On the protection of extrasolar Earth-like planets around K/M stars against galactic cosmic rays

Previous studies have shown that extrasolar Earth-like planets in close-in habitable zones around M-stars are weakly protected against galactic cosmic rays (GCRs), leading to a strongly increased particle flux to the top of the planetary atmosphere. Two main effects were held responsible for the weak shielding of such an exoplanet: (a) For a close-in planet, the planetary magnetic moment is strongly reduced by tidal locking. Therefore, such a close-in extrasolar planet is not protected by an extended magnetosphere. (b) The small orbital distance of the planet exposes it to a much denser stellar wind than that prevailing at larger orbital distances. This dense stellar wind leads to additional compression of the magnetosphere, which can further reduce the shielding efficiency against GCRs. In this work, we analyse and compare the effect of (a) and (b), showing that the stellar wind variation with orbital distance has little influence on the cosmic ray shielding. Instead, the weak shielding of M star planets can be attributed to their small magnetic moment. We further analyse how the planetary mass and composition influence the planetary magnetic moment, and thus modify the cosmic ray shielding efficiency. We show that more massive planets are not necessarily better protected against galactic cosmic rays, but that the planetary bulk composition can play an important role.     

Orbital dynamics and equilibrium points around an asteroid with gravitational orbit–attitude coupling perturbation

The strongly perturbed dynamical environment near asteroids has been a great challenge for the mission design. Besides the non-spherical gravity, solar radiation pressure, and solar tide, the orbital motion actually suffers from another perturbation caused by the gravitational orbit–attitude coupling of the spacecraft. This gravitational orbit–attitude coupling perturbation (GOACP) has its origin in the fact that the gravity acting on a non-spherical extended body, the real case of the spacecraft, is actually different from that acting on a point mass, the approximation of the spacecraft in the orbital dynamics. We intend to take into account GOACP besides the non-spherical gravity to improve the previous close-proximity orbital dynamics. GOACP depends on the spacecraft attitude, which is assumed to be controlled ideally with respect to the asteroid in this study. Then, we focus on the orbital motion perturbed by the non-spherical gravity and GOACP with the given attitude. This new orbital model can be called the attitude-restricted orbital dynamics, where restricted means that the orbital motion is studied as a restricted problem at a given attitude. In the present paper, equilibrium points of the attitude-restricted orbital dynamics in the second degree and order gravity field of a uniformly rotating asteroid are investigated. Two kinds of equilibria are obtained: on and off the asteroid equatorial principal axis. These equilibria are different from and more diverse than those in the classical orbital dynamics without GOACP. In the case of a large spacecraft, the off-axis equilibrium points can exist at an arbitrary longitude in the equatorial plane. These results are useful for close-proximity operations, such as the asteroid body-fixed hovering.     

SDSS J233325.92+152222.1 and the evolution of intermediate polars

Intermediate polars (IPs) are cataclysmic variables which contain magnetic white dwarfs with a rotational period shorter than the binary orbital period. Evolutionary theory predicts that IPs with long orbital periods evolve through the 2–3 h period gap, but it is very uncertain what the properties of the resulting objects are. Whilst a relatively large number of long-period IPs are known, very few of these have short orbital periods. We present phase-resolved spectroscopy and photometry of SDSS J233325.92+152222.1 (SDSS J2333) and classify it as the IP with the shortest-known orbital period (83.12 ± 0.09 min), which contains a white dwarf with a relatively long spin period (41.66 ± 0.13 min). We estimate the white dwarf's magnetic moment to be μ_WD≈ 2 × 10³³ G cm³, which is not only similar to three of the other four confirmed short-period IPs but also to those of many of the long-period IPs. We suggest that long-period IPs conserve their magnetic moment as they evolve towards shorter orbital periods. Therefore, the dominant population of long-period IPs, which have white dwarf spin periods roughly 10 times shorter than their orbital periods, will likely end up as short-period IPs like SDSS J2333, with spin periods a large fraction of their orbital periods.     

Orbital period modulation and magnetic cycles in close binaries

We discuss the observed orbital period modulations in close binaries, and focus on the mechanism proposed by Applegate relating the changes of the stellar internal rotation associated with a magnetic activity cycle with the variation of the gravitational quadrupole moment of the active component; the variation of this quadrupole moment in turn forces the orbital motion of the binary stars to follow the activity level of the active star. We generalize this approach by considering the details of this interaction, and develop some illustrative examples in which the problem can be easily solved in analytical form. Starting from such results, we consider the interplay between rotation and magnetic field generation in the framework of different types of dynamo models, which have been proposed to explain solar and stellar activity. We show how the observed orbital period modulation in active binaries may provide new constraints for discriminating between such models. In particular, we study the case of the prototype active binary RS Canum Venaticorum, and suggest that torsional oscillations — driven by a stellar magnetic dynamo — may account for the observed behaviour of this star. Further possible applications of the relationship between magnetic activity and orbital period modulation, related to the recent discovery of binary systems containing a radio pulsar and a convecting upper main-sequence or a late-type low-mass companion, are discussed.     

V4633 Sgr – a probable second asynchronous polar classical nova

Photometric observations of V4633 Sgr (Nova Sagittarii 1998) during 1998–2005 reveal the presence of a stable photometric periodicity at   P ₁= 180.8 min  which is probably the orbital period of the underlying binary system. A second period was present in the light curve of the object for 6 yr. Shortly after the nova eruption it was measured as   P ₂= 185.6 min  . It has decreased monotonically in the following few years reaching the value   P ₂= 183.9 min  in 2003. In 2004 it was no longer detectable. We suggest that the second periodicity is the spin of the magnetic white dwarf of this system that rotates nearly synchronously with the orbital revolution. According to our interpretation, the post-eruption evolution of Nova V4633 Sgr follows a track similar to the one taken by V1500 Cyg (Nova Cygni 1975) after that nova eruption, on a somewhat longer time-scale. The asynchronism is probably the result of the nova outburst that led to a considerable expansion of the white dwarf's photosphere. The increase in the moment of inertia of the star was associated with a corresponding decrease in its spin rate. Our observations have followed the spinning-up of the white dwarf resulting from the contraction of its outer envelope as the star is slowly returning to its pre-outburst state. It is thus the second known asynchronous polar classical nova.     

Photometric and spectroscopic study of nova Cassiopeiae 1995 (V723 Cas)

We report an 11-year long series of U BV RI observations and the results of our monitoring of the classical slow nova V723 Cas. We analyze the spectra of this star taken using the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences with a spectral resolution of 3.5–8.5 Å during the nebular stage and at the supersoft X-ray source phase (SSS). This systemhas a large orbital inclination and its orbital period is equal to 0.693265 days. The orbital period increases. We found low-amplitude light variations with the orbital period during the early stages of the outburst and even at the pre-maximum stage. The orbital light curve at the nebular stage is asymmetric and gradually increases its amplitude up to V=2 ^m in 2006. The asymmetry of the light curve of V723 Cas can be explained by the reflection effect, eclipse of the extended accretion disk, and high rate of mass transfer in the system. The light curve of V723 Cas has developed a plateau due to the SSS phase. In the spectrum of V723 Cas the transition to the SSS phase shows up in an order-of-magnitude increase of the flux of the [Fe X] λ 6374 Å emission, which forms in the expanding envelope. In addition, narrow emission lines λ 6466.4 Å (O V) and λ 6500.5 Å (Fe XVII) also emerged in the spectrum.     

On the chaotic orbital dynamics of the planet in the system 16 Cyg

The chaotic orbital dynamics of the planet in the wide visual binary star system 16 Cyg is considered. The only planet in this system has a significant orbital eccentricity, e = 0.69. Previously, Holman et al. suggested the possibility of chaos in the orbital dynamics of the planet due to the proximity of 16 Cyg to the separatrix of the Lidov–Kozai resonance. We have calculated the Lyapunov characteristic exponents on the set of possible orbital parameters for the planet. In all cases, the dynamics of 16 Cyg is regular with a Lyapunov time of more than 30 000 yr. The dynamics is considered in detail for several possible models of the planetary orbit; the dependences of Lyapunov exponents on the time of their calculation and the time dependences of osculating orbital elements have been constructed. Phase space sections for the system dynamics near the Lidov–Kozai resonance have been constructed for all models. A chaotic behavior in the orbital motion of the planet in 16 Cyg is shown to be unlikely, because 16 Cyg in phase space is far from the separatrix of the Lidov–Kozai resonance at admissible orbital parameters, with the chaotic layer near the separatrix being very narrow.     

Formation of terrestrial planets in disks with different surface density profiles

We present the results of an extensive study of the final stage of terrestrial planet formation in disks with different surface density profiles and for different orbital configurations of Jupiter and Saturn. We carried out simulations in the context of the classical model with disk surface densities proportional to \({r^{-0.5}}, {r^{-1}}\) and \({r^{-1.5}}\), and also using partially depleted, non-uniform disks as in the recent model of Mars formation by Izidoro et al. (Astrophys J 782:31, 2014). The purpose of our study is to determine how the final assembly of planets and their physical properties are affected by the total mass of the disk and its radial profile. Because as a result of the interactions of giant planets with the protoplanetary disk, secular resonances will also play important roles in the orbital assembly and properties of the final terrestrial planets, we will study the effect of these resonances as well. In that respect, we divide this study into two parts. When using a partially depleted disk (Part 1), we are particularly interested in examining the effect of secular resonances on the formation of Mars and orbital stability of terrestrial planets. When using the disk in the classical model (Part 2), our goal is to determine trends that may exist between the disk surface density profile and the final properties of terrestrial planets. In the context of the depleted disk model, results of our study show that in general, the \(\nu _5\) resonance does not have a significant effect on the dynamics of planetesimals and planetary embryos, and the final orbits of terrestrial planets. However, \(\nu _6\) and \(\nu _{16}\) resonances play important roles in clearing their affecting areas. While these resonances do not alter the orbits of Mars and other terrestrial planets, they strongly deplete the region of the asteroid belt ensuring that no additional mass will be scattered into the accretion zone of Mars so that it can maintain its mass and orbital stability. In the context of the classical model, the effects of these resonances are stronger in disks with less steep surface density profiles. Our results indicate that when considering the classical model (Part 2), the final planetary systems do not seem to show a trend between the disk surface density profile and the mean number of the final planets, their masses, time of formation, and distances to the central star. Some small correlations were observed where, for instance, in disks with steeper surface density profiles, the final planets were drier, or their water contents decreased when Saturn was added to the simulations. However, in general, the final orbital and physical properties of terrestrial planets seem to vary from one system to another and depend on the mass of the disk, the spatial distribution of protoplanetary bodies (i.e., disk surface density profile), and the initial orbital configuration of giant planets. We present results of our simulations and discuss their implications for the formation of Mars and other terrestrial planets, as well as the physical properties of these objects such as their masses and water contents.     

The dynamical stability of a Kuiper Belt-like region

The dynamics of the Kuiper Belt region between 33 and 63 au is investigated just taking into account the gravitational influence of Neptune. Indeed the aim is to analyse the information which can be drawn from the actual exoplanetary systems, where typically physical and orbital data of just one or two planets are available. Under this perspective we start our investigation using the simplest three-body model (with Sun and Neptune as primaries), adding at a later stage the eccentricity of Neptune and the inclinations of the orbital planes to evaluate their effects on the Kuiper Belt dynamics. Afterwards we remove the assumption that the orbit of Neptune is Keplerian by adding the effect of Uranus through the Lagrange–Laplace solution or through a suitable resonant normal form. Finally, different values of the mass ratios of the primary to the host star are considered in order to perform a preliminary analysis of the behaviour of exoplanetary systems. In all cases, the stability is investigated by means of classical tools borrowed from dynamical system theory, like Poincaré mappings and Lyapunov exponents.     

Period studies of classical Algol-type binaries II: UX Leo,RW Mon,EQ Ori,XZ UMa and AX Vul

This study presents an investigation of the orbital period variations of five Algol type binaries, UX Leo, RW Mon, EQ Ori, XZ UMa and AX Vul based on all available minima times. The O–C diagrams of all systems exhibit a periodic variation superimposed on a downward parabolic segment. The mass loss due to magnetic braking effect in the cooler components is assumed to account for the parabolic variation with a downward shape, while it is suggested that the light-time effect (LITE) due to an unseen component around the eclipsing binaries explains the tilted sinusoidal changes in their O–C diagrams. The orbital period decrease rates for the systems are estimated as approximately between about 0.7 and 2.5 s per century. It is clearly seen that mass loss effect is more dominant than the expected mass transfer for classical Algols in this study. The minimum mass of the probable third bodies around the eclipsing pairs was calculated to be ?0.5 M_⊙ except for UX Leo, in which it was estimated to be approximately 0.9 M_⊙. In order to search for third lights in the light curves of five systems, the V-light curves of the systems were analyzed and their physical and photometric parameters were determined. For UX Leo, a significant third light contribution was determined. We found a very small third light that can be tested using multi-color light curves, for RW Mon, EQ Ori and XZ UMa, while a third light for AX Vul could not be exposed.     

Averaged model to study long-term dynamics of a probe about Mercury

This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from \(J_2\) up to \(J_6\), and the tesseral harmonics \(\overline{C}_{22}\) that is of the same magnitude than zonal \(J_2\). In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury–Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury’s gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits.     

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.     

Allowance for the geometry of solar wind interaction with the Earth’s magnetic field in geoeffective parameters and in the prediction of geomagnetic activity

We suggest geoeffective independent parameters that can be calculated on the basis of conventional measurements of the solar wind, which allows them to be used to forecast space weather. We present the results of our analysis of the ground variations in planetary geomagnetic activity (K _p ) and geoeffective parameters calculated on the basis of solar wind and interplanetary magnetic field measurements in the Earth’s orbit for the period 1964–1996 by taking into account the change in the orientation of the geomagnetic moment during the Earth’s diurnal and annual motions.     

Orbital structure of the GJ876 extrasolar planetary system based on the latest Keck and HARPS radial velocity data

We use full available array of radial velocity data, including recently published HARPS and Keck observatory sets, to characterize the orbital configuration of the planetary system orbiting GJ876. First, we propose and describe in detail a fast method to fit perturbed orbital configuration, based on the integration of the sensitivity equations inferred by the equations of the original N-body problem. Further, we find that it is unsatisfactory to treat the available radial velocity data for GJ876 in the traditional white noise model, because the actual noise appears autocorrelated (and demonstrates non-white frequency spectrum). The time scale of this correlation is about a few days, and the contribution of the correlated noise is about 2 m/s (i.e., similar to the level of internal errors in the Keck data). We propose a variation of the maximum-likelihood algorithm to estimate the orbital configuration of the system, taking into account the red noise effects. We show, in particular, that the non-zero orbital eccentricity of the innermost planet d, obtained in previous studies, is likely a result of misinterpreted red noise in the data. In addition to offsets in some orbital parameters, the red noise also makes the fit uncertainties systematically underestimated (while they are treated in the traditional white noise model). Also, we show that the orbital eccentricity of the outermost planet is actually ill-determined, although bounded by ~0.2. Finally, we investigate possible orbital non-coplanarity of the system, and limit the mutual inclination between the planets b and c orbits by 5°?C15°, depending on the angular position of the mutual orbital nodes.     

A phenomenological study of the timing of solar activity minima of the last millennium through a physical modeling of the Sun–Planets Interaction

We numerically integrate the Sun’s orbital movement around the barycenter of the solar system under the persistent perturbation of the planets from the epoch J2000.0, backward for about one millennium, and forward for another millennium to 3000 AD. Under the Sun–Planets Interaction (SPI) framework and interpretation of Wolff and Patrone (2010), we calculated the corresponding variations of the most important storage of the specific potential energy (PE) within the Sun that could be released by the exchanges between two rotating, fluid-mass elements that conserve its angular momentum. This energy comes about as a result of the roto-translational dynamics of the cell around the solar system barycenter. We find that the maximum variations of this PE storage correspond remarkably well with the occurrences of well-documented Grand Minima (GM) solar events throughout the available proxy solar magnetic activity records for the past 1000 yr. It is also clear that the maximum changes in PE precede the GM events in that we can identify precursor warnings to the imminent weakening of solar activity for an extended period. The dynamical explanation of these PE minima is connected to the minima of the Sun’s position relative to the barycenter as well as the significant amount of time the Sun’s inertial motion revolving near and close to the barycenter. We presented our calculation of PE forward by another 1000 yr until 3000 AD. If the assumption of the solar activity minima corresponding to PE minima is correct, then we can identify quite a few significant future solar activity GM events with a clustering of PE minima pulses starting at around 2150 AD, 2310 AD, 2500 AD, 2700 AD and 2850 AD.     

Possible third body effects in the period changes of four Algol binaries: RY Aqr,SZ Her,RV Lyr and V913 Oph

An investigation of the orbital period changes of the neglected eclipsing binaries, RY Aqr, SZ Her, RV Lyr and V913 Oph, is presented based on all published minima times. Although the explanation of magnetic activity on the surface of the secondaries of the studied Algols is still open, the preferred light‐time effect due to the unseen components around the systems seems more plausible in explaining the tilted sinusoidal variations with relatively high‐amplitudes. The minimal mass values of possible tertiary components have been estimated to be about 1.06, 0.25, 0.78 and 2.85 M_⊙ for RY Aqr, SZ Her, RV Lyr and V913 Oph, respectively and the results indicate that their contributions to the total light of the eclipsing pairs are measurable with high accuracy photometric and spectroscopic data, if they exist. Applegate's (1992) model has been discussed as an alternative mechanism assuming that the cooler components have magnetic cycles. It is found that the model parameters of RY Aqr and V913 Oph are consistent with the required values in Applegate's model. In addition to the first detailed orbital study on these systems, a statistical survey on the character of the O – C variations of classical Algols has revealed that about 50 percent of the systems show cyclic behavior. This means that the presence of possible third bodies around classical Algols should be tested with careful analysis using new data. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stellar and gas dynamics of late-type barred-spiral galaxies: NGC 3359, a test case

We study the dynamics of a model for the late-type barred-spiral galaxy NGC 3359 by using both observational and numerical techniques. The results of our modelling are compared with photometric and kinematical data. The potential used is estimated directly from observations of the galaxy. It describes with a single potential function, a barred-spiral system with an extended spiral structure. Thus, the study of the dynamics in this potential has an interest by itself. We apply orbital theory and response models for the study of the stellar component, and smoothed particle hydrodynamics for modelling the gas. In particular, we examine the pattern speed of the system and the orbital character (chaotic or ordered) of the spiral arms. We conclude that the spiral pattern rotates slowly, in the sense that its corotation is close to or even beyond the end of the arms. Although a single, slow pattern speed could, under certain assumptions, characterize the whole disc, the comparison with the observational data indicates that probably the bar and the spirals have different angular velocities. In our two pattern speeds model, the best fit is obtained with a bar ending close to its 4:1 resonance and a more slowly rotating spiral. Assuming an 11 Mpc distance to the galaxy, a match of our models with the observed data indicates a pattern speed of about  39 km s⁻¹ kpc⁻¹  for the bar and about  15 km s⁻¹ kpc⁻¹  for the spiral. We do not find any indication for a chaotic character of the arms in this barred-spiral system. The flow in the region of the spirals can best be described as a regular 'precessing-ellipses flow'.     

A comprehensive photometric study of the Algol-type eclipsing binary: BG Pegasi

This study presents new photometric observations of classical Algol type binary BG Peg with a δ Scuti component. The light curve modeling was provided with the physical parameters of the component stars in the BG Peg system for the first time. After modeling light curves in B and V filters, the eclipse and proximity effects were removed from the light curve to analyze intrinsic variations caused by the hotter component of the system. Frequency analysis of the residuals light represents the multi-mode pulsation of the more massive component of the BG Peg system at periods of 0.039 and 0.047 days. Two frequencies could be associated with non-radial (l = 2) modes. The total amplitude of the pulsational variability in the V light curve was found to be about 0.045 mag. The long-term orbital period variation of the system was also investigated for the first time. The O–C analysis indicates periodic variation superimposed on a downward parabola. The secular period variation means that the orbital period of the system is decreasing at a rate of ?5.5 seconds per century, probably due to the magnetic activity of the cooler component. The tilted sinusoidal O–C variation may be caused by the gravitational effect of an unseen component around the system.     

Role of the solar wind parameters in changing orbital motion of the Earth’s satellites

The investigation of the solar wind and geomagnetic activity parameters' effect on variations of the orbital motion periods of artificial satellites has been continued. The periods of orbital motion of uncontrolled satellites from the database of the Ukrainian network of optical stations (UNOS) for 2012–2014 was used. The data have been compared with the values of geomagnetic planetary index K and the energy spectra of protons and electrons obtained by the GEOS satellites in events during which the orbital periods have changed. It is shown that, in the energy spectra of the proton and electron fluxes, there is no effect of softening the spectrum with time at the time of the flare appearance. This indicates the possibility of particle accumulation above the active region (AR), which entails further continuous energy emission of the solar flare from AR. Dependences have been obtained between the geomagnetic activity and the solar wind speed at a given interplanetary magnetic field strength during the periods under study for the changes in the orbital motion periods of satellites. The corresponding correlation coefficients are 0.93–0.96.     

Small-scale high-temperature structures in flare regions

When analyzing YOHKOH/SXT, HXT (soft and hard X-ray) images of solar flares against the background of plasma with a temperature T?6 MK, we detected localized (with minimum observed sizes of ≈2000 km) high-temperature structures (HTSs) with T≈(20–50) MK with a complex spatial-temporal dynamics. Quasi-stationary, stable HTSs form a chain of hot cores that encircles the flare region and coincides with the magnetic loop. No structures are seen in the emission measure. We reached conclusions about the reduced heat conductivity (a factor of ～10³ lower than the classical isotropic one) and high thermal insulation of HTSs. The flare plasma becomes collisionless in the hottest HTSs (T>20 MK). We confirm the previously investigated idea of spatial heat localization in the solar atmosphere in the form of HTSs during flare heating with a volume nonlocalized source. Based on localized soliton solutions of a nonlinear heat conduction equation with a generalized flare-heating source of a potential form including radiative cooling, we discuss the nature of HTSs.