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As there is a strong degeneracy between luminosity and density it is difficult to disentangle the effects of luminosity and density evolution (Loveday et al. 2012). A luminosity density (LD) estimate is often reported instead (e.g. Blanton et al. 2003c; Montero-Dorta & Prada 2009; Loveday et al. 2012) as that can be better constrained. The LD evolution observed in the GAMA Hα star forming population is shown in Figure 3.17. The filled diamonds

FIGURE 3.17: The evolution of LDs of all and photometrically classified blue and red Hα star forming galaxies as a

function of redshift (filled symbols), compared to the evolution of luminosity density of all, blue and red GAMA galaxies as a function of redshift (shaded regions; Loveday et al. 2012). Also shown are the LD measurements at low–z from Blanton et al. (2003c) (open circle) and Montero-Dorta & Prada (2009) (open triangle). The GAMA measurements shown by the filled diamonds indicate the LDs derived by integrating the best–fitting Schechter functional forms shown in Figure 3.11, and the filled stars indicate the values obtained from integrating the best–fitting bivariate analytical forms shown in Figures 3.15 and 3.16. The three colours, black, blue and red, indicate all and photometrically classified blue and red galaxies respectively. All published measurements are converted to our assumed cosmology.

indicate the GAMA LDs derived from integrating the four Schechter functions shown in Figure 3.11. The densities indicated by filled stars are estimated from the best–fitting bivariate LHα–Mr functions shown in Figure 3.16.

Only the integrated value for0.1 < z < 0.15 is shown as the bivariate functional fitting for the higher–z LFs cannot be constrained accurately due to the narrow range in LHα and Mrprobed. Also shown are the confidence

limits from Figure 20 of Loveday et al. (2012) and low redshift density estimates from Blanton et al. (2003c) and Montero-Dorta & Prada (2009). We see a result here that is consistent with the SF proportions of the broadband blue and red LFs shown in Figure 3.10. LDs estimated from the best–fitting Schechter functional forms indicate a decrease in LD with redshift, in contrast to Loveday et al. (2012). This is a natural consequence of the SF populations comprising only a small fraction (10–20%) of the total red galaxy population. The decrease in LD of photometrically classified blue SF population at higher–z (z > 0.17) is likely due to the difficulty in measuring Hα in higher–z galaxy spectra, which are likely dustier than their low–z counterparts. Given our sample is already biased against photometrically classified red galaxies, mainly as a result of the Hα flux limit, the drop in LD corresponding to those galaxies is not unexpected.

Figure 3.18 shows the SFRD versus Mr relationship with redshift for the two lowest redshift ranges, obtained by

integrating the analytical bivariate function fit shown in Figures 3.15 and 3.16. Significant evolution in SFRD can be seen for both optically faint and bright galaxies, while for those just faintward of M∗there is little change. The evolution in the SFRD at the optically bright end is directly supported by the evolution seen in the measured BLF (Figure 3.7). The implied evolution at faint optical magnitudes seen here, however, is a direct result of fixing the

88 BIVARIATE DISTRIBUTION FUNCTIONS OFHαSTAR FORMING GALAXIES

FIGURE3.18: The SFR density as a function of Mrfor thez < 0.1 and 0.1 < z < 0.15 ranges. The solid lines indicate

M∗values for the two redshift ranges.

TABLE3.5: The SFRDs (Schechter–Saunders function).

Redshift log ˙ρ(0,0)−(Lb,Mb) log ˙ρ(Lf,z1,Mf,z1)−(Lb,Mb) log ˙ρ(Lf,zx,Mf,zx)−(Lb,Mb))

range (M_yr−1Mpc−3) (M_yr−1Mpc−3) (M_yr−1Mpc−3)

0.1 < z < 0.15 −2.00 −2.00 −2.03 (-14.25, 33.1)

0.17 < z < 0.24 −1.75 −1.77 −2.03 (-18.75, 33.5)

0.24 < z < 0.34 −1.72 −1.77 −2.14 (-19.25, 33.9)

shape of the faint end of the bivariate LF, combined with the increase inΨ∗ as fit to the 0.1 < z < 0.15 bivariate LF. Without more direct measurement of the faint end shape of the BLF at these redshifts, we can’t make any strong claims about evolution in the SFRD at such faint optical magnitudes.

As mentioned previously, our primary motivation behind modelling the bivariate LHα–MrLFs is to overcome the

bivariate sample effects introduced by the dual Hα flux and magnitude selection imposed on our sample. As a result of this effect, the SFRDs presented in paper I are underestimates. In Figure 3.19 we reproduce Figure 15 of paper I to show the SFRDs derived not by integrating the Saunders functional fit to a univariate Hα LF but by integrating the bivariate analytic fit to LHα–MrLF. By modelling the low–redshift LHα–Mrdistribution covering

−24 <Mr < −10 and 30 <log LHα < 36 and assuming the faint–end bivariate distribution is similar for the

higher–z samples (Figures 3.15 and 3.16), we can estimate a correction for the missing optically faint star forming galaxies. The resultant SFRDs are shown in Figure 3.19, and given in Table 3.5. It can be seen that the resulting SFRD is much more consistent with that from other published measurements (e.g. Hopkins & Beacom 2006), than the direct estimates from paper I. This implies that our assumptions regarding the faint end slope of the bivariate LF are not unreasonable, and can be used as a reliable model for the shape and normalisation of the bivariate LHα–

Mr LF. Even so, the highest redshift range probed still appears to be somewhat underestimated. This suggests

that there may well be some non–negligible evolution in the faint–end shape of the bivariate LF over this redshift range.

FIGURE3.19: The cosmic SF history, reproduced from Figure 15 of paper I, with our new measurements shown as blue

stars. The GAMA SFR densities are based on integrating the analytic fits to the bivariate LHα–MrLFs (Figures 3.15 and

3.16). Published estimates based on narrowband/slitless spectroscopy data are shown as open symbols and those based on broadband surveys as filled symbols. Different colours correspond to different SFR indicators.