Momentum Distribution for Bosons with Positive Scattering Length in a Trap

The coordinate-momentum double distribution function $\rho ({\bf r}, {\bf p}) d^{3}rd^{3}p$ is calculated in the local density approximation for bosons with positive scattering length $a$ in a trap. The calculation is valid to the first order of $a$. To clarify the meaning of the result, it is compared for a special case with the double distribution function $\rho_{w}d^{3} rd^{3}p$ of Wigner.Comment: Latex fil

A Survey of Merger Remnants II: The Emerging Kinematic and Photometric Correlations

This paper is the second in a series exploring the properties of 51 {\it optically} selected, single-nuclei merger remnants. Spectroscopic data have been obtained for a sub-sample of 38 mergers and combined with previously obtained infrared photometry to test whether mergers exhibit the same correlations as elliptical galaxies among parameters such as stellar luminosity and distribution, central stellar velocity dispersion ($\sigma$$_{\circ}$), and metallicity. Paramount to the study is to test whether mergers lie on the Fundamental Plane. Measurements of $\sigma$$_{\circ}$ have been made using the Ca triplet absorption line at 8500 {\AA} for all 38 mergers in the sub-sample. Additional measurements of $\sigma$$_{\circ}$ were made for two of the mergers in the sub-sample using the CO absorption line at 2.29 \micron. The results indicate that mergers show a strong correlation among the parameters of the Fundamental Plane but fail to show a strong correlation between $\sigma$$_{\circ}$ and metallicity (Mg$_{2}$). In contrast to earlier studies, the $\sigma$$_{\circ}$ of the mergers are consistent with objects which lie somewhere between intermediate-mass and luminous giant elliptical galaxies. However, the discrepancies with earlier studies appears to correlate with whether the Ca triplet or CO absorption lines are used to derive $\sigma$$_{\circ}$, with the latter almost always producing smaller values. Finally, the photometric and kinematic data are used to demonstrate for the first time that the central phase-space density of mergers are equivalent to elliptical galaxies. This resolves a long-standing criticism of the merger hypothesis.Comment: Accepted Astronomical Journal (to appear in January 2006

K band Spectroscopy of Ultraluminous Infrared Galaxies: The 2 Jy Sample

We present near-infrared spectroscopy for a complete sample of 33 ultraluminous infrared galaxies at a resolution of R\approx 1000. Most of the wavelength range from 1.80-2.20 microns in the rest frame is covered, including the Pa-alpha and Br-gamma hydrogen recombination lines, and the molecular hydrogen vibration-rotation 1-0 S(1) and S(3) lines. Other species, such as He I, [Fe II], and [Si VI] appear in the spectra as well, in addition to a number of weaker molecular hydrogen lines. Nuclear extractions for each of the individual galaxies are presented here, along with spectra of secondary nuclei, where available. The Pa-alpha emission is seen to be highly concentrated on the nuclei, typically with very little emision extending beyond a radius of 1 kpc. Signatures of active nuclei are rare in the present sample, occurring in only two of the 33 galaxies. It is found that visual extinctions to the nuclei via the Pa-alpha/Br-gamma line ratio in excess of 10 magnitudes are relatively common among ULIRGs, and that visual extinctions greater than 25 mag are necessary to conceal a QSO emitting half the total bolometric luminosity. The vibration-rotation lines of molecular hydrogen appear to be predominantly thermal in origin, with effective temperatures generally around 2200 K. The relative nuclear velocities between double nucleus ULIRGs are investigated, through which it is inferred that the maximum deprojected velocity difference is about 200 km/s. This figure is lower than the velocities predicted by physical models of strong interactions/mergers of large, gas-rich galaxies.Comment: 52 pages (19 with just figures), 9 figures, accepted for publication in the Astronomical Journal; Table 3 not formatted properly on astro-ph: get source and print Murphy.tab3.p

A Second Luminous Blue Variable in the Quintuplet Cluster

H and K band moderate resolution and 4 $\mu$m high resolution spectra have been obtained for FMM#362, a bright star in the Quintuplet Cluster near the Galactic Center. The spectral features in these bands closely match those of the Pistol Star, a luminous blue variable and one of the most luminous stars known. The new spectra and previously-obtained photometry imply a very high luminosity for FMM#362, L $\geq 10^6$ \Lsun, and a temperature of 10,000 - 13,000 K. Based on its luminosity, temperature, photometric variability, and similarities to the Pistol Star, we conclude that FMM#362 is a luminous blue variable.Comment: Accepted for publication in The Astrophysical Journal Letters, 4 PostScript figures, 2 table

Bose-Einstein Condensation of Atoms in a Trap

We point out that the local density approximation (LDA) of Oliva is an adaptation of the Thomas-Fermi method, and is a good approximation when $\varepsilon = \hbar\omega/kT 0$, the LDA leads to a quantitative result (14') easily checked by experiments. Critical remarks are made about the physics of the many body problem in terms of the scattering length $a$.Comment: 9 pages, latex. one figure, available from author

Dynamical properties of Ultraluminous Infrared Galaxies. II. Traces of dynamical evolution and end products of local ultraluminous mergers

We present results from our Very Large Telescope large program to study the dynamical evolution of local Ultraluminous Infrared Galaxies (ULIRGs) and QSOs. This paper is the second in a series presenting the stellar kinematics of 54 ULIRGs, derived from high resolution, long-slit H- and K-band spectroscopy. The data presented here, including observations of 17 new targets, are mainly focused on sources that have coalesced into a single nucleus. The stellar kinematics, extracted from the CO ro-vibrational bandheads in our spectra, indicate that ULIRG remnants are dynamically heated systems with a mean dispersion of 161 km/s. The combination of kinematic, structural, and photometric properties of the remnants indicate that they mostly originate from major mergers and that they result in the formation of systems supported by random motions, therefore, elliptical galaxies. The peak of the velocity dispersion distribution and the locus of ULIRGs on the fundamental plane of early-type galaxies indicate that the end products of ultraluminous mergers are typically moderate-mass ellipticals (of stellar mass ~10^10 - 10^11 M_sun). Converting the host dispersion into black hole mass with the aid of the M_BH-sigma relation yields black hole mass estimates of the order 10^7 - 10^8 M_sun and high accretion rates with Eddington efficiencies often >0.5.Comment: Accepted for publication in the Astrophysical Journa

Gender differences in motivation and perception of utility of the scholar spot

El principal objetivo del estudio es analizar las diferencias entre el nivel de autodeterminación y la satisfacción de las necesidades psicológicas básicas en función del género y su incidencia sobre la percepción de utilidad del deporte. Participaron en el estudio 1897 jóvenes jugadores de baloncesto, balonmano, fútbol y voleibol (1378 chicos y 519 chicas). Diferentes instrumentos fueron utilizados para medir las distintas variables abordadas en el estudio. Los resultados mostraron que los chicos presentan puntuaciones más altas en todos los tipos de motivación y que su sentimiento de competencia es más elevado que el de las chicas. Por otro lado, la motivación autodeterminada y la satisfacción de las necesidades conducen a percibir mayor utilidad del deporte en ambos génerosThe aim of the study was to analyze the differences between self-determination level and satisfaction of the three psychological needs with respect to gender and their influence on the perception of utility of the sport. The sample comprised 1897 basketball, handball, football and volleyball young players (1378 boys and 519 girls). Different measures were used to examine the differences between the variables contained in the study. Results showed that boys were more intrinsically and extrinsically motivated and showed less a motivation than girls, as well as their scored higher in competence than girls. However, both for boys and girls, self-determined motivation and psychological needs satisfaction led to a greater perception of utility of the spor

Analysis of the group process and the performance in semiprofessional soccer

El principal objetivo del estudio es aplicar un modelo teórico analizando dos de los antecedentes de la eficacia colectiva, el clima motivacional y la cohesión grupal, y su principal consecuencia como es el rendimiento. Los participantes fueron 203 futbolistas que participaban en el grupo XIV de la Liga Nacional de Tercera División, que rellenaron diversos instrumentos para valorar el clima motivacional, la cohesión y la eficacia colectiva. Los resultados obtenidos señalan que el modelo teórico que se aplica confirma que el clima que implica a la tarea predice la cohesión grupal. Además, la cohesión tarea se manifiesta como el principal predictor de la eficacia colectiva, y ésta a su vez del rendimiento. La principal conclusión es que para optimizar la percepción de eficacia colectiva y con ello, la mejora del rendimiento, parece fundamental que los entrenadores planteen estrategias para fomentar los aspectos tarea del clima motivacional y la cohesión grupal en los jugadores.The main aim of the study was to test a theoretical model examining two of the antecedents of the collective efficacy, motivational climate and group cohesion, as well as performance as their principal consequence. Participants were 203 footballers who played in the XIV group of National League in Third Division and filled several instruments to assess motivational climate, cohesion and collective efficacy. The theoretical model showed that mastery climate predicted group cohesion. Furthermore, task cohesion emerged as the strongest predictor of collective efficacy, and this variable predicted performance. The main conclusion is that to optimize perception of collective efficacy and so, increase performance, it seems important that coaches promote strategies to enhance task related motivational climate and group cohesion in players