Discovery of deep eclipses in the cataclysmic variable IPHAS J051814.33+294113.0

Performing the photometric observations of the cataclysmic variable IPHAS J051814.33+294113.0, we discovered very deep eclipses. The observations were obtained over 14 nights, had a total duration of 56 hours and covered one year. The large time span, during which we observed the eclipses, allowed us to measure the orbital period in IPHAS J051814.33+294113.0 with high precision, \(P_{\mathrm{orb}}=0.20603098\pm 0.00000025\) d. The prominent parts of the eclipses lasted \(0.1\pm 0.01\) phases or \(30\pm 3~\mbox{min}\). The depth of the eclipses was variable in the range 1.8–2.9 mag. The average eclipse depth was equal to \(2.42\pm 0.06~\mbox{mag}\). The prominent parts of the eclipses revealed a smooth and symmetric shape. We derived the eclipse ephemeris, which, according to the precision of the orbital period, has a formal validity time of 500 years. This ephemeris can be useful for future investigations of the long-term period changes. During the latter four observational nights in 2017 January, we observed the sharp brightness decrease of IPHAS J051814.33+294113.0 by 2.3 mag. This brightness decrease imitated the end of the dwarf nova outburst. However, the long-term light curve of IPHAS J051814.33+294113.0 obtained in the course of the Catalina Sky Survey during 8 years showed no dwarf nova outbursts. From this we conclude that IPHAS J051814.33+294113.0 is a novalike variable. Moreover, the sharp brightness decrease, which we observed in IPHAS J051814.33+294113.0, suggests that this novalike variable belongs to the VY Scl-subtype. Due to very deep eclipses, IPHAS J051814.33+294113.0 is suitable to study the accretion disc structure using eclipse mapping techniques. Because this novalike variable has the long orbital period, it is of interest to determine the masses of the stellar components from radial velocity measurements. Then, our precise eclipse ephemeris can be useful to the phasing of spectroscopic data.     

Eigenfrequencies of rotationally and tidally distorted white dwarf models of stars

In the present paper we have studied the eigenfrequencies of small adiabatic barotropic pseudo-radial and nonradial modes of oscillations of the white dwarf models of rotating stars in binary systems. In this work the methodology of Mohan and Saxena (in Astrophys. Space Sci. 113:155, 1985) has been used that utilizes the averaging technique of Kippenhahn and Thomas (in Proc. IAU Colloq., vol. 4, p. 20, 1970) and certain results on Roche equipotential as that given by Kopal (in Advances in Astronomy and Astrophysics, Academic Press, 1972). The objective of this study is to investigate the effects of rotation and/or tidal distortion on the periods of oscillations of rotationally and/or tidally distorted white dwarf models of stars assuming it to be the primary component of the binary system and rotating uniformly. The results of present study show that the eigenfrequencies (both radial and nonradial modes) of the rotationally distorted and rotationally and tidally distorted white dwarf model of stars in binary systems tend to decrease under the influence of rotational distortions and rotational and tidal distortions, respectively. However, results are contrary for tidally distorted white dwarf model of stars.     

Fourier analysis of the light curves of eclipsing variables,XXIII

The method of evaluating the photometric perturbationsB _2m of eclipsing variables in the frequency domain, developed by Kopal (1959, 1975e, 1978) for an interpretation of mutual eclipses in systems whose components are distorted by axial rotation and mutual tidal action. The aim of the present paper has been to establish explicit expressions for the photometric perturbationB _2m in such systems, regardless of the kind of eclipses and non-integral values ofm. Recently, Kopal (1978) introduced two different kinds of integrals with respect to associated α-functions andI-integrals which have been expressed in terms of certain general types of series that can be easily programmed for automatic computation within seconds of real time on highspeed computers. Following a brief introduction (Section 1) in which the need of this new approach will be expounded, in Section 3 we shall deduce the integral $$\int_0^{\theta \prime } {\tfrac{{\alpha _n^\prime }}{\delta }} d(sin^{2m} \theta )$$ in terms of a certain general type of series and also β-function, which should enable us to evaluate explicit expressions forf _* ^(h) ,f ₁ ^(h) ,f ₂ ^(h) as well asB _2m .     

High precision predictions for near-Earth asteroids: the strange case of (3908) Nyx

In November 2004 radar delay measurements of near-Earth asteroid (3908) Nyx obtained at the Arecibo radio telescope turned out to be \(7.5\sigma \) away from the orbital prediction. We prove that this discrepancy was caused by a poor astrometric treatment and an incomplete dynamical model, which did not account for nongravitational perturbations. To improve the astrometric treatment, we remove known star catalog biases, apply suitable weights to the observations, and use an aggressive outlier rejection scheme. The main issue related to the dynamical model is having not accounted for the Yarkovsky effect. Including the Yarkovsky perturbation in the model makes the orbital prediction and the radar measurements statistically consistent by both reducing the offset and increasing the prediction uncertainty to a more realistic level. This analysis shows the sensitivity of high precision predictions to the astrometric treatment and the Yarkovsky effect. By using the full observational dataset we obtain a \(5\sigma \) detection of the Yarkovsky effect acting on Nyx corresponding to an orbital drift \(da/dt = (142 \pm 29)\)  m/year. In turn, we derive constraints on thermal inertia and bulk density. In particular, we find that the bulk density of Nyx is around 1 g/cm \(^3\) , possibly less. To make sure that our results are not corrupted by an asteroid impact or a close approach with a perturbing asteroid not included in our dynamical model, we show that the astrometry provides no convincing evidence of an impulsive variation of Nyx’s velocity while crossing the main belt region.     

Exoplanet atmospheres with EChO: spectral retrievals using EChOSim

We demonstrate the effectiveness of the Exoplanet Characterisation Observatory mission concept for constraining the atmospheric properties of hot and warm gas giants and super Earths. Synthetic primary and secondary transit spectra for a range of planets are passed through EChOSim [13] to obtain the expected level of noise for different observational scenarios; these are then used as inputs for the NEMESIS atmospheric retrieval code and the retrieved atmospheric properties (temperature structure, composition and cloud properties) compared with the known input values, following the method of [1]. To correctly retrieve the temperature structure and composition of the atmosphere to within 2 σ, we find that we require: a single transit or eclipse of a hot Jupiter orbiting a sun-like (G2) star at 35 pc to constrain the terminator and dayside atmospheres; 20 transits or eclipses of a warm Jupiter orbiting a similar star; 10 transits/eclipses of a hot Neptune orbiting an M dwarf at 6 pc; and 30 transits or eclipses of a GJ1214b-like planet.     

Secular period decreasing of detached chromospherically active binaries

The long-term orbital period changes of a large sample of detached chromospherically active binaries (CABs) were studied. Eleven such systems were found to be undergoing secular period decreases with the rates of ?6.3×10^?9 to ?1.1×10^?6 days per year. The period decreasing rates are found to vary depending on the orbital period. The longer the orbital period is, the more rapidly the period decreases. Following Stepien (Mon. Not. R. Astron. Soc. 274:1019, 1995), the period decreasing rate predicted by angular momentum loss (AML) caused by magnetic wind is computed for each system. A comparison between the observed and calculated period decreasing rates shows that the former values are obviously larger than the latter by 1–3 orders of magnitude. It suggests that the magnetic wind is not likely the determinant mechanism driving the AML in these systems. Finally, the orbital angular momentum (AM) and the rate of AML, $\dot{J}$ , are computed for each system. It shows that the AM have a similar change with the orbital period like dP/dt does, but $\log\dot{J}/J$ presents no strict changing with the kinematical ages.     

Coupling between corotation and Lindblad resonances in the presence of secular precession rates

We investigate the dynamics of two satellites with masses $\mu _s$ and $\mu '_s$ orbiting a massive central planet in a common plane, near a first order mean motion resonance $m+1{:}m$ (m integer). We consider only the resonant terms of first order in eccentricity in the disturbing potential of the satellites, plus the secular terms causing the orbital apsidal precessions. We obtain a two-degrees-of-freedom system, associated with the two critical resonant angles $\phi = (m+1)\lambda ' -m\lambda - \varpi $ and $\phi '= (m+1)\lambda ' -m\lambda - \varpi '$ , where $\lambda $ and $\varpi $ are the mean longitude and longitude of periapsis of $\mu _s$ , respectively, and where the primed quantities apply to $\mu '_s$ . We consider the special case where $\mu _s \rightarrow 0$ (restricted problem). The symmetry between the two angles $\phi $ and $\phi '$ is then broken, leading to two different kinds of resonances, classically referred to as corotation eccentric resonance (CER) and Lindblad eccentric Resonance (LER), respectively. We write the four reduced equations of motion near the CER and LER, that form what we call the CoraLin model. This model depends upon only two dimensionless parameters that control the dynamics of the system: the distance $D$ between the CER and LER, and a forcing parameter $\epsilon _L$ that includes both the mass and the orbital eccentricity of the disturbing satellite. Three regimes are found: for $D=0$ the system is integrable, for $D$ of order unity, it exhibits prominent chaotic regions, while for $D$ large compared to 2, the behavior of the system is regular and can be qualitatively described using simple adiabatic invariant arguments. We apply this model to three recently discovered small Saturnian satellites dynamically linked to Mimas through first order mean motion resonances: Aegaeon, Methone and Anthe. Poincaré surfaces of section reveal the dynamical structure of each orbit, and their proximity to chaotic regions. This work may be useful to explore various scenarii of resonant capture for those satellites.     

On some long time dynamical features of the Trojan asteroids of Jupiter

The equation of motion of long periodic libration around the Lagrangian point $L_4$ L 4 in the restricted three-body problem is investigated. The range of validity of an approximate analytical solution in the tadpole region is determined by numerical integration. The predictions of the model of libration are tested on the Trojan asteroids of Jupiter. The long time evolution of the orbital eccentricity and the longitude of the perihelion of the Trojan asteroids, under the effect of the four giant planets, is also investigated and a slight dynamical asymmetry is shown between the two groups of Trojans at $L_4$ L 4 and $L_5$ L 5 .     

Secular dynamics of a lunar orbiter: a global exploration using Prony’s frequency analysis

We study the secular dynamics of lunar orbiters, in the framework of high-degree gravity models. To achieve a global view of the dynamics, we apply a frequency analysis (FA) technique which is based on Prony’s method. This allows for an extensive exploration of the eccentricity ( $e$ )—inclination ( $i$ ) space, based on short-term integrations ( $\sim $ 8 months) over relatively high-resolution grids of initial conditions. Different gravity models are considered: 3rd, 7th and 10th degree in the spherical harmonics expansion, with the main perturbations from the Earth being added. Since the dynamics is mostly regular, each orbit is characterised by a few parameters, whose values are given by the spectral decomposition of the orbital elements time series. The resulting frequency and amplitude maps in ( $e_0,i_0$ ) are used to identify the dominant perturbations and deduce the “minimum complexity” model necessary to capture the essential features of the long-term dynamics. We find that the 7th degree zonal harmonic ( $J_7$ term) is of profound importance at low altitudes as, depending on the initial secular phases, it can lead to collision with the Moon’s surface within a few months. The 3rd-degree non-axisymmetric terms are enough to describe the deviations from the 1 degree-of-freedom zonal problem; their main effect is to modify the equilibrium value of the argument of periselenium, $\omega $ , with respect to the “frozen” solution ( $\omega =\pm 90^{\circ }, \forall \Omega $ , where $\Omega $ is the nodal longitude). Finally, we show that using FA on a fine grid of initial conditions, set around a suitably chosen ‘first guess’, one can compute an accurate approximation of the initial conditions of a periodic orbit.     

Binary pulsars in magnetic field versus spin period diagram

We analyzed 186 binary pulsars (BPSRs) in the magnetic field versus spin period (B-P) diagram, where their relations to the millisecond pulsars (MSPs) can be clearly shown. Generally, both BPSRs and MSPs are believed to be recycled and spun-up in binary accreting phases, and evolved below the spin-up line setting by the Eddington accretion rate ( $\dot{M}{\simeq}10^{18}~\mbox{g/s}$ ). It is noticed that most BPSRs are distributed around the spin-up line with mass accretion rate $\dot{M}=10^{16}~\mbox{g/s}$ and almost all MSP samples lie above the spin-up line with $\dot{M}\sim10^{15}~\mbox{g/s}$ . Thus, we calculate that a minimum accretion rate ( $\dot{M}\sim10^{15}~\mbox{g/s}$ ) is required for the MSP formation, and physical reasons for this are proposed. In the B-P diagram, the positions of BPSRs and their relations to the binary parameters, such as the companion mass, orbital period and eccentricity, are illustrated and discussed. In addition, for the seven BPSRs located above the limit spin-up line, possible causes are suggested.     

The broad band spectral index of TeV blazars detected by Fermi LAT

Using γ-ray data detected by Fermi Large Area Telescope (LAT) and multi-wave band data for 35 TeV blazars sample, we have studied the possible correlations between different broad band spectral indices ( $\alpha_{\rm r.ir}$ , $\alpha_{\rm{r.o}}$ , $\alpha_{\rm r.x}$ , $\alpha_{\rm r.\gamma}$ , $\alpha_{\rm{ir.o}}$ , $\alpha_{\rm ir.x}$ , $\alpha_{\rm ir.\gamma}$ , $\alpha_{\rm o.x}$ , $\alpha_{\rm o.\gamma}$ , $\alpha_{\rm r.x}$ , $\alpha_{\rm x.\gamma}$ ) in all states (average/high/low). Our results are as follows: (1) For our TeV blazars sample, the strong positive correlations were found between $\alpha_{\rm r.ir}$ and $\alpha_{\rm{r.o}}$ , between $\alpha_{\rm r.ir}$ and $\alpha_{\rm r.x}$ , between $\alpha_{\rm r.ir}$ and $\alpha_{\rm r.\gamma}$ in all states (average/high/low); (2) For our TeV blazars sample, the strong anti-correlations were found between $\alpha_{\rm r.ir}$ and $\alpha_{\rm x.\gamma}$ , between $\alpha_{\rm{r.o}}$ and $\alpha_{\rm ir.\gamma}$ , between $\alpha_{\rm{r.o}}$ and $\alpha_{\rm o.\gamma}$ , between $\alpha_{\rm{r.o}}$ and $\alpha_{\rm x.\gamma}$ , between $\alpha_{\mathrm{ir.o}}$ and $\alpha_{\rm o.\gamma}$ , between $\alpha_{\rm r.x}$ and $\alpha_{\rm x.\gamma}$ , between $\alpha_{\rm ir.x}$ and $\alpha_{\rm x.\gamma}$ in all states (average/high/low). The results suggest that the synchrotron self-Compton radiation (SSC) is the main mechanism of high energy γ-ray emission and the inverse Compton scattering of circum-nuclear dust is likely to be a important complementary mechanism for TeV blazars. Our results also show that the possible correlations vary from state to state in the same pair of indices, Which suggest that there may exist differences in the emitting process and in the location of the emitting region for different states.     

Retrograde resonance in the planar three-body problem

We continue the investigation of the dynamics of retrograde resonances initiated in Morais and Giuppone (Mon Notices R Astron Soc 424:52–64, doi:10.1111/j.1365-2966.2012.21151.x, 2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/ $-$ 1, 1/ $-$ 1 and 1/ $-$ 2). In the case of the 1/ $-$ 1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.     

Spectroscopic studies of the small-amplitude Cepheid SU Cas

A new set of 16 high-resolution spectra for the small-amplitude Cepheid SU Cas obtained in 2007–2009 has allowed us to determine its atmospheric parameters (T _eff = 6345 ± 30 K, log g = 2.40, V _t = 3.25 km s^?1) and to measure its radial velocities. The latter were added to the general list of radial velocities (375 estimates) obtained in the last 90 years. Using a frequency analysis, we have refined the pulsation and orbital periods of the Cepheid. Apart from the well-known fundamental pulsation period , we have detected a possible secondary period of . Their ratio of 0.96 suggests the existence of nonradial pulsations in the Cepheid’s atmosphere. Based on photoelectric photometry in the last 60 years, we have shown that the effective temperature undergoes cyclic secular changes of ±200 K with an unknown period. The mean effective temperature T _eff = 6395 ± 52 K estimated from photometric data agrees well with our estimate from spectroscopic data. The variations of the mean color index, effective temperature, and γ-velocity (in 90 years of observations) point to a possible orbital motion of the well-known hot companion with the most probable periods of , , and . The elemental abundances in the atmosphere of SU Cas confirm the conclusion that this Cepheid is a typical yellow supergiant after the first dredge-up. Our T _eff estimate gives a radius of 32R _⊙ and a distance of 455 pc for it, which is inconsistent with its membership in the open cluster Alessi 95. The question about the pulsation mode of SU Cas still remains open.     

Fourier analysis of light curves of eclipsing variable stars

The photometric perturbationsB _h ^(l) arising from both tidal and rotational distortion of a close eclipsing binary have been given in two previous papers (Livaniou, 1977; Rovithis-Livaniou, 1977). The aim of the present paper will be to find the eclipse perturbationsB _2m =B _{2m, tid} +B _{2m, rot} of a close binary exhibiting partial eclipses. This will be done giving the suitable combinations of theB _h ^(l) 's and will make easier the application to real stars. After a very brief introduction, Section 2 gives both theB _{2m, tid} andB _{2m, rot} for uniformly bright discs; while in Sections 3 and 4 they are given for linear and quadratic limb-darkening, respectively. Finally, Section 5 gives a brief discussion of the results.     

Comparative analysis of photometric variability of TT ARI in the years 1994–1995 and 2001, 2004

We present the results of photometric observations of a bright cataclysmic variable TT Ari with an orbital period of 0.13755 days. CCD observations were carried out with the Russian-Turkish RTT 150 telescope in 2001 and 2004 (13 nights). Multi-color photoelectric observations of the system were obtained with the Zeiss 600 telescope of SAO RAS in 1994–1995 (6 nights). In 1994–1995, the photometric period of the system was smaller than the orbital one (0 _. ^d 132 and 0 _. ^d 134), whereas it exceeded the latter (0 _. ^d 150 and 0 _. ^d 148) in 2001, 2004. An additional period exceeding the orbital one (0 _. ^d 144) is detected in 1995 modulations. We interpret it as indicating the elliptic disc precession in the direction of the orbital motion. In 1994, the variability in colors shows periods close to the orbital one (0 _. ^d 136, b-v), as well as to the period indicating the elliptic disk precession (0 _. ^d 146, w-b). We confirm that during the epochs characterized by photometric periods shorter than the orbital one, the quasi-periodic variability of TT Ari at time scales about 20 min is stronger than during epochs with long photometric periods. In general, the variability of the system can be described as a “red” noise with increased amplitudes of modulations at characteristic time scales of 10–40 min.     

Solving Kepler’s equation via Smale’s \alpha -theory

We obtain an approximate solution $\tilde{E}=\tilde{E}(e,M)$ of Kepler’s equation $E-e\sin (E)=M$ for any $e\in [0,1)$ and $M\in [0,\pi ]$ . Our solution is guaranteed, via Smale’s $\alpha $ -theory, to converge to the actual solution $E$ through Newton’s method at quadratic speed, i.e. the $n$ -th iteration produces a value $E_n$ such that $|E_n-E|\le (\frac{1}{2})^{2^n-1}|\tilde{E}-E|$ . The formula provided for $\tilde{E}$ is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near $e=1$ and $M=0$ , where a single cubic root is used. We also show that the root operation is unavoidable, by proving that no approximate solution can be computed in the entire region $[0,1)\times [0,\pi ]$ if only rational functions are allowed in each branch.     

The planetary spin and rotation period: a modern approach

Using a new approach, we have obtained a formula for calculating the rotation period and radius of planets. In the ordinary gravitomagnetism the gravitational spin (S) orbit (L) coupling, $\vec{L}\cdot\vec{S}\propto L^{2}$ , while our model predicts that $\vec{L}\cdot\vec{S}\propto\frac{m}{M}L^{2}$ , where M and m are the central and orbiting masses, respectively. Hence, planets during their evolution exchange L and S until they reach a final stability at which MS∝mL, or $S\propto\frac{m^{2}}{v}$ , where v is the orbital velocity of the planet. Rotational properties of our planetary system and exoplanets are in agreement with our predictions. The radius (R) and rotational period (D) of tidally locked planet at a distance a from its star, are related by, $D^{2}\propto\sqrt{\frac{M}{m^{3}}}R^{3}$ and that $R\propto\sqrt{\frac {m}{M}}a$ .     

Effective stability around the Cassini state in the spin-orbit problem

We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay variables, we construct a high-order Birkhoff normal form and give an estimate of the effective stability time in the Nekhoroshev sense. By extensively using algebraic manipulations on a computer, we explicitly apply our method to the rotation of Titan. We obtain physical bounds of Titan’s latitudinal and longitudinal librations, finding a stability time greatly exceeding the estimated age of the Universe. In addition, we study the dependence of the effective stability time on three relevant physical parameters: the orbital inclination, $i$ , the mean precession of the ascending node of Titan orbit, $\dot{\varOmega }$ , and the polar moment of inertia, $C$ .     

A simple procedure to extend the Gauss method of determining orbital parameters from three to N points

A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit determination, an initial set of heliocentric state vectors r _i and $\dot{\mathbf{r}}_{i}$ is calculated. Then using the fact that the object follows the path that keep the constants of motion unchanged, I derive conserved quantities by applying simple linear regression method on state vectors r _i and $\dot{\mathbf{r}}_{i}$ . The best orbital plane is fixed by applying an iterative procedure which minimize the variation in magnitude of angular momentum of the orbit. Same procedure is used to fix shape and orientation of the orbit in the plane by minimizing variation in total energy and Laplace Runge Lenz vector. The method is tested using simulated data for a hypothetical planet rotating around the sun.