Upper estimates for the element number of non-redundant antenna configurations on square and hexagonal grids

Estimates for the maximum number of elements of non-redundant configurations on integer square and hexagonal grids of given sizes are derived (a “non-redundant” configuration implies that the vector differences between its elements are all distinct). When projecting a large 2-D interferometer or a telescope, such an estimate can be used as a guide for evaluating the maximum possible number of antennas in a non-redundant configuration that can be arranged within a given area. The suggested estimates are empirical and based on the available data. They are obtained by reducing the problem to the linear case and by generalizing the method applied therein. Examples of applying the method are presented.     

Temporal Evolution of a Rapidly-Moving Umbral Dot

We performed two-dimensional spectroscopic observations of the preceding sunspot of NOAA 10905 located off disk center (S8 E36, μ≈0.81) by using the Interferometric BI-dimensional Spectrometer (IBIS) operated at the Dunn Solar Telescope (DST) of the National Solar Observatory, New Mexico. The magnetically insensitive Fe I line at 709.04 nm was scanned in wavelength repetitively at an interval of 37 s to calculate sequences of maps of the line-wing and line-core intensity, and the line-of-sight Doppler velocity at different line depths (3% to 80%). Visual inspection of movies based on speckle reconstructions computed from simultaneous broadband data and the local continuum intensity at 709.04 nm revealed an umbral dot (UD) intruding rapidly from the umbral boundary to the center of the umbra. The apparent motion of this object was particularly fast (1.3 km s⁻¹) when compared to typical UDs. The lifetime and size of the UD was 8.7 min and 240 km, respectively. The rapid UD was visible even in the line-core intensity map of Fe I 709.04 nm and was accompanied by a persistent blueshift of about 0.06 km s⁻¹.     

A real-time software backend for the GMRT

The new era of software signal processing has a large impact on radio astronomy instrumentation. Our design and implementation of a 32 antennae, 33 MHz, dual polarization, fully real-time software backend for the GMRT, using only off-the-shelf components, is an example of this. We have built a correlator and a beamformer, using PCI-based ADC cards and a Linux cluster of 48 nodes with dual gigabit inter-node connectivity for real-time data transfer requirements. The highly optimized compute pipeline uses cache efficient, multi-threaded parallel code, with the aid of vectorized processing. This backend allows flexibility in final time and frequency resolutions, and the ability to implement algorithms for radio frequency interference rejection. Our approach has allowed relatively rapid development of a fairly sophisticated and flexible backend receiver system for the GMRT, which will greatly enhance the productivity of the telescope. In this paper we describe some of the first lights using this software processing pipeline. We believe this is the first instance of such a real-time observatory backend for an intermediate sized array like the GMRT.     

Comparison of Five Numerical Codes for Automated Tracing of Coronal Loops

The three-dimensional (3D) modeling of coronal loops and filaments requires algorithms that automatically trace curvilinear features in solar EUV or soft X-ray images. We compare five existing algorithms that have been developed and customized to trace curvilinear features in solar images: i) the oriented-connectivity method (OCM), which is an extension of the Strous pixel-labeling algorithm (developed by Lee, Newman, and Gary); ii) the dynamic aperture-based loop-segmentation method (developed by Lee, Newman, and Gary); iii) unbiased detection of curvilinear structures (developed by Steger, Raghupathy, and Smith); iv) the oriented-direction method (developed by Aschwanden); and v) ridge detection by automated scaling (developed by Inhester). We test the five existing numerical codes with a TRACE image that shows a bipolar active region and contains over 100 discernable loops. We evaluate the performance of the five codes by comparing the cumulative distribution of loop lengths, the median and maximum loop length, the completeness or detection efficiency, the accuracy, and flux sensitivity. These algorithms are useful for the reconstruction of the 3D geometry of coronal loops from stereoscopic observations with the STEREO spacecraft, or for quantitative comparisons of observed EUV loop geometries with (nonlinear force-free) magnetic field extrapolation models.     

Position and velocity perturbations for the determination of geopotential from space geodetic measurements

Although space geodetic observing systems have been advanced recently to such a revolutionary level that low Earth Orbiting (LEO) satellites can now be tracked almost continuously and at the unprecedented high accuracy, none of the three basic methods for mapping the Earth’s gravity field, namely, Kaula linear perturbation, the numerical integration method and the orbit energy-based method, could meet the demand of these challenging data. Some theoretical effort has been made in order to establish comparable mathematical modellings for these measurements, notably by Mayer-Gürr et al. (J Geod 78:462–480, 2005). Although the numerical integration method has been routinely used to produce models of the Earth’s gravity field, for example, from recent satellite gravity missions CHAMP and GRACE, the modelling error of the method increases with the increase of the length of an arc. In order to best exploit the almost continuity and unprecedented high accuracy provided by modern space observing technology for the determination of the Earth’s gravity field, we propose using measured orbits as approximate values and derive the corresponding coordinate and velocity perturbations. The perturbations derived are quasi-linear, linear and of second-order approximation. Unlike conventional perturbation techniques which are only valid in the vicinity of reference mean values, our coordinate and velocity perturbations are mathematically valid uniformly through a whole orbital arc of any length. In particular, the derived coordinate and velocity perturbations are free of singularity due to the critical inclination and resonance inherent in the solution of artificial satellite motion by using various types of orbital elements. We then transform the coordinate and velocity perturbations into those of the six Keplerian orbital elements. For completeness, we also briefly outline how to use the derived coordinate and velocity perturbations to establish observation equations of space geodetic measurements for the determination of geopotential.     

Secular influence of change in the heliocentric gravitation constant <Emphasis Type="Italic">GM</Emphasis><Subscript>⊙</Subscript> on evolution of orbits of Meteor Streams

The Secular influence of the change in the heliocentric gravitational constant on the evolution of orbits of Meteor Streams is examined by using the method of celestial mechanics with variable mass and variable gravitational constant. The change in the heliocentric gravitational constant includes the combined changes in the sun’s mass and gravitational constant obtained from the modern observation of planets and spacecraft. The perturbation equations are solved by expanding series with mean anomaly. The solutions of the secular and periodic variation of orbital elements are derived. The theoretical results for the secular variables of the semi-major axes, solar distances at perihelion and orbital periods are given for three Meteor Streams: Dracorids, Quadrantids, and Ursids. The numerical results are shown in Table 2. The discussion and conclusion are drawn.     

Adaptive particle swarm optimization for optimal orbital elements of binary stars

The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability.     

The causality between the rapid rotation of a sunspot and an X3.4 flare

Using multi-wavelength data of Hinode, the rapid rotation of a sunspot in ac-tive region NOAA 10930 is studied in detail. We found extraordinary counterclockwise rotation of the sunspot with positive polarity before an X3.4 flare. From a series of vector magnetograms, it is found that magnetic force lines are highly sheared along the neu-tral line accompanying the sunspot rotation. Furthermore, it is also found that sheared loops and an inverse S-shaped magnetic loop in the corona formed gradually after the sunspot rotation. The X3.4 flare can be reasonably regarded as a result of this movement. A detailed analysis provides evidence that sunspot rotation leads to magnetic field linestwisting in the photosphere. The twist is then transported into the corona and triggers flares.