Fig 4.14 shows the BBDs summed to produce luminosity functions (LFs). There is good agreement between the four MGC luminosity functions for M < —17.5. Beyond that, the volume over which galaxies can be seen becomes tiny, see Figs 4.2 & 4.5. The dotted lines show the Schechter function fits to the data. While the bright end is well determined, there
is a large variation in the faint end slope (—0.770 > ck> —1.00). The dashed line shows the
Nor berg et al. (2002) line calculated using Einstein-de Sitter cosmology. The bright end is slightly fainter 0.075 ± 0.025 mag, and the faint end slope is much steeper. From Fig 2.15 we would expect the bright end to be slightly fainter, and there to be a slight steepening of the faint end slope, if the 2dF magnitudes used by Norberg are not as close to total magnitudes as
the MGC magnitudes. Since the 2dFGRS uses Gaussian corrected magnitudes that are then calibrated to deeper CCD photometry, we expect that the offsets for corrected magnitudes at
Tlim ~ 26.0mag arcsec~^ in Table 2.3 will match the difference between our results and the Norberg results. Thus we predict a decrease in M* of 0.06 mag and a decrease in (j)* of 5.5% and no significant change in a. However, since the Norberg et al. (2002) LF is normalised to the number counts, their value of is reliable. This accounts for the small error in M*.
In Norberg et al. (2002), the luminosity function is shallower in the Northern Galactic Pole (NGP) region than the Southern Galactic Pole (SGP) region. For the A-CDM case the NGP has a faint end slope gradient a = —1.14 and the SGP has a — —1.28 (Norberg, private communication). Since there is little variation between the values of a in the different
Chapter 4: The MGC/2dFGRS/SDSS EDR BED. 140 0.1 •r \- -©• 0.001 -22 -21 -20 19 18 -17 16 Mg / (m a g )
Figure 4.14: This plot shows 4 LFs produced using the MGC data. The blue lines show the LFs produced using the empirical method, with subsample 1 shown as a dotted line and subsample 2 as a solid line. The red lines show LFs produced using the SWML method. There
is good agreement within the selection limits. The shaded regions show the limits for each subsample and method. Subsample 1, with the empirical method is valid for M < —17.5, and with SWML it is valid to M < —16.9. The equivalent limits for subsample 2 are M < —16.85 and M < —16.4. The Norberg et al. (2002) result is shown by the dashed line.
cosmologies, this difference is true for the Einstein-de Sitter cosmology. The MGC is located in
the NGP, so this difference could explain some of the variation seen between the Norberg et al. (2002) results and the MGC LFs. Finally, the faint end slope is dominated by an apparent dip in the LF at M = —17, which is very close to the limits of the survey. In Chapter 5 we will probe deeper into the faint end of the LF, so we will be able to test whether this is real substructure or not. This substructure may well have been missed by Norberg et al. (2002) because of the errors in magnitudes. While they corrected their magnitudes for the overall offset compared to the SDSS-EDR, they did not correct for the non-linearities in surface brightness. This will underestimate the magnitudes of high surface brightness galaxies, but will overestimate the magnitudes of low-surface brightness galaxies, or galaxies at high redshift.
The parameters and fits are detailed in Table 4.1. The fits are very good apart from subsample 2 calculated by the empirical method. The errors are a combination of the random errors and the errors in the K-t-e corrections listed in Norberg et al. (2002). The errors in our result are of the same order of magnitude as those quoted in Norberg et al. (2002). Their error
CV&opfer STAe j&DJR iLBU?. 141
Table 4.1: A comparison of the fits found both subsamples using both methods. All results are converted to Johnson B and are calculated for an Einstein-de Sitter cosmology, unless stated.
Method/Sample Slog h a X u j7 lO^^L©Mpc
EM P/Subl -19.30 0.07 (2 .0 2 ± 0.09) -0.940 ± 0.04 6.81 7 (1.64 ± 0.17) EMP/Sub2 -19.08 ± 0.07 (2 .6 6 ± 0.09) -0.770 ± 0.04 16.25 8 (1.61 ± 0.16) SWML/Subl -19.24i 0.07 (2.15 d= 0.09) -1.00 ±0.04 5.50 1 2 (1 .6 6 ± 0.19) SWML/Sub2 -19.18 ± 0.07 (2.36 J: 0.09) -0.922 ± 0.04 5.63 15 (1 .6 6 ± 0.18) 2dF* -19.20 d=0.07 (2.15 ± 0.09) -1.18 ± 0 .0 2 (1.83 ± 0.17) e s p*2 -19.33 ih 0.08 (2 .0 0 ± 0.04) - 1 .2 2 ±0.06 (1.99 ± 0.2 0) 8DSS*3 -19.42 i 0.04 (2.69 ± 0.34) -1.22 ±0.05 (2.91 ± 0.40) EM P/Sub2/i -18.98 0.07 (&84 ± 0.09) -0.72 ±0.02 1&76 8 (1.56 ± 0.17) SW ML/8ub2/i -19.32 ± 0.07 (1.91 ± 0.09) -0.977 ± 0 .0 2 3.84 13 (1.56 ± 0.17) Sim/Sub2/**'i -18.96 d=0.07 (2 .8 8 ± 0.09) -0.956 ± 0.02 25.8 15 (1 .6 8 ± 0.17)
2dF*i -19.38 ± 0.07 (1 .6 8 ±0.09) - 1 .2 1 ± 0 .0 2 (1.74 ± 0.17)
SDSB^i -19.40 ± 0.07 (1.63 ±0.09) -1.26 ± 0 .0 2 (1.81 ± 0.40)
berg et al. (2002). ** In this case a luminosity function, without surface brightness corrections was calculated, using the SWML methodology. ^ A-CDM cosmology. 0,^ = 0.3, = 0.7,
is dominated by errors in the zero point and the completeness whereas our error is dominated by random errors due to the sample size.
In Table 4.1 and Fig 4.15 we compare 3 recent LFs to the MGC LFs. We compare the 2dFGRS LF (Norberg et al. 2002), the ESP LF (Zucca et al. 2001) and the SDSS LF (Blanton et al. 2001). As we discussed above the MGC does not penetrate far into the faint end of the LF, so we will concentrate on the bright end, where the deep CCD photometry using Kron magnitudes (see § A.l for a comparison of magnitude systems) will provide tight constraints. The ESP gives the best fit to the bright end of the MGC while the SDSS gives the worst fit. Only the ESP fits the MGC within the error bars at the bright end. It would be expected that the SDSS would give a close fit, as it is based on Petrosian CCD magnitudes in 5 colours, and gives an excellent match to the MGC magnitudes, see § 3.5.3. Norberg et al. (2002) have analysed the SDSS LF and conclude that when the correct colour equation is applied to the g' LF, the over-density in the LF within the SDSS region is taken into account and pure luminosity evolution is factored in, the 2dFGRS and SDSS LF are consistent. Norberg et al.
(2 0 0 2) did the analysis of the two surveys using a A-CDM cosmology, and so we will compare
the Norberg calibrated SDSS LF with a MGC LF generated assuming a A-CDM cosmology. The luminosity density calculated for the MGC LFs is consistent compared to each other. There are no noticeable differences between the two subsamples. The mean value is j s = (1.64 ± 0.17) X 10®/iL©Mpc~^ for the Einstein-de Sitter cosmology. This compares with the 2dFGRS value Jb = (1.83 ± 0.17) x 10®hL©Mpc~^. The ESP which fits the MGC better at the bright end gives a higher value (1.99 ± 0.20) x 10®/iL©Mpc“ ^.
The surface brightness functions are shown in Fig 4.16. While the new LFs are similar to the Cross et al. (2001) luminosity function, the surface brightness functions are significantly wider and flatter. This is likely to be due to the improved measurement of surface brightness, allowing for different profile shapes and inclination. In § A. 1.2 and Fig. A.6 we discuss the effects of
Chapter 4- The MGC/2dFGRS/SDSS EDR BED. 142 0.001 -17 -16 -20 -19 -18 -22 -21
Mg / (me
Figure 4.15: This plot shows 4 Schechter Function fits to the MGC subsamples in Fig 4.14 compared to 3 recent surveys. The solid lines are the MGC LFs, the dotted line is the 2dFGRS LF (Norberg et al. 2002), the short dashed line is the ESP LF (Zucca et al. 1997) and the long dashed line is the SDSS LF (Blanton et al. 2001). While the MGC cannot probe the faint end due to the redshift incompleteness and small survey area, it gives excellent constraints on the bright end. The ESP LF fits the bright end best, and the SDSS fits it worst.
Chapter 4' The MGC/2dFGRS/SDSS EDR BED. 143
0.001
21 22 28 24
20
Ai, / ( m a g a r cse c ”®)
Figure 4.16: This plot shows 4 SBFs produced using the MGC data. The blue lines show the LFs produced using the empirical method, with subsample 1 shown as a dotted line and subsample 2 as a solid line. The red lines show LFs produced using the SWML method. The higher values for the SWML reflect the fact that these contain more intrinsically faint galaxies. The green dashed lines show previous results. The green dashed line with points is the Cross et al. (2001) result, and the green dashed line without points is the O’Neil & Bothun (2000) result. The O’Neil & Bothun have been normalised so that 0(/ie = 21.65) = 0.04. The MGC seems to support the O’Neil & Bothun (2000) result. The black shaded regions are the limits where the volume falls below 5000Mpc^.
effective surface brightness of ellipticals while overestimating the effective surface brightness of early type spirals. Thus if both types of galaxy had the same surface brightness when measured using a fitted exponential profile, the elliptical would in reality have a higher surface
brightness than the spiral. The surface brightness distribution can become wider or narrower when the surface brightness is calculated from the half-light radius measurement, rather than the method used in Chapter 2.
The inclination correction will reduce the surface brightness of highly inclined galaxies, since a highly inclined, optically thin spiral galaxy will appear to have a higher surface brightness than the same galaxy viewed face on.
The surface brightness distribution appears to be consistent with a flat distribution, as O’Neil & Bothun (2000) found. However brighter than the Freeman value (/ig < 21.65), where the space density is usually found to significantly decrease, is where the star galaxy separation line limits the volume over which these galaxies can be seen. The difference between the
Chapter 4: The MGC/2dFGRS/SDSS EDR BED. 144 0.1 0.001 19 -20 18 -17 -22 -21 -16 Mg / ( ma g )
Figure 4.17: This plot shows 2 LFs produced using the MGC data and A-CDM cosmology. The blue line shows the LF produced using the empirical method, and the red lines shows the LF produced using the SWML method. There is good agreement within the selection limits. The cyan curve shows a LF calculated using the traditional SWML of Efstathiou, Ellis &; Peterson (1988). The shaded regions show the limits for each subsample and method. The solid curves are the Schechter function fits to the MGC LFs. The dotted line shows the best fit 2dFGRS LF (Norberg et al. 2002) and the dashed line shows the best fit SDSS LF, modified by Norberg et al. (2 0 0 2).
results from the empirical method and the SWML is due to the magnitude range that they sum galaxies over. The SWML BBDs are summed to M = —13, whilst the empirical BBDs are only summed to M = —IQ due to the different Zmin limits. The surface brightness distribution appears to get flatter as the magnitude range over which it is summed increases.