Cost-effective aperture arrays for SKA Phase 1: single or dual-band?

An important design decision for the first phase of the Square Kilometre Array is whether the low frequency component (SKA1-low) should be implemented as a single or dual-band aperture array; that is, using one or two antenna element designs to observe the 70-450 MHz frequency band. This memo uses an elementary parametric analysis to make a quantitative, first-order cost comparison of representative implementations of a single and dual-band system, chosen for comparable performance characteristics. A direct comparison of the SKA1-low station costs reveals that those costs are similar, although the uncertainties are high. The cost impact on the broader telescope system varies: the deployment and site preparation costs are higher for the dual-band array, but the digital signal processing costs are higher for the single-band array. This parametric analysis also shows that a first stage of analogue tile beamforming, as opposed to only station-level, all-digital beamforming, has the potential to significantly reduce the cost of the SKA1-low stations. However, tile beamforming can limit flexibility and performance, principally in terms of reducing accessible field of view. We examine the cost impacts in the context of scientific performance, for which the spacing and intra-station layout of the antenna elements are important derived parameters. We discuss the implications of the many possible intra-station signal transport and processing architectures and consider areas where future work could improve the accuracy of SKA1-low costing.Comment: 64 pages, 23 figures, submitted to the SKA Memo serie

Method For Making 2-Electron Response Reduced Density Matrices Approximately N-representable

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schr\"odinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not $N$-representable. That is, the response 2-RDM does not correspond to an actual physical $N$-electron wave function. We present a new algorithm for making these non-$N$-representable 2-RDMs approximately $N$-representable, i.e. it has the right symmetry and normalization and it fulfills the $P$-, $Q$- and $G$-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties that is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between the initial 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, $Q$- and $G$-matrices are positive semidefinite, i.e. their eigenvalues are non-negative. Our method is suitable for fixing non-N-respresentable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.Comment: 13 pages, 8 figure

Imaging Jupiter's radiation belts down to 127 MHz with LOFAR

Context. Observing Jupiter's synchrotron emission from the Earth remains today the sole method to scrutinize the distribution and dynamical behavior of the ultra energetic electrons magnetically trapped around the planet (because in-situ particle data are limited in the inner magnetosphere). Aims. We perform the first resolved and low-frequency imaging of the synchrotron emission with LOFAR at 127 MHz. The radiation comes from low energy electrons (~1-30 MeV) which map a broad region of Jupiter's inner magnetosphere. Methods (see article for complete abstract) Results. The first resolved images of Jupiter's radiation belts at 127-172 MHz are obtained along with total integrated flux densities. They are compared with previous observations at higher frequencies and show a larger extent of the synchrotron emission source (>=4 $R_J$). The asymmetry and the dynamic of east-west emission peaks are measured and the presence of a hot spot at lambda_III=230 {\deg} $\pm$ 25 {\deg}. Spectral flux density measurements are on the low side of previous (unresolved) ones, suggesting a low-frequency turnover and/or time variations of the emission spectrum. Conclusions. LOFAR is a powerful and flexible planetary imager. The observations at 127 MHz depict an extended emission up to ~4-5 planetary radii. The similarities with high frequency results reinforce the conclusion that: i) the magnetic field morphology primarily shapes the brightness distribution of the emission and ii) the radiating electrons are likely radially and latitudinally distributed inside about 2 $R_J$. Nonetheless, the larger extent of the brightness combined with the overall lower flux density, yields new information on Jupiter's electron distribution, that may shed light on the origin and mode of transport of these particles.Comment: 10 pages, 12 figures, accepted for publication in A&A (27/11/2015) - abstract edited because of limited character

Signal processing aspects of the low frequency array

In the Northern part of the Netherlands ASTRON is building the largest radio telescope in the world for low frequencies. The telescope is based on phased array principles and is known as the LOw Frequency ARray (LOFAR). LOFAR is optimized for detecting astronomical signals in the 30-80 MHz and 120-240 MHz frequency window. LOFAR detects the incoming radio signals by using an array of simple omni-directional antennas. The antennas are grouped in so called stations mainly to reduce the amount of data generated. More than fifty stations will be built, mainly within a circle of 150 kilometres in diameter but also internationally. The signals of all the stations are distributed to the central processor facility, where all the station signals are correlated with each other. In this paper the signal processing aspects on system level will be presented mainly for the astronomical application.\ud \u

First LOFAR observations at very low frequencies of cluster-scale non-thermal emission: the case of Abell 2256

Abell 2256 is one of the best known examples of a galaxy cluster hosting large-scale diffuse radio emission that is unrelated to individual galaxies. It contains both a giant radio halo and a relic, as well as a number of head-tail sources and smaller diffuse steep-spectrum radio sources. The origin of radio halos and relics is still being debated, but over the last years it has become clear that the presence of these radio sources is closely related to galaxy cluster merger events. Here we present the results from the first LOFAR Low band antenna (LBA) observations of Abell 2256 between 18 and 67 MHz. To our knowledge, the image presented in this paper at 63 MHz is the deepest ever obtained at frequencies below 100 MHz in general. Both the radio halo and the giant relic are detected in the image at 63 MHz, and the diffuse radio emission remains visible at frequencies as low as 20 MHz. The observations confirm the presence of a previously claimed ultra-steep spectrum source to the west of the cluster center with a spectral index of -2.3 \pm 0.4 between 63 and 153 MHz. The steep spectrum suggests that this source is an old part of a head-tail radio source in the cluster. For the radio relic we find an integrated spectral index of -0.81 \pm 0.03, after removing the flux contribution from the other sources. This is relatively flat which could indicate that the efficiency of particle acceleration at the shock substantially changed in the last \sim 0.1 Gyr due to an increase of the shock Mach number. In an alternative scenario, particles are re-accelerated by some mechanism in the downstream region of the shock, resulting in the relatively flat integrated radio spectrum. In the radio halo region we find indications of low-frequency spectral steepening which may suggest that relativistic particles are accelerated in a rather inhomogeneous turbulent region.Comment: 13 pages, 13 figures, accepted for publication in A\&A on April 12, 201

A very brief description of LOFAR - the Low Frequency Array

LOFAR (Low Frequency Array) is an innovative radio telescope optimized for the frequency range 30-240 MHz. The telescope is realized as a phased aperture array without any moving parts. Digital beam forming allows the telescope to point to any part of the sky within a second. Transient buffering makes retrospective imaging of explosive short-term events possible. The scientific focus of LOFAR will initially be on four key science projects (KSPs): 1) detection of the formation of the very first stars and galaxies in the universe during the so-called epoch of reionization by measuring the power spectrum of the neutral hydrogen 21-cm line (Shaver et al. 1999) on the ~5' scale; 2) low-frequency surveys of the sky with of order $10^8$ expected new sources; 3) all-sky monitoring and detection of transient radio sources such as gamma-ray bursts, x-ray binaries, and exo-planets (Farrell et al. 2004); and 4) radio detection of ultra-high energy cosmic rays and neutrinos (Falcke & Gorham 2003) allowing for the first time access to particles beyond 10^21 eV (Scholten et al. 2006). Apart from the KSPs open access for smaller projects is also planned. Here we give a brief description of the telescope.Comment: 2 pages, IAU GA 2006, Highlights of Astronomy, Volume 14, K.A. van der Hucht, e

LOFAR tied-array imaging and spectroscopy of solar S bursts

Context. The Sun is an active source of radio emission that is often associated with energetic phenomena ranging from nanoflares to coronal mass ejections (CMEs). At low radio frequencies (<100 MHz), numerous millisecond duration radio bursts have been reported, such as radio spikes or solar S bursts (where S stands for short). To date, these have neither been studied extensively nor imaged because of the instrumental limitations of previous radio telescopes. Aims. Here, LOw Frequency ARray (LOFAR) observations were used to study the spectral and spatial characteristics of a multitude of S bursts, as well as their origin and possible emission mechanisms. Methods. We used 170 simultaneous tied-array beams for spectroscopy and imaging of S bursts. Since S bursts have short timescales and fine frequency structures, high cadence (~50 ms) tied-array images were used instead of standard interferometric imaging, that is currently limited to one image per second. Results. On 9 July 2013, over 3000 S bursts were observed over a time period of ~8 h. S bursts were found to appear as groups of short-lived (<1 s) and narrow-bandwidth (~2.5 MHz) features, the majority drifting at ~3.5 MHz s-1 and a wide range of circular polarisation degrees (2−8 times more polarised than the accompanying Type III bursts). Extrapolation of the photospheric magnetic field using the potential field source surface (PFSS) model suggests that S bursts are associated with a trans-equatorial loop system that connects an active region in the southern hemisphere to a bipolar region of plage in the northern hemisphere. Conclusions. We have identified polarised, short-lived solar radio bursts that have never been imaged before. They are observed at a height and frequency range where plasma emission is the dominant emission mechanism, however, they possess some of the characteristics of electron-cyclotron maser emission

Optimized Trigger for Ultra-High-Energy Cosmic-Ray and Neutrino Observations with the Low Frequency Radio Array

When an ultra-high energy neutrino or cosmic ray strikes the Lunar surface a radio-frequency pulse is emitted. We plan to use the LOFAR radio telescope to detect these pulses. In this work we propose an efficient trigger implementation for LOFAR optimized for the observation of short radio pulses.Comment: Submitted to Nuclear Instruments and Methods in Physics Research Section