et al. 2012), which may affect some of the spectra adopted in our analysis.
## Appendix D: Abundances in the pulsation cycle

Figure D.1 shows the O and S abundances plotted as a function of the pulsation phase for the 20 calibrating CCs provided by da Silva et al. (2022). This is a selection of Cepheids from our sample for which high-resolution spectra cover either the entire cycle or a significant portion of the pulsation cycle.

The phases ($\phi$) in the pulsation cycle were calculated by using the following equation and the ephemerides that we previously published in da Silva et al. (2022):

$$ \phi = \begin{cases} x - \text{int}(x) - 1 & \text{if } x - \text{int}(x) > 0 \\ x - \text{int}(x) + 1 & \text{if } x - \text{int}(x) < 0 \\ x - \text{int}(x) & \text{otherwise} \end{cases} $$

$$ x = \frac{\text{MJD} - (T_0 - 2400000) + 0.5}{P}, \qquad (\text{D.1}) $$

where MJD is the modified Julian date from their Table 4, while $T_0$ (as defined in that paper) and the pulsation period ($P$) are from their Table 5. For Cepheids for which more than one value of $T_0$ was available, we adopted the first one (ephemeris source = 0). We note that a shift was applied to the phases of VY Sgr (-0.05), RZ Vel (+0.03), and WZ Sgr (-0.03) for the reasons mentioned in the notes to Table 5. Finally, we mention that the oxygen abundance for the variable Y Oph was not included in our current study. Although the S/N of the spectra available for this variable is quite high (from ~70 to more than 180), there are several emission features close to the oxygen line at 6300.3 Å. This means that the position of the continuum could not be assessed accurately. This oxygen line is relatively weak, which makes the abundance measurements very sensible to the continuum definition. The observed features might be related to airglow emission lines (see Noll et al. 2012), which may affect some of the spectra adopted in our analysis.
<figure><img src="image_15.png" /><figcaption>**Fig. D.1.** Abundance ratios as a function of the pulsation phase. Measurements from different spectrographs are indicated with different colors and symbols. The error bars are smaller than the symbol size in some cases. The weighted mean (dashed line) and the standard error of the abundances are also shown, together with the pulsation period.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. D.1.** Abundance ratios as a function of the pulsation phase. Measurements from different spectrographs are indicated with different colors and symbols. The error bars are smaller than the symbol size in some cases. The weighted mean (dashed line) and the standard error of the abundances are also shown, together with the pulsation period.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. D.1. continued.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. D.1. continued.</figcaption></figure>