Luminosity function parameters for RXCJ0014.3-3022

Overall the cluster environment comprises its core and the two filaments (see Braglia et al. (2007) and Braglia et al. 2008a). Here a third region is associated with it: an annular ring centred on the X-ray centroid and limited by radii of 3 and 5 arcmin, excluding the filaments. This region extends to where the overdensity of red galaxies is still significant at more than 5σ. It contains 128 objects, bringing the total number of cluster members to 1165. The regions are summarized in Table 4.4.2:

We determine the luminosity function in each of the rest-frame B, V, and R bands for the cluster environment, the cluster core, the filaments, and the field. Best-fit parameters, uncertainties, and values of the reducedχ2 _{(i.e., the value ofχ}2 _divided

by the degrees of freedom of the fit minus the number of parameters,ν−p) are listed in Table 4.4.2 for the individual bands and the individual regions. Figure 4.7 reproduces the LF as a function of broad-band filter and surveyed regions, while Fig. 4.8 shows the associated error contours in the parameter space. Both Table 4.4.2 Fig. 4.8 show that the best-fit solutions are robust. For the cluster as a whole, our best-fit values for slopes and characteristic magnitudes of the LFs in V and R bands are consistent with those quoted by Busarello et al. ((2002)), within the errors. The number of objects is similar (i.e., 1165 vs. 1206), but the combination of photo-z selection and robust characterization of the background allow smaller uncertainties to be reached for the best-fit parameters listed in Table 4.4.2.

Region N.Objects R band α ∆α M∗ ∆M∗ χ2/(ν−p) Full cluster 1165 −0.89 0.03 −22.51 0.21 3.46/9 Core 304 −0.78 0.06 −21.91 0.29 5.98/9 NW filament 359 −0.91 0.12 −22.69 0.59 4.21/7 S filament 374 −0.94 0.09 −23.09 0.73 3.00/9 Field 488 −1.07 0.01 −23.13 0.28 12.37/9 V band α ∆α M∗ ∆M∗ χ2/(ν−p) Full cluster 1165 −0.92 0.03 −22.14 0.23 8.34/9 Core 304 −0.93 0.04 −22.16 0.34 5.88/8 NW filament 359 −0.84 0.09 −22.69 0.29 4.86/6 S filament 374 −0.99 0.08 −23.70 0.72 8.70/8 Field 488 −1.17 0.01 −23.58 0.23 5.33/9 B band α ∆α M∗ ∆M∗ χ2/(ν−p) Full cluster 1165 −0.95 0.02 −21.88 0.19 4.44/9 Core 304 −0.90 0.04 −21.36 0.29 8.42/9 NW filament 359 −1.02 0.05 −22.79 0.35 10.74/7 S filament 374 −0.98 0.06 −22.87 0.43 5.25/8 Field 488 −1.19 0.01 −23.40 0.23 4.39/9

Table 4.2: Summary of luminosity function parameters for RXCJ0014.3-3022 and its components in the B, V and R bands.

There is a robust evidence for the slope of the faint end of the LF to flatten moving from the field to the cluster environment. At the same time, the characteristic magnitude becomes fainter. This holds for all bands. The difference is more evident when comparing the field to the cluster core. Accordingly, the distribution of the fit parameters in the parameter space (see Fig. 4.8) describes, within error contours, an almost continuous evolution of the values of the fit from the field through the filaments towards the core. These results are consistent with previous ones, whether they were obtained for this cluster or for other systems at different redshifts.

The new result is that the LF in the filaments exhibits characteristic parameters that are in between those of the field and the cluster core. In fact, the fit to the filaments shows unexpectedly large contours, even in comparison with those of other regions with similar number of objects. The contours for the cluster, core and field have well-defined and limited regions in the parameters space, confirming the robust-

4.4 Optical luminosity function

Figure 4.7: Luminosity functions of the cluster RXCJ0014.3-3022 and for its com- ponents. Left column is for R band, central column for V band and right column for B band. From top to bottom, the background-corrected magnitude distribution of cluster members and Schechter function best fit are shown for the full cluster sample, cluster core, NW filament, S filament and field.

ness of the fit. On the other hand, the filaments contours have large and irregular shapes. This is also reflected in the bumpy distributions shown in Fig. 4.7. This sug- gests that the best-fit could be not a single function, but a combination of different behaviours. In Braglia et al. ((2007)) a sudden increase in the blue-to-red objects was found in the outer part of the filaments. The increase is dramatically evident in the denser southern filament, while the northern one shows a gentler trend still towards high values. Based on this results, luminosity functions for the inner and outer part of the filaments are independently re-fitted to check whether the popula-

Figure 4.8: Error contours for the fits of all regions of RXCJ0014.3-3022. From left to right, the panels show results for the R, V and B band respectively. Black continuous contours are for the full cluster, black dashed contours for the field, red dotted for the core, blue short dashed for the N filament and green long dashed for the S filament. In the R and V band, the filament error contours are large and irregular, shrinking only in the B band to comparable values and areas. The full cluster and its core always show well-defined and compact contours, as the field does. The field contours are well separated from the cluster and its components, and in V and B basically occupy the same region in the parameters space.

tion in the two parts can be different. To obtain higher counts for a better fit the two filaments are stacked together to form a composite filament, whose population is then splitted with respect to cluster-centric radius. The inner and outer part of the composite are defined as below or beyond a radius of 8′

, respectively. This value is chosen to separate the filament sections where the ratio of blue-to-red galaxies is below or beyond the typical field values (cfr. Fig. 6 in BPB07). At the cluster’s redshift, it corresponds to about 2.2 Mpc or 0.82R200.

The inner part of the composite filament shows a luminosity function globally comparable with the main cluster. Although errors are still relatively large, the error contours now are smooth and well-defined. Thus, we can consider the inner part of the filaments as following the overall population in the cluster. The same result is seen if the LF is evaluated for each filament’s inner part, although uncertainties become larger. The outer part proves instead difficult to fit with a Schechter function, appearing instead as an almost flat distribution of objects across the full magnitude

4.4 Optical luminosity function

Figure 4.9: Luminosity functions for the composite filament in RXCJ0014.3-3022. From left to right, the plots for the three bands (R, V and B respectively) are shown. Top row shows the LF for the inner part of the filament, where galaxies follow the overall trend of the cluster population. Bottom row is instead the magnitude distri- bution for the outer filaments, where the shape of the LF is globally transformed. Overplotted to the points in the bottom panels is the mean count value.

R V B Region L ∆L L ∆L L ∆L Full cluster 2.290 0.028 1.337 0.038 0.786 0.028 Core 0.910 0.014 0.514 0.019 0.279 0.014 NW Filament 0.256 0.013 0.154 0.018 0.099 0.013 S Filament 0.926 0.014 0.578 0.019 0.374 0.013

Table 4.3: Total luminosity and errors for RXCJ0014.3-3022 and for its com- ponents in the R, V and B bands. All luminosities are expressed in multiples of 1013

L⊙.

interval sampled.

The total luminosity is calculated for the full cluster environment, as well as for each cluster component (core, NW filament and S filament). Table 4.4.2 lists the values of

Band M/L ∆M/L

B 370 58

V 214 32

R 124 18

Table 4.4: M/L ratio and error for RXCJ0014.3-3022, calculated in the three bands atR200. All values are expressed in units ofM⊙/L⊙. Errors are calculated by standard error propagation.

the total optical luminosity and associated errors for the cluster and its components in each band. The full cluster luminosity also accounts for contribution from the additional annulus around the core. These results provide a consistent picture of RXCJ0014.3-3022 as an extremely large system: its total optical luminosity is at the very high end of the values reported for clusters at intermediate redshifts (e.g. Popesso et al. (2004)). The southern filament, that we already know to be denser and richer in blue galaxies (see Braglia et al. (2007); Braglia et al. 2008, in prep.), has a total luminosity about three times of the north-western filament, and is found to be brighter than the core in B band by about 35%. The total optical luminosity decreases from the R band to the B band. This is not surprising, as for cluster galaxies (i.e., at z∼0.3) R band samples a region of the spectrum mainly powered by old stars, while B band samples the region bluewards of the 4000 ˚A break, where the largest part of the emission is due to younger stars. Thus, mainly actively star- forming galaxies (i.e. a fraction of the total number of galaxies in the cluster) will contribute to the radiation detected in the B band.

4.4.2.1 Cluster mass-to-light ratio

The results obtained from the study of dynamics and the behaviour of the LF in the different cluster components can be easily combined to obtain a reliable evalua- tion of the cluster mass-to-light (M/L) ratio in the three bands and to examine its dependence with radius. The value of M/L ratio within R200 (as determined from

dynamical analysis) is given in Table 4.4.2.1:

We calculate the radial behaviour of the M/L ratio in the three bands from the cluster core to its outskirts (1.5R200). The total cluster luminosity is calculated

within concentric radii in the same way as for the dynamical mass (constant bin of 0.1R200, starting from 0.2R200; cfr. Sect. 4.3) and considering all cluster photometric

members (the core with additional objects out to 5’ and the two filaments). The M/L ratio is constant within errors below 0.5R200and beyond 0.7R200(a slight decreasing

trend is barely noticeable in the B band), whereas it increases steadily by about 40% in between (i.e., within 0.54 Mpc). Interestingly, this is the region where the two filaments connect to the cluster main body and their population is dominated by red

4.4 Optical luminosity function

Figure 4.10: Radial behaviour of M/L ratio for RXCJ0014.3-3022 in the three bands. The vertical dashed line marks the position ofr200=2.69 Mpc. Top panel, B band; middle panel, V band; bottom panel, R band.

galaxies (see Braglia et al. (2007), 2008a).

The differential mass-to-light radial profile (i.e., δM(R)/δL(R)) provides a more precise picture of the M/L profile of the cluster (see e.g. Rines et al. (2000)). The profile obtained is shown in Fig. 4.11. In all bands, the differential M/L profile is seen to be decreasing (within errors) for increasing cluster-centric radii below 0.85R200,

as already shown in several previous works (e.g. Katgert et al. (1994); Rines et al. (2000) and (2001); Biviano & girardi (2003)). However, beyond 0.85R200 a

sudden increase in the M/L ratio is detected. This distance precisely corresponds to the region where Braglia et al. ((2007); also see Braglia et al. 2008a, in prep.) found a strong increase in the star formation activity of galaxies belonging to the two

Figure 4.11: Radial behaviour of differential M/L ratio forRXCJ0014.3-3022 in the three bands. The vertical dashed line marks the position of r200=2.69 Mpc. Top panel, B band; middle panel, V band; bottom panel, R band.

filaments, both from colour information and spectral index analysis. Thus, we suggest that this increase in the M/L ratio is due to the presence of the two filaments that bring new matter into the cluster. This is also partly in agreement with the excess mass and luminosity profiles found by Sheldon et al. ((2007)) in clusters drawn from the MaxBCG sample, where they found a steady increase in the deprojected radial M/L ratio profile using weak lensing mass profiles.