Equatorial Ellipticity Research Articles

Mercury׳s global shape and topography from MESSENGER limb images

We derive models for the global shape and topography of Mercury from limb images obtained by the MESSENGER spacecraft during flybys and from orbit. Crossover heights of 225 individual limb profiles were adjusted by least-squares techniques to establish a rigid global topographic network. Mercury is confirmed to possess an equatorial ellipticity and a polar oblateness. Several large impact basins and craters can be identified in the topographic model, including one basin that was earlier proposed but unconfirmed. Comparisons with absolute height data from laser altimetry indicate that the limb model appears to overestimate planetary radius by ~900m on average. Limb profiles and local digital terrain models derived from stereo-photogrammetry show good agreement.

Resonance in a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity

Resonances in a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity have been investigated. The resonance at two points resulting from the commensurability between the mean motion of the satellite and Γ (angle measured from the minor axis of the Earth’s equatorial ellipse to the projection of the satellite on the plane of the equator) is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. We have observed that the amplitude and the time period of the oscillation decrease as Γ increases in the first quadrant. The radial deviation (Δr) and the tangential deviation (rcΔθ) have been determined. Here rc represents the synchronous altitude. The effects of the arithmetic sum of amplitudes λi involved in the perturbation equations on orbital inclination 0∘≤α0≤90∘ are shown. It is observed that \(\sum_{i = 1}^{46} \lambda_{i}\) increases as α0 increases. We have also determined the displacement ΔD (called drift) due to the oscillatory terms under the summation sign involved in the equations of motion of the satellite. We have observed that the value of ΔD is less than 0.5∘.

Resonance in the earth-moon system around the sun including earth’s equatorial ellipticity

We have investigated the resonances in the earth-moon system around the sun including earth’s equatorial ellipticity. The resonance resulting from the commensurability between the mean motion of the moon and Γ (angle measured from the minor axis of the earth’s equatorial ellipse to the projection of the moon on the plane of the equator) is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. We have shown the effects of Γ on the amplitude and the time period of the resonance oscillation using the data of the moon. It is observed that the amplitude decreases and the time period also decreases as Γ increases from 0∘ to 45∘.

Resonance in a geo-centric satellite due to earth’s equatorial ellipticity

The resonances in a geocentric satellite due to earth’s equatorial ellipticity have been investigated. The resonance at five points resulting from the commensurability between the mean motion of the satellite and the earth’s equatorial ellipticity is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. A comparison of their effects on the orbital elements has also been studied. It is observed that the amplitude and the time period of the oscillation decrease as Γ (angle measured from the minor axis of the earth’s equatorial ellipse to the projection of the satellite on the plane of the equator) increases in the first quadrant for all the resonance cases.

Experimental study of libration-driven zonal flows in non-axisymmetric containers

Orbital dynamics that lead to longitudinal libration of celestial bodies also result in an elliptically deformed equatorial core–mantle boundary. The non-axisymmetry of the boundary leads to a topographic coupling between the assumed rigid mantle and the underlying low viscosity fluid. The present experimental study investigates the effect of non axisymmetric boundaries on the zonal flow driven by longitudinal libration. For large enough equatorial ellipticity, we report intermittent space-filling turbulence in particular bands of resonant frequency correlated with larger amplitude zonal flow. The mechanism underlying the intermittent turbulence has yet to be unambiguously determined. Nevertheless, recent numerical simulations in triaxial and biaxial ellipsoids suggest that it may be associated with the growth and collapse of an elliptical instability (Cébron et al., 2012). Outside of the band of resonance, we find that the background flow is laminar and the zonal flow becomes independent of the geometry at first order, in agreement with a non linear mechanism in the Ekman boundary layer (e.g., Calkins et al., 2010; Sauret and Le Dizès, submitted for publication).

Low-altitude, near-polar and near-circular orbits around Europa

The dynamics of orbits around planetary satellites, taking into account the gravitational attraction of a third-body and the non-uniform distribution of mass of the planetary satellite, is studied. The Hamiltonian considered is explicitly time-dependent. Conditions for frozen orbits are presented. Low-altitude, near-polar orbits, very desirable for scientific missions to study planetary satellites such as the Jupiter’s moon Europa, are analyzed. Lifetimes for these orbits are computed through the single and double averaged method. Comparison between the results obtained by the single and double averaged method is presented. The single-averaged model is more realistic, since it does not eliminate the term due to the equatorial ellipticity of the planetary satellite as done by the double-averaged problem. Considering the single-averaged method, we found unstable frozen orbits where the satellite does not impact with the surface of Europa for at least 200days. We present an approach using the unaveraged disturbing potential to analyze the effects of these terms in the amplitude of the eccentricity.

Structural properties of disk galaxies

<i>Context. <i/> Knowledge of the intrinsic shapes of galaxy components provides crucial information when constraining phenomena driving their formation and evolution.<i>Aims. <i/> We analize the structural parameters of a magnitude-limited sample of 148 unbarred S0–Sb galaxies to derive the intrinsic shape of their bulges.<i>Methods. <i/> We developed a new method to derive the intrinsic shapes of bulges based on geometrical relationships between the apparent and intrinsic shapes of bulges and disks. Bulges were assumed to be triaxial ellipsoids sharing the same center and polar axis of their surrounding disks. Disks were assumed to be circular, infinitesimally thin, and to lie on the equatorial plane of bulges. The equatorial ellipticity and intrinsic flattening of bulges were obtained from the length of the apparent major and minor semi-axes of the bulge, the twist angle between the apparent major axis of the bulge and the galaxy line of nodes, and the galaxy inclination.<i>Results. <i/> We find that the intrinsic shape is well constrained for a subsample of 115 bulges with favorable viewing angles. A large fraction of them are characterized by an elliptical section (<i>B<i/>/<i>A<i/> < 0.9). This fraction is 33%, 55%, and 43% if using their maximum, mean, or median equatorial ellipticity, respectively. Most are flattened along their polar axis (<i>C<i/> < (<i>A<i/>+<i>B<i/>)/2). Only 18% of the observed bulges have a probability > 50% and none has a probability > 90% of being elongated along the polar axis. The distribution of triaxiality is strongly bimodal. This bimodality is driven by bulges with Sérsic index <i>n<i/> > 2, or equivalently, by the bulges of galaxies with a bulge-to-total ratio <i>B<i/>/<i>T<i/> > 0.3. Bulges with <i>n<i/> <i>≤<i/> 2 and with <i>B<i/>/<i>T<i/> <i>≤<i/> 0.3 follow a similar distribution, which differs from that of bulges with <i>n<i/> > 2 and <i>B<i/>/<i>T<i/> > 0.3. In particular, bulges with <i>n<i/> <i>≤<i/> 2 and <i>B<i/>/<i>T<i/> <i>≤<i/> 0.3 exhibit a larger fraction of oblate axisymmetric (or nearly axisymmetric) bulges, a smaller fraction of triaxial bulges, and fewer prolate axisymmetric (or nearly axisymmetric) bulges with respect to bulges with <i>n<i/> > 2 and with <i>B<i/>/<i>T<i/> > 0.3, respectively. No correlation is found between the intrinsic shape and either the luminosity or velocity dispersion of bulges.<i>Conclusions. <i/> According to predictions of the numerical simulations of bulge formation, bulges with <i>n<i/> <i>≤<i/> 2, which show a high fraction of oblate axisymmetric (or nearly axisymmetric) shapes and have <i>B<i/>/<i>T<i/> <i>≤<i/> 0.3, may be the result of dissipational minor mergers. Both major dissipational and dissipationless mergers seem to be required to explain the variety of shapes found for bulges with <i>n<i/> > 2 and <i>B<i/>/<i>T<i/> > 0.3.

FIRST SEARCH FOR GRAVITATIONAL WAVES FROM THE YOUNGEST KNOWN NEUTRON STAR

We present a search for periodic gravitational waves from the neutron star in the supernova remnant Cassiopeia A. The search coherently analyzes data in a 12-day interval taken from the fifth science run of the Laser Interferometer Gravitational-Wave Observatory. It searches gravitational wave frequencies from 100 to 300 Hz, and covers a wide range of first and second frequency derivatives appropriate for the age of the remnant and for different spin-down mechanisms. No gravitational wave signal was detected. Within the range of search frequencies, we set 95% confidence upper limits of 0.7--1.2e-24 on the intrinsic gravitational wave strain, 0.4--4e-4 on the equatorial ellipticity of the neutron star, and 0.005--0.14 on the amplitude of r-mode oscillations of the neutron star. These direct upper limits beat indirect limits derived from energy conservation and enter the range of theoretical predictions involving crystalline exotic matter or runaway r-modes. This is the first gravitational wave search to present upper limits on r-modes.

The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0–90°E, is greater than that seen during flyby 2 in the longitude range 180–270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field , C 2,2, is well determined and correlates with the equatorial shape. The S 2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J 2, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C 2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment ( C m/C ), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.

All-Sky LIGO Search for Periodic Gravitational Waves in the Early Fifth-Science-Run Data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

Nonsphericity of the Moon and Near Sun‐Synchronous Polar Lunar Orbits

Herein, we consider the problem of a lunar artificial satellite perturbed by the nonuniform distribution of mass of the Moon taking into account the oblateness (J2) and the equatorial ellipticity (sectorial term C22). Using Lie‐Hori method up to the second order short‐period terms of the Hamiltonian are eliminated. A study is done for the critical inclination in first and second order of the disturbing potential. Coupling terms due to the nonuniform distribution of mass of the Moon are analyzed. Numerical simulations are presented with the disturbing potential of first and second order is. It an approach for the behavior of the longitude of the ascending node of a near Sun‐synchronous polar lunar orbit is presented.

Structural properties of disk galaxies

(Abridged) A variety of formation scenarios was proposed to explain the diversity of properties observed in bulges. Studying their intrinsic shape can help in constraining the dominant mechanism at the epochs of their assembly. The structural parameters of a magnitude-limited sample of 148 unbarred S0--Sb galaxies were derived in order to study the correlations between bulges and disks as well as the probability distribution function (PDF) of the intrinsic equatorial ellipticity of bulges. It is presented a new fitting algorithm (GASP2D) to perform the two-dimensional photometric decomposition of galaxy surface-brightness distribution. This was assumed to be the sum of the contribution of a bulge and disk component characterized by elliptical and concentric isophotes with constant (but possibly different) ellipticity and position angles. Bulge and disk parameters of the sample galaxies were derived from the J-band images which were available in the Two Micron All Sky Survey. The PDF of the equatorial ellipticity of the bulges was derived from the distribution of the observed ellipticities of bulges and misalignments between bulges and disks. Strong correlations between the bulge and disk parameters were found. About 80% of bulges in unbarred lenticular and early-to-intermediate spiral galaxies are not oblate but triaxial ellipsoids. Their mean axial ratio in the equatorial plane is <B/A> = 0.85. There is not significant dependence of their PDF on morphology, light concentration, and luminosity. The interplay between bulge and disk parameters favors scenarios in which bulges assembled from mergers and/or grew over long times through disk secular evolution. But all these mechanisms have to be tested against the derived distribution of bulge intrinsic ellipticities.

Structural properties of disk galaxies

Context. A variety of formation scenarios have been proposed to explain the diversity of properties observed in bulges. Studying their intrinsic shape can help to constrain the dominant mechanisms at the epochs of their assembly. Aims. The structural parameters of a magnitude-limited sample of 148 unbarred S0–Sb galaxies were derived in order to study the correlations between bulges and disks, as well as the probability distribution function of the intrinsic equatorial ellipticity of bulges. Methods. We present a new fitting algorithm (GASP2D) to perform two-dimensional photometric decomposition of the galaxy surface-brightness distribution. This was assumed to be the sum of the contribution of a bulge and disk component characterized by elliptical and concentric isophotes with constant (but possibly different) ellipticity and position angles. Bulge and disk parameters of the sample galaxies were derived from the J-band images, which were available in the Two Micron All Sky Survey. The probability distribution function of the equatorial ellipticity of the bulges was derived from the distribution of the observed ellipticities of bulges and misalignments between bulges and disks. Results. Strong correlations between the bulge and disk parameters were found. About 80% of bulges in unbarred lenticular and early

Constraining crystalline color superconducting quark matter with gravitational-wave data

We estimate the maximum equatorial ellipticity sustainable by compact stars composed of crystalline color-superconducting quark matter. For the theoretically allowed range of the gap parameter $\ensuremath{\Delta}$, the maximum ellipticity could be as large as ${10}^{\ensuremath{-}2}$, which is about 4 orders of magnitude larger than the tightest upper limit obtained by the recent science runs of the LIGO and GEO600 gravitational-wave detectors based on the data from 78 radio pulsars. We point out that the current gravitational-wave strain upper limit already has some implications for the gap parameter. In particular, the upper limit for the Crab pulsar implies that $\ensuremath{\Delta}$ is less than $O(20)\text{ }\text{ }\mathrm{MeV}$ for a range of quark chemical potential accessible in compact stars, assuming that the pulsar has a mass $1.4{M}_{\ensuremath{\bigodot}}$, radius 10 km, breaking strain ${10}^{\ensuremath{-}3}$, and that it has the maximum quadrupole deformation it can sustain without fracturing.

Upper limits on gravitational wave emission from 78 radio pulsars

We present upper limits on the gravitational wave emission from 78 radio pulsars based on data from the third and fourth science runs of the LIGO and GEO 600 gravitational wave detectors. The data from both runs have been combined coherently to maximize sensitivity. For the first time, pulsars within binary (or multiple) systems have been included in the search by taking into account the signal modulation due to their orbits. Our upper limits are therefore the first measured for 56 of these pulsars. For the remaining 22, our results improve on previous upper limits by up to a factor of 10. For example, our tightest upper limit on the gravitational strain is 2.6×10-25 for PSR J1603-7202, and the equatorial ellipticity of PSR J2124–3358 is less than 10-6. Furthermore, our strain upper limit for the Crab pulsar is only 2.2 times greater than the fiducial spin-down limit.

The intrinsic equatorial ellipticity of bulges

AbstractTraditionally, the study of the structural parameters of galaxies have been used to understand the bulge formation processes. However, one piece lost in this study is the three-dimensional shape of the bulges. In this work, the structural parameters of a magnitude-limited sample of 148 unbarred S0-Sb galaxies were derived to study the correlations between bulge and disk parameters as well as the probability distribution function (PDF) of the intrinsic equatorial ellipticity of bulges. A new algorithm (GASP-2D) was used to perform the bidimensional bulge-disk decomposition of J-band galaxy images extracted from the archive of the 2MASS survey. The PDF of intrinsic ellipticities was derived from the distribution of the observed ellipticities of bulges and misalignments between bulges and disks. About 80% of bulges in S0-Sb galaxies are not oblate but triaxial ellipsoids. Their mean axial ratio in the equatorial plane is 〈B/A〉=0.85. There is not significant dependence of their PDF on morphology, light concentration, and luminosity. The scenarios in which bulges assembled from mergers and/or grew over long times through disk secular evolution have to be tested against the derived PDF of bulge intrinsic ellipticities.

Searching for gravitational waves from known pulsars

We present upper limits on the amplitude of gravitational waves from 28 isolated pulsars using data from the second science run of LIGO. The results are also expressed as a constraint on the pulsars' equatorial ellipticities. We discuss a new way of presenting such ellipticity upper limits that takes account of the uncertainties of the pulsar moment of inertia. We also extend our previous method to search for known pulsars in binary systems, of which there are about 80 in the sensitive frequency range of LIGO and GEO 600.

Limits on Gravitational-Wave Emission from Selected Pulsars Using LIGO Data

We place direct upper limits on the amplitude of gravitational waves from 28 isolated radio pulsars by a coherent multidetector analysis of the data collected during the second science run of the LIGO interferometric detectors. These are the first direct upper limits for 26 of the 28 pulsars. We use coordinated radio observations for the first time to build radio-guided phase templates for the expected gravitational-wave signals. The unprecedented sensitivity of the detectors allows us to set strain upper limits as low as a few times 10(-24). These strain limits translate into limits on the equatorial ellipticities of the pulsars, which are smaller than 10(-5) for the four closest pulsars.

Setting upper limits on the strength of periodic gravitational waves from PSRJ1939+2134using the first science data from the GEO 600 and LIGO detectors

Data collected by the GEO 600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar J1939+2134 at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsar’s gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsar’s equatorial ellipticity.

Cosmic background of gravitational waves from rotating neutron stars

The extragalactic background of gravitational waves produced by tri-axial rotating neutron stars was calculated, under the assumption that the properties of the underlying pulsar population are the same of those of the galactic population, recently derived by Regimbau & de Freitas Pacheco (2000). For an equatorial ellipticity of $\epsilon$ = 10$^{-6}$, the equivalent density parameter due to gravitational waves has a maximum amplitude in the range 2$\times10^{-11}-3\times10^{-9}$, around 0.9-1.5 kHz. The main reasons affecting the theoretical predictions are discussed. This background is comparable to that produced by the ''ring-down'' emission from distorted black holes. The detection possibility of this background by a future generation of gravitational antennas is also examined.