Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them

WASP-33 is a fast rotating, main sequence star which hosts a hot Jupiter moving along a retrograde and almost polar orbit with semi-major axis a=0.02 au and eccentricity provisionally set to e=0. The quadrupole mass moment J₂^*J_{2}^{\star} and the proper angular momentum S _⋆ of the star are 1900 and 400 times, respectively, larger than those of the Sun. Thus, huge classical and general relativistic non-Keplerian orbital effects should take place in such a system. In particular, the large inclination Ψ_⋆ of the orbit of WASP-33b to the star’s equator allows to consider the node precession [(W)\dot]\dot{\Omega} and the related time variation dt _d /dt of the transit duration t _d . The WASP-33b node rate due to J₂^*J_{2}^{\star} is 9×10⁹ times larger than the same effect for Mercury induced by the Sun’s oblateness, while the general relativistic gravitomagnetic node precession is 3×10⁵ times larger than the Lense-Thirring effect for Mercury due to the Sun’s rotation. We also consider the effect of the centrifugal oblateness of the planet itself and of a putative distant third body X. The magnitudes of the induced time change in the transit duration are of the order of 3×10⁻⁶,2×10⁻⁷,8×10⁻⁹ for J₂^*J_{2}^{\star}, the planet’s rotational oblateness and general relativity, respectively. A yet undiscovered planet X with the mass of Jupiter orbiting at more than 1 au would induce a transit duration variation of less than 4×10⁻⁹. A conservative evaluation of the accuracy in measuring dt _d /dt over 10 yr points towards ≈10⁻⁸. The analysis presented here will be applicable also to other exoplanets with similar features if and when they will ne discovered.     

Relativistic effects and solar oblateness from radar observations of planets and spacecraft

We used more than 250 000 high-precision American and Russian radar observations of the inner planets and spacecraft obtained in the period 1961–2003 to test the relativistic parameters and to estimate the solar oblateness. Our analysis of the observations was based on the EPM ephemerides of the Institute of Applied Astronomy, Russian Academy of Sciences, constructed by the simultaneous numerical integration of the equations of motion for the nine major planets, the Sun, and the Moon in the post-Newtonian approximation. The gravitational noise introduced by asteroids into the orbits of the inner planets was reduced significantly by including 301 large asteroids and the perturbations from the massive ring of small asteroids in the simultaneous integration of the equations of motion. Since the post-Newtonian parameters and the solar oblateness produce various secular and periodic effects in the orbital elements of all planets, these were estimated from the simultaneous solution: the post-Newtonian parameters are β = 1.0000 ± 0.0001 and γ = 0.9999 ± 0.0002, the gravitational quadrupole moment of the Sun is J₂ = (1.9 ± 0.3) × 10^?7, and the variation of the gravitational constant is ?/G = (?2 ± 5) × 10^?14 yr^?1. The results obtained show a remarkable correspondence of the planetary motions and the propagation of light to General Relativity and narrow significantly the range of possible values for alternative theories of gravitation.     

Changes in the Sun’s mass and gravitational constant estimated using modern observations of planets and spacecraft

More than 635 thousand positional observations of planets and spacecraft of various types (mostly radiotechnical ones, 1961–2010) were used to estimate possible changes in the gravitational constant, Sun’s mass, and semi-major axes of planetary orbits, as well as the associated value of the astronomical unit. The observations were analyzed based on the EPM2010 ephemerides constructed at the Institute of Applied Astronomy (Russian Academy of Sciences) in a post-Newtonian approximation as a result of simultanious numerical integration of the equations of motion of nine major planets, the Sun, the Moon, asteroids, and trans-Neptunian objects. The heliocentric gravitational constant GM _⊙ was found to vary with a rate of (GṀ _⊙/GM _⊙ = (−5.0 ± 4.1)) × 10⁻¹⁴ per year (at the 3σ level). The positive secular changes in the semimajor axes ȧ _i /a _i were found for Mercury, Venus, Mars, Jupiter, and Saturn provided by high-precision observations. These changes also correspond to the decrease in the heliocentric gravitational constant. The changing of GM _⊙, itself is probably caused by the loss of the mass M _⊙ of the Sun due to its radiation and solar wind; these effects are partly compensated by the material falling onto the Sun. Allowing for the maximum bounds on the possible change in the Sun’s mass M _⊙, it has been found from the change obtained in GM _⊙ that the annual change Ġ/G of the gravitational constant G falls within the interval −4.2 × 10⁻¹⁴ < ȧ/G < +7.5 × 10⁻¹⁴ with a 95% probability. The astronomical unit (AU) is connected by its definition only with the heliocentric gravitational constant. The decrease of GM _⊙ obtained in this paper should correspond to a secular decrease in the AU. It is shown, however, that the modern level of accuracy does not allow us to determine a change in the AU. The attained posibility of determining changes in GM _⊙ using high-accuracy observations encourages us to have a relation between GM _⊙ and the AU fixed for a certain moment in time, since it is inconvenient to have a time-dependent length for the AU.     

Galactic rotation curve from the space velocities of selected masers

Based on currently available observations of 28 maser sources in 25 star-forming regions with measured trigonometric parallaxes, proper motions, and radial velocities, we have constructed the rotation curve of the Galaxy. Taking different distances to the Galactic center R ₀, we have estimated the peculiar velocity of the Sun, the angular velocity of Galactic rotation, and its three derivatives. For R ₀ = 8 kpc, we have found the circular velocity of the Sun to be V ₀ = 243 ± 16 km s⁻¹, which corresponds to a revolution period of 202 ± 10 Myr. We have obtained the Oort constants A = 16.9 ± 1.2 km s⁻¹ kpc⁻¹ and B = −13.5 ± 1.4 km s⁻¹ kpc⁻¹. Our simulation of the influence of a spiral density wave has shown that the peculiar velocity of the Sun with respect to the local standard of rest and the component (V _⊙)_LSR depend significantly on the Sun’s phase in the spiral wave.     

WR 140 (=V1687 Cyg): Infrared photometry, 2001–2010

We present the results of our infrared observations of WR 140 (=V1687 Cyg) in 2001–2010. Analysis of the observations has shown that the J brightness at maximum increased near the periastron by about 0 ^m .3; the M brightness increased by ∼2 ^m in less than 50 days. The minimum J brightness and the minimum L and M brightnesses were observed 550–600 and 1300–1400 days after the maximum, respectively. The JHKLM brightness minimum was observed in the range of orbital phases 0.7–0.9. The parameters of the primary O5 component of the binary have been estimated to be the following: R(O5) ≈ 24.7R _⊙, L(O5) ≈ 8 × 10⁵ L _⊙, and M _bol(O5) ≈ −10 ^m . At the infrared brightness minimum, T _g ∼ 820–880 K, R _g ≈ 2.6 × 10⁵ R _⊙, the optical depth of the shell at 3.5 μm is ∼5.3 × 10⁻⁶, and its mass is ≈1.4 × 10⁻⁸ M _⊙. At the maximum, the corresponding parameters are ∼1300 K, 8.6 × 10⁴ R _⊙, ∼2 × 10⁻⁴, and ∼6 × 10⁻⁸ M _⊙; the mean rate of dust inflow (condensation) into the dust structure is ∼3.3 × 10⁻⁸ M _⊙ yr⁻¹. The mean escape velocity of the shell from the heating source is ∼10³ km s⁻¹ and the mean dispersal rate of the shell is ∼1.1 × 10⁻⁸ M _⊙ yr⁻¹.     

CCD BV and 2MASS photometric study of the open cluster NGC 1513

We present CCD BV and JHK _s 2MASS photometric data for the open cluster NGC 1513. We observed 609 stars in the direction of the cluster up to a limiting magnitude of V∼19 mag. The star-count method showed that the centre of the cluster lies at α ₂₀₀₀=04 ^h 09 ^m 36 ^s , δ ₂₀₀₀=49°28^′43^″ and its angular size is r=10 arcmin. The optical and near-infrared two-colour diagrams revealed the colour excesses in the direction of the cluster as E(B−V)=0.68±0.06, E(J−H)=0.21±0.02 and E(J−K _s )=0.33±0.04 mag. These results are consistent with normal interstellar extinction values. Optical and near-infrared Zero Age Main-Sequences (ZAMS) provided an average distance modulus of (m−M)₀=10.80±0.13 mag, which can be translated into a distance of 1440±80 pc. Finally, using Padova isochrones we determined the metallicity and age of the cluster as Z=0.015±0.004 ([M/H]=−0.10±0.10 dex) and log (t/yr)=8.40±0.04, respectively.     

A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars

Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS) mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W ₀ = (12,654,875 ± 69) (m²/s²), is used as one of the four fundamental gravity parameters of Mars namely, {W ₀, GM, ω, J ₂₀}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid is presented with respect to the computed reference ellipsoid.     

Electron Temperatures and Flow Speeds of the Low Solar Corona: MACS Results from the Total Solar Eclipse of 29 March 2006 in Libya

An experiment was conducted in conjunction with the total solar eclipse on 29 March 2006 in Libya to measure both the electron temperature and its flow speed simultaneously at multiple locations in the low solar corona by measuring the visible K-coronal spectrum. Coronal model spectra incorporating the effects of electron temperature and its flow speed were matched with the measured K-coronal spectra to interpret the observations. Results show electron temperatures of (1.10±0.05) MK, (0.70±0.08) MK, and (0.98±0.12) MK, at 1.1 R _⊙ from Sun center in the solar north, east and west, respectively, and (0.93±0.12) MK, at 1.2 R _⊙ from Sun center in the solar west. The corresponding outflow speeds obtained from the spectral fit are (103±92) km s⁻¹, (0+10) km s⁻¹, (0+10) km s⁻¹, and (0+10) km s⁻¹. Since the observations were taken only at 1.1 R _⊙ and 1.2 R _⊙ from Sun center, these speeds, consistent with zero outflow, are in agreement with expectations and provide additional confirmation that the spectral fitting method is working. The electron temperature at 1.1 R _⊙ from Sun center is larger at the north (polar region) than the east and west (equatorial region).     

Analytical Approach to the Motion of a Lunar Artificial Satellite

The canonical equations of motion of an artificial lunar satellite are formulated including the effects of the asphericity of the Moon comprising the harmonics J ₂, J ₂₂, J ₃, J ₃₁, J ₄ andJ ₅, the oblateness of the Earth up to the second zonal harmonic, as well as the disturbing function due to the attractions of the Earth and of the Sun (terms are retained up to order 10^-6 for the higher orbits and 10^-8 for the lower orbits). This revised version was published online in July 2006 with corrections to the Cover Date.     

The kinematics of Trapezium-type systems

Summary In this paper the results of the research of the stars proper motions Trapezium components are reported. They are: the galactic coordinates of the solar aprx and the Sun velocity (L _⊙=43±18°,B _⊙=+28±13°,V _⊙=13±4 km s⁻¹), the dispersion of peculiar velocities in the direction of the galactic coordinates for the above mentioned stars (σ _l =±11 km s⁻¹, σ _b =±7 km s⁻¹).The attained accuracy of the proper motions (±0.005″ yr⁻¹) is shown to be insufficient to the study of internal space motions in these systems. At present the work to increase the relative proper motions accuracy for multiple system components and to improve reductions from the relative to absolute proper motions, is being carried out in the Main Astronomical Observatory (Academy of Sciences of the Ukrainian SSR). The new catalogue of the AGK3 stars is composed now in the vicinity of the galactic equator in order to improve reductions from the relative to absolute proper motions. The r.m.s. errors of the proper motions, obtained in the AGK3 system, are ±0.005″ yr⁻¹.     

Galactic kinematics from OB3 stars with distances determined from interstellar Ca II lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation Ω′₀ and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R ₀ = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components (u _⊙, v _⊙, ω _⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s⁻¹; (2) the Galactic rotation parameters Ω₀ = −31.5 ± 0.9 km s⁻¹ kpc⁻¹, Ω′₀ = +4.49 ± 0.12 km s⁻¹ kpc⁻², Ω″₀ = −1.05 ± 0.38 km s⁻¹ kpc⁻³ (the corresponding Oort constants are A = 17.9 ± 0.5 km s⁻¹ kpc⁻¹, B = −13.6 ± 1.0 km s⁻¹ kpc⁻¹ and the circular rotation velocity of the solar neighborhood is |V ₀| = 252 ± 14 km s⁻¹); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f _R = −12.5±1.1 km s⁻¹ and f _ϑ = 2.0 ± 1.6 km s⁻¹; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x _⊙ = −91° ± 4°.     

Solar Polarity Dependence of Cosmic Ray Power Spectra Observed with Mawson Underground Muon Telescopes

Power spectral density (PSD) of cosmic rays has been calculated from hourly averaged counts observed by underground muon telescopes located at Mawson over the low-frequency range 2.7×10⁻⁷ – 1.4×10⁻⁴ Hz. The first two harmonics of the solar daily variation are well defined for even cycles (20 and 22) whereas only the first harmonic is defined in cycle 21. The amplitude of the diurnal variation is lower for even cycles than for the odd cycle. The spectral power of the odd cycle exceeds those of the even cycles. The spectra are flatter and have lower power when the interplanetary magnetic field (IMF) is directed away from the Sun above the current sheet (A>0) than when the IMF is directed toward the Sun above the current sheet (A<0). The spectra imply that heliospheric magnetic turbulence may be more variable on time scales of several years than previously suspected.     

Parameters of the local warp of the stellar-gaseous galactic disk from the kinematics of Tycho-2 nearby red giant clump stars

We analyze the three-dimensional kinematics of about 82 000 Tycho-2 stars belonging to the red giant clump (RGC). First, based on all of the currently available data, we have determined new, most probable components of the residual rotation vector of the optical realization of the ICRS/HIPPARCOS system relative to an inertial frame of reference, (ω _x , ω _y , ω _z ) = (−0.11, 0.24, −0.52) ± (0.14, 0.10, 0.16) mas yr⁻¹. The stellar proper motions in the form μ_α cos δ have then be corrected by applying the correction ω _z = −0.52 mas yr⁻¹. We show that, apart from their involvement in the general Galactic rotation described by the Oort constants A = 15.82 ± 0.21 km s⁻¹ kpc⁻¹ and B = −10.87 ± 0.15 km s⁻¹ kpc⁻¹, the RGC stars have kinematic peculiarities in the Galactic yz plane related to the kinematics of the warped stellar-gaseous Galactic disk. We show that the parameters of the linear Ogorodnikov-Milne model that describe the kinematics of RGC stars in the zx plane do not differ significantly from zero. The situation in the yz plane is different. For example, the component of the solid-body rotation vector of the local solar neighborhood around the Galactic x axis is M ₃₂⁻ = −2.6 ± 0.2 km s⁻¹ kpc⁻¹. Two parameters of the deformation tensor in this plane, namely M ₂₃⁺ = 1.0 ± 0.2 km s⁻¹ kpc⁻¹ and M ₃₃ − M ₂₂ = −1.3 ± 0.4 km s⁻¹ kpc⁻¹, also differ significantly from zero. On the whole, the kinematics of the warped stellar-gaseous Galactic disk in the local solar neighborhood can be described as a rotation around the Galactic x axis (close to the line of nodes of this structure) with an angular velocity −3.1 ± 0.5 km s⁻¹ kpc⁻¹ ≤ Ω_W ≤ −4.4 ± 0.5 km s⁻¹ kpc⁻¹.     

Tritium chain of the hydrogen cycle of thermonuclear reactions in the solar interior

The tritium chain of the hydrogen cycle on the Sun including the reactions ³He(e⁻, ν _e) ³H(p, γ)⁴He is considered. The flux of tritium neutrinos at a distance of 1 AU is 8.1 × 10⁴ cm⁻² s⁻¹. It exceeds the neutrino flux from the (hep)-reaction by one order of magnitude. The radial distribution of the yield of ³H neutrinos inside the Sun and their energy spectrum, which has the form of a line at an energy of 2.5–3.0 keV, have also been calculated. The flux of thermal tritium neutrinos is accompanied by a very weak flux of antineutrinos (∼10³ cm⁻² yr⁻¹) with an energy below 18.6 keV. These antineutrinos are produced in the URCA processes ³He ⇆ ³H.     

A diffraction limit on the gravitational lens effect

The focussing of gravitational radiation by the interior and exterior gravitational field of a Newtonian gravitational lens is considered. A graphical method for determining the caustic structure of a Newtonian gravitational lens is presented and the caustic structure of a solar type gravitational lens is discussed. Estimates of the amplitude magnification in the caustic region indicate that waves with frequencies less than a critical cutoff frequency ω _c are not amplified significantly. For a lens of massM this cutoff frequency is ω _c ≈(10^-1πM)^-1; for the Sun ω _c ≈10⁴s^-1. Work supported in part by National Science Foundation Grant PHY78-05368.     

Equivalence principle (EP) and solar system constraints on $R(1\pm\epsilon\ln({R \over R_{c}}))$ model of gravity

Experiments on the violation of equivalence principle (EP) and solar system give a number of constraints in which any modified gravity model must satisfy them. We study these constraints on a kind of f(R) gravity as f(R) = R(1±eln([(R)/(R_c)]))f(R) = R(1\pm\epsilon\ln({R \over R_{c}})). For this investigation we use of chameleon mechanism and show that a spherically body has thin-shell in this model. So that we obtain an effective coupling of the fifth force which is suppressed through a chameleon mechanism. Also, we obtain γ _PPN =1±1.13×10⁻⁵ which is agreement with experiment results. At last, we show that for R _c ≈ρ _c this model is consistent with EP, thin shell condition and fifth force of chameleon mechanism for ε⋍10⁻¹⁴.     

Allan Sandage and the cosmic expansion

This is an account of Allan Sandage’s work on (1) The character of the expansion field. For many years he has been the strongest defender of an expanding Universe. He later explained the CMB dipole by a local velocity of 220±50 km s⁻¹ toward the Virgo cluster and by a bulk motion of the Local supercluster (extending out to ∼3500 km s⁻¹) of 450–500 km s⁻¹ toward an apex at l=275, b=12. Allowing for these streaming velocities he found linear expansion to hold down to local scales (∼300 km s⁻¹). (2) The calibration of the Hubble constant. Probing different methods he finally adopted—from Cepheid-calibrated SNe Ia and from independent RR Lyr-calibrated TRGBs—H ₀=62.3±1.3±5.0 km s⁻¹ Mpc⁻¹.     

Dissipation of modified entropic gravitational energy through gravitational waves

The phenomenological nature of a new gravitational type interaction between two different bodies derived from Verlinde’s entropic approach to gravitation in combination with Sorkin’s definition of Universe’s quantum information content, is investigated. Assuming that the energy stored in this entropic gravitational field is dissipated under the form of gravitational waves and that the Heisenberg principle holds for this system, one calculates a possible value for an absolute minimum time scale in nature t = \frac1516 \fracL^1/2(^h/_2p) Gc⁴ ~ 9.27×10^-105\tau=\frac{15}{16} \frac{\Lambda^{1/2}\hbar G}{c^{4}}\sim9.27\times10^{-105} seconds, which is much smaller than the Planck time t _P =(ħG/c ⁵)^1/2∼5.38×10⁻⁴⁴ seconds. This appears together with an absolute possible maximum value for Newtonian gravitational forces generated by matter F_g=\frac3230\fracc⁷L (^h/_2p) G² ~ 3.84×10¹⁶⁵F_{g}=\frac{32}{30}\frac{c^{7}}{\Lambda \hbar G^{2}}\sim 3.84\times 10^{165} Newtons, which is much higher than the gravitational field between two Planck masses separated by the Planck length F _gP =c ⁴/G∼1.21×10⁴⁴ Newtons.     

Determining the orientation parameters of the ICRS/UCAC2 system using the Kharkov catalog of absolute stellar proper motions

The absolute proper motions of about 275 million stars from the Kharkov XPM catalog have been obtained by comparing their positions in the 2MASS and USNO-A2.0 catalogs with an epoch difference of about 45 yr for northern-hemisphere stars and about 17 yr for southern-hemisphere stars. The zero point of the system of absolute proper motions has been determined using 1.45 million galaxies. The equatorial components of the residual rotation vector of the ICRS/UCAC2 coordinate system relative to the system of extragalactic sources have been determined by comparing the XPM and UCAC2 stellar proper motions: ω _x,y,z = (−0.06, 0.17, −0.84) ± (0.15, 0.14, 0.14) mas yr⁻¹. These parameters have been calculated using about 1 million faintest UCAC2 stars with magnitudes R _UCAC2 > 16 ^m and J > 14 ^m . 7, for which the color and magnitude equation effects are negligible.     

A high galactic latitude HI 21 cm-line absorption survey using the GMRT: II. Results and interpretation

We have carried out a sensitive high-latitude (|b| > 15°) HI 21 cm-line absorption survey towards 102 sources using the GMRT. With a 3σ detection limit in optical depth of ∼ 0.01, this is the most sensitive HI absorption survey. We detected 126 absorption features most of which also have corresponding HI emission features in the Leiden Dwingeloo Survey of Galactic neutral Hydrogen. The histogram of random velocities of the absorption features is well-fit by two Gaussians centered at V_1sr ∼ 0 km s⁻¹ with velocity dispersions of 7.6 ± 0.3 km s⁻¹ and 21 ± 4 km s⁻¹ respectively. About 20% of the HI absorption features form the larger velocity dispersion component. The HI absorption features forming the narrow Gaussian have a mean optical depth of 0.20 ± 0.19, a mean HI column density of (1.46 ± 1.03) × 10²⁰ cm⁻², and a mean spin temperature of 121 ± 69 K. These HI concentrations can be identified with the standard HI clouds in the cold neutral medium of the Galaxy. The HI absorption features forming the wider Gaussian have a mean optical depth of 0.04 ± 0.02, a mean HI column density of (4.3 ± 3.4) × 10¹⁹ cm⁻², and a mean spin temperature of 125 ± 82 K. The HI column densities of these fast clouds decrease with their increasing random velocities. These fast clouds can be identified with a population of clouds detected so far only in optical absorption and in HI emission lines with a similar velocity dispersion. This population of fast clouds is likely to be in the lower Galactic Halo.