Thermal and transport properties of mantle rock at high pressure: Applications to super-Earths

In the present study, the temperature- and pressure-dependent transport and thermal properties, i.e., viscosity, phonon thermal conductivity, thermal expansivity and heat capacities, as well as electronic and radiative thermal conductivities, have been derived for the mantles of super-Earths. These properties are necessary to understand the interior dynamics and the thermal evolution of those planets. We assume that the mantles consist of MgSiO₃ perovskite (pv), but we discuss the effects of the post-perovskite transition, and we elaborate on an addition of periclase MgO and incorporated Fe. However, MgO is found to only significantly influence the phonon thermal conductivity – the viscosities, heat capacities and thermal expansivities of pv and MgO remain comparable. We use the Keane theory of solids, which takes into account the behavior of solid matter at the infinite pressure limit, adopt the Keane equations of state, and adjust for pv and MgO by comparison with experimental high-pressure and high-temperature data. We find the theory of the infinite pressure limit of Keane to be in excellent agreement with recent ab initio studies and experiments. To calculate the melting curve, we further use the Lindemann–Stacey scaling law and fit it to available experimental data. The best data fitting melting temperature for pv reaches 5700 K at 135 GPa and increases to 20,000 K at 1.1 TPa, corresponding to the core-mantle boundary of a 10 Earth mass super-Earth (10M_Earth). We find the pv adiabatic temperature (with a potential temperature of 1700 K) to reach 2570 K at 135 GPa and 5000 K at 1.1 TPa. To calculate the pressure-and temperature-dependent viscosity, we use the semi-empirical homologous temperature scaling to relate enthalpy change, and hence viscosity, to the melting temperature. We find that the resulting activation volume of pv decreases from 2.8 cm³/mol at 25 GPa to 1.4 cm³/mol at 1.1 TPa-resulting in a viscosity increase by ～15 orders of magnitude through the adiabatic mantle of a 10M_Earth planet. Furthermore, the thermal expansivity (of pv and MgO) decreases by a factor of eight, and the total thermal conductivity (phonon, radiative and electronic) of an Earth-like pv/MgO composite increases by a factor of seven through an adiabatic mantle of a 10M_Earth super-Earth. At higher temperatures, i.e., for super-adiabatic temperature profiles, the electronic and radiative thermal conductivities strongly increase and dominate the conductive heat transport. All findings indicate an increase of heat transfer solely by conduction in the lower mantles of super-Earths. Thus our results disagree with Earth-biased full-mantle convection assumptions made by previous models for super-Earths, and additionally raise questions about the differentiation of massive rocky exoplanets and their ability to generate magnetic fields or sustain plate tectonics.     

Penetration of nearby supernova dust in the inner solar system

We investigate the method by which nearby supernovae – within a few tens of pc of the solar system – can penetrate the solar system and deposit live radioactivities on earth. The radioactive isotopic signatures that could potentially leave an observable geological imprint are in the form of refractory metals; consequently, it is likely they would arrive in the form of supernova-produced dust grains. Such grains can penetrate into the solar system more easily than the bulk supernova plasma, which gets stalled and deflected near the solar system due to the solar wind plasma pressure. We therefore examine the motion of charged grains as they decouple from the supernova plasma and are influenced by the solar magnetic, radiation, and gravitational fields. We characterize the dust trajectories with analytical approximations which display the roles of grain size, initial velocity, and surface voltage. These results are verified with full numerical simulations for wide ranges of dust properties. We find that supernova dust grains traverse the inner solar system nearly undeflected, if the incoming grain velocity – which we take to be that of the incident supernova remnant – is comparable to the solar wind speeds and much larger than the escape velocity at 1 AU. Consequently, the dust penetration to 1 AU has essentially 100% transmission probability and the dust capture onto the earth should have a geometric cross section. Our results cast in a new light the terrestrial deposition of radioisotopes from nearby supernovae in the geological past. For explosions beyond ～10 pc from earth, dust grains can still deliver supernova ejecta to earth, and thus the amount of supernova material deposited is set by the efficiency of dust condensation and survival in supernovae. Turning the problem around, we use observations of live ⁶⁰Fe in both deep-ocean and lunar samples to infer a conservative lower bound iron condensation efficiency of M_dust,Fe/M_tot,Fe ? 4  × 10^?4 for the supernova which apparently produced these species 2–3 Myr ago.     

Io: Volcanic thermal sources and global heat flow

We have examined thermal emission from 240 active or recently-active volcanic features on Io and quantified the magnitude and distribution of their volcanic heat flow during the Galileo epoch. We use spacecraft data and a geological map of Io to derive an estimate of the maximum possible contribution from small dark areas not detected as thermally active but which nevertheless appear to be sites of recent volcanic activity. We utilize a trend analysis to extrapolate from the smallest detectable volcanic heat sources to these smallest mapped dark areas. Including the additional heat from estimates for “outburst” eruptions and for a multitude of very small (“myriad”) hot spots, we account for ～62 × 10¹² W (～59 ± 7% of Io’s total thermal emission). Loki Patera contributes, on average, 9.6 × 10¹² W (～9.1 ± 1%). All dark paterae contribute 45.3 × 10¹² W (～43 ± 5%). Although dark flow fields cover a much larger area than dark paterae, they contribute only 5.6 × 10¹² W (～5.3 ± 0.6%). Bright paterae contribute ～2.6 × 10¹² W (～2.5 ± 0.3%). Outburst eruption phases and very small hot spots contribute no more than ～4% of Io’s total thermal emission: this is probably a maximum value. About 50% of Io’s volcanic heat flow emanates from only 1.2% of Io’s surface. Of Io’s heat flow, 41 ± 7.0% remains unaccounted for in terms of identified sources. Globally, volcanic heat flow is not uniformly distributed. Power output per unit surface area is slightly biased towards mid-latitudes, although there is a stronger bias toward the northern hemisphere when Loki Patera is included. There is a slight favoring of the northern hemisphere for outbursts where locations were well constrained. Globally, we find peaks in thermal emission at ～315°W and ～105°W (using 30° bins). There is a minimum in thermal emission at around 200°W (almost at the anti-jovian longitude) which is a significant regional difference. These peaks and troughs suggest a shift to the east from predicted global heat flow patterns resulting from tidal heating in an asthenosphere. Global volcanic heat flow is dominated by thermal emission from paterae, especially from Loki Patera (312°W, 12°N). Thermal emission from dark flows maximises between 165°W and 225°W. Finally, it is possible that a multitude of very small hot spots, smaller than the present angular resolution detection limits, and/or cooler, secondary volcanic processes involving sulphurous compounds, may be responsible for at least part of the heat flow that is not associated with known sources. Such activity should be sought out during the next mission to Io.     

Lunar heat flow experiments: Science objectives and a strategy for minimizing the effects of lander-induced perturbations

Reliable measurements of the Moon's global heat flow would serve as an important diagnostic test for models of lunar thermal evolution and would also help to constrain the Moon's bulk abundance of radioactive elements and its differentiation history. The two existing measurements of lunar heat flow are unlikely to be representative of the global heat flow. For these reasons, obtaining additional heat flow measurements has been recognized as a high priority lunar science objective. In making such measurements, it is essential that the design and deployment of the heat flow probe and of the parent spacecraft do not inadvertently modify the near-surface thermal structure of the lunar regolith and thus perturb the measured heat flow. One type of spacecraft-related perturbation is the shadow cast by the spacecraft and by thermal blankets on some instruments. The thermal effects of these shadows propagate by conduction both downward and outward from the spacecraft into the lunar regolith. Shadows cast by the spacecraft superstructure move over the surface with time and only perturb the regolith temperature in the upper 0.8 m. Permanent shadows, such as from thermal blankets covering a seismometer or other instruments, can modify the temperature to greater depth. Finite element simulations using measured values of the thermal diffusivity of lunar regolith show that the limiting factor for temperature perturbations is the need to measure the annual thermal wave for 2 or more years to measure the thermal diffusivity. The error induced by permanent spacecraft thermal shadows can be kept below 8% of the annual wave amplitude at 1 m depth if the heat flow probe is deployed at least 2.5 m away from any permanent spacecraft shadow. Deploying the heat flow probe 2 m from permanent shadows permits measuring the annual thermal wave for only one year and should be considered the science floor for a heat flow experiment on the Moon. One way to meet this separation requirement would be to deploy the heat flow and seismology experiments on opposite sides of the spacecraft. This result should be incorporated in the design of future lunar geophysics spacecraft experiments. Differences in the thermal environments of the Moon and Mars result in less restrictive separation requirements for heat flow experiments on Mars.     

Enceladus: A hypothesis for bringing both heat and chemicals to the surface

The eruptive plumes and large heat flow (～15 GW) observed by Cassini in the South Polar Region of Enceladus may be expressions of hydrothermal activity inside Enceladus. We hypothesize that a subsurface ocean is the heat reservoir for thermal anomalies on the surface and the source of heat and chemicals necessary for the plumes. The ocean is believed to contain dissolved gases, mostly CO₂ and is found to be relatively warm (～0 °C). Regular tidal forces open cracks in the icy crust above the ocean. Ocean water fills these fissures. There, the conditions are met for the upward movement of water and the dissolved gases to exsolve and form bubbles, lowering the bulk density of the water column and making the pressure at its bottom less than that at the top of the ocean. This pressure difference drives ocean water into and up the conduits toward the surface. This transportation mechanism supports the thermal anomalies and delivers heat and chemicals to the chambers from which the plumes erupt. Water enters these chambers and there its bubbles pop and loft an aerosol mist into the ullage. The exiting plume gas entrains some of these small droplets. Thus, nonvolatile chemical species in ocean water can be present in the plume particles. A CO₂ equivalent-gas molar fraction of ～4 × 10^?4 for the ocean is sufficient to support the circulation. A source of heat is needed to keep the ocean warm at ～0 °C (about two degrees above its freezing point). The source of heat is unknown, but our hypothesis is not dependent on any particular mechanism for producing the heat.     

Downflow-induced brightening following a filament eruption

The plasma from solar filament eruptions sometimes falls down to the lower solar atmosphere. These interesting events can help us to understand the properties of downflows, such as the temperature and the conversion between kinetic energy and thermal energy. We analyze the case of a filament eruption in active region NOAA 11283 and brightening caused by the return of filament material on September 7 and 8, 2011, observed by the Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO). Magnetic flux cancellation was observed as a result of the eruption after the eruptive filament started to ascend. Another filament near the eruptive filament was disturbed by an extreme ultraviolet (EUV) wave that was triggered by the eruptive filament, causing it to oscillate. Based on coronal seismology, the mean magnetic field strength in the oscillatory filament was estimated to be approximately 18 ± 2 G. Some plasma separated from the filament and fell down to the solar northwest surface after the filament eruption. The velocities of the downflows increased at accelerations lower than the gravitational acceleration. The main characteristic temperature of the downflows was about 5 × 10⁴ K. When the plasma blobs fell down to lower atmospheric heights, the high-speed downward-travelling plasma collided with plasma at lower atmospheric heights, causing the plasma to brighten. The brightening was observed in all 8 AIA channels, demonstrating that the temperature of the plasma in the brightening covered a wide range of values, from 10⁵ K to 10⁷ K. This brightening indicates the conversion between kinetic energy and thermal energy.     

The impact of a weak south pole on thermal convection in Enceladus’ ice shell

Enceladus exhibits a strong hemispheric dichotomy of tectonism and heat flux, with geologically young, heavily tectonized terrains and a high heat flux in the South Polar Terrain (SPT) and relatively ancient terrains with presumably lower heat fluxes over the rest of the satellite. To understand the convective pattern and its relationship with surface tectonics, we present three-dimensional numerical models of convection in Enceladus’ ice shell including basal heating and tidal heating. Our thermal boundary conditions exhibit no north–south asymmetries, but because the tectonism at the SPT may weaken the ice there, we impose a mechanically weak lithosphere within the SPT. The weakening is parameterized by adopting a reduced viscosity contrast within the SPT. Without such a weak zone, convection (if any) resides in stagnant-lid mode and exhibits no hemispheric dichotomy. In the presence of such an SPT weak zone, however, we find vigorous convection in the ice underneath the SPT, with convective plumes rising close to the surface. In contrast, only stagnant lid convection, or no convection at all, occurs elsewhere over the satellite. Away from the SPT, the heat flux in our models is small (5–10 mW m^?2) and the surface strains are small enough to imply surface ages >10⁹ years. Within the SPT, however, our models yield peak heat fluxes of ～70–200 mW m^?2, implying heat flows integrated across the SPT of up to 5 GW, similar to that inferred from Cassini thermal observations. The surface strains in our models are high enough near the south pole to cause intense tectonism and imply surface ages of ～10⁶–10⁷ years, consistent with age estimates of the SPT.     

A whole-moon thermal history model of Europa: Impact of hydrothermal circulation and salt transport

A whole-moon numerical model of Europa is developed to simulate its thermal history. The thermal evolution covers three phases: (i) an initial, roughly 0.5 Gyr-long period of radiogenic heating and differentiation, (ii) a long period from 0.5 Gyr to 4 Gyr with continuing radiogenic heating but no tidal dissipative heating (TDH), and (iii) a final period covering the last 0.5 Gyr until the present, during which TDH is active. Hydrothermal plumes develop after the initial period of heating and differentiation and transport heat and salt from Europa’s silicate mantle to its ice shell. We find that, even without TDH, vigorous hydrothermal convection in the rocky mantle can sustain flow in an ocean layer throughout Europa’s history. When TDH becomes active, the ice shell melts quickly to a thickness of about 20 km, leaving an ocean 80 km or more deep. Parameterized convection in the ice shell is non-uniform spatially, changes over time, and is tied to the deeper ocean–mantle dynamics. We also find that the dynamics are affected by salt concentrations. An initially non-uniform salt distribution retards plume penetration, but is homogenized over time by turbulent diffusion and time-dependent flow driven by initial thermal gradients. After homogenization, the uniformly distributed salt concentrations are no longer a major factor in controlling plume transport. Salt transport leads to the formation of a heterogeneous brine layer and salt inclusions at the bottom of the ice shell; the presence of salt in the ice shell could strongly influence convection in that layer.     

Solar modulation of galactic cosmic rays during 19–23 solar cycles

We make a detailed analysis of cross-correlation and time-lag between monthly data of galactic cosmic rays (GCRs) intensity and different solar activity indices (e.g., sunspot number, sunspot area, green coronal Fe line and 10.7 cm solar radio flux) during 19–23 solar cycles. GCRs time-series data from Kiel neutron monitor station and solar data from the last 50 years period, covering five solar cycles (19–23), and alternating solar polarity states (i.e., five A < 0 and four A > 0) have been investigated. We find a clear asymmetry in the cross-correlation between GCRs and solar activity indicators for both odd and even-numbered solar cycles. The time-lags between GCRs and solar parameters are found different in different solar cycles as well as in the opposite polarity states (A < 0 and A > 0) within the same solar cycle. Possible explanations of the observed results are discussed in light of modulation models, including drift effects.     

The heat flow during the formation of ribbon terrains on Venus

Ribbons are regularly spaced, between 2 and 6 km, troughs that exist on venusian tesserae, which are mainly located in, and characterize to, venusian crustal plateaus. Independent of the geological or temporal relations with other features, regularly and similarly spaced ribbons on several tesserae strongly suggest a thermal control on the thickness of the deformed layer. This can be used to constraint the heat flow at the time of ribbon formation, which holds important implications for the viability of the hypotheses that address the origin and evolution of crustal plateaus. For a brittle–ductile transition ∼1–3 km deep (as proposed from ribbon spacing), realistic strain rates, and a present-day surface temperature of 740 K, the implied heat flow is very high, 130–780 mW m⁻². If Venus has experienced higher surface temperatures due to climate forcing by massive volcanism, then the heat flow could be greatly reduced. For surface temperatures of 850–900 K the heat flow is 190–560, 60–230 and 20–130 mW m⁻² for brittle–ductile transition depths of 1, 2 and 3 km, respectively. Heat flow values around 80–100 mW m⁻² are reasonable for venusian hotspots, based on terrestrial analogs, but hardly consistent with coldspot settings. High surface temperatures are also required to maintain the crustal solidus deeper than a few kilometers during the formation of ribbon terrains. For the obtained heat flows, a solidus deeper than ∼30 km (the likely mean value for the crustal thickness) is difficult to achieve. This suggests that a substantial proportion of the crust beneath crustal plateaus was emplaced subsequently to the time when ribbon terrains were formed. Alternatively, at that time a magma reservoir inside the crust could have existed.     

Thermally driven escape from Pluto’s atmosphere: A combined fluid/kinetic model

A combined fluid/kinetic model is developed to calculate thermally driven escape of N₂ from Pluto’s atmosphere for two solar heating conditions: no heating above 1450 km and solar minimum heating conditions. In the combined model, one-dimensional fluid equations are applied for the dense part of the atmosphere, while the exobase region is described by a kinetic model and calculated by the direct simulation Monte Carlo method. Fluid and kinetic parts of the model are iteratively solved in order to maintain constant total mass and energy fluxes through the simulation region. Although the atmosphere was found to be highly extended, with an exobase altitude at ～6000 km at solar minimum, the outflow remained subsonic and the escape rate was within a factor of two of the Jeans rate for the exobase temperatures determined. This picture is drastically different from recent predictions obtained solely using a fluid model which, in itself, requires assumptions about atmospheric density, flow velocity and energy flux carried away by escaping molecules at infinity. Gas temperature, density, velocity and heat flux versus radial distance are consistent between the hydrodynamic and kinetic model up to the exobase, only when the energy flux across the lower boundary and escape rate used to solve the hydrodynamic equations is obtained from the kinetic model. This limits the applicability of fluid models to atmospheric escape problems. Finally, the recent discovery of CO at high altitudes, the effect of Charon and the conditions at the New Horizon encounter are briefly considered.     

The solar wind interaction with Venus through the eyes of the Pioneer Venus Orbiter

Venus has no internal magnetic dynamo and thus its ionosphere and hot oxygen exosphere dominate the interaction with the solar wind. The solar wind at 0.72 AU has a dynamic pressure that ranges from 4.5 nPa (at solar max) to 6.6 nPa (at solar min), and its flow past the planet produces a shock of typical magnetosonic Mach number 5 at the subsolar point. At solar maximum the pressure in the ionospheric plasma is sufficient to hold off the solar wind at an altitude of 400 km above the surface at the subsolar point, and 1000 km above the terminators. The deflection of the solar wind occurs through the formation of a magnetic barrier on the inner edge of the magnetosheath, or shocked solar wind. Under typical solar wind conditions the time scale for diffusion of the magnetic field into the ionosphere is so long that the ionosphere remains field free and the barrier deflects almost all the incoming solar wind. Any neutral atoms of the hot oxygen exosphere that reach the altitude of the magnetosheath are accelerated by the electric field of the flowing magnetized plasma and swept along cycloidal paths in the antisolar direction. This pickup process, while important for the loss of the Venus atmosphere, plays a minor role in the deceleration and deflection of the solar wind. Like at magnetized planets, the Venus shock and magnetosheath generate hot electrons and ions that flow back along magnetic field lines into the solar wind to form a foreshock. A magnetic tail is created by the magnetic flux that is slowed in the interaction and becomes mass-loaded with thermal ions.The structure of the ionosphere is very much dependent on solar activity and the dynamic pressure of the solar wind. At solar maximum under typical solar wind conditions, the ionosphere is unmagnetized except for the presence of thin magnetic flux ropes. The ionospheric plasma flows freely to the nightside forming a well-developed night ionosphere. When the solar wind pressure dominates over the ionospheric pressure the ionosphere becomes completely magnetized, the flow to the nightside diminishes, and the night ionosphere weakens. Even at solar maximum the night ionosphere has a very irregular density structure. The electromagnetic environment of Venus has not been well surveyed. At ELF and VLF frequencies there is noise generated in the foreshock and shock. At low altitude in the night ionosphere noise, presumably generated by lightning, can be detected. This paper reviews the plasma environment at Venus and the physics of the solar wind interaction on the threshold of a new series of Venus exploration missions.     

The convective boundary layer on Mars: Some 1-D simulation results

The daytime convective boundary layer (CBL) of Mars and the transition to it after the cold night is studied on a warm dusty sol at the rover Spirit using temperature profiles from the miniature thermal emission spectrometer (mini-TES) and a 1-D model. The model’s net solar fluxes are linear in z in the CBL while the thermal fluxes decay logarithmically from about 8 m upward, due mainly to the emissivity properties and density of CO₂. The induced strong radiative heating of the lower CBL is so well compensated by turbulent cooling (with an elevated maximum in the sensible heat flux H) that the growth of the CBL is uniform by the model, as observed by the mini-TES. Hence the net energy fluxes are linear and the shape of H in the lower CBL can be obtained as a residual. Moisture evolution is also considered although without validation.     

Latest results on Jovian disk X-rays from XMM-Newton

We present the results of a spectral study of the soft X-ray emission (0.2–2.5 keV) from low-latitude (‘disk’) regions of Jupiter. The data were obtained during two observing campaigns with XMM-Newton in April and November 2003. While the level of the emission remained approximately the same between April and the first half of the November observation, the second part of the latter shows an enhancement by about 40% in the 0.2–2.5 keV flux. A very similar, and apparently correlated increase, in time and scale, was observed in the solar X-ray and EUV flux.The months of October and November 2003 saw a period of particularly intense solar activity, which appears reflected in the behavior of the soft X-rays from Jupiter's disk. The X-ray spectra, from the XMM-Newton EPIC CCD cameras, are all well fitted by a coronal model with temperatures in the range 0.4–0.5 keV, with additional line emission from Mg XI (1.35 keV) and Si XIII (1.86 keV): these are characteristic lines of solar X-ray spectra at maximum activity and during flares.The XMM-Newton observations lend further support to the theory that Jupiter's disk X-ray emission is controlled by the Sun, and may be produced in large part by scattering, elastic and fluorescent, of solar X-rays in the upper atmosphere of the planet.     

Contamination of the 5394 Å spectral region by telluric lines

The spectral region in the vicinity of 5394 Å contains three prominent photospheric spectral lines, which can be used as a solar plasma diagnostic tool. The occurrence of telluric lines in this region is a potential source of systematic and random errors in these solar spectral lines. The goal of our investigation was to determine the telluric line contamination of this interesting spectral region. Several series of high-resolution solar spectra within an interval of about 4 Å around the 5394 Å wavelength were observed at different zenith distances of the Sun. Comparison of these spectra has permitted identification of telluric lines in this spectral interval. The observations were carried out with the horizontal solar spectrograph of the Heliophysical Observatory in Debrecen. Telluric feature blending was identified in the blue and red wings of the Fe I 5393.2 Å line, and in the local continuum of the Mn I 5394.7 Å line. The blue wing of the Fe I 5395.2 Å line is contaminated by a weak telluric feature too. The red continuum of this line has a more prominent telluric contamination. A dozen of water vapor telluric lines that determined the observed telluric features were identified in this spectral interval. The profiles of three telluric lines that have a significant influence on both the profiles of solar spectral lines and the level of local continuum were derived, and the variation of their parameters (equivalent width and central depth) with air mass were analyzed.     

Charting thermal emission variability at Pele,Janus Patera and Kanehekili Fluctus with the Galileo NIMS Io Thermal Emission Database (NITED)

Using the NIMS Io Thermal Emission Database (NITED), a collection of over 1000 measurements of radiant flux from Io’s volcanoes (Davies, A.G. et al. [2012]. Geophys. Res. Lett. 39, L01201. doi:10.1029/2011GL049999), we have examined the variability of thermal emission from three of Io’s volcanoes: Pele, Janus Patera and Kanehekili Fluctus. At Pele, the 5-μm thermal emission as derived from 28 night time observations is remarkably steady at 37 ± 10 GW μm^?1, re-affirming previous analyses that suggested that Pele an active, rapidly overturning silicate lava lake. Janus Patera also exhibits relatively steady 5-μm thermal emission (≈20 ± 3 GW μm^?1) in the four observations where Janus is resolved from nearby Kanehekili Fluctus. Janus Patera might contain a Pele-like lava lake with an effusion rate (Q_F) of ≈40–70 m³ s^?1. It should be a prime target for a future mission to Io in order to obtain data to determine lava eruption temperature. Kanehekili Fluctus has a thermal emission spectrum that is indicative of the emplacement of lava flows with insulated crusts. Effusion rate at Kanehekili Fluctus dropped by an order of magnitude from ≈95 m³ s^?1 in mid-1997 to ≈4 m³ s^?1 in late 2001.     

Characteristics of the Expansion of Magnetic Funnels in Solar Quiet Regions

Via the potential field extrapolation of the observed photospheric magnetic field, the structure of the photospheric magnetic fields above solar quiet regions is renewed. As revealed by the result, below 20 Mm the open magnetic lines exhibit many obvious small funnel structures. These funnels expand with height and at the height of about 20 Mm they combine into large funnel structures. By a systematic study of the tendency of change of the cross section areas of funnels, it is discovered that the cross section areas of funnels in solar quiet regions expand approximately linearly. The velocity of expansion of magnetic funnels at rather low altitudes (< 20 Mm) is larger than that at high altitudes (> 20 Mm). This phenomenon has important significance for the two-dimensional numerical simulations of the origin of solar wind and the mass flow in magnetic loops. At the same time it is found that the number of closed magnetic lines decreases in the form of exponential function.     

Depth of faulting and ancient heat flows in the Kuiper region of Mercury from lobate scarp topography

Mercurian lobate scarps are interpreted to be the surface expressions of thrust faults formed by planetary cooling and contraction, which deformed the crust down to the brittle–ductile transition (BDT) depth at the time of faulting. In this work we have used a forward modeling procedure in order to analyze the relation between scarp topography and fault geometries and depths associated with a group of prominent lobate scarps (Santa Maria Rupes and two unnamed scarps) located in the Kuiper region of Mercury for which Earth-based radar altimetry is available. Also a backthrust associated with one of the lobate scarps has been included in this study. We have obtained best fits for depths of faulting between 30 and 39 km; the results are consistent with the previous results for other lobate scarps on Mercury.The so-derived fault depths have been used to calculate surface heat flows for the time of faulting, taking into account crustal heat sources and a heterogeneous surface temperature due to the variable insolation pattern. Deduced surface heat flows are between 19 and 39 mW m^?2 for the Kuiper region, and between 22 and 43 mW m^?2 for Discovery Rupes. Both BDT depths and heat flows are consistent with the predictions of thermal history models for the range of time relevant for scarp formation.     

A local interstellar spectrum for galactic electrons

A heliopause spectrum at 122 AU from the Sun is presented for galactic electrons over an energy range from 1 MeV to 50 GeV that can be considered the lowest possible local interstellar spectrum (LIS). The focus of this work is on the spectral shape of the LIS below ∼1.0 GeV. The study is done by using a comprehensive numerical model for solar modulation in comparison with Voyager 1 observations at ∼112 AU from the Sun and PAMELA data at Earth. Below ∼1.0 GeV, this LIS exhibits a power law with E^{−(1.55 ± 0.05)}, where E is the kinetic energy of these electrons. However, reproducing the PAMELA electron spectrum averaged for 2009, requires a LIS with a different power law of the form E^{−(3.15 ± 0.05)} above ∼5 GeV. Combining the two power laws with a smooth transition from low to high energies yields a LIS over the full energy range that is relevant and applicable to the modulation of cosmic ray electrons in the heliosphere. The break occurs between ∼800 MeV and ∼2 GeV as a characteristic feature of this LIS. The power-law form below ∼1 GeV produces a challenge to the origin of these low energy galactic electrons. On the other hand, the results of this study can be used as a gauge for astrophysical modeling of the local interstellar spectrum for electrons.     

Radiative heating of carbonaceous near-Earth objects as a cause of thermal metamorphism for CK chondrites

Metamorphic CK carbonaceous chondrites display matrix textures that are best explained by a transient thermal event with temperatures in the 550–950 K range and durations in the order of days to years, longer than what is commonly admitted for shock events but shorter than what is required for nuclide decay. We propose that radiative heating of small carbonaceous meteoroids with perihelia close to the Sun could account for the petrological features observed in CK chondrites. Numerical thermal modeling, using favorable known NEOs orbital parameters (perihelion distances between 0.07 and 0.15 AU) and physical properties of CV and CK chondrites (albedo in the range 0.01–0.1, 25% porosity, thermal diffusivity of 0.5–1.5 W m^?1 K^?1), shows that radiative heating can heat carbonaceous meteoroids in the meter size range to core temperatures up to 1050 K, consistent with the metamorphic temperatures estimated for CK chondrites. Sizes of known CV and CK chondrites indicate that all these objects were small meteoroids (radii from a few cm to 2.5 m) prior to their atmospheric entry. Simulations of dynamic orbits for NEO objects suggest that there are numerous such bodies with suitable orbits and properties, even if they are only a small percentage of all NEOs. Radiative heating would be a secondary process (superimposed on parent-body processes) affecting meteoroids formed by the disruption of an initially homogeneous CV3-type parent body. Different petrologic types can be accounted for depending on the sizes and heliocentric distances of the objects in such a swarm.