The PROFUSE estimator and its application to the ALHAMBRA B-band LF is presented on López-Sanjuan et al. 2016.

The rest-frame B-band is well covered by extragalactic optical surveys, allowing the study of non-extrapolated luminosities up to z ~ 1 (see Beare et al. 2015 for a recent compilation of B-band luminosity functions).

We compute the posterior luminosity function in ALHAMBRA using the redshift - spectral template and the I-band magnitude posteriors. We first derive the z - M_B posterior of each ALHAMBRA source (see an example in Fig. 1), and combine them to estimate the ALHAMBRA LF of both quiescent and star-forming galaxies at 0.2 < z < 1.0. We compute the LF for three different photometric redshift priors (BPZ, constant, and cosmic volume) and redshift bin sizes (Δz = 0.05, 0.1, and 0.2). These derived LFs and their full covariance matrices are accessible here.

Figure 1 – Posterior probability in the z – M_B space of an ALHAMBRA galaxy. The red solid line shows the I₀ = 24 limiting magnitude, and the grey area marks the accessible volume in z - M_B space.

We present the ALHAMBRA luminosity functions, both for star-forming and quiescent galaxies, and our median models in Fig. 2. We modelled the observed LFs with redshift-dependent Schechter functions, one for star-forming galaxies and two for quiescent galaxies. The redshift-magnitude-galaxy type covariance matrices, including shot noise and cosmic variance, were used in the modelling.

Figure 2 – Top panels: Posterior luminosity function of star-forming (left) and quiescent (right) galaxies in ALHAMBRA. Bottom panels : Median luminosity function model for star-forming (left) and quiescent (right) galaxies. These luminosity functions are complete for I₀ < 24 galaxies.

The comparison with previous work is presented in Figs. 3 and 4. The ALHAMBRA LFs nicely agree with the literature. We find a significant population of faint quiescent galaxies with M_B > -18, modelled by a second Schechter function.

Figure 3 – ALHAMBRA luminosity function of star-forming galaxies in four redshift bins (labelled in the panels). The blue squares are the observed luminosity functions and the blue solid lines the median model. Other lines and symbols are from the literature.

Figure 4 – ALHAMBRA luminosity function of quiescent galaxies in four redshift bins (labelled in the panels). The red dots are the observed luminosity functions and the red lines the median model. Other lines and symbols are from the literature.

Finally, the redshift evolution of the Schechter function parameters and the derived luminosity density are also satisfactory, as shown in Figs. 5 and 6. The measured faint-end slopes are α_SF = -1.29 ± 0.02 and α_Q = -0.53 ± 0.04. The faint quiescent population has a characteristic magnitude M_f = -17.00 ± 0.09, slope β = -1.31 ± 0.11, and the same Φ^* evolution than the bright population. The luminosity density of star-forming galaxies decreases by a factor 2.55 ± 0.14 since z = 1 to the present, and the luminosity density of quiescent galaxies increases by a factor 1.25 ± 0.16 in the same time lapse.

Figure 5 – Redshift evolution for star-forming galaxies of M_B^* ∝ Q_SF z (top left panel), Φ^* ∝ 10^{{P_SF z}} (top right panel), and the B-band luminosity density j_B (bottom left panel). In all panels the blue dashed line show the median model from ALHAMBRA data, with the coloured areas enclosing 95% of the solutions. The median of the parameters with their associated 68% (1σ) probability intervals are labelled in the panels. The other symbols, labelled in the bottom right panel, are from the literature. Their error bars mark 2σ confidence intervals.

Figure 6 – The same as previous figure, but for quiescent galaxies. In all panels the red dashed line show the median model from ALHAMBRA data, with the coloured areas enclosing 95% of the solutions. The red dotted line in the bottom left panel shows the median model for the bright Schechter component alone.

In addition to the B-band luminosity function, we also measured the galaxy bias function both for star-forming and quiescent galaxies. The results are summarised here.