Exact solutions for the spatial de Vaucouleurs and Sersic laws and related quantities

Using the Mathematica package, we find exact analytical expressions for the so-called de-projected De Vaucouleurs and Sersic laws as well as for related spatial (3D) quantities, such the mass, gravitational potential, the total energy and the central velocity dispersion, generally involved in astronomical calculations expressed in terms of the Meijer G functions.Comment: 11 pages, accepted in A

Collisionless evaporation from cluster elliptical galaxies

We describe a particular aspect of the effects of the parent cluster tidal field (CTF) on stellar orbits inside cluster Elliptical galaxies. In particular we discuss, with the aid of a simple numerical model, the possibility that collisionless stellar evaporation from elliptical galaxies is an effective mechanism for the production of the recently discovered intracluster stellar populations. A preliminary investigation, based on very idealized galaxy density profiles (Ferrers density distributions), showed that over an Hubble time, the amount of stars lost by a representative galaxy may sum up to the 10% of the initial galaxy mass, a fraction in interesting agreement with observational data. The effectiveness of this mechanism is due to the fact that the galaxy oscillation periods near equilibrium configurations in the CTF are comparable to stellar orbital times in the external galaxy regions. Here we extend our previous study to more realistic galaxy density profiles, in particular by adopting a triaxial Hernquist model.Comment: 6 pages, 2 figures. To appear on "Lecture Notes in Physics", proceedings of the Workshop on "Galaxies and Chaos. Theory and Observations", Athens (September 16-19, 2002), G. Contopoulos and N. Voglis, ed

X-ray emission and internal kinematics in early-type galaxies. I. Observations

Long slit spectroscopic data for 7 early-type galaxies with X-ray emission have been analyzed to derive velocity dispersion and radial velocity profiles. Major axis rotation curves out to $R\sim R_e$ are presented. Adding these new data to those available in the literature, we have built a sample of early-type galaxies with detected X-ray emission and known kinematics (central velocity dispersion $\sigma_0$ and maximum rotational velocity $v_r$). Using this sample we investigate from an observational point of view the role of rotation and flattening on the X-ray emission, particularly with regard to the X-ray underluminosity of flat systems. The trend between the X-ray to optical ratio $L_X/L_B$, a measure of the hot gas content of the galaxies, and $v_r/\sigma_0$ is L-shaped, with the X-ray brightest objects confined at $v_r/\sigma_0 <0.4$, both for Es and S0s. Neither for low or intermediate, nor for high $L_X/L_B$, there is any clear correlation between X-ray emission and rotational properties. The trend between $L_X/L_B$ and the ellipticity $\epsilon$ is also L-shaped: there are no high $L_X/L_B$ objects with high $\epsilon$. The existence of a relation between $v_r/\sigma_0$ and $\epsilon$ makes it difficult to assess whether rotation or flattening is at the basis of the trends found. Our observational findings are finally discussed in connection with the effects that rotation and flattening are predicted to have in the cooling flow and in the wind/outflow/inflow scenarios.Comment: 10 pages, plain tex, plus 7 .ps figures and tex-macro mn.tex -- accepted by MNRAS (main journal

Predicting success in the worldwide start-up network

By drawing on large-scale online data we construct and analyze the time-varying worldwide network of professional relationships among start-ups. The nodes of this network represent companies, while the links model the flow of employees and the associated transfer of know-how across companies. We use network centrality measures to assess, at an early stage, the likelihood of the long-term positive performance of a start-up, showing that the start-up network has predictive power and provides valuable recommendations doubling the current state of the art performance of venture funds. Our network-based approach not only offers an effective alternative to the labour-intensive screening processes of venture capital firms, but can also enable entrepreneurs and policy-makers to conduct a more objective assessment of the long-term potentials of innovation ecosystems and to target interventions accordingly

A More Fundamental Plane

We combine strong-lensing masses with SDSS stellar velocity dispersions and HST-ACS effective (half-light) radii for 36 lens galaxies from the Sloan Lens ACS (SLACS) Survey to study the mass dependence of mass-dynamical structure in early-type galaxies. We find that over a 180--390 km/s range in velocity dispersion, structure is independent of lensing mass to within 5%. This result suggests a systematic variation in the total (i.e., luminous plus dark matter) mass-to-light ratio as the origin of the tilt of the fundamental plane (FP) scaling relationship between galaxy size, velocity dispersion, and surface brightness. We construct the FP of the lens sample, which we find to be consistent with the FP of the parent SDSS early-type galaxy population, and present the first observational correlation between mass-to-light ratio and residuals about the FP. Finally, we re-formulate the FP in terms of surface mass density rather than surface brightness. By removing the complexities of stellar-population effects, this mass-plane formulation will facilitate comparison to numerical simulations and possible use as a cosmological distance indicator.Comment: 4+epsilon pages, 1 figure, emulateapj. Revised version accepted for publication in the ApJ Letter

Chemical abundances and radial velocities in the extremely metal-poor galaxy DDO 68

We present chemical abundances and radial velocities of six HII regions in the extremely metal-poor star-forming dwarf galaxy DDO 68. They are derived from deep spectra in the wavelength range 3500 - 10,000 {\AA}, acquired with the Multi Object Double Spectrograph (MODS) at the Large Binocular Telescope (LBT). In the three regions where the [O III]$\lambda$4363 {\AA} line was detected, we inferred the abundance of He, N, O, Ne, Ar, and S through the "direct" method. We also derived the oxygen abundances of all the six regions adopting indirect method calibrations. We confirm that DDO 68 is an extremely metal-poor galaxy, and a strong outlier in the luminosity - metallicity relation defined by star-forming galaxies. With the direct-method we find indeed an oxygen abundance of 12+log(O/H)=7.14$\pm$0.07 in the northernmost region of the galaxy and, although with large uncertainties, an even lower 12+log(O/H)=6.96$\pm$0.09 in the "tail". This is, at face value, the most metal-poor direct abundance detection of any galaxy known. We derive a radial oxygen gradient of -0.06$\pm$0.03 dex/kpc (or -0.30 dex $R_{25}^{-1}$) with the direct method, and a steeper gradient of -0.12$\pm$0.03 dex/kpc (or -0.59 dex $R_{25}^{-1}$) from the indirect method. For the $\alpha$-element to oxygen ratios we obtain values in agreement with those found in other metal-poor star-forming dwarfs. For nitrogen, instead, we infer much higher values, leading to log(N/O)$\sim-1.4$, at variance with the suggested existence of a tight plateau at $-1.6$ in extremely metal poor dwarfs. The derived helium mass fraction ranges from Y=0.240$\pm$0.005 to Y=0.25$\pm$0.02, compatible with standard big bang nucleosynthesis. Finally, we measured HII region radial velocities in the range 479$-$522 km/s from the tail to the head of the "comet", consistent with the rotation derived in the HI.Comment: Accepted for publication in MNRA

The internal structure and formation of early-type galaxies: the gravitational--lens system MG2016+112 at z=1.004

[Abridged] We combine our measurements of the velocity dispersion and the surface brightness profile of the lens galaxy D in the system MG2016+112 (z=1.004) with constraints from gravitational lensing to study its internal mass distribution. We find that: (i) dark matter accounts for >50% of the total mass within the Einstein radius (99% CL), excluding at the 8-sigma level that mass follows light inside the Einstein radius with a constant mass-to-light ratio (M/L). (ii) the total mass distribution inside the Einstein radius is well-described by a density profile ~r^-gamma' with an effective slope gamma'=2.0+-0.1+-0.1, including random and systematic uncertainties. (iii) The offset of galaxy D from the local Fundamental Plane independently constrains the stellar M/L, and matches the range derived from our models, leading to a more stringent lower limit of >60% on the fraction of dark matter within the Einstein radius (99%CL). Under the assumption of adiabatic contraction, the inner slope of the dark matter halo before the baryons collapsed is gamma_i<1.4 (68 CL), marginally consistent with the highest-resolution cold dark matter simulations that indicate gamma_i~1.5. This might indicate that either adiabatic contraction is a poor description of E/S0 formation or that additional processes play a role as well. Indeed, the apparently isothermal density distribution inside the Einstein radius, is not a natural outcome of adiabatic contraction models, where it appears to be a mere coincidence. By contrast, we argue that isothermality might be the result of a stronger coupling between luminous and dark-matter, possibly the result of (incomplete) violent relaxation processes. Hence, we conclude that galaxy D appears already relaxed 8 Gyr ago.Comment: 8 pages, 4 figures, ApJ, in press, minor change

The MOND Fundamental Plane

Modified Newtonian Dynamics (MOND) has been shown to be able to fit spiral galaxy rotation curves as well as giving a theoretical foundation for empirically determined scaling relations, such as the Tully - Fisher law, without the need for a dark matter halo. As a complementary analysis, one should investigate whether MOND can also reproduce the dynamics of early - type galaxies (ETGs) without dark matter. As a first step, we here show that MOND can indeed fit the observed central velocity dispersion $\sigma_0$ of a large sample of ETGs assuming a simple MOND interpolating functions and constant anisotropy. We also show that, under some assumptions on the luminosity dependence of the Sersic n parameter and the stellar M/L ratio, MOND predicts a fundamental plane for ETGs : a log - linear relation among the effective radius $R_{eff}$, $\sigma_0$ and the mean effective intensity $\langle I_e \rangle$. However, we predict a tilt between the observed and the MOND fundamental planes.Comment: 16 pages, 2 figures, 2 tables, accepted for publication on MNRA