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

Tracing the Mass-Assembly History of Galaxies with Deep Surveys

We use the optical and near-infrared galaxy samples from the Munich Near-Infrared Cluster Survey (MUNICS), the FORS Deep Field (FDF) and GOODS-S to probe the stellar mass assembly history of field galaxies out to z ~ 5. Combining information on the galaxies' stellar mass with their star-formation rate and the age of the stellar population, we can draw important conclusions on the assembly of the most massive galaxies in the universe: These objects contain the oldest stellar populations at all redshifts probed. Furthermore, we show that with increasing redshift the contribution of star-formation to the mass assembly for massive galaxies increases dramatically, reaching the era of their formation at z ~ 2 and beyond. These findings can be interpreted as evidence for an early epoch of star formation in the most massive galaxies in the universe.Comment: 3 pages, 2 figures; published in B. Aschenbach, V. Burwitz, G. Hasinger, B. Leibundgut (eds.): "Relativistic Astrophysics and Cosmology - Einstein's Legacy. Proceedings of the Conference held in Munich, 2006", ESO Astrophysics Symposia, Springer Verlag, 2007, p. 310. Replaced to match final published versio

Theory of continuum percolation II. Mean field theory

I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems. This is done by introducing a new variational principle, the basis of which has to be taken, for now, as heuristic. The critical exponents obtained are $\beta= 1$, $\gamma= 1$ and $\nu = 0.5$, which are identical with the mean field exponents of lattice percolation. The critical density in this approximation is \rho_c = 1/\ve where \ve = \int d \x \, p(\x) \{ \exp [- v(\x)/kT] - 1 \}. p(\x) is the binding probability of two particles separated by \x and v(\x) is their interaction potential.Comment: 25 pages, Late

The stellar-subhalo mass relation of satellite galaxies

We extend the abundance matching technique (AMT) to infer the satellite-subhalo and central-halo mass relations (MRs) of galaxies, as well as the corresponding satellite conditional mass functions (CMFs). We use the observed galaxy stellar mass function (GSMF) decomposed into centrals and satellites and the LCDM halo/subhalo mass functions as inputs. We explore the effects of defining the subhalo mass at the time of accretion (m_acc) vs. at the time of observation (m_obs). We test the standard assumption that centrals and satellites follow the same MRs, showing that this assumption leads to predictions in disagreement with observations, specially for m_obs. Instead, when the satellite-subhalo MRs are constrained following our AMT, they are always different from the central-halo MR: the smaller the stellar mass (Ms), the less massive is the subhalo of satellites as compared to the halo of centrals of the same Ms. On average, for Ms<2x10^11Msol, the dark mass of satellites decreased by 60-65% with respect to their masses at accretion time. The resulting MRs for both definitions of subhalo mass yield satellite CMFs in agreement with observations. Also, when these MRs are used in a HOD model, the predicted correlation functions agree with observations. We show that the use of m_obs leads to less uncertain MRs than m_acc, and discuss implications of the obtained satellite-subhalo MR. For example, we show that the tension between abundance and dynamics of MW satellites in LCDM gives if the slope of the GSMF faint-end slope upturns to -1.6.Comment: 13, pages, 4 figures. Accepted for publication in ApJ. Minor changes to previous versio

Theory of continuum percolation III. Low density expansion

We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair connectedness and the mean cluster size. We prove that given an adequate identification of functions, the result is equivalent to the density expansion derived from a completely different point of view by Coniglio et al. [J. Phys A 10, 1123 (1977)] to describe physical clustering in a gas. We then apply our expansion to a system of hypercubes with a hard core interaction. The calculated critical density is within approximately 5% of the results of simulations, and is thus much more precise than previous theoretical results which were based on integral equations. We suggest that this is because integral equations smooth out overly the partition function (i.e., they describe predominantly its analytical part), while our method targets instead the part which describes the phase transition (i.e., the singular part).Comment: 42 pages, Revtex, includes 5 EncapsulatedPostscript figures, submitted to Phys Rev

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

The halo mass function conditioned on density from the Millennium Simulation: insights into missing baryons and galaxy mass functions

The baryon content of high-density regions in the universe is relevant to two critical unanswered questions: the workings of nurture effects on galaxies and the whereabouts of the missing baryons. In this paper, we analyze the distribution of dark matter and semianalytical galaxies in the Millennium Simulation to investigate these problems. Applying the same density field reconstruction schemes as used for the overall matter distribution to the matter locked in halos we study the mass contribution of halos to the total mass budget at various background field densities, i.e., the conditional halo mass function. In this context, we present a simple fitting formula for the cumulative mass function accurate to ~ 5% for halo masses between 10^{10} and 10^{15}Msol/h. We find that in dense environments the halo mass function becomes top heavy and present corresponding fitting formulae for different redshifts. We demonstrate that the major fraction of matter in high-density fields is associated with galaxy groups. Since current X-ray surveys are able to nearly recover the universal baryon fraction within groups, our results indicate that the major part of the so-far undetected warm-hot intergalactic medium resides in low-density regions at low temperatures. Similarly, we show that the differences in galaxy mass functions with environment seen in observed and simulated data stem predominantly from differences in the mass distribution of halos. In particular, the hump in the galaxy mass function is associated with the central group galaxies, and the bimodality observed in the galaxy mass function is therefore interpreted as that of central galaxies versus satellites.Comment: aligned with version published in Ap

The Disk Mass of Spiral Galaxies

We derive the disk masses of 18 spiral galaxies of different luminosity and Hubble Type, both by mass modelling their rotation curves and by fitting their SED with spectro-photometric models. The good agreement of the estimates obtained from these two different methods allows us to quantify the reliability of their performance and to derive very accurate stellar mass-to-light ratio vs color (and stellar mass) relationships.Comment: 5 pages, 4 Figures accepted to M

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