The Faber-Jackson relation for early-type galaxies: Dependence on the magnitude range

We take a sample of early-type galaxies from the Sloan Digital Sky Survey (SDSS-DR7, $\sim$ 90 000 galaxies) spanning a range of approximately 7 $mag$ in both $g$ and $r$ filters and analyse the behaviour of the Faber-Jackson relation parameters as functions of the magnitude range. We calculate the parameters in two ways: i) We consider the faintest (brightest) galaxies in each sample and we progressively increase the width of the magnitude interval by inclusion of the brighter (fainter) galaxies (increasing-magnitude-intervals), and ii) we consider narrow-magnitude intervals of the same width ($\Delta M = 1.0$ $mag$) over the whole magnitude range available (narrow-magnitude-intervals). Our main results are that: i) in both increasing and narrow-magnitude-intervals the Faber-Jackson relation parameters change systematically, ii) non-parametric tests show that the fluctuations in the values of the slope of the Faber-Jackson relation are not products of chance variations. We conclude that the values of the Faber-Jackson relation parameters depend on the width of the magnitude range and the luminosity of galaxies within the magnitude range. This dependence is caused, to a great extent by the selection effects and because the geometrical shape of the distribution of galaxies on the $M - \log (\sigma_{0})$ plane depends on luminosity. We therefore emphasize that if the luminosity of galaxies or the width of the magnitude range or both are not taken into consideration when comparing the structural relations of galaxy samples for different wavelengths, environments, redshifts and luminosities, any differences found may be misinterpreted.Comment: 15 pages, 5 figures. A&A. Accepte

Caustics of Compensated Spherical Lens Models

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.Comment: 21 pages, 5 ps figures, eps

The Kormendy Relation for early-type galaxies. Dependence on the magnitude range

Previous studies indicate that faint and bright early-type galaxies (ETGs) present different coefficients and dispersion for their Kormendy relation (KR). A recently published paper states that the intrinsic dispersion of the KR depends on the magnitude range within which the galaxies are contained, therefore, we investigate here whether the magnitude range has also an influence over the values of the coefficients of the KR; $\alpha$ (zero point) and $\beta$ (slope). We perform numerical simulations and analysis of these coefficients for 4 samples of galaxies, which contain an approximate total of 9400 ETGs in a relatively ample magnitude range ($$ $\sim 6 mag$). The analysis of the results makes us conclude that the values of the KR coefficients depend on the width of the magnitude range and the brightness of galaxies within the magnitude range. This dependence is due to the fact that the distribution of galaxies in the $\log (r_{e}) - _{e}$ plane depends on luminosity and that this distribution is not symmetrical, that is, the geometric shape of the distribution of galaxies in the $\log (r_{e}) - _{e}$ plane plays an important role in the determination of the values of the coefficients of the KR.Comment: 22 pages, 10 figures. A&A. Accepte

Probing the cosmic acceleration history and the properties of dark energy from the ESSENCE supernova data with a model independent method

With a model independent method the expansion history $H(z)$, the deceleration parameter $q(z)$ of the universe and the equation of state $w(z)$ for the dark energy are reconstructed directly from the 192 Sne Ia data points, which contain the new ESSENCE Sne Ia data and the high redshift Sne Ia data. We find that the evolving properties of $q(z)$ and $w(z)$ reconstructed from the 192 Sne Ia data seem to be weaker than that obtained from the Gold set, but stronger than that from the SNLS set. With a combination of the 192 Sne Ia and BAO data, a tight constraint on $\Omega_{m0}$ is obtained. At the $1\sigma$ confidence level $\Omega_{m0}=0.278^{+0.024}_{-0.023}$, which is highly consistent with that from the Gold+BAO and SNLS+BAO.Comment: 11 pages, 5 figures, to appear in JCA

On the interpretation of the spectral--energy correlations in long Gamma--Ray Bursts

Recently, Liang & Zhang (2005) found a tight correlation involving only observable quantities, namely the isotropic emitted energy $E_{\gamma,iso}$, the energy of the peak of the prompt spectrum $E^\prime_{p}$, and the jet break time $t^\prime_{j}$. This phenomenological correlation can have a first explanation in the framework of jetted fireballs, whose semiaperture angle $\theta_{j}$ is measured by the jet break time $t^\prime_{j}$. By correcting $E_{\gamma, iso}$ for the angle $\theta_{j}$ one obtains the so called Ghirlanda correlation linking the collimation corrected energy $E_\gamma$ and $E^\prime_{p}$. There are two ways to derive $\theta_{j}$ from $t^\prime_{j}$ in the standard scenario, corresponding to an homogeneous or to a wind-like circumburst medium. We show that the Ghirlanda correlation with a wind-like medium is as tight as (if not tighter) than the Ghirlanda correlation found in the case of an homogeneous medium. There are hence two Ghirlanda correlations, both entirely consistent with the phenomenological Liang & Zhang relation. We consider the difference between the observed correlations and the ones one would see in the comoving frame (i.e. moving with the same bulk Lorentz factor of the fireball). Since both $E_{p}$ and $E_\gamma$ transform in the same way, the wind-like Ghirlanda relation, which is linear, remains linear also in the comoving frame, no matter the distribution of bulk Lorentz factors. Instead, in the homogeneous density case, one is forced to assume the existence of a strict relation between the bulk Lorentz factor and the total energy, which in turn put constraints on the radiation mechanisms of the prompt emission. The wind-like Ghirlanda correlation, being linear, corresponds to different bursts having the same number of photons.Comment: 12 pages, 8 figures, 2 tables. Accepted for publication in Astronomy & Astrophysic

The Fundamental Plane for early-type galaxies. Dependence on the magnitude range

Studying 3 samples of early-type galaxies, which include approximately 8800 galaxies and cover a relatively ample magnitude range ($$ $\sim 5$ $mag$), we find that the coefficients as well as the intrinsic dispersion of the Fundamental Plane depend on the width of the magnitude range within which the galaxies are distributed. We analyse this dependence and the results show that it could be due to the fact that the distribution of galaxies in the space defined by the variables $\log (r_{e}), _{e}, \log(\sigma)$ depends on the luminosity.Comment: 11 pages, 5 figures. MNRAS. Accepte

The population of early-type galaxies at 1<z<2 - New clues on their formation and evolution

[Abridged]We present the morphological analysis based on HST-NICMOS observations in the F160W filter of a sample of 32 early-type galaxies (ETGs) at 1<z<2 with spectroscopic confirmation of their redshift and spectral type. We find that ETGs at are composed of two distinct populations, an older population (oETGs) and a younger population (yETGs) whose mean ages differ by about 1.5-2 Gyr. Young ETGs are not denser than local ones since they follow the size-mass relation of local ETGs and luminosity evolution brings them onto the local Kormendy and size-luminosity relations. On the constrary, old ETGs do not follow the size-mass relation of local ETGs and luminosity evolution does not account for the discrepancy they show with respect to the local size-luminosity and Kormendy relations. An increase of their effective radius R_e by a factor 2.5-3 (a density decrease by a factor 15-30) from z~1.5-2 to z~0 is required to bring these galaxies onto the local scaling relations. The different behaviour shown by the two populations implies different formation and evolution scenarios. The older population must have formed at higher-z in a sort of dissipative gas-rich collapse ables to produce remnants which at z~2 are old and compact. The size evolution they must experience from z~2 to z~0 has to leave unchanged their mass to not exceed the local number of high-mass ETGs. Thus, major merging cannot fit this requirement. The younger population of ETGs can be formed later through subsequent episodes of merging which increased progressively their size and assembled their mass down to z~2. At z<2 they evolve purely in luminosity since episodes of major merging would bring them far from the local scaling relations.Comment: Accepted for publication in MNRAS; 16 pages, 10 figures 2 table