235 research outputs found

    Nonlinear stability analysis of the Emden-Fowler equation

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    In this paper we qualitatively study radial solutions of the semilinear elliptic equation Δu+un=0\Delta u + u^n = 0 with u(0)=1u(0)=1 and uâ€Č(0)=0u'(0)=0 on the positive real line, called the Emden-Fowler or Lane-Emden equation. This equation is of great importance in Newtonian astrophysics and the constant nn is called the polytropic index. By introducing a set of new variables, the Emden-Fowler equation can be written as an autonomous system of two ordinary differential equations which can be analyzed using linear and nonlinear stability analysis. We perform the study of stability by using linear stability analysis, the Jacobi stability analysis (Kosambi-Cartan-Chern theory) and the Lyapunov function method. Depending on the values of nn these different methods yield different results. We identify a parameter range for nn where all three methods imply stability.Comment: 12 pages; new reference added; 3 new references added; fully revised versio

    Shape modeling technique KOALA validated by ESA Rosetta at (21) Lutetia

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    We present a comparison of our results from ground-based observations of asteroid (21) Lutetia with imaging data acquired during the flyby of the asteroid by the ESA Rosetta mission. This flyby provided a unique opportunity to evaluate and calibrate our method of determination of size, 3-D shape, and spin of an asteroid from ground-based observations. We present our 3-D shape-modeling technique KOALA which is based on multi-dataset inversion. We compare the results we obtained with KOALA, prior to the flyby, on asteroid (21) Lutetia with the high-spatial resolution images of the asteroid taken with the OSIRIS camera on-board the ESA Rosetta spacecraft, during its encounter with Lutetia. The spin axis determined with KOALA was found to be accurate to within two degrees, while the KOALA diameter determinations were within 2% of the Rosetta-derived values. The 3-D shape of the KOALA model is also confirmed by the spectacular visual agreement between both 3-D shape models (KOALA pre- and OSIRIS post-flyby). We found a typical deviation of only 2 km at local scales between the profiles from KOALA predictions and OSIRIS images, resulting in a volume uncertainty provided by KOALA better than 10%. Radiometric techniques for the interpretation of thermal infrared data also benefit greatly from the KOALA shape model: the absolute size and geometric albedo can be derived with high accuracy, and thermal properties, for example the thermal inertia, can be determined unambiguously. We consider this to be a validation of the KOALA method. Because space exploration will remain limited to only a few objects, KOALA stands as a powerful technique to study a much larger set of small bodies using Earth-based observations.Comment: 15 pages, 8 figures, 2 tables, accepted for publication in P&S

    The second flight of the SUNRISE balloon-borne solar observatory: overview of instrument updates, the flight, the data and first results

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    The SUNRISE balloon-borne solar observatory, consisting of a 1~m aperture telescope that provided a stabilized image to a UV filter imager and an imaging vector polarimeter, carried out its second science flight in June 2013. It provided observations of parts of active regions at high spatial resolution, including the first high-resolution images in the Mg~{\sc ii}~k line. The obtained data are of very high quality, with the best UV images reaching the diffraction limit of the telescope at 3000~\AA\ after Multi-Frame Blind Deconvolution reconstruction accounting for phase-diversity information. Here a brief update is given of the instruments and the data reduction techniques, which includes an inversion of the polarimetric data. Mainly those aspects that evolved compared with the first flight are described. A tabular overview of the observations is given. In addition, an example time series of a part of the emerging active region NOAA AR~11768 observed relatively close to disk centre is described and discussed in some detail. The observations cover the pores in the trailing polarity of the active region, as well as the polarity inversion line where flux emergence was ongoing and a small flare-like brightening occurred in the course of the time series. The pores are found to contain magnetic field strengths ranging up to 2500~G and, while large pores are clearly darker and cooler than the quiet Sun in all layers of the photosphere, the temperature and brightness of small pores approach or even exceed those of the quiet Sun in the upper photosphere.Comment: Accepted for publication in The Astrophysical Journa

    IBIS: The Imager on-board INTEGRAL

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    The IBIS telescope is the high angular resolution gamma-ray imager on-board the INTEGRAL Observatory, successfully launched from Baikonur (Kazakhstan) the 17th of October 2002. This medium size ESA project, planned for a 2 year mission with possible extension to 5, is devoted to the observation of the gamma-ray sky in the energy range from 3 keV to 10 MeV (Winkler 2001). The IBIS imaging system is based on two independent solid state detector arrays optimised for low ( 15-1000 keV) and high ( 0.175-10.0 MeV) energies surrounded by an active VETO System. This high efficiency shield is essential to minimise the background induced by high energy particles in the highly excentric out of van Allen belt orbit. A Tungsten Coded Aperture Mask, 16 mm thick and ~1 squared meter in dimension is the imaging device. The IBIS telescope will serve the scientific community at large providing a unique combination of unprecedented high energy wide field imaging capability coupled with broad band spectroscopy and high resolution timing over the energy range from X to gamma rays. To date the IBIS telescope is working nominally in orbit since more than 9 month.Reglero Velasco, Victor, [email protected]

    Jacobi stability of the vacuum in the static spherically symmetric brane world models

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    We analyze the stability of the structure equations of the vacuum in the brane world models, by using both the linear (Lyapunov) stability analysis, and the Jacobi stability analysis, the Kosambi-Cartan-Chern (KCC) theory. In the brane world models the four dimensional effective Einstein equations acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. Generally, the spherically symmetric vacuum solutions of the brane gravitational field equations, have properties quite distinct as compared to the standard black hole solutions of general relativity. We close the structure equations by assuming a simple linear equation of state for the dark pressure. In this case the vacuum is Jacobi stable only for a small range of values of the proportionality constant relating the dark pressure and the dark radiation. The unstable trajectories on the brane behave chaotically, in the sense that after a finite radial distance it would be impossible to distinguish the trajectories that were very near each other at an initial point. Hence the Jacobi stability analysis offers a powerful method for constraining the physical properties of the vacuum on the brane.Comment: 21 pages, 3 figures, accepted for publication in PR

    The Sunrise Mission

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    The first science flight of the balloon-borne \Sunrise telescope took place in June 2009 from ESRANGE (near Kiruna/Sweden) to Somerset Island in northern Canada. We describe the scientific aims and mission concept of the project and give an overview and a description of the various hardware components: the 1-m main telescope with its postfocus science instruments (the UV filter imager SuFI and the imaging vector magnetograph IMaX) and support instruments (image stabilizing and light distribution system ISLiD and correlating wavefront sensor CWS), the optomechanical support structure and the instrument mounting concept, the gondola structure and the power, pointing, and telemetry systems, and the general electronics architecture. We also explain the optimization of the structural and thermal design of the complete payload. The preparations for the science flight are described, including AIV and ground calibration of the instruments. The course of events during the science flight is outlined, up to the recovery activities. Finally, the in-flight performance of the instrumentation is briefly summarized.Comment: 35 pages, 17 figure

    The on-board calibration system of the X-ray Imaging Polarimetry Explorer (XIPE)

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    The calibration system for XIPE is aimed at providing a way to check and correct possible variations of performance of the Gas Pixel Detector during the three years of operation in orbit (plus two years of possible extended operation), while facilitating the observation of the celestial sources. This will be performed by using a filter wheel with a large heritage having a set of positions for the calibration and the observation systems. In particular, it will allow for correcting possible gain variation, for measuring the modulation factor using a polarized source, for removing non interesting bright sources in the field of view and for observing very bright celestial sources. The on-board calibration system is composed of three filter wheels, one for each detector and it is expected to operate for a small number of times during the year. Moreover, since it operates once at a time, within the observation mode, it allows for simultaneous calibration and acquisition from celestial sources on different detectors. In this paper we present the scope and the requirements of the on-board calibration system, its design, and a description of its possible use in space

    A collision in 2009 as the origin of the debris trail of asteroid P/2010 A2

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    The peculiar object P/2010 A2 was discovered by the LINEAR near-Earth asteroid survey in January 2010 and given a cometary designation due to the presence of a trail of material, although there was no central condensation or coma. The appearance of this object, in an asteroidal orbit (small eccentricity and inclination) in the inner main asteroid belt attracted attention as a potential new member of the recently recognized class of 'Main Belt Comets' (MBCs). If confirmed, this new object would greatly expand the range in heliocentric distance over which MBCs are found. Here we present observations taken from the unique viewing geometry provided by ESA's Rosetta spacecraft, far from the Earth, that demonstrate that the trail is due to a single event rather than a period of cometary activity, in agreement with independent results from the Hubble Space Telescope (HST). The trail is made up of relatively large particles of millimetre to centimetre size that remain close to the parent asteroid. The shape of the trail can be explained by an initial impact ejecting large clumps of debris that disintegrated and dispersed almost immediately. We determine that this was an asteroid collision that occurred around February 10, 2009.Comment: Published in Nature on 14/10/2010. 25 pages, includes supplementary materia
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