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Paty C, Arridge CS, Cohen IJ, DiBraccio GA, Ebert RW, Rymer AM. Ice giant magnetospheres. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190480. [PMID: 33161869 DOI: 10.1098/rsta.2019.0480] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/16/2020] [Indexed: 05/20/2023]
Abstract
The ice giant planets provide some of the most interesting natural laboratories for studying the influence of large obliquities, rapid rotation, highly asymmetric magnetic fields and wide-ranging Alfvénic and sonic Mach numbers on magnetospheric processes. The geometries of the solar wind-magnetosphere interaction at the ice giants vary dramatically on diurnal timescales due to the large tilt of the magnetic axis relative to each planet's rotational axis and the apparent off-centred nature of the magnetic field. There is also a seasonal effect on this interaction geometry due to the large obliquity of each planet (especially Uranus). With in situ observations at Uranus and Neptune limited to a single encounter by the Voyager 2 spacecraft, a growing number of analytical and numerical models have been put forward to characterize these unique magnetospheres and test hypotheses related to the magnetic structures and the distribution of plasma observed. Yet many questions regarding magnetospheric structure and dynamics, magnetospheric coupling to the ionosphere and atmosphere, and potential interactions with orbiting satellites remain unanswered. Continuing to study and explore ice giant magnetospheres is important for comparative planetology as they represent critical benchmarks on a broad spectrum of planetary magnetospheric interactions, and provide insight beyond the scope of our own Solar System with implications for exoplanet magnetospheres and magnetic reversals. This article is part of a discussion meeting issue 'Future exploration of ice giant systems'.
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Affiliation(s)
- Carol Paty
- Department of Earth Sciences, University of Oregon, 100 Cascade Hall, Eugene, OR 97403-1272, USA
| | - Chris S Arridge
- Department of Physics, Lancaster University, Bailrigg, Lancaster LA1 4YW, UK
| | - Ian J Cohen
- The Johns Hopkins University Applied Physics Laboratory, 11000 Johns Hopkins Road, Laurel, MD 20723, USA
| | - Gina A DiBraccio
- Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
| | - Robert W Ebert
- Department of Space Research, Southwest Research Institute, San Antonio, TX 78228-0510, USA
- Department of Physics and Astronomy, University of Texas, San Antonio, TX 78249-0600, USA
| | - Abigail M Rymer
- The Johns Hopkins University Applied Physics Laboratory, 11000 Johns Hopkins Road, Laurel, MD 20723, USA
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Livadiotis G. Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities. ENTROPY 2020; 22:e22060594. [PMID: 33286366 PMCID: PMC7517129 DOI: 10.3390/e22060594] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Revised: 05/20/2020] [Accepted: 05/21/2020] [Indexed: 11/27/2022]
Abstract
The concept of duality of probability distributions constitutes a fundamental “brick” in the solid framework of nonextensive statistical mechanics—the generalization of Boltzmann–Gibbs statistical mechanics under the consideration of the q-entropy. The probability duality is solving old-standing issues of the theory, e.g., it ascertains the additivity for the internal energy given the additivity in the energy of microstates. However, it is a rather complex part of the theory, and certainly, it cannot be trivially explained along the Gibb’s path of entropy maximization. Recently, it was shown that an alternative picture exists, considering a dual entropy, instead of a dual probability. In particular, the framework of nonextensive statistical mechanics can be equivalently developed using q- and 1/q- entropies. The canonical probability distribution coincides again with the known q-exponential distribution, but without the necessity of the duality of ordinary-escort probabilities. Furthermore, it is shown that the dual entropies, q-entropy and 1/q-entropy, as well as, the 1-entropy, are involved in an identity, useful in theoretical development and applications.
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Affiliation(s)
- George Livadiotis
- Division of Space Science and Engineering, Southwest Research Institute, San Antonio, TX 78238, USA
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Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas. UNIVERSE 2018. [DOI: 10.3390/universe4120144] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Kappa distributions received impetus as they provide efficient modelling of the observed particle distributions in space and astrophysical plasmas throughout the heliosphere. This paper presents (i) the connection of kappa distributions with statistical mechanics, by maximizing the associated q-entropy under the constraints of the canonical ensemble within the framework of continuous description; (ii) the derivation of q-entropy from first principles that characterize space plasmas, the additivity of energy, and entropy; and (iii) the derivation of the characteristic first order differential equation, whose solution is the kappa distribution function.
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Bennett CJ, Pirim C, Orlando TM. Space-Weathering of Solar System Bodies: A Laboratory Perspective. Chem Rev 2013; 113:9086-150. [DOI: 10.1021/cr400153k] [Citation(s) in RCA: 107] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Chris J. Bennett
- Department of Chemistry & Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive, Atlanta, Georgia 30332, United States
| | - Claire Pirim
- Department of Chemistry & Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive, Atlanta, Georgia 30332, United States
| | - Thomas M. Orlando
- Department of Chemistry & Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive, Atlanta, Georgia 30332, United States
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Affiliation(s)
- B. H. Mauk
- Johns Hopkins University Applied Physics Laboratory; Laurel Maryland USA
| | - N. J. Fox
- Johns Hopkins University Applied Physics Laboratory; Laurel Maryland USA
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Broadfoot AL, Atreya SK, Bertaux JL, Blamont JE, Dessler AJ, Donahue TM, Forrester WT, Hall DT, Herbert F, Holberg JB, Hunter DM, Krasnopolsky VA, Linick S, Lunine JI, McConnell JC, Moos HW, Sandel BR, Schneider NM, Shemansky DE, Smith GR, Strobel DF, Yelle RV. Ultraviolet spectrometer observations of neptune and triton. Science 2010; 246:1459-66. [PMID: 17756000 DOI: 10.1126/science.246.4936.1459] [Citation(s) in RCA: 286] [Impact Index Per Article: 19.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Results from the occultation of the sun by Neptune imply a temperature of 750 +/- 150 kelvins in the upper levels of the atmosphere (composed mostly of atomic and molecular hydrogen) and define the distributions of methane, acetylene, and ethane at lower levels. The ultraviolet spectrum of the sunlit atmosphere of Neptune resembles the spectra of the Jupiter, Saturn, and Uranus atmospheres in that it is dominated by the emissions of H Lyman alpha (340 +/- 20 rayleighs) and molecular hydrogen. The extreme ultraviolet emissions in the range from 800 to 1100 angstroms at the four planets visited by Voyager scale approximately as the inverse square of their heliocentric distances. Weak auroral emissions have been tentatively identified on the night side of Neptune. Airglow and occultation observations of Triton's atmosphere show that it is composed mainly of molecular nitrogen, with a trace of methane near the surface. The temperature of Triton's upper atmosphere is 95 +/- 5 kelvins, and the surface pressure is roughly 14 microbars.
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Abstract
The National Aeronautics and Space Administration Goddard Space Flight Center-University of Delaware Bartol Research Institute magnetic field experiment on the Voyager 2 spacecraft discovered a strong and complex intrinsic magnetic field of Neptune and an associated magnetosphere and magnetic tail. The detached bow shock wave in the supersonic solar wind flow was detected upstream at 34.9 Neptune radii (R(N)), and the magnetopause boundary was tentatively identified at 26.5 R(N) near the planet-sun line (1 R(N) = 24,765 kilometers). A maximum magnetic field of nearly 10,000 nanoteslas (1 nanotesla = 10(-5) gauss) was observed near closest approach, at a distance of 1.18 R(N). The planetary magnetic field between 4 and 15 R(N) can be well represented by an offset tilted magnetic dipole (OTD), displaced from the center of Neptune by the surprisingly large amount of 0.55 R(N) and inclined by 47 degrees with respect to the rotation axis. The OTD dipole moment is 0.133 gauss-R(N)(3). Within 4 R(N), the magnetic field representation must include localized sources or higher order magnetic multipoles, or both, which are not yet well determined. The obliquity of Neptune and the phase of its rotation at encounter combined serendipitously so that the spacecraft entered the magnetosphere at a time when the polar cusp region was directed almost precisely sunward. As the spacecraft exited the magnetosphere, the magnetic tail appeared to be monopolar, and no crossings of an imbedded magnetic field reversal or plasma neutral sheet were observed. The auroral zones are most likely located far from the rotation poles and may have a complicated geometry. The rings and all the known moons of Neptune are imbedded deep inside the magnetosphere, except for Nereid, which is outside when sunward of the planet. The radiation belts will have a complex structure owing to the absorption of energetic particles by the moons and rings of Neptune and losses associated with the significant changes in the diurnally varying magnetosphere configuration. In an astrophysical context, the magnetic field of Neptune, like that of Uranus, may be described as that of an "oblique" rotator.
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Sittler EC, Hartle RE. Triton's ionospheric source: Electron precipitation or photoionization. ACTA ACUST UNITED AC 1996. [DOI: 10.1029/96ja00398] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Krasnopolsky VA, Cruikshank DP. Photochemistry of Triton's atmosphere and ionosphere. JOURNAL OF GEOPHYSICAL RESEARCH 1995; 100:21271-86. [PMID: 11541126 DOI: 10.1029/95je01904] [Citation(s) in RCA: 78] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The photochemistry of 32 neutral and 21 ion species in Triton's atmosphere is considered. Parent species N2, CH4, and CO (with a mixing ratio of 3 x 10(-4) in our basic model) sublime from the ice with rates of 40, 208, and 0.3 g/cm2/b.y., respectively. Chemistry below 50 km is driven mostly by photolysis of methane by the solar and interstellar medium Lyman-alpha photons, producing hydrocarbons C2H4, C2H6, and C2H2 which form haze particles with precipitation rates of 135, 28, and 1.3 g/cm2/b.y., respectively. Some processes are discussed which increase the production of HCN (by an order of magnitude to a value of 29 g/cm2/b.y.) and involve indirect photolysis of N2 by neutrals. Reanalysis of the measured methane profiles gives an eddy diffusion coefficient K = 4 x 10(3) cm2/s above the tropopause and a more accurate methane number density near the surface, (3.1 +/- 0.8) x 10(11) cm-3. Chemistry above 200 km is driven by the solar EUV radiation (lambda < 1000 angstroms) and by precipitation of magnetospheric electrons with a total energy input of 10(8) W (based on thermal balance calculations). The most abundant photochemical species are N, H2, H, O, and C. They escape with the total rates of 7.7 x 10(24) s-1, 4.5 x 10(25) s-1, 2.4 x 10(25) s-1, 4.4 x 10(22) s-1, and 1.1 x 10(24) s-1, respectively. Atomic species are transported to a region of 50-200 km and drive the chemistry there. Ionospheric chemistry explains the formation of an E region at 150-240 km with HCO+ as a major ion, and of an F region above 240 km with a peak at 320 km and C+ as a major ion. The ionosphere above 500 km consists of almost equal densities of C+ and N+ ions. The model profiles agree with the measured atomic nitrogen and electron density profiles. A number of other models with varying rate coefficients of some reactions, differing properties of the haze particles (chemically passive or active), etc., were developed. These models show that there are four basic unknown values which have strong impacts on the composition and structure of the atmosphere and ionosphere. These values and their plausible ranges are the CO mixing ratio fco = 10(-4)-10(-3), the magnetospheric electron energy input (1 +/- 0.5) x 10(8) W, the rate coefficient of charge-exchange reaction N2(+) + C k = 10(-11)-10(-10) cm3/s, and the ion escape velocity Vi approximately equal to 150 cm/s.
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Affiliation(s)
- V A Krasnopolsky
- National Research Council/NASA Goddard Space Flight Center, Greenbelt, Maryland, USA
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Mauk BH, Krimigis SM, Acuña MH. Neptune's inner magnetosphere and aurora: Energetic particle constraints. ACTA ACUST UNITED AC 1994. [DOI: 10.1029/94ja00735] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Acuña MH, Connerney JEP, Ness NF. Neptune's magnetic field: Calculation of field geometric invariants derived from the I8E1 GSFC/BRI model. ACTA ACUST UNITED AC 1993. [DOI: 10.1029/92ja02981] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Sawyer CB, Warwick JW, Romig JH. The effect of magnetic topography on high-latitude radio emission at Neptune. ACTA ACUST UNITED AC 1992. [DOI: 10.1029/91ja02390] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Neubauer FM, Lüttgen A, Ness NF. On the lack of a magnetic signature of Triton's magnetospheric interaction on the Voyager 2 flyby trajectory. ACTA ACUST UNITED AC 1991. [DOI: 10.1029/91ja00377] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Cairns IH, Smith CW, Kurth WS, Gurnett DA, Lepping RP. Remote sensing of Neptune's bow shock: Evidence for large-scale shock motions. ACTA ACUST UNITED AC 1991. [DOI: 10.1029/91ja01929] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Paranicas CP, Cheng AF. Satellite sweeping of energetic particles at Neptune. ACTA ACUST UNITED AC 1991. [DOI: 10.1029/91ja01652] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Mauk BH, Keath EP, Kane M, Krimigis SM, Cheng AF, Acuña MH, Armstrong TP, Ness NF. The magnetosphere of Neptune: Hot plasmas and energetic particles. ACTA ACUST UNITED AC 1991. [DOI: 10.1029/91ja01820] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Richardson JD, Belcher JW, Zhang M, McNutt RL. Low-energy ions near Neptune. ACTA ACUST UNITED AC 1991. [DOI: 10.1029/91ja01598] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Belcher JW, Bridge HS, Bagenal F, Coppi B, Divers O, Eviatar A, Gordon GS, Lazarus AJ, McNutt RL, Ogilvie KW, Richardson JD, Siscoe GL, Sittler EC, Steinberg JT, Sullivan JD, Szabo A, Villanueva L, Vasyliunas VM, Zhang M. Plasma Observations Near Neptune: Initial Results from Voyager 2. Science 1989; 246:1478-83. [PMID: 17756003 DOI: 10.1126/science.246.4936.1478] [Citation(s) in RCA: 92] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The plasma science experiment on Voyager 2 made observations of the plasma environment in Neptune's magnetosphere and in the surrounding solar wind. Because of the large tilt of the magnetic dipole and fortuitous timing, Voyager entered Neptune's magnetosphere through the cusp region, the first cusp observations at an outer planet. Thus the transition from the magnetosheath to the magnetosphere observed by Voyager 2 was not sharp but rather appeared as a gradual decrease in plasma density and temperature. The maximum plasma density observed in the magnetosphere is inferred to be 1.4 per cubic centimeter (the exact value depends on the composition), the smallest observed by Voyager in any magnetosphere. The plasma has at least two components; light ions (mass, 1 to 5) and heavy ions (mass, 10 to 40), but more precise species identification is not yet available. Most of the plasma is concentrated in a plasma sheet or plasma torus and near closest approach to the planet. A likely source of the heavy ions is Triton's atmosphere or ionosphere, whereas the light ions probably escape from Neptune. The large tilt of Neptune's magnetic dipole produces a dynamic magnetosphere that changes configuration every 16 hours as the planet rotates.
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Gurnett DA, Kurth WS, Poynter RL, Granroth LJ, Cairns IH, Macek WM, Moses SL, Coroniti FV, Kennel CF, Barbosa DD. First Plasma Wave Observations at Neptune. Science 1989; 246:1494-8. [PMID: 17756006 DOI: 10.1126/science.246.4936.1494] [Citation(s) in RCA: 85] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The Voyager 2 plasma wave instrument detected many familiar plasma waves during the encounter with Neptune, including electron plasma oscillations in the solar wind upstream of the bow shock, electrostatic turbulence at the bow shock, and chorus, hiss, electron cyclotron waves, and upper hybrid resonance waves in the inner magnetosphere. Low-frequency radio emissions, believed to be generated by mode conversion from the upper hybrid resonance emissions, were also observed propagating outward in a disklike beam along the magnetic equatorial plane. At the two ring plane crossings many small micrometer-sized dust particles were detected striking the spacecraft. The maximum impact rates were about 280 impacts per second at the inbound ring plane crossing, and about 110 impacts per second at the outbound ring plane crossing. Most of the particles are concentrated in a dense disk, about 1000 kilometers thick, centered on the equatorial plane. However, a broader, more tenuous distribution also extends many tens of thousands of kilometers from the equatorial plane, including over the northern polar region.
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