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Appendix A: Derivation of the UV continuum slope from spectra

	Fig. A.1 Comparison between β26, β18, and β26s, for the galaxies whose spectrum covers the wavelength range 1250−2600 Å. See the text for more details about the definitions of β. Blue dashed lines indicate the linear fits to the data.
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In Sect. 5.1 we studied the relation between the UV continuum slope and dust attenuation. In galaxies dominated by a young stellar population, the shape of the UV continuum can be fairly accurately approximated by a power law F_λ ∝ λ^β, where F_λ is the observed flux (erg s^-1 cm^-2 Å^-1) and β is the continuum slope (Calzetti et al. 1994). The wavelength range in which β is defined goes from ~1250 Å to ~2600 Å. In this range, Calzetti et al. (1994) defined ten windows to be used to measure the continuum, chosen to avoid the strongest spectral features. For galaxies at z ≥ 1.6β was derived through an error-weighted OLS (Y | X), by fitting the average fluxes in the ten windows defined by Calzetti et al. (1994), in the log (F_λ) − log (λ) plane. More details about the procedure can be found also in Talia et al. (2012). We define the slope computed using all the ten windows as β₂₆. Since not all spectra cover the entire 1250−2600 Å range, we define also two shorter versions of β: β₁₈, ranging from ~1250 Å to ~1800 Å, and β_26s, ranging from ~1550 Å to ~2600 Å. With respect to the ten original windows, β₁₈ is measured using the 7 bluer windows (1st to 7th), while β_26s is measured using the 6 redder ones (5th to 10th).

In Table A.1 we indicate the number of galaxies for which each version of the slope could be computed, depending on the wavelength range covered by the spectra.

In Fig. A.1 we compare the three definitions of β for the galaxies whose spectrum covers the entire wavelength range 1250−2600 Å. β₁₈ is always redder (more positive) than β₂₆, and the discrepancy increases for increasing value of the slopes (Calzetti 2001).

There is a strong correlation between the two definitions of the slope. In particular, applying an error-weighted linear fit we obtain the following relation (r_xy ~ 0.9): (A.1)On the other hand, β_26s is systematically slightly bluer (more negative) than β₂₆, which is quite intuitive, since β₁₈ and β_26s basically sample the two halves of β₂₆. In this case, a linear fit gives: (A.2)with a slightly larger dispersion than in the previous case and no dependence on β₂₆. The likely explanation of the discrepancy between the three definitions is the presence of a large number of closely spaced Fe absorption lines in the 2300−2800 Å range (Leitherer et al. 1999; Calzetti 2001). For each spectrum in the UV sample the appropriate definition of the slope was computed, depending on the wavelength coverage. Then all the β₁₈ and β_26s values were scaled to β₂₆ using Eqs. (A.1) and (A.2): these homogenised values are the ones that were plotted in Fig. 11 and used to derive the relation given in Sect. 5.1.

As explained in Sect. 5.1, β can be derived also from photometry. In the [OII]-sample the available photometry forced us to adopt a short wavelength baseline and we defined β_phot in the range λ_rest ~ 1500−2600 Å. As we did with the spectroscopic determination of the slope, we used the galaxies in the UV-sample to test the effect of different wavelength baselines also in the computation of the slope from photometry. We found that the values of β_phot derived using, respectively, the total baseline (1250−2600 Å) and a shorter one (1500−2600 Å) are broadly consistent with one another, with the short-based values being on average slightly bluer than the long-based ones, though to a lesser extent than in the case of β_spec. Since the short wavelength baseline is available from photometry for the entire galaxy sample, we used directly the values of β_phot in the range λ_rest ~ 1500−2600 Å to obtain the relations presented in Sects. 5.1 and 5.4, without the need to scale them to the total wavelength baseline.

© ESO, 2015