Heavy ion reflection and heating by collisionless shocks in polar solar corona

We propose a new model for explaining the observations of preferential heating of heavy ions in the polar solar corona. We consider that a large number of small scale shock waves can be present in the solar corona, as suggested by recent observations of polar coronal jets by the Hinode and STEREO spacecraft. The heavy ion energization mechanism is, essentially, the ion reflection off supercritical quasi-perpendicular collisionless shocks in the corona and the subsequent acceleration by the motional electric field E=−(1/c)V ×B. The acceleration due to E is perpendicular to the magnetic field, giving rise to large temperature anisotropy with T_⊥?T_∥, which can excite ion cyclotron waves. Also, heating is more than mass proportional with respect to protons, because the heavy ion orbit is mostly upstream of the quasi-perpendicular shock foot. The observed temperature ratios between O⁵⁺ ions and protons in the polar corona, and between α particles and protons in the solar wind are easily recovered. We also discuss the mechanism of heavy ion reflection, which is based on ion gyration in the magnetic overshoot of the shock.     

Electrodynamic heating and movement of the thermosphere

The theory of dissipation of ionospheric electric currents is extended to include viscosity. In a steady state (i.e. usually above about 140 km altitude) the joule plus viscous heating may be calculated by μ∇²v. E × B/B². At lower altitudes where viscosity may, in some circumstances, be relatively unimportant the joule dissipation is calculated by the usual formula j. (E + v × B). In a prevalent model of the auroral electrojets it is found that the joule heating can be much more intense outside auroral forms than within them. Heating due to auroral electrojets cause a semi-annual variation in the thermosphere. Movement caused by auroral electric fields make a contribution to the super-rotation of the midlatitude upper atmosphere. Random electric fields lead to an eddy ‘viscosity’ or ‘exchange coefficientrs in the upper thermosphere of magnitude ρE_R²/B³t_R²|∇E|. where t_R is the correlation time of the random component of electric fields E_R and ρ is air density. Theoretical conditions for significant heating by field-aligned currents are derived.     

Constraints to Uranus' Great Collision III: The Origin of the Outer Satellites

The theory of satellite loss resulting from a giant impact on Uranus (Parisi and Brunini 1997, Planet. Space Sci.45, 181-187) is revisited, in the light of the discovery of its five outer moons (Gladman et al. 1998, Nature392, 897-899; Gladman et al. 2000, Icarus147, 320-324; erratum 148, 320). Physical conditions and dynamical constraints in the great collision scenario and restrictions in the possible mechanisms for the origin of the outer uranian satellites are obtained from the knowledge of their actual orbital properties. We conclude that the existence of these moons implies that their origin must be connected to a breakup process. Other scenarios for their origin cast serious doubts on the occurrence of a giant collision at the end of Uranus' formation process to account for its large spin axis obliquity.     

The evolution of nighttime mid-latitude mesoscale F-region structures: A case study utilizing numerical solution of the Perkins instability equations

In recent years, all-sky camera airglow observations of evolving nighttime F-region structures have raised questions regarding the formation and apparent motion of these often wave-like structures. We address these issues using a pseudo-spectral method code developed to numerically solve the Perkins (1973. Spread F and ionospheric currents. J. Geophys. Res. 78, 218-226) moment equations modeling F-region electrodynamics. To aid in interpretation of the results, we utilize a Gaussian shape initial condition of the (geomagnetic field, B, parallel) integrated conductivity under the homogeneous TEC (B-parallel total electron content) condition and a northeastward DC electric field (E-field). We find that the initial Gaussian shape conductivity structure gradually evolves into banded structures oriented along the northwest-southeast direction while the amplitude of the banded structures continues growing and the peak of the structure moves to the northwest due to the E×B drift. The potential distribution corresponding to the initial Gaussian conductivity distribution is more complex but also becomes banded with the same orientation and growing trend as the conductivity. Wave vector domain plots show structure growth in approximately the first and third quadrants and damping in the second and fourth quadrants for both the conductivity and potential, as Perkins predicts—this leads to the orientation of the structures. We note that the evolved banded structures in conductivity and potential are oriented perpendicular to the direction given by half the angle between the DC E-field and east—the direction of maximum instability growth rate predicted by Perkins. The polarization (perturbation) E-field is seen mainly perpendicular to the long axis of the banded structures—i.e., no obvious structure-parallel E-field is observed in the simulation. By tracking the maximum point of the conductivity as a function of time, it is found that the localized structures move northwestward at a nearly constant speed that corresponds to the E×B drift velocity (to within relative errors on the direction and magnitude of ?4%). We also note that the E×B drift velocity has a dominant effect on the speed and propagation direction of the wave-like bands. The “wave” velocity is the projection of the E×B drift velocity on the line perpendicular to the wave front. Thus, the movement of a northwest-southeast oriented band can be decomposed into two components—parallel (to the band, northwestward) and perpendicular (southwestward) motions. A preliminary comparison of these results with an Arecibo all-sky camera observations shows good agreement.     

Iron(VI) Seems an Unlikely Explanation for Viking Labeled Release Results

Tsapin et al. (2000, Icarus147, 68-78) propose the strong oxidant ferrate(VI) to explain the Viking Labeled Release Mars life detection results. However, their data do not support that theory. Further, sensitive IR searches for oxidants on Mars found none, and Viking produced physical evidence against an oxidizing surface. Finally, Tsapin et al. (2000, Icarus147, 68-78) report no precautions to prevent microbial contamination from confounding their results.     

The Existence of a Planet beyond 50 AU and the Orbital Distribution of the Classical Edgeworth-Kuiper-Belt Objects

We study the effects of a Mars-like planetoid with a semimajor axis at about ∼60 AU orbiting embedded in the primordial Edgeworth-Kuiper belt (EKB). The origin of such an object can be explained in the framework of our current understanding of the origin of the outer Solar System, and a scenario for the orbital transport mechanism to its present location is given. The existence of such an object would produce a gap in the EKB distribution with an edge at about 50 AU, which seems to be in agreement with the most recent observations. No object at low eccentricity with semimajor axis beyond 50 AU has been detected so far, even though the present observing capabilities would allow an eventual detection (B. Gladman et al. 1998, Astron. J.116, 2042-2054; D. Jewitt et al. 1998, Astron. J.115, 2125-2135; E. I. Chiang and M. E. Brown 1999, Astron. J.118, 1411-1422; R. L. Allen et al. 2000, Astrophys. J.549, 241-244; C. A. Trujillo et al. 2001, Astron. J.122, 457-473; B. Gladman et al. 2001, Astron. J.122, 1051-1066; C. A. Trujillo and M. E. Brown 2001, Astrophys. J.554, 95-98). Finally, ranges for the magnitude and proper motion of the proposed object are given.     

Shear Instabilities as a Probe of Jupiter's Atmosphere

Linear wave patterns in Jupiter's clouds with wavelengths strongly clustered around 300 km are commonly observed in the planet's equatorial atmosphere (F. M. Flasar and P. J. Gierasch, 1986, J. Atmos. Sci.43, 2683-2707). We propose that the preferred wavelength is related to the thickness of an unstable shear layer within the clouds (A. P. Ingersoll and D. W. Koerner 1989, Bull. Am. Astron. Soc.21, 943). We numerically analyze the linear stability of wavelike disturbances that have nonzero horizontal phase speeds in Jupiter's atmosphere and find that, if the static stability in the shear layer is very low (but still nonnegative), a deep vertical shear layer like the one measured by the Galileo probe (D. H. Atkinson et al. 1998, J. Geophys. Res.103, 22911-22928) can generate the instabilities. The fastest growing waves grow exponentially within an hour, and their wavelengths match the observations. Close to zero values of static stability that permit the growth of instabilities are within the range of values measured by the Galileo probe in a hot spot (A. Seiff et al. 1998, J. Geophys. Res.103, 22857-22889). Our model probes Jupiter's equatorial atmosphere below the cloud deck and suggests that thick regions of wind shear and low static stability exist outside hot spots.     

Drift theory of charged particles in electric and magnetic fields

In this paper we review the drift theory of charged particles in electric and magnetic fields. No new physical interpretations are added to this classical topic, but through an alternative, simplified derivation of the guiding centre velocity, several complexities are eliminated and possible misconceptions of the theory are clarified. It is shown that:

1. The curvature/gradient drift velocity in the magnetic field, averaged over a particle distribution function is to lowest order in the direction of?×B/B ², while the average particle velocity is in the direction ofB×? P withP the scalar particle pressure.
2. These drift directions are correct for first-order expansions of the particle distribution function, and only second-order or higher expansions change these directions.
3. The?×B/B ² drift, which is the standard gradient plus curvature drift, and which is usually considered as a ‘single particle’ drift, need not be ‘reconciled’ with theB×? P, or ‘macroscopic, collective’ drift, as is often asserted in the literature. They are in fact related per definition and we show how.
4. When viewed in fixed momentum intervals (p,p+dp), the so-called Compton-Getting factor enters into the electric field (E×B)/B ² drift term.
5. The results are independent of the scale length of variation ofE andB, in contrast to existing drift theory. We discuss the implications of this result for three important cases.

     

Carbon Monoxide on Jupiter: Evidence for Both Internal and External Sources

Thirteen lines of the CO band near 4.7 μm have been observed on a jovian hot spot at a resolution of 0.045 cm⁻¹. The measured line profiles indicate that the CO mole fraction is 1.0±0.2 ppb around the 6-bar level and is larger in the upper troposphere and/or stratosphere. An external source of CO providing an abundance of 4⁺³₋₂×10¹⁶ molecules cm⁻² is implied by the observations in addition to the amount deposited at high altitude by the Shoemaker-Levy 9 collision. From a simple diffusion model, we estimate that the CO production rate is (1.5-10)×10⁶ molecules cm⁻² s⁻¹ assuming an eddy diffusion coefficient around the tropopause between 300 and 1500 cm² s⁻¹. Precipitation of oxygen atoms from the jovian magnetosphere or photochemistry of water vapor from meteoroidal material can only provide a negligible contribution to this amount. A significant fraction of the CO in Jupiter's upper atmosphere may be formed by shock chemistry due to the infall of kilometer- to subkilometer-size Jupiter family comets. Using the impact rate from Levison et al. (2000, Icarus143, 415-420) rescaled by Bottke et al. (2002, Icarus156, 399-433), this source can provide the observed stratospheric CO only if the eddy diffusion coefficient around the tropopause is 100-300 cm² s⁻¹. Higher values, ∼700 cm² s⁻¹, would require an impact rate larger by a factor of 5-10, which cannot be excluded considering uncertainties in the distribution of Jupiter family comets. Such a large rate is indeed consistent with the observed cratering record of the Galilean satellites (Zahnle et al. 1998, Icarus136, 202-222). On the other hand, the ∼1 ppb concentration in the lower troposphere requires an internal source. Revisiting the disequilibrium chemistry of CO in Jupiter, we conclude that rapid vertical mixing can provide the required amount of CO at ∼6 bar for a global oxygen abundance of 0.2-9 times the solar value considering the uncertainties in the convective mixing rate and in the chemical constants.     

Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

Advanced method to derive the IMF direction near Mars from cycloidal proton distributions

In a previous paper, we showed a method for deriving the interplanetary magnetic field (IMF) orientation from the velocity distribution of ring-like distributed ions as measured by the Ion Mass Analyser (IMA) on board Mars Express (MEX). This method has been improved so that one can derive the IMF orientation from a very limited portion of the ring distributions, i.e., only the highest energy portion of the ring distribution. This method uses the maximum variance direction L instead of the minimum variance direction N, which are derived from manually selected ring data. Because IMA's count rate for a semi-persistent ring distribution is nearly proportional to energy squire, L is most likely aligned to the tangential direction of the ring distribution at its highest energy, and this tangential direction is parallel or anti-parallel to the electric field. A vector product of L and the solar wind direction (X) gives the IMF orientation projected to the Y-Z plane. The tilt angle of IMF toward the X direction from the Y-Z plane is the same as the angle between the X direction and the ring plane, and is obtained from two methods when the initial speed of the ring ions is estimated to be much smaller than the solar wind speed: (1) angle between the velocity of ring's maximum energy portion and the solar wind vector, and (2) energy ratio between the solar wind and the maximum energy of the ring. The present method is applied to the IMA data from 3 June 2005 (0605-0640 UT) when the Mars Global Surveyor (MGS) magnetometer data are available. Using these data, we also tried to determine the sign of the IMF direction by estimating the evolution direction of the ring ions.     

Multifractal Fits to the Observed Main Belt Asteroid Distribution

Dohnanyi's (J. W. Dohnanyi, 1969, J. Geophys. Res.74, 2531-2554) theory predicts that a collisional system such as the asteroidal population of the main belt should rapidly relax to a power-law stationary size distribution of the kind N(m)∝m^−α, with α very close to 11/6, provided all the collisional response parameters are independent of size. The actual asteroid belt distribution at observable sizes, instead, does not exhibit such a simple fractal size distribution.We investigate in this work the possibility that the corresponding cumulative distribution may be instead fairly fitted by multifractal distributions. This multifractal behavior, in contrast with the Dohnanyi fractal distribution, is related to the release of his hypothesis of self-similarity.     

The Unusual Dynamics of Northern Dark Spots on Neptune

Hubble Space Telescope (HST) and ground-based observations of Neptune from 1991 to 2000 show that Neptune's northern Great Dark Spots (NGDS) remained remarkably stable in latitude and longitudinal drift rate, in marked contrast to the 1989 southern Great Dark Spot (GDS), which moved continuously equatorward during 1989 and dissipated unseen during 1990. NGDS-32, discovered in October 1994 HST images, (H. B. Hammel et al., 1995, Science268, 1740-1742), stayed at ∼32°N from 1994 through at least 1996, and possibly through 2000. The second northern GDS (NGDS-15), discovered in August 1996 HST images, (L. A. Sromovsky et al. 2001, Icarus146, 459-488), appears to have existed as early as 8 March 1996 and remained near 15°N for the 16 months over which it was observed. NGDS-32 had a very uniform longitudinal drift rate averaging −36.28±0.04°/day from 10 October 1994 to 2 November 1995, and −35.84±0.02°/day from 1 September 1995 through 24 November 1995. A single circulation feature certainly exists during each of the first two periods, though it is not certain that it is the same feature. It is probable, but less certain, that only a single circulation feature was tracked during the 1996-1998 period, during which positions are consistent with a modulated drift rate averaging −35.401±0.001°/day, but with a peak-to-peak modulation of 1.5°/day with an ∼760-day period. If NDS-32 varied its drift rate in accord with the local latitudinal shear in the zonal wind, then all its drift-rate changes might be due to only ∼0.4° of latitudinal motion. The movement of NGDS-15 is also not consistent with a uniform longitudinal drift rate, but the nature of its variation cannot be estimated from the limited set of observations. The relatively stable latitudinal positions of both northern dark spots are not consistent with current numerical model calculations treating them as anticyclonic vortices in a region of uniform potential vorticity gradient (R. P. Lebeau and T. E. Dowling 1998, Icarus132, 239-265). Possible explanations include unresolved latitudinal structure in the zonal wind background or unaccounted-for variations in vertical stability structure.     

Comparison between the Shkuratov and Hapke Scattering Theories for Solid Planetary Surfaces: Application to the Surface Composition of Two Centaurs

This project examines the different approaches which deal with the theory of radiative transfer on atmosphereless bodies. We present the relative merits of two scattering theories based on the equivalent slab model: the extensively used Hapke theory (Hapke 1981, J. Geophys. Res.86, 3039-3054) and the Shkuratov theory (Shkuratov et al. 1999, Icarus141, 132-155). We found that their main difference is the role of the phase function of individual particles of regolith, which is predicted (and generally forward directed) in the case of the Shkuratov model instead of being a free parameter as formulated in the Hapke model. We also emphasize that different assumptions as to the manner in which different constituents are physically mixed in either model have a substantial effect on the synthetic spectra inferred. This leads to a significant extension of the validity of Hapke's or similar practical approaches to areas where these approaches are valid.We used two objects (the Centaurs 5145 Pholus and 8405 Asbolus) as examples. Previous modeling of the spectra of these two bodies with the Hapke approach gave suspect results in terms of the derived grain sizes, which were smaller than the wavelength, violating key assumptions of the model (Cruikshank et al. 1998, Icarus135, 389-407 for Pholus; Barucci et al. 2000, Astron. Astrophys.357, L53-56 for Asbolus). We considered several different types of powdered surfaces to interpret the surface composition of these two Centaurs. The effect of fine-scale contamination of water ice grains by small amounts of carbon and/or tholins is also explored. We can explain the strong red color and the rich near-infrared spectral signatures of Pholus using a five-component surface (contaminated water ice, amorphous carbon, Titan tholin, olivine, and methanol ice) where the grain sizes are consistent with the model assumptions. These components are similar to those inferred by Cruikshank et al. (1998), but we obtain very different grain sizes and relative abundances. For example, we obtain a relative abundance of water ice on the surface of Pholus of about 40% instead of 6% found with the Hapke model. Organic and carbonaceous components change by similar amounts. In the case of Asbolus, a tholin and amorphous carbon areal mixture can reproduce the spectrum, with water remaining at 9% or less. Using the albedo published by Fernandez et al. (2002, Astron. J.123, 1050-1055) which is higher than most workers assume for Centaurs and Kuiper belt objects, a surface composition similar to that of Pholus is found. It appears that model-based uncertainties in relative compositions must be regarded with more attention.     

The influence of fluctuation fields on the force-free field

In Paper I (Hu, 1982), we discussed the the influence of fluctuation fields on the force-free field for the case of conventional turbulence and demonstrated the general relationships. In the present paper, by using the approach of local expansion, the equation of average force-free field is obtained as (1+b)?×B ₀=(α#x002B;a)B ₀#x002B;a ⁽¹⁾×B ₀#x002B;K. The average coefficientsa,a ⁽¹⁾,b, andK show the influence of the fluctuation fields in small scale on the configurations of magnetic field in large scale. As the average magnetic field is no longer parallel to the average electric current, the average configurations of force-free fields are more general and complex than the usual ones. From the view point of physics, the energy and momentum of the turbulent structures should have influence on the equilibrium of the average fields. Several examples are discussed, and they show the basic features of the fluctuation fields and the influence of fluctuation fields on the average configurations of magnetic fields. The astrophysical environments are often in the turbulent state, the results of the present paper may be applied to the turbulent plasma where the magnetic field is strong.     

Perihelion evolution of observed new comets implies the dominance of the galactic tide in making Oort cloud comets discernable

For an Oort cloud comet to be seen as a new comet, its perihelion must be moved from a point exterior to the loss cylinder boundary to a point interior to observable limits in a single orbit. The galactic tide can do this continuously, in a non-impulsive manner. Near-parabolic comets, with specific angular momentum , will most easily be made observable. Therefore, to reduce the perihelion distance H must decrease. Since weakly perturbed comets are, in general, more numerous than strongly perturbed comets, we can anticipate that new comets made observable by a weak tidal torque will more likely be first observed when their slowly changing perihelion distances are approaching their minimum osculating values under the action of the tide, rather than receding from their minimum values. That is, defining ΔH_tide as the vector change due to the galactic tidal torque during the prior orbit, and H_obs as the observed vector, the sign S≡Sign(H_obs·ΔH_tide) will more likely be −1 than +1 if a weak galactic tidal perturbation indeed dominates in making comets observable. Using comet data of the highest quality class (1A) for new comets (a>10,000 AU), we find that 49 comets have S=−1 and 22 have S=+1. The binomial probability that as many or more would exhibit this characteristic if in fact S=?1 were equally likely is only 0.0009. This characteristic also persists in other long-period comet populations, lending support to the notion that they are dominated by comets recently arrived from the outer Oort cloud. The preponderance of S=−1 also correlates with weakly perturbed (i.e., smaller semimajor axis) new comets in a statistically significant manner. This is strong evidence that the data are of sufficiently high quality and sufficiently free of observational selection effects to detect this unique imprint of the tide.     

The Diagnosis of Complex Rotation in the Lightcurve of 4179 Toutatis and Potential Applications to Other Asteroids and Bare Cometary Nuclei

The analysis of radar observations of the asteroid 4179 Toutatis by Hudson and Ostro (1995, Science270, 84-86) yielded a complex spin state. We revisit the visible lightcurve data on Toutatis (Spencer et al. 1995, Icarus117, 71-89) to explore the feasibility of using a rotational lightcurve to recover the signature of an excited spin state. For this, we apply Fourier transform and CLEAN algorithm (WindowCLEAN). WindowCLEAN yields clear and precise frequency signatures associated with the precession of the long axis about the total angular momentum vector and a combination of this precession and rotation about the long axis. For a long-axis mode state, our periodicities for Toutatis yield a mean long-axis precession period, P_φ, of 7.38 days and a rotation period around the long axis, P_ψ, of 5.38 days, which compare well with the respective periods of 7.42 and 5.37 days derived by Ostro et al. (1999, Icarus137, 122-139) and represent an independent confirmation of these values. We explain why the dramatic change in the Earth-Toutatis-Sun geometry during the time that the lightcurve was obtained has little effect on the final results obtained. Using the Toutatis example as a guide, we discuss the capabilities as well as the limitations on deriving information about complex spin states from asteroidal lightcurves.     

Measurement of Impact Ejecta from Regolith Targets in Oblique Impacts

This paper reports the results of experiments on projectile impact into regolith targets at various impact angles. Copper projectiles of 240 mg are accelerated to 197 to 272 m s⁻¹ using an electromagnetic gun. The ejecta are detected by thin Al foil targets as secondary targets, and the resulting holes on the foil are measured to derive the spatial distribution of the ejecta. The ejecta that penetrated the foil are concentrated toward the downrange azimuths of impacting projectiles in oblique impacts. In order to investigate the ejecta velocity distribution, the nondimensional volume of ejecta with velocities higher than a given value is calculated from the spatial distribution. In the case of the vertical impact of the projectile, most ejecta have velocities lower than 24% of the projectile speed (∼50 m s⁻¹), and there are only several ejecta with velocities higher than 72 m s⁻¹. This result confirms the existence of an upper limit to the ejection velocity in the ejecta velocity distribution (Hartmann cutoff velocity) (W. K. Hartmann, 1985, Icarus63, 69-98). On the other hand, it is found that, in the oblique impacts, there are a large number of ejecta with velocities higher than the Hartmann cutoff velocity. The relative quantity of ejecta above the Hartmann cutoff velocity increases as the projectile impact angle decreases. Taking these results with the results of S. Yamamoto and A. M. Nakamura (1997, Icarus128, 160-170) from impact experiments using an impact angle of 30°, it can be concluded that the ejecta from these regolith targets exhibit a bimodal velocity distribution. Below a few tens of m s⁻¹, we see the expected velocity distribution of ejecta, but above this velocity we see a separate group of high-velocity ejecta.     

Numerical Evaluation of the General Yarkovsky Effect: Effects on Eccentricity and Longitude of Periapse

J. N. Spitale and R. Greenberg (2001, Icarus149, 222-234) developed a nonlinearized, finite-difference solution to the heat equation that yields orbital rates of change due to the Yarkovsky effect for small, spherical, bare-rock asteroids and used it to investigate changes in semimajor axis caused by the Yarkovsky effect. Here, we present results for changes in eccentricity and longitude of periapse. These results may be useful as benchmarks for simplified analytical solutions. Moreover, we explore a range of parameters, some of which are inaccessible to most other approaches. Instantaneous rates can be quite fast: For a 1-m scale body rotating with a 5-h period, de/dt can be as fast as 0.1 per million years (da/dt rates for similar test bodies were reported in J. N. Spitale and R. Greenberg (2001, Icarus149, 222-234)). For more typical rotation periods, these rates would be considerably slower. Output from our calculation method could be used in simulations of asteroid population evolution such as that by W. F. Bottke, D. P. Rubincam, and J. A. Burns (2000, Icarus145, 301-331). On long time scales, impacts would randomize the spin axis before significant orbital evolution could occur. Nevertheless, occasional favorable rotation states might persist long enough for substantial eccentricity changes to accumulate (1) if the body is decoupled from the main belt (e.g., many near-Earth asteroids), (2) if the population of very small (mm-scale) main-belt impactors is less than expected, or (3) if our numerical results are scaled up to km-size bodies.     

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory

We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components B _x (x), B _y (x), B _z (x), the force-free parameter α(x), the electric current density j(x), and are accurate to second-order (of the nonlinear force-free α-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena.