Relative equilibria of a satellite subjected to gravitational and aerodynamic torques

The problem of determining all equilibria of a satellite in a circular orbit is solved in the case where the satellite is subjected to gravitational and aerodynamic torques. The number of isolated equilibria is shown to be no less than eight and no more than 24. The existence proof of one-parameter families of stationary solutions is given. Using Lyapunov's method sufficient conditions for stability of isolated equilibria are obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the baseline flux determination of microlensing events detectable with the difference image analysis method

To improve photometric precision by removing the blending effect, a newly developed technique of difference image analysis (DIA) has been adopted by several gravitational microlensing experiment groups. However, the principal problem of the DIA method is that, by its nature, it has difficulties in measuring the baseline flux F ₀ of a source star, causing a degeneracy problem in determining the lensing parameters of an event. Therefore, it is often believed that the DIA method is not as powerful as the classical method based on PSF photometry for determining the Einstein time-scales t _E of events.
In this paper, we demonstrate that the degeneracy problem in microlensing events, detectable from searches using the DIA method, is not as serious as is often thought. This is because a substantial fraction of events will be high amplification events for which the deviations of the amplification curves, constructed with the wrong baseline fluxes from their corresponding best-fit standard amplification curves, will be considerable, even for a small amount of the fractional baseline flux deviation Δ F ₀ F ₀. With a model luminosity function of source stars and under realistic observational conditions, we find that ∼30 per cent of detectable Galactic bulge events are expected to have high amplifications and their baseline fluxes can be determined with uncertainties Δ F ₀ F ₀≤0.5.     

Distribution of caustic-crossing intervals for Galactic binary-lens microlensing events

Detection of caustic crossings of binary-lens gravitational microlensing events is important because by detecting them one can obtain useful information about both the lens and the source star. In this paper, we compute the distribution of the intervals between two successive caustic crossings, f ( t _cc), for Galactic bulge binary-lens events to investigate the observational strategy for the optimal detection and resolution of caustic crossings. From this computation, we find that the distribution is highly skewed towards short t _cc and peaks at t _cc∼1.5 d. For the maximal detection of caustic crossings, therefore, prompt initiation of follow-up observations for intensive monitoring of events will be important. We estimate that, under the strategy of the current follow-up observations with a second caustic-crossing preparation time of ∼2 d, the fraction of events with resolvable caustic crossing is ∼80 per cent. We find that if the follow-up observations can be initiated within 1 d after the first caustic crossing by adopting more aggressive observational strategies, the detection rate can be improved to ∼90 per cent.     

The effects of resolved sources and blending on the detection of planets via gravitational microlensing

It has been shown that gravitational microlensing events towards the Galactic Bulge are sensitive to the presence of a planet orbiting the lensing star. The probability of planet detection is calculated here as a function of the binary geometry for mass ratios of     taking the effects of resolving the source and the inclusion of unlensed light (blending) into account. Source radii up to     θ _E are considered, at which point the detection probability becomes negligible. Small     mass ratio planets become undetectable at source radii of     θ _E . Blending has a slight adverse effect on planet detection. It is worst when the unblended detection probability is small and causes planets to become undetectable at smaller source radii than would be the case in the absence of blending. An alternative to current gravitational microlensing follow-up observations is investigated, where only the peaks of high amplification events are followed. Such a strategy promises to be at least twice as efficient at detecting planets as current observations, but requires a large number of high amplification events.     

The non-Gaussian tail of cosmic-shear statistics

Owing to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of high-redshift galaxy images because of the tidal gravitational field of the large-scale matter distribution, called cosmic shear, can be used to investigate the statistical properties of the large‐scale structure (LSS) . In particular, non-Gaussian properties of the LSS will lead to a non-Gaussian distribution of cosmic-shear statistic. The aperture mass ( M _ap) statistics, recently introduced as a measure for cosmic shear, is particularly well suited for measuring these non-Gaussian properties. In this paper we calculate the highly non-Gaussian tail of the aperture mass probability distribution, assuming Press–Schechter theory for the halo abundance and the 'universal' density profile of haloes as obtained from numerical simulations. We find that for values of M _ap much larger than its dispersion, this probability distribution is closely approximated by an exponential, rather than a Gaussian. We determine the amplitude and shape of this exponential for various cosmological models and aperture sizes, and show that wide-field imaging surveys can be used to distinguish between some of the currently most popular cosmogonies. Our study here is complementary to earlier cosmic-shear investigations, which focused more on two- and three-point statistical properties.     

用Kaula线性摄动方法恢复CHAMP重力场模型

介绍了Kau la线性摄动方法的基本原理和算法,基于CHAMP几何法轨道和动力法轨道,给出了利用该方法恢复地球重力场模型的实现过程,分析了Kau la线性摄动方法在实际应用中需要注意的问题。基于德国慕尼黑技术大学提供的一个月的CHAMP几何法轨道和德国GFZ数据中心提供的快速科学轨道,计算出了50×50阶地球重力场模型CHAMP-Kau la1S,并与EIGEN-CG03C、EIGEN-CHAMP03S、EIGEN2、ENIGN1S、EGM96模型进行了比较。结果表明:X ISM-CHAMP1S模型精度明显优于相同阶次EIGEN1S模型,前40阶明显优于EGM96模型,而低于同阶次的EIGEN2和EIGEN-CHAMP03S模型精度。     

Weak gravitational lensing in the standard cold dark matter model, using an algorithm for three-dimensional shear

We investigate the effects of weak gravitational lensing in the standard cold dark matter cosmology, using an algorithm that evaluates the shear in three dimensions. The algorithm has the advantage of variable softening for the particles, and our method allows the appropriate angular diameter distances to be applied to every evaluation location within each three-dimensional simulation box. We investigate the importance of shear in the distance–redshift relation, and find it to be very small. We also establish clearly defined values for the smoothness parameter in the relation, finding its value to be at least 0.83 at all redshifts in our simulations. From our results, obtained by linking the simulation boxes back to source redshifts of 4, we are able to observe the formation of structure in terms of the computed shear, and also note that the major contributions to the shear come from a very broad range of redshifts. We show the probability distributions for the magnification, source ellipticity and convergence, and also describe the relationships amongst these quantities for a range of source redshifts. We find a broad range of magnifications and ellipticities; for sources at a redshift of 4, 97.5 per cent of all lines of sight show magnifications up to 1.39 and ellipticities up to 0.23. There is clear evidence that the magnification is not linear in the convergence, as might be expected for weak lensing, but contains contributions from higher order terms in both the convergence and the shear. Our results for the one-point distribution functions are generally different from those obtained by other authors using two-dimensional (planar) approaches, and we suggest reasons for the differences. Our magnification distributions for sources at redshifts of 1 and 0.5 are also very different from the results used by other authors to assess the effect on the perceived value of the deceleration parameter, and we briefly address this question.