Exact solution of a one-dimensional continuum percolation model

I consider a one dimensional system of particles which interact through a hard core of diameter \si and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$ until it diverges at some critical density, the percolation threshold. This system can be mapped onto an off-lattice generalization of the Potts model which I have called the Potts fluid, and in this way, the mean cluster size, pair connectedness and percolation probability can be calculated exactly. The mean cluster size is S = 2 \exp[ \rho (d -\si)/(1 - \rho \si)] - 1 and diverges only at the close packing density \rho_{cp} = 1 / \si . This is confirmed by the behavior of the percolation probability. These results should help in judging the effectiveness of approximations or simulation methods before they are applied to higher dimensions.Comment: 21 pages, Late

The stellar mass function of galaxies to z ~ 5 in the Fors Deep and GOODS-S fields

We present a measurement of the evolution of the stellar mass function (MF) of galaxies and the evolution of the total stellar mass density at 0<z<5. We use deep multicolor data in the Fors Deep Field (FDF; I-selected reaching I_AB=26.8) and the GOODS-S/CDFS region (K-selected reaching K_AB=25.4) to estimate stellar masses based on fits to composite stellar population models for 5557 and 3367 sources, respectively. The MF of objects from the GOODS-S sample is very similar to that of the FDF. Near-IR selected surveys hence detect the more massive objects of the same principal population as do I-selected surveys. We find that the most massive galaxies harbor the oldest stellar populations at all redshifts. At low z, our MF follows the local MF very well, extending the local MF down to 10^8 Msun. The faint end slope is consistent with the local value of alpha~1.1 at least up to z~1.5. Our MF also agrees very well with the MUNICS and K20 results at z<2. The MF seems to evolve in a regular way at least up to z~2 with the normalization decreasing by 50% to z=1 and by 70% to z=2. Objects having M>10^10 Msun which are the likely progenitors of todays L* galaxies are found in much smaller numbers above z=2. However, we note that massive galaxies with M>10^11 Msun are present even to the largest redshift we probe. Beyond z=2 the evolution of the mass function becomes more rapid. We find that the total stellar mass density at z=1 is 50% of the local value. At z=2, 25% of the local mass density is assembled, and at z=3 and z=5 we find that at least 15% and 5% of the mass in stars is in place, respectively. The number density of galaxies with M>10^11 Msun evolves very similarly to the evolution at lower masses. It decreases by 0.4 dex to z=1, by 0.6 dex to z=2, and by 1 dex to z=4.Comment: Accepted for publication in ApJ

Measuring Dark Matter Profiles Non-Parametrically In Dwarf Spheroidals: An Application To Draco

We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal galaxy (dSph) Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7 m telescope at McDonald Observatory. Our non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 = 20 pc is well fit by a power law with slope alpha = -1.0 +/- 0.2, consistent with predictions from cold dark matter simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.NSF-0908639Astronom

The Kormendy relation of massive elliptical galaxies at z~1.5. Evidence for size evolution ?

We present the morphological analysis based on HST-NIC2 (0.075 arcsec/pixel) images in the F160W filter of a sample of 9 massive field (> 10^{11} M_\odot) galaxies spectroscopically classified as early-types at 1.2<z<1.7. Our analysis shows that all of them are bulge dominated systems. In particular, 6 of them are well fitted by a de Vaucouleurs profile (n=4) suggesting that they can be considered pure elliptical galaxies. The remaining 3 galaxies are better fitted by a Sersic profile with index 1.9<n<2.3 suggesting that a disk-like component could contribute up to 30% to the total light of these galaxies. We derived the effective radius R_e and the mean surface brightness within R_e of our galaxies and we compared them with those of early-types at lower redshifts. We find that the surface brightness of our galaxies should get fainter by 2.5 mag from z~1.5 to z~0 to match the surface brightness of the local ellipticals with comparable R_e, i.e. the local Kormendy relation. Luminosity evolution without morphological changes can only explain half of this effect, as the maximum dimming expected for an elliptical galaxy is ~1.6 mag in this redshift range. Thus, other parameters, possibly structural, may undergo evolution and play an important role in reconciling models and observations. Hypothesizing an evolution of the effective radius of galaxies we find that R_e should increase by a factor 1.5 from z~1.5 to z~0.Comment: Accepted for publication in MNRAS, 15 pages, 8 figure

The Bimodal Galaxy Stellar Mass Function in the COSMOS Survey to z~1: A Steep Faint End and a New Galaxy Dichotomy

We present a new analysis of stellar mass functions (MF) in the COSMOS field to fainter limits than has been previously probed to z~1. Neither the total nor the passive or star-forming MF can be well fit with a single Schechter function once one probes below 3e9 Msun. We observe a dip or plateau at masses ~1e10 Msun, and an upturn towards a steep faint-end slope of -1.7 at lower mass at any z<1. This bimodal nature of the MF is not solely a result of the blue/red dichotomy. The blue MF is by itself bimodal at z~1. This suggests a new dichotomy in galaxy formation that predates the appearance of the red sequence. We propose two interpretations for this bimodality. If the gas fraction increases towards lower mass, galaxies with M_baryon~1e10 Msun would shift to lower stellar masses, creating the observed dip. This would indicate a change in star formation efficiency, perhaps linked to supernovae feedback becoming much more efficient. Therefore, we investigate whether the dip is present in the baryonic (stars+gas) MF. Alternatively, the dip could be created by an enhancement of the galaxy assembly rate at ~1e11 Msun, a phenomenon that naturally arises if the baryon fraction peaks at M_halo ~1e12 Msun. In this scenario, galaxies occupying the bump around M* would be identified with central galaxies and the second fainter component having a steep faint-end slope with satellites. While the dip is apparent in the total MF at any z, it appears to shift from the blue to red population, likely as a result of transforming high-mass blue galaxies into red ones. At the same time, we detect a drastic upturn in the number of low-mass red galaxies. Their increase with time reflects a decrease in the number of blue systems and so we tentatively associate them with satellite dwarf galaxies that have undergone quenching.Comment: 16 pages, 10 figures, accepted for publication in Ap

The star formation rate history in the FORS Deep and GOODS South Fields

We measure the star formation rate (SFR) as a function of redshift z up to z \~4.5, based on B, I and (I+B) selected galaxy catalogues from the FORS Deep Field (FDF) and the K-selected catalogue from the GOODS-South field. Distances are computed from spectroscopically calibrated photometric redshifts accurate to (Delta_z / (z_spec+1)) ~0.03 for the FDF and ~0.056 for the GOODS-South field. The SFRs are derived from the luminosities at 1500 Angstroem. We find that the total SFR estimates derived from B, I and I+B catalogues agree very well (\lsim 0.1 dex) while the SFR from the K catalogue is lower by ~0.2 dex. We show that the latter is solely due to the lower star-forming activity of K-selected intermediate and low luminosity (L<L_*) galaxies. The SFR of bright (L>L_*) galaxies is independent of the selection band, i.e. the same for B, I, (I+B), and K-selected galaxy samples. At all redshifts, luminous galaxies (L>L_*) contribute only ~1/3 to the total SFR. There is no evidence for significant cosmic variance between the SFRs in the FDF and GOODs-South field, ~0.1 dex, consistent with theoretical expectations. The SFRs derived here are in excellent agreement with previous measurements provided we assume the same faint-end slope of the luminosity function as previous works (alpha ~ -1.6). However, our deep FDF data indicate a shallower slope of alpha=-1.07, implying a SFR lower by ~0.3 dex. We find the SFR to be roughly constant up to z ~4 and then to decline slowly beyond, if dust extinctions are assumed to be constant with redshift.Comment: 6 pages, 2 figures, Accepted for publication in ApJ

MOIRCS Deep Survey IV: Evolution of Galaxy Stellar Mass Function Back to z ~ 3

We use very deep near-infrared (NIR) imaging data obtained in MOIRCS Deep Survey (MODS) to investigate the evolution of the galaxy stellar mass function back to z~3. The MODS data reach J=24.2, H=23.1, K=23.1 (5sigma, Vega magnitude) over 103 arcmin^2 (wide) and J=25.1, H=23.7, K=24.1 over 28 arcmin^2 (deep) in the GOODS-North region. The wide and very deep NIR data allow us to measure the number density of galaxies down to low stellar mass (10^9-10^10 Msun) even at high redshift with high statistical accuracy. The normalization of the mass function decreases with redshift and the integrated stellar mass density becomes ~ 8-18% of the local value at z~2 and ~ 4-9% at z~3, which are consistent with results of previous studies in general fields. Furthermore, we found that the low-mass slope becomes steeper with redshift from alpha ~- 1.3 at z~1 to alpha ~- 1.6 at z~3, and that the evolution of the number density of low-mass (10^9-10^10 Msun) galaxies is weaker than that of M* (~10^11 Msun) galaxies. This indicates that the contribution of low-mass galaxies to the total stellar mass density has been significant at high redshift. The steepening of the low-mass slope with redshift is opposite trend expected from the stellar mass dependence of the specific star formation rate reported in previous studies. The present result suggests that the hierarchical merging process overwhelmed the effect of the stellar mass growth by star formation and was very important for the stellar mass assembly of these galaxies at 1<~z<~3.Comment: 21 pages, 18 figures, accepted for publication in Ap

Extremely compact massive galaxies at z~1.4

The optical rest-frame sizes of 10 of the most massive (~5x10^{11}h_{70}^{-2}M_sun) galaxies found in the near-infrared MUNICS survey at 1.2<z<1.7 are analysed. Sizes were estimated both in the J and K' filters. These massive galaxies are at least a factor of 4_{-1.0}^{+1.9} (+-1 sigma) smaller in the rest-frame V-band than local counterparts of the same stellar mass. Consequently, the stellar mass density of these objects is (at least) 60 times larger than massive ellipticals today. Although the stellar populations of these objects are passively fading, their structural properties are rapidly changing since that redshift. This observational fact disagrees with a scenario where the more massive and passive galaxies are fully assembled at z~1.4 (i.e. a monolithic scenario) and points towards a dry merger scenario as the responsible mechanism for the subsequent evolution of these galaxies.Comment: 5 pages, 2 figures, 1 table, accepted for publication in MNRAS letter