Conformal gravity: light deflection revisited and the galactic rotation curve failure

We show how Conformal Gravity (CG) has to satisfy a fine-tuning condition to describe the rotation curves of disk galaxies without the aid of dark matter. Interpreting CG as a gauge natural theory yields conservation laws and their associated superpotentials without ambiguities. We consider the light deflection of a point-like lens and impose that the two Schwarzschild-like metrics with and without the lens are identical at infinite distances from the lens. The energy conservation law implies that the parameter $\gamma$ in the linear term of the metric has to vanish, otherwise the two metrics are physically inaccessible from each other. This linear term is responsible to mimic the role of dark matter in disk galaxies and gravitational lensing systems. Our analysis shows that removing the need of dark matter with CG thus relies on a fine-tuning condition on $\gamma$. We also illustrate why the results of previous investigations of gravitational lensing in CG largely disagree. These discrepancies derive from the erroneous use of the deflection angle definition adopted in General Relativity, where the vacuum solution is asymptotically flat, unlike CG. In addition, the lens mass is identified with various combinations of the metric parameters. However, these identifications are arbitrary, because the mass is not a conformally invariant quantity, unlike the conserved charge associated to the energy conservation law. Based on this conservation law and by removing the fine-tuning condition on $\gamma$, i.e. by setting $\gamma=0$, the energy difference between the metric with the point-like lens and the metric without it defines a conformally invariant quantity that can in principle be used for (1) a proper derivation of light deflection in CG, and (2) the identification of the lens mass with a function of the parameters $\beta$ and $k$ of the Schwarzschild-like metric.Comment: 16 pages, 1 figure. Revised version according to the referees comments. The results reported in the original version remain unchange

Clusters and Groups of Galaxies in the Simulated Local Universe

We compare the properties of galaxy groups extracted from the Updated Zwicky Catalogue (UZC) with those of groups extracted from N-body simulations of the local Universe, in a LambdaCDM and a tauCDM cosmology. In the simulations, the initial conditions of the dark matter density field are set to reproduce the present time distribution of the galaxies within 80 Mpc/h from the Milky Way. These initial conditions minimize the uncertainty originated by cosmic variance, which has affected previous analyses of this small volume of the Universe. The simulations also model the evolution of the photometric properties of the galaxy population with semi-analytic prescriptions. The models yield a galaxy luminosity function sensibly different from that of the UZC and are unable to reproduce the distribution of groups and their luminosity content. The discrepancy between the model and the UZC reduces substantially, if we redistribute the luminosity among the galaxies in the simulation according to the UZC luminosity function while preserving the galaxy luminosity rank. The modified LambdaCDM model provides the best match to the UZC: the abundances of groups by harmonic radius, velocity dispersion, mass and luminosity are consistent with observations. We find that this model also reproduces the halo occupation number of groups and clusters. However, the large-scale distribution of groups is marginally consistent with the UZC and the redshift-space correlation function of galaxies on scales larger than 6 Mpc/h is still more than 3-sigma smaller than observed. We conclude that reproducing the properties of the observed groups certainly requires a more sophisticated treatment of galaxy formation, and possibly an improvement of the dark matter model.Comment: 20 pages, 18 figures, accepted by MNRAS. Minor revisions according to referee's comments. Conclusions unchange

Deep spectroscopy in nearby galaxy clusters: III Orbital structure of galaxies in Abell 85

Galaxies in clusters are strongly affected by their environment. They evolve according to several physical mechanisms that are active in clusters. Their efficiency can strongly depend on the orbital configuration of the galaxies. Our aim is to analyse the orbits of the galaxies in the cluster Abell 85, based on the study of the galaxy velocity anisotropy parameter. We have solved the Jeans equation under the assumption that the galaxies in A85 are collisionless objects, within the spherically symmetric gravitational potential of the virialized cluster. The mass of the cluster was estimated with X-ray and caustic analyses. We find that the anisotropy profile of the full galaxy population in A85 is an increasing monotonic function of the distance from the cluster centre: on average, galaxies in the central region (r/r200 < 0.3) are on isotropic orbits, while galaxies in the outer regions are on radial orbits. We also find that the orbital properties of the galaxies strongly depend on their stellar colour. In particular, blue galaxies are on less radial orbits than red galaxies. The different families of cluster galaxies considered here have the pseudo phase-space density profiles Q(r) and Qr(r) consistent with the profiles expected in virialized dark matter halos in $N$-body simulations. This result suggests that the galaxies in A85 have reached dynamical equilibrium within the cluster potential. Our results indicate that the origin of the blue and red colour of the different galaxy populations is the different orbital shape rather than the accretion time.Comment: 15 pages, 15 figures. Accepted for publication at MNRA

The radial metallicity gradients in the Milky Way thick disk as fossil signatures of a primordial chemical distribution

In this letter we examine the evolution of the radial metallicity gradient induced by secular processes, in the disk of an $N$-body Milky Way-like galaxy. We assign a [Fe/H] value to each particle of the simulation according to an initial, cosmologically motivated, radial chemical distribution and let the disk dynamically evolve for 6 Gyr. This direct approach allows us to take into account only the effects of dynamical evolution and to gauge how and to what extent they affect the initial chemical conditions. The initial [Fe/H] distribution increases with R in the inner disk up to R ~ 10 kpc and decreases for larger R. We find that the initial chemical profile does not undergo major transformations after 6 Gyr of dynamical evolution. The final radial chemical gradients predicted by the model in the solar neighborhood are positive and of the same order of those recently observed in the Milky Way thick disk. We conclude that: 1) the spatial chemical imprint at the time of disk formation is not washed out by secular dynamical processes, and 2) the observed radial gradient may be the dynamical relic of a thick disk originated from a stellar population showing a positive chemical radial gradient in the inner regions.Comment: 10 pages, 5 figures, Accepted for publication on Astrophysical Journal Letter

The Spatial and Kinematic Distributions of Cluster Galaxies in a LCDM Universe -- Comparison with Observations

We combine dissipationless N-body simulations and semi-analytic models of galaxy formation to study the spatial and kinematic distributions of cluster galaxies in a LCDM cosmology. We investigate how the star formation rates, colours and morphologies of galaxies vary as a function of distance from the cluster centre and compare our results with the CNOC1 survey of galaxies from 15 X-ray luminous clusters in the redshift range 0.18 to 0.55. In our model, gas no longer cools onto galaxies after they fall into the cluster and their star formation rates decline on timescales of 1-2 Gyr. Galaxies in cluster cores have lower star formation rates and redder colours than galaxies in the outer regions because they were accreted earlier. Our colour and star formation gradients agree with those those derived from the data. The difference in velocity dispersions between red and blue galaxies observed in the CNOC1 clusters is also well reproduced by the model. We assume that the morphologies of cluster galaxies are determined solely by their merging histories. Morphology gradients in clusters arise naturally, with the fraction of bulge- dominated galaxies highest in cluster cores. We compare these gradients with the CNOC1 data and find excellent agreement for bulge-dominated galaxies. The simulated clusters contain too few galaxies of intermediate bulge-to-disk ratio, suggesting that additional processes may influence the morphological evolution of disk-dominated galaxies in clusters. Although the properties of the cluster galaxies in our model agree extremely well with the data, the same is not true of field galaxies. Both the star formation rates and the colours of bright field galaxies appear to evolve much more strongly from redshift 0.2 to 0.4 in the CNOC1 field sample than in our simulations.Comment: 17 pages, sumitted to MNRAS. Simulation outputs, halo catalogs, merger trees and galaxy catalogs are now available at http://www.mpa-garching.mpg.de/GIF

Deep spectroscopic luminosity function of Abell 85: no evidence for a steep upturn of the faint-end slope

We present a new deep determination of the spectroscopic LF within the virial radius of the nearby and massive Abell\,85 (A85) cluster down to the dwarf regime (M* + 6) using VLT/VIMOS spectra for $\sim 2000$ galaxies with m$_r \leq 21$ mag and $\langle \mu_{e,r} \rangle \leq 24$ mag arcsec$^{-2}$. The resulting LF from 438 cluster members is best modelled by a double Schechter function due to the presence of a statistically significant upturn at the faint-end. The amplitude of this upturn ($\alpha_{f} = -1.58^{+0.19}_{-0.15}$), however, is much smaller than that of the SDSS composite photometric cluster LF by Popesso et al. 2006, $\alpha_{f} \sim$ -2. The faint-end slope of the LF in A85 is consistent, within the uncertainties, with that of the field. The red galaxy population dominates the LF at low luminosities, and is the main responsible for the upturn. The fact that the slopes of the spectroscopic LFs in the field and in a cluster as massive as A85 are similar suggests that the cluster environment does not play a major role in determining the abundance of low-mass galaxies.Comment: 6 pages, 4 figures, accepted at MNRAS lette

X-ray Emitting GHz-Peaked Spectrum Galaxies: Testing a Dynamical-Radiative Model with Broad-Band Spectra

In a dynamical-radiative model we recently developed to describe the physics of compact, GHz-Peaked-Spectrum (GPS) sources, the relativistic jets propagate across the inner, kpc-sized region of the host galaxy, while the electron population of the expanding lobes evolves and emits synchrotron and inverse-Compton (IC) radiation. Interstellar-medium gas clouds engulfed by the expanding lobes, and photoionized by the active nucleus, are responsible for the radio spectral turnover through free-free absorption (FFA) of the synchrotron photons. The model provides a description of the evolution of the spectral energy distribution (SED) of GPS sources with their expansion, predicting significant and complex high-energy emission, from the X-ray to the gamma-ray frequency domain. Here, we test this model with the broad-band SEDs of a sample of eleven X-ray emitting GPS galaxies with Compact-Symmetric-Object (CSO) morphology, and show that: (i) the shape of the radio continuum at frequencies lower than the spectral turnover is indeed well accounted for by the FFA mechanism; (ii) the observed X-ray spectra can be interpreted as non-thermal radiation produced via IC scattering of the local radiation fields off the lobe particles, providing a viable alternative to the thermal, accretion-disk dominated scenario. We also show that the relation between the hydrogen column densities derived from the X-ray (N_H) and radio (N_HI) data of the sources is suggestive of a positive correlation, which, if confirmed by future observations, would provide further support to our scenario of high-energy emitting lobes.Comment: 29 pages, 3 figures, 6 tables; to appear in ApJ. A few clarifications included, according to referee's suggestion

Implications for dwarf spheroidal mass content from interloper removal

Using the caustic method, we identify the member stars of five dwarf spheroidal (dSph) galaxies of the Milky Way, the smallest dark matter (DM) dominated systems in the Universe. After our interloper rejection, we compute line-of-sight velocity dispersion profiles that are substantially smoother than previous results. Moreover, two dSphs have line-of-sight velocity dispersions 20% smaller than previous calculations suggested. Our Jeans modelling confirms that the DM content interior to 300pc is roughly constant with satellite luminosity. Finally, if we assume that MOND provides the true law of gravity, our identification of interlopers implies that four dSphs have mass-to-light ratios in agreement with stellar population synthesis models, whereas Carina still has a mass-to-light ratio a factor of two too large and remains a problem for MOND.Comment: A&A accepted, 13 pages, 14 figures, 4 table