Giant cluster arcs as a constraint on the scattering cross-section of dark matter

We carry out ray tracing through five high-resolution simulations of a galaxy cluster, to study how its ability to produce giant gravitationally lensed arcs is influenced by the collision cross-section of its dark matter. In three cases typical dark matter particles in the cluster core undergo between 1 and 100 collisions per Hubble time; two more explore the long ('collisionless') and short ('fluid') mean free path limits. We study the size and shape distributions of arcs and compute the cross-section for producing 'extreme' arcs of various sizes. Even a few collisions per particle modifies the core structure enough to destroy the ability of the cluster to produce long, thin arcs. For larger collision frequencies the cluster must be scaled up to unrealistically large masses before it regains the ability to produce giant arcs. None of our models with self-interacting dark matter (except the 'fluid' limit) is able to produce radial arcs; even the case with the smallest scattering cross-section must be scaled to the upper limit of observed cluster masses before it produces radial arcs. Apparently the elastic collision cross-section of dark matter in clusters must be very small, below 0.1 cm² g⁻¹, to be compatible with the observed ability of clusters to produce both radial arcs and giant arcs.     

Application of variance component estimation to precise orbit determination for ERS-2

Variance component estimation (VCE) is applied to precise orbit determination (POD) of the ERS-2 satellite. Twenty 5-day long arcs in the early three months in 1998 were calculated using the SLR and PRARE data. In the data the adjacent arcs overlap for two days except the intervals for orbit maneuver. The effect of VCE orbit determination on the calculation is investigated by an analysis of residuals and comparison of overlapping arcs, and the mean a posteriori standard deviation of each group of measured residuals is given. It is shown by the residuals analysis that the fitting of the measurements is significantly improved by VCD. However, according to Abbey criterion, VCD is not able to eliminate the systematic errors due to errors in the dynamic and geometric models. The results of the comparison of the overlapping arcs show that (1) VCE reduces the mean range deviation of overlapping arcs, especially where there are obviously unreasonable deviations, so that the orbit obtained has a more uniform precision; (2) By using VCE, adjacent arcs tend to close up and this is more apparent in the transverse direction. From the mean a posteriori standard error of each group of measurements, it can be seen that as far as the single normal point measurement is concerned, the data of some SLR stations are more important than other measurements in POD calculation. Generally speaking, determination of weighting by using VCE is more reasonable than by using initial standard deviation.     

Boundary layer plasmas as a source for high-latitude, early afternoon, auroral arcs

Simultaneous measurements of hot boundary layer plasma from PROGNOZ-7 and particle precipitation from the TIROS/NOAA satellite in nearly magnetically conjugate regions have been used to study the dynamo process responsible for the formation of high latitude, early afternoon, auroral arcs.

Characteristic for the PROGNOZ-7 observations in the dayside boundary layer at high latitudes is the frequent occurrence of regions with injected magnetosheath plasma embedded in a “halo” of antisunward flowing magnetosphere plasma. The injected magnetosheath plasma have several features which indicate that it also acts as a local source of EMF in the boundary layer. The process resembles that of a local MHD dynamo driven by the excess drift velocity of the injected magnetosheath plasma relative to the background magnetospheric plasma.

The dynamo region is capable of driving field-aligned currents that couple to the ionosphere, where the upward current is associated with the high latitude auroral arcs.

We demonstrate that the large-scale morphology as well as the detailed data intercomparison between PROGNOZ-7 and TIROS-N both agree well with a local injection of magnetosheath plasma into the dayside boundary layer as the main dynamo process powering the high-latitude, early afternoon auroral arcs.     

Arc(let)s in clusters of galaxies

Summary The discovery of giant gravitational arcs and arclets in rich clusters of galaxies is one of the major events of the last decade in observational cosmology. High resolution imaging in subarcsecond seeing conditions of giant arcs gives information on the cluster potential and the matter distribution within the inner regions of clusters. Ultra-deep photometry of the clusters reveals numerous arclets with an orthoradial orientation from which one can infer the projected mass profile at large distance and the redshift distribution of the faintest distant background galaxies which are unobservable with standard spectroscopic techniques. Thanks to the strong magnification factor, the spectroscopy of giant arcs is possible and we can therefore observe with great detail a few very distant galaxies. Individual redshifts of arcs give the total mass of the lens, whereas the spectroscopy of a large sample of arcs also gives information on the redshift distribution of distant galaxies. It is obvious that cluster lenses play an important role as large natural telescopes for probing the distant universe. Finally, observations of multiple-arc configurations due to different sources may even constrain the cosmological parameters. We are now confident that gravitational lensing will be an essential tool within the next decade for observing very high redshift galaxies and the weak shear generated by the largest structures of the universe.In this review we summarize the present status of gravitational arc(let)s surveys with particular emphasis on the most important issues which have arisen during the last years and on the prospects for the future, regarding the rebirth of the Hubble Space Telescope, the coming of a new generation of Very Large Telescopes, and the development of large CCDs in the optical and the infrared.     

Minor planet short periodic perturbations: The indirect part of the disturbing function

Leverrier's development of the indirect part of the disturbing function has been extended to include terms up to degree 4 in eccentricity and inclination; the resulting series has been expressed with respect to a fixed plane, and in a computer readable form (a list of integers). Tests have been performed for the relative significance of the terms of degrees 2, 3 and 4, and estimates have been obtained for the accuracy of the short periodic perturbations of a minor planet, and of the corresponding mean orbital elements. It was found that: (i) even in extreme cases, the indirect part of the disturbing function gives rise to very small short periodic perturbations; (ii) bodies of very high eccentricity/inclination and those close to mean motion resonances are most significantly affected; (iii) indirect perturbations for minor planets can be computed up to the degree 2 terms only, without any significant loss of accuracy; and (iv) higher degree indirect perturbations appear to be important only for their contribution to the long periodic effects of higher order (with respect to the perturbing mass).     

Cluster strong lensing in the Millennium simulation: the effect of galaxies and structures along the line-of-sight

We use ray-tracing through the Millennium simulation to study how secondary matter structures along the line-of-sight and the stellar mass in galaxies affect strong cluster lensing, in particular the cross-section for giant arcs. Furthermore, we investigate the distribution of the cluster Einstein radii and the radial distribution of giant arcs. We find that additional structures along the line-of-sight increase the strong-lensing optical depth by  ∼10–25 per cent  , while strong-lensing cross-sections of individual clusters are frequently boosted by as much as  ∼50 per cent  . The enhancement is mainly due to structures that are not correlated with the lens. Cluster galaxies increase the strong-lensing optical depth by up to a factor of 2, while interloping galaxies are not significant. We conclude that these effects need to be taken into account for predictions of the giant arc abundance, but they are not large enough to fully account for the reported discrepancy between predicted and observed abundances.
Furthermore, we find that Einstein radii defined via the area enclosed by the critical curve are 10–30 per cent larger than those defined via radial surface mass density profiles. The contributions of radial and tangential arcs to the radial distribution of arcs can be clearly distinguished. The radial distribution of tangential arcs is very broad and extends out to several Einstein radii. Thus, individual arcs are not well suited for constraining Einstein radii.     

Calculation of the intermediate perturbed orbit from three or more positions of a small body on the celestial sphere

Two new methods are described for finding the orbit of a small celestial body from three or more pairs of angular measurements and the corresponding time points. The methods are based on, first, the approach that has been developed previously by the author to the determination, from a minimum number of observations, of intermediate orbit considering most of the perturbations in the bodies’ motion and, second, Herget’s algorithmic procedure enabling the introduction of additional observations. The errors of orbital parameters calculated by the proposed methods are two orders of magnitude smaller than the corresponding errors of the traditional approach based on the construction of an unperturbed Keplerian orbit. The thus-calculated orbits of the minor planets 1566 Icarus, 2002 EC1, and 2010 TO48 are used to compare the results of Herget’s multiposition procedure and the new methods. The comparison shows that the new methods are highly effective in the study of perturbed motion. They are particularly beneficial if high-precision observational data covering short orbital arcs are available.     

Estimation of the chord length and relative height of tracking stations from single pass satellite ranging data

We describe here a technique of determining the chord length and the relative height between two laser tracking stations using single-pass satellite ranging data over very short arcs. Numerical examples show that this technique can supplement the conventional technique which requires data over much longer arcs by providing a capability for checking the accuracy of the geodetic network of laser tracking stations.     

方差分量估计方法在ERS—2卫星精密定轨中的应用

将方差分量估计（VCE）方法应用于ERS－2卫星的精密定轨,用SLR和PRARE资料计算了1998年前3个月的23个长度为5天的弧段（除了调整轨道的时段外,相邻弧段有两天的重叠）,从观测值残差分析和重叠弧段比较两个方面,考察VCE方法对定轨计算的影响,并给出了各组观测值的平均验后均方差,对观测值残差的分析表明,使用VCE方法明显地改善了观测值的拟合程度,但从阿卑（Abbey)标准对观测值残差的检验结果来看,使用VCE方法不能消除轨道中由力学模型和几何模型误差引入的系统差,重叠弧段比较的结果表明：（1）使用VCE方法缩小了重叠弧段的平均距离差,并改善了一部分权段明显不合理的偏离,使最后得到的轨道具有更均匀的精度,（2）相比较而言,VCE方法使相邻弧段靠拢的趋势在轨道切向体现得较为明显,由各组观测值的平均验后方差可见,说单个标准点观测值而言,部分SLR台站的观测资料在定轨计算中占有比其他观测资料更重的地位,纵观全文,使用VCE后得到的观测值的平衡验后均方差来确定资料的双重将比使用均方差更为合理。     

Four-neutrino mixing and Big-Bang Nucleosynthesis

We investigate the Big-Bang Nucleosynthesis constraints on the elements of the neutrino mixing matrix which connect sterile with massive neutrino fields, in the framework of the two four-neutrino schemes that are favored by the results of neutrino oscillation experiments. We discuss the implications of these constraints for terrestrial short and long-baseline neutrino oscillation experiments and we present several possibilities of testing them in these experiments. In particular, we show that from the Big-Bang Nucleosynthesis constraints it follows that the transition is severely suppressed in short-baseline experiments, whereas its oscillation amplitude in long-baseline experiments is of order 1. We also propose a new parameterization of the four-neutrino mixing matrix U which is appropriate for the schemes under consideration.     

Time evolution of orbital uncertainties for the impactor candidate 2004 AS1

We evaluate the asteroid impact risk from the discovery night onwards using six-dimensional statistical orbit computation techniques to examine the a posteriori probability density of the orbital elements. Close to the discovery moment the observational data of an object are typically exiguous: the number of observations is very small and/or the covered orbital arc is very short. For such data, the covariance matrices computed in the linear approximation (e.g., with the least-squares technique) are known to fail to describe the uncertainties in the orbital parameters. The technique of statistical ranging gives us rigorous means to assess the orbital uncertainties already on the discovery night. To examine the time evolution of orbital uncertainties, we make use of a new nonlinear Monte Carlo technique of phase-space sampling using volumes of variation, which complements the ranging technique for exiguous data and the least-squares technique for extensive observational data. We apply the statistical techniques to the near-Earth Asteroid 2004 AS₁, which grabbed the attention of asteroid scientists because, for one day, it posed the highest and most immediate impact risk so far recorded. We take this extreme case to illustrate the ambiguities in the impact risk assessment for short arcs. We confirm that the weighted fraction of the collision orbits at discovery was large but conclude that this was mostly due to the discordance of the discovery-night observations. This case study highlights the need to introduce a regularization in terms of an a priori probability density to secure the invariance of the probabilistic analysis especially in the nonlinear orbital inversion for short arcs. We remark that a predominant role of the a priori can give indications of the feasibility of the probabilistic interpretation, that is, how reliable the results derived from the a posteriori probability density are. Nevertheless, the strict mathematical definition of, e.g., the collision probability remains valid, and our nonlinear statistical techniques give us the means to always deduce, at the very least, order-of-magnitude-estimates for the collision probability.     

Asteroid detection at millimetric wavelengths with the PLANCK survey

The PLANCK mission, originally devised for cosmological studies, offers the opportunity to observe Solar System objects at millimetric and submillimetric wavelengths. In this paper we concentrate on the asteroids of the Main Belt, a large class of minor bodies in the Solar System. At present, more that 40 000 of these asteroids have been discovered and their detection rate is rapidly increasing. We intend to estimate the number of asteroids that can be detected during the mission and to evaluate the strength of their signal. We have rescaled the instrument sensitivities, calculated by the LFI and HFI teams for sources fixed in the sky, introducing some degradation factors to properly account for moving objects. In this way a detection threshold is derived for asteroidal detection that is related to the diameter of the asteroid and its geocentric distance. We have developed a numerical code that models the detection of asteroids in the LFI and HFI channels during the mission. This code performs a detailed integration of the orbits of the asteroids in the timespan of the mission and identifies those bodies that fall in the beams of PLANCK and their signal strength. According to our simulations, a total of 397 objects will be observed by PLANCK and an asteroidal body will be detected in some beam in 30% of the total sky scan-circles. A significant fraction (in the range from 50 to 100 objects) of the 397 asteroids will be observed with a high S/N ratio. Flux measurements of a large sample of asteroids in the submillimeter and millimeter range are relevant since they allow to analyze the thermal emission and its relation to the surface and regolith properties. Furthermore, it will be possible to check on a wider base, the two standard thermal models, based on a nonrotating or rapidly rotating sphere. Our method can also be used to separate Solar System sources from cosmological sources in the survey. This work is based on PLANCK LFI activities.     

Searching for tidal tails – investigating galaxy harassment

Galaxy harassment has been proposed as a physical process that morphologically transforms low surface density disc galaxies into dwarf elliptical galaxies in clusters. It has been used to link the observed very different morphology of distant cluster galaxies (relatively more blue galaxies with 'disturbed' morphologies) with the relatively large numbers of dwarf elliptical galaxies found in nearby clusters. One prediction of the harassment model is that the remnant galaxies should lie on low surface brightness tidal streams or arcs. We demonstrate in this paper that we have an analysis method that is sensitive to the detection of arcs down to a surface brightness of 29 B μ and we then use this method to search for arcs around 46 Virgo cluster dwarf elliptical galaxies. We find no evidence for tidal streams or arcs and consequently no evidence for galaxy harassment as a viable explanation for the relatively large numbers of dwarf galaxies found in the Virgo cluster.     

The dynamic nature of the Adams ring arcs—Fraternite,Egalite (2,1), Liberte,Courage

By considering the finite mass of Fraternite, the dynamic nature of the Adams ring arcs is regarded as caused by the reaction of a test body (a minor arc) through the Lindblad resonance (LR). Assuming the eccentricity of the test body is larger than that of Galatea, this generates several locations along the ring in the neighborhood of Fraternite where the time averaged force on a test body vanishes. These locations appear to correspond to the time dependent configuration of Egalite (2,1), Liberte, and Courage, and seem to be able to account for the dynamics of the arcs. Such a configuration is a dynamic one because the minor arcs are not bounded by the corotation eccentricity resonance (CER) externally imposed by Galatea, but are self-generated by LR reacting to the external fields.     

From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs

Contemporary surveys provide a huge number of detections of small solar system bodies, mostly asteroids. Typically, the reported astrometry is not enough to compute an orbit and/or perform an identification with an already discovered object. The classical methods for preliminary orbit determination fail in such cases: a new approach is necessary. When the observations are not enough to compute an orbit we represent the data with an attributable (two angles and their time derivatives). The undetermined variables range and range rate span an admissible region of solar system orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by an optimal triangulation. The attributable results from a fit and has an uncertainty represented by a covariance matrix, thus the predictions of future observations can be described by a quasi-product structure (admissible region times confidence ellipsoid), which can be approximated by a triangulation with each node surrounded by a confidence ellipsoid. The problem of identifying two independent short arcs of observations has been solved. For each VA in the admissible region of the first arc we consider prediction at the time of the second arc and the corresponding covariance matrix, and we compare them with the attributable of the second arc with its own covariance. By using the penalty (increase in the sum of squares, as in the algorithms for identification) we select the VAs which can fit together both arcs and compute a preliminary orbit. Even two attributables may not be enough to compute an orbit with a convergent differential corrections algorithm. The preliminary orbits are used as first guess for constrained differential corrections, providing solutions along the Line Of Variations (LOV) which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a least squares orbit, with uncertainty described by the covariance matrix.     

440 keV proton precipitation at middle latitudes during the recovery phase of magnetic storms

Quasitrapped (H_min < 100 km) protons with energies E > 440 keV have been detected during magnetic storms by the IK-5 satellite in a narrow zone with a center at L = 3.0−3.2; this zone is well separated from the region of Isotropie fluxes at L > 4. Data for five moderate storms have been analysed in detail. It was found that the quasitrapped proton peaks appear during the recovery phase of magnetic storms and that the scattering of protons toward low mirror points takes place in all local time sectors. The relation between the observed precipitation of the E > 440 keV protons and the intraplasmaspheric precipitation of low-energy protons has been discussed in the light of the theory of generation of ion-cyclotron waves by the ring current and the theory of parasitic interaction of these waves with the radiation belt protons. A series of arguments indicates that the phenomenon under study is connected with the magnetopheric process which generates the SAR arcs.     

Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies

The equilibrium points of the gravitational potential field of minor celestial bodies, including asteroids, comets, and irregular satellites of planets, are studied. In order to understand better the orbital dynamics of massless particles moving near celestial minor bodies and their internal structure, both internal and external equilibrium points of the potential field of the body are analyzed. In this paper, the location and stability of the equilibrium points of 23 minor celestial bodies are presented. In addition, the contour plots of the gravitational effective potential of these minor bodies are used to point out the differences between them. Furthermore, stability and topological classifications of equilibrium points are discussed, which clearly illustrate the topological structure near the equilibrium points and help to have an insight into the orbital dynamics around the irregular-shaped minor celestial bodies. The results obtained here show that there is at least one equilibrium point in the potential field of a minor celestial body, and the number of equilibrium points could be one, five, seven, and nine, which are all odd integers. It is found that for some irregular-shaped celestial bodies, there are more than four equilibrium points outside the bodies while for some others there are no external equilibrium points. If a celestial body has one equilibrium point inside the body, this one is more likely linearly stable.     

Cometary masses derived from non-gravitational forces

We compute masses and densities for 10 periodic comets with known sizes: 1P/Halley, 2P/Encke, 6P/d'Arrest, 9P/Tempel 1, 10P/Tempel 2, 19P/Borrelly, 22P/Kopff, 46P/Wirtanen, 67P/Churyumov–Gerasimenko and 81P/Wild 2. The method follows the one developed by Rickman and colleagues, which is based on the gas production curve and on the change in the orbital period due to the non-gravitational force. The gas production curve is inferred from the visual light curve. We found that the computed masses cover more than three orders of magnitude:  ≃(0.3–400) × 10¹²  kg. The computed densities are in all cases very low (≲0.8 g cm⁻³), with an average value of 0.4 g cm⁻³, in agreement with previous results and models of the cometary nucleus depicting it as a very porous object. The computed comet densities turn out to be the lowest among the different populations of Solar system minor bodies, in particular as compared to those of near-Earth asteroids (NEAs). We conclude that the model applied in this paper, in spite of its simplicity (as compared to more sophisticated thermophysical models applied to very few comets), is useful for a statistical approach to the mean density of the cometary nuclei. However, we cannot assess from this simple model if there is a real dispersion among the bulk densities of comets that could tell us about differences in physical structure (porosity) and/or chemical composition.     

Keplerian integrals,elimination theory and identification of very short arcs in a large database of optical observations

Modern asteroid surveys produce an increasingly large number of observations, which are grouped into very short arcs (VSAs) each containing a few observations of the same object in one single night. To decide whether two VSAs collected in different nights correspond to the same observed object we can attempt to compute an orbit with the observations of both arcs: this is called the linkage problem. Since the number of linkages to be attempted is very large, we need efficient methods of orbit determination. Using the first integrals of Kepler’s motion we can write algebraic equations for the linkage problem, which can be put in polynomial form. In Gronchi et al. (Celest Mech Dyn Astron 123(2):105–122, 2015) these equations are reduced to a polynomial equation of degree 9: the unknown is the topocentric distance of the observed body at the mean epoch of one VSA. Here we derive the same equations in a more concise way, and show that the degree 9 is optimal in a sense that will be specified in Sect. 3.3. We also introduce a procedure to join three VSAs: from the conservation of angular momentum we obtain a polynomial equation of degree 8 in the topocentric distance at the mean epoch of the second VSA. For both identification methods, with two and three VSAs, we discuss how to discard solutions. Finally, we present some numerical tests showing that the new methods give satisfactory results and can be used also when the time separation between the VSAs is large. The low polynomial degree of the new methods makes them well suited to deal with the very large number of asteroid observations collected by the modern surveys.