The Function of the Second Postulate in Special Relativity

Many authors noted that the principle of relativity, together with space-time symmetries, suffices to derive Lorentz-like coordinate transformations between inertial frames. These contain a free parameter, $k$, (equal to $c^{-2}$ in special relativity) which is usually claimed to be empirically determinable, so that special relativity does not need the postulate of constancy of the speed of light. I analyze this claim and find that all methods destined to measure $k$ fail without further assumptions, similar to the second postulate. Specifically, measuring $k$ requires a signal that travels identically in opposite directions (this is unrelated to the conventionality of synchronization, as the one-postulate program implicitly selects the standard synchronization convention). Positing such a property about light is logically weaker than Einstein's second postulate but suffices to recover special relativity in full

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

Bulgeless Giant Galaxies Challenge our Picture of Galaxy Formation by Hierarchical Clustering

We dissect giant Sc-Scd galaxies with Hubble Space Telescope photometry and Hobby-Eberly Telescope spectroscopy. We use HET's High Resolution Spectrograph (resolution = 15,000) to measure stellar velocity dispersions in the nuclear star clusters and pseudobulges of the pure-disk galaxies M33, M101, NGC 3338, NGC 3810, NGC 6503, and NGC 6946. We conclude: (1) Upper limits on the masses of any supermassive black holes are MBH <= (2.6+-0.5) * 10**6 M_Sun in M101 and MBH <= (2.0+-0.6) * 10**6 M_Sun in NGC 6503. (2) HST photometry shows that the above galaxies contain tiny pseudobulges that make up <~ 3 % of the stellar mass but no classical bulges. We inventory a sphere of radius 8 Mpc centered on our Galaxy to see whether giant, pure-disk galaxies are common or rare. In this volume, 11 of 19 galaxies with rotation velocity > 150 km/s show no evidence for a classical bulge. Four may contain small classical bulges that contribute 5-12% of the galaxy light. Only 4 of the 19 giant galaxies are ellipticals or have classical bulges that contribute 1/3 of the galaxy light. So pure-disk galaxies are far from rare. It is hard to understand how they could form as the quiescent tail of a distribution of merger histories. Recognition of pseudobulges makes the biggest problem with cold dark matter galaxy formation more acute: How can hierarchical clustering make so many giant, pure-disk galaxies with no evidence for merger-built bulges? This problem depends strongly on environment: the Virgo cluster is not a puzzle, because >2/3 of its stellar mass is in merger remnants.Comment: 28 pages, 16 Postscript figures, 2 tables; requires emulateapj.sty and apjfonts.sty; accepted for publication in ApJ; for a version with full resolution figures, see http://chandra.as.utexas.edu/~kormendy/kdbc.pd