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Register a new userFurther constraining galaxy evolution models through the Size Function of SDSS Early-type galaxies
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Francesco Shankar
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We discuss how the effective radius Phi(Re) function (ERF) recently worked out by Bernardi et al. (2009) represents a new testbed to improve the current understanding of Semi-analytic Models of Galaxy formation. In particular, we here show that a detailed hierarchical model of structure formation can broadly reproduce the correct peak in the size distribution of local early-type galaxies, although it significantly overpredicts the number of very compact and very large galaxies. This in turn is reflected in the predicted size-mass relation, much flatter than the observed one, due to too large (~3 kpc) low-mass galaxies (<10^11 msun), and to a non-negligible fraction of compact (< 0.5-1 kpc) and massive galaxies (> 10^11 msun). We also find that the latter discrepancy is smaller than previously claimed, and limited to only ultracompact (Re < 0.5 kpc) galaxies when considering elliptical-dominated samples. We explore several causes behind these effects. We conclude that the former problem might be linked to the initial conditions, given that large and low-mass galaxies are present at all epochs in the model. The survival of compact and massive galaxies might instead be linked to their very old ages and peculiar merger histories. Overall, knowledge of the galactic stellar mass {em and} size distributions allows a better understanding of where and how to improve models.
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We analyze 40 cosmological re-simulations of individual massive galaxies with present-day stellar masses of $M_{*} > 6.3 times 10^{10} M_{odot}$ in order to investigate the physical origin of the observed strong increase in galaxy sizes and the decrease of the stellar velocity dispersions since redshift $z approx 2$. At present 25 out of 40 galaxies are quiescent with structural parameters (sizes and velocity dispersions) in agreement with local early type galaxies. At z=2 all simulated galaxies with $M_* gtrsim 10^{11}M_{odot}$ (11 out of 40) at z=2 are compact with projected half-mass radii of $approx$ 0.77 ($pm$0.24) kpc and line-of-sight velocity dispersions within the projected half-mass radius of $approx$ 262 ($pm$28) kms$^{-1}$ (3 out of 11 are already quiescent). Similar to observed compact early-type galaxies at high redshift the simulated galaxies are clearly offset from the local mass-size and mass-velocity dispersion relations. Towards redshift zero the sizes increase by a factor of $sim 5-6$, following $R_{1/2} propto (1+z)^{alpha}$ with $alpha = -1.44$ for quiescent galaxies ($alpha = -1.12$ for all galaxies). The velocity dispersions drop by about one-third since $z approx 2$, following $sigma_{1/2} propto (1+z)^{beta}$ with $beta = 0.44$ for the quiescent galaxies ($beta = 0.37$ for all galaxies). The simulated size and dispersion evolution is in good agreement with observations and results from the subsequent accretion and merging of stellar systems at $zlesssim 2$ which is a natural consequence of the hierarchical structure formation. A significant number of the simulated massive galaxies (7 out of 40) experience no merger more massive than 1:4 (usually considered as major mergers). On average, the dominant accretion mode is stellar minor mergers with a mass-weighted mass-ratio of 1:5. (abridged)
The dramatic size evolution of early-type galaxies from z ~ 2 to 0 poses a new challenge in the theory of galaxy formation, which may not be explained by the standard picture. It is shown here that the size evolution can be explained if the non-baryonic cold dark matter is composed of compact objects having a mass scale of ~10^5 M_sun. This form of dark matter is consistent with or only weakly constrained by the currently available observations. The kinetic energy of the dark compact objects is transferred to stars by dynamical friction, and stars around the effective radius are pushed out to larger radii, resulting in a pure size evolution. This scenario has several good properties to explain the observations, including the ubiquitous nature of size evolution and faster disappearance of higher density galaxies.
Using data drawn from the DEEP2 and DEEP3 Galaxy Redshift Surveys, we investigate the relationship between the environment and the structure of galaxies residing on the red sequence at intermediate redshift. Within the massive (10 < log(M*/Msun) < 11) early-type population at 0.4 < z <1.2, we find a significant correlation between local galaxy overdensity (or environment) and galaxy size, such that early-type systems in higher-density regions tend to have larger effective radii (by ~0.5 kpc or 25% larger) than their counterparts of equal stellar mass and Sersic index in lower-density environments. This observed size-density relation is consistent with a model of galaxy formation in which the evolution of early-type systems at z < 2 is accelerated in high-density environments such as groups and clusters and in which dry, minor mergers (versus mechanisms such as quasar feedback) play a central role in the structural evolution of the massive, early-type galaxy population.
Early-type galaxies (ETGs) are observed to be more compact, on average, at $z gtrsim 2$ than at $zsimeq 0$, at fixed stellar mass. Recent observational works suggest that such size evolution could reflect the similar evolution of the host dark matter halo density as a function of the time of galaxy quenching. We explore this hypothesis by studying the distribution of halo central velocity dispersion ($sigma_0$) and half-mass radius ($r_{rm h}$) as functions of halo mass $M$ and redshift $z$, in a cosmological $Lambda$-CDM $N$-body simulation. In the range $0lesssim zlesssim 2.5$, we find $sigma_0propto M^{0.31-0.37}$ and $r_{rm h}propto M^{0.28-0.32}$, close to the values expected for homologous virialized systems. At fixed $M$ in the range $10^{11} M_odot lesssim Mlesssim 5.5 times 10^{14} M_odot$ we find $sigma_0propto(1+z)^{0.35}$ and $r_{rm h}propto(1+z)^{-0.7}$. We show that such evolution of the halo scaling laws is driven by individual haloes growing in mass following the evolutionary tracks $sigma_0propto M^{0.2}$ and $r_{rm h}propto M^{0.6}$, consistent with simple dissipationless merging models in which the encounter orbital energy is accounted for. We compare the $N$-body data with ETGs observed at $0lesssim zlesssim3$ by populating the haloes with a stellar component under simple but justified assumptions: the resulting galaxies evolve consistently with the observed ETGs up to $z simeq 2$, but the model has difficulty reproducing the fast evolution observed at $zgtrsim 2$. We conclude that a substantial fraction of the size evolution of ETGs can be ascribed to a systematic dependence on redshift of the dark matter haloes structural properties.
Observational studies are showing that the galaxy-wide stellar initial mass function are top-heavy in galaxies with high star-formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR of a galaxy, it follows that galaxies which have or which formed with SFRs > 10 Msol yr^-1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher M/L ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar initial mass function (IMF). For the Milky Way, the IGIMF yields very good agreement with the disk- and the bulge-IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a pc and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index beta of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.
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