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At least 343 records · Page 19

Full-waveform tomography reveals iron spin crossover in Earth’s lower mantle

Abstract Three-dimensional models of Earth’s seismic structure can be used to identify temperature-dependent phenomena, including mineralogical phase and spin transformations, that are obscured in 1-D spherical averages. Full-waveform tomography maps seismic wave-speeds inside the Earth in three dimensions, at a higher resolution than classical methods. By providing absolute wave speeds (rather than perturbations) and simultaneously constraining bulk and shear wave speeds over the same frequency range, it becomes feasible to distinguish variations in temperature from changes in composition or spin state. We present a quantitative joint interpretation of bulk and shear wave speeds in the lower mantle, using a recently published full-waveform tomography model. At all depths the diversity of wave speeds cannot be explained by an isochemical mantle. Between 1000 and 2500 km depth, hypothetical mantle models containing an electronic spin crossover in ferropericlase provide a significantly better fit to the wave-speed distributions, as well as more realistic temperatures and silica contents, than models without a spin crossover. Below 2500 km, wave speed distributions are explained by an enrichment in silica towards the core-mantle boundary. This silica enrichment may represent the fractionated remains of an ancient basal magma ocean.

58 GEOSCIENCES↗

The ionization structure of the Orion nebula: Infrared line observations and models

Observations of the (O III) 52 and 88 micron lines and the (N III) 57 micron line have been made at 6 positions and the (Ne III) 36 micron line at 4 positions in the Orion Nebula to probe its ionization structure. The measurements, made with a -40" diameter beam, were spaced every 45" in a line south from and including the Trapezium. The wavelength of the (Ne III) line was measured to be 36.013 + or - 0.004 micron. Electron densities and abundance ratios of N(++)/O(++) have been calculated and compared to other radio and optical observations. Detailed one component and two component (bar plus halo) spherical models were calculated for exciting stars with effective temperatures of 37 to 40,000K and log g = 4.0 and 4.5. Both the new infrared observations and the visible line measurements of oxygen and nitrogen require T sub eff approx less than 37,000K. However, the double ionized neon requires a model with T sub eff more than or equal to 39,000K, which is more consistent with that inferred from the radio flux or spectral type. These differences in T sub eff are not due to effects of dust on the stellar radiation field, but are probably due to inaccuracies in the assumed stellar spectrum. The observed N(++)/O(++) ratio is almost twice the N(+)/O(+) ratio. The best fit models give N/H = 8.4 x 10 to the -5 power, O/H = 4.0 x 10 to the -4 power, and Ne/H = 1.3 x 10 to the -4 power. Thus neon and nitrogen are approximately solar, but oxygen is half solar in abundance. From the infrared O(++) lines it is concluded that the ionization bar results from an increase in column depth rather than from a local density enhancement.

Simpson, J. P.↗

Mini Micropulse Lidar measurements in vertical and scanning modes

The Atmospheric Radiation Measurement (ARM) program operates ten Sigma Space (currently Droplet Measurement Technologies/DMT) micropulse lidar systems (MPL-4B-IDS/POL-FS series), which detect the backscattered light in two orthogonal linear polarization channels allowing to distinguish between spherical (e.g. water) and non-spherical (e.g. ice) scattering particles. The ARM MPLs have been providing valuable measurements to the aerosol and cloud research community for well over a decade. DMT’s Mini-Micropulse lidar (MiniMPL) is a compact version of the standard MPL. It reduces the power-aperture product to minimize cost, size, weight, power requirements and has all the electronics integrated with optics in a single box. Although as a result, it has a lower detection range than the MPL, limiting the measurements to the troposphere, its performance is promised to match that of the standard MPL within the troposphere. The MiniMPL weighs 13 kg, and the complete system, consisting of an optical transceiver and a laptop running the data acquisition and post-processing software, fits in a storm case, allowing its transport on domestic or international flights. This can be especially valuable for short field campaigns or Intensive Operational Periods, where time is of the essence when replacing a faulty instrument. In addition, the scanning polarization lidar capability (MiniMPL-SCAN option) could be of great interest for satisfying ARM measurement needs for certain research topics related to clouds and precipitation. To evaluate its full potential in comparison with co-located remote sensing instruments including the ARM MPL-4B-IDS/POL-FS at SGP, a miniMPL was hosted at the ARM Southern Great Plains (SGP) mega-site in 2020 for approximately 3 months. During this time the miniMPL was tested in both vertical sampling and scanning modes.

54 ENVIRONMENTAL SCIENCES↗

Analysis of fast-ion losses measured in MAST-U via infrared thermography and a Fast Ion Loss Detector

Fast-ion losses need to be monitored to avoid damage to plasma facing components. In existing experimental devices, the scintillator-based fast-ion loss detector (FILD) is the most advanced diagnostic for measuring fast-ion losses. However, FILDs provide only local information about the losses. Infrared (IR) thermography can be used as a complementary tool for more global monitoring of the deposition of fast-ion losses on the wall, at the expense of no velocity-space resolution. IR cameras measure the temperature of the plasma facing components. This measurement, determined by a combined effect of the thermal plasma, radiation, neutrons and fast-ion losses, can be decomposed to infer the fast-ion load on the tokamak wall. In this manuscript, a workflow to estimate fast-ion losses via IR thermography is applied to the MAST-U spherical tokamak, using a 1D approximation to extract the experimental heat flux on the FILD front face from IR data. To numerically estimate the different contributions to this total heat flux, the field-line tracing environment SMITER is used to calculate the thermal plasma contribution, the orbit-following Monte-Carlo code ASCOT to estimate the fast-ion losses, and bolometry measurements for the radiation. To validate the workflow, two discharges, L-mode plasmas with low MHD activity, were executed using on and off-axis beams, respectively. The experimentally and numerically estimated heat flux are of the same order of magnitude for the on-axis heated scenario, with a strong dependence of the estimated fast-ion losses contribution on the fit to the kinetic profiles used as input. This is also true for the off-axis heated scenario, where the total numerically estimated heat flux is 2.1 or 1.3 times higher than the maximum experimentally estimated heat flux, depending on the ASCOT input used.

FILD↗

Energy density functional and sensitivity of energies of giant resonances to bulk nuclear matter properties

The development of a modern and more realistic nuclear energy density functional (EDF) for accurate predictions of properties of nuclei is the subject of enhanced activity, since it is very important for the study of properties of nuclear matter (NM), giant resonances and, in particular, of properties of rare nuclei with unusual neutron-to-proton ratios. Here, we provide a short review of the current status of the nuclear EDF and the theoretical results obtained for properties of nuclei and nuclear matter. We will first describe a method for determining the parameters of the EDF, associated with the Skyrme type effective interaction, by carrying out a Hartree-Fock based fit to extensive set of data of ground state properties and constraints. Next we will describe the fully self-consistent Hartree-Fock (HF) based random-phase-approximation (RPA) theory for calculating the strength functions S(E) and centroid energies E CEN of giant resonances and the folding model (FM) distorted wave Вorn approximation (DWBA) to calculate the excitation cross section of giant resonances by α scattering. Then we will provide results for: (i) the Skyrme parameters of the KDE0v1 EDF; (ii) consequences of violation of self-consistently in HF-based RPA; (iii) FM-DWBA calculation of excitation cross section; (iv) values of the E CEN of isoscalar and isovector giant resonances of multipolarities L=0–3 for a wide range of spherical nuclei, using 33 EDFs associated with standard form of the Skyrme type interactions, commonly employed in the literature; and (v) the sensitivities E CEN of the giant resonances to bulk properties of NM. We also determine constraints on NM properties, such as the incompressibility coefficient and effective mass, by comparing with experimental data on E CEN of giant resonances.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Results of the Fluid Merging Viscosity Measurement International Space Station Experiment

The purpose of FMVM is to measure the rate of coalescence of two highly viscous liquid drops and correlate the results with the liquid viscosity and surface tension. The experiment takes advantage of the low gravitational free floating conditions in space to permit the unconstrained coalescence of two nearly spherical drops. The merging of the drops is accomplished by deploying them from a syringe and suspending them on Nomex threads followed by the astronaut s manipulation of one of the drops toward a stationary droplet till contact is achieved. Coalescence and merging occurs due to shape relaxation and reduction of surface energy, being resisted by the viscous drag within the liquid. Experiments were conducted onboard the International Space Station in July of 2004 and subsequently in May of 2005. The coalescence was recorded on video and down-linked near real-time. When the coefficient of surface tension for the liquid is known, the increase in contact radius can be used to determine the coefficient of viscosity for that liquid. The viscosity is determined by fitting the experimental speed to theoretically calculated contact radius speed for the same experimental parameters. Recent fluid dynamical numerical simulations of the coalescence process will be presented. The results are important for a better understanding of the coalescence process. The experiment is also relevant to liquid phase sintering, free form in-situ fabrication, and as a potential new method for measuring the viscosity of viscous glass formers at low shear rates.

Ethridge, Edwin C.↗

Sunlight Transmission through Desert Dust and Marine Aerosols: Diffuse Light Corrections to Sun Photometry and Pyrheliometry

Desert dust and marine aerosols are receiving increased scientific attention because of their prevalence on intercontinental scales and their potentially large effects on Earth radiation and climate, as well as on other aerosols, clouds, and precipitation. The relatively large size of desert dust and marine aerosols produces scattering phase functions that are strongly forward- peaked. Hence, Sun photometry and pyrheliometry of these aerosols are more subject to diffuse-light errors than is the case for smaller aerosols. Here we quantify these diffuse-light effects for common Sun photometer and pyrheliometer fields of view (FOV), using a data base on dust and marine aerosols derived from (1) AERONET measurements of sky radiance and solar beam transmission and (2) in situ measurements of aerosol layer size distribution and chemical composition. Accounting for particle non-sphericity is important when deriving dust size distribution from both AERONET and in situ aerodynamic measurements. We express our results in terms of correction factors that can be applied to Sun photometer and pyrheliometer measurements of aerosol optical depth (AOD). We find that the corrections are negligible (less than approximately 1% of AOD) for Sun photometers with narrow FOV (half-angle eta less than degree), but that they can be as large as 10% of AOD at 354 nm wavelength for Sun photometers with eta = 1.85 degrees. For pyrheliometers (which can have eta up to approximately 2.8 degrees), corrections can be as large as 16% at 354 nm. We find that AOD correction factors are well correlated with AOD wavelength dependence (hence Angstrom exponent). We provide best-fit equations for determining correction factors from Angstrom exponents of uncorrected AOD spectra, and we demonstrate their application to vertical profiles of multiwavelength AOD.

Russell, P. B.↗

The ellipticity parameterization for an NFW profile: An overlooked angular structure in strong lens modeling

Galaxy-scale gravitational lenses are often modeled with two-component mass profiles where one component represents the stellar mass and the second is a Navarro Frenk White (NFW) profile representing the dark matter. Outside of the spherical case, the NFW profile is costly to implement, and so it is approximated via two different methods; ellipticity can be introduced via the lensing potential (NFWp) or via the mass by approximating the NFW profile as a sum of analytical profiles (NFWm). While the NFWp method has been the default for lensing applications, it gives a different prescription of the azimuthal structure, which we show introduces ubiquitous gradients in ellipticity and boxiness in the mass distribution rather than having a constant elliptical shape. Because an unmodeled azimuthal structure has been shown to be able to bias lens model results, we explored the degree to which this azimuthal structure that was introduced can affect the model accuracy. We constructed input profiles using composite models using both the NFWp and NFWm methods and fit these mocks with a power-law elliptical mass distribution (PEMD) model with external shear. As a measure of the accuracy of the recovered lensing potential, we calculated the value of the Hubble parameter H 0 one would determine from the lensing fit. We found that the fits to the NFWp input return H 0 values that are systematically biased by about 3% lower than the NFWm counterparts. We explored whether such an effect is attributable to the mass sheet transformation (MST) by using an MST-independent quantity, ξ 2 . We show that, as expected, the NFWm mocks are degenerate with PEMD through an MST. For the NFWp, an additional bias was found beyond the MST due to the azimuthal structure exterior to the Einstein radius. We recommend modelers use an NFWm prescription in the future, such that the azimuthal structure can be introduced explicitly rather than implicitly.

79 ASTRONOMY AND ASTROPHYSICS↗

The Thomas theorem and the Efimov States within a generalized Bohr model

Using a generalized Bohr model and the hyper-spherical formalism for a three-body system, we derive the universal energy functions. We apply our model to 4He atom where only the Coulomb potential is dominant and find that its binding energy is well reproduced (less than 5.5% difference). Later, we focus on the equal mass three-body systems and derive the Thomas theorem assuming a simple interaction depending on the range of the potential. We discuss the conditions for which an unbound two-body system produces a bound three-body system and apply our model to 4He and triton atoms as well as to the triton nucleus. Using their scattering lengths and effective ranges, we are able to reproduce the two-body or the three-body binding energies (less than 5% difference) with only one parameter fitted. Prediction for excited (Efimov) levels are also given and in particular we demonstrate that for some hyper-angles two equal minima appear which indicate a phase (shape) transition similar to the Landau's theory of phase transition. We suggest that the observed excited levels in two different experiments for the triton nucleus are indeed Efimov levels and there may be more surprises.

74 ATOMIC AND MOLECULAR PHYSICS↗

HST-STIS Spectra of Saturn's Rings and Implications for Their Reddening Agent

We obtained HST-STIS spectra of Saturn's main rings in May 2011, using the G230L (and G430L) gratings, with final averaged radial resolution of 160 (and 330) km/pixel. The dataset filled a previous 200-330nm "spectral gap" between Cassini and ground-based spectra. The data provide radial profiles as a function of wavelength, but our most basic product at this point is a set of very low-noise spectra, radially averaged over broad regions of the rings (A, B, C, and Cassini Division). The raw spectra required special processing to remove artifacts due to extended-source grating scatter. We have modeled the spectra using a new particle surface model, which corrects for on-surface shadowing due to the likely very rough ring particle surfaces, and avoids overestimation of intra-mixed "neutral absorber". We correct for non-classical layer effects and finite ring optical depth, and relate our observed reflectivities to the spherical albedos of individual smooth particles. We model these smooth particle albedos using standard Hapke theory for regolith grain mixtures that are either homogeneous and "intramixed" (nonicy absorbers dispersed in water ice regolith grains) or heterogeneous "intimate" mixtures. As candidates for the nonicy contaminants we have considered amorphous carbon, aromatic-rich and aliphatic-rich organic tholins, silicates, hematite and iron metal. For the A and B rings, we find that iron metal (including a new theoretical estimate of the refractive indices of nanometer-sized grains of iron) is not spectrally steep enough in the 200-300nm range, and that aliphatic-rich tholins are either too steep at short wavelengths or too flat at long wavelengths. However, less than 1% by mass of aromatic-rich tholins provides a very good fit across the entire spectral range with no gratuitous "neutral absorber" needed, and a minimum of additional free parameters. The best fits require forward-scattering regolith grains. For the C Ring and Cassini Division, additional absorbers are needed (updated results will be given).

Saturn's Rings↗

Interstellar Dust Models

A viable interstellar dust model - characterized by the composition, morphology, and size distribution of the dust grains and by the abundance of the different elements locked up in the dust - should fit all observational constraints arising primarily from the interactions of the dust with incident radiation or the ambient gas. As a minimum, these should include the average interstellar extinction, the infrared emission from the diffuse interstellar medium (ISM), and the observed interstellar abundances of the various refractory elements. The last constraint has been largely ignored, resulting in dust models that require more elements to be in the dust phase than available in the ISM. In this talk I will describe the most recent advances towards the construction of a comprehensive dust model made by Zubko, Dwek, and Arendt, who, for the first time, included the interstellar abundances as explicit constraints in the construction of interstellar dust models. The results showed the existence of many distinct models that satisfy the basic set of observational constraints, including bare spherical silicate and graphite particles, PAHs, as well as spherical composite particles containing silicate, organic refractories, water ice, and voids. Recently, a new interstellar dust constituent has emerged, consisting of metallic needles. These needles constitute a very small fraction of the interstellar dust abundance, and their existence is primarily manifested in the 4 to 8 micron wavelength region, where they dominate the interstellar extinction. Preliminary studies show that these models may be distinguished by their X-ray halos, which are produced primarily by small angle scattering off large dust particles along the line of sight to bright X-ray sources, and probe dust properties largely inaccessible at other wavelengths.

Dwek, Eli↗

The Far-Infrared Emission Line and Continuum Spectrum of the Seyfert Galaxy NGC 1068

We report on the analysis of the first complete far-infrared spectrum (43-197 microns) of the Seyfert 2 galaxy NGC 1068 as observed with the Long Wavelength Spectrometer (LWS) onboard the Infrared Space Observatory (ISO). In addition to the 7 expected ionic fine structure emission lines, the OH rotational lines at 79, 119 and 163 microns were all detected in emission, which is unique among galaxies with full LWS spectra, where the 119 micron line, where detected, is always in absorption. The observed line intensities were modelled together with IS0 Short Wavelength Spectrometer (SWS) and optical and ultraviolet line intensities from the literature, considering two independent emission components: the AGN component and the starburst component in the circumnuclear ring of approximately 3kpc in size. Using the UV to mid-IR emission line spectrum to constrain the nuclear ionizing continuum, we have confirmed previous results: a canonical power-law ionizing spectrum is a poorer fit than one with a deep absorption trough, while the presence of a big blue bump is ruled out. Based on the instantaneous starburst age of 5 Myr constrained by the Br gamma equivalent width in the starburst ring, and starburst synthesis models of the mid- and far-infrared fine-structure line emission, a low ionization parameter (U=10(exp -3.5)) and low densities (n=100 cm (exp -3)) are derived. Combining the AGN and starburst components, we succeed in modeling the overall UV to far-IR atomic spectrum of SGC 1068, reproducing the line fluxes to within a factor 2.0 on average with a standard deviation of 1.4. The OH 119 micron emission indicates that the line is collisionally excited, and arises in a warm and dense region. The OH emission has been modeled using spherically symmetric, non-local, non-LTE radiative transfer models. The models indicate that the bulk of the emission arises from the nuclear region, although some extended contribution from the starburst is not ruled out. The OH abundance in the nuclear region is expected to be approximately 10(exp -5), characteristic of X-ray dominated regions.

Spinoglio, Luigi↗

Using Cassini CIRS Data to Constrain Enceladus' Libration State

Given the non-spherical shape of Enceladus, the satellite may experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical libration would produce a diurnal oscillation in the longitude of Enceladus' tidal bulge, which could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus' libration amplitude, small amplitude librations may have geologically significant consequences. For example, a physical libration will affect heat production along the tiger stripes as produced by tidal shear heating. We have modeled the expected power emitted along the tiger stripes for various types of physical libration and have quantified which types of physical libration best reproduce the observed power f1ux as detailed in Cassini CIRS data. We find that including a physical libration does allow better fits to the observations and we have identified regions of the libration phase space that where these fits are optimized. A physical libration has important implications for tidal dissipation within Ence1adus and if identified may provide an additional constraint on its interior mass distribution.

Hurford, T. A.↗

Chain trajectories, domain shapes, and terminal boundaries in block copolymers

The packing geometry of macromolecules in complex mesophases is of key importance to self-organization in synthetic and biological soft materials. While approximate or heuristic models rely on often-untested assumptions about how flexible molecules “fit in” to distinct locations of complex assemblies, physical assemblies derive from ensembles of fluctuating conformations, obscuring the connection between mesophase geometry and the underlying arrangements. Here, we present an approach to extract and analyze features of molecular packing in diblock block copolymer (BCP) melts, a prototypical soft matter system, based on the statistical description of chain conformations in self-consistent field (SCF) theory. We show how average BCP chain trajectories in ordered morphologies can be analyzed from the SCF-derived orientational order parameter of chain segments. We use these extracted trajectories to analyze the features of local packing geometry, including chain bending and tilt, as well as the terminal boundaries that delineate distinct domains in ordered BCP morphologies. In conclusion, we illustrate this analysis by focusing on measurable features of packing frustration in 2D (columnar) and 3D (spherical and bicontinuous) morphologies, notably establishing an explicit link between chain conformations in complex morphologies and their medial geometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using Cassini CIRS Data to Constrain Enceladus' Libration State

Given the non-spherical shape of Enceladus, the satellite may experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical Libration would produce a diurnal oscillation in the longitude of Enceladus' tidal bulge, which could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus' libration amplitude, small amplitude librations may have geologically significant consequences. For example, a physical libration will affect heat production. along the tiger stripes as produced by tidal shear heating. We have modeled the expected power en-litted along the tiger stripes for various types of physical libration and have quantified which types of physical libration best reproduce the observed power flux as detailed in Cassini CIRS data. We find that including a physical libration does allow better fits to the observations and we have identified regions of the libration phase space that where these fits are optimized. A physical libration has important implications for tidal dissipation within Enceladus and if identified may provide an additional constraint on its interior mass distribution.

Hurford, T. A.↗

Toward a NASA Deep Space Optical Communications System

As discussed at SpaceOps in 2016, we expect the data rates from deep space missions to increase approximately one order of magnitude per decade for the next 50 years. The first order of magnitude improvement will come from existing plans for radio frequency (RF) communications including enhancements to both spacecraft and Deep Space Network (DSN) facilities. The next two orders of magnitude are predicted to come from the introduction of deep space optical communications. Studies indicate that optical receive apertures of between 8m12m are desired. The large cost of dedicated receive telescopes makes this method unrealistic – at least in the near-term. The cost of large optical ground terminals is driven primarily by the cost of the optics and by the cost of a stable structure for the telescope. We propose a novel hybrid design in which existing DSN 34m beam waveguide (BWG) radio antennas can be modified to include an 8m equivalent optical primary. By utilizing a low-cost segmented spherical mirror optical design, pioneered by the optical astronomical community, and by exploiting the already existing extremely stable large radio aperture structures in the DSN, we can minimize both of these cost drivers for implementing large optical communications ground terminals. Two collocated hybrid RF/optical antennas could be arrayed to synthesize the performance of an 11.3m receive aperture to support more capable or more distant space missions or used separately to communicate with two optical spacecraft simultaneously. NASA is in the midst of building six new 34m BWG antennas in the DSN. The final two are planned to be built at the DSN Goldstone, California and Canberra complexes. We are now investigating building these last two antennas as RF/optical hybrids. By delaying their operational dates by two years, we would be able to add the 8m optical receive capability for these two antennas while fitting within existing budgetary constraints. This paper describes the hybrid antenna design, the technical challenges being addressed, and plan for using this concept, together with ongoing work on optical flight terminals, to infuse operation optical communications into deep space missions.

Cornwell, Donald M.↗

High-degree Gravity Models from GRAIL Primary Mission Data

We have analyzed Ka‒band range rate (KBRR) and Deep Space Network (DSN) data from the Gravity Recovery and Interior Laboratory (GRAIL) primary mission (1 March to 29 May 2012) to derive gravity models of the Moon to degree 420, 540, and 660 in spherical harmonics. For these models, GRGM420A, GRGM540A, and GRGM660PRIM, a Kaula constraint was applied only beyond degree 330. Variance‒component estimation (VCE) was used to adjust the a priori weights and obtain a calibrated error covariance. The global root‒mean‒square error in the gravity anomalies computed from the error covariance to 320×320 is 0.77 mGal, compared to 29.0 mGal with the pre‒GRAIL model derived with the SELENE mission data, SGM150J, only to 140×140. The global correlations with the Lunar Orbiter Laser Altimeter‒derived topography are larger than 0.985 between l = 120 and 330. The free‒air gravity anomalies, especially over the lunar farside, display a dramatic increase in detail compared to the pre‒GRAIL models (SGM150J and LP150Q) and, through degree 320, are free of the orbit‒track‒related artifacts present in the earlier models. For GRAIL, we obtain an a posteriori fit to the S‒band DSN data of 0.13 mm/s. The a posteriori fits to the KBRR data range from 0.08 to 1.5 micrometers/s for GRGM420A and from 0.03 to 0.06 micrometers/s for GRGM660PRIM. Using the GRAIL data, we obtain solutions for the degree 2 Love numbers, k20=0.024615+/-0.0000914, k21=0.023915+/-0.0000132, and k22=0.024852+/-0.0000167, and a preliminary solution for the k30 Love number of k30=0.00734+/-0.0015, where the Love number error sigmas are those obtained with VCE.

Primary 1↗

Crustal Magnetic Spectra from Correlated Sources on Mars

The spectral method for distinguishing crustal from core-source magnetic fields has been re-examined, modified and applied to both a comprehensive geomagnetic field model and an altitude normalized magnetic map of Mars. These observational spectra are fairly fitted by theoretical forms expected from certain elementary classes of magnetic sources. For Earth we found fields from a core radius 3512 +/- 64 km and a crust represented by a shell of random dipolar sources at radius 6367 +/- 14 km. For Mars we found only a field from a crust represented in the same way, but 46 +/- 10 km below the planetary menu radius. More realistic theoretical spectra, allowing for crustal thickness, oblateness and magnetization by a planet centered dipole, were derived and discussed, as were spectral effects of laterally correlated sources. The main effect of laterally correlated sources is to soften the spectrum at high degrees. We tend to over-estimate source shell depth when this is omitted. To include this effect simply size and magnetization distribution functions for extended sources are recast as a characteristic diameter and mean square magnetization amplitude for an ensemble of vertically magnetized spherical caps on a shell. For small caps, and at moderated degrees, the practical derivatives of the log-theoretical spectrum with respect to amplitude, shell radius, and cap diameter are approximately proportional to l, n, and -n **2, respectively. Separation of diameter from amplitude from layer thickness. Results from applications to observational spectra are discussed, noting that there are now several fine field models for Mars; moreover, the terrestrial magnetic spectrum at high degrees, as revised, updated with high precision Oerstad data, and upgrade with high resolution Champ data, appears softer than before.

Voorhies, Coerte V.↗