Capture of comets from the Oort cloud into Halley-type and Jupiter-family orbits

This paper analyzes the capture of comets into Halley-type and Jupiter-family orbits from the nearparabolic flux of the Oort cloud. Two types of capture into Halley-type orbits are found. The first type is the evolution of near-parabolic orbits into short-period orbits (with heliocentric orbital periods P < 200 years) as a result of close encounters with giant planets. This process is followed by a very slow drift of cometary orbits into the inner part of the Solar System. Only those comets may pass from short-period orbits into Halley-type and Jupiter-family orbits, which move in orbits with perihelion distances q < 13 au. In the second type of capture, the perihelion distances of cometary orbits become rather small (< 1.5 au) during the first stage of dynamic evolution under the action of perturbations from the Galaxy, and then their semimajor axes decrease as a result of diffusion. The capture takes place, on average, in 500 revolutions of the comet about the Sun, whereas in the first case, the comet is captured, on average, after 12500 revolutions. The region of initial orbital perihelion distances q > 4 au is found to be at least as important a source of Halley-type comets as the region of perihelion distances q < 4 au. More than half of the Halley-type comets are captured from the nearly parabolic flux with q > 4 au. The analysis of the dynamic evolution of objects moving in short-period orbits shows that the distribution of Centaurs orbits agrees well with the observed distribution corrected for observational selection effects. Hence, the hypothesis associating the origin of Centaurs with the Edgeworth-Kuiper belt and the trans-Neptunian region exclusively should be rejected.     

Orbital stability of systems of closely-spaced planets,II: configurations with coorbital planets

We numerically investigate the stability of systems of 1 \({{\rm M}_{\oplus}}\) planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 10⁸, 5 × 10⁵, and 2 × 10⁵ years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log(t _c /t ₀) = b β + c, where t _c is the crossing time, t ₀ = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively.     

New orbits of wide visual double stars

Based on photographic and CCD observations with the Pulkovo 26-inch refractor, radial velocity measurements with the 1.5-m RTT-150 telescope (TUBITAK National Observatory, Turkey), and highly accurate observations published in the WDS catalog, we have obtained the orbits of ten wide visual double stars by the apparent motion parameter method. The orientation of the orbits in the Galactic coordinate system has been determined. For the outer pair of the multiple star HIP 12780 we have calculated a family of orbits with a minimum period P = 4634 yr. Two equivalent solutions with the same period have been obtained for the stars HIP 50 (P = 949 yr) and HIP 66195 (P = 3237 yr). We have unambiguously determined the orbits of six stars: HIP 12777 (P = 3327 yr), HIP 15058 (P = 420 yr), HIP 33287 (P = 1090 yr), HIP 48429 (P = 1066 yr), HIP 69751 (P = 957 yr), and HIP 73846 (P = 1348 yr). The orbit of HIP 55068 is orientated perpendicularly to the plane of the sky, P >1000 yr. The star HIP 48429 is suspected to have an invisible companion.     

Effect of the darkforce on the extra-anomalous apsidal precession of solar planets

We demonstrate that, while the proposed Gravitational Dark-force Theory (of Nyambuya (New Astron. 67:1, 2019b) here-in Paper II) predicts an extra-anomalous apsidal precession for Solar planets due to the gravitational dark-force on the orbits of these planets, the predicted extra-anomalous apsidal precession is so small—so much that—it can not account for the observed extra-anomalous apsidal precession of Solar planets. This null result is important in that it informs us that whatever may be the cause of the extra-anomalous apsidal precession, it is not the proposed gravitational dark-force.     

Open cluster ASCC21 as a probable birthplace of the neutron star Geminga

We analyze the encounters of the neutron star (pulsar) Geminga with open star clusters in the OB association Ori OB1a through the integration of epicyclic orbits into the past by taking into account the errors in the data. The open cluster ASCC21 is shown to be the most probable birthplace of either a single progenitor star for the Geminga pulsar or a binary progenitor system that subsequently broke up. Monte Carlo simulations of Geminga-ASCC21 encounters with the pulsar radial velocity V _r = ?100±50 km s^?1 have shown that close encounters could occur between them within ≤10 pc at about t = ?0.52 Myr. In addition, the trajectory of the neutron star Geminga passes at a distance of ≈25 pc from the center of the compact OB association λ Ori at about t = ?0.39 Myr, which is close to the age of the pulsar estimated from its timing.     

Catalog of candidates for quasars at 3 &lt; <Emphasis Type="Italic">z</Emphasis> &lt; 5.5 selected among X-Ray sources from the 3XMM-DR4 survey of the XMM-Newton observatory

We have compiled a catalog of 903 candidates for type 1 quasars at redshifts 3 < z < 5.5 selected among the X-ray sources of the “serendipitous” XMM-Newton survey presented in the 3XMMDR4 catalog (the median X-ray flux is ≈5 × 10^?15 erg s^?1 cm^?2 in the 0.5–2 keV energy band) and located at high Galactic latitudes |b| > 20° in Sloan Digital Sky Survey (SDSS) fields with a total area of about 300 deg². Photometric SDSS data as well infrared 2MASS and WISE data were used to select the objects. We selected the point sources from the photometric SDSS catalog with a magnitude error δ _mz′ < 0.2 and a color i′ ? z′ < 0.6 (to first eliminate the M-type stars). For the selected sources, we have calculated the dependences χ²(z) for various spectral templates from the library that we compiled for these purposes using the EAZY software. Based on these data, we have rejected the objects whose spectral energy distributions are better described by the templates of stars at z = 0 and obtained a sample of quasars with photometric redshift estimates 2.75 < z _phot < 5.5. The selection completeness of known quasars at z _spec > 3 in the investigated fields is shown to be about 80%. The normalized median absolute deviation (Δz = |z _spec ? z _phot|) is σ _Δz /(1+z _spec) = 0.07, while the outlier fraction is η = 9% when Δz/(1 + z _спек.) > 0.2. The number of objects per unit area in our sample exceeds the number of quasars in the spectroscopic SDSS sample at the same redshifts approximately by a factor of 1.5. The subsequent spectroscopic testing of the redshifts of our selected candidates for quasars at 3 < z < 5.5 will allow the purity of this sample to be estimated more accurately.     

Close encounters of nearly parabolic comets and planets

An overview is given of close encounters of nearly parabolic comets (NPCs; with periods of P > 200 years and perihelion distances of q > 0.1 AU; the number of the comets is N = 1041) with planets. The minimum distances Δ_min between the cometary and planetary orbits are calculated to select comets whose Δ_min are less than the radius of the planet’s sphere of influence. Close encounters of these comets with planets are identified by numerical integration of the comets’ equations of motion over an interval of ±50 years from the time of passing the perihelion. Close encounters of NPCs with Jupiter in 1663–2011 are reported for seven comets. An encounter with Saturn is reported for comet 2004 F2 (in 2001).     

Forbidden Zones for Circular Regular Orbits of the Moons in Solar System,R3BP

Previously, we have considered the equations of motion of the three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each other). Analysing such a system of equations, we considered the case of small-body motion of negligible mass m ₃ around the second of two giant-bodies m ₁, m ₂ (which are rotating around their common centre of masses on Kepler’s trajectories), the mass of which is assumed to be less than the mass of central body. In the current development, we have derived a key parameter η that determines the character of quasi-circular motion of the small third body m ₃ relative to the second body m ₂ (planet). Namely, by making several approximations in the equations of motion of the three-body problem, such the system could be reduced to the key governing Riccati-type ordinary differential equations. Under assumptions of R3BP (restricted three-body problem), we additionally note that Riccati-type ODEs above should have the invariant form if the key governing (dimensionless) parameter η remains in the range 10^?2 Open image in new window 10^?3. Such an amazing fact let us evaluate the forbidden zones for Moon’s orbits in the inner solar system or the zones of distances (between Moon and Planet) for which the motion of small body could be predicted to be unstable according to basic features of the solutions of Riccati-type.     

Comparison of the X-ray and optical variabilities in the Seyfert galaxy 3C 120

Based on our UBV RI observations and X-ray data from the RXTE satellite, we have investigated the variability of the galaxy 3C 120 over the period 1996–2008. The relative variability amplitude in the U and B bands without any subtraction of the contribution from the underlying galaxy is 23 and 22%, respectively, against 21% in the X-ray band. The autocorrelation function based on the B-band data is considerably wider than that based on the X-ray data. The structure functions on a time scale from 1 to ～100–300 days in the X-ray and optical spectral ranges have the form of a power law (SF ～ τ ^b ). However, their indices differ significantly: b = 0.42 in the X-ray band and b = 1.36 in the B band. Considering the X-ray and optical variabilities as a superposition of independent flares in a wide range of durations, we may conclude that the amplitudes of short flares in the X-ray band are higher than those in the optical one and, conversely, the relative amplitudes of long flares in the X-ray band are slightly lower than those in the optical one, i.e., short events dominate in the X-ray band. The optical flux variations in the R _c and I _c bands lag significantly behind those in the B band, by 3.9 _?0.7 ^+1.0 and 6.2 _?0.6 ^+1.1 days, respectively, if the lag is estimated from the centroid of the cross-correlation function. The X-ray variability on a time scale of about 1800 days (～5 yr) lags behind the B-band variations by 5.3 _?3.3 ^+2.7 days, but the confidence level of this estimate is only 87%. A more detailed analysis of the correlation between the X-ray and optical emissions has revealed a fairly complex picture: different degrees of correlation between the optical and X-ray fluxes are observed at different times.     

Families <Emphasis Type="Italic">c</Emphasis> and <Emphasis Type="Italic">i</Emphasis> of periodic solutions of the restricted problem for μ = 5 × 10<Superscript>−5</Superscript>

We consider the circular planar restricted three-body problem with the mass parameter μ = 5 × 10^?5. Two families of periodic solutions are calculated: family c, starting from the collinear fixed point L ₁, and the initial part of familyi, which begins by direct circular orbits of an infinitely small radius around the body of bigger mass. The calculated families are very close to the generating ones, which we described earlier. In particular, the existence of the predicted zigzag structure of characteristics of family iis verified. New properties of the planar and vertical traces are discovered.     

Dynamical lifetime survey of geostationary transfer orbits

In this paper, we study the long-term dynamical evolution of highly elliptical orbits in the medium-Earth orbit region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrations (up to 200 years) within a realistic dynamical model, aimed primarily at recording the dynamical lifetime of such orbits (defined as the time needed for atmospheric reentry) and understanding its dependence on initial conditions and other parameters, such as the area-to-mass ratio (A / m). Our results are presented in the form of 2-D lifetime maps, for different values of inclination, A / m, and drag coefficient. We find that the majority of small debris (\(>70\%\), depending on the inclination) can naturally reenter within 25–90 years, but these numbers are significantly less optimistic for large debris (e.g., upper stages), with the notable exception of those launched from high latitude (Baikonur). We estimate the reentry probability and mean dynamical lifetime for different classes of GTOs and we find that both quantities depend primarily and strongly on initial perigee altitude. Atmospheric drag and higher A / m values extend the reentry zones, especially at low inclinations. For high inclinations, this dependence is weakened, as the primary mechanisms leading to reentry are overlapping lunisolar resonances. This study forms part of the EC-funded (H2020) “ReDSHIFT” project.     

Astrometric Study of Two Multiple Stars: ADS 2668 and ADS 8236

Based on CCD observations with the Pulkovo 26-inch refractor in 2003–2018, we have obtained the orbit of the visual double star ADS 2668 AB (P = 947 yr, a = 2.9″, e = 0.41, ω = 246°, Ω = 131°, i = 114°, T = 1456 yr) for the first time by the apparent motion parameter (AMP) method, which is consistent with the inner orbit of ADS 2668 Aa-Ab, and improved the orbit of ADS 8236 AB (P = 1996 yr, a = 4.69″, e = 0.39, ω = 201°, Ω = 166°, i = 110°, T = 1246 yr). The inner orbit of the photocenter of ADS 8236 with a period of 4.627 yr has been calculated from the residuals. This orbit of ADS 8236 Ba–Bb supplements the spectroscopic orbit by the elements specifying the orbital plane (i and Ω). In both cases, the planes of the inner and outer orbits are noncoplanar. The presence of an additional companion in the system ADS 2668 is discussed.     

Plane Symmetric Dark Energy Models in the Form of Wet Dark Fluid in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) Gravity

In this paper, we have investigated the plane symmetric space-time with wet dark fluid (WDF), which is a candidate for dark energy, in the framework of f (R,T) gravity Harko et al. 2011, Phys. Rev. D, 84, 024020), where R and T denote the Ricci scalar and the trace of the energy–momentum tensor respectively. We have used the equation of state in the form of WDF for the dark energy component of the Universe. It is modeled on the equation of state p = ω(ρ ? ρ ^?). The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied. Also, we have discussed the well-known astrophysical phenomena, namely the look-back time, proper distance, the luminosity distance and angular diameter distance with red shift.     

Long-period comet flux in the planetary region: Dynamical evolution from the Oort cloud

This study analyzes the evolution of 2 × 10⁵ orbits with initial parameters corresponding to the orbits of comets of the Oort cloud under the action of planetary, galactic, and stellar perturbations over 2 × 10⁹ years. The dynamical evolution of comets of the outer (orbital semimajor axes a > 10⁴ AU) and inner (5 × 10³ < a (AU) < 10⁴) parts of the comet cloud is analyzed separately. The estimates of the flux of “new” and long-period comets for all perihelion distances q in the planetary region are reported. The flux of comets with a > 10⁴ AU in the interval 15 AU < q < 31 AU is several times higher than the flux of comets in the region q < 15 AU. We point out the increased concentration of the perihelia of orbits of comets from the outer cloud, which have passed several times through the planetary system, in the Saturn-Uranus region. The maxima in the distribution of the perihelia of the orbits of comets of the inner Oort cloud are located in the Uranus-Neptune region. “New” comets moving in orbits with a < 2 × 10⁴ AU and arriving at the outside of the planetary system (q > 25 AU) subsequently have a greater number of returns to the region q < 35 AU. The perihelia of the orbits of these comets gradually drift toward the interior of the Solar System and accumulate beyond the orbit of Saturn. The distribution of the perihelia of long-period comets beyond the orbit of Saturn exhibits a peak. We discuss the problem of replenishing the outer Oort cloud by comets from the inner part and their subsequent dynamical evolution. The annual rate of passages of comets of the inner cloud, which replenish the outer cloud, in the region q < 1 AU in orbits with a > 10⁴ AU (～ 5.0 × 10^?14 yr^?1) is one order of magnitude lower than the rate of passage of comets from the outer Oort cloud (～ 9.1 × 10^?13 yr^?1).     

The orbital dust torus as an enveloping surface of a family of trajectories of isotropically ejected particles

Meteorite impacts onto a small satellite lead to the ejection of a regolith mass, which is much greater than the impactor mass, into cosmic space. Assume that an isotropic ejection with velocities smaller than the maximum possible velocity b took place at the time moment t ₀. Since the orbital periods are unequal, the particle trajectories will densely fill a certain domain D. The same domain will be filled after an explosion of an artificial satellite moving in a high orbit. One to three months later, the node and pericenter longitudes will be distributed over the entire circle and the domain D will become a body of revolution, a topological solid torus. We examine the domain of possible particle motion and its boundary S immediately after the impact event (an unperturbed case) and the same domain under the assumption that the initial longitudes of nodes and pericenters were already a result of considerable changes (a perturbed case). In both cases, we managed to construct the domain D and its boundary S analytically: parametric equations containing only relatively simple functions were obtained for S. The basic topologic and differential-geometric properties of S were studied completely.     

Results of a long-term monitoring of the multiple system SZ Cam

We present the results of the reduction of our photometric and spectroscopic observations for the eclipsing binary SZ Cam performed with the telescopes at the Astronomical Observatory of the Ural Federal University and the Special Astrophysical Observatory of the Russian Academy of Sciences in 1996–2014. Based on an 11-year-long photometric monitoring of SZ Cam, we have obtained new elements of its photometric orbit and parameters of its components. We have detected low-amplitude periodic light variations in SZ Cam that are possibly related to the ellipsoidal shape of the components of the spectroscopic binary third body. Based on published data and our new spectroscopy, we have found new values for the mass ratio, q = 0.72 ± 0.01, and parameters of the radial velocity curves of the components, V ₀ = ?3.6 ± 1.7 km s^?1, K ₁ = 190.2 ± 1.9 km s^?1, and K ₂ = 263.0 ± 2.4 km s^?1. The component masses have been estimated to be M ₁ = 16.1 M _⊙ and M ₂ = 11.6 M _⊙. We have obtained new light elements and parameters of the radial velocity curves for the third body, V ₀ ^3b = 4.2 ± 0.6 km s^?1 and K ₁ ^3b = 26.6 ± 0.8 km s^?1. We have improved the period of the relative orbit of SZ Cam and the third body, P _orb = 55.6 ± 1.5 yr.     

Soft proton flux on <Emphasis Type="Italic">ATHENA</Emphasis> focal plane and its impact on the magnetic diverter design

The experience gained with the current generation of X-ray telescopes like Chandra and XMM-Newton has shown that low energy “soft” protons can pose a severe threat to the possibility to exploit scientific data, reducing the available exposure times by up to 50% and introducing a poorly reproducible background component. These soft protons are present in orbits outside the radiation belts and enter the mirrors, being concentrated towards the focal plane instruments, losing energy along their path and finally depositing their remaining energy in the detectors. Their contribution to the residual background will be even higher for ATHENA with respect to previous missions, given the much higher collecting area of the mirrors, even if the instruments will likely suffer no significant radiation damage from this particles flux. As a consequence this soft proton flux shall be damped with the use of a magnetic diverter to avoid excess background loading on the WFI or X-IFU instruments. We present here a first complete evaluation of this background component for the two focal plane instruments of the ATHENA mission in absence of a magnetic diverter, and derive the requirements for such device to reduce the soft protons induced background below the level required to enable the mission science. We estimate the soft proton flux expected in L2 for the interplanetary component and for the component generated locally by acceleration processes in the magnetotail. We produce a proton response matrix for each of the two instruments of ATHENA focal plane, exploiting two independent Monte Carlo simulations to estimate the optics concentration efficiency, and Geant4 simulations to evaluate the energy loss inside the radiation filters and deposited in the detector. With this modular approach we derive the expected fluxes and spectra for the soft protons component of the background. Finally, we calculate the specifics of a magnetic diverter able to reduce such flux below the required level for both X-IFU and WFI.     

Modeling infrared absorption bands with nonspherical particles

We investigated the two deepest absorption bands observed in the spectra of stars and protostars, the water-ice band with the center near 3.1 μm and the silicate band with the center near 9.7 μm, by using a core-mantle confocal spheroid model with various axial ratios and relative volumes of the core material. We considered the effect of grain size, shape, structure, chemical composition, and orientation on the central wavelengths of the two bands, their full widths at half maximum (FWHMs), the ratio of the optical depths at their centers, and the polarization. We found that the observed relationships between the FWHMs of the bands and the ratio of their optical depths at the band centers could be explained if we chose slightly oblate or prolate particles (a/b ? 2) of small sizes (r_v ? 0.35 μm) with a silicate core and a thin ice mantle (V_core/V_total ? 0.7).     

Broad-band spectral evolution and temporal variability of IGR J17091-3624 during its 2016 outburst: <Emphasis Type="Italic">SWIFT</Emphasis> and <Emphasis Type="Italic">NuSTAR</Emphasis> results

We report on the 2016 outburst of the transient Galactic Black Hole candidate IGR J17091-3624 based on the observation campaign carried out with SWIFT and NuSTAR. The outburst profile, as observed with SWIFT-XRT, shows a typical ‘q’-shape in the Hardness Intensity Diagram (HID). Based on the spectral and temporal evolution of the different parameters, we are able to identify all the spectral states in the q-profile of HID and the Hardness-RMS diagram (HRD). Both XRT and NuSTAR observations show an evolution of low frequency Quasi periodic oscillations (QPOs) during the low hard and hard intermediate states of the outburst rising phase. We also find mHz QPOs along-with distinct coherent class variabilities (heartbeat oscillations) with different timescales, similar to the \(\rho \)-class (observed in GRS 1915+105). Phenomenological modelling of the broad-band XRT and NuSTAR spectra also reveals the evolution of high energy cut-off and presence of reflection from ionized material during the rising phase of the outburst. Further, we conduct the modelling of X-ray spectra of SWIFT and NuSTAR in 0.5–79 keV to understand the accretion flow dynamics based on two component flow model. From this modelling, we constrain the mass of the source to be in the range of \(10.62\mbox{--}12.33~\mbox{M}_{\odot }\) with 90% confidence, which is consistent with earlier findings.