Volume 579, July 2015
|Number of page(s)||23|
|Published online||19 June 2015|
If the feeding in gas is driven by the growth of the dark matter halos and if the fraction of the infalling gas converted into stars stays constant, we expect that . However, only a fraction of the mass created stays trapped in an old stellar population. Therefore, is different from the sSFR defined as with R the return fraction depending on the age of the stellar populations (Renzini & Buzzoni 1986).
Assuming a constant R value, we expect sSFR′ = sMIRDM/ (1−R). For the Chabrier (2003) IMF, the maximum value of R is 0.5. Therefore, we use this value to define the upper bound of the green area in Figs. 12 and 13.
However, R depends on time. The value of the stellar mass lost by a given galaxy depends on its SFH. In order to determine the mass lost along the galaxy history, for each galaxy in our sample we measure the difference between the total mass obtained by integrating the SFH (without taking into account the stellar mass loss) and the stellar mass. Then, we measure the median of these differences as a function of redshift. Figure A.1 shows the median stellar mass effectively lost as a function of redshift Rmed(z). The lower bound of the green shaded area in Figs. 12 and 13 corresponds to sMIRDM/ (1−Rmed(z)) measured for low-mass galaxies. We check that the averaged stellar mass effectively lost in the higher mass bin would be within our two boundaries.
Open triangles and open circles represent the median (1−R) obtained for a low-mass galaxy sample (9.5 < log (M⋆) < 10) and high-mass sample (11 < log (M⋆) < 11.5), respectively. The green curves correspond to the mass loss parametrized by Conroy & Wechsler (2009) assuming the same redshift of formation z = 10 for all the stars. The black line is the parametrization that we adopt as a lower limit for the return fraction.
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We note that the evolution of is flatter than sMIRDM/ 2 (i.e., taking R as a constant), since Rmed(z) is smaller at high redshift than at low redshift (stellar populations are younger).
In this appendix, we investigate wether the criterion used to select star-forming galaxies could artificially create a broadening of the sSFR function with the mass.
We first check that the intrinsic evolution of the sSFR does not enlarge our estimate of σ significantly (e.g., Speagle et al. 2014). Using a simple model with sSFR ∝ (1 + z)3.8 (our extreme value of b), we find that the broadening cannot be overestimated by more than 0.02 dex in our redshift bins owing to the sSFR intrinsic evolution.
Since the rest-frame colors are closely correlated with the sSFR, one could artificially modify the shape of the sSFR function depending on the rest-frame color cut used to separate quiescent and star-forming galaxies. In particular, it is unclear if the population that is transitioning from the star-forming to the quiescent population should be included in the analysis, and how it affects the sSFR function. As shown in Fig. B.1, the most massive galaxies tend to lie much closer to the transitioning area than the other star-forming galaxies. This result is not surprising since Peng et al. (2010) show that the probability of a star-forming galaxy being quenched is proportional to its SFR and mass (their Eq. (17)). In order to investigate the impact of the selection criterion, we move down and up the selection criterion by 0.3 mag which are the extreme values we could adopt (dotted lines in Fig. B.1). We find that this change has no impact on the sSFR functions of galaxies less massive than M⋆ < 1011 M⊙ and the value of σ remains above 0.4 dex at M⋆ > 1011 M⊙. While the measurements are slightly modified for the most massive galaxies, the overall shape of the sSFR functions is not affected. Therefore, our conclusions are not sensitive to the adopted limit used to select star-forming galaxies.
We also investigate if the uncertainties associated with the stellar mass could artificially create such broadening of the sSFR function. Indeed, uncertainties in the stellar mass could move the galaxies from one mass bin to another. Since the sSFR depends on the mass, it could artificially broaden the sSFR distribution. The galaxies at M⋆ < 1011 M⊙ could contaminate the most massive galaxies and artificially add galaxies with a larger sSFR since the sSFR decreases with the stellar mass. In order to test this effect, we use the semi-analytical model described in Sect. 7. We add random errors using a Gaussian distribution having a standard deviation of 0.1 dex (already larger than our expected uncertainties) to the predicted SFR and to the predicted mass. We find that the sSFR functions predicted by the model are almost unmodified. If we adopt uncertainties of 0.2 dex in mass and in SFR, we get unrealistic predictions at all masses. We note that systematic uncertainties are not discussed here since they shift the full distribution.
Same as Fig. 2, except that the red circles are the massive 24 μm sources (11 < log (M⋆) < 11.5) and the size of the sources is proportional to the 24 μm flux. The contours refer to the full galaxy sample at log (M⋆) > 9.5. The largest fraction of massive galaxies are well below the selection criterion and the brightest ones are located in top right part of the diagram with the most extinguished sources.
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© ESO, 2015
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