We quantify the systematics in the size-luminosity relation of galaxies in the SDSS main sample which arise from fitting different 1- and 2-component model profiles to the images. In objects brighter than L*, fitting a single Sersic profile to what i
s really a two-component SerExp system leads to biases: the half-light radius is increasingly overestimated as n of the fitted single component increases; it is also overestimated at B/T ~ 0.6. However, the net effect on the R-L relation is small, except for the most luminous tail, where it curves upwards towards larger sizes. We also study how this relation depends on morphological type. Our analysis is one of the first to use Bayesian-classifier derived weights, rather than hard cuts, to define morphology. Crudely, there appear to be only two relations: one for early-types (Es, S0s and Sas) and another for late-types (Sbs and Scds). However, closer inspection shows that within the early-type sample S0s tend to be 15% smaller than Es of the same luminosity, and, among faint late types, Sbs are more than 25% smaller than Scds. Neither the early- nor the late-type relations are pure power-laws: both show significant curvature, which we quantify. However, the R-L relations of the bulges of early-types are almost pure power laws. Our analysis confirms that two mass scales are special for early-type galaxies: M* = 3e10 and 2e11 Msun. These same mass scales are also special for late types: there is almost no correlation between R and M* below the former, and almost no late-types above the latter. We also show that the intrinsic scatter around the relation decreases at large luminosity and/or stellar mass; this should provide additional constraints on models of how the most massive galaxies formed.
For early-type galaxies, the correlations between stellar mass and size, velocity dispersion, surface brightness, color, axis ratio and color-gradient all indicate that two mass scales, M* = 3 x 10^10 Msun and M* = 2 x 10^11 Msun, are special. The sm
aller scale could mark the transition between wet and dry mergers, or it could be related to the interplay between SN and AGN feedback, although quantitative measures of this transition may be affected by morphological contamination. At the more massive scale, mean axis ratios and color gradients are maximal, and above it, the colors are redder, the sizes larger and the velocity dispersions smaller than expected based on the scaling at lower M*. In contrast, the color-sigma relation, and indeed, most scaling relations with sigma, are not curved: they are well-described by a single power law, or in some cases, are almost completely flat. When major dry mergers change masses, sizes, axis ratios and color gradients, they are expected to change the colors or velocity dispersions much less. Therefore, the fact that scaling relations at sigma > 150 km/s show no features, whereas the size-M*, b/a-M*, color-M* and color gradient-M* relations do, suggests that M* = 2 x 10^11 Msun is the scale above which major dry mergers dominate the assembly histories of early-type galaxies.
We analyze a sample of 23 supermassive elliptical galaxies (central velocity dispersion larger than 330 km s-1), drawn from the SDSS. For each object, we estimate the dynamical mass from the light profile and central velocity dispersion, and compare
it with the stellar mass derived from stellar population models. We show that these galaxies are dominated by luminous matter within the radius for which the velocity dispersion is measured. We find that the sizes and stellar masses are tightly correlated, with Re ~ M*^{1.1}$, making the mean density within the de Vaucouleurs radius a steeply declining function of M*: rho_e ~ M*^{-2.2}. These scalings are easily derived from the virial theorem if one recalls that this sample has essentially fixed (but large) sigma_0. In contrast, the mean density within 1 kpc is almost independent of M*, at a value that is in good agreement with recent studies of z ~ 2 galaxies. The fact that the mass within 1 kpc has remained approximately unchanged suggests assembly histories that were dominated by minor mergers -- but we discuss why this is not the unique way to achieve this. Moreover, the total stellar mass of the objects in our sample is typically a factor of ~ 5 larger than that in the high redshift (z ~ 2) sample, an amount which seems difficult to achieve. If our galaxies are the evolved objects of the recent high redshift studies, then we suggest that major mergers were required at z > 1.5, and that minor mergers become the dominant growth mechanism for massive galaxies at z < 1.5.
The color-magnitude relation of early-type galaxies differs slightly but significantly from a pure power-law, curving downwards at low and upwards at large luminosities (Mr>-20.5 and Mr<-22.5). This remains true of the color-size relation, and is eve
n more apparent with stellar mass (M* < 3x10^10 Msun and M* > 2x10^11 Msun). The upwards curvature at the massive end does not appear to be due to stellar population effects. In contrast, the color-sigma relation is well-described by a single power law. Since major dry mergers change neither the colors nor sigma, but they do change masses and sizes, the clear features observed in the scaling relations with M*, but not with sigma > 150 km/s, suggest that M* > 2x10^11 Msun is the scale above which major dry mergers dominate the assembly history. We discuss three models of the merger histories since z ~ 1 which are compatible with our measurements. In all three models, dry mergers are responsible for the flattening of the color-M* relation at M* > 3x10^10 Msun - wet mergers only matter at smaller masses. At M* > 2 x 10^11 Msun, the merger histories in one model are dominated by major rather than minor dry mergers, as suggested by the axis ratio and color gradient trends. In another, although both major and minor mergers occur at the high mass end, the minor mergers contribute primarily to the formation of the ICL, rather than to the mass growth of the central massive galaxy. A final model assumes that the reddest objects were assembled by a mix of major and minor dry mergers.
From a sample of ~50000 early-type galaxies from the SDSS, we measured the traditional Fundamental Plane in four bands. We then replaced luminosity with stellar mass, and measured the stellar mass FP. The FP steepens slightly as one moves from shorte
r to longer wavelengths: the orthogonal fit has slope 1.40 in g and 1.47 in z. The FP is thinner at longer wavelengths: scatter is 0.062 dex in g, 0.054 dex in z. The scatter is larger at small galaxy sizes/masses; at large masses measurement errors account for essentially all of the observed scatter. The FP steepens further when luminosity is replaced with stellar mass, to slope ~ 1.6. The intrinsic scatter also reduces further, to 0.048 dex. Since color and stellar mass-to-light ratio are closely related, this explains why color can be thought of as the fourth FP parameter. However, the slope of the stellar mass FP remains shallower than the value of 2 associated with the virial theorem. This is because the ratio of dynamical to stellar mass increases at large masses as M_d^0.17. The face-on view of the stellar mass kappa-space suggests that there is an upper limit to the stellar density for a given dynamical mass, and this decreases at large masses: M_*/R_e^3 ~ M_d^-4/3. We also study how the estimated coefficients a and b of the FP are affected by other selection effects (e.g. excluding small sigma biases a high; excluding fainter L biases a low). These biases are seen in FPs which have no intrinsic curvature, so the observation that a and b scale with L and sigma is not, by itself, evidence that the Plane is warped. We show that the FP appears to curve sharply downwards at the small mass end, and more gradually downwards towards larger masses. Whereas the drop at small sizes is real, most of the latter effect is due to correlated errors.
We select a sample of about 50,000 early-type galaxies from the Sloan Digital Sky Survey (SDSS), calibrate fitting formulae which correct for known problems with photometric reductions of extended objects, apply these corrections, and then measure a
number of pairwise scaling relations in the corrected sample. We show that, because they are not seeing corrected, the use of Petrosian-based quantities in magnitude limited surveys leads to biases, and suggest that this is one reason why Petrosian-based analyses of BCGs have failed to find significant differences from the bulk of the early-type population. These biases are not present when seeing-corrected parameters derived from deVaucouleur fits are used. Most of the scaling relations we study show evidence for curvature: the most luminous galaxies have smaller velocity dispersions, larger sizes, and fainter surface brightnesses than expected if there were no curva-ture. These statements remain true if we replace luminosities with stellar masses; they suggest that dissipation is less important at the massive end. There is curvature in the dynamical to stellar mass relation as well: the ratio of dynamical to stellar mass increases as stellar mass increases, but it curves upwards from this scaling both at small and large stellar masses. In all cases, the curvature at low masses becomes apparent when the sample becomes dominated by objects with stellar masses smaller than 3 x 10^10 M_Sun. We quantify all these trends using second order polynomials; these generally provide significantly better description of the data than linear fits, except at the least luminous end.
We used the Advanced Camera for Surveys on board the Hubble Space Telescope to obtain high resolution i-band images of the centers of 23 single galaxies, which were selected because they have SDSS velocity dispersions larger than 350 km/s. The surfac
e brightness profiles of the most luminous of these objects (M_i<-24) have well-resolved `cores on scales of 150-1000 pc, and share similar properties to BCGs. The total luminosity of the galaxy is a better predictor of the core size than is the velocity dispersion. The correlations of luminosity and velocity dispersion with core size agree with those seen in previous studies of galaxy cores. Because of high velocity dispersions, our sample of galaxies can be expected to harbor the most massive black holes, and thus have large cores with large amounts of mass ejection. The mass-deficits inferred from core-Sersic fits to the surface-brightness profiles are approximately double the black-hole masses inferred from the M_bh-sigma relation and the same as those inferred from the M_bh-L relation. The less luminous galaxies (M_i>-23) tend to have steeper `power-law inner profiles, higher-ellipticity, diskier isophotes, and bulge-to-total ratios of order 0.5 -- all of which suggest that they are `fast-rotators and rotational motions could have contaminated the velocity dispersion estimate. There are obvious dust features within about 300 pc of the center in about 35% of the sample, predominantly in power-law rather than core galaxies.
We study a sample of 43 early-type galaxies, selected from the SDSS because they appeared to have velocity dispersion > 350 km/s. High-resolution photometry in the SDSS i passband using HRC-ACS on board the HST shows that just less than half of the s
ample is made up of superpositions of two or three galaxies, so the reported velocity dispersion is incorrect. The other half of the sample is made up of single objects with genuinely large velocity dispersions. None of these objects has sigma larger than 426 +- 30 km/s. These objects define rather different relations than the bulk of the early-type galaxy population: for their luminosities, they are the smallest, most massive and densest galaxies in the Universe. Although the slopes of the scaling relations they define are rather different from those of the bulk of the population, they lie approximately parallel to those of the bulk at fixed sigma. These objects appear to be of two distinct types: the less luminous (M_r>-23) objects are rather flattened and extremely dense for their luminosities -- their properties suggest some amount of rotational support and merger histories with abnormally large amounts of gaseous dissipation. The more luminous objects (M_r<-23) tend to be round and to lie in or at the centers of clusters. Their properties are consistent with the hypothesis that they are BCGs. Models in which BCGs form from predominantly radial mergers having little angular momentum predict that they should be prolate. If viewed along the major axis, such objects would appear to have abnormally large sigma for their sizes, and to be abnormally round for their luminosities. This is true of the objects in our sample once we account for the fact that the most luminous galaxies (M_r<-23.5), and BCGs, become slightly less round with increasing luminosity.
