Low Frequency Array Research Articles

A low-frequency study of linear polarization in radio galaxies

ABSTRACTRadio galaxies are linearly polarized – an important property that allows us to infer the properties of the magnetic field of the source and its environment. However, at low frequencies, Faraday rotation substantially depolarizes the emission, meaning that comparatively few polarized radio galaxies are known at low frequencies. Using the LOFAR Two-metre Sky Survey at 150 MHz and at a resolution of 20 arcsec, we select 342 radio galaxies brighter than 50 mJy and larger than 100 arcsec in angular size, of which 67 are polarized (18 per cent detection fraction). These are predominantly Fanaroff–Riley type II sources. The detection fraction increases with total flux density, and exceeds 50 per cent for sources brighter than 1 Jy. We compare the sources in our sample detected by the LOw Frequency ARray (LOFAR) to those also detected in NRAO VLA Sky Survey at 1400 MHz, and find that our selection bias towards bright radio galaxies drives a tendency for sources depolarized between 1400 and 150 MHz to have flatter spectra over that frequency range than those that remain polarized at 150 MHz. By comparing observed rotation measures with an analytic model, we find that we are preferentially sensitive to sources in low-mass environments. We also infer that sources with one polarized hotspot are inclined by a small angle to the line of sight, while sources with hotspots in both lobes lie in the plane of the sky. We conclude that low-frequency polarization in radio galaxies is related to a combination of environment, flux density, and jet orientation.

Finding the Ionospheric Fluctuations Reflection in the Pulsar Signals' Characteristics Observed with LOFAR.

Pulsars’ signals reaching the atmosphere can be considered being stable under certain assumptions. In such a case the ionosphere remains the main factor distorting signal from the extraterrestrial sources, particularly if we observe them at long radio waves. In this article we present the results of the analysis of relative peak flux changes for two selected pulsars: PSR J0332+5434 (B0329+54) and PSR J1509+5531 (B1508+55), observed with the long radio wave sensor (The PL612 Low Frequency Array (LOFAR) station in Bałdy), together with the analysis of Rate of TEC (ROT) parameter changes measured with the Global Navigation Satellite Systems (GNSS) sensor (IGS LAMA station (IGS: International GSSN Service)). The main objective of the work is to find if the rapid plasma density (observed with the Rate of Total Electron Content (TEC)) has a counterpart in the pulsar observation characteristics. This focuses the attention on ionosphere influence during pulsar investigations at low radio frequencies. Additionally, what was the aim of this work, our results give reasons for using pulsar signals from LOFAR together with GNSS data as multi instrumental ionosphere state probes. Our results show a clear anti-correlation between the ROT and the pulsar profile’s peak flux trends.

LOFAR observations of radio burst source sizes and scattering in the solar corona

Low frequency radio wave scattering and refraction can have a dramatic effect on the observed size and position of radio sources in the solar corona. The scattering and refraction is thought to be due to fluctuations in electron density caused by turbulence. Hence, determining the true radio source size can provide information on the turbulence in coronal plasma. However, the lack of high spatial resolution radio interferometric observations at low frequencies, such as with the LOw Frequency ARray (LOFAR), has made it difficult to determine the true radio source size and level of radio wave scattering. Here we directly fit the visibilities of a LOFAR observation of a Type IIIb radio burst with an elliptical Gaussian to determine its source size and position. This circumvents the need to image the source and then de-convolve LOFAR’s point spread function, which can introduce spurious effects to the source size and shape. For a burst at 34.76 MHz, we find full width at half maximum (FWHM) heights along the major and minor axes to be 18.8′ ± 0.1′ and 10.2′ ± 0.1′, respectively, at a plane of sky heliocentric distance of 1.75 R⊙. Our results suggest that the level of density fluctuations in the solar corona is the main cause of the scattering of radio waves, resulting in large source sizes. However, the magnitude of ε may be smaller than what has been previously derived in observations of radio wave scattering in tied-array images.

Gaussian process foreground subtraction and power spectrum estimation for 21 cm cosmology

ABSTRACT One of the primary challenges in enabling the scientific potential of 21 cm intensity mapping at the epoch of reionization (EoR) is the separation of astrophysical foreground contamination. Recent works have claimed that Gaussian process regression (GPR) can robustly perform this separation, particularly at low Fourier k wavenumbers where the EoR signal reaches its peak signal-to-noise ratio. We revisit this topic by casting GPR foreground subtraction (GPR-FS) into the quadratic estimator formalism, thereby putting its statistical properties on stronger theoretical footing. We find that GPR-FS can distort the window functions at these low k modes, which, without proper decorrelation, make it difficult to probe the EoR power spectrum. Incidentally, we also show that GPR-FS is in fact closely related to the widely studied inverse covariance weighting of the optimal quadratic estimator. As a case study, we look at recent power spectrum upper limits from the Low-Frequency Array (LOFAR) that utilized GPR-FS. We pay close attention to their normalization scheme, showing that it is particularly sensitive to signal loss when the EoR covariance is misestimated. This has possible ramifications for recent astrophysical interpretations of the LOFAR limits, because many of the EoR models ruled out do not fall within the bounds of the covariance models explored by LOFAR. Being more robust to this bias, we conclude that the quadratic estimator is a more natural framework for implementing GPR-FS and computing the 21 cm power spectrum.

Dispersion measure variability for 36 millisecond pulsars at 150 MHz with LOFAR

Context. Radio pulses from pulsars are affected by plasma dispersion, which results in a frequency-dependent propagation delay. Variations in the magnitude of this effect lead to an additional source of red noise in pulsar timing experiments, including pulsar timing arrays (PTAs) that aim to detect nanohertz gravitational waves. Aims. We aim to quantify the time-variable dispersion with much improved precision and characterise the spectrum of these variations. Methods. We use the pulsar timing technique to obtain highly precise dispersion measure (DM) time series. Our dataset consists of observations of 36 millisecond pulsars, which were observed for up to 7.1 yr with the LOw Frequency ARray (LOFAR) telescope at a centre frequency of ~150 MHz. Seventeen of these sources were observed with a weekly cadence, while the rest were observed at monthly cadence. Results. We achieve a median DM precision of the order of 10−5 cm−3 pc for a significant fraction of our sources. We detect significant variations of the DM in all pulsars with a median DM uncertainty of less than 2 × 10−4 cm−3 pc. The noise contribution to pulsar timing experiments at higher frequencies is calculated to be at a level of 0.1–10 μs at 1.4 GHz over a timespan of a few years, which is in many cases larger than the typical timing precision of 1 μs or better that PTAs aim for. We found no evidence for a dependence of DM on radio frequency for any of the sources in our sample. Conclusions. The DM time series we obtained using LOFAR could in principle be used to correct higher-frequency data for the variations of the dispersive delay. However, there is currently the practical restriction that pulsars tend to provide either highly precise times of arrival (ToAs) at 1.4 GHz or a high DM precision at low frequencies, but not both, due to spectral properties. Combining the higher-frequency ToAs with those from LOFAR to measure the infinite-frequency ToA and DM would improve the result.

Radio observations of HD 80606 near planetary periastron

Context. All the giant planets in the Solar System generate radio emission via electron cyclotron maser instability, giving rise most notably to Jupiter’s decametric emissions. An interaction with the solar wind is at least partially responsible for all of these Solar System electron cyclotron masers. HD 80606b is a giant planet with a highly eccentric orbit, leading to predictions that its radio emission may be enhanced substantially near periastron. Aims. This paper reports observations with the Low Frequency Array (LOFAR) of HD 80606b near its periastron in an effort to detect radio emissions generated by an electron cyclotron maser instability in the planet’s magnetosphere. Methods. The reported observations are at frequencies between 30 and 78 MHz, and they are distinguished from most previous radio observations of extrasolar planets by two factors: (i) they are at frequencies near 50 MHz, much closer to the frequencies at which Jupiter emits (ν < 40 MHz) and lower than most previously reported observations of extrasolar planets; and (ii) sensitivities of approximately a few millijanskys have been achieved, an order of magnitude or more below nearly all previous extrasolar planet observations below 100 MHz. Results. We do not detect any radio emissions from HD 80606b and use these observations to place new constraints on its radio luminosity. We also revisit whether the observations were conducted at a time when HD 80606b was super-Alfvénic relative to the host star’s stellar wind, which experience from the Solar System illustrates is a state in which an electron cyclotron maser emission can be sustained in a planet’s magnetic polar regions.

Reaching small scales with low-frequency imaging: applications to the Dark Ages.

The initial conditions for the density perturbations in the early Universe, which dictate the large-scale structure and distribution of galaxies we see today, are set during inflation. Measurements of primordial non-Gaussianity are crucial for distinguishing between different inflationary models. Current measurements of the matter power spectrum from the cosmic microwave background only constrain this on scales up to k ∼ 0.1 Mpc-1. Reaching smaller angular scales (higher values of k) can provide new constraints on non-Gaussianity. A powerful way to do this is by measuring the HI matter power spectrum at [Formula: see text]. In this paper, we investigate what values of k can be reached for the Low-Frequency Array (LOFAR), which can achieve [Formula: see text]1″ resolution at approximately 50 MHz. Combining this with a technique to isolate the spectrally smooth foregrounds to a wedge in [Formula: see text]-k⊥ space, we demonstrate what values of k we can feasibly reach within observational constraints. We find that LOFAR is approximately five orders of magnitude away from the desired sensitivity, for 10 years of integration time. This article is part of a discussion meeting issue 'Astronomy from the Moon: the next decades'.

Interpreting LOFAR 21-cm signal upper limits at z ≈ 9.1 in the context of high-z galaxy and reionization observations

ABSTRACT Using the latest upper limits on the 21-cm power spectrum at z ≈ 9.1 from the Low Frequency Array (LOFAR), we explore the regions of parameter space which are inconsistent with the data. We use 21cmmc, a Monte Carlo Markov chain sampler of 21cmfast which directly forward models the three dimensional (3D) cosmic 21-cm signal in a fully Bayesian framework. We use the astrophysical parametrization from 21cmfast, which includes mass-dependent star formation rates and ionizing escape fractions as well as soft-band X-ray luminosities to place limits on the properties of the high-z galaxies. Further, we connect the disfavoured regions of parameter space with existing observational constraints on the Epoch of Reionization such as ultra-violet (UV) luminosity functions, background UV photoionization rate, intergalactic medium (IGM) neutral fraction, and the electron scattering optical depth. We find that all models exceeding the 21-cm signal limits set by LOFAR at z ≈ 9.1 are excluded at ≳2σ by other probes. Finally, we place limits on the IGM spin temperature from LOFAR, disfavouring at 95 per cent confidence spin temperatures below ∼2.6 K across an IGM neutral fraction range of $0.15 \lesssim \bar{x}_{\rm H\, \rm {\small I}} \lesssim 0.6$. Note, these limits are only obtained from 141 h of data in a single redshift bin. With tighter upper limits, across multiple redshift bins expected in the near future from LOFAR, more viable models will be ruled out. Our approach demonstrates the potential of forward modelling tools such as 21cmmc in combining 21-cm observations with other high-z probes to constrain the astrophysics of galaxies.

LOFAR detection of a low-power radio halo in the galaxy cluster Abell 990

ABSTRACT Radio haloes are extended (∼Mpc), steep spectrum sources found in the central region of dynamically disturbed clusters of galaxies. Only a handful of radio haloes have been reported to reside in galaxy clusters with a mass $M_{500}\lesssim 5\times 10^{14}\, \mathrm{ M}_\odot$. In this paper, we present a LOw Frequency ARray (LOFAR) 144 MHz detection of a radio halo in the galaxy cluster Abell 990 with a mass of $M_{500}=(4.9\pm 0.3)\times 10^{14}\, \mathrm{ M}_\odot$. The halo has a projected size of ${\sim} 700\, {\rm kpc}$ and a flux density of $20.2\pm 2.2\, {\rm mJy}$ or a radio power of $1.2\pm 0.1\times 10^{24}\, {\rm W\, Hz}^{-1}$ at the cluster redshift (z = 0.144) that makes it one of the two haloes with the lowest radio power detected to date. Our analysis of the emission from the cluster with Chandra archival data using dynamical indicators shows that the cluster is not undergoing a major merger but is a slightly disturbed system with a mean temperature of $5\, {\rm keV}$. The low X-ray luminosity of $L_{\mathrm{ X}}=(3.66\pm 0.08)\times 10^{44}\, {\rm erg\, s}^{-1}$ in the 0.1–2.4 keV band implies that the cluster is one of the least luminous systems known to host a radio halo. Our detection of the radio halo in Abell 990 opens the possibility of detecting many more haloes in poorly explored less massive clusters with low-frequency telescopes such as LOFAR, Murchison Widefield Array (MWA, Phase II), and upgraded Giant Metrewave Radio Telescope (uGMRT).

The great Kite in the sky: A LOFAR observation of the radio source in Abell 2626

Context.The radio source at the center of the galaxy cluster Abell 2626, also known as the Kite, stands out for its unique morphology composed of four symmetric arcs. Previous studies have probed the properties of this source at different frequencies and its interplay with the surrounding thermal plasma, but the puzzle of its origin is still unsolved.Aims.We use a new LOw-Frequency ARray (LOFAR) observation from the LOFAR Two-meter Sky Survey at 144 MHz to investigate the origin of the Kite.Methods.We present a detailed analysis of the new radio data, which we combined with archival radio and X-ray observations. We produced a new, resolved spectral index map of the source with a resolution of 7″ and we studied the spatial correlation of radio and X-ray emission to investigate the interplay between thermal and nonthermal plasma.Results.The new LOFAR data changed our view of the Kite because we discovered two steep-spectrum (α < −1.5) plumes of emission connected to the arcs. The spectral analysis shows, for the first time, a spatial trend of the spectrum along the arcs with evidence of curved synchrotron spectra and a spatial correlation with the X-ray surface brightness. On the basis of our results, we propose that the Kite was originally an X-shaped radio galaxy whose fossil radio plasma, after the end of the activity of the central active galactic nucleus, has been compressed as a consequence of motions of the thermal plasma encompassing the galaxy. The interplay between the compression and advection of the fossil plasma, with the restarting of the nuclear activity of the central galaxy, could have enhanced the radio emission of the fossil plasma producing the arcs of the Kite. We also present the first, low-frequency observation of a jellyfish galaxy in the same field, in which we detect extended, low-frequency emission without a counterpart at higher frequencies.

Direct Radio Discovery of a Cold Brown Dwarf

Abstract Magnetospheric processes seen in gas giants such as aurorae and circularly polarized cyclotron maser radio emission have been detected from some brown dwarfs. However, previous radio observations targeted known brown dwarfs discovered via their infrared emission. Here we report the discovery of BDR J1750+3809, a circularly polarized radio source detected around 144 MHz with the Low-Frequency Array (LOFAR) telescope. Follow-up near-infrared photometry and spectroscopy show that BDR J1750+3809 is a cold methane dwarf of spectral type T6.5 ± 1 at a distance of . The quasi-quiescent radio spectral luminosity of BDR J1750+3809 is ≈5 × 1015 erg s−1 Hz−1, which is over two orders of magnitude larger than that of the known population of comparable spectral type. This could be due to a preferential geometric alignment or an electrodynamic interaction with a close companion. In addition, as the emission is expected to occur close to the electron gyrofrequency, the magnetic field strength at the emitter site in BDR J1750+3809 is B ≳ 25 G, which is comparable to planetary-scale magnetic fields. Our discovery suggests that low-frequency radio surveys can be employed to discover substellar objects that are too cold to be detected in infrared surveys.

The Significance of Low-frequency Interferometric Observations for the GPS Pulsar Flux Estimation: The Case of J1740+1000

Abstract In this paper we present recent Low Frequency Array observations of the pulsar J1740+1000. We confirm that its spectrum has a turnover at 260 MHz, which is unusual for a typical pulsar. We argue that in this case interferometric imaging provides more accurate pulsar flux estimates than other, more traditional, means such as beamformed observations. We conclude that existing calibration and imaging techniques can be used for a more comprehensive study of the influence of the interstellar medium on the point-like sources at very low frequencies in the near future.

Alternating Current Poling on Sliver-Mode Rhombohedral Pb(Mg1/3nb2/3)O3-Pbtio3 Single Crystals

Sliver-mode 0.73Pb(Mg1/3Nb2/3)O3-0.27PbTiO3 single crystals were poled by alternating current poling (ACP) along [001] direction for low-frequency transducer applications. Under ACP with optimized conditions, dielectric permittivity and piezoelectric coefficient are 36% higher than those under traditional direct current poling. The piezoresponse force microscopy observation and phase-field simulation show that domain morphology changed from ‘4R’ configuration into ‘2R’ one quickly and finally became stable as stripe-like layered structures with near-parallel 109° domain walls, along with the correlation between the domain structure and the coercive field. These findings on the effect and mechanism of ACP will help develop advanced low-frequency single crystal transducer arrays.

The LOFAR view of FR 0 radio galaxies

We explore the low-frequency radio properties of the sources in the Fanaroff-Riley class 0 catalog (FR0CAT) as seen by the Low-Frequency ARray (LOFAR) observations at 150 MHz. This sample includes 104 compact radio active galactic nuclei (AGN) associated with nearby (z < 0.05) massive early-type galaxies. Sixty-six FR0CAT sources are in the sky regions observed by LOFAR and all of them are detected, usually showing point-like structures with sizes of ≲3–6 kpc. However, 12 FR 0s present resolved emission of low surface brightness, which contributes between 5% and 40% of the total radio power at 150 MHz, usually with a jetted morphology extending between 15 and 50 kpc. No extended emission is detected around the other FR 0s, with a typical luminosity limit of ≲5 × 1022 W Hz−1 over an area of 100 kpc × 100 kpc. The spectral slopes of FR 0s between 150 MHz and 1.4 GHz span a broad range (−0.7 ≲ α ≲ 0.8) with a median value of ᾱ ∼ 0.1; 20% of them have a steep spectrum (α ≳ 0.5), which is an indication of the presence of substantial extended emission confined within the spatial resolution limit. The fraction of FR 0s showing evidence for the presence of jets, by including both spectral and morphological information, is at least ∼40%. This study confirms that FR 0s and FR Is can be interpreted as two extremes of a continuous population of jetted sources, with the FR 0s representing the low end in size and radio power.

Reaching thermal noise at ultra-low radio frequencies

Context. Ultra-low frequency observations (< 100 MHz) are particularly challenging because they are usually performed in a low signal-to-noise ratio regime due to the high sky temperature and because of ionospheric disturbances whose effects are inversely proportional to the observing frequency. Nonetheless, these observations are crucial for studying the emission from low-energy populations of cosmic rays. Aims. We aim to obtain the first thermal-noise limited (∼1.5 mJy beam−1) deep continuum radio map using the Low Frequency Array’s Low Band Antenna (LOFAR LBA) system. Our demonstration observation targeted the galaxy cluster RX J0603.3+4214 (known as the Toothbrush cluster). We used the resulting ultra-low frequency (39–78 MHz) image to study cosmic-ray acceleration and evolution in the post shock region considering the presence of a radio halo. Methods. We describe the data reduction we used to calibrate LOFAR LBA observations. The resulting image was combined with observations at higher frequencies (LOFAR 150 MHz and VLA 1500 MHz) to extract spectral information. Results. We obtained the first thermal-noise limited image from an observation carried out with the LOFAR LBA system using all Dutch stations at a central frequency of 58 MHz. With eight hours of data, we reached an rms noise of 1.3 mJy beam−1 at a resolution of 18″ × 11″. Conclusions. The procedure we developed is an important step towards routine high-fidelity imaging with the LOFAR LBA. The analysis of the radio spectra shows that the radio relic extends to distances of 800 kpc downstream from the shock front, larger than what is allowed by electron cooling time. Furthermore, the shock wave started accelerating electrons already at a projected distance of < 300 kpc from the crossing point of the two clusters. These results may be explained by electrons being re-accelerated downstream by background turbulence, possibly combined with projection effects with respect to the radio halo.

Alignment in the orientation of LOFAR radio sources

Various studies have laid claim to finding an alignment of the polarization vectors or radio jets of active galactic nuclei over large distances, but these results have proven controversial and so far, there is no clear explanation for this observed alignment. To investigate this case further, we tested the hypothesis that the position angles of radio galaxies are randomly oriented in the sky by using data from the Low-Frequency Array (LOFAR) Two-metre Sky Survey (LoTSS). A sample of 7555 double-lobed radio galaxies was extracted from the list of 318 520 radio sources in the first data release of LoTSS at 150 MHz. We performed statistical tests for uniformity of the two-dimensional (2D) orientations for the complete 7555 source sample. We also tested the orientation uniformity in three dimensions (3D) for the 4212 source sub-sample with photometric or spectroscopic redshifts. Our sample shows a significant deviation from uniformity (p-value < 10−5) in the 2D analysis at angular scales of about four degrees, mainly caused by sources with the largest flux densities. No significant alignment was found in the 3D analysis. Although the 3D analysis has access to fewer sources and suffers from uncertainties in the photometric redshift, the lack of alignment in 3D points towards the cause of the observed effect being unknown systematics or biases that predominantly affect the brightest sources, although this has yet to be demonstrated irrefutably and should be the subject of subsequent studies.

A Review of Recent Solar Type III Imaging Spectroscopy

Solar type III radio bursts are the most common impulsive radio signatures from the Sun, stimulated by electron beams travelling through the solar corona and solar wind. Type III burst analysis provides us with a powerful remote sensing diagnostic tool for both the electron beams and the plasma they travel through. Advanced radio telescopes like the LOw Frequency ARray (LOFAR), the Murchison Widefield Array (MWA) and the Karl G. Jansky Very Large Array (VLA) are now giving us type III imaging spectroscopy with orders of magnitude better resolution than before. In this review, the recent observational progress provided by the new observations is discussed, including how this enhanced resolution has facilitated study of type III burst fine structure. The new results require more detailed theoretical understanding of how type III bursts are produced. Consequently, recent numerical work is discussed which improves our understanding of how electron beams, Langmuir waves and radio waves evolve through the turbulent solar system plasma. Looking towards the future, some theoretical challenges are discussed that we need to overcome on our quest to understand type III bursts and the electron beams that drive them.

FEEDBACK: a SOFIA Legacy Program to Study Stellar Feedback in Regions of Massive Star Formation

FEEDBACK is a SOFIA (Stratospheric Observatory for Infrared Astronomy) legacy program dedicated to study the interaction of massive stars with their environment. It performs a survey of 11 galactic high mass star-forming regions in the 158 μm (1.9 THz) line of [C ii] and the 63 μm (4.7 THz) line of [O i]. We employ the 14 pixel Low Frequency Array and 7 pixel High Frequency Array upGREAT heterodyne instrument to spectrally resolve (0.24 MHz) these far-infrared fine structure lines. With a total observing time of 96h, we will cover ∼6700 arcmin2 at 14.″1) angular resolution for the [C ii] line and 6.″3 for the [O i] line. The observations started in spring 2019 (Cycle 7). Our aim is to understand the dynamics in regions dominated by different feedback processes from massive stars such as stellar winds, thermal expansion, and radiation pressure, and to quantify the mechanical energy injection and radiative heating efficiency. This is an important science topic because feedback of massive stars on their environment regulates the physical conditions and sets the emission characteristics in the interstellar medium (ISM), influences the star formation activity through molecular cloud dissolution and compression processes, and drives the evolution of the ISM in galaxies. The [C ii] line provides the kinematics of the gas and is one of the dominant cooling lines of gas for low to moderate densities and UV fields. The [O i] line traces warm and high-density gas, excited in photodissociations regions with a strong UV field or by shocks. The source sample spans a broad range in stellar characteristics from single OB stars, to small groups of O stars, to rich young stellar clusters, to ministarburst complexes. It contains well-known targets such as Aquila, the Cygnus X region, M16, M17, NGC7538, NGC6334, Vela, and W43 as well as a selection of H ii region bubbles, namely RCW49, RCW79, and RCW120. These [C ii] maps, together with the less explored [O i] 63 μm line, provide an outstanding database for the community. They will be made publically available and will trigger further studies and follow-up observations.

Vibration Mode Analysis for a Suspension Bridge by Using Low-Frequency Cantilever-Based FBG Accelerometer Array

In this article, we present a vibration measurement system based on low-frequency cantilever-based fiber Bragg grating accelerometers (CFAs) for a suspension bridge. Each accelerometer has an end-loaded cantilever beam, specifically tailored to achieve a uniform sensitivity for a frequency range of 0-4 Hz, a suitable detection range for the vibration analysis. In the field test, seven CFAs were installed at specific positions along the deck of a 110-m-long suspension bridge for synchronous multipoint vibration measurements. The reflection spectra of the CFA array were recorded and processed using the pseudo-high-resolution scheme to improve the signal quality and measurement accuracy. Three natural vibration frequencies: 1.15, 1.54, and 3.17 Hz have been identified from the measurement. Following that, the acquired time-domain signals were processed by a digital bandpass filter to retrieve the waveform at each natural frequency to determine the corresponding mode shapes. The results are in agreement with the phase difference between the frequency domain signal for each natural frequency. This investigation has shown the feasibility of the proposed measurement system for determining the mode shapes and dynamic frequency analysis of a suspension bridge. It is a potential method for structural health monitoring for other similar civil structures.

Tools21cm: A python package to analyse the large-scale 21-cm signal from the Epoch of Reionization and Cosmic Dawn

Giri et al., (2020). Tools21cm: A python package to analyse the large-scale 21-cm signal from the Epoch of Reionization and Cosmic Dawn. Journal of Open Source Software, 5(52), 2363, https://doi.org/10.21105/joss.02363