The evolution of the Fundamental Plane can be characterised in terms of its zero-point. In turn, the zero-point of the FP is related to the mean M/L ratio. Thus, if the FP zero-point for a sample of early-type galaxies changes as a func-tion of redshift z, this implies an evolution of the mean M/L ratio and hence an evolution in the luminosity-weighted stellar population prop-erties of the galaxies under consideration.
For the present-day zero-point of the FP a boot-strap bisector fit to the early-type Coma galax-ies in rest-frame Gunn r-band was performed.
This yielded a slope of 1.048±0.038 and a zero-point of −0.029±0.010. The early-type galax-ies of A 2390 show a small shift with respect to the Coma galaxies (see Fig. 6.11). As the veloc-ity dispersions and effective radii of the galax-ies in A 2390 span similar ranges like their local
counterparts (apart from the Coma cD galax-ies with Re >∼ 30 kpc) and the surface bright-nesses are slightly increased with respect to the local sample, at least a fraction of the shift in the M/L ratio is due to luminosity evolution.
However, when deriving an exact amount of lu-minosity evolution, one has to be careful as ad-ditional combined effects also contribute to the total derived luminosity offset. Some studies found different FP slopes at intermediate red-shift compared to the local slope, but they suf-fer from low number statistics (van Dokkum &
Franx 1996; Kelson et al. 1997; van Dokkum et al. 1998). However, more recent investigations based on larger samples reported similarly only a modest change in the FP slope (Kelson et al.
2000b; Treu et al. 2001b). Thus, the lack of a strong slope change gives evidence against the hypothesis of the FP being solely an age-mass re-lation. The Fundamental Plane is mainly a rela-tion between theM/Lratio and galaxy massM.
Therefore, when comparing small samples with significantly different ranges in galaxy mass, an offset in the M/L ratio can heavily depend on the adopted FP slope. The M/Loffset will be a combination of three items: (i) the difference in the slope of the FP, (ii) the mean mass range of the sample and (iii) the ‘true’ offset. By reducing the differences in the mass distribution, theM/L results become insensitive to the adopted slope of the FP and any derived evolution for the dis-tant galaxies is valid for a given range of galaxy masses (Kelson et al. 2000b). For this reason, the local Coma sample was restricted to a sim-ilar mass function as for the galaxies in A 2218 and A 2390 and this reference was applied for the entire analyses within the FP and the M/L evolution.
A comparison of the mass distributions of the distant early-type galaxies of A 2390 and A 2218 with the local Coma galaxies within the logσ− logReplane is shown in Fig. 6.17. The distribu-tions of galaxy masses for the Low–LX E+S0 galaxies are illustrated in Fig. 6.18. Regions
Figure 6.17: The log σ −log Re plane for the A 2390 and A 2218 early-type galaxies, compared to the Coma galaxies of J99. Symbol notations as in Fig.6.11. Dashed lines indicate contours of constant mass 5G−1σ2Re= 1010, 1011 and 1012M (Bender et al. 1992). The early-type galaxy masses of A 2390 and A 2218 atz∼0.2 are similarly distributed as the early-type Coma sample.
of constant mass, ranging from 1012M over 1011M down to 1010M, derived with the re-lation M = 5σ2Re/G in units of M (Bender, Burstein & Faber 1992) where G is the gravi-tational constant, are indicated as dashed lines.
For the absolute magnitude in Gunn r of the Sun,Mr,= 4.87m was adopted, which was de-rived from MV, = 5.72 and (V −R) = 0.52 (Schaifers et al. 1981) and the transformation r =R+ 0.41 + 0.21(V −R) (Kent 1985). Both samples exhibit similar ranges in mass (σ) and size (Re), assuring that a possible M/L evolu-tion will not be driven mainly by any differ-ences between the galaxy mass ranges of the samples. The restrictions to the local Coma reference as defined for the rich cluster sam-ple were also adopted for the early-type galaxies in the poor clusters (cf. section 6.2). To test the effects of different limits in velocity
disper-Chapter 6: Galaxy Scaling Relations at z∼0.2 149
Figure 6.18: The log σ−log Re plane for the the Cl 0849, Cl 1701 and Cl 1702 early-type galaxies, com-pared to the Coma galaxies of J99. Symbol notations as in Fig. 6.12. Dashed lines indicate contours of constant mass 5G−1σ2Re = 1010, 1011and 1012M (Bender et al. 1992). The early-type galaxy masses of poor cluster galaxies between 0.22≤z≤0.24 are similarly distributed as the early-type Coma sample.
sion on the amount of derived luminosity evo-lution for the Low–LX galaxies, the selection boundaries of the Coma cluster were modified.
The largest effect was detected for a limit of logσJ99 >2.10 (corresponding to a ∼22 km s−1 higher cutoff value), which yields a change in the amount of derived luminosity evolution of less than 0.0033m. This difference is negligible and assures that the assumption to use one definition of selection boundaries is also valid for the poor cluster sample.
Adopting a constant slope with redshift, the median zero-point offset for the combined sam-ple of 34 E+S0 rich cluster galaxies yielded
∆γE+S0,z=0.2 = 0.10±0.06. Alternatively using a variable slope in the FP for the distant cluster sample, negligible changes in the FP parameters α andβ compared to the locally defined param-eters by the Coma data are found. In particular,
a bootstrap bisector fit to all 34 E+S0 galaxies gives a slightly steeper slope of 1.152±0.047 and a zero-point of −0.153±0.018, with a 3σ confi-dence level for a slope change. This comparison and the results based on the M/L ratios may give some evidence for a mass-dependent evolu-tion which is stronger for low-mass galaxies.
Fig.6.19 shows the observed mass-to-light M/L ratio of the distant clusters A 2218 and A 2390 as a function of velocity dispersion σ (left) and versus mass M (right). The Coma sample was limited to galaxies with logσ > 2.02 (indi-cated by the vertical dotted lines in Fig. 6.19) in order to match the area of parameter space covered by the distant galaxies of A 2390 and A 2218. An analysis based on bootstrap bi-sector fits to M/L = a σm revealed differ-ent M/L slopes for the distant (hashed area) and the local (solid lines) samples. The slope difference between A 2218 and Coma is
∆mA2218 = 0.27 ± 0.17 and an offset in the zero-point of ∆aA2218 = 0.040 ± 0.027. For A 2390 ∆mA2390 = 0.11 ± 0.21 is detected and ∆aA2390 = 0.157 ± 0.019. The com-bined sample of distant clusters has a slope difference of ∆mz=0.2 = 0.36 ± 0.17 and
∆az=0.2 = 0.036± 0.024. With a 2σ confi-dence different slopes for both are measured, the intermediate clusters and the Coma cluster (Coma slope value is m = 0.59±0.15). How-ever, a systematic zero-point offset of the dis-tant M/L relation is detected, which is not in agreement with the proposed change due to pas-sive evolution. Adopting a formation redshift of zform = 2 for all stars in early-type galaxies, the BC96 models predict ∆a = 0.12. Ellipti-cals and S0 galaxies seem to have different M/L slope changes, with a steeper slope for the ellipti-cal galaxies. Elliptiellipti-cals: ∆mE= 0.54±0.30 and
∆aE= 0.041±0.037; S0s: ∆mS0 = 0.06±0.23 and ∆aS0 = 0.141±0.026.
The M/L ratios as a function of mass M are shown in the right plot of Fig. 6.19. In a similar manner as for the velocity
disper-Figure 6.19: TheM/Lratio in Gunnr for A 2390 and A 2218. Left: M/Lratio as a function of velocity dispersion σ, Right: M/L ratio as a function of mass in solar units. Symbol notations as in Fig. 6.11.
Solid lines show the 100 iteration bootstrap bisector fits to the local Coma sample of J99 within selection boundaries of the distant samples (1 σerrors). The hashed area denotes the bisector fits within 1σerrors to the combined distant sample of A 2390 and A 2218.
sions, the two samples are analysed in terms of bootstrap bisector fits. For the reduced Coma cluster alone M/L∝M0.59±0.07 is found.
With respect to Coma, the slope difference for A 2218 is ∆mA2218 = 0.025 ± 0.060 with a zero-point offset of ∆aA2218 = 0.048± 0.029.
For A 2390 a similar slope change is found
∆mA2390 = 0.057±0.063, but a larger offset of
∆aA2390 = 0.165±0.028. The two distant clus-ters as a whole have ∆mz=0.2 = 0.071±0.039 and ∆az=0.2 = 0.037±0.021. Dividing the sam-ple into elliptical and S0 galaxies gives no signifi-cant slope changes, for Es: ∆mE= 0.049±0.056 and for S0s: ∆mS0 = 0.087±0.089. However, the S0s exhibit a larger offset in the zero-point of
∆aS0= 0.138±0.030, compared to the ellipticals
∆aE= 0.050±0.034.
Analogous to the cluster galaxies, the M/L ra-tios for the poor clusters Cl 0849, Cl 1701 and Cl 1702 were computed. Fig. 6.20 displays the M/L ratios as a function of velocity disper-sion σ (left panel) and as a function of mass in solar units (right panel). Unfortunately, an
analysis for the morphological types of ellip-ticals and lenticulars cannot be performed as the latter class comprises only one galaxy. Un-der assumption of a non–changing local slope with redshift, the mean residuals from the lo-cal logM/L−logσ relation of the Low–LX clus-ter galaxies are investigated and their mean evo-lution in the M/L ratio is derived. The M/L ratios of the distant poor galaxies are on aver-age offset by ∆M/L = 0.138±0.049 compared to the Coma M/L ratios. In the right part of Fig. 6.20, the M/L ratios are shown as a func-tion of galaxy mass M. The low–mass cluster galaxies occupy a larger range in theM/Lratios than the rich cluster galaxies in Fig.6.19. In ad-dition a larger offset to the local logM/L−logM relation with ∆logM/L= 0.216±0.059 for the poor sample than for the rich cluster sample with
∆logM/L= 0.109±0.021 is found, where for the latter also the Coma slope was assumed.
In both illustrations of Fig.6.20theM/Lratios of the Low–LX E+S0 galaxies feature on average a larger scatter withσM/L Poor= 0.29 than their
Chapter 6: Galaxy Scaling Relations at z∼0.2 151
Figure 6.20: TheM/Lratio in Gunnrfor the poor clusters Cl 0849, Cl 1701 and Cl 1702. Left: M/Lratio as a function of velocity dispersionσ,Right: M/Lratio as a function of mass in solar units. Symbol notations as in Fig.6.12. The linear bisector fit to the Coma galaxies was restricted to the range encompassed by the distant rich cluster galaxies. The area bounded by dotted lines indicates the mean ±1σ of the local M/L relation. The solid line shows the mean evolution of the poor cluster sample assuming the local slope.
counterparts in rich clusters σM/L Rich = 0.23 and theirM/L are slightly more offset from the galaxies in Coma compared to the M/L ratios in rich clusters. For a comparison, the reduced local reference sample has a dispersion in the M/L ratios of σM/L Coma = 0.14. In both, the FP (Fig.6.12) and the logM/L−logM diagram (Fig. 6.20), it seems that there are two different groups of cluster galaxies, one class which fol-lows the local relation and another one which is clearly offset from the Coma reference. An ex-planation could be that the Low–LX E+S0 gal-axies have larger variations in their stellar pop-ulations or that star formation processes work differently in these galaxies. Such effects should also be detectable in an analysis of the forma-tion redshift for the galaxies which gives also clues on the global star formation histories in these systems (cf. section 7.2). Furthermore, in case of the bright cD galaxies, differences be-tween the Low–LX E+S0 galaxies and the rich cluster members are found. Two of three cen-tral cluster galaxies in the poor clusters (# 24
with Re ≈ 14 kpc in CL 0849 and # 81 with Re≈16 kpc in CL 1702) havehigher velocity dis-persions with ∆σ≈118 km s−1, but at the same time smaller half-light radii of ∆Re ≈ 2.6 kpc than their counterparts in the A 2218 cluster.
The third cD galaxy of the cluster CL 1701 (# 123) at σ = 244 km s−1 and Re = 8.8 kpc has a double nucleus and cannot be regarded as a typical cD galaxy as it is an ongoing merger of two galaxies. Another galaxy which shows an offset in the logσ−logRe diagram is the object
# 62 (Re = 15.5 kpc) which is a large elliptical galaxy but not massive enough to be a central cluster galaxy as it has a low velocity dispersion of ∼155 km s−1. Together with the findings in the KR, the signs of interaction processes give further evidence, that the cD galaxies in low–
mass clusters have longer formation timescales up to the recent past and therefore represent a different galaxy population compared to the cD galaxies in rich galaxy clusters.
Morphological transformation from late-type spiral to S0 galaxies as observed from redshift of
z = 0.55 to the present day Universe (Dressler et al. 1997) can have significant effects on the evolution of colours and luminosities of early-type galaxies with redshift. If early-early-type galaxies were transformed from late-type galaxies in the recent past, the youngest progenitors of present-day early-type galaxies will drop out from an observed sample of early-type galaxies at high redshift. The samples at high and low redshift differ and the high-z data set may be biased towards the oldest progenitors of present-day early-type galaxies. The correction for this so-called ‘progenitor bias’ (van Dokkum & Franx 2001b) increases as a function of redshift and can be quoted in terms of the M/L ratio as
∆lnhM/LBi ≈ 0.2×z. It has a small (<∼20%) but non-negligible effect on the measured evo-lution of the mean the M/L ratios. For the results in the FP and on the M/L ratios at z = 0.2 the effect is insignificant, the true evo-lution in the M/L ratio is underestimated by
∆lnhM/LBi ≈0.04 and was therefore not con-sidered. This effect comes into play at a red-shift of z >∼0.4 and has dramatic effect at high redshifts of about z ≥ 0.8. In the analysis of the field early–type galaxies and the derivation of the formation epochs in the following chap-ter, the correction of the progenitor bias will be accounted for.
As a conclusion from the results of the scaling re-lations so far, for the whole sample of 34 E+S0 cluster galaxies in A 2218 and A 2390 and 10 early–type galaxies in the Low–LX clusters on average only a moderate amount of luminosity evolution is derived. From these findings it can be inferred that at a look-back time of∼2.8 Gyrs most early–type galaxies in the rich clusters con-sist of an old stellar population with the bulk of the stars formed at a high formation redshift of about zform ≥ 2. The elliptical galaxies in the poor clusters however, suggest a trend for a stronger evolution which favours a lower forma-tion epoch. A detailed discussion on the stellar population ages will be presented in section 7.2.
In the following, the findings for the early–type cluster galaxies will be compared to previous re-sults in the literature.