LOFAR Transient Detection with a Bispectrum Algorithm

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astronomical institute

Anton Pannekoek

Master’s Thesis

LOFAR Transient Detection

with a Bispectrum Algorithm

Author:

Georgi Kokotanekov

Supervisors:

Dr. John Swinbank

Prof. Dr. Ralph A. M. J. Wijers

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Abstract

Transients are exciting to study because they are likely locations of very explosive and dynamic events. The new generation of radio astronomy facilities offers the opportunity not only to explore the extreme physics of known transient events but also to discover completely new classes of astrophysical phenomena. In this research we focus on the de-tection of short-timescale transients at low radio frequencies. Such sources include pulsars, rotating radio transients, soft gamma repeaters, flare stars, “Lorimer”-like bursts, and any unanticipated phenomena that may occur in this parameter space.

The standard method for detecting transients in correlated “visibility” data involves making an image of every timestep. However, this is computationally expensive, particu-larly when dealing with a large data sets such as those provided by the new Low Frequency Array (LOFAR) telescope. Law and Bower (2012) recently proposed a new method of de-tecting transients based on the “bispectrum”: the product of visibilities on a closed triple of antennas. In this strategy the computational load is significantly reduced by the fact that imaging is only required for localization and confirmation when a candidate transient is detected through the bispectra.

The aim of this master thesis project was to adapt the bispectrum algorithm for LOFAR and test its transient detection capabilities. For this purpose we used datasets produced by MSSS (LOFAR’s first all-sky, multi-epoch survey) and derived a robust technique for making one-second images with LOFAR. We modified and improved the bispectrum algo-rithm to make it suitable for use with LOFAR data. We developed a procedure to simulate short-timescale transients as they might appear in LOFAR observations and used the re-sults to study the detection properties of the bispectrum.

Our analysis proves that the bispectrum method is fully applicable for LOFAR. It shows that this new algorithm is capable of detecting 10-Jy transients in low-frequency MSSS ob-servations, practically reaching its theoretical sensitivity. Through a comparison between the computation time of the standard imaging method and the bispectrum algorithm, our work demonstrates that the bispectrum approach is at least an order of magnitude more efficient than the standard procedure.

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Acknowledgements

I would like to express my gratefulness to Ralph Wijers for attracting me to the tran-sient science and for offering me to work with him on my master’s project. I thank him for his support throughout my research and for meticulously reading the draft version of this thesis.

I would like to acknowledge the passionate supervision of John Swinbank. I sincerely thank him for introducing me to this exciting project and for guiding my progress in the right direction. I value his positive attitude towards my work and I appreciate the time we spent in interesting discussions. John responded to any meeting request and whenever I needed advice we spent enough time to go through all my questions. It is an amazing experience to work with John!

I also express my gratitude to Casey Law for giving me the opportunity to work on his bispectrum code and for being an active part of this project. I highly appreciate his willingness to meet me during his short visits to Amsterdam. I also thank him for being always ready to discuss my progress online and especially for his patience to clarify various technical and astronomical concepts concerning my work.

Finally, I would like to acknowledge Antonia Rowlinson, Alexander van der Horst, and Dario Carbone for being always open for discussions. Sharing experience and different materials, they significantly aided my project.

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Chapter 1 Introduction

Exploration of the transient Universe is an exciting area of research. Known transient phenomena emerge from diverse physical processes and their timescales range from sub-nanosecond to years. Transient sources are likely locations of explosive or dynamic events, thus offering great potential to uncover a wide range of new astrophysics.

While the transient sky is well explored in X- and γ-rays, the lack of suitable instru-ments has left the transient radio Universe a largely unexplored field. The new-generation radio facilities are overcoming this technological limitation and are opening a new era in radio astronomy. Examples of such new projects include the Low Frequency Array (LOFAR) and the Square Kilometer Array (SKA), as well as its precursor instruments – the Australian SKA Pathfinder (ASKAP) in Western Australia and MeerKAT in South Africa. LOFAR, in particular, is already operational. It consists of many low-frequency dipole antennas distributed over baselines of thousands of kilometers across Europe. With its unprecedented capabilities, LOFAR opens a new parameter space for investigation and presents enormous discovery potential. The digital nature of the LOFAR system makes it inherently agile and an ideal instrument for rapidly detecting and reacting to transient sources.

The data rates and volumes will significantly grow with the new radio interferometric arrays, which have many antennas, wide bandwidths, and large fields of view. One of the biggest challenges of contemporary research is how to efficiently process these large data volumes. A promising strategy is to first use a simple algorithm to identify candidate transients and later apply more detailed analysis to the selected events. To perform the initial check Law and Bower (2012) proposed a transient detection algorithm based on the bispectrum, the product of three visibilities from baselines that form a closed loop. This strategy is computationally efficient, sensitive to sources over a wide field of view, and immune to antenna-based gain phase errors. The bispectrum also offers a simple way of quantifying whether the selected candidate is a point-like celestial source or is an artifact due to, for example, ground-based radio frequency interference. Since the bispectrum does not provide localization, imaging is used to identify the position of the detected transients.

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The main goal of this thesis project is to determine if the transient detection strategy proposed by Law and Bower (2012) is applicable to LOFAR. In our research we focus mainly on the class of phenomena detectable on second timescales. The detection of these events involves considerable signal processing due to the high time and frequency resolution needed in the transient explorations and the need to overcome radio frequency interference. These requirements necessitate adaptation of new, non-imaging algorithms for transient detection that directly rely on the visibilities.

In order to study the proposed strategy we tested both the transient detection algorithm and short-timescale imaging with LOFAR. Through dedicated tests we derived a list of the optimal imaging and calibration parameters for consistent 1-second images with LOFAR. To study the detection capabilities of the bispectrum algorithm we employed simulated transients.

In Chapter 2 of this thesis we explain the main principles of radio astronomy obser-vations. Chapter 3 presents LOFAR and its first full-sky survey, MSSS. In Chapter 4 we discuss the LOFAR transient science and review some of the known types of transient radio sources at low frequencies. The next chapter is concerned with the difficulties of short-timescale imaging and describes in detail our experiments on producing series of 1-second images with LOFAR.

Through the rest of the work we focus on the bispectrum algorithm. In Chapter 6 we present the method from theoretical point of view and in the next unit we discuss the computer code which realizes the transient search. In order to test the transient detection capabilities of the bispectrum algorithm we develop a procedure to simulate short-timescale transients in LOFAR observations. This process is explained in Chapter 8. The following chapter presents our results on the sensitivity of the bispectrum algorithm and gives an estimate of the efficiency of this new detection strategy. In the last part of this thesis we summarize the outcomes of our research and discuss the potential of the bispectrum algorithm for future transient detection campaigns.

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Chapter 2 Radio Astronomy Techniques

Radio astronomy is the study of radio waves originating outside the Earth. The radio range of frequencies or wavelengths is loosely defined by three factors: atmospheric transparency, current technology, and fundamental limitations imposed by quantum noise. Together they yield a boundary between radio and far-infrared astronomy at frequency ν ≡ 1 THz or wavelength λ = c/ν ∼ 0.3 mm. The lower limit on frequency is at ∼10 MHz (λ ∼ 30 m) since below this value the ionosphere is radio opaque.

In this chapter we start by describing the single-element radio telescope. In subsequent sections we explain the technique of radio interferometry, used to achieve higher sensitivity and spatial resolution. We present the image acquisition processes and finish with a short discussion on the complications of wide-field imaging. The outline in this chapter mainly derives from the detailed descriptions by Condon and Ransom (2010) and Burke (2002).

2.1 Single-dish antenna

An antenna is a device for converting electromagnetic radiation into electrical currents or vice-versa. Radio telescopes use receiving antennas. Their main purpose is to collect the radiation and direct it to the receiver.

Most radio telescopes operating at shorter wavelengths (λ < 1 m) use large reflectors to collect signal. The most common reflector shape is a paraboloid of revolution because it focuses the plane wave from a distant point source onto a single point. In parabolic telescopes the incoming electric field induces voltage oscillations at the antenna focus, in a device called a feed. The most important characteristics of the parabolic antennas are:

• direction-dependent gain (Figure 2.1, left panel)

• angular resolution given by θ ∼ λ/D, where λ is the wavelength and D is the diameter of the dish

• sidelobes – portions of the antenna response which deviate from a Gaussian point-spread function (PSF) (Figure 2.1).

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Figure 2.1: Left: Primary beam - the power pattern of an individual antenna. The main lobe depicts the direction of greatest sensitivity. The beam has a number of sidelobes (local peaks of response away from the main lobe). The dish is maximally sensitive to radiation from the direction of the main lobe, but is also slightly sensitive to sources in the direction of the side lobes. Right: Power response of a single dish. Due to the sidelobes the antenna response deviates from a Gaussian. The local maxima away from the central peak (at offset between 500 and 1000) depict the sidelobe power sensitivity. Credit: Bertoldi (2009).

2.2 Two-element and N-element narrow-band

inter-ferometer

The simplest interferometer consists of a pair of radio telescopes whose voltage outputs are correlated (multiplied and averaged). In this section we present the case of a two-element narrow-band interferometer. This is the most fundamental concept since any complicated interferometer with N 2 elements can be simplified to a set of N (N − 1)/2 independent element pairs.

Figure 2.2 shows two identical dishes separated by a baseline vector ~b. Both dishes are pointing in the direction specified by ˆs. Plane waves from a distant point source in this direction must travel an extra distance ~b · ˆs = b cos θ to reach antenna 1. Thus, the output of antenna 1 is the same as that of antenna 2, but it lags by a geometric delay τg = ~b · ˆs/c. Let us assume that our interferometer is quasi-monochromatic, i.e. responding only to radiation in a very narrow band centered on frequency ν = ω/2π. The electromagnetic waves coming from a point source will induce voltages V1 and V2 in each antenna receiver:

V1 = V cos[ω(t − τg)] (2.1)

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Figure 2.2: Block diagram of the components of a two-element interferometer. Credit: Condon and Ransom (2010).

where t denotes time and V is voltage amplitude.

The correlator multiplies the two voltage responses V1 and V2: V1V2 = V2cos(ωt) cos[ω(t − τg)] =

V2 2

[cos(2ωt − ωτg) + cos(ωτg)]. (2.3)

Afterwards, time average ∆t _2ω1 is taken in order to remove the high-frequency term cos(2ωt − ωτg): Rc= hV1V2i = V2 2 cos(ωτg). (2.4)

The uncorrelated noise is also eliminated through the correlation process and does not appear in the correlator output. Compared to the observations with a single dish, this leads to significantly decreased fluctuations in receiver gain and atmospheric emission.

The cosine correlator can be thought of projecting a sinusoidal fringe pattern onto the sky (Fig. 2.3). The correlator multiplies the source brightness by this wave pattern, and integrates the result over the sky. The fringes have an angular scale of λ/b radians. Their phase φ depends on direction θ as

dφ dθ = d(ωτg) dθ = ω cb sin θ = 2π b sin θ λ . (2.5)

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Figure 2.3: Sinusoidal fringe pattern on the sky with period ∆θ. Credit: Gary (2012).

The fringe period (∆φ = 2π) corresponds to an angular change ∆θ = λ/(b sin θ). Thus, a longer baseline b leads to a more accurate measure of the source position and therefore better resolution.

On the other hand, improving the instantaneous point-source response of an interferom-eter requires more baselines. Figure 2.4 shows the point-source responses of a two-, three-, and four-element interferometer. This comparison nicely demonstrates how the number of antennas constrains the response. Although the sidelobes are still significant and there is a broad negative “bowl” (caused by the lack of spacings shorter than the diameter of an individual antenna), the synthesized main beam of the four-element interferometer is nearly Gaussian and has an angular resolution ≈ λ/b.

2.3 Extended sources and the complex correlator

In the case of an extended emission, the source is treated as the sum of independent point sources and the response of the two-element interferometer with “cosine” correlator (with output as in Equation 2.4) takes the form

Rc= Z

Iν(ˆs) cos(2πν~b · ˆs/c)dΩ = Z

Iν(ˆs) cos(2π~b · ˆs/λ)dΩ, (2.6)

where Iν(ˆs) is the source brightness distribution and Ω is the solid angle on the sky. However, the even cosine function of the cosine correlator responds only to the even part of the source brightness distribution, which consists of a sum of even and odd part. In order to measure the odd part we need to introduce a “sine” correlator which has a phase shift 90◦ and output Rs = (V2/2) sin(ωτg). The response of the the sine correlator to an extended source is

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Figure 2.4: The instantaneous point-source responses of interferometers with overall projected length b and two, three, or four antennas distributed as shown are indicated by the thick curves. The individual responses of the three two-element interferometers comprising the three-element interferometer and the six two-element interferometers comprising the four-element interferometer are plotted as thin curves. Credit: Condon and Ransom (2010).

Rs= Z

Iν(ˆs) sin(2π~b · ˆs/λ)dΩ. (2.7)

Since it is convenient to write cosines and sines as complex exponentials using Euler’s formula eiφ _{= cos φ + i sin φ, we can define the so called “complex” correlator, which is a} combination of “cosine” and “sine” correlators. We can further define the complex visibility function V as the complex sum of the sine and cosine correlator outputs:

V ≡ Rc− iRs = Ae−iφ, (2.8)

where A =p(R2

c+ R2s) is the visibility amplitude and φ = arctan(Rs/Rc) is the visibility phase. Thus, the relationship between the source brightness distribution Iν(ˆs) and the response of an interferometer, given by the complex visibility Vν, is

Vν = Z

Iν(ˆs)e−i2π~b·ˆs/λdΩ. (2.9)

Furthermore, we can introduce a plane perpendicular to the source direction. This is known as the u, v-plane (Figure 2.5, left). Its coordinates are (u, v, w), where w coincides with the ˆs-direction and u and v are projected easterly and northerly, respectively. In the u, v-plane visibilities can be expressed as

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Figure 2.5: The u, v-plane (left ) and twelve-hours Earth-rotation aperture synthesis (right ). Credit: Burke (2002) and Condon and Ransom (2010), respectively.

Vν(u, v, w) = Z Z

Iν(l, m)e−i2π(ul+vm−w(l

2_+m2_)/2)

dldm, (2.10)

where (u, v, w) are the projected baseline coordinates, and (l, m) are the sines of the angles between the phase center and the emission.

If all antenna elements are situated on a plane, a simple phase shift can ensure that the w-component becomes zero. In this case, the visibilities measured in the u, v-plane turn out to be a two-dimensional Fourier transform of the source brightness Iν:

Vν(u, v) = Z Z _I ν(l, m) √ 1 − l2_{− m}2e −i2π(ul+vm)_dldm. _(2.11)

Each observation of the source with a given baseline length brings one measure of the visibility. Provided that enough measures of V are available, one can derive Iν, performing an inverse Fourier transform:

Iν(l, m) = √

1 − l2 _{− m}2 Z Z

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2.4 Earth-rotation aperture synthesis

The sequential use of a series of baselines or the simultaneous use of many baselines of an array of radio telescopes is called aperture synthesis. The technique of Earth-rotation aperture synthesis utilizes the rotation of the Earth to vary the projected baseline coverage of an interferometer whose elements are fixed on the ground.

Seen from a distant source at positive declination, the Earth rotates counterclockwise with a period of one sidereal day. The right panel of Figure 2.5 demonstrates Earth-rotation aperture synthesis of an east-west two-element interferometer at latitude +40◦. The two antennas are shown as they appear at hour angles −6h, −3h, 0h, +3h, and +6h (from left to right). As seen from the diagram, in the plane perpendicular to the line of sight the interferometer baseline rotates from north-south (at −6h_{) through east-west (at 0}h_{) to} south-north (at +6h). Besides the orientation, the projected baseline length is also changed. Projected onto the u, v-plane the baseline traces an ellipse in a period of 12 hours. This is shown by the dashed curve on the small u, v-plot in the right end of Figure 2.5. The points on the u, v-ellipse designate the instantaneous coverage at −6h_{, −3}h_{, 0}h_{, +3}h_{, and} +6h_{. The ratio of the v-axis to the u-axis of the ellipse is determined by cos δ, where δ is} the declination of the source.

2.5 Standard data processing and image acquisition

2.5.1 Flagging

At radio frequencies, the data are often corrupted by stray electromagnetic transmissions which interfere with the incoming radiation from the observed celestial source. Origins of Radio Frequency Interference (RFI) may be internal, such as antenna cross-talk and imperfect Faraday cages, or external. The latter case can be due to deliberately radiating equipment, such as satellite/aircraft radars and TV/radio broadcasting antennas, or unin-tentionally radiating devices such as cars, electrical fences, power lines, and wind turbines (Offringa et al. 2013). Flagging involves the identification and masking of RFI-affected data points such that they are excluded from further analysis. Flagging is a useful first step in the data analysis process.

Traditionally, RFI identification and removal has been done by hand through visual inspection of the data. Modern radio telescopes produce large amounts of data for which manual examination is infeasible. Therefore, automatic routines have been developed to provide flagging of contemporary radio observations. Such techniques are generally based on the assumption that the astronomical signal is smooth and therefore aim to detect significant jumps and discontinuities in the data (Offringa 2012).

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2.5.2 Calibration

An interferometer observes the true sky distorted by characteristics of the instrument (sta-tion beam, clock synchroniza(sta-tion, etc) and the environment (ionosphere). The goal of calibration is to compute an accurate estimate of the true sky from the obtained distorted measurements.

The second step of the standard data processing is to calibrate the gathered signals from the individual antennas. Two calibration techniques are frequently used – cross-calibration and self-calibration. The first one is performed by observations of a reference source and the second one uses redundant information within the synthesis observations.

Cross-calibration

The cross-calibration technique is realized through dedicated calibration observations of a part of the sky that contains a single known, relatively strong point source. Given the measured signal and the known properties of the source, calibration aims to find the set of parameter values that minimize the difference between the model and the observations. Afterwards, these calibration solutions can be applied to the target observation.

Not only the gain of the main beam of each antenna needs to be estimated, but also the phase differences between the antennas. For this purpose two classes of calibration sources are needed: phase calibrators and flux calibrators. The flux calibrators are sources with accurately known fluxes which do not vary with time (or vary very slowly). These sources should be reasonably compact and unresolved by the interferometer because for such objects visibilities are easily predictable. Phase calibrators are also compact sources which not necessarily have constant flux but whose position is stable. Since the phases are stable only over a short time, there must be frequent breaks in the main observations of the science targets in order to observe a phase calibrator.

Self-calibration

Self-calibration also corrects for antenna based phase and amplitude errors. It is, however, performed at a later stage, together with imaging. It starts from an initial estimate of the parameters and adapts them until the resulting image matches a prior parametric model of the field of interest (Boonstra and van der Veen 2003). This technique requires sufficient signal-to-noise at each solution interval, which makes it unreliable in many cases. Self-calibration is an iterative, non-linear relaxation process which means that it is very computationally demanding.

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2.5.3 Gridding

After cross-calibration, the data are transformed into a form suitable for the Fourier in-version. Since these operations for data obtained with large arrays are very demanding on computer capacity and time, it is advantageous to use a Fast Fourier Transform (FFT; Cooley and Tukey 1965). To accomplish that, the data need to be gridded, i.e., to be in-terpolated so that the u, v-plane is regularly covered by data points. Weighting is applied to the Fourier components to help suppress sidelobe-like artifacts generated by the transfer function (Briggs et al. 1999).

2.5.4 Imaging

An inverse-Fourier transform of the gridded visibilities gives the dirty image. The dirty beam is the transform of the unevenly sampled u, v-plane. Thus, the dirty image is simply the convolution of the true sky brightness distribution with the dirty beam.

The PSF of a dirty map, synthesized by a single transformation of the gridded data, contains large sidelobes, which present themselves in the form of arcs and radial lines. Fortunately, the form of the dirty beam is known from the u, v-plane distribution and corrections can be applied in order to deconvolve the dirty beam from the dirty image and eventually increase the quality of the map.

Thus, if a dirty map contains a single prominent point-like source, the first step is to subtract a dirty beam centered on that source. This way the sidelobes disappear and smaller sources, which may have been obscured before, are revealed. The same process is repeated until no sources are clearly distinguished. At the end, the resulting point source model is convolved with a clean beam, a Gaussian with an idealized PSF similar to that of the dirty beam. This process is known as cleaning (H¨ogbom 1974) and is the most commonly used technique to improve radio interferometric images.

2.6 Complications of wide-field imaging

The new generation of radio interferometers, like LOFAR and SKA (see Chapter 3), are being built with wide fields of view. In order to achieve high resolution, their antennas also span large distances, over which Earth’s curvature becomes important. These two features have many benefits but also lead to a number of significant complications. Dealing accu-rately with large fields of view and non-coplanarity of the antennas requires sophisticated algorithms and substantial computational resources.

Traditional synthesis imaging assumes visibility measurements lying on a plane. When baselines are thousands of kilometers long, we can no longer consider the antennas to be

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Figure 2.6: Left: Radio array with small field of view, whose antennas are closely situated and can be approximated to sit in a plane. Right: The antennas have wide field of view and a situated at large distances from each other. Curvature of Earth breaks the approximation of plane array. The wide primary beam patterns cause the antennas to experience ionospheric variations across the field of view. Large FoV requires corrections far from the phase center. Credit: Intema et al. (2009).

situated on a flat surface (Fig. 2.6). In this case, the w-term in Equation 2.10 becomes im-portant and cannot be disregarded. This means that the visibilities cannot be considered as a simple Fourier transform of the sky brightness, as Equation 2.11 implies. The correc-tions of the w-term are difficult to incorporate since they must be applied during imaging (Bhatnagar et al. 2008). The most relevant method removing the effects of non-coplanar baselines is the w-projection algorithm (Cornwell et al. 2008).

The wide primary beam patterns cause the antennas to experience ionospheric varia-tions across the field of view (2.6, right panel). Antennas also have intrinsically varying sensitivity to the different regions of the large FoV. This means that gain changes signifi-cantly inside the primary beam, introducing direction-dependent effects. The A-projection algorithm (Bhatnagar et al. 2008) is used to correct for the direction-dependent effects of the antenna primary beams. The w-projection and A-projection techniques significantly improve the results from the new generation radio arrays but inevitably bring additional computational demand on the imaging process.

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Chapter 3 LOFAR and MSSS

This chapter is divided in two main parts. The first section presents the purpose, layout, and parameters of the new LOFAR radio telescope. The second part focuses on MSSS, LOFAR’s first all-sky survey.

3.1 LOFAR

LOFAR, the LOw Frequency ARray, is a new generation software-driven radio telescope built in the Netherlands and with additional antenna stations throughout Europe (Fig. 3.1 and 3.4). It consists of antennas grouped into stations distributed over hundreds of kilometers. LOFAR operates in two frequency ranges: 10 – 80 MHz, using the Low Band Antennas (LBA), and 100 – 240 MHz, using the High Band Antennas (HBA). This new facility not only opens a new unexplored window of the lowest frequency radio emission observable from Earth’s surface, but also provides unprecedented wide field of view and very high sensitivity. LOFAR therefore represents an important new capability for observing transient sources at low radio frequencies. With its unique capabilities, LOFAR is an important pathfinder of the ambitious Square Kilometer Array (SKA; Ekers 2012).

3.1.1 Science case

After the discoveries in radio astronomy in the last several decades were dominated by higher frequencies, using aperture synthesis arrays (like Westerbork, VLA, and GMRT) or large monolithic dishes (like Effelsberg, Arecibo, and Green Bank), LOFAR is meant to open the lowest frequency radio regime to the study of a broad range of astrophysical phenomena. One of the main science goals for the array is the detection of highly red-shifted 21-cm line emission from the epoch of reionization (HI redshifts z=6 to 20) and a phase called Cosmic Dawn (HI redshifts from 50 to 20; Zaroubi et al. 2012). The LO-FAR project also aims to perform deep surveys in search for high redshift radio sources (R¨ottgering et al. 2011) and to include detections of exoplanets (Zarka 2011) and radio flashes from ultra-high energy cosmic rays (CRs, Falcke et al. 2005). The great sensitivity

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Figure 3.1: The Superterp - the central core section of LOFAR.

and broad fractional bandwidth are also favorable for studies of cosmic magnetic fields (Beck 2010). The large effective area of LOFAR’s central region, the support for wide-field observing, and the high time resolution make LOFAR particularly suitable for all-sky monitoring of transient radio sources.

3.1.2 Technical challenges

To achieve its unprecedented capabilities at low radio frequencies, LOFAR faces several non-trivial technical challenges. The most obvious example is the excising of man-made interference (Section 2.5.1). High dynamic range analog-to-digital converters are needed since RFI may appear orders of magnitude stronger than the astronomical signal. Due to the often narrow-band frequency nature of man-made contamination, optimal RFI removal requires high frequency resolution. If this is not available, the RFI-induced amplitude spike is smeared out throughout the broad channel. This not only makes the RFI more difficult to recognize but also means that more data will have to be removed in order to eliminate the pollution. Since RFI is typically short-lived, the similar situation occurs in the time domain. This implies that high time resolution is also needed to correctly identify RFI and eliminate it while losing a minimal amount of good data.

Another major challenge for LOFAR is the high data rate (up to 13 Tbit/s for the entire array), which implies fast transportation and huge storage capacity. A significant part of LOFAR’s design is dedicated to reducing this data rate. In this sense, LOFAR is one of the first astronomical facilities which has to cope with the new-generation data-intensive astronomy.

The requirements of LOFAR observations have triggered not only a new approach to ra-dio array hardware but also improvement of the existing signal handling algorithms. Being very sensitive to the variations of the ionosphere, low-frequency radio signals required the

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Figure 3.2: LOFAR low-band antenna (left ) and high-band antenna tile (right ).

development of advanced calibration techniques that can simultaneously determine multi-directional station gain solutions and to operate in the near-real-time regime. Likewise, since LOFAR’s wide FoV breaks the traditional interferometric assumption of a coplanar array, advanced imaging procedures were to be implemented in order to image data in which the w-term in the measured visibilities is not negligible.

3.1.3 Antennas

Since angular resolution of dishes scales as λ/D (Section 2.1), lower frequency dishes must achieve unrealistic sizes in order to attain resolutions capable to serve the purposes of con-temporary research. “Filled aperture” paraboloidal reflectors become impractically large at wavelengths longer than ∼1 meter, and simple dipole antenna elements are used instead (Ellingson 2005). Thus, LOFAR receivers are not monolithic dishes but consist of many dipoles which build up a large collecting area. The output of each antenna is individually digitized and then combined with the signals from other antennas. The group of antennas whose output is combined is referred to as a station. Each such station is the functional equivalent of a dish in the traditional (higher frequency) aperture synthesis radio telescope. Unlike the conventional higher frequency interferometric radio telescope, LOFAR an-tennas have no moving parts (Fig. 3.2). Pointing is achieved by combining signals from the individual antenna elements in order to form a phased array. Thus, all LOFAR stations contain significant local computing resources. These features make the LOFAR system both flexible and agile. Station-level beamforming allows for rapid repointing of the tele-scope and simultaneous observation of multiple areas of the sky. The ability to create beams pointing at different directions of the sky at once is called multi-beaming.

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Figure 3.3: Median averaged spectrum for all LBA (left ) and all HBA (right ) dipoles in station CS003. The strong peaks are due to RFI. Left: LBA antennas are most sensitive at 58 MHz. RFI is clearly visible below 30 MHz and is partly due to ionospheric reflection of sub-horizon RFI back toward the ground. The RFI above 80 MHz is due to the commercial FM band. Right: Various prominent RFI sources are visible across the frequency range. The strong peak near 170 MHz corresponds to an emergency pager signal. Credit: van Haarlem et al. (2013).

LBA

At the lowest frequencies, LOFAR utilizes the LBAs (Low-Band Antennas). They are de-signed to operate from the ionospheric cutoff near 10 MHz up to about 90 MHz. However, their work is by default limited to 30 – 80 MHz due to low sensitivity of the antennas and the presence of strong RFI outside this range (Fig. 3.3, left panel). LBA antennas have almost omnidirectional response which allows simultaneous observation of the entire visible sky. This design is particularly useful for all-sky monitoring for radio transients.

HBA

High-band antennas (HBAs; Fig. 3.3, right panel) have different mechanical design and are capable of observing between 110 and 250 MHz. Since the frequency range above 240 MHz is heavily contaminated by RFI the band is limited to 110 – 240 MHz. Each high-band antenna is a so called ”tile” (Fig. 3.2, right panel), which includes 16 antenna elements, initial analog amplification, and the first analog stage of beamforming.

3.1.4 Stations

LOFAR antennas are grouped into stations. A total of 40 LOFAR stations are being de-ployed in the Netherlands, with additional 8 international stations distributed in Germany, France, the UK, and Sweden.

LOFAR stations are classified as either core, remote, or international, according to their design and the distance from the center of the array. The so called “core” of LOFAR

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Figure 3.4: Left: Distribution of the Dutch LOFAR stations. Right: Distribution of the LOFAR stations on a Euro-scale. Green dots outside the Netherlands show the 8 international stations. Yellow dots are stations still under construction. Credit: ASTRON and van Haarlem et al. (2013), respectively.

consists of 24 densely sampled stations situated within 2-km-wide central part of LOFAR, located close to the village of Exloo, the Netherlands. At the core, the station distribution is optimized to achieve the good instantaneous uv-coverage required by many of the science cases, including the radio transient searches.

At the center of the core, six stations reside on a 320 m diameter island referred to as the “Superterp” (Fig. 3.1). Beyond the core, the 16 “remote” Dutch LOFAR stations extend out to a radius of 90 km (Fig. 3.4), and are arranged so as to enhance the u, v-coverage. The positions of the international stations have not been chosen to maximize the filling of the uv-coverage, but duplicate baselines have been avoided. With baseline lengths ranging from a few tens of meters to over one thousand kilometers, the angular resolution of LOFAR extends from 0.5◦ to sub-arcsecond scales (van Haarlem et al. 2013).

3.1.5 Data processing and storage (CEP and LTA)

The signals from all LOFAR stations are sent via high-speed optical fibers to the central processing (CEP) facility located in Groningen, the Netherlands. There, data are aligned, combined, and further processed using an IBM Blue Gene/P supercomputer with ∼28

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Tflop/s of processing power. When this is accomplished, raw data products are moved to a storage cluster for additional post-processing. The final step is to transfer the scientific data to the LOFAR long-term archive (LTA), where they should become accessible to the community (van Haarlem et al. 2013). The visibilities from LOFAR observations are stored in the so called measurement sets (MS), which use the casacore table format1_.

3.1.6 Tools of the standard LOFAR imaging pipeline

The LOFAR imaging pipeline follows the main steps of the standard radio data reduc-tion procedure (Secreduc-tion 2.5) and utilizes tools specially developed to serve the specifics of LOFAR.

NDPPP

The software accomplishing the first step is called NDPPP, the New Default Pre-Processing Pipeline. It is used to flag the data, i.e. to identify RFI and exclude it from further analy-sis (Section 2.5.1). Additionally, it can perform averaging in time or frequency. This first stage of the processing may also include a subtraction of the contributions of the brightest sources in the sky (Cygnus A, Cassiopeia A, etc.), using a demixing technique (van der Tol et al. 2007).

Since LOFAR is situated in densely populated area, it has been designed to provide extremely high frequency- and time-resolution in order to overcome the influence of the terrestrial RFI in the local low-frequency radio spectrum (van Haarlem et al. 2013). The flagging of the data in both time and frequency is carried out using the AOFlagger (Of-fringa et al. 2012a,b), a post-correlation RFI mitigation pipeline included in NDPPP. For both the low- and high-band systems, the median level of RFI is estimated to be around 2% of the data (van Haarlem et al. 2013).

BBS

The calibration step is typically performed using BlackBoard Selfcal (BBS; Pandey et al. 2009), a package specifically developed for LOFAR. As input, BBS requires an observation, a source catalog (also called sky model), and a configuration file (also called parset) which specifies the operations that need to be applied on the observation as a whole (Pizzo 2012). BSS performs a least square fit between the Fourier-inversed sky model and the original data in order to find the calibration solutions leading to the best estimate of the true sky. The currently used sky models are based on the cataloged values from the VLA Low-frequency Sky Survey (VLSS and VLSSr; Cohen et al. (2007) and Lane et al. (2012), respectively), the Westerbork Northern Sky Survey (WENSS; Rengelink et al. (1997)),

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and the NRAO VLA Sky Survey (NVSS; Condon et al. (1998)). The next generation of LOFAR sky models will be supplemented by the Multifrequency Snapshot Sky Survey (MSSS, Heald 2011) (see Section 3.2).

AWImager

After the pre-processing stage, the calibrated data are imaged with the AWImager, which is a modified version of the CASA imager (Tasse et al. 2013). It is specially adapted to image wide fields of view and data produced by non-coplanar arrays, where the w-term in the measured visibilities is not negligible. Unlike CASA, AWImager also corrects for direction dependent effects using the A-projection technique (see Section 2.6).

3.2 MSSS

The Multifrequency Snapshot Sky Survey (MSSS) is the first major observing program to be carried out with LOFAR (Heald et al. 2012). The main goal of MSSS is to produce a broadband catalog of the brightest sources in the low-frequency sky, creating a calibration sky model for future observations with LOFAR.

MSSS provides a higher areal density of sources than the VLSS catalog and includes well-sampled spectral information. It covers two frequency windows: one within the LBA range (30 – 74 MHz) and the other in the HBA range (120 – 160 MHz). LOFAR’s multi-beaming capability is utilized to observe several fields simultaneously in order to increase the survey speed. At the early testing phase only three beams were used at the same time. Currently, HBA observes six target fields simultaneously and LBA observes five target fields plus a calibrator field at the same time. Each beam consists of 8 bands divided into 10 subbands (Table 3.1). A subband has a bandwidth of about 200 kHz and a band has a bandwidth of 2 MHz (Heald 2013c).

The time cadence of the MSSS observations is 1 second. This is determined by the shortest dump time achievable with the LOFAR correlator and provides the fundamental limit on visibility-based LOFAR observations.

The number of fields required to survey the entire northern sky is 660 for LBA and 3616 for HBA. The layout of these fields is chosen to provide nearly uniform coverage at the optimized frequencies 60 MHz (LBA) and 150 MHz (HBA). The nominal spacings of 2.42◦ in HBA and 5.77◦ in LBA are used as upper limits in each of several declination slices (Heald 2011).

To ensure good uv-coverage while using the limited array for short observing blocks, each field is observed in snapshots (9 snapshots per field in LBA and 2 snapshots per field in HBA). The time per field is 9 × 11 min and 2 × 7 min, respectively (Table 3.2). MSSS

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Band Central Frequency (MHz) LBA HBA 0 31 120 1 37 125 2 43 129 3 49 135 4 54 143 5 60 147 6 66 151 7 74 157

Table 3.1: Central frequencies for the different bands of the MSSS. Credit: Heald (2013c).

MSSS-LBA MSSS-HBA

Field of view per field (FWHM, degrees) 5.77 at 60 MHz 2.42 at 150 MHz

Bandwidth per field (MHz) 16 16

Number of simultaneous fields 5 (+calibrator) 6

Time per field 9 × 11 min 2 × 7 min

Required number of fields 660 3616

Required on-source observing time (hr) 218 141

Table 3.2: MSSS project overview. Credit: Heald (2013b).

is expected to have sensitivity of ≤ 15 mJy/beam for LBA and ≥ 5 mJy/beam for HBA, and angular resolution ≤ 10000and ≤ 12000, respectively (Table 3.3).

MSSS observing runs began in late 2011 and were nearly half completed during 2012 (Heald 2013b). The schedule focused on the LBA in 2012, and switched to MSSS-HBA in early 2013. The MSSS survey should be complete in 2013 (Heald 2013a). Figure 3.5 shows a map of the covered fields of MSSS-LBA and MSSS-HBA.

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Survey (Telescope) Frequency Sensitivity Resolution Area Part of Sky

(MHz) (mJy/beam) (arcsec) (deg2₎

MSSS-LBA 30–74 ≤15 ≤100 20 000 δ > 0◦ VLSS (VLA) 74 100 80 30 000 δ > −30◦ MSSS-HBA 120–160 ≤5 ≤120 20 000 δ > 0◦ TGSS (GMRT) 140–156 7-9 20 32 000 δ > −30◦ WENSS (WSRT) 330 3.6 54 10 000 δ > +30◦ NVSS (VLA) 1400 0.45 45 35 000 δ > −40◦

Table 3.3: MSSS output characteristics in comparison with existing surveys. Credit: Heald (2013b).

Figure 3.5: Status of MSSS-LBA (left ) and MSSS-HBA (right ) as of July 26, 2013. Color code: purple – data archived, green – data available on CEP, blue – partial data available, red – data missing, orange – not yet observed. Credit: http://msss.astron.nl.

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Chapter 4 Transients Key Science Project and

Transient Radio Sky

LOFAR is a new system which combines an unprecedentedly wide field of view, high sen-sitivity at low frequencies, and remarkably flexible data-processing tools. These unique capabilities will be exploited to carry out a large-scale transients monitoring program lead by the Transients Key Science Project (TKP). In this chapter we outline the main approaches and goals of the TKP and review the transient radio sources which will be studied as part of the TKP monitoring programs and with a potential bispectrum survey.

4.1 Transients Key Science Project (TKP)

The Transient Key Science Project (TKP) is one of the six key projects which comprise the core LOFAR science case. The remit of the TKP is to detect and study variable and transient events in the unexplored low-frequency radio sky on timescales from milliseconds to years. The beamformed technique (not reviewed here) is typically used for phenomena shorter than a second. At longer timescales, the TKP focuses on image-plane analysis, searching for transients in the output of the standard tools described in the previous chap-ter.

4.1.1 Radio Sky Monitor (RSM)

One of the key observational modes of LOFAR for the transient key project will be the Radio Sky Monitor (RMS; Fender 2007). This mode of observation will be capable of sur-veying the majority of the visible sky to a depth of tens of mJy in a 24-hour period. Taking advantage of the flexible LOFAR system, multiple beams will be pointed simultaneously from the core stations to tile out a large fraction of the sky. At the same time, separate beams from the remote stations will be formed to observe in targeted mode (Fig. 4.1).

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Figure 4.1: Schematic of the Radio Sky Monitor (RSM) mode of LOFAR. Credit: Scheers (2011).

Using multiple (100 – 600) pointings, the powerful sky monitor will be able to survey the visible sky once a day, going as deep as 2 – 180 mJy with resolution of 3 – 70 at the high and low frequency band, respectively (Scheers 2011).

4.1.2 Transient Pipeline (TraP)

The transient detection pipeline (TraP) consists of a near real-time pipeline which monitors the incoming stream of images, searching for both known variable sources and previously unobserved transients. The TraP is currently under development and its ultimate goal is to be capable of detecting radio transients down to 1-second timescales with a response time latency of order 10 seconds (van Haarlem et al. 2013). The TKP has been developing the TraP to respond to the large amounts of data generated by LOFAR observations.

In order to provide real-time transient alerts, and if necessary reconfigure the telescope, all data processing is fully automated. The TraP is tightly coupled with an optimized ver-sion of LOFAR’s standard imaging pipeline (section 3.1.6), which performs data flagging, compression, calibration and imaging. As a result, the so called “image cube” (a group of simultaneous images of the same area of sky at different frequencies and Stokes parameters) is provided for analysis. Source fitting routines extract sources and related properties from the images, after which the results are stored into a database (Scheers 2011). Inside the database, the results are compared with cataloged source properties, the new detections are associated with known objects, and lightcurves are generated. Interesting lightcurves are extracted from the database and fed to a source classification and response system (Swinbank 2011). The parameters of known sources are used to update the monitoring database (Fender et al. 2006). Significant differences are reported back, and triggers for further specific follow-up actions may be sent (Scheers 2011).

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MonetDB Database Imaging

Pipeline

Image

Cube Quality Control

Lightcurve Storage Transient & Variability Analysis Source Association Archive Database Classification & Analysis Response Scheduling Send External Alert Re-run Image Analysis Schedule New Observation Other Facilities Receive External Alert Real-time Processing Off-line & External Systems

On-line Processing Visibility Data Scheduler Source Finding

Figure 4.2: Schematic flowchart of the LOFAR transients detection pipeline (TraP). Data are initially processed by a modified version of the standard imaging pipeline (Section 3.1.6). Transients analysis is performed using a combination of source-finding and analysis routines and a high-performance MonetDB database. Credit: John Swinbank (priv. comm.).

Classification of discoveries is essential for facilitating responses to dynamic events in real time. Potential actions may include re-running the pipeline with a different config-uration, scheduling a follow-up observation, or sending a notification of the event to the community (Swinbank 2011). Since for transient sources any follow-up with other tele-scopes or particle detectors needs to be fast, LOFAR has been set up to send and receive alerts of new events via the so called VOEvent network (Scheers 2011).

4.2 LOFAR transient and variable sources

Transient radio science is vast (Fig. 4.3). The distances to detected objects, as well as the timescale for transient behavior, vary dramatically. Giant kilo-Jansky micro-second radio pulses have been detected from the relatively nearby Crab Pulsar. In contrast, month-timescale variations are commonly observed in the radio emission produced by powerful jets driven by accretion onto super-massive black holes in distant AGN. Through studying the transient and variable nature of these exotic and energetic objects, we obtain a pow-erful laboratory to probe extreme conditions on a variety of distance scales and physical environments.

The time scales to explore transients can span a huge range of almost 20 orders of mag-nitude. Within this context a rough distinction can be made between “slow” and “fast”

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Figure 4.3: Artist’s impressions of some transient sources. Top left: Gamma-ray burst, Top middle: Supernova, Top right: Active galactic nucleus, Bottom left: X-ray binary, Bottom middle: Flare star, Bottom right: Pulsar. Credit: hiddenleaves.wordpress.com, smithsonianscience.org, imagine.gsfc.nasa.gov, paolobonfini.wordpress.com, universetoday.com, spaceinimages.esa.int, respectively.

transients. Fast transients are the ones with sub-second timescales, which are normally studied by time-domain signal processing of data sampled at high time and frequency res-olutions. Slow transients have timescales of hours, days, or years and require imaging on a wide range of time integrations.

Based on experiences with previous new telescopes, it is strongly believed that new types of phenomena are very likely to be discovered by LOFAR. Probing such a large re-gion of unexplored parameter space will almost certainly lead to serendipitous discoveries of new classes of astrophysical objects. This opportunity is especially enhanced by the wide-field monitoring mode of the RSM.

4.2.1 Long-timescale transients

Of particular interest to the TKP is the class of jet sources, which show radio emission due to synchrotron radiation produced by magnetized relativistic particle outflows interacting with the environment. The class of jet sources includes the active galactic nuclei (AGN), gamma-ray bursts (GRBs), radio supernovae, and microquasars.

Galactic microquasars have outbursts that may last from days to months, but their rise times can be much shorter. The flux levels range from hundreds of Jy down to the mJy level. AGN flares typically have much longer time scales due to the scaling of black-hole phenomena with mass. The peak fluxes of radio supernovae and GRBs at LOFAR frequen-cies are below a mJy. Their variability reaches timescales of years and decades.

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Observing different types of slow radio transients offers unique insights into the physics that plays a role in the jet evolution. One of the obstacles in deciphering the radiation mechanisms is, however, the fact that only few sources of each class are known. LOFAR, with its very wide FoV and high sensitivity, is expected to find many more slow transient representatives. For these transients the challenge in data analysis comes from the need of careful analysis of deep images and supporting data in order to distinguish the different types of slow radio transients (van Haarlem et al. 2013). The long-timescale transients are the main focus of the TraP (Section 4.1.2).

GRBs

Gamma-ray bursts (GRBs) are extremely bright, distant, short lived bursts. All of the proposed GRB progenitors are connected with the end phase of the evolution of a star. One candidate involves the collapse of a star. Another possibility is a binary merger of either neutron star binary, or neutron star – black hole binary.

The GRBs are isotropically distributed across the sky and their redshifts show that they originate from cosmological distances. GRB afterglows have been detected in the X-ray, optical, and radio wavebands. The dominant radio emission mechanism is considered to be synchrotron radiation emitted by shock accelerated electrons within a jet. At LOFAR frequencies, the rise time for a typical GRB is predicted to be in the order of years, with a peak flux less than 1 mJy (van der Horst et al. 2008).

The GRBs are also believed to produce coherent prompt emission. One proposed mech-anism involves gravitationally excited MHD waves in the case of merging compact neutron-star binaries (Moortgat and Kuijpers 2003). The model of Usov and Katz (2000) suggests that early interaction of the magnetized relativistic wind with the ambient medium gives rise to a very low-frequency radio pulse. The bulk of this radiation is expected to be below 1 MHz, but the high-frequency tail of the emission is possibly detectable with LOFAR.

Radio supernovae

A Supernova is the explosive death of a massive star. The resulting explosion and subse-quent shock wave results in a short lived astronomical source which is extremely luminous at all wavelengths.

The classification of type I and type II divides supernovae based on the detection or non-detection of optical hydrogen emission lines. Further subdivision is provided by the presence of certain emission lines. Supernovae of class Ia exhibit a strong ionized silicon absorption line. Type I supernovae without strong silicon line are classified as types Ib and Ic (with type Ib showing strong neutral helium lines and type Ic lacking them). Type

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Ib, Ic, and II are all associated with core-collapse mechanisms and can be radio luminous. The emission mechanism for core-collapse supernovae is the non-thermal synchrotron process. Typical radio lightcurves go through an initial fast rise due to electrons in the circumstellar medium which are accelerated by the propagating shock wave. This rise is followed by an expansion phase, which gives a slower decay in the lightcurve. Since the peak radio emission evolves from high to low frequencies, LOFAR will be able to explore the later stages of radio supernovae evolution.

AGN

An active galactic nucleus (AGN) is an extremely energetic compact region at the center of a galaxy. Seyfert galaxies and quasars are the most abundant objects associated with AGN activity. AGN harbor some of the most massive black holes in the universe. Due to accretion and jet production AGN undergo bright transient outbursts at all frequencies. The radio emission is produced in large collimated jets through synchrotron process, either within shock regions or through steadily evolving relativistic outflows. Typical timescales at radio frequencies range from months to years.

Radio loud classes of AGN are some of the earliest studied variable radio sources. The main reason for that is that they are bright at all radio frequencies. Their fluxes can reach kJy scales at low frequencies.

X-ray binaries

Low-Mass X-ray Binaries (LMXBs), or microquasars, are the smaller (∼10M) Galactic versions of AGN. LMXBs consist of a compact object, either a black hole or neutron star, in a binary system with a companion star. Matter is accreted from the companion star through an accretion disk onto the black hole.

The timescales for LMXBs to evolve are significantly shorter compared with AGN. This allows to track complete cycles, from the low flux quiescent state to the high state (of mas-sive accretion and ejection events), which exhibits transient outbursts at both X-ray and radio frequencies. These state changes can last from days to months, compared to many thousands of years for the AGN. This is the reason why AGN are typically observed in a constant state.

LOFAR provides a new radio frequency window to observe LMXBs and allows for long-term, wide-field monitoring of the low frequency sky coupled with dedicated observations of interesting cases. This will significantly expand our knowledge of LMXBs and will lead to deeper understanding of the accretion and ejection mechanisms driving them.

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4.2.2 Short-timescale transients

LOFAR’s ability to observe very wide fields with high sensitivity opens up a very large dis-covery space in fast-transient astronomy. Transients on short timescales are mainly linked to coherent radiation and to sources in extreme matter states. Such short-duration tran-sients are naturally affected by plasma propagation effects such as dispersion, multi-path scattering and scintillation by the intervening media. For these reasons, they may also serve as excellent probes of the interstellar and intergalactic medium (Bhat 2011).

Coherent emitters are the only ones reaching detectable fluxes. Giant pulses of regu-lar radio pulsars can attain 100 Jy over microseconds. Fregu-lares from soft gamma repeaters (SGRs) reach similarly high fluxes. Millisecond single pulses of RRATs have a wide range of flux levels up to 1 Jy. Stellar radio flares have lower fluxes and durations from minutes to hours.

LOFAR will also study radio emission from planets within the Solar System. This includes imaging Jupiter’s magnetosphere and radiation belts at high spatial and time res-olution, and studying planetary lightning from the other planets within the Solar System. It is hoped that radio bursts from nearby hot-Jupiter exoplanets might also be detected, although their signals are expected to be very weak (Grießmeier et al. 2007).

Short-timescale transients are often studied by the time-domain beamformed method because it allows very fast sampling. Beamforming over a wide field of view, however, is extremely computationally demanding, leading to low survey speeds. In this thesis we test the effective bispectrum algorithm and study its suitability to perform large surveys for second-timescale transients using correlated visibilities. Due to their high fluxes, the pulsars, RRATs, flare stars, Lorimer bursts, and the giant flares from SGRs are the main targets of the bispectrum algorithm.

Flare stars

Flare stars are typically late type stars (often referred to as dM or dMe stars) that undergo transient outbursts. This increases their radio flux density by a factor of ∼500 (from mJy quiescent levels). A sub-division of the flare star class includes active binaries of types RS CVn and BY Dra, which share similar characteristics to standard flare stars.

Due to the high brightness temperatures, steep spectral index, and short timescale of variability a coherent emission mechanism is favored over synchrotron for frequencies below ∼5 GHz. The outbursts are often characterized by:

1. a high degree of circular polarization (up to 100%) 2. a high spectral index, typically α ∼ −2.5

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3. high brightness temperatures, typically Tb > 1012 K

4. bursts that can last from tens of seconds to tens of minutes

Based on previous statistics, flare stars are expected to be abundant in routine monitor-ing with LOFAR. Due to LOFAR’s one second cadence and wide-field of view, a broadband census of nearby flare star activity will be achieved.

Pulsars

Pulsars emit pulsed emission across the electromagnetic spectrum, with periods typically less than a second. The pulsed emission is a consequence of a rapidly rotating neutron star, which creates beamed radio emission at the poles. Pulsars usually have a steep spectral index α ∼ −2 and flux densities ranging from 0.1 mJy to 5 Jy at 400 MHz. As well as emitting pulsed emission, pulsars have also been shown to emit giant radio pulses. For example, the Crab pulsar (PSR B0532+21) has emitted a number of ∼105 Jy pulses (at 430 MHz) lasting only 100 µs.

There are currently ∼2000 known radio pulsars. LOFAR is expected to significantly increase that number, deliver the true pulsar population in the nearby Galaxy, and poten-tially detect single giant pulses from greater distances. Previous surveys for radio pulsars have typically been conducted at 450 MHz or 1.4 GHz. In this sense LOFAR opens a new observing window to study pulsar properties. Observations in the range of 30 – 240 MHz will be very beneficial for addressing some longstanding issues about the pulsar emission mechanism and the conditions of the ISM.

RRATs

Rotating radio transients (RRATs) are a class of recently discovered transient sources (McLaughlin et al. 2006). They are not a distinct object population but are extreme examples of radio pulsars. RRATs are believed to be pulsars that only emit a pulse of radio emission once per very many rotation periods. The pulses have peak flux densities at 1.4 GHz ranging from 100 mJy up to 10 Jy and pulse widths of 2 – 30 ms. A number of individual millisecond pulses are received followed by hours or days of non-detections. The long periods observed are comparable to the magnetars rather than the radio pulsars. The narrow pulse widths and high brightness temperatures of 1020 _{– 10}24 _{K are similar to} individual pulses from radio pulsars.

As pulses are detected only occasionally, RRATs are easier to find in single-pulse stud-ies (Bagchi et al. 2012). After their discovery by McLaughlin et al. (2006), more searches for non-repetitive, dispersed signals in radio pulsar survey data have led to new RRAT discoveries. With their nature of sporadic strong pulses, RRATs are also very suitable for detection by the bispectrum algorithm.

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Figure 4.4: Intensity of the Lorimer burst as a function of radio frequency versus time. Inner panel: Integrated pulse profile. Credit: Lorimer et al. (2007).

Soft Gamma Repeaters

Other expected LOFAR transient events are the flares from soft gamma repeaters (SGRs). These sources represent a rare class of strongly magnetized neutron stars exhibiting two types of gamma-ray burst emission.

Occasionally, SGRs enter an active stage and emit repeated short bursts. The burst-ing activity typically lasts from several days to a year. This regime is followed by a long quiescent period taking up to several years. Much more rarely, perhaps every 50 years, an SGR may emit a giant flare with enormous intensity. The energy released in such a flare in gamma-rays is comparable to the total energy emitted by the Sun over 104 – 105 years (Mazets et al. 2008).

Observations have established that SGRs are isolated, and hence the extra energy can-not be provided by accretion from a companion. The most successful explanation for their activity is the magnetar model. SGRs are believed to be powered by ultra-strong magnetic fields of 1014 – 1015 G.

Lorimer bursts

The Lorimer bursts are highly dispersed isolated radio bursts with properties suggestive of extragalactic origin. The true origin of these events is not yet understood, although there are various suggestions.

In 2007, the discovery of the so-called “Lorimer Burst” was announced – a single 5-ms 30-Jy radio pulse that was so dispersed that it could only originate outside the Galaxy (Fig. 4.4). The high value of the dispersion measure indicates distances of 500 – 1000 Mpc. The energy needed to provide such a large amount of flux, in such a short time duration is vast.

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Lorimer et al. (2007) derived a brightness temperature of Tb ∼ 1034 K and energy released of δE ∼ 1033 _{J. These results rule out many astrophysical progenitors (like synchrotron} emitters) and leave only extreme cataclysmic possibilities, such as binary neutron-star merger and coalescing black holes.

The results of Lorimer et al. (2007) showed the importance of short duration bursts. Crude estimates of the rates of such events predict that many such bursts should be detectable in archived pulsar-survey data. Some of the searches conducted so far lead to new discoveries. Studies of extreme radio pulses is also one of the priorities for LOFAR. Due to their spontaneity, short timescales, and high brightness, Lorimer burst are one of the main targets of the bispectrum and the 1-sec imaging method discussed in this thesis.

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Chapter 5 Short-timescale Imaging with

LOFAR

Short-timescale imaging is always a formidable challenge since it deals with small quan-tities of data. It makes proper calibration essential in order to achieve the quality and consistency of images sufficient for further research.

Short timescale imaging has vast applications for transient science and its feasibility with LOFAR is a question of great interest. Since LOFAR is a new instrument, short-timescale imaging is largely unexplored by current research. No dedicated tests had been reported before the current work.

As will be shown in Chapter 6, imaging is needed in the procedure suggested by Law and Bower (2012) in order to localize sources detected by the bispectrum algorithm. Since our main goal is to test the bispectrum algorithm and prove it useful for LOFAR, we have to make sure that short-timescale imaging with high level of consistency is possible. In the early testing phase of the bispectrum algorithm, we also need images to check its per-formance, i.e. to examine if the pulses detected by the bispectra correspond to real point sources.

Due to all these considerations, at the beginning of the project presented in this the-sis we devoted special attention to imaging in order to test LOFAR’s capabilities on a 1-second timescale – the shortest cadence achievable with the LOFAR correlator. This chapter opens the experimental part of our research and presents the tests performed to achieve stable one-second images with LOFAR.

For the tests described below we use MSSS data, more precisely the calibrator field (targeted at 3C295) of observation ID (ObsID) L40022 from 2011-12-24. This is an 11-min observation as part of MSSS-LBA, which was performed with 41 stations (24 core, 9 re-mote, and 8 international) with longest baseline stretching to 1 100 km. For the analysis in this chapter only the four lowest-frequency subbands were used. Thus, all images discussed

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here have reference frequency of 30.4 MHz and bandwidth of 0.8 MHz.

The procedure used to obtain one-second images of the calibrator field is the following. After flagging, the subbands are calibrated independently with BBS. To achieve that we do neither the standard cross- nor the self-calibration (Section 2.5.2). Since we only work with calibrator fields we apply a single calibration step based on comparing the observa-tions to a model of the known sky. This is done by running the calibrate-stand-alone script (providing the MS name, a skymodel file, and a configuration file with predefined parameters). After calibration, the four subbands are combined into one measurement set using NDPPP. The combined MS is sliced into 660 1-second measurement sets which are finally imaged with CASA1_.

5.1 Flagging and averaging

Initially, each subband of the raw measurement sets was “preflagged”. This is done in order to exclude useless information from the observation. In our case, those were all autocorrelations since they do not carry phase information. After preflagging, the data were flagged with the AOFlagger. Both steps were performed in NDPPP by running the following configuration file:

msin=L40022 SAP002 SB### uv.MS msin.autoweight=true

msin.datacolumn=DATA msin.nchan=60

msin.startchan=2

msout=L40022 SAP002 SB### uv.MS.dppp1 msout.datacolumn=DATA steps=[preflag,aoflagger] uselogger=True preflag.corrtype=auto preflag.type=preflagger aoflagger.memoryperc=50 aoflagger.overlap=0 aoflagger.overlapperc=0 aoflagger.type=aoflagger,

where ### stands for the subband number, ranging from 160 to 163.

With this process 5% of all visibilities were flagged, which is very close to the expected fraction of corrupted data (Offringa et al. 2013). Later analysis showed that only 1% of

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the data is flagged for baselines shorter than 6 km.

Since we are using only 1-sec data for imaging, in order to increase the SNR we aver-aged the 60 frequency channels of each subband. This was done again in NDPPP with the help of the following parset:

msin=L40022 SAP002 SB### uv.MS.dppp1 msout=L40022 SAP002 SB### uv.MS.dppp2 steps=[avg]

avg.type=averager avg.freqstep=60 avg.timestep=1

5.2 Choice of imager

After calibration the measurement sets were sliced into separated 1-sec MS, each contain-ing only one integration of the original observation. In other words, the calibrated MS was divided into 660 individual MSs.

Since AWImager is specially developed for LOFAR data, we initially decided to use it for our short-timescale imaging. We started testing AWImager by trying to image 10-, 5-, and 1-sec data (corresponding to 10, 5, and 1 integrations, respectively). While the tool was easily producing dirty maps of 10 or 5 integrations, it was constantly crashing when 1-sec data was used. Our many attempts to cope with this problem led to failure, which came to prove that AWImager was incapable of imaging one-second snapshots.

Since the bug of AWImager was fixed only a few weeks before the submission of this thesis, throughout our data analysis we utilized CASA to produce LOFAR 1-sec images. This software was more robust and successfully treated data of just one integration. We used the following parameters for the CASA CLEAN procedure for obtaining the dirty images analyzed throughout our research:

selectdata = True uvrange = ’< 6km’ gridmode = ’widefield’ wprojplanes = 64 niter = 0 imsize = [512, 512]

cell = [’40arcsec’, ’40arcsec’] weighting = ’briggs’

LOFAR Transient Detection with a Bispectrum Algorithm

Anton Pannekoek

Master’s Thesis

LOFAR Transient Detection

with a Bispectrum Algorithm

Author:

Georgi Kokotanekov

Supervisors:

Dr. John Swinbank

Prof. Dr. Ralph A. M. J. Wijers

Acknowledgements

Contents

Chapter 1

Introduction

Chapter 2

Radio Astronomy Techniques

2.1

Single-dish antenna

2.2

Two-element and N-element narrow-band

inter-ferometer

2.3

Extended sources and the complex correlator

2.4

Earth-rotation aperture synthesis

2.5

Standard data processing and image acquisition

2.5.1

Flagging

2.5.2

Calibration

2.5.3

Gridding

2.5.4

Imaging

2.6

Complications of wide-field imaging

Chapter 3

LOFAR and MSSS

3.1

LOFAR

3.1.1

Science case

3.1.2

Technical challenges

3.1.3

Antennas

3.1.4

Stations

3.1.5

Data processing and storage (CEP and LTA)

3.1.6

Tools of the standard LOFAR imaging pipeline

3.2

MSSS

Chapter 4

Transients Key Science Project and

Transient Radio Sky

4.1

Transients Key Science Project (TKP)

4.1.1

Radio Sky Monitor (RSM)

4.1.2

Transient Pipeline (TraP)

4.2

LOFAR transient and variable sources

4.2.1

Long-timescale transients

4.2.2

Short-timescale transients

Chapter 5

Short-timescale Imaging with

LOFAR

5.1

Flagging and averaging

5.2

Choice of imager