The dark matter distribution in disc galaxies

We use high-quality optical rotation curves of nine low-luminosity disc galaxies to obtain the velocity profiles of the surrounding dark matter haloes. We find that they increase linearly with radius at least out to the edge of the stellar disc, implying that, over the entire stellar region, the density of the dark halo is about constant.
The properties of the mass structure of these haloes are similar to those found for a number of dwarf and low surface brightness galaxies, but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the cold dark matter scenario and those actually detected around galaxies. We find that the density law proposed by Burkert reproduces the halo rotation curves, with halo central densities ( ρ ₀∼1–4×10⁻²⁴ g cm⁻³) and core radii ( r ₀∼5–15 kpc) scaling as ρ ₀∝ r ₀^−2/3.     

Dust-induced chemical differentiation in dense regions

Dust grains respond to the physical and chemical conditions of the interstellar region in which they are embedded. The interaction produces an extinction curve which depends on the local environment and on the past history of the dust grains. In this work we present a theoretical study of the effects of radial variations of dust extinction properties on gas-phase chemistry in spherical core–halo clouds. We use observational constraints on the variation range of the extinction curve, and we analyse if the degree of dust environmental processing could be reflected by chemical signatures in the gas-phase molecular concentrations. The results of this work show that significant variations in the photodestruction rates and in the thermal profile of the cloud might induce chemical patterns otherwise excluded in the standard dense-cloud chemistry. Some discrepancies between observations and theoretical provisions are discussed in the light of the present results.     

A real-time spectrum analyser with on-line definition of the confidence levels

This paper describes a real-time spectrum analyser with on-line definition of the confidence levels built at Trieste Observatory for a research program on periodical components of unknown period in optical sources. The system is realized by a photon counting photometer on-line to a computer that elaborates in real-time the data from the photometer and displays the spectrum of the source measured. The spectrum is normalized to unity mean value and the display is calibrated by the confidence levels relative to the distribution of the spectrum displayed. Some experimental data show the performance of the machine that operates in real-time at full efficiency up to 160 Hz. Work supported by Consiglio Nazionale delle Ricerche, Gruppo Nazionale di Astronomia, Settore Tecnologie Astronomiche. Trieste Observatory — Instruments and Data Processing Group (1/76).     

Certain particular solutions of the clairaut equation

A study has been conducted to ascertain conditions on the density distribution within a fluid, rotating planet in order that the deformation of its outer shell be expressible in terms of the Bessel functions of the first kind and the Gaussian hypergeometric series.It has been established that (1) the density must be a solution to an ordinary differential equation of the Riccati type, and (2) two already considered density distributions are the only closed-form solutions of physical relevance.     

The equilibrium of a rotating body of arbitrary density

This paper extends Clairaut's theory of rotational equilibrium to third order terms in a small parameter and is meant to be a sequel to a 1962 publication by the author bearing on the same topic. It has been feasible to obtain the Clairaut equation, which governs the deformation of the equipotential surfaces within a rapidly rotating mass in hydrostatic equilibrium, as an ordinary differential equation. This has been achieved by eliminating the two integral terms which appeared in the original formulation. It is expected that the numerical integration of this newly obtained equation will contribute toward a more precise solution of certain geophysical problems — e.g., the determination of the geoid to an accuracy of ±1 m, and the correction to the travel-time of seismic waves; it should also assist in some planetary questions like the determination of the exterior shape for the rapidly rotating planets Jupiter and Saturn.     

Dynamical evolution of NEAs: Close encounters, secular perturbations and resonances

We discuss the main mechanisms affecting the dynamical evolution of Near-Earth Asteroids (NEAs) by analyzing the results of three numerical integrations over 1 Myr of the NEA (4179) Toutatis. In the first integration the only perturbing planet is the Earth. So the evolution is dominated by close encounters and looks like a random walk in semimajor axis and a correlated random walk in eccentricity, keeping almost constant the perihelion distance and the Tisserand invariant. In the second integration Jupiter and Saturn are present instead of the Earth, and the 3/1 (mean motion) and v ₆ (secular) resonances substantially change the eccentricity but not the semimajor axis. The third, most realistic, integration including all the three planets together shows a complex interplay of effects, with close encounters switching the orbit between different resonant states and no approximate conservation of the Tisserand invariant. This shows that simplified 3-body or 4-body models cannot be used to predict the typical evolution patterns and time scales of NEAs, and in particular that resonances provide some fast-track dynamical routes from low-eccentricity to very eccentric, planet-crossing orbits.On leave from the Department of Mathematics, University of Pisa, Via Buonarroti 2, 56127 Pisa, Italy, thanks to the G. Colombo fellowships of the European Space Agency.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

XMM–Newton observations of soft gamma-ray repeaters

All the confirmed Soft Gamma-ray Repeaters have been observed with the EPIC instrument on the XMM–Newton satellite. We review the results obtained in these observations, providing the most accurate spectra on the persistent X-ray emission in the 1–10 keV range for these objects, and discuss them in the context of the magnetar interpretation.