Thermal conductivity measurements of porous dust aggregates: I. Technique, model and first results

We present a non-invasive technique for measuring the thermal conductivity of fragile and sensitive materials. In the context of planet-formation research, the investigation of the thermal conductivity of porous dust aggregates provide important knowledge about the influence of heating processes, like internal heating by radioactive decay of short-lived nuclei, e.g. ²⁶Al, on the evolution and growth of planetesimals. The determination of the thermal conductivity was performed by a combination of laboratory experiments and numerical simulations. An IR camera measured the temperature distribution of the sample surface heated by a well-characterized laser beam. The thermal conductivity as free parameter in the model calculations, exactly emulating the experiment, was varied until the experimental and numerical temperature distributions showed best agreement. Thus, we determined for three types of porous dust samples, consisting of spherical, 1.5 μm-sized SiO₂ particles, with volume filling factors in the range of 15-54%, the thermal conductivity to be 0.002-0.02 W m⁻¹ K⁻¹, respectively. From our results, we can conclude that the thermal conductivity mainly depends on the volume filling factor. Further investigations, which are planned for different materials and varied contact area sizes (produced by sintering), will prove the appropriate dependencies in more detail.     

Accurate and approximate calculations of Raman scattering in the atmosphere of Neptune

Raman scattering by H₂ in Neptune's atmosphere has significant effects on its reflectivity for λ<0.5 μm, producing baseline decreases of ∼20% in a clear atmosphere and ∼10% in a hazy atmosphere. However, few accurate Raman calculations are carried out because of their complexity and computational costs. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH₄ bands is mainly Raman scattered is not valid for current estimates of the CH₄ vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by ∼6% in the 0.22-0.26 μm range and by ∼13% in the 0.35-0.45 μm range. A sample haze model with 0.2 optical depths of 0.2-μm radius particles between 0.1 and 0.8 bars fits reasonably well, but is not a unique solution. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, 174-192) method of applying Raman corrections to calculated spectra and removing Raman effects from observed spectra is shown to have limited applicability and to undercorrect the depths of weak CH₄ absorption bands. The relatively large Q-branch contribution observed by Karkoschka is shown to be consistent with current estimates of Raman cross-sections. The Wallace (1972, Astrophys. J. 176, 249-257) approximation, produces geometric albedo ∼5% low as originally proposed, but can be made much more accurate by including a scattering contribution from the vibrational transition. The original Pollack et al. (1986, Icarus 65, 442-466) approximation is inaccurate and unstable, but can be greatly improved by several simple modifications. A new approximation based on spectral tuning of the effective molecular single scattering albedo provides low errors for zenith angles below 70° in a clear atmosphere, although intermediate clouds present problems at longer wavelengths.     

Calculated atmospheric color refraction and observed stellar positions

Astrometric observations at different zenith distances have been performed in Dresden in an area centered atNGC 6791 where there are some stars with reliable color information (widely dispersed spectral types in the MK systemand color indices B_T – V_T) as well as with accurate positions from Tycho‐2 catalog. The results are used to estimate how significant improvements in stellar positions may be when accurate corrections for color refraction are taken into account. We have treated two cases for refraction calculations: (1) a photometric case for color indices and (2) a spectral case for spectral types and luminosity classes. To calculate refraction we use Stone's modified computer code (Malyuto & Meinel 2000). To treat the photometric case we have calculated the synthetic color indices for the spectral energy distributions of Sviderskiene (1988). The positional improvements due to including color refraction corrections are significant and slightly larger in the spectral case. An improvement of about 15% is reached at a zenith distance of 65°. Our basic conclusion is that color refraction should be taken into account for obtaining accurate stellar positions from ground based observations at larger zenith distances. Reliable refraction corrections may be calculated from spectral and/or photometric data.     

He Conductivity in Cool White Dwarf Atmospheres

We investigate the conductivity of warm dense helium under conditions found in the atmospheres of cool white dwarfs using ab initio simulations. The calculations performed consist of quantum molecular dynamics simulations where the electronic wavefunction at each time step is obtained using density functional theory, while the ion trajectories are calculated using the resulting quantum mechanical forces. We use both conventional DFT (PW91) and hybrid (PBE0) functionals to calculate the conductivities that provide an estimate of the ionization fraction. While the calculations are in good agreement with the measurements for the equation of state, a significant discrepancy exists with the recently measured conductivity.     

A simple analytic model of reconnection in a high-temperature turbulent sheet

We present a simple model of high-temperature (T≥10⁸ K) turbulent current sheets forming in magnetic-reconnection regions on the Sun. The model is based on an empirical formula by de Kluiver et al. (1991) for turbulent plasma conductivity and is apparently valid over a wide range of physical conditions. A comparison of the new results with known test calculations suggests agreement between the theoretical and empirical approaches to calculating the anomalous conductivity in turbulent plasma. The energy release in current sheets is powerful enough for flares, coronal transients, and coronal mass ejections to be interpreted.     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – II. Solution of the induction equations

We have solved numerically the general relativistic induction equations in the interior background space–time of a slowly rotating magnetized neutron star. The analytic form of these equations was discussed recently (Paper I), where corrections due to both the space–time curvature and the dragging of reference frames were shown to be present. Through a number of calculations we have investigated the evolution of the magnetic field with different rates of stellar rotation, different inclination angles between the magnetic moment and the rotation axis, as well as different values of the electrical conductivity. All of these calculations have been performed for a constant-temperature relativistic polytropic star and make use of a consistent solution of the initial-value problem which avoids the use of artificial analytic functions. Our results show that there exist general relativistic effects introduced by the rotation of the space–time which tend to decrease the decay rate of the magnetic field. The rotation-induced corrections are however generally hidden by the high electrical conductivity of the neutron star matter, and when realistic values for the electrical conductivity are considered, these corrections become negligible even for the fastest known pulsar.     

Numerical simulation of cometary nuclei: III. Internal temperatures of cometary nuclei

A one-dimensional heat-diffusion model was used to calculate internal temperatures in cometary nuclei composed of either crystalline or amorphous ice, and for a range of orbits. It was found that the final central temperature, T_c, was a complex function of the comet's orbital semimajor axis, a, and eccentricity, e, as well as the functional form of the thermal conductivity. For cometary nuclei with identical thermal properties, T_c was found to decrease with eccentricity for a short-period orbit with a = 3 AU. For an intermediate-period orbit with a = 20 AU, T_c initially increased with eccentricity but then declined at large values of e for a crystalline ice nucleus, while for amorphous ice T_c increased monotonically. In addition, it was found that for conductivities of similar magnitude, crystalline ice (for which the conductivity varies inversely proportional to temperature) reached the final central temperature twice as fast as amorphouslike ice (for which the conductivity is proportional to temperature). T_c also depended on the magnitude of the conductivity. A four- to fivefold decrease in the conductivity resulted in a 3–4°K decrease in T_c at large eccentricities, while at small eccentricities T_c was only weakly dependent on the conductivity. Finally, the numerical results are compared to the analytical solutions of J. Klinger (1981, Icarus 47, 320–324) and C. P. McKay, S. W. Squyres, and R. T. Reynolds (1986, Icarus, 66, 625–629), and a numerical correction factor is derived for the McKay et al. expression for the central temperature.     

Unipolar induction in the moon and a lunar limb shock mechanism

The unipolar induction mechanism is employed to calculate electric field profiles in the interior of a chemically homogeneous Moon possessing a steep radial thermal gradient characteristic of long-term radioactive heating. The thermal models used are those of Fricker, Reynolds, and Summers. From the magnetic field, the magnetic back pressure upon the solar wind is found. The electric field profile is shown to depend only upon the activation energy,E _o, of the geological material and the radial gradient of the reciprocal temperature. The current is additionally dependent upon the coefficient of the electrical conductivity function but only by a scale factor. Since the Moon is experimentally known to correspond to the case of weak interaction with the solar wind, the magnetic back pressure is calculated without the need for an iterative procedure. The results indicate that a hot Moon can yield sufficient current flow so that the magnetic back pressure is observable as a vestigial limb shock wave using an activation energy of about 2/3 eV together with a conductivity coefficient of about 10³ mhos/m. Such matter is approximated by diabase-like composition, although the result that both the activation energy and coefficient enter into the current determination does not rule out the possibility of a match with other similar substances. The calculations are entirely consistent with earlier results which indicated a model where the unipolar current density is dominated by a high impedance surface layer and a strong shock wave is inhibited. In addition to the magnetic back pressure, the integration of the current continuity equation permits current densities and joule heating rates to be calculated, though the magnitude of the latter for present solar wind conditions is not thermally important.On leave from NASA Ames Research Center     

Thermophysical properties of Almahata Sitta meteorites (asteroid 2008 TC3) for high‐fidelity entry modeling

Asteroid 2008 TC₃ was characterized in a unique manner prior to impacting Earth's atmosphere, making its October 7, 2008, impact a suitable field test for or validating the application of high‐fidelity re‐entry modeling to asteroid entry. The accurate modeling of the behavior of 2008 TC₃ during its entry in Earth's atmosphere requires detailed information about the thermophysical properties of the asteroid's meteoritic materials at temperatures ranging from room temperature up to the point of ablation (T ~ 1400 K). Here, we present measurements of the thermophysical properties up to these temperatures (in a 1 atm. pressure of argon) for two samples of the Almahata Sitta meteorites from asteroid 2008 TC₃: a thick flat‐faced ureilite suitably shaped for emissivity measurements and a thin flat‐faced EL6 enstatite chondrite suitable for diffusivity measurements. Heat capacity was determined from the elemental composition and density from a 3‐D laser scan of the sample. We find that the thermal conductivity of the enstatite chondrite material decreases more gradually as a function of temperature than expected, while the emissivity of the ureilitic material decreases at a rate of 9.5 × 10^?5 K^?1 above 770 K. The entry scenario is the result of the actual flight path being the boundary to the load the meteorite will be affected with when entering. An accurate heat load prediction depends on the thermophysical properties. Finally, based on these data, the breakup can be calculated accurately leading to a risk assessment for ground damage.     

Non‐equilibrium concepts lead to a unified explanation of the formation of chondrules and chondrites

Abstract— Calculations of the formation of seven types of chondrules in Semarkona from a gas of solar composition were performed with the FACT computer program to predict the chemistries of oxides (including silicates), developed by the authors and their colleagues. The constrained equilibrium theory was used in the calculations with two nucleation constraints suggested by nucleation theory. The first constraint was the blocking of Fe and other metal gaseous atoms from condensing to form solids or liquids because of very high surface free energies and high surface tensions of the solid and liquid metals, respectively. The second constraint was the blocking of the condensation of solids and the formation of metastable liquid oxides (including silicates) well below their liquidus temperatures. Our laboratory experiments suggested subcooling of type IIA chondrule compositions of 400 degrees or more below the liquidus temperature. The blocking of iron leads to a supersaturation of Fe atoms, so that the partial pressure of Fe (p_Fe) is larger than the partial pressure at equilibrium (p_Fe(eq)). The supersaturation ratio S = p_Fe/p_Fe(eq) becomes larger than 1 and increases rapidly with a decrease in temperature. This drives the reaction Fe + H₂O ? H₂ + FeO to the right. With S = 100, the activity of FeO in the liquid droplet is 100 times as large as the value at equilibrium. The FeO activities are a function of temperature and provide relative average temperatures of the crystallization of chondrules. Our calculations for the LL3.0 chondrite Semarkona and our study of some non‐equilibrium effects lead to accurate representations of the compositions of chondrules of types IA, IAB, IB, IIA, IIAB, IIB, and CC. Our concepts readily explain both the variety of FeO concentrations in the different chondrule types and the entire process of chondrule formation. Our theory is unified and could possibly explain the formation of chondrules in all chondritic meteorites as well as provide a simple explanation for the complex chemistries of chondrites, and especially for type 3 chondrites.     

The compressed geomagnetic field as a function of dipole tilt

The currents on the precisely calculated magnetosphere surface previously reported have been integrated with the same accuracy as used in the surface calculation to give the magnetic field at 688 points within the magnetosphere for each of eight surfaces for the tilt of the Earth's dipole in steps of 5° between 0° and 35°. The magnetic fields have then been used to fit the coefficients of a 35 term spherical harmonic expansion of the scalar magnetic potential representing the field by the method of least squares fit. The coefficients for each of the eight surfaces were then represented as a power series in dipole tilt angle, λ so that the complete field can be given very conveniently for any λ. For λ = 0, the first two coefficients g₁₀ and g₂₁ are the dominant terms and the azimuthally dependent term g₂₁ is 30 per cent less than that calculated by Mead and Midgley from older less accurate surface and field calculations.     

Self‐similar evolutionary solutions for an accreting magneto‐fluid around a compact object with finite electrical conductivity

In this paper, we investigate the time evolution of an accreting magneto‐fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell's equations are derived in a simplified, one‐dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity of the plasma is taken into account by Ohm's law; however, the shear viscous stress is neglected, as well as the self‐gravity of the disk. In order to solve the integrated equations that govern the dynamical behaviour of the magneto‐fluid, we have used a self‐similar solution. We introduce two dimensionless variables, S₀ and ε_ϱ, which represent the size of the electrical conductivity and the density behaviour with time, respectively. The effect of each of these on the structure of the disk is studied. While the pressure is obtained simply by solving an ordinary differential equation, the density, the magnetic field, the radial velocity, and the rotational velocity are presented analytically. The solutions show that the S0 and ε_ϱ parameters affect the radial thickness of the disk. Also, radial velocity and gas pressure are more sensitive to the electrical conductivity in the inner regions of disk. Moreover, the parameter ε_ϱ has a more significant effect on the physical quantities for small radii. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Predictions of the electrical conductivity and charging of the aerosols in Titan's atmosphere

The electrical conductivity and electrical charge on the aerosols in atmosphere of Titan are computed for altitudes between 0 and 400 km. Ionization of methane and nitrogen due to galactic cosmic rays (GCR) is important at night where these ions are converted to ion clusters such as CH⁺₅CH₄, C₇H⁺₇, C₄H⁺₇, and H₄C₇N⁺. The ubiquitous aerosols observed also play an important role in determining the charge distribution in the atmosphere. Because polycyclic aromatic hydrocarbons (PAHs) are expected in Titan's atmosphere and have been observed in the laboratory and found to be electrophilic, we consider the formation of negative ions. During the night, the very smallest molecular complexes accept free electrons to form negative ions. This results in a large reduction of the electron abundance both in the region between 150 and 350 km over that predicted when such aerosols are not considered. During the day time, ionization by photoemission from aerosols irradiated by solar ultraviolet (UV) radiation overwhelms the GCR-produced ionization. The presence of hydrocarbon and nitrile minor constituents substantially reduces the UV flux in the wavelength band from the cutoff of CH₄ at 155 to 200 nm. These aerosols have such a low ionization potential that the bulk of the solar radiation at longer wavelengths is energetic enough to produce a photoionization rate sufficient to create an ionosphere even without galactic cosmic ray (GCR) bombardment. At altitudes below 60 km, the electron and positive ion abundances are influenced by the three-body recombination of ions and electrons. The addition of this reaction significantly reduces the predicted electron abundance over that previously predicted. Our calculations for the dayside show that the peaks of the charge distributions move to larger values as the altitude increases. This variation is the result of the increased UV flux present at the highest altitudes. Clearly, the situation is quite different than that for the night where the peak of the distribution for a particular size is nearly constant with altitude when negative ions are not present. The presence of very small aerosol particles (embryos) may cause the peak of the distribution to decrease from about 8 negative charges to as little as one negative charge or even zero charge. This dependence on altitude will require models of the aerosol formation to change their algorithms to better represent the effect of charged aerosols as a function of altitude. In particular, the charge state will be much higher than previously predicted and it will not be constant with altitude during the day time. Charging of aerosol particles, whether on the dayside or nightside, has a major influence on both the electron abundance and electrical conductivity. The predicted conductivities are within the measurement range of the HASI PWA instrument over most but not all, of the altitude range sampled.     

Predicted electrical conductivity between 0 and 80 km in the Venusian atmosphere

Calculations of the space charge, ion density, and conductivity in the Venus atmosphere were made. The presence of the cloud particles on Venus causes a profound reduction in the calculated values of the ion density and conductivity compared to the values that are obtained without consideration of the cloud particles. When the cloud particles are included in the calculations, the results for the ion density and conductivity are approximately the same as those of the terrestrial atmosphere at the same pressure-altitude. Because the particles span such a large range of sizes and are abundant over a substantial range of pressure, the space charge varies strongly with altitude and particle size. Differential settling of the particles is expected to produce weak electric fields in the clouds.     

The physics of thermal instability in two dimensions

Previous studies of a thermal (radiative) instability in a sheared magnetic field have shown that, under solar coronal conditions, cool condensations can form in a small neighborhood about the shear layer. Such results have served to model the formation of solar filaments (or prominences) observed to occur above photospheric magnetic polarity-inversion lines. A surprising conclusion of these studies is that the width of the condensation does not depend on the thermal conductivity (). By examining the mass-flow patterns of two-dimensional condensations in the absence of thermal conduction, we demonstrate that local plasma dynamics and the constraints imposed by boundary conditions are together sufficient to explain the size of the condensation width. In addition we present the results of a series of numerical calculations which illustrate the characteristic mode structure of sheared-field condensations.     

A dynamic model of the mesosphere and lower thermosphere

A one-dimensional, time-dependent calculation which includes the dynamics of turbulence has been developed. The dynamical parameters together with the mass density and temperature structure measured during the ALADDIN I program are inputs to the calculations of the vertical distribution of [O], [O₂], [O₂(¹Δ_g)], [OH] and [Ar] between 50 and 150 km. The results of the calculations are compared with measurements of these species distributions made during the ALADDIN I program and are also related to reported results at other times. Good to excellent agreement is found when the calculated profiles are compared with the measurements. This agreement supports the contention of the authors that the turbulent parameters measured from chemical trail fluctuations are due to atmospheric turbulence and are appropriate for use in model calculations. Significant changes in species concentrations occur when the eddy diffusion coefficient is increased. In particular, an increase in molecular oxygen and a reduction in atomic oxygen and helium are noted.     

Electrical conductivity in sunspots and the quiet photosphere

The electrical conductivity, thermal conductivity and viscosity of models of the quiet photosphere and the umbra of a sunspot have been calculated using LTE ionization equilibria and the Chapman-Enskog theory of transport coefficients. The results are presented in tabular form, and compared with previous calculations.     

Titan impacts and escape

We report on hydrodynamic calculations of impacts of large (multi-kilometer) objects on Saturn’s moon Titan. We assess escape from Titan, and evaluate the hypothesis that escaping ejecta blackened the leading hemisphere of Iapetus and peppered the surface of Hyperion.We carried out two- and three-dimensional simulations of impactors ranging in size from 4 to 100 km diameter, impact velocities between 7 and 15 km s⁻¹, and impact angles from 0° to 75° from the vertical. We used the ZEUSMP2 hydrocode for the calculations. Simulations were made using three different geometries: three-dimensional Cartesian, two-dimensional axisymmetric spherical polar, and two-dimensional plane polar. Three-dimensional Cartesian geometry calculations were carried out over a limited domain (e.g. 240 km on a side for an impactor of size d_i = 10 km), and the results compared to ones with the same parameters done by Artemieva and Lunine (2005); in general the comparison was good. Being computationally less demanding, two-dimensional calculations were possible for much larger domains, covering global regions of the satellite (from 800 km below Titan’s surface to the exobase altitude 1700 km above the surface). Axisymmetric spherical polar calculations were carried out for vertical impacts. Two-dimensional plane-polar geometry calculations were made for both vertical and oblique impacts. In general, calculations among all three geometries gave consistent results.Our basic result is that the amount of escaping material is less than or approximately equal to the impactor mass even for the most favorable cases. Amounts of escaping material scaled most strongly as a function of velocity, with high-velocity impacts generating the largest amount, as expected. Dependence of the relative amount of escaping mass f_esc = m_esc/M_i on impactor diameter d_i was weak. Oblique impacts (impact angle θ_i > 45°) were more effective than vertical or near-vertical impacts; ratios of m_esc/M_i ∼ 1-2 were found in the simulations.     

Gravitational instability of partially-ionized plasma in an oblique magnetic field

The effects of Hall currents, finite conductivity, and collision with neutrals have been studied on the gravitational instability of a partially-ionized plasma. It is assumed that plasma is permeated by an oblique magnetic field. The dispersion relation has been obtained and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitationally unstable mode on the various physical parameters involved. It is found that Jeans's criterion remains unchanged in the presence of Hall currents, finite conductivity, and collisions. The Hall currents, finite conductivity, and collisions have destabilizing influence on the unstable mode of wave propagation of a gravitational instability of partially-ionized plasma.