The Two-Component Virial Theorem and the Physical Properties of Stellar Systems

Motivated by present indirect evidences that galaxies are surrounded by dark matter halos, we investigate whether their physical properties can be described by a formulation of the virial theorem which explicitly takes into account the gravitational potential term representing the interaction of the dark halo with the barionic or luminous component. Our analysis shows that the application of such a ``two-component virial theorem'' not only accounts for the scaling relations displayed, in particular, by elliptical galaxies, but also for the observed properties of all virialized stellar systems, ranging from globular clusters to galaxy clusters.Comment: 13 pages, 2 figures, LaTeX, corrected few typos. This version matches the published versio

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

The cluster of galaxies Abell 376

We present a dynamical analysis of the galaxy cluster Abell 376 based on a set of 73 velocities, most of them measured at Pic du Midi and Haute-Provence observatories and completed with data from the literature. Data on individual galaxies are presented and the accuracy of the determined velocities is discussed as well as some properties of the cluster. We obtained an improved mean redshift value z=0.0478^{+0.005}_{-0.006} and velocity dispersion sigma=852^{+120}_{-76}km/s. Our analysis indicates that inside a radius of 900h_{70}^{-1}kpc (15 arcmin) the cluster is well relaxed without any remarkable feature and the X-ray emission traces fairly well the galaxy distribution. A possible substructure is seen at 20 arcmin from the centre towards the Southwest direction, but is not confirmed by the velocity field. This SW clump is, however, kinematically bound to the main structure of Abell 376. A dense condensation of galaxies is detected at 46 arcmin (projected distance 2.6h_{70}^{-1}Mpc) from the centre towards the Northwest and analysis of the apparent luminosity distribution of its galaxies suggests that this clump is part of the large scale structure of Abell 376. X-ray spectroscopic analysis of ASCA data resulted in a temperature kT = 4.3+/-0.4 keV and metal abundance Z = 0.32+/-0.08 Z_solar. The velocity dispersion corresponding to this temperature using the T_X-sigma scaling relation is in agreement with the measured galaxies velocities.Comment: 11 pages, 10 figures, accepted for publication in A&

The structure and dynamics of the AC114 galaxy cluster revisited

We present a dynamical analysis of the galaxy cluster AC114 based on a catalogue of 524 velocities. Of these, 169 (32%) are newly obtained at ESO (Chile) with the VLT and the VIMOS spectrograph. Data on individual galaxies are presented and the accuracy of the measured velocities is discussed. Dynamical properties of the cluster are derived. We obtain an improved mean redshift value z= 0.31665 +/- 0.0008 and velocity dispersion \sigma= 1893+73-82 \kms. A large velocity dispersion within the core radius and the shape of the infall pattern suggests that this part of the cluster is in a radial phase of relaxation with a very elongated radial filament spanning 12000 \kms. A radial foreground structure is detected within the central 0.5/h Mpc radius, recognizable as a redshift group at the same central redshift value. We analyze the color distribution for this archetype Butcher-Oemler galaxy cluster and identify the separate red and blue galaxy sequences. The latter subset contains 44% of confirmed members of the cluster, reaching magnitudes as faint as R_{f}= 21.1 (1.0 magnitude fainter than previous studies). We derive a mass M_{200}= (4.3 \pm 0.7) x 10^15 Msun/h. In a subsequent paper we will utilize the spectral data presented here to explore the mass-metallicity relation for this intermediate redshift cluster.Comment: 17 pages, 11 figures, 4 tables, accepted for publication in MNRA

Círculos matemáticos: uma experiência com alunos ingressantes no ensino superior no contexto da pandemia Covid-19

Os círculos matemáticos são tradicionais em Moscou há mais de cem anos. Eles não formam um conjunto de aulas para uma disciplina, mas fomentam o encontro de alunos com professores e monitores para estudar matemática em grupos. Inspirados em seu funcionamento realizamos, junto aos alunos ingressantes do curso de Ciências Econômicas de uma universidade pública do estado de São Paulo, o projeto de ensino intitulado “círculos matemáticos da economia”. O objetivo do projeto é contribuir com a melhoria da aprendizagem dos alunos que chegam à universidade com diferentes níveis de proficiência em matemática. Assim, este texto descreve e analisa a experiência da realização deste projeto no contexto da pandemia Covid-19. Para tal, lançamos mão de atividades digitais dirigidas aos participantes e das reflexões trazidas pela narrativa do monitor do projeto, através de uma produção escrita. Do ponto de vista metodológico, a discussão realizada a partir das respostas dos alunos em atividades digitais tem natureza quantitativa e mostram dados como o engajamento dos estudantes no projeto e suas percepções com respeito às atividades remotas. Já a discussão realizada em relação à narrativa tem natureza qualitativa e fundamenta-se em uma análise interpretativa, a qual nos leva a conclusão de que o convívio escolar, ainda que digital, é o ponto de partida para a construção da aprendizagem

Dissipationless Collapse of Spherical Protogalaxies and the Fundamental Plane

Following on from the numerical work of Capelato, de Carvalho & Carlberg (1995, 1997), where dissipationless merger simulations were shown to reproduce the "Fundamental Plane" (FP) of elliptical galaxies, we investigate whether the end products of pure, spherically symmetric, one-component dissipationless {\it collapses} could also reproduce the FP. Past numerical work on collisionless collapses have addressed important issues on the dynamical/structural characteristics of collapsed equilibrium systems. However, the study of collisionless collapse in the context of the nature of the FP has not been satisfactorily addressed yet. Our aim in this paper is to focus our attention on the resulting collapse of simple one-component spherical models with a range of different initial virial coefficients. We find that the characteristic correlations of the models are compatible with virialized, centrally homologous systems. Our results strengthen the idea that merging may be a fundamental ingredient in forming non-homologous objects.Comment: 9 pages, 4 Postscript figures, Astronomy & Astrophysics in press (2002). Abstract placement correcte

Intelectuais latino-americanos: o “caráter nacional” em questão

The most recent discussions over national identity refuse the concept of “national feature” understood as changeless essence and as homogeneous phenomenon. However, over the 1930’s and the 1969’s, many Latin-American authors devoted to this kind of study, and tried to define the constituent elements of “being national” in their respective countries, the harms they caused and the chances to overcome them in order to achieve a superior identity.As discussões mais atuais sobre identidade nacional recusam o conceito de “caráter nacional” entendido como essência imutável e como fenômeno homo-gêneo. No entanto, entre as décadas de 1930 e 1960, inúmeros autores latino-americanos se dedicaram a esse tipo de estudo, procurando definir os elementos constitutivos do “ser nacional” em seus respectivos países, os males que eles produziam e as possibilidades de superá-los com o intuito de atingir uma cultura superior. Tal perspectiva indica uma nova forma de relação entre cultura e identidade nacional