Effects of low-viscous layers and a non-zero obliquity on surface stresses induced by diurnal tides and non-synchronous rotation: The case of Europa

In this study we present a semi-analytical Maxwell-viscoelastic model of the variable tidal stress field acting on Europa’s surface. In our analysis, we take into account surface stresses induced by the small eccentricity of Europa’s orbit, the non-zero obliquity of Europa’s spin axis - both acting on a diurnal 3.55-days timescale - and the reorientation of the ice shell as a result of non-synchronous rotation (NSR). We assume that Europa’s putative ocean is covered by an ice shell, which we subdivide in a low-viscous and warm lower ice layer (asthenosphere, viscosity 10¹²-10¹⁷ Pa s), and a high-viscous and cold upper ice layer (lithosphere, viscosity 10²¹ Pa s).Viscoelastic relaxation influences surface stresses in two ways: (1) through viscoelastic relaxation in the lithosphere and (2) through the viscoelastic tidal response of Europa’s interior. The amount of relaxation in the lithosphere is proportional to the ratio between the period of the forcing mechanism and the Maxwell time of the high-viscous lithosphere. As a result, this effect is only relevant to surface stresses caused by the slow NSR mechanism. On the other hand, the importance of the viscoelastic response on surface stresses is proportional to the ratio between the relaxation time (τ_j) of a given viscoelastic mode j and the period of the forcing function. On a diurnal timescale the fast relaxation of transient modes related to the low viscosity of the asthenosphere can alter the magnitude and phase shift of the diurnal stress field at Europa’s surface. The effects are largest, up to 20% in magnitude and 7° in phase for ice rigidities lower than 3.487 GPa, when the relaxation time of the aforementioned transient modes approaches the inverse of the average angular rate of Europa’s orbit. On timescales relevant for NSR (>10⁴ years) the magnitude and phase shift of NSR surface stresses can be affected by viscoelastic relaxation of the ocean-ice boundary. This effect, however, becomes only important when the behavior of the lithosphere w.r.t. NSR approaches the fluid limit, i.e. for strong relaxation in the lithosphere. The combination of NSR and diurnal stresses for different amounts of viscoelastic relaxation of NSR stresses in the lithosphere leads to a large variety of global stress fields that can explain the formation of the large diversity of lineament morphologies observed on Europa’s surface. Variation of the amount of relaxation in the lithosphere is likely due to changes in the spin rate of Europa and/or the rheological properties of the surface.In addition, we show that a small obliquity(<1°) can have a considerable effect on Europa’s diurnal stress field. A non-zero obliquity breaks the symmetric distribution of stress patterns with respect to the equator, thereby affecting the magnitude and orientation of the principal stresses at the surface. As expected, increasing the value of Europa’s obliquity leads to larger diurnal stresses at the surface, especially when Europa is located 90° away from the nodes formed by the intersection of its orbital and equatorial planes.     

Constraints on Europa’s rotational dynamics from modeling of tidally-driven fractures

Cycloids, arcuate features observed on Europa’s surface, have been interpreted as tensile cracks that form in response to diurnal tidal stress caused by Europa’s orbital eccentricity. Stress from non-synchronous rotation may also contribute to tidal stress, and its influence on cycloid shapes has been investigated as well. Obliquity, fast precession, and physical libration would contribute to tidal stress but have often been neglected because they were expected to be negligibly small. However, more sophisticated analyses that include the influence of Jupiter’s other large satellites and the state of Europa’s interior indicate that perhaps these rotational parameters are large enough to alter the tidal stress field and the formation of tidally-driven fractures. We test tidal models that include obliquity, fast precession, stress due to non-synchronous rotation, and physical libration by comparing how well each model reproduces observed cycloids. To do this, we have designed and implemented an automated parameter-searching algorithm that relies on a quantitative measure of fit quality, which we use to identify the best fits to observed cycloids. We then apply statistical techniques to determine the tidal model best supported by the data. By incorporating obliquity, fits to observed southern hemisphere cycloids improve, and we can reproduce equatorial and equator-crossing cycloids. Furthermore, we find that obliquity plus physical libration is the tidal model best supported by the data. With this model, the obliquities range from 0.32° to 1.35°. The libration amplitudes are 0.72–2.44°, and the libration phases are −6.04° to 17.72° with one outlier at 84.5°. The variability in obliquity is expected if Europa’s ice shell is mechanically decoupled from the interior, and the libration amplitudes are plausible in the presence of a subsurface ocean. Indeed, the presence of a decoupling ocean may result in feedbacks that cause all of these rotational parameters to become time-variable.     

Heat flow, lenticulae spacing, and possibility of convection in the ice shell of europa

Two opposing models to explain the geological features observed on Europa’s surface have been proposed. The thin-shell model states that the ice shell is only a few kilometers thick, transfers heat by conduction only, and can become locally thinner until it exposes an underlying ocean on the satellite’s surface. According to the thick-shell model, the ice shell may be several tens of kilometers thick and have a lower convective layer, above which there is a cold stagnant lid that dissipates heat by conduction. Whichever the case, from magnetic data there is strong support for the presence of a layer of salty liquid water under the ice. The present study was performed to examine whether the possibility of convection is theoretically consistent with surface heat flows of ∼100-200 mW m⁻², deduced from a thin brittle lithosphere, and with the typical spacing of 15-23 km proposed for the features usually known as lenticulae. It was obtained that under Europa’s ice shell conditions convection could occur and also account for high heat flows due to tidal heating of the convective (nearly isothermal) interior, but only if the dominant water ice rheology is superplastic flow (with activation energy of 49 kJ mol⁻¹; this is the rheology thought dominant in the warm interior of the ice shell). In this case the ice shell would be ∼15-50 km thick. Furthermore, in this scenario explaining the origin of the lenticulae related to convective processes requires ice grain size close to 1 mm and ice thickness around 15-20 km.     

Coupled convection and tidal dissipation in Europa’s ice shell using non-Newtonian grain-size-sensitive (GSS) creep rheology

We present self-consistent, fully coupled two-dimensional (2D) numerical models of thermal evolution and tidal heating to investigate how convection interacts with tidal dissipation under the influence of non-Newtonian grain-size-sensitive creep rheology (plausibly resulting from grain boundary sliding) in Europa’s ice shell. To determine the thermal evolution, we solved the convection equations (using finite-element code ConMan) with the tidal dissipation as a heat source. For a given heterogeneous temperature field at a given time, we determined the tidal dissipation rate throughout the ice shell by solving for the tidal stresses and strains subject to Maxwell viscoelastic rheology (using finite-element code Tekton). In this way, the convection and tidal heating are fully coupled and evolve together. Our simulations show that the tidal dissipation rate can have a strong impact on the onset of thermal convection in Europa’s ice shell under non-Newtonian GSS rheology. By varying the ice grain size (1-10 mm), ice-shell thickness (20-120 km), and tidal-strain amplitude (0-4 × 10⁻⁵), we study the interrelationship of convection and conduction regimes in Europa’s ice shell. Under non-Newtonian grain-size-sensitive creep rheology and ice grain size larger than 1 mm, no thermal convection can initiate in Europa’s ice shell (for thicknesses <100 km) without tidal dissipation. However, thermal convection can start in thinner ice shells under the influence of tidal dissipation. The required tidal-strain amplitude for convection to occur decreases as the ice-shell thickness increases. For grain sizes of 1-10 mm, convection can occur in ice shells as thin as 20-40 km with the estimated tidal-strain amplitude of 2 × 10⁻⁵ on Europa.     

Can redistribution of material by sputtering explain the hemispheric dichotomy of europa?

Sputtering and redeposition make up a significant geologic process on Europa and may contribute to the observed color differences between the leading and trailing hemispheres. Sputtering is particularly efficient on Europa as an erosive process, due to the high rate of ion bombardment from the Io plasma torus, together with Europa’s easily sputtered icy surface. We estimate the global average sputtering erosion rate on Europa at 14.7 mm Myr⁻¹. However, 42% to 86% of sputtered water molecules survive to redeposit onto the surface again. Due to gravitational escape and removal by electron-impact ionization, the number of redepositing particles cannot overcome sputtering erosion, and the global average result of sputtering is net erosion. However, neither sputtering nor redeposition is globally uniform, and differences in the global distributions of the two processes can result locally in net deposition.We propose that Europa’s hemispheric color dichotomy might be explained by net deposition on the leading hemisphere, which may obscure the non-ice signature by covering it with a thin water frost. To test this hypothesis, we have created a simulated model of the sputtering erosion/redeposition process on Europa. Our objectives are to determine the conditions under which net deposition occurs on the leading hemisphere and to evaluate the effects on this process of Jupiter’s gravity, of Europa’s rotation, and of the loss of water molecules to the jovian magnetosphere. We have followed the trajectories of hundreds of thousands of simulated sputtered water molecules in a Monte Carlo process, evolving their orbits under the gravity of both Europa and Jupiter. We have performed this model multiple times, in order to explore the effects of different assumptions of the global distribution of impacting ions, as well as of the sputtered particle ejection velocity. Based upon our results, we conclude that net deposition occurs under a wide range of conditions, making sputtering erosion and redeposition a plausible explanation for the hemispheric color dichotomy of Europa.     

Multi-frequency electromagnetic sounding of the Galilean moons

Induced magnetic fields provide the unique possibility to sound the conductive interior of planetary bodies. Such fields are caused by external time-variable magnetic fields. We investigate temporal variations of the jovian magnetospheric field at multiple frequencies at the positions of the Galilean moons and analyze possible responses due to electromagnetic induction within multi-layered interior models of all four satellites. At the jovian satellites the magnetic field varies with the synodic rotation period of Jupiter’s internal field (about 10 h), fractions of this period (e.g., 1/2 and 1/3) due to higher order harmonics of the internal field, the orbital periods of the satellites (∼40 h at Io to ∼400 h at Callisto) and the solar rotation period (about 640 h) and its harmonics due to variabilities of the magnetopause field. To analyze these field variations, we use a magnetospheric model that includes the jovian internal field, the current sheet field and fields due to the magnetopause boundary currents. With this model we calculate magnetic amplitude spectra for each satellite orbit. These spectra provide the strengths of the inducing signals at the different frequencies for all magnetic components. The magnetic fields induced in the interiors of the satellites are then determined from response functions computed for different multi-layer interior models including conductive cores and ocean layers of various conductivities and thicknesses. Based on these results we discuss what information about the ocean and core layers can be deduced from the analysis of induction signals at multiple frequencies. Even moderately thick and conductive oceans produce measurable signal strengths at several frequencies for all satellites. The conductive cores cause signals which will be hardly detectable. Our results show that mutual induction occurs between the core and the ocean. We briefly address this effect and its implications for the analysis of induced field data. We further note that close polar orbits are preferable for future Jupiter system missions to investigate the satellites interiors.     

Subsurface oceans and deep interiors of medium-sized outer planet satellites and large trans-neptunian objects

The detection of induced magnetic fields in the vicinity of the jovian satellites Europa, Ganymede, and Callisto is one of the most surprising findings of the Galileo mission to Jupiter. The observed magnetic signature cannot be generated in solid ice or in silicate rock. It rather suggests the existence of electrically conducting reservoirs of liquid water beneath the satellites' outermost icy shells that may contain even more water than all terrestrial oceans combined. The maintenance of liquid water layers is closely related to the internal structure, composition, and thermal state of the corresponding satellite interior. In this study we investigate the possibility of subsurface oceans in the medium-sized icy satellites and the largest trans-neptunian objects (TNO's). Controlling parameters for subsurface ocean formation are the radiogenic heating rate of the silicate component and the effectiveness of the heat transfer to the surface. Furthermore, the melting temperature of ice will be significantly reduced by small amounts of salts and/or incorporated volatiles such as methane and ammonia that are highly abundant in the outer Solar System. Based on the assumption that the satellites are differentiated and using an equilibrium condition between the heat production rate in the rocky cores and the heat loss through the ice shell, we find that subsurface oceans are possible on Rhea, Titania, Oberon, Triton, and Pluto and on the largest TNO's 2003 UB₃₁₃, Sedna, and 2004 DW. Subsurface oceans can even exist if only small amounts of ammonia are available. The liquid subsurface reservoirs are located deeply underneath an ice-I shell of more than 100 km thickness. However, they may be indirectly detectable by their interaction with the surrounding magnetic fields and charged particles and by the magnitude of a satellite's response to tides exerted by the primary. The latter is strongly dependent on the occurrence of a subsurface ocean which provides greater flexibility to a satellite's rigid outer ice shell.     

Coupled convection and tidal dissipation in Europa’s ice shell

We performed 2D numerical simulations of oscillatory tidal flexing to study the interrelationship between tidal dissipation (calculated using the Maxwell model) and a heterogeneous temperature structure in Europa’s ice shell. Our 2D simulations show that, if the temperature is spatially uniform, the tidal dissipation rate peaks when the Maxwell time is close to the tidal period, consistent with previous studies. The tidal dissipation rate in a convective plume encased in a different background temperature depends on both the plume and background temperature. At a fixed background temperature, the dissipation increases strongly with plume temperature at low temperatures, peaks, and then decreases with temperature near the melting point when a melting-temperature viscosity of 10¹³ Pa s is used; however, the peak occurs at significantly higher temperature in this heterogeneous case than in a homogeneous medium for equivalent rheology. For constant plume temperature, the dissipation rate in a plume decreases as the surrounding temperature increases; plumes that are warmer than their surroundings can exhibit enhanced heating not only relative to their surroundings but relative to the Maxwell-model prediction for a homogeneous medium at the plume temperature. These results have important implications for thermal feedbacks in Europa’s ice shell.To self-consistently determine how convection interacts with tidal heating that is correctly calculated from the time-evolving heterogeneous temperature field, we coupled viscoelastic simulations of oscillatory tidal flexing (using Tekton) to long-term simulations of the convective evolution (using ConMan). Our simulations show that the tidal dissipation rate resulting from heterogeneous temperature can have a strong impact on thermal convection in Europa’s ice shell. Temperatures within upwelling plumes are greatly enhanced and can reach the melting temperature under plausible tidal-flexing amplitude for Europa. A pre-existing fracture zone (at least 6 km deep) promotes the concentration of tidal dissipation (up to ∼20 times more than that in the surroundings), leading to lithospheric thinning. This supports the idea that spatially variable tidal dissipation could lead locally to high temperatures, partial melting, and play an important role in the formation of ridges, chaos, or other features.     

Europa’s ridged plains and smooth low albedo plains: Distinctive compositions and compositional gradients at the leading side-trailing side boundary

This investigation uses linear mixture modeling employing cryogenic laboratory reference spectra to estimate surface compositions and water ice grain sizes of Europa’s ridged plains and smooth low albedo plains. Near-infrared spectra for 23 exposures of ridged plains materials are analyzed along with 11 spectra representing low albedo plains. Modeling indicates that these geologic units differ both in the relative abundance of non-ice hydrated species and in the abundance and grain sizes of water ice. The background ridged plains in our study area appear to consist predominantly of water ice (∼46%) with approximately equal amounts (on average) of hydrated sulfuric acid (∼27%) and hydrated salts (∼27%). The solutions for the smooth low albedo plains are dominated by hydrated salts (∼62%), with a relatively low mean abundance of water ice (∼10%), and an abundance of hydrated sulfuric acid similar to that found in ridged plains (∼27%). The model yields larger water ice grain sizes (100 μm versus 50-75 μm) in the ridged plains. The 1.5-μm water ice absorption band minimum is found at shorter wavelengths in the low albedo plains deposits than in the ridged plains (1.498 ± .003 μm versus 1.504 ± .001 μm). The 2.0-μm band minimum in the low albedo plains exhibits a somewhat larger blueshift (1.964 ± .006 μm versus 1.983 ± .006 μm for the ridged plains).The study area spans longitudes from 168° to 185°W, which includes Europa’s leading side-trailing side boundary. A well-defined spatial gradient of sulfuric acid hydrate abundance is found for both geologic units, with concentrations increasing in the direction of the trailing side apex. We associate this distribution with the exogenic effects of magnetospheric charged particle bombardment and associated chemical processing of surface materials (the radiolytic sulfur cycle). However, one family of low albedo plains exposures exhibits sulfuric acid hydrate abundances up to 33% lower than found for adjacent exposures, suggesting that these materials have undergone less processing, thus implying that these deposits may have been emplaced more recently.Modeling identifies high abundances (to 30%) of magnesium sulfate brines in the low albedo plains exposures. Our investigation marks the first spectroscopic identification of MgSO₄ brine on Europa. We also find significantly higher abundances of sodium-bearing species (bloedite and mirabilite) in the low albedo plains. The results illuminate the role of radiolytic processes in modifying the surface composition of Europa, and may provide new constraints for models of the composition of Europa’s putative subsurface ocean.     

On the “rotational angular momentum” of the oceans and the corresponding polar motion

Periodic polar motions caused by ocean tides are predicted. In the Liouville equations for rotational motion the complete excitation functions for the ocean tides have to be used. This does not depend on the fact that hydrodynamical ocean tide models do not consider the centrifugal acceleration. The observable polar motion of the Celestial Ephemeris Pole CEP (more exactly: the terrestrial location of the CEP) is tabulated for the ten ocean tides M₂, S₂, N₂, K₁, O₁, P₁, M f, M f′, M m, Ssa. Typical amplitudes for the largest ocean tides are 0.4 milliarcseconds. This is within the reach of geodetic VLBI and SLR observations.     

Nonresonant generation of MHD disturbances during supernova explosions in an inhomogeneous interstellar medium

We analyze the nonresonant generation of large-scale magnetic inhomogeneities near a shock front by accelerated particles. The MHD disturbances are generated by the electric current excited by relativistic particles in the preshock medium in the presence of weak large-scale density inhomogeneities. The MHD modes considered can be amplified by other resonant and nonresonant mechanisms related to the presence of relativistic particles. We estimate the magnetic fields and the energies to which charged particles can be accelerated in different phases of the interstellar medium by taking into account the random magnetic fields generated by the mechanism considered.     

Elastic ice shells of synchronous moons: Implications for cracks on Europa and non-synchronous rotation of Titan

A number of synchronous moons are thought to harbor water oceans beneath their outer ice shells. A subsurface ocean frictionally decouples the shell from the interior. This has led to proposals that a weak tidal or atmospheric torque might cause the shell to rotate differentially with respect to the synchronously rotating interior. Applications along these lines have been made to Europa and Titan. However, the shell is coupled to the ocean by an elastic torque. As a result of centrifugal and tidal forces, the ocean would assume an ellipsoidal shape with its long axis aligned toward the parent planet. Any displacement of the shell away from its equilibrium position would induce strains thereby increasing its elastic energy and giving rise to an elastic restoring torque. In the investigation reported on here, the elastic torque is compared with the tidal torque acting on Europa and the atmospheric torque acting on Titan.Regarding Europa, it is shown that the tidal torque is far too weak to produce stresses that could fracture the ice shell, thus refuting an idea that has been widely advocated. Instead, it is suggested that the cracks arise from time-dependent stresses due to non-hydrostatic gravity anomalies from tidally driven, episodic convection in the satellite’s interior.Two years of Cassini RADAR observations of Titan’s surface have been interpreted as implying an angular displacement of ∼0.24° relative to synchronous rotation. Compatibility of the amplitude and phase of the observed non-synchronous rotation with estimates of the atmospheric torque requires that Titan’s shell be decoupled from its interior. We find that the elastic torque balances the seasonal atmospheric torque at an angular displacement ?0.05°, effectively coupling the shell to the interior. Moreover, if Titan’s surface were spinning faster than synchronous, the tidal torque tending to restore synchronous rotation would almost certainly be larger than the atmospheric torque. There must either be a problem with the interpretation of the radar observations, or with our basic understanding of Titan’s atmosphere and/or interior.     

Tidal dynamical considerations constrain the state of an ocean on Enceladus

In previous work, solutions to the non-dissipative Laplace Tidal Equations (LTE) were used to provide bounds on the heat generated by the response of a subsurface ocean on Enceladus to an obliquity component of tidal forces. Here we improve these bounds using solutions from the LTE with a generic dissipation term explicitly added. We find solutions for a wider range of ocean tidal responses that include both unstratified (barotropic) and stratified (baroclinic) flow responses to obliquity as well as eccentricity components of the tidal forces. We consolidate the results in three ocean tidal scenarios on Enceladus that can explain the high heat fluxes (∼7 mW/m² globally averaged) inferred from measurements by the Cassini spacecraft: (1) a deep (1-50 km) barotropic ocean responding to obliquity tidal forces, where obliquity is at least 0.1°; (2) a shallow (∼360 m) barotropic ocean responding to eccentricity tidal forces; (3) a stratified (baroclinic) ocean responding to eccentricity tidal forces where the density-weighted “equivalent depth” (typically much smaller than the ocean’s physical depth) is near 360 m. The ocean is assumed to be global, but extensions for a semi-global case are also described. A more general result which is independent of the specific scenarios proposed is that an ocean attempting to freeze (with an associated decrease in its liquid depth, which affects the ocean’s dynamical response to the tidal forcing) must first pass through resonant configurations with a greatly increased generation of ocean tidal heat (exceeding 1 W/m² to 1 kW/m²) that would act to halt further freezing and stagnate the ocean state in this configuration so long as there is still orbital energy to provide the tidal forces. With an additional assumption that the ocean has evolved from a more energetic state where the depth of the liquid ocean was greater, we obtain the three scenarios proposed.     

Galileo PPR observations of Europa: Hotspot detection limits and surface thermal properties

The Galileo photopolarimeter–radiometer (PPR) made over 100 observations of Europa’s surface temperature. We have used these data to constrain a diurnal thermal model and, thus, map the thermal inertia and bolometric albedo over 20% of the surface. We find an increased thermal inertia at mid-latitudes that is widespread in longitude and does not appear to correlate with geology, albedo, or other observables. Our derived thermophysical properties can be used to predict volatile stability across the surface over the course of a day and in planning of infrared instruments on future missions. Furthermore, while observations in the thermal infrared can and have been used to find endogenic activity, no such activity was detected at Europa. We have calculated the detection limits of these PPR observations and find that 100 km² hotspots with temperatures of 116–1200 K could exist undetected on the surface, depending on the location.     

Neutral particle release from Europa’s surface

In this paper, we look at space weathering processes on the icy surface of Jupiter’s moon Europa. The heavy energetic ions of the jovian plasma (H⁺, O⁺, S⁺, C⁺) can erode the surface of Europa via ion sputtering (IS), ejecting up to 1000 H₂O molecules per ion. UV photons impinging the Europa’s surface can also result in neutral atom release via photon-stimulated desorption (PSD) and chemical change (photolysis). In this work, we study the efficiency of the IS and PSD processes for ejecting water molecules, simulating the resulting neutral H₂O density. We also estimate the contribution to the total neutral atom release by the Ion Backscattering (IBS) process. Moreover, we estimate the possibility of detecting the sputtered high energy atoms, in order to distinguish the action of the IS process from other surface release mechanisms. Our main results are: (1) The most significant sputtered-particle flux and the largest contribution to the neutral H₂O density come from the incident S⁺ ions; (2) the H₂O density produced via PSD is lower than that due to sputtering by ∼1.5 orders of magnitude; (3) in the energy range below 1 keV, the IBS can be considered negligible for the production of neutrals, whereas in the higher energy range it becomes the dominant neutral emission mechanism; (4) the total sputtering rate for Europa is 2.0 × 10²⁷ H₂O s⁻¹; and (5) the fraction of escaping H₂O via IS is 22% of the total sputtered population, while the escape fraction for H₂O produced by PSD is 30% of the total PSD population. Since the PSD exosphere is lower than the IS one, the major agent for Europa’s surface total net erosion is IS on both the non-illuminated and illuminated side. Lastly, the exospheric neutral density, estimated from the Galileo electron density measurements appears to be higher than that calculated for H₂O alone; this favors the scenario of the presence of O₂ produced by radiolysis and photolysis.     

Accretion onto stars with octupole magnetic fields: Matter flow, hot spots and phase shifts

Recent measurements of the surface magnetic fields of classical T Tauri stars (CTTSs) and magnetic cataclysmic variables show that their magnetic fields have a complex structure. Investigation of accretion onto such stars requires global three-dimensional (3D) magnetohydrodynamic (MHD) simulations, where the complexity of simulations strongly increases with each higher-order multipole. Previously, we were able to model disc accretion onto stars with magnetic fields described by a superposition of dipole and quadrupole moments. However, in some stars, like CTTS V2129 Oph and BP Tau, the octupolar component is significant and it was necessary to include the next octupolar component. Here, we show results of global 3D MHD simulations of accretion onto stars with superposition of the dipole and octupole fields, where we vary the ratio between components. Simulations show that if octupolar field strongly dominates at the disc-magnetosphere boundary, then matter flows into the ring-like octupolar poles, forming ring-shape spots at the surface of the star above and below equator. The light-curves are complex and may have two peaks per period. In case where the dipole field dominates, matter accretes in two ordered funnel streams towards poles, however the polar spots are meridionally-elongated due to the action of the octupolar component. In the case when the fields are of similar strengths, both, polar and belt-like spots are present. In many cases the light-curves show the evidence of complex fields, excluding the cases of small inclinations angles, where sinusoidal light-curve is observed and ‘hides’ the information about the field complexity.We also propose new mechanisms of phase shift in stars with complex magnetic fields. We suggest that the phase shifts can be connected with: (1) temporal variation of the star’s intrinsic magnetic field and subsequent redistribution of main magnetic poles; (2) variation of the accretion rate, which causes the disc to interact with the magnetic fields associated with different magnetic moments. We use our model to demonstrate these phase shift mechanisms, and we discuss possible applications of these mechanisms to accreting millisecond pulsars and young stars.     

The origin of galactic magnetic fields

In this article it is argued that galactic magnetic fields are generated in the earliest moments of galaxy collapse. Our model proposes that provided, even if only briefly, a supermassive star is formed early on in the galaxy formation process, this star can produce a strong centrally localized magnetic field which may act as the seed field from which a galactic field can grow. In order to substantiate this model, detailed numerical calculations will be required.     

Segmented lineaments on Europa: Implications for the formation of ridge complexes and bright bands

We describe several segmented lineaments on Europa’s surface. These lineaments are extensive, stretching for 100s-1000s of km, and have ridge complex or bright band morphologies. The geometries of the segmented portions of these features are diagnostic of the remote normal and shear stress environment in which they formed and, therefore, constrain ridge complex and bright band formation mechanisms. Analysis of four ridge complexes indicates that they formed in a remote normal stress environment that was tensile and isotropic (or nearly so) and that these lineaments may have formed in a manner more analogous to bands on Europa than to ridges. The stress environment associated with these ridge complexes may also explain the anastomosing nature of their interior morphology. Analysis of two bright bands indicate that one formed in a remote normal stress environment that was tensile and the other was reactivated under a combination of remote tensile normal stress and remote sinistral shear stress. Aspects of the morphologies of these features also indicate that bright bands likely have complex deformation histories that can include multiple episodes of reactivation.     

Linkage between accretion disks and blazars

The magnetic field in an accretion disk is estimated assuming that all of the angular momentum within prescribed accretion disk radii is removed by a jet. The magnetic field estimated at the base of the jet is extrapolated to the blazar emission region using a model for a relativistic axisymmetric jet combined with some simplifying assumptions based on the relativistic nature of the flow. The extrapolated magnetic field is compared with estimates based upon the synchrotron and inverse Compton emission from three blazars, MKN 501, MKN 421 and PKS 2155-304. The magnetic fields evaluated from pure synchrotron self-Compton models are inconsistent with the magnetic fields extrapolated in this way. However, in two cases inverse Compton models in which a substantial part of the soft photon field is generated locally agree well, mainly because these models imply magnetic field strengths consistent with an important Poynting Flux component. This comparison is based on estimating the mass accretion rate from the jet energy flux. Further comparisons along these lines will be facilitated by independent estimates of the mass accretion rate in blazars and by more detailed models for jet propagation near the black hole.     

Tidal effects on the LAGEOS–LARES satellites and the LARASE program

The effects of solid and ocean tides have been computed on the right ascension of the ascending node of the two LAGEOS and LARES satellites and on the argument of pericenter of LAGEOS II. Their effects—together with the possible mis-modeling related to systematic errors in the estimate of the tidal coefficients, especially in the case of ocean tides—are quite important to be well established for the key role of the LAGEOS satellites, as well as of the newly LARES, in space geodesy and geophysics as well as in fundamental physics measurements. In the case of the measurement of the Lense–Thirring effect, the mis-modeling of long-period tides may mimic a secular effect on the cited orbital elements, thus producing a degradation in the measurement of the relativistic precession. A suitable combination of the orbital elements of the three satellites can help in avoiding the effects of the long-period tides of degree \(\ell =2\) (as for the Lunar solid tides with periods of 18.6 and 9.3 years) and \(\ell =4\), but other long-period tides, as the ocean \(K_1\) tide, which has the same periodicities of the right ascension of the ascending node \(\varOmega \) of the satellites, may strongly influence the measurement, especially if it is performed over a relatively short time span. These results are particularly important in the case of LARES, since they are new and because of the role that the orbit of LARES, and especially of its ascending node right ascension, will have in a new measurement of the Lense–Thirring effect by the joint analysis of its orbit with that of the two LAGEOS.