Cloud Models for Solar Faculae

Assuming the clouds as plane parallel structures above the photosphere, center-to-limb contrast variations of various cloud models for solar faculae with approximations such as optically thin or thick, hot or cold, and with or without surface reflections, have been investigated. It has been found that the observed facular contrast data from Frazier (1971) and Taylor et al. (1998) at the 525 nm continuum is best represented by a cloud which is 230 K hotter than the undisturbed photosphere, with an optical depth =0.4283, and with isotropic surface reflections causing 11% of the background photons to be lost before penetrating into the cloud. This model and some other cloud models are shown to provide a fit better than the other physical and non-physical facular models presented previously.     

The phase variations of the solar cycle

It has previously been shown that the statistics of the phase fluctuation of the sunspot cycle are compatible with the assumption that the solar magnetic field is generated deep in the Sun by a frequency stable oscillator and that the observed substantial phase fluctuation in the sunspot cycle is due to variation in the time required for the magnetic field to move to the solar surface (Dicke, 1978, 1979). It was shown that the observed phase shifts are strongly correlated with the amplitude of the solar cycle. It is shown here that of two empirical models for the transport of magnetic flux to the surface, the best fit to the data is obtained with a model for which the magnetic flux is carried to the surface by convection with the convection velocity proportional to a function of the solar cycle amplitude. The best fit of this model to the data is obtained for a 12-yr transit time. The period obtained for the solar cycle is T = 22.219 ± 0.032 yr. It is shown that the great solar anomaly of 1760–1800 is most likely real and not due to poor data.     

Effects of variableC min on gamma-ray burstC max/C min distributions

Claims continue to be made that detector selection effects can explain the deviation of the gamma-ray burst brightness distributions from the -3/2 power law expected for homogeneous burst sources. However, these effects are insufficient to explain the BATSE observations. The BATSE sensitivity threshold does vary with time, independent of the burst brightness; however, a homogeneous distribution of standard candle sources would still produce a -3/2 power law. The variation in the threshold does affect inhomogeneous source models. As an example, the effect of a time-varyingC _min on theC _max/C _min distribution of an extended Galactic halo model is shown here. To fit the BATSEC _max/C _min distribution including a varyingC _min requires a larger observing distance (relative to the scale-height of the halo) than for a constantC _min; however, the observations can still be fit using the halo models.     

On the interpretation of the observed angular-size-flux-density relation for extragalactic radio sources

The interpretation of the observed relation between median angular sizes (θ _m) of extragalactic radio sources and flux density at 408 MHz has been examined. The predictedθ _m-S relations based on well-observed strong sources in parent samples selected at 178 and 1400 MHz, and existing models of the evolving radio luminosity function can be made to fit the observed relation only by invoking cosmological evolution in linear sizes even for theq ₀ = 0 universe. Predictions based on a parent sample at 2.7 GHz are shown to overestimate the contribution of steep-spectrum, compact (SSC) sources in low-frequency samples unless the downward curvature in the spectra of such sources is taken into account. When approximate corrections are made for this effect, predictions based on the 2.7 GHz parent sample cannot obviate the need for linear size evolution as claimed in the literature.     

The G-dwarf problem: A tentative analytical approach,relaxing instantaneous recycling

Starting from a general solution for the birth functionB(m, t) of stars described in detail in Casusoet al. (1989), we have obtained a first-order analytical approximation to this function as a function of metallicityZ. Using this, we obtained a fit to the observational curve compiled by Tinsley (1980) for the cumulative function of stars with metallicity lower than a given value in the solar neighbourhood. In addition, using the same expression, with its numerical fit to previous data, we obtain a good fit to the differential distributions of stars at low metallicity given in the review by Pagel (1987), given a bifurcation in the birth function at low values ofZ, which would correspond to two distinct epochs of onset of star formation. The analysis gives an infall of gas towards the solar neighbourhood up to the epoch of metallicityZ=6.7×10^–3 with a correspondingly increased star formation rate, which subsequently stabilized, and another similar inflow up toZ=1.2×10^–3, followed again by a steady star formation rate for largerZ. Although the assumptions made are still relatively crude, and the numbers should be considered tentative, the flexibility of the model in handling the problem is that we wish to show here.     

Relativistic dynamics for three charged particles

The motions of three charged particles under non-Newtonian assumptions are shown to be expressed by differential equations of order up to 1/c ² in relative coordinates. These equations are then shown to satisfy Lagrange's special solutions, i.e. the equilateral triangle and the collinear ones.     

Can elliptical galaxies be equilibrium systems?

This paper deals with the question of whether elliptical galaxies can be considered as equilibrium systems (i.e., the gravitational+centrifugal potential is constant on the external surface). We find that equilibrium models such as Emden-Chandrasekhar polytropes and Roche polytropes withn=0 can account for the main part of observations relative to the ratio of maximum rotational velocity to central velocity dispersion in, elliptical systems. More complex models involving, for example, massive halos could lead to a more complete agreement. Models that are a good fit to the observed data are characterized by an inner component (where most of the mass is concentrated) and a low-density outer component. A comparison is performed between some theoretical density distributions and the density distribution observed by Younget al. (1978) in NGC 4473, but a number of limitations must be adopted. Alternative models, such as triaxial oblate non-equilibrium configurations with coaxial shells, involve a number of problems which are briefly discussed. We conclude that spheroidal oblate models describing elliptical glaxies cannot be ruled out until new analyses relative to more refined theoretical equilibrium models (involving, for example, massive halos) and more detailed observations are performed.     

The warped disc of NGC 4258

We consider the properties of the warped accretion disc in NGC 4258 which is delineated by maser emission. We use our analytical models to consider whether the disc could be warped by Lense–Thirring precession. We show that such models fit the shape of the disc well and we determine the goodness of fit for various combinations of the warp radius and the disc and black hole configurations. Though the fits are compelling evidence, we note that such a model has implications for the formation and longevity of the disc which might be problematic for the current understanding of Seyfert galaxies.     

Galactic mass determinations from incomplete rotation curves

Given an incomplete rotation curve of a spiral galaxy, various assumptions about the Galaxy beyond the last observed point are made: (A) the force falls off as 1/r ², (B) the mass density is zero, and (C) the mass density falls off as 1/r ³. The msss distributions obtained from each of these assumptions are all well behaved, and it is impossible to choose the correct curve from considerations of the resulting mass distributions alone. The correct mass distribution in the disk system of a galaxy cannot be deduced from an incomplete rotation curve.     

Atmospheric thermal structures of the giant planets

Thermal models of planetary atmospheres can be calculated from assumptions of the energy budget of the atmosphere and from the knowledge of the effective temperature of the studied planet. On the other hand, the retrieval of the thermal atmospheric profiles from infrared measurements by means of the numerical inversion of the radiative transfer equation presents the advantages of not requiring such assumptions. The extent of the atmospheric range which can then be sounded is examined and the vertical resolution of the inferred profiles is discussed. Comparisons of thermal models and retrieved thermal profiles are made for the four giant planets. The retrieved profiles lead to brightness temperature spectra which fit all the available infrared measurements fairly well for Jupiter and Saturn but only part of them for Uranus and Neptune. The values of the planetary effective temperatures calculated from the retrieved profiles show that Jupiter, Saturn, and Neptune have strong internal heating sources while Uranus probably has a very small or null one.     

Pleiades luminosity function: fine structure and new Pre‐MS models

In order to study a model‐dependence of the results achieved in the previous investigations of the Pleiades luminosity function using D'Antona and Mazzitelli (1994) evolutionary tracks, we repeated the computations with the new track system by D'Antona and Mazzitelli (1997). The following main conclusions can be drawn: the new models agree better with observations; the helium abundance needed to fit the Hipparcos distance modulus is reduced to a more reasonable value of Y = 0.31; the cluster age becomes slightly higher and the slope of the initial mass function somewhat lower. The conclusions on the fine structure of the luminosity function do not change significantly due to the application of the new models.     

On the Lifetime of Hot Coronal Plasmas Arising from Nanoflares

The cooling of plasmas in closed coronal loops by thermal conduction is important when considering their detectability at X-ray and EUV wavelengths. A non-local formalism of thermal conduction originating in laboratory plasmas is used and it is shown that while the effect is unlikely to be important for loops that are in a steady state, it does play a significant role in loops that are impulsively heated (e.g., by nanoflares). Such loops are “under-dense”, and so hot electrons have a relatively long mean free path. Analytic and numerical models are presented, and it is shown that conduction cooling times are lengthened quite considerably. A comparison of various cooling times with ionisation times is also presented, and it is noted that this conductive physics may enhance the chances of observing hot nanoflare-heated plasma.     

Geo-Neutrinos: A Systematic Approach to Uncertainties and Correlations

Geo-neutrinos emitted by heat-producing elements (U, Th and K) represent a unique probe of the Earth interior. The characterization of their fluxes is subject, however, to rather large and highly correlated uncertainties. The geochemical covariance of the U, Th and K abundances in various Earth reservoirs induces positive correlations among the associated geo-neutrino fluxes, and between these and the radiogenic heat. Mass-balance constraints in the Bulk Silicate Earth (BSE) tend instead to anti-correlate the radiogenic element abundances in complementary reservoirs. Experimental geo-neutrino observables may be further (anti)correlated by instrumental effects. In this context, we propose a systematic approach to covariance matrices, based on the fact that all the relevant geo-neutrino observables and constraints can be expressed as linear functions of the U, Th and K abundances in the Earth’s reservoirs (with relatively well-known coefficients). We briefly discuss here the construction of a tentative “geo-neutrino source model” (GNSM) for the U, Th, and K abundances in the main Earth reservoirs, based on selected geophysical and geochemical data and models (when available), on plausible hypotheses (when possible), and admittedly on arbitrary assumptions (when unavoidable). We use then the GNSM to make predictions about several experiments (“forward approach”), and to show how future data can constrain a posteriori the error matrix of the model itself (“backward approach”). The method may provide a useful statistical framework for evaluating the impact and the global consistency of prospective geo-neutrino measurements and Earth models.     

Empirical chemical stratifications in magnetic Ap stars: questions of uniqueness

Over the last decades, modelling of the inhomogeneous vertical abundance distributions of various chemical elements in magnetic peculiar A type has largely relied on simple step-function approximations. In contrast, the recently introduced regularized vertical inversion procedure (VIP) is not based on parametrized stratification profiles and has been claimed to yield unique solutions without a priori assumptions as to the profile shapes. It is the question of uniqueness of empirical stratifications which is at the centre of this article. An error analysis establishes confidence intervals about the abundance profiles and it is shown that many different step functions of sometimes widely different amplitudes give fits to the observed spectra which equal the VIP fits in quality. Theoretical arguments are advanced in favour of abundance profiles that depend on magnetic latitude, even in moderately strong magnetic fields. Including cloud, cap and ring models in the discussion, it is shown that uniqueness of solutions cannot be achieved without phase-resolved high signal-to-noise ratio and high spectral resolution ( R ) spectropolarimetry in all four Stokes parameters.     

Power law relating 10.7 cm flux to sunspot number

To investigate the relation between observations of the 10.7 cm flux and the international sunspot number so that a physical unit may be ascribed to historical records, both polynomial and power law models are developed giving the radio flux as a function of sunspot number and vice versa. Bayesian data analysis is used to estimate the model parameters and to discriminate between the models. The effect on the parameter uncertainty and on the relative evidence of normalizing the measure of fit is investigated. The power law giving flux as a function of sunspot number is found to be the most plausible model and may be used to estimate the radio flux from historical sunspot observations.     

Selection Effect in Semimajor Axes of Orbits of Extrasolar Planets

We present a detailed analysis of the distribution of semimajor axes of orbits of extrasolar planets detected by the method of radial velocity measurements. The relation obtained enables one to calculate the probability of the discovery of a planet at a distance r from a star, knowing the masses of the star and the planet and the threshold radial velocity. The selection effect is manifested in the transformation of the distribution functions. A relation is found between the true and observable distributions of the quantity r. The domain of detectability of extrasolar planets is examined under various assumptions about the form of the distribution functions. The available statistical data on observable extrasolar systems are shown to be inadequate to draw detailed conclusions about their structure. Although substantial differences are found between the structures of all detected planetary systems and that of the Solar System, it would be premature to assert the uniqueness of the latter.     

The stellar populations of starburst galaxies through near-infrared spectroscopy

We study the central (inner few hundred parsecs) stellar populations of four starburst galaxies (NGC 34, 1614, 3310 and 7714) in the near-infrared (NIR), from 0.8 to 2.4 μm, by fitting combinations of stellar population models of various ages and metallicities. The NIR spectra of these galaxies feature many absorption lines. For the first time, we fit simultaneously as much as 15 absorption features in the NIR. The observed spectra are best explained by stellar populations containing a sizable amount (20–56 per cent by mass) of ∼1-Gyr-old stellar population with thermally pulsing asymptotic giant branch stars. We found that the metallicity of the stars which dominates the light is solar. Metallicities substantially different from solar give a worse fit. Though the ages and metallicities we estimate using the NIR spectroscopy are in agreement with values from the literature based on the ultraviolet/optical, we find older ages and a larger age spread. This may be due to the fact that the optical is mostly sensitive to the last episode of star formation, while the NIR better maintains the record of previous stellar generations. Another interesting result is that the reddening estimated from the whole NIR spectrum is considerably lower than that based on emission lines. Finally, we find a good agreement of the free emission-line spectrum with photoionization models, using as input spectral energy distribution the synthetic composite template we derived as best fit.     

Inversions for axisymmetric galactic disks

We use two models for the distribution function to solve an inverse problem for axisymmetric disks. These systems may be considered - under certain assumptions - as galactic disks. In some cases the solutions of the resulting integral equations are simple, which allows the determination of the kinematic properties of self-consistent models for these systems. These properties for then = 1 Toomre disk are presented in this study.     

Simulations of stellar disks in galaxies with non-Newtonian interactions

We describe gravitationalN-body simulations to investigate whether various non-Newtonian interactions between the stars of a system could explain the flat rotational curves which are characteristic of actual isolated spiral galaxies. It is shown that replacing the standard Newtonian interaction by the models of Sanders (1984), Kuhn and Kruglyak (1987) and Milgrom (1983), no massive halo (or dark matter) is required to produce the flat rotational curves of the systems under consideration. All models also generate the exponential surface mass density distribution which is in agreement with that observed in disk-shaped galaxies. In relation to the spiral structure of galaxies, we present the evidence that the non-Newtonian interactions can reproduce the multiple armed patterns in stellar disks without dark matter.