On the photo-gravitational restricted four-body problem with variable mass

This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393–394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86–97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses \(m_{1}\), \(m_{2}\) and \(m_{3}\) in an equilateral triangle with \(m_{2}=m_{3}\) will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters \(\gamma (\frac{m \ \text{at time} \ t}{m \ \text{at initial time}}, 0<\gamma\leq1 )\), \(\alpha\) (the proportionality constant in Jeans’ law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), \(0\leq\alpha\leq2.2\)), the mass parameter \(\mu=0.005\) and radiation parameters \(q_{i}, (0< q_{i}\leq1, i=1, 2, 3)\). All the libration points are non-collinear if \(q_{2}\neq q_{3}\). It has been observed that the collinear and out-of-plane libration points also exist for \(q_{2}=q_{3}\). In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton–Raphson basins of attraction are also discussed.     

Dust color temperature distribution of two FIR cavities at IRIS and AKARI maps

By systematically searching the region of far infrared loops, we found a number of huge cavity-like dust structures at \(60\,\mu \hbox {m}\) and \(100\,\mu \hbox {m}\) IRIS maps. By checking these with AKARI maps (\(90\,\mu \hbox {m}\) and \(140\,\mu \hbox {m}\)), two new cavity-like structures (sizes \(\sim \) \( 2.7\,\hbox {pc} \times 0.8\,\hbox {pc}\) and \(\sim \) \( 1.8\,\hbox {pc} \times 1\,\hbox {pc}\)) located at R.A. (\(\hbox {J}2000)=14^{h}41^{m}23^{s}\) and Dec. \((\hbox {J}2000)=-64^{\circ }04^{\prime }17^{{\prime }{\prime }}\) and R.A. \((\hbox {J}2000)=05^{h}05^{m}35^{s}\) and Dec. \((\hbox {J}2000)=-\,69^{\circ }35^{\prime } 25^{{\prime }{\prime }}\) were selected for the study. The difference in the average dust color temperatures calculated using IRIS and AKARI maps of the cavity candidates were found to be \(3.2\pm 0.9\,\hbox {K}\) and \(4.1\pm 1.2\,\hbox {K}\), respectively. Interestingly, the longer wavelength AKARI map gives larger values of dust color temperature than that of the shorter wavelength IRIS maps. Possible explanation of the results will be presented.     

Addendum to: Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

This addendum uses an alternate fit for the electron density distribution \(N(r)\) (see Figure 1) and estimates the coronal magnetic field using the new model. We find that the estimates of the magnetic field are in close agreement using both the models.

We have fit the \(N(r)\) distribution obtained from STEREO-A/COR1 and SOHO/LASCO-C2 using a fifth-order polynomial (see Figure 1). The expression can be written as

$$\begin{aligned} N_{\text{cor}}(r) &= 1.43 \times 10^{9} r^{-5} - 1.91 \times 10^{9} r^{-4} + 1.07 \times 10^{9} r^{-3} - 2.87 \times 10^{8} r^{-2} \\ &\quad {} + 3.76 \times 10^{7} r^{-1} - 1.91 \times 10^{6} , \end{aligned}$$

(1)

where \(N_{\text{cor}}(r)\) is in units of cm^?3 and \(r\) is in units of \(\mathrm{R}_{\odot}\). The background coronal electron density is enhanced by a factor of 5.5 at 2.63 \(\mathrm{R}_{\odot}\) during the coronal mass ejection (CME). The estimated coronal magnetic field strength (\(B\)) using radio data indicates that \(B(r) \approx(0.51\text{\,--\,}0.48) \pm 0.02\ \mathrm{G}\) in the range \(r \approx2.65\text{\, --\,}2.82\ \mathrm{R}_{\odot}\). The field strengths for STEREO-A/COR1 and SOHO/LASCO-C2 are ≈?0.32 G at \(r \approx 3.11\ \mathrm{R}_{\odot}\) and ≈?0.12 G at \(r \approx 4.40\ \mathrm{R}_{\odot}\), respectively.

     

Markarian galaxies in UV and multiwavelength studies

The UV properties of 1152 Markarian galaxies have been investigated based on GALEX data. These objects have been investigated also in other available wavelengths using multi-wavelength data from X-ray to radio. Using our classification for activity types for 779 Markarian galaxies based on SDSS spectroscopy, we have investigated these objects on the GALEX, 2MASS and WISE color-magnitude and color-color diagrams by the location of objects of different activity types and have revealed a number of loci. UV contours overplotted on the optical images revealed additional structures, particularly spiral arms of a number of Markarian galaxies. UV (FUV and NUV) and optical absolute magnitudes and luminosities have been calculated showing graduate transition from AGN to Composites, HIIs and Absorption line galaxies from (average \(M\)) \(-17.56^{m}\) to \(-15.20^{m}\) in FUV, from \(-18.07^{m}\) to \(-15.71^{m}\) in NUV and from AGN to Composites, Absorption line galaxies and HII from \(-21.14^{m}\) to \(-19.42^{m}\) in optical wavelengths and from (average \(L\)) \(7\times10^{9}\) to \(4 \times 10^{8}\) in FUV, from \(1\times 10^{10}\) to \(5\times10^{8}\) in NUV and from AGN to Composites, Absorption line galaxies and HII from \(7\times10^{10}\) to \(1\times10^{10}\) in optical wavelengths.     

An analysis of the convergence of Newton iterations for solving elliptic Kepler’s equation

In this note a study of the convergence properties of some starters \( E_0 = E_0(e,M)\) in the eccentricity–mean anomaly variables for solving the elliptic Kepler’s equation (KE) by Newton’s method is presented. By using a Wang Xinghua’s theorem (Xinghua in Math Comput 68(225):169–186, 1999) on best possible error bounds in the solution of nonlinear equations by Newton’s method, we obtain for each starter \( E_0(e,M)\) a set of values \( (e,M) \in [0, 1) \times [0, \pi ]\) that lead to the q-convergence in the sense that Newton’s sequence \( (E_n)_{n \ge 0}\) generated from \( E_0 = E_0(e,M)\) is well defined, converges to the exact solution \(E^* = E^*(e,M)\) of KE and further \( \vert E_n - E^* \vert \le q^{2^n -1}\; \vert E_0 - E^* \vert \) holds for all \( n \ge 0\). This study completes in some sense the results derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014) by using Smale’s \(\alpha \)-test with \(q=1/2\). Also since in KE the convergence rate of Newton’s method tends to zero as \( e \rightarrow 0\), we show that the error estimates given in the Wang Xinghua’s theorem for KE can also be used to determine sets of q-convergence with \( q = e^k \; \widetilde{q} \) for all \( e \in [0,1)\) and a fixed \( \widetilde{q} \le 1\). Some remarks on the use of this theorem to derive a priori estimates of the error \( \vert E_n - E^* \vert \) after n Kepler’s iterations are given. Finally, a posteriori bounds of this error that can be used to a dynamical estimation of the error are also obtained.     

The Origin of Sequential Chromospheric Brightenings

Sequential chromospheric brightenings (SCBs) are often observed in the immediate vicinity of erupting flares and are associated with coronal mass ejections. Since their initial discovery in 2005, there have been several subsequent investigations of SCBs. These studies have used differing detection and analysis techniques, making it difficult to compare results between studies. This work employs the automated detection algorithm of Kirk et al. (Solar Phys. 283, 97, 2013) to extract the physical characteristics of SCBs in 11 flares of varying size and intensity. We demonstrate that the magnetic substructure within the SCB appears to have a significantly smaller area than the corresponding \(\mbox{H}\upalpha\) emission. We conclude that SCBs originate in the lower corona around \(0.1~R_{\odot}\) above the photosphere, propagate away from the flare center at speeds of \(35\,\mbox{--}\,85~\mbox{km}\,\mbox{s}^{-1}\), and have peak photosphere magnetic intensities of \(148\pm2.9~\mbox{G}\). In light of these measurements, we infer SCBs to be distinctive chromospheric signatures of erupting coronal mass ejections.     

Secondary resonances and the boundary of effective stability of Trojan motions

One of the most interesting features in the libration domain of co-orbital motions is the existence of secondary resonances. For some combinations of physical parameters, these resonances occupy a large fraction of the domain of stability and rule the dynamics within the stable tadpole region. In this work, we present an application of a recently introduced ‘basic Hamiltonian model’ \(H_\mathrm{b}\) for Trojan dynamics (Páez and Efthymiopoulos in Celest Mech Dyn Astron 121(2):139, 2015; Páez et al. in Celest Mech Dyn Astron 126:519, 2016): we show that the inner border of the secondary resonance of lowermost order, as defined by \(H_\mathrm{b}\), provides a good estimation of the region in phase space for which the orbits remain regular regardless of the orbital parameters of the system. The computation of this boundary is straightforward by combining a resonant normal form calculation in conjunction with an ‘asymmetric expansion’ of the Hamiltonian around the libration points, which speeds up convergence. Applications to the determination of the effective stability domain for exoplanetary Trojans (planet-sized objects or asteroids) which may accompany giant exoplanets are discussed.     

Density variation effect on multi-ions with kinetic Alfven wave around cusp region—a kinetic approach

The kinetic Alfven waves in the presence of homogeneous magnetic field plasma with multi-ions effect are investigated. The dispersion relation and normalised damping rate are derived for low-\(\beta\) plasma using kinetic theory. The effect of density variation of \(\text{H}^{+}\), \(\text{He}^{+}\) and \(\text{O}^{+}\) ions is observed on frequency and damping rate of the wave. The variation of frequency (\(\omega\)) and normalised damping rate (\(\gamma / \varOmega_{H^{ +}} \)) of the wave are studied with respect to \(k_{ \bot} \rho_{j}\), where \(k_{ \bot} \) is the perpendicular wave number, \(\rho_{j}\) is the ion gyroradius and \(j \) denotes \(\text{H}^{+}\), \(\text{He}^{+}\) and \(\text{O}^{+}\) ions. The variation with \(k_{ \bot} \rho_{j}\) is considered over wide range. The parameters appropriate to cusp region are used for the explanation of results. It is found that with hydrogen and helium ions gyration, the frequency of wave is influenced by the density variation of \(\text{H}^{+}\) and \(\text{He}^{+}\) ions but remains insensitive to the change in density of \(\text{O}^{+}\) ions. For oxygen ion gyration, the frequency of wave varies over a short range only for \(\text{O}^{+}\) ion density variation. The wave shows damping at lower altitude due to variation in density of lighter \(\text{H}^{+}\) and \(\text{He}^{+}\) ions whereas at higher altitude only heavy \(\text{O}^{+}\) ions contribute in wave damping. The damping of wave may be due to landau damping or energy transfer from wave to particles. The present study signifies that the both lighter and heavier ions dominate differently to change the characteristics of kinetic Alfven wave and density variation is also an important parameter to understand wave phenomena in cusp region.     

Formation of Thorne–Żytkow objects in close binaries

Thorne–?ytkow objects (T?Os), originally proposed by Thorne and ?ytkow, may form as a result of unstable mass transfer in a massive X-ray binary after a neutron star (NS) is engulfed in the envelope of its companion star. Using a rapid binary evolution program and the Monte Carlo method, we simulated the formation of T?Os in close binary stars. The Galactic birth rate of T?Os is about \(1.5\times 10^{-4}~\hbox {yr}^{-1}\). Their progenitors may be composed of a NS and a main-sequence star, a star in the Hertzsprung gap or a core-helium burning, or a naked helium star. The birth rates of T?Os via the above different progenitors are \(1.7\times 10^{-5}\), \(1.2\times 10^{-4}\), \(0.7\times 10^{-5}\), \(0.6\times 10^{-5}~\hbox {yr}^{-1}\), respectively. These progenitors may be massive X-ray binaries. We found that the observational properties of three massive X-ray binaries (SMC X-1, Cen X-3 and LMC X-4) in which the companions of NSs may fill their Roche robes were consistent with those of their progenitors.     

Discovery of GeV gamma-ray emission from the LMC B0443-6657 with the <Emphasis Type="Italic">Fermi</Emphasis> Large Area Telescope

We report the discovery of gamma-ray detection from the Large Magellanic Cloud (LMC) B0443-6657 using the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. LMC B0443-6657 is a flat-spectrum radio source, possibly associated with a supernova remnant in the Large Magellanic Cloud (LMC N4). Employing the LAT data of 8 years, our results show a significant excess (\(>9.4\sigma \)) of gamma rays in the range of 0.2–100 GeV above the gamma-ray background. A power-law function is found to adequately describe the 0.2–\(100\mbox{ GeV}\)\(\gamma \)-ray spectrum, which yields a photon flux of \(3.27\pm 0.53\ \text{photon}\,\mbox{cm}^{2}\,\mbox{s}^{-1}\) with a photon index of \(2.35\pm 0.11\), corresponding to an isotropic gamma-ray luminosity of \(5.3\times 10^{40}~\mbox{erg}\,\mbox{s}^{-1}\). The hadronic model predicts a low X-ray and TeV flux while the leptonic model predicts an observable flux in these two energy bands. The follow-up observations of the LMC B0443-6657 in X-ray or TeV band would distinguish the radiation models of gamma rays from this region.     

Quantum scattering of KCl with He/para-$\mbox{H}_{2}$: potential energy surface and rate coefficients at low temperature

We present new two- and four-dimensional potential energy surfaces for the KCl(\(\mbox{X}^{1} \varSigma ^{+}\))-He and KCl(\(\mbox{X}^{1} \varSigma ^{+}\))-para-H₂ systems calculated with the internuclear distances of KCl and H₂ frozen at their experimental minimum energy. The CCSD(T) level of theory with aug-cc-pVQZ/AQZP basis sets is used. The potential surfaces present well depths of about \(78~\mbox{cm}^{-1}\) and \(235~\mbox{cm}^{-1}\) below the dissociation limit of the above interacting systems respectively. With these potential surfaces, cross sections are obtained in the close coupling scheme and rate coefficients inferred by averaging the cross sections over a Maxwell-Boltzmann velocity distribution for temperature below 50 K. A propensity towards \(\Delta J = 1\) transitions is observed.     

$$M_{\bullet } - \sigma $$ relation in spherical systems

To investigate the \(M_\bullet -\sigma \) relation, we consider realistic elliptical galaxy profiles that are taken to follow a single power-law density profile given by \(\rho (r) = \rho _{0}(r/ r_{0})^{-\gamma }\) or the Nuker intensity profile. We calculate the density using Abel’s formula in the latter case by employing the derived stellar potential; in both cases. We derive the distribution function f(E) of the stars in the presence of the supermassive black hole (SMBH) at the center and hence compute the line-of-sight (LoS) velocity dispersion as a function of radius. For the typical range of values for masses of SMBH, we obtain \(M_{\bullet } \propto \sigma ^{p}\) for different profiles. An analytical relation \(p = (2\gamma + 6)/(2 + \gamma )\) is found which is in reasonable agreement with observations (for \(\gamma = 0.75{-}1.4\), \(p = 3.6{-}5.3\)). Assuming that a proportionality relation holds between the black hole mass and bulge mass, \(M_{\bullet } =f M_\mathrm{b}\), and applying this to several galaxies, we find the individual best fit values of p as a function of f; also by minimizing \(\chi ^{2}\), we find the best fit global p and f. For Nuker profiles, we find that \(p = 3.81 \pm 0.004\) and \(f = (1.23 \pm 0.09)\times 10^{-3}\) which are consistent with the observed ranges.     

The Most Intense Electron-Scale Current Sheets in the Solar Wind

Previous analysis of magnetohydrodynamic-scale currents in high-speed solar wind near 1 AU suggests that the most intense current-carrying structures occur at electron scales and are characterized by average current densities on the order of \(1~\mbox{pA}/\mbox{cm}^{2}\). Here, this prediction is verified by examining the effects of the measurement bandwidth and/or measurement resolution on the analysis of synthetic solar wind signals. Assuming Taylor’s hypothesis holds for the energetically dominant fluctuations at kinetic scales, the results show that when \(\nu_{c}\gg \nu_{b}\), where \(\nu_{c}\) is the measurement bandwidth and \(\nu_{b} \approx 1/3~\mbox{Hz}\) is the break frequency, the average scale of the most intense fluctuations in the current density proxy is approximately \(1/\nu_{c}\), and the average peak current density is a weakly increasing function that scales approximately like \(\nu_{c}^{0.1}\).     

Subsurface Zonal and Meridional Flow During Cycles 23 and 24

We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have used ring-diagram analysis to analyze Dopplergrams obtained with the Michelson Doppler Imager (MDI) Dynamics Program, the Global Oscillation Network Group (GONG), and the Helioseismic and Magnetic Imager (HMI) instrument. We combined the zonal and meridional flows from the three data sources and scaled the flows derived from MDI and GONG to match those from HMI observations. In this way, we derived their temporal variation in a consistent manner for Solar Cycles 23 and 24. We have corrected the measured flows for systematic effects that vary with disk positions. Using time-depth slices of the corrected subsurface flows, we derived the amplitudes and times of the extrema of the fast and slow zonal and meridional flows during Cycles 23 and 24 at every depth and latitude. We find an average difference between maximum and minimum amplitudes of \(8.6 \pm0.4~\mbox{m}\,\mbox{s}^{-1}\) for the zonal flows and \(7.9 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flows associated with Cycle 24 averaged over a depth range from 2 to 12 Mm. The corresponding values derived from GONG data alone are \(10.5 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the zonal and \(10.8 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flow. For Cycle 24, the flow patterns are precursors of the magnetic activity. The timing difference between the occurrence of the flow pattern and the magnetic one increases almost linearly with increasing latitude. For example, the fast zonal and meridional flow appear \(2.1 \pm 0.6\) years and \(2.5\pm 0.6\) years, respectively, before the magnetic pattern at \(30^{\circ}\) latitude in the northern hemisphere, while in the southern hemisphere, the differences are \(3.2 \pm 1.2\) years and \(2.6 \pm 0.6\) years. The flow patterns of Cycle 25 are present and have reached \(30^{\circ}\) latitude. The amplitude differences of Cycle 25 are about 22% smaller than those of Cycle 24, but are comparable to those of Cycle 23. Moreover, polynomial fits of meridional flows suggest that equatorward meridional flows (counter-cells) might exist at about \(80^{\circ}\) latitude except during the declining phase of the solar cycle.     

Motion of the fast exoplanets

It is shown that a number of superfast, with periods \(< 2\) d, exoplanets revolve around parent stars with periods, near-commensurate with \(P_{E}\) and/or \(2 P_{E} / \pi\), where the exoplanet resonance timescale \(P_{E}=9603(85)\) s agrees fairly well with the period \(P_{0}= 9600.606(12)\) s of the so-called “cosmic oscillation” (the probability that the two timescales would coincide by chance is near \(3 \times10^{-4}\); the \(P_{0}\) period was discovered first in the Sun, and later on—in other objects of Cosmos). True nature of the exoplanet \(P_{0}\) resonance is unknown.     

The Na <Emphasis Type="SmallCaps">i</Emphasis> and Sr <Emphasis Type="SmallCaps">ii</Emphasis> Resonance Lines in Solar Prominences

We estimate the electron density, \(n_{\mathrm{e}}\), and its spatial variation in quiescent prominences from the observed emission ratio of the resonance lines Na?i?5890 Å (D₂) and Sr?ii?4078 Å. For a bright prominence (\(\tau_{\alpha}\approx25\)) we obtain a mean \(n_{\mathrm{e}}\approx2\times10^{10}~\mbox{cm}^{-3}\); for a faint one (\(\tau _{\alpha }\approx4\)) \(n_{\mathrm{e}}\approx4\times10^{10}~\mbox{cm}^{-3}\) on two consecutive days with moderate internal fluctuation and no systematic variation with height above the solar limb. The thermal and non-thermal contributions to the line broadening, \(T_{\mathrm{kin}}\) and \(V_{\mathrm{nth}}\), required to deduce \(n_{\mathrm{e}}\) from the emission ratio Na?i/Sr?ii cannot be unambiguously determined from observed widths of lines from atoms of different mass. The reduced widths, \(\Delta\lambda_{\mathrm{D}}/\lambda_{0}\), of Sr?ii?4078 Å show an excess over those from Na?D₂ and \(\mbox{H}\delta\,4101\) Å, assuming the same \(T_{\mathrm{kin}}\) and \(V_{\mathrm{nth}}\). We attribute this excess broadening to higher non-thermal broadening induced by interaction of ions with the prominence magnetic field. This is suggested by the finding of higher macro-shifts of Sr?ii?4078 Å as compared to those from Na?D₂.     

Study and application of the resonant secular dynamics beyond Neptune

We use a secular representation to describe the long-term dynamics of transneptunian objects in mean-motion resonance with Neptune. The model applied is thoroughly described in Saillenfest et al. (Celest Mech Dyn Astron, doi: 10.1007/s10569-016-9700-5, 2016). The parameter space is systematically explored, showing that the secular trajectories depend little on the resonance order. High-amplitude oscillations of the perihelion distance are reported and localised in the space of the orbital parameters. In particular, we show that a large perihelion distance is not a sufficient criterion to declare that an object is detached from the planets. Such a mechanism, though, is found unable to explain the orbits of Sedna or \(2012\text {VP}_{113}\), which are insufficiently inclined (considering their high perihelion distance) to be possibly driven by such a resonant dynamics. The secular representation highlights the existence of a high-perihelion accumulation zone due to resonances of type 1:k with Neptune. That region is found to be located roughly at \(a\in [100;300]\) AU, \(q\in [50;70]\) AU and \(I\in [30;50]^{\circ }\). In addition to the flux of objects directly coming from the Scattered Disc, numerical simulations show that the Oort Cloud is also a substantial source for such objects. Naturally, as that mechanism relies on fragile captures in high-order resonances, our conclusions break down in the case of a significant external perturber. The detection of such a reservoir could thus be an observational constraint to probe the external Solar System.     

Analysis of the exoplanet containing system Kepler-13

We have applied the close binary system analysis program WinFitter, with its physically detailed fitting function, to an intensive study of the complex multiple system Kepler-13 using photometry data from all 13 short cadence quarters downloaded from the NASA Exoplanet Archive (NEA) (http://exoplanetarchive.ipac.caltech.edu). The data-point error of our normalized, phase-sequenced and binned (380 points per bin: 0.00025 phase interval) flux values, at 14 ppm, allows the model’s specification for the mean reference flux level of the system to a precision better than 1 ppm. Our photometrically derived values for the mass and radius of KOI13.01 are \(6.8\pm0.6~\mbox{M}_{\mathrm{J}}\) and \(1.44\pm0.04~\mbox{R}_{\mathrm{J}}\). The star has a radius of \(1.67\pm0.05~\mbox{R}_{\odot}\). Our modelling sets the mean of the orbital inclination \(i\) at \(94.35\pm0.14^{\circ}\), with the star’s mean precession angle \(\phi_{p}\)—\(49.1\pm5.0^{\circ}\) and obliquity \(\theta_{o}\)\(67.9 \pm 3.0^{\circ}\), though there are known ambiguities about the sense in which such angles are measured.Our findings did not confirm secular variation in the transit modelling parameters greater than their full correlated errors, as argued by previous authors, when each quarter’s data was best-fitted with a determinable parameter set without prejudice. However, if we accept that most of the parameters remain the same for each transit, then we could confirm a small but steady diminution in the cosine of the orbital inclination over the 17 quarter timespan. This is accompanied by a slight increase of the star’s precession angle (less negative), but with no significant change in the obliquity of its spin axis. There are suggestions of a history of strong dynamical interaction with a highly distorted planet rotating in a 3:2 resonance with its revolution, together with a tidal lag of \(\sim30~\mbox{deg}\). The mean precessional period is derived to be about 1000 y, but at the present time the motion of the star’s rotation axis appears to be supporting the gravitational torque, rather than providing the balance against it that would be expected over long periods of time.The planet has a small but detectable backwarming effect on the star, which helps to explain the difference in brightness just after transit and just before occultation eclipses. In assessing these findings it is recognized that sources of uncertainty remain, notably with possible inherent micropulsational effects, variations from other components of the multiple star, stellar activity, differential rotation and the neglect of higher order terms (than \(r_{1}^{5}\)) in the fitting function, where \(r_{1}\) is the ratio of the radius of the star to the mean orbital separation of planet and host star.     

The global modulation of Galactic and Jovian electrons in the heliosphere

A full three-dimensional, numerical model is used to study the modulation of Jovian and Galactic electrons from 1 MeV to 50 GeV, and from the Earth into the heliosheath. For this purpose the very local interstellar spectrum and the Jovian electron source spectrum are revisited. It is possible to compute the former with confidence at kinetic energies \(E < 50~\mbox{MeV}\) since Voyager 1 crossed the heliopause in 2012 at \(\sim 122~\mbox{AU}\), measuring Galactic electrons at these energies. Modeling results are compared with Voyager 1 observations in the outer heliosphere, including the heliosheath, as well as observations at or near the Earth from the ISSE3 mission, and in particular the solar minimum spectrum from the PAMELA space mission for 2009, also including data from Ulysses for 1991 and 1992, and observations above 1 MeV from SOHO/EPHIN. Making use of the observations at or near the Earth and the two newly derived input functions for the Jovian and Galactic electrons respectively, the energy range over which the Jovian electrons dominate the Galactic electrons is determined so that the intensity of Galactic electrons at Earth below 100 MeV is calculated. The differential intensity for the Galactic electrons at Earth for \(E = 1~\mbox{MeV}\) is \(\sim 4\) electrons \(\mbox{m}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{MeV}^{-1}\), whereas for Jovian electrons it is \(\sim 350\) electrons \(\mbox{m}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{MeV}^{-1}\). At \(E = 30~\mbox{MeV}\) the two intensities are the same; above this energy the Jovian electron intensity quickly subsides so that the Galactic intensity completely dominates. At 6 MeV, in the equatorial plane the Jovian electrons dominate but beyond \(\sim 15~\mbox{AU}\) the Galactic intensity begins to exceed the Jovian intensity significantly.     

Local stellar kinematics from RAVE data—VIII. Effects of the Galactic disc perturbations on stellar orbits of red clump stars

We aim to probe the dynamic structure of the extended Solar neighborhood by calculating the radial metallicity gradients from orbit properties, which are obtained for axisymmetric and non-axisymmetric potential models, of red clump (RC) stars selected from the RAdial Velocity Experiment’s Fourth Data Release. Distances are obtained by assuming a single absolute magnitude value in near-infrared, i.e. \(M_{Ks}=-1.54\pm0.04\) mag, for each RC star. Stellar orbit parameters are calculated by using the potential functions: (i) for the MWPotential2014 potential, (ii) for the same potential with perturbation functions of the Galactic bar and transient spiral arms. The stellar age is calculated with a method based on Bayesian statistics. The radial metallicity gradients are evaluated based on the maximum vertical distance (\(z_{max}\)) from the Galactic plane and the planar eccentricity (\(e_{p}\)) of RC stars for both of the potential models. The largest radial metallicity gradient in the \(0< z_{max} \leq0.5\) kpc distance interval is \(-0.065\pm0.005~\mbox{dex}\,\mbox{kpc}^{-1}\) for a subsample with \(e_{p}\leq0.1\), while the lowest value is \(-0.014\pm0.006~\mbox{dex}\,\mbox{kpc}^{-1}\) for the subsample with \(e_{p}\leq0.5\). We find that at \(z_{max}>1\) kpc, the radial metallicity gradients have zero or positive values and they do not depend on \(e_{p}\) subsamples. There is a large radial metallicity gradient for thin disc, but no radial gradient found for thick disc. Moreover, the largest radial metallicity gradients are obtained where the outer Lindblad resonance region is effective. We claim that this apparent change in radial metallicity gradients in the thin disc is a result of orbital perturbation originating from the existing resonance regions.