A physical model of Titan's aerosols

Microphysical simulations of Titan's stratospheric haze show that aerosol microphysics is linked to organized dynamical processes. The detached haze layer may be a manifestation of 1 cm sec-1 vertical velocities at altitudes above 300 km. The hemispherical asymmetry in the visible albedo may be caused by 0.05 cm sec-1 vertical velocities at altitudes of 150 to 200 km, we predict contrast reversal beyond 0.6 micrometer. Tomasko and Smith's (1982, Icarus 51, 65-95) model, in which a layer of large particles above 220 km altitude is responsible for the high forward scattering observed by Rages and Pollack (1983, Icarus 55, 50-62), is a natural outcome of the detached haze layer being produced by rising motions if aerosol mass production occurs primarily below the detached haze layer. The aerosol's electrical charge is critical for the particle size and optical depth of the haze. The geometric albedo, particularly in the ultraviolet and near infrared, requires that the particle size be near 0.15 micrometer down to altitudes below 100 km, which is consistent with polarization observations (Tomasko and Smith 1982, West and Smith 1991, Icarus 90, 330-333). Above about 400 km and below about 150 km Yung et al.'s (1984, Astrophys. J. Suppl. Ser. 55, 465-506) diffusion coefficients are too small. Dynamical processes control the haze particles below about 150 km. The relatively large eddy diffusion coefficients in the lower stratosphere result in a vertically extensive region with nonuniform mixing ratios of condensable gases, so that most hydrocarbons may condense very near the tropopause rather than tens of kilometers above it. The optical depths of hydrocarbon clouds are probably less than one, requiring that abundant gases such as ethane condense on a subset of the haze particles to create relatively large, rapidly removed particles. The wavelength dependence of the optical radius is calculated for use in analyzing observations of the geometric albedo. The lower atmosphere and surface should be visible outside of regions of methane absorption in the near infrared. Limb scans at 2.0 micrometers wavelength should be possible down to about 75 km altitude.     

A physical model of quasi-electrostatic whistler-mode propagation

The process of quasi-electrostatic whistler-mode propagation is interpreted in terms of the periodic energy exchange between wave field and perturbed electron currents.     

A physical model of Titan's clouds

We have constructed a model of the physical processes controlling Titan's clouds. Our model produces clouds that qualitatively match the present observational constraints in a wide variety of model atmospheres, including those with low atmospheric pressures (25 mbar) and high atmospheric pressures. We find the following: (1) high atmospheric temperatures (160°K) are important so that there is a large scale height in the first few optical depths of cloud; (2) the aerosol mass production occurs at very low aerosol optical depth so that the cloud particles do not directly affect the photochemistry producing them; (3) the production rate of aerosol mass by chemical processes is probably greater than 3.5 × 10^?14 g cm^?2 sec^?1; (4) and the eddy diffusion coefficient is less than 5 × 10⁶ cm² sec^?1 except perhaps in the top optical depth of the cloud. Our model is not extremely sensitive to particle shape, but it is sensitive to particle density. Higher particle densities require larger aerosol mass production rates to produce satisfactory clouds. Particle densities of unity require a mass production rate on the order of 3.5 × 10^?13 g cm^?2 sec^?1. We also show that an increase in mass input causes a decrease in the mean particle size, as required by J. B. Pollack et al. (1980, Geophys. Res. Lett. 7, 829–832), to explain the observed correlation between the solar cycle and Titan's albedo; that coagulation need not be extremely inefficient in order to obtain realistic clouds as proposed by M. Podolak and E. Podolak (1980, Icarus43, 73–83); that coagulation could be inefficient due to photoelectric charging of the particles; and, that the lifetime of particles near the altitude of unit optical depth is a few months, as required to explain the temporal variability observed by S. T. Suess and G. W. Lockwood and D. P. Cruikshank and J. S. Morgan (1979, Bull. Amer. Astron. Soc.11, 564). Although Titan's aerosols are ottically thick in the vertical direction, the atmosphere is so extended that the horizontal visibility is greater than that found anywhere at Earth's surface.     

Towards a physical model for galactic rotation curves

Extensive and meticulous observations of the rotation curves of galaxies show that they are either flat or gently going up, but rarely decreasing, at large galactocentric distances. Here we show that the gravitational potential which would lead to such rotation curves arises naturally when the visible matter modelled as a collisionless Maxwellian gas is embedded in a dark halo of collisionless particles with a much higher dispersion in velocities.     

Radar observations and a physical model of Asteroid 1580 Betulia

We report Arecibo (2380-MHz, 13-cm) observations of Asteroid 1580 Betulia in May-June 2002. We combine these continuous-wave Doppler spectra and delay-Doppler images with optical lightcurves from the 1976 and 1989 apparitions in order to estimate Betulia's shape and spin vector. We confirm the spin vector solution of Kaasalainen et al. [Kaasalainen, M., and 21 colleagues, 2004. Icarus 167, 178-196], with sidereal period P=6.13836 h and ecliptic pole direction (λ,β)=(136°,+22°), and obtain a model that resembles the Kaasalainen et al. convex-definite shape reconstruction but is dominated by a prominent concavity in the southern hemisphere. We find that Betulia has a maximum breadth of 6.59±0.66 km and an effective diameter of 5.39±0.54 km. These dimensions are in accord with reanalyzed polarimetric and radar data from the 1970s. Our effective diameter is 15% larger than the best radiometric estimate of Harris et al. [Harris, A.W., Mueller, M., Delbó, M., Bus, S.J., 2005. Icarus 179, 95-108], but this difference is much smaller than the size differences between past models. Considering orbits of test particles around Betulia, we find that this asteroid's unusual shape results in six equilibrium points close to its equatorial plane rather than the usual four points; two of these six points represent stable synchronous orbits while four are unstable. Betulia's close planetary encounters can be predicted for over four thousand years into the future.     

A mathematical magnetospheric field model with independent physical parameters

A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings.The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplace's equation with Neumann's boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earth's dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions.The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earth's dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma.The models for the equatorial ring current depend on the D_st-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.     

The physical properties of an analytic model for a relativistic star

An exact solution of Einstein's equations for a static isentropic perfect fluid sphere is examined in detail. The analysis yields a strong indication that the model isstable with respect to infinitesimal radial pulsations. This means that the temperature is decreasing outwards. We prove that the adiabatic speed of sound is everywhere less than the speed of light if and only if the radius of the sphere is larger than 1.61 times its Schwarzschild radius. We further show that the strong energy condition is fulfilled everywhere if and only if the radius is larger than 1.76 times the Schwarzschild radius. The necessary and sufficient condition for the speed of sound to be decreasing outwards is given, and we find that this criterion is fulfilled if the fluid is causal. Taking the values of the pressure and the density to be somewhere given by the maximum values from Baymet al.'s equation of state, i.e., ₀=5.1×10¹⁴ g cm^–3 andp ₀=7.4×10³³ dyne cm^–2, we find the maximum mass of the fluid sphere to be 2.5 solar masses.Dedicated to the memory of the late George Cunliffe McVittie (1904–1988).     

Understanding the behaviour of X-shooter via the application of a physical model

We show how traditional instrument quality control trending can be augmented by the use of a physical instrument model. The ESO VLT archive contains a detailed record of instrument diagnostics and calibration parameters while ESO quality control monitors changes in critical parameters. The physical model allows changes in positions, orientations and other physical properties of a spectrograph to be determined from standard wavelength calibration exposures via an optimisation process that seeks the physical model parameters that best reproduce the calibration features in the data. We introduce physical model parameters to the quality control monitoring. When applying this technique to archived calibration exposures, we find that the results are sensitive to the combination of parameters open to the optimisation process. Therefore we determine the most favourable set of physical parameters to optimise for each arm. We then show correlations between several physical parameters and instrument temperature sensor readings and epoch. In addition we find clear discontinuities in some physical parameter values that correspond to known maintenance events.     

Radar observations and a physical model of contact binary Asteroid 4486 Mithra

Arecibo (2380 MHz, 12.6 cm) and Goldstone (8560 MHz, 3.5 cm) delay-Doppler radar images obtained in July and August of 2000 reveal that 4486 Mithra is an irregular, significantly bifurcated object, with a central valley ∼380 m deep and a long axis potentially exceeding 2 km. With its bimodal appearance, Mithra is a strong candidate for a contact binary asteroid. Sequences of Goldstone images spanning up to 3 h per day show very little rotation and establish that Mithra is an unusually slow rotator. We used Goldstone and Arecibo data to estimate Mithra’s 3D shape and spin state. We obtain prograde (λ = 337°, β = 19°) and retrograde (λ = 154°, β = −19°) models that give comparable fits, have very similar shapes roughly resembling an hourglass, and have a rotation period of 67.5 ± 6.0 h. The dimensions of these two models are very similar; for the prograde solution the maximum dimensions are X = 2.35 ± 0.15 km, Y = 1.65 ± 0.10 km, Z = 1.44 ± 0.10 km. Dynamical analysis of our models suggests that in the past, Mithra most likely went through a period of even slower rotation with its obliquity close to 90°. The spin rate is predicted to be increasing due to thermal torque (YORP), while the obliquity, which is currently +68° and +106° for the prograde and retrograde models, respectively, is predicted to move away from 90°.     

Application of the X‐shooter physical model to flexure analysis

We use the large number of available X‐shooter automatic flexure compensation exposures that have accumulated in the archive to constrain parameters of the instrument physical model. This enables us to establish which physical model parameters vary with instrument orientation and hence directly identify physical mechanisms that give rise to flexure effects in the spectral format (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some results of model calculations of the solar S-component radio emission

Numerical calculations of special characteristics of the solar S-component microwave radiation are presented on the basis of recent sunspot and plage models. Quantitative results are discussed and can be used for the plasma diagnostics of solar active regions by comparisons with observations with high spatial and spectral resolution . The possibility of generalized applications to magnetic stars and stellar activity is briefly noted.     

De Draconis: Spectroscopic orbit,rotation effect and physical model

New spectroscopic observations are used for the determination of orbital elements and for a study of the rotation effect of DE Draconis. The primary component is found to rotate much faster than the synchronous rate and with its axis of rotation possibly inclined with respect to the perpendicular to the orbital plane. The system is fully detached and the stars are relatively young and unevolved.     

Some physical properties and stability of an exact model of a relativistic star

An exact solution of Einstein's field equations for an isentropic fluid sphere is examined. It turns out that the crucial factor for the physical properties and the stability of this model is the degree of incompressibility. Necessary and sufficient conditions are given for the weak and the strong energy conditions to be fulfilled and for the speed of sound to be less than the speed of light. The speed of sound always has a minimum at the center of the fluid sphere. But two possibilities exist: either the speed of sound is increasing all the way outwards to the surface of the sphere, or the speed of sound is first increasing, then reaching a maximum when still inside the fluid sphere, and thereafter decreasing outwards to the surface. The adiabatic index is investigated and is found to be increasing outwards for the actual degrees of compressibility. This adiabatic index is always greater than unity, and the temperature is thus decreasing throughout the sphere. The necessary and sufficient condition for the adiabatic index to be greater than 4/3 is also given. (This is a necessary condition for the fluid sphere to be stable.) Chandrasekhar's pulsation equation with boundary conditions is investigated, and the fluid sphere is found to bestable if and only if the degree of incompressibility is greater than a certain value.Dedicated to the memory of the late Bronislaw Kuchowicz.     

A realistic model for point-sources imaged on array detectors: The model and initial results

We have constructed a computer model for simulation of point-sources imaged on two-dimensional detectors. An attempt has been made to ensure that the model produces data that mimic real data taken with 2-D detectors. To be realistic, such simulations must include randomly generated noise of the appropriate type from all sources (e.g. source, background, and detector). The model is generic and accepts input values for parameters such as pixel size, read noise, source magnitude, and sky brightness. Point-source profiles are then generated with noise and detector characteristics added via our model. The synthetic data are output as simple integrations (onedimensional), as radial slices (two-dimensional), and as intensity-contour plots (three-dimensional). Each noise source can be turned on or off so that they can be studied separately as well as in combination to yield a realistic view of an image. This paper presents the basic properties of the model and some examples of how it can be used to simulate the effects of changing image position, image scale, signal strength, noise characteristics, and data reduction procedures.Use of the model has allowed us to confirm and quantify three points: 1) The use of traditionalsize apertures for photometry of faint point-sources adds substantial noise to the measurement which can significantly degrade the quality of the observation; 2) The number of pixels used to estimate the background is important and must be considered when estimating errors; and 3) The CCD equation normally used by the astronomical community consistently overestimates the signal-to-noise obtainable by a measurement while a revised equation, discussed here, provides a better estimator.     

Analytical and numerical results on the stability of a planetary precessional model

A model for planetary precession is investigated using analytical and numerical techniques. A Hamiltonian function governing the model is derived in terms of action-angle Andoyer-Déprit variables under the assumption of equatorial symmetry. As a first approximation a simplified Hamiltonian with zero-eccentricity is considered and stability estimates are derived using KAM theory. A validation of the analytical results is performed computing Poincaré surfaces of section for the circular and elliptical model. We also investigate the role of the eccentricity and its connection with the appearance of resonances. Special attention is devoted to the particular case of the Earth–Moon system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Report on the physical characteristics of Vaidya-Tikekar's exact relativistic model for a superdense star

We report here the results of our examination of the physical properties of Vaidya-Tikekar's model for a relativistic star. Full details will be published elsewhere. The analysis yields a strong indication that the model is stable with respect to infinitesimal radial oscillations. We find that the adiabatic speed of sound is smaller than the speed of light everywhere inside the fluid sphere if the radius of the sphere is larger than 1.46 times its Schwarzschild radius. We also find that the fluid must necessarily be supraluminal somewhere if the speed of sound is decreasing outwards close to the center. We further find that the strong energy condition is fulfilled everywhere if it is fulfilled at the center. Since the ratio of the pressure p and the density ⋅ is decreasing outwards, this indicates that the temperature gradient is negative. We also find that the relativistic adiabatic index is larger than two. Demanding the fluid to be causal, and taking the pressure and the density to be somewhere given by 7.4 ⋅ 10³³ dynes/cm³ and 5.1 ⋅ 10¹⁴ g/cm³, we calculate the maximum mass of the fluid sphere to be 3 solar masses.     

Chicxulub central crater structure: Initial results from physical property measurements and combined velocity and gravity modeling

Abstract The Chicxulub crater in Mexico is a nearly pristine example of a large impact crater. Its slow burial has left the central impact basin intact, within which there is an apparently uneroded topographic peak ring. Its burial, however, means that we must rely on drill holes and geophysical data to interpret the crater form. Interpretations of crater structures using geophysical data are often guided by numerical modeling and observations at other large terrestrial craters. However, such endeavors are hindered by uncertainties in current numerical models and the lack of any obvious progressive change in structure with increasing crater size. For this reason, proposed structural models across Chicxulub remain divergent, particularly within the central crater region, where the deepest well is only ?1.6 km deep. The shape and precise location of the stratigraphic uplift are disputed. The spatial extent and distribution of the allogenic impact breccias and melt rocks remain unknown, as do the lithological nature of the peak ring and the mechanism for its formation. The objective of our research is to provide a well‐constrained 3D structural and lithological model across the central region of the Chicxulub crater that is consistent with combined geophysical data sets and drill core samples. With this in mind, we present initial physical property measurements made on 18 core samples from the Yaxcopoil‐1 (Yax‐1) drill hole between 400 and 1500 m deep and present a new density model that is in agreement with both the 3D velocity and gravity data. Future collation of petrophysical and geochemical data from Yax‐1 core, as well as further seismic surveys and drilling, will allow us to calibrate our geophysical models—assigning a suite of physical properties to each lithology. An accurate 3D model of Chicxulub is critical to our understanding of large craters and to the constraining of the environmental effects of this impact.     

On the physical conditions in the photospheric network: An improved model of solar faculae

Semi-empirical models of solar faculae, cospatial with strong photospheric magnetic fields, have been constructed from continuum observations. The center-to-limb contrast of the various models was computed taking into account their geometrical shape. The adopted model whose horizontal size was taken to be 750 km, indicates that, in field regions, the temperature begins to rise outwards at z -125 km (above ₅₀₀₀ = 1) and that the extrapolated temperature at z -400 km is about 1500 K above that of the undisturbed atmosphere; the electron density is higher by a factor of about 30.