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The turbulent ionosphere causes phase shifts to incoming radio waves on a broad range of temporal and spatial scales. When an interferometer is not sufficiently calibrated for the direction-dependent ionospheric effects, the time-varying phase shifts can cause the signal to decorrelate. The ionosphere's influence over various spatiotemporal scales introduces a baseline-dependent effect on the interferometric array. We study the impact of baseline-dependent decorrelation on high-redshift observations with the Low Frequency Array (LOFAR). Datasets with a range of ionospheric corruptions are simulated using a thin-screen ionosphere model, and calibrated using the state-of-the-art LOFAR Epoch of Reionisation pipeline. For the first time ever, we show the ionospheric impact on various stages of the calibration process including an analysis of the transfer of gain errors from longer to shorter baselines using realistic end-to-end simulations. We find that direction-dependent calibration for source subtraction leaves excess power of up to two orders of magnitude above the thermal noise at the largest spectral scales in the cylindrically averaged auto-power spectrum under normal ionospheric conditions. However, we demonstrate that this excess power can be removed through Gaussian process regression, leaving no excess power above the ten per cent level for a $5~$km diffractive scale. We conclude that ionospheric errors, in the absence of interactions with other aggravating effects, do not constitute a dominant component in the excess power observed in LOFAR Epoch of Reionisation observations of the North Celestial Pole. Future work should therefore focus on less spectrally smooth effects, such as beam modelling errors., Comment: 22 pages, 20 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS)

Current radio interferometers output multi-petabyte-scale volumes of data per year making the storage, transfer, and processing of this data a sizeable challenge. This challenge is expected to grow with the next-generation telescopes such as the Square Kilometre Array. Lossy compression of interferometric data post-correlation can abate this challenge. However, since high-redshift 21-cm studies impose strict precision requirements, the impact of such lossy data compression on the 21-cm signal power spectrum statistic should be understood. We apply Dysco visibility compression, a technique to normalize and quantize specifically designed for radio interferometric data. We establish the level of the compression noise in the power spectrum in comparison to the thermal noise as well as its coherency behavior. Finally, for optimal compression results, we compare the compression noise obtained from different compression settings to a nominal 21-cm signal power. From a single night of observation, we find that the noise introduced due to the compression is more than five orders of magnitude lower than the thermal noise level in the power spectrum. The noise does not affect calibration. The compression noise shows no correlation with the sky signal and has no measurable coherent component. The level of compression error in the power spectrum ultimately depends on the compression settings. Dysco visibility compression is found to be of insignificant concern for 21-cm power spectrum studies. Hence, data volumes can be safely reduced by factors of $\sim 4$ and with insignificant bias to the final power spectrum. Data from SKA-low will likely be compressible by the same factor as LOFAR, owing to the similarities of the two instruments. The same technique can be used to compress data from other telescopes, but a small adjustment of the compression parameters might be required., Comment: 12 pages, 9 figures, and 3 tables; submitted to Astronomy and Astrophysics (A&A)

One of the main obstacles preventing the detection of the redshifted 21-cm signal from neutral hydrogen in the early Universe is the astrophysical foreground emission, which is several orders of magnitude brighter than the signal. The foregrounds, due to their smooth spectra, are expected to predominantly occupy a region in the cylindrical power spectrum known as the foreground wedge. However, the conventional equations describing the extent of the foreground wedge are derived under a flat-sky approximation. This assumption breaks down for tracking wide-field instruments, thus rendering these equations inapplicable in these situations. In this paper, we derive equations for the full sky foreground wedge and show that the foregrounds can potentially extend far beyond what the conventional equations suggest. We also derive the equations that describe a specific bright source in the cylindrical power spectrum space. The validity of both sets of equations is tested against numerical simulations. Many current and upcoming interferometers (e.g., LOFAR, NenuFAR, MWA, SKA) are wide-field phase-tracking instruments. These equations give us new insights into the nature of foreground contamination in the cylindrical power spectra estimated using wide-field instruments. Additionally, they allow us to accurately associate features in the power spectrum to foregrounds or instrumental effects. The equations are also important for correctly selecting the "EoR window" for foreground avoidance analyses, and for planning 21-cm observations. In future analyses, it is recommended to use these updated horizon lines to indicate the foreground wedge in the cylindrical power spectrum accurately. The new equations for generating the updated wedge lines are made available in a Python library, pslines., Comment: 21 pages, 13 figures, and 2 tables; submitted to Astronomy and Astrophysics (A&A)

The upcoming Square Kilometer Array (SKA) will set a new standard regarding data volume generated by an astronomical instrument, which is likely to challenge widely adopted data-analysis tools that scale inadequately with the data size. The aim of this study is to develop a new source detection and characterization method for massive radio astronomical datasets based on modern deep-learning object detection techniques. For this, we seek to identify the specific strengths and weaknesses of this type of approach when applied to astronomical data. We introduce YOLO-CIANNA, a highly customized deep-learning object detector designed specifically for astronomical datasets. In this paper, we present the method and describe all the elements introduced to address the specific challenges of radio astronomical images. We then demonstrate the capabilities of this method by applying it to simulated 2D continuum images from the SKA observatory Science Data Challenge 1 (SDC1) dataset. Using the SDC1 metric, we improve the challenge-winning score by +139% and the score of the only other post-challenge participation by +61%. Our catalog has a detection purity of 94% while detecting 40 to 60% more sources than previous top-score results, and exhibits strong characterization accuracy. The trained model can also be forced to reach 99% purity in post-process and still detect 10 to 30% more sources than the other top-score methods. It is also computationally efficient, with a peak prediction speed of 500 images of 512x512 pixels per second on a single GPU. YOLO-CIANNA achieves state-of-the-art detection and characterization results on the simulated SDC1 dataset and is expected to transfer well to observational data from SKA precursors., Comment: 42 pages. Custom layout edit of the corresponding in press A&A paper

The critical behaviour of laser-induced changes in magnetic ordering is studied experimentally in two-dimensional zigzag antiferromagnets $XY$-like NiPS$_3$ and Ising-like FePS$_3$. To examine laser-induced dynamics in flakes of these compounds, we employ time-resolved exchange linear dichroism effect sensitive to zigzag magnetic ordering and independent of the orientation of the antiferromagnetic vector. In both compounds laser excitation in the vicinity of the absorption edge induces partial quenching of the antiferromagnetic ordering manifested by exchange linear dichroism reduction. The amplitude of the effect varies with temperature as the derivative of the antiferromagnetic vector and exhibits a critical behaviour with the exponents corresponding to $XY$- and Ising-models for NiPS$_3$ and FePS$_3$, respectively. Critical slowing down of the demagnetization in the vicinity of N\'eel temperature is found, however, only in FePS$_3$. In contrast, the increase of the demagnetization time near the ordering temperature in NiPS$_3$ is minor. We show that the difference in the demagnetization times correlates well with the spin specific heat in both compounds. Beyond the range of slowing down, the demagnetization times in NiPS$_3$ and FePS$_3$ are comparable, about 5 - 10 ps, and are longer than those reported earlier for CoPS$_3$ and considerably shorter than for MnPS$_3$. This points to the importance of the unquenched angular momentum of transition-metal ions in laser-induced demagnetization process., Comment: 12 pages, 6 figures

The redshifted 21 cm signal from neutral hydrogen is a direct probe of the physics of the early universe and has been an important science driver of many present and upcoming radio interferometers. In this study we use a single night of observations with the New Extension in Nan\c{c}ay Upgrading LOFAR (NenuFAR) to place upper limits on the 21 cm power spectrum from cosmic dawn at a redshift of $z$ = 20.3. NenuFAR is a new low-frequency radio interferometer, operating in the 10-85 MHz frequency range, currently under construction at the Nan\c{c}ay Radio Observatory in France. It is a phased array instrument with a very dense uv coverage at short baselines, making it one of the most sensitive instruments for 21 cm cosmology analyses at these frequencies. Our analysis adopts the foreground subtraction approach, in which sky sources are modeled and subtracted through calibration and residual foregrounds are subsequently removed using Gaussian process regression. The final power spectra are constructed from the gridded residual data cubes in the uv plane. Signal injection tests are performed at each step of the analysis pipeline, the relevant pipeline settings are optimized to ensure minimal signal loss, and any signal suppression is accounted for through a bias correction on our final upper limits. We obtain a best 2$\sigma$ upper limit of $2.4\times 10^7$ $\text{mK}^{2}$ at $z$ = 20.3 and $k$ = 0.041 $h\,\text{cMpc}^{-1}$. We see a strong excess power in the data, making our upper limits two orders of magnitude higher than the thermal noise limit. We investigate the origin and nature of this excess power and discuss further improvements to the analysis pipeline that can potentially mitigate it and consequently allow us to reach thermal noise sensitivity when multiple nights of observations are processed in the future., Comment: 27 pages, 21 figures, and 6 tables; accepted for publication in Astronomy and Astrophysics (A&A); language edits implemented; typos corrected

Measurement of the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn (CD) and Epoch of Reionisation (EoR) promises to unveil a wealth of information about the astrophysical processes during the first billion years of evolution of the universe. The AARTFAAC Cosmic Explorer (ACE) utilises the AARTFAAC wide-field imager of LOFAR to measure the power spectrum of the intensity fluctuations of the redshifted 21-cm signal from the CD at z~18. The RFI from various sources contaminates the observed data and it is crucial to exclude the RFI-affected data in the analysis for reliable detection. In this work, we investigate the impact of non-ground-based transient RFI using cross-power spectra and cross-coherence metrics to assess the correlation of RFI over time and investigate the level of impact of transient RFI on the ACE 21-cm power spectrum estimation. We detected moving sky-based transient RFI sources that cross the field of view within a few minutes and appear to be mainly from aeroplane communication beacons at the location of the LOFAR core in the 72-75 MHz band, by inspecting filtered images. This transient RFI is mostly uncorrelated over time and is only expected to dominate over the thermal noise for an extremely deep integration time of 3000 hours or more with a hypothetical instrument that is sky temperature dominated at 75 MHz. We find no visible correlation over different k-modes in Fourier space in the presence of noise for realistic thermal noise scenarios. We conclude that the sky-based transient RFI from aeroplanes, satellites and meteorites at present does not pose a significant concern for the ACE analyses at the current level of sensitivity and after integrating over the available 500 hours of observed data. However, it is crucial to mitigate or filter such transient RFI for more sensitive experiments aiming for significantly deeper integration., Comment: 13 pages, 9 figures, and 3 tables; accepted for publication in Astronomy and Astrophysics (A&A)

We present a new method, called "forced-spectrum fitting", for physically-based spectral modelling of radio sources during deconvolution. This improves upon current common deconvolution fitting methods, which often produce inaccurate spectra. Our method uses any pre-existing spectral index map to assign spectral indices to each model component cleaned during the multi-frequency deconvolution of WSClean, where the pre-determined spectrum is fitted. The component magnitude is evaluated by performing a modified weighted linear least-squares fit. We test this method on a simulated LOFAR-HBA observation of the 3C196 QSO and a real LOFAR-HBA observation of the 4C+55.16 FRI galaxy. We compare the results from the forced-spectrum fitting with traditional joined-channel deconvolution using polynomial fitting. Because no prior spectral information was available for 4C+55.16, we demonstrate a method for extracting spectral indices in the observed frequency band using "clustering". The models generated by the forced-spectrum fitting are used to improve the calibration of the datasets. The final residuals are comparable to existing multi-frequency deconvolution methods, but the output model agrees with the provided spectral index map, embedding correct spectral information. While forced-spectrum fitting does not solve the determination of the spectral information itself, it enables the construction of accurate multi-frequency models that can be used for wide-band calibration and subtraction., Comment: 17 pages, 9 figures, 5 tables. Accepted for publication in MNRAS

Detecting the 21-cm signal from the Epoch of Reionisation (EoR) is challenging due to the strong astrophysical foregrounds, ionospheric effects, radio frequency interference and instrumental effects. Understanding and calibrating these effects are crucial for the detection. In this work, we introduce a newly developed direction-dependent (DD) calibration algorithm DDECAL and compare its performance with an existing algorithm, SAGECAL, in the context of the LOFAR-EoR 21-cm power spectrum experiment. In our data set, the North Celestial Pole (NCP) and its flanking fields were observed simultaneously. We analyse the NCP and one of its flanking fields. The NCP field is calibrated by the standard pipeline, using SAGECAL with an extensive sky model and 122 directions, and the flanking field is calibrated by DDECAL and SAGECAL with a simpler sky model and 22 directions. Additionally, two strategies are used for subtracting Cassiopeia A and Cygnus A. The results show that DDECAL performs better at subtracting sources in the primary beam region due to the application of a beam model, while SAGECAL performs better at subtracting Cassiopeia A and Cygnus A. This indicates that including a beam model during DD calibration significantly improves the performance. The benefit is obvious in the primary beam region. We also compare the 21-cm power spectra on two different fields. The results show that the flanking field produces better upper limits compared to the NCP in this particular observation. Despite the minor differences between DDECAL and SAGECAL due to the beam application, we find that the two algorithms yield comparable 21-cm power spectra on the LOFAR-EoR data after foreground removal. Hence, the current LOFAR-EoR 21-cm power spectrum limits are not likely to depend on the DD calibration method., Comment: 28 pages, 14 figures, accepted for publication in A&A; a few equations in section 3 were corrected in this version

The detection of the 21 cm signal of neutral hydrogen from the Epoch of Reionization (EoR) is challenging due to bright foreground sources, radio frequency interference (RFI), the ionosphere, and instrumental effects. Even after correcting for these effects in the calibration step and applying foreground removal techniques, the remaining residuals in the observed 21 cm power spectra are still above the thermal noise, which is referred to as the "excess variance." We study potential causes of this excess variance based on 13 nights of data obtained with the Low-Frequency Array (LOFAR). We focused on the impact of gain errors, the sky model, and ionospheric effects on the excess variance by correlating the relevant parameters such as the gain variance over time or frequency, local sidereal time (LST), diffractive scale, and phase structure-function slope with the level of excess variance. Our analysis shows that excess variance has an LST dependence, which is related to the power from the sky. And the simulated Stokes I power spectra from bright sources and the excess variance show a similar progression over LST with the minimum power appearing at LST bin 6h to 9h. This LST dependence is also present in sky images of the residual Stokes I of the observations. In very-wide sky images, we demonstrate that the extra power comes exactly from the direction of bright and distant sources Cassiopeia A and Cygnus A with the array beam patterns. These results suggest that the level of excess variance in the 21 cm signal power spectra is related to sky effects and, hence, it depends on LST. In particular, very bright and distant sources such as Cassiopeia A and Cygnus A can dominate the effect. This is in line with earlier studies and offers a path forward toward a solution since the correlation between the sky-related effects and the excess variance is non-negligible., Comment: 29 pages, 14 figures, accepted for publication in A&A

Aims: Contamination from bright diffuse Galactic thermal and non-thermal radio emission poses crucial challenges in experiments aiming to measure the 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionization. If not included in calibration, this diffuse emission can severely impact the analysis and signal extraction in 21-cm experiments. We examine large-scale diffuse Galactic emission at 122~MHz, around the North Celestial Pole, using the AARTFAAC-HBA system. Methods: In this pilot project, we present the first-ever wide-field image produced with a single sub-band of the data recorded with the AARTFAAC-HBA. We demonstrate two methods: multiscale CLEAN and shapelet decomposition, to model the diffuse emission revealed in the image. We use angular power spectrum metrics to quantify different components of the emission and compare the performance of the two diffuse structure modelling approaches. Results: We observe that the point sources dominate the angular power spectrum ($\ell(\ell+1)C_{\ell}/2\pi\equiv \Delta^2(\ell)$) of the emission in the field on scales $\ell\gtrsim 60$ ($\lesssim 3$~degree). The angular power spectrum after subtraction of compact sources is flat within $20\lesssim \ell \lesssim200$ range, suggesting that the residual power is dominated by the diffuse emission on scales $\ell\lesssim200$. The residual diffuse emission has a brightness temperature variance of $\Delta^2_{\ell=180} = (145.64 \pm 13.61)~{\rm K}^2$ at 122~MHz on angular scales of 1~degree, and is consistent with a power-law following $C_{\ell}\propto \ell^{-2.0}$ in $20\lesssim \ell \lesssim200$ range. We also find that, in the current setup, the multiscale CLEAN is suitable to model the compact and diffuse structures on a wide range of angular scales, whereas the shapelet decomposition method better models the large scales, which are of the order of a few degrees and wider., Comment: 11 pages, 9 figures, accepted (A&A)

We investigate systematic effects in direction dependent gain calibration in the context of the Low-Frequency Array (LOFAR) 21-cm Epoch of Reionization (EoR) experiment. The LOFAR EoR Key Science Project aims to detect the 21-cm signal of neutral hydrogen on interferometric baselines of $50-250 \lambda$. We show that suppression of faint signals can effectively be avoided by calibrating these short baselines using only the longer baselines. However, this approach causes an excess variance on the short baselines due to small gain errors induced by overfitting during calibration. We apply a regularised expectation-maximisation algorithm with consensus optimisation (sagecal-co) to real data with simulated signals to show that overfitting can be largely mitigated by penalising spectrally non-smooth gain solutions during calibration. This reduces the excess power with about a factor 4 in the simulations. Our results agree with earlier theoretical analysis of this bias-variance trade off and support the gain-calibration approach to the LOFAR 21-cm signal data., Comment: This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review

The exploration of the Cosmic Dawn, the period of the Universe during which the first stars and galaxies were formed, is one of the last frontiers of modern astronomy and cosmology. The redshifted 21-cm line emission from neutral hydrogen is a unique probe and can open this era for astrophysical and cosmological studies. The tentative detection of the 21-cm global signal by the EDGES team at $z \sim 17$ underlines the need for an interferometric detection of this signal to discriminate between the numerous models trying to explain this unexpected discovery. The NenuFAR Cosmic-Dawn Key-Science Program aims to perform this detection in the redshift range $z \sim 15 - 31$ with a novel SKA precursor, the NenuFAR radio telescope located at the Station de Radioastronomie de Nan\c{c}ay and that started operating in 2019. Due to its compactness it is particularly sensitive to the large scale of the 21-cm signal. Only 100 hours of observation are needed to reach the level of the most extreme models, while 1000 hours are needed for the more standard models. Observations have already started, accumulating to almost 500 hours on the North Celestial Pole field. In this contribution, we introduce the project, our first results and the developments in calibration and RFI mitigation specific to this new instrument., Comment: 4 pages, SF2A 2021 proceeding

We investigate the role of domain walls in the ultrafast magnon dynamics of an antiferromagnetic NiO single crystal in a pump-probe experiment with variable pump photon energy. Analysing the amplitude of the energy-dependent photo-induced ultrafast spin dynamics, we detect a yet unreported coupling between the material's characteristic THz- and a GHz-magnon modes. We explain this unexpected coupling between two orthogonal eigenstates of the corresponding Hamiltonian by modelling the magneto-elastic interaction between spins in different domains. We find that such interaction, in the non-linear regime, couples the two different magnon modes via the domain walls and it can be optically exploited via the exciton-magnon resonance., Comment: 6 pages, 4 figures

We performed temperature-dependent optical pump - THz emission measurements in Y3Fe5O12 (YIG)|Pt from 5 K to room temperature in the presence of an externally applied magnetic field. We study the temperature dependence of the spin Seebeck effect and observe a continuous increase as temperature is decreased, opposite to what is observed in electrical measurements where the spin Seebeck effect is suppressed as 0K is approached. By quantitatively analysing the different contributions we isolate the temperature dependence of the spin-mixing conductance and observe features that are correlated to the bands of magnon spectrum in YIG., Comment: 11 pages, 9 figures

We compare various foreground removal techniques that are being utilised to remove bright foregrounds in various experiments aiming to detect the redshifted 21cm signal of neutral hydrogen from the Epoch of Reionization. In this work, we test the performance of removal techniques (FastICA, GMCA, and GPR) on 10 nights of LOFAR data and investigate the possibility of recovering the latest upper limit on the 21cm signal. Interestingly, we find that GMCA and FastICA reproduce the most recent 2$\sigma$ upper limit of $\Delta^2_{21} <$ (73)$^2$ mK$^2$ at $k=0.075~ h \mathrm{cMpc}^{-1}$, which resulted from the application of GPR. We also find that FastICA and GMCA begin to deviate from the noise-limit at \textit{k}-scales larger than $\sim 0.1 ~h \mathrm{cMpc}^{-1}$. We then replicate the data via simulations to see the source of FastICA and GMCA's limitations, by testing them against various instrumental effects. We find that no single instrumental effect, such as primary beam effects or mode-mixing, can explain the poorer recovery by FastICA and GMCA at larger \textit{k}-scales. We then test scale-independence of FastICA and GMCA, and find that lower \textit{k}-scales can be modelled by a smaller number of independent components. For larger scales ($k \gtrsim 0.1~h \mathrm{cMpc}^{-1}$), more independent components are needed to fit the foregrounds. We conclude that, the current usage of GPR by the LOFAR collaboration is the appropriate removal technique. It is both robust and less prone to overfitting, with future improvements to GPR's fitting optimisation to yield deeper limits., Comment: 15 pages, 11 figures, accepted by MNRAS on 02 November 2020

The 21-cm absorption feature reported by the EDGES collaboration is several times stronger than that predicted by traditional astrophysical models. If genuine, a deeper absorption may lead to stronger fluctuations on the 21-cm signal on degree scales (up to 1~Kelvin in rms), allowing these fluctuations to be detectable in nearly 50~times shorter integration times compared to previous predictions. We commenced the "AARTFAAC Cosmic Explorer" (ACE) program, that employs the AARTFAAC wide-field imager, to measure or set limits on the power spectrum of the 21-cm fluctuations in the redshift range $z = 17.9-18.6$ ($\Delta\nu = 72.36-75.09$~MHz) corresponding to the deep part of the EDGES absorption feature. Here, we present first results from two LST bins: 23.5-23.75h and 23.5-23.75h, each with 2~h of data, recorded in `semi drift-scan' mode. We demonstrate the application of the new ACE data-processing pipeline (adapted from the LOFAR-EoR pipeline) on the AARTFAAC data. We observe that noise estimates from the channel and time-differenced Stokes~$V$ visibilities agree with each other. After 2~h of integration and subtraction of bright foregrounds, we obtain $2\sigma$ upper limits on the 21-cm power spectrum of $\Delta_{21}^2 < (8139~\textrm{mK})^2$ and $\Delta_{21}^2 < (8549~\textrm{mK})^2$ at $k = 0.144~h\,\textrm{cMpc}^{-1}$ for the two LST bins. Incoherently averaging the noise bias-corrected power spectra for the two LST bins yields an upper limit of $\Delta_{21}^2 < (7388~\textrm{mK})^2$ at $k = 0.144~h\,\textrm{cMpc}^{-1}$. These are the deepest upper limits thus far at these redshifts., Comment: 16 pages, 10 figures, accepted for publication in MNRAS

The ARCADE2 and LWA1 experiments have claimed an excess over the Cosmic Microwave Background (CMB) at low radio frequencies. If the cosmological high-redshift contribution to this radio background is between 0.1% and 22% of the CMB at 1.42 GHz, it could explain the tentative EDGES Low-Band detection of the anomalously deep absorption in the 21-cm signal of neutral hydrogen. We use the upper limit on the 21-cm signal from the Epoch of Reionization ($z=9.1$) based on 141 hours of observations with LOFAR to evaluate the contribution of the high redshift Universe to the detected radio background. Marginalizing over astrophysical properties of star-forming halos, we find (at 95% C.L.) that the cosmological radio background can be at most 9.6% of the CMB at 1.42 GHz. This limit rules out strong contribution of the high-redshift Universe to the ARCADE2 and LWA1 measurements. Even though LOFAR places limit on the extra radio background, excess of $0.1-9.6$% over the CMB (at 1.42 GHz) is still allowed and could explain the EDGES Low-Band detection. We also constrain the thermal and ionization state of the gas at $z = 9.1$ and put limits on the properties of the first star-forming objects. We find that, in agreement with the limits from EDGES High-Band data, LOFAR data constrain scenarios with inefficient X-ray sources and cases where the Universe was ionized by stars in massive halos only., Comment: Published in Monthly Notices of the Royal Astronomical Society (MNRAS). Available at https://doi.org/10.1093/mnras/staa2422

We derive constraints on the thermal and ionization states of the intergalactic medium (IGM) at redshift $\approx$ 9.1 using new upper limits on the 21-cm power spectrum measured by the LOFAR radio-telescope and a prior on the ionized fraction at that redshift estimated from recent cosmic microwave background (CMB) observations. We have used results from the reionization simulation code GRIZZLY and a Bayesian inference framework to constrain the parameters which describe the physical state of the IGM. We find that, if the gas heating remains negligible, an IGM with ionized fraction $\gtrsim 0.13$ and a distribution of the ionized regions with a characteristic size $\gtrsim 8 ~h^{-1}$ comoving megaparsec (Mpc) and a full width at the half maximum (FWHM) $\gtrsim 16 ~h^{-1}$ Mpc is ruled out. For an IGM with a uniform spin temperature $T_{\rm S} \gtrsim 3$ K, no constraints on the ionized component can be computed. If the large-scale fluctuations of the signal are driven by spin temperature fluctuations, an IGM with a volume fraction $\lesssim 0.34$ of heated regions with a temperature larger than CMB, average gas temperature 7-160 K and a distribution of the heated regions with characteristic size 3.5-70 $h^{-1}$ Mpc and FWHM of $\lesssim 110$ $h^{-1}$ Mpc is ruled out. These constraints are within the 95 per cent credible intervals. With more stringent future upper limits from LOFAR at multiple redshifts, the constraints will become tighter and will exclude an increasingly large region of the parameter space., Comment: 22 pages, 15 Figures, 5 tables, Accepted for publication in MNRAS

A new upper limit on the 21-cm signal power spectrum at a redshift of $z \approx 9.1$ is presented, based on 141 hours of data obtained with the Low-Frequency Array (LOFAR). The analysis includes significant improvements in spectrally-smooth gain-calibration, Gaussian Process Regression (GPR) foreground mitigation and optimally-weighted power spectrum inference. Previously seen `excess power' due to spectral structure in the gain solutions has markedly reduced but some excess power still remains with a spectral correlation distinct from thermal noise. This excess has a spectral coherence scale of $0.25 - 0.45$\,MHz and is partially correlated between nights, especially in the foreground wedge region. The correlation is stronger between nights covering similar local sidereal times. A best 2-$\sigma$ upper limit of $\Delta^2_{21} < (73)^2\,\mathrm{mK^2}$ at $k = 0.075\,\mathrm{h\,cMpc^{-1}}$ is found, an improvement by a factor $\approx 8$ in power compared to the previously reported upper limit. The remaining excess power could be due to residual foreground emission from sources or diffuse emission far away from the phase centre, polarization leakage, chromatic calibration errors, ionosphere, or low-level radio-frequency interference. We discuss future improvements to the signal processing chain that can further reduce or even eliminate these causes of excess power., Comment: 27 pages, 14 figues, accepted in MNRAS (updated with reference to accompanying paper)

We analyse the accuracy of radio interferometric gridding of visibilities with the aim to quantify the Epoch of Reionization (EoR) 21-cm power spectrum bias caused by gridding, ultimately to determine the suitability of different imaging algorithms and gridding settings for 21-cm power spectrum analysis. We simulate realistic LOFAR data, and construct power spectra with convolutional gridding and w-stacking, w-projection, image domain gridding and without w-correction. These are compared against directly Fourier transformed data. The influence of oversampling, kernel size, w-quantization, kernel windowing function and image padding are quantified. The gridding excess power is measured with a foreground subtraction strategy, for which foregrounds have been subtracted using Gaussian progress regression, as well as with a foreground avoidance strategy. Constructing a power spectrum that has a bias significantly lower compared to the expected EoR signals is possible with the tested methods, but requires a kernel oversampling factor > 4000 and, when using w-correction, > 500 w-quantization levels. These values are higher than typical values used for imaging, but are computationally feasible. The kernel size and padding factor parameters are less crucial. Among the tested methods, image domain gridding shows the highest accuracy with the lowest imaging time. LOFAR 21-cm power spectrum results are not affected by gridding. Image domain gridding is overall the most suitable algorithm for 21-cm EoR experiments, including for future SKA EoR analyses. Nevertheless, convolutional gridding with tuned parameters results in sufficient accuracy. This holds also for w-stacking for wide-field imaging. The w-projection algorithm is less suitable because of the kernel oversampling requirements, and a faceting approach is unsuitable due to the resulting spatial discontinuities., Comment: Accepted for publication in A&A ; abstract abridged

In March 2018, Mukherjee (2018) reported the detection by VERITAS of very-high-energy emission (VHE; > 100 GeV) from 3C 264. This is the sixth, and second most distant, radio galaxy ever detected in the TeV regime. In this article we present a radio and X-ray analysis of the jet in 3C 264. We determine the main physical parameters of the parsec-scale flow and explore the implications of the inferred kinematic structure for radiative models of this gamma-ray emitting jet. The radio data set is comprised of VLBI observations at 15 GHz from the MOJAVE program, and cover a time period of ~2 years. Through a segmented wavelet decomposition method we estimate the apparent displacement of individual plasma features; we then perform a pixel-based analysis of the stacked image to determine the jet shape. The X-ray data set includes all available observations from the Chandra, XMM, and Swift satellites, and is used, together with archival data in the other bands, to build the SED. Proper motion is mostly detected along the edges of the flow, which appears strongly limb-brightened. The apparent speeds increase as a function of distance from the core up to a maximum of ~$11.5$ c. This constrains the jet viewing angle to assume relatively small values ($\theta\lesssim10^{\circ}$). In the acceleration region, extending up to a de-projected distance of ~$4.8\times10^4$ Schwarzschild radii (~$11$ pc), the jet is collimating ($r\propto z^{0.40\pm 0.04}$), as predicted for a magnetically-driven plasma flow. By assuming that the core region is indeed magnetically dominated ($U_B/U_e>1$), the SED and the jet power can be well reproduced in the framework of leptonic models, provided that the high-energy component is associated to a second emitting region. The possibility that this region is located at the end of the acceleration zone, either in the jet layer or in the spine, is explored in the modeling., Comment: 12 pages, 10 figures. Accepted for publication in Astronomy and Astrophysics

We investigate the implications of interference detection for experiments that are pursuing a detection of the redshifted 21-cm signals from the Epoch of Reionization. Interference detection causes samples to be sporadically flagged and rejected. As a necessity to reduce the data volume, flagged samples are typically (implicitly) interpolated during time or frequency averaging or uv-gridding. This so-far unexplored systematic biases the 21-cm power spectrum, and it is important to understand this bias for current 21-cm experiments as well as the upcoming SKA Epoch of Reionization experiment. We analyse simulated data using power spectrum analysis and Gaussian process regression. We find that the combination of flagging and averaging causes tiny spectral fluctuations, resulting in `flagging excess power'. This excess power does not substantially average down over time and, without extra mitigation techniques, can exceed the power of realistic models of the 21-cm reionization signals in LOFAR observations. We mitigate the bias by i) implementing a novel way to average data using a Gaussian-weighted interpolation scheme; ii) using unitary instead of inverse-variance weighting of visibilities; and iii) using low-resolution forward modelling of the data. After these modifications, which have been integrated in the LOFAR EoR processing pipeline, the excess power reduces by approximately three orders of magnitude, and is no longer preventing a detection of the 21-cm signals., Comment: 11 pages, 8 figures, accepted for publication in MNRAS

Observations of the redshifted 21-cm hyperfine line of neutral hydrogen from early phases of the Universe such as Cosmic Dawn and the Epoch of Reionization promise to open a new window onto the early formation of stars and galaxies. We present the first upper limits on the power spectrum of redshifted 21-cm brightness temperature fluctuations in the redshift range $z = 19.8 - 25.2$ ($54-68$ MHz frequency range) using 14 hours of data obtained with the LOFAR-Low Band Antenna (LBA) array. We also demonstrate the application of a multiple pointing calibration technique to calibrate the LOFAR-LBA dual-pointing observations centred on the North Celestial Pole and the radio galaxy 3C220.3. We observe an unexplained excess of $\sim 30-50\%$ in Stokes $I$ noise compared to Stokes $V$ for the two observed fields, which decorrelates on $\gtrsim 12$ seconds and might have a physical origin. We show that enforcing smoothness of gain errors along frequency direction during calibration reduces the additional variance in Stokes $I$ compared Stokes $V$ introduced by the calibration on sub-band level. After subtraction of smooth foregrounds, we achieve a $2\sigma$ upper limit on the 21-cm power spectrum of $\Delta_{21}^2 < (14561\,\text{mK})^2$ at $k\sim 0.038\,h\,\text{cMpc}^{-1}$ and $\Delta_{21}^2 < (14886\,\text{mK})^2$ at $k\sim 0.038 \,h\,\text{cMpc}^{-1}$ for the 3C220 and NCP fields respectively and both upper limits are consistent with each other. The upper limits for the two fields are still dominated by systematics on most $k$ modes., Comment: 19 pages, 16 figures, accepted for publication in MNRAS

Nuclear spin coherence and relaxation dynamics of all constituent isotopes of an n-doped CdTe/(Cd,Mg)Te quantum well structure are studied employing optically detected nuclear magnetic resonance. Using time-resolved pump-probe Faraday ellipticity, we generate and detect the coherent spin dynamics of the resident electrons. The photogenerated electron spin polarization is transferred into the nuclear spin system, which becomes polarized and acts back on the electron spins as the Overhauser field. Under the influence of resonant radio frequency pulses, we trace the coherent spin dynamics of the nuclear isotopes $^{111}$Cd, $^{113}$Cd, and $^{125}$Te. We measure nuclear Rabi oscillations, the inhomogeneous dephasing time $T_2^*$, the spin coherence time $T_2$, and the longitudinal relaxation time $T_1$. Furthermore, we investigate the influence of the laser excitation and the corresponding electron spin polarization on the nuclear spin relaxation time and find a weak extension of this time induced by interaction with the electron spins., Comment: 5 pages, 2 figures

We introduce a prototypical nonlinear Weyl equation, motivated by recent developments in massless Dirac fermions, topological semimetals and photonics. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time $t_s$ this pulse moves with the speed of light (or Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the results to a broader class of nonlinearities and on their emerging potential for observation in different areas of application., Comment: 7 pages, 6 figures

Direct detection of the Epoch of Reionization via the redshifted 21-cm line will have unprecedented implications on the study of structure formation in the early Universe. To fulfill this promise current and future 21-cm experiments will need to detect the weak 21-cm signal over foregrounds several order of magnitude greater. This requires accurate modeling of the galactic and extragalactic emission and of its contaminants due to instrument chromaticity, ionosphere and imperfect calibration. To solve for this complex modeling, we propose a new method based on Gaussian Process Regression (GPR) which is able to cleanly separate the cosmological signal from most of the foregrounds contaminants. We also propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere. Using this method, chromatic effects causing the so-called "wedge" are effectively eliminated (i.e. deconvolved) in the cylindrical ($k_{\perp}, k_{\parallel}$) power spectrum., Comment: Subbmited to the Proceedings of the IAUS333, Peering Towards Cosmic Dawn, 4 pages, 2 figures

Detecting and characterizing the Epoch of Reionization and Cosmic Dawn via the redshifted 21-cm hyperfine line of neutral hydrogen will revolutionize the study of the formation of the first stars, galaxies, black holes and intergalactic gas in the infant Universe. The wealth of information encoded in this signal is, however, buried under foregrounds that are many orders of magnitude brighter. These must be removed accurately and precisely in order to reveal the feeble 21-cm signal. This requires not only the modeling of the Galactic and extra-galactic emission, but also of the often stochastic residuals due to imperfect calibration of the data caused by ionospheric and instrumental distortions. To stochastically model these effects, we introduce a new method based on `Gaussian Process Regression' (GPR) which is able to statistically separate the 21-cm signal from most of the foregrounds and other contaminants. Using simulated LOFAR-EoR data that include strong instrumental mode-mixing, we show that this method is capable of recovering the 21-cm signal power spectrum across the entire range $k = 0.07 - 0.3 \ \rm{h\, cMpc^{-1}}$. The GPR method is most optimal, having minimal and controllable impact on the 21-cm signal, when the foregrounds are correlated on frequency scales $\gtrsim 3$\,MHz and the rms of the signal has $\sigma_{\mathrm{21cm}} \gtrsim 0.1\,\sigma_{\mathrm{noise}}$. This signal separation improves the 21-cm power-spectrum sensitivity by a factor $\gtrsim 3$ compared to foreground avoidance strategies and enables the sensitivity of current and future 21-cm instruments such as the {\sl Square Kilometre Array} to be fully exploited., Comment: 15 pages, accepted to MNRAS, augmented with new subsection and appendix, no changes to conclusion

Very long baseline interferometry (VLBI) imaging of radio emission from extragalactic jets provides a unique probe of physical mechanisms governing the launching, acceleration, and collimation of relativistic outflows. The two-dimensional structure and kinematics of the jet in M\,87 (NGC\,4486) have been studied by applying the Wavelet-based Image Segmentation and Evaluation (WISE) method to 11 images obtained from multi-epoch Very Long Baseline Array (VLBA) observations made in January-August 2007 at 43 GHz ($\lambda = 7$ mm). The WISE analysis recovers a detailed two-dimensional velocity field in the jet in M\,87 at sub-parsec scales. The observed evolution of the flow velocity with distance from the jet base can be explained in the framework of MHD jet acceleration and Poynting flux conversion. A linear acceleration regime is observed up to $z_{obs} \sim 2$\,mas. The acceleration is reduced at larger scales, which is consistent with saturation of Poynting flux conversion. Stacked cross correlation analysis of the images reveals a pronounced stratification of the flow. The flow consists of a slow, mildly relativistic layer (moving at $\beta \sim 0.5\,c$), associated either with instability pattern speed or an outer wind, and a fast, accelerating stream line (with $\beta \sim 0.92$, corresponding to a bulk Lorentz factor $\gamma \sim 2.5$). A systematic difference of the apparent speeds in the northern and southern limbs of the jet is detected, providing evidence for jet rotation. The angular velocity of the magnetic field line associated with this rotation suggests that the jet in M87 is launched in the inner part of the disk, at a distance $r_0 \sim 5\, R_\mathrm{s}$ from the central engine. The combined results of the analysis imply that MHD acceleration and conversion of Poynting flux to kinetic energy play the dominant roles in collimation and acceleration of the flow in M\,87., Comment: 20 pages, accepted in A&A

Velocity measurements made from multiple-epoch astronomical images of evolving objects with optically thin continuum emission (e.g. as relativistic jets or expanding supernova shells) may be confused as a result of the overlap of semi-transparent features moving at different speeds. Multi-scale wavelet decomposition can be effectively applied to identify and track such overlapping features, provided that their respective structural responses can be separated over the spatial scales used for the decomposition. We developed a new method that combines the stacked cross-correlation with the wavelet-based image segmentation and evaluation (WISE) technique of decomposition of two-dimensional structures, to separate and track dominant spatial responses of overlapping evolving features. The method is tested on a set of simulated images of a stratified relativistic jet, demonstrating the robust detection of both the faster spine and the slower sheath speeds. The method is applied to mutliple-epoch images from the MOJAVE survey, revealing two different superluminal streams inside the jet in 3C 273 and the acceleration of the flow in 3C 120. The method can be applied to densely monitored objects with composite structural evolution such as the parsec-scale jet in M87 or heavily resolved expanding supernova shells., Comment: Accepted in A&A, 6 pages, 5 figures

High-resolution Very-Long-Baseline Interferometry observations of relativistic jets are essential to constrain fundamental parameters of jet formation models. At a distance of 249 Mpc, Cygnus A is a unique target for such studies, being the only Fanaroff-Riley Class II radio galaxy for which a detailed sub-parsec scale imaging of the base of both jet and counter-jet can be obtained. Observing at millimeter wavelengths unveils those regions which appear self-absorbed at longer wavelengths and enables an extremely sharp view towards the nucleus to be obtained. We performed 7 mm Global VLBI observations, achieving ultra-high resolution imaging on scales down to 90 $\mu$as. This resolution corresponds to a linear scale of only ${\sim}$400 Schwarzschild radii (for $M_{\mathrm{BH}}=2.5 \times 10^9 M_{\odot}$). We studied the kinematic properties of the main emission features of the two-sided flow and probed its transverse structure through a pixel-based analysis. We suggest that a fast and a slow layer, with different acceleration gradients, exist in the flow. The extension of the acceleration region is large (${\sim} 10^4 R_{\mathrm{S}}$), indicating that the jet is magnetically-driven. The limb brightening of both jet and counter-jet and their large opening angles ($\phi_\mathrm{J}{\sim} 10^{\circ}$) strongly favor a spine-sheath structure. In the acceleration zone, the flow has a parabolic shape ($r\propto z^{0.55\pm 0.07}$). The acceleration gradients and the collimation profile are consistent with the expectations for a jet in "equilibrium'' (Lyubarsky 2009), achieved in the presence of a mild gradient of the external pressure ($p\propto z^{-k}, k\leq2$).}, Comment: 9 pages, 8 figures. Accepted for publication in Astronomy and Astrophysics

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system.

Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices were recently generalized to the case of dispersive long-range interactions (LRI) of the Kac-Baker form. The position variance of the soliton shows a stronger than linear time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with nearest neighbour interactions (NNI). In contrast to the NNI case where the position variance at moderate soliton velocities has a considerable linear time-dependence (normal diffusion), the solitons with LRI are dominated by a superdiffusive mechanism where the position variance mainly depends quadratic and cubic on time. Since the superdiffusion seems to be generic for nontopological solitons, we want to illuminate the role of the soliton shape on the superdiffusive mechanism. Therefore, we concentrate on a FPU-like lattice with a certain class of power-law long-range interactions where the solitons have algebraic tails instead of exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI). A collective variable (CV) approach in the continuum approximation of the system leads to stochastic integro-differential equations which can be reduced to Langevin-type equations for the CV position and width. We are able to derive an analytical result for the soliton diffusion which agrees well with the simulations of the discrete system. Despite of structurally similar Langevin systems for the two soliton types, the algebraic solitons reach the superdiffusive long-time limit with a characteristic $t^{1.5}$ time-dependence much faster than exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor of $\pi$ smaller for algebraic solitons., Comment: 7 figures

We extend our studies of thermal diffusion of non-topological solitons to anharmonic FPU-type chains with additional long-range couplings. The observed superdiffusive behavior in the case of nearest neighbor interaction (NNI) turns out to be the dominating mechanism for the soliton diffusion on chains with long-range interactions (LRI). Using a collective variable technique in the framework of a variational analysis for the continuum approximation of the chain, we derive a set of stochastic integro-differential equations for the collective variables (CV) soliton position and the inverse soliton width. This set can be reduced to a statistically equivalent set of Langevin-type equations for the CV, which shares the same Fokker-Planck equation. The solution of the Langevin set and the Langevin dynamics simulations of the discrete system agree well and demonstrate that the variance of the soliton increases stronger than linearly with time (superdiffusion). This result for the soliton diffusion on anharmonic chains with long-range interactions reinforces the conjecture that superdiffusion is a generic feature of non-topological solitons., Comment: 11 figures

Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of solitons in two dimensions. We investigate numerically and analytically the dynamics of such vortex pairs. In particular we simulate numerically the head-on collision of two pairs with different velocities for a wide range of the total linear momentum of the system. If the momentum difference of the two pairs is small, the vortices exchange partners, scatter at an angle depending on this difference, and form two new identical pairs. If it is large, the pairs pass through each other without losing their identity. We also study head-tail collisions. Two identical pairs moving in the same direction are bound into a moving quadrupole in which the two vortices as well as the two antivortices rotate around each other. We study the scattering processes also analytically in the frame of a collective variable theory, where the equations of motion for a system of four vortices constitute an integrable system. The features of the different collision scenarios are fully reproduced by the theory. We finally compare some aspects of the present soliton scattering with the corresponding situation in one dimension., Comment: 13 pages (RevTeX), 8 figures

We investigate the dynamics of a lattice soliton on a monatomic chain in the presence of damping and external forces. We consider Stokes and hydrodynamical damping. In the quasi-continuum limit the discrete system leads to a damped and forced Boussinesq equation. By using a multiple-scale perturbation expansion up to second order in the framework of the quasi-continuum approach we derive a general expression for the first-order velocity correction which improves previous results. We compare the soliton position and shape predicted by the theory with simulations carried out on the level of the monatomic chain system as well as on the level of the quasi-continuum limit system. For this purpose we restrict ourselves to specific examples, namely potentials with cubic and quartic anharmonicities as well as the truncated Morse potential, without taking into account external forces. For both types of damping we find a good agreement with the numerical simulations both for the soliton position and for the tail which appears at the rear of the soliton. Moreover we clarify why the quasi-continuum approximation is better in the hydrodynamical damping case than in the Stokes damping case.

Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry. There are two types of vortices, characterized by their polarization (a second topological charge in addition to the vorticity): Planar vortices have Newtonian dynamics (even-order equations of motion) and exhibit strong discreteness effects, while non-planar vortices have non-Newtonian dynamics (odd-order equations of motion) and smooth trajectories. The influence of thermal fluctuations on single vortices is investigated. Different types of noise and damping are discussed and implemented into the microscopic equations which yields stochastic equations of motion for the vortices. The solutions of the these equations are compared with Langevin dynamics simulations. Moreover, noise-induced transitions between opposite polarizations of a vortex are investigated. For temperatures above the Kosterlitz-Thouless vortex-antivortex unbinding transition, a phenomenological theory, namely the vortex gas approach, yields central peaks in the dynamic form factors for the spin correlations. Such peaks are observed both in combined Monte Carlo- and Spin Dynamics-Simulations and in inelastic neutron scattering experiments. However, the assumption of ballistic vortex motion appears questionable., Comment: 34 pages, 11 figures, to appear in "Nonlinear Science at the Dawn of the 21th Century" edited by Peter Leth Christiansen and Mads Peter Soerensen, Springer Verlag (http://www.springer-ny.com/), Berlin

Starting from a travelling wave ansatz we show successively that the shape of a nonlinear excitation generally depends also on the 1st, 2nd, ... time derivative of the position X of the excitation. From the Hamilton equations we derive a hierarchy of equations of motion for X. The type of the excitation determines on which levels the hierarchy can be truncated consistently: "Gyrotropic" excitations are governed by odd-order equations, non-gyrotropic ones by even-order equations. Examples for the latter case are kinks in 1-dimensional models and planar vortices of the 2D anisotropic (easy-plane) Heisenberg model. The non-planar vortices of this model are the simplest gyrotropic example. For this case we solve the Hamilton equations for a finite system with one vortex and free boundary conditions and calculate the parameters of the 3rd-order equation of motion. This equation yields trajectories which are a superposition of two cycloids with different frequencies, which is in full agreement with computer simulations of the full many-spin model. Finally we demonstrate that the additional effects from the 5th-order equation are negligible., Comment: 22 pages, 7 figures

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons., Comment: 12 pages, 14 figures