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Vibor Jelić

Publications and source records attributed to Vibor Jelić.

At least 19 recordsLinked to original sources

Faraday depth similarities across scales with LoTSS & DRAGONS

Faraday rotation of diffuse Galactic synchrotron emission is a powerful tracer of the complex, magnetised interstellar medium (ISM), whose structures span a wide range of spatial scales, requiring both interferometric and single-antenna broadband radio polarisation observations for full characterisation. We compare Faraday rotation in the interferometric LOw-Frequency ARray Two-Metre Sky Survey (LoTSS; 120-168 MHz) and the single-antenna Dominion Radio Astrophysical Observatory Global Magneto-Ionic Medium Survey of the Northern Sky (DRAGONS; 350-1030 MHz), which are complementary in their sensitivity to spatial and Faraday-depth scales. We calculate first moments (M1) of polarised intensity versus Faraday depth, producing polarised-intensity-weighted mean Faraday depth maps of the regions common to both surveys. These maps show remarkable agreement between the surveys despite the lack of overlap in frequency or spatial-scale coverage. In the northern Galactic region, the M1 maps are morphologically similar with only small spatial shifts in the boundaries between positive and negative M1, and strong pixel-by-pixel correlation. In the southern Galactic region, both surveys trace the Faraday-depth gradient with Galactic longitude previously identified in LoTSS. Faraday depth spectra show consistent numbers and locations of peaks for more than half of the pixels. The strong structural similarity between the surveys, demonstrated by computing structure functions, suggests coupling across spatial scales in the magnetised ISM, enabling both interferometric and single-antenna observations to trace the same features. Instances of differences point to ISM configurations where observational effects such as depolarisation dominate or where this coupling breaks down due to local physical conditions.

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Faraday tomography of LoTSS-DR2 data: III. Revealing the Local Bubble and the complex of local interstellar clouds in the high-latitude inner Galaxy

In this work, we present a new mosaic created with the second release of LOFAR Two-Metre Sky Survey data (LoTSS-DR2), which probes polarised synchrotron emission in the high-latitude inner Galaxy. Our objective is to characterise the observed emission through multi-tracer analysis to better understand the volume and the structures that may be observed with LOFAR. Furthermore, we exploit Faraday depth as a unique tool to probe the diffuse magnetised structure in the local ISM. We produced a mosaic Faraday cube of LoTSS-DR2 data by applying a rotation measure synthesis algorithm. From the cube, we constructed Faraday moment maps to characterise the nature of spectra. Additionally, we quantified the linear depolarisation canals using the Rolling Hough transform and used them to search for alignment with other data sets. Utilising LoTSS-DR2 observations alongside complementary data sets including Planck polarisation data, HI emission maps, and starlight polarisation measurements, we estimated the distance to the Faraday structures. The Faraday cube reveals an ordered structure across two-thirds of the observed area, whose orientation aligns well with that of both the HI filaments and the magnetic field. We estimate the minimum distance to the Faraday structures to be between 40 and 80 pc, which puts them in the vicinity of the Local Bubble wall. The emission is organised in a large gradient in Faraday depth whose origin we associate with the curved wall of the Local Bubble. Comparing our data with a model of the Local Bubble wall, we conclude that we might be probing a contribution of the medium inside the Local Bubble cavity as well, corresponding to the complex of local interstellar clouds. Moreover, we propose a toy model incorporating an ionised front of finite thickness into the Local Bubble wall, as a curved, cold neutral shell alone is insufficient to produce the observed gradient.

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Faraday tomography of LoTSS-DR2 data: II. Multi-tracer analysis in the high-latitude outer Galaxy

We conducted a follow-up study on the analysis of the LOw Frequency ARray (LOFAR) Two-metre Sky Survey (LoTSS) mosaic in the high-latitude outer Galaxy presented in the first paper of this series. Here, we focus on the search for alignment between the magnetic field traced by dust, HI filaments, starlight optical linear polarisation, and linear depolarised structures (depolarisation canals) observed in low-frequency synchrotron polarisation. This alignment was previously found in several smaller fields observed with LOFAR, offering valuable insights into the nature of the interstellar medium and the 3D spatial distribution of the diffuse ionised medium. We aim to determine whether the alignment of the interstellar medium (ISM) phases observed through multiple tracers is a common occurrence or an exception. Additionally, in areas where depolarisation canals align with the magnetic field, we use starlight polarisation to constrain the distance to the structures associated with the observed canals. We employed the Rolling Hough Transform (RHT) and projected Rayleigh statistics (PRS) to identify and quantify the alignment between the different tracers. On the scale of the whole mosaic, we did not find any evidence of a universal alignment among the three tracers. However, in one particular area, the western region (Dec between $29^\circ$ and $70^\circ$ and RA between $\mathrm{7^h44^m}$ and $\mathrm{9^h20^m}$), we do find a significant alignment between the magnetic field, depolarisation canals, and HI filaments. Based on this alignment, we used the starlight polarisation of stars with known parallax distances to estimate that the minimum distance to the structures observed by LOFAR in this region lies within the range of 200 to 240 pc. We associate these structures with the edge of the Local Bubble.

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Comparison of distance measurements to dust clouds using GRB X-ray halos and 3D dust extinction

X-ray photons from energetic sources such as gamma-ray bursts (GRBs) can be scattered on dust clouds in the Milky Way, creating a time-evolving halo around the GRB position. X-ray observations of such halos allow the measurement of dust clouds distances in the Galaxy on which the scattering occurs. We present the first systematic comparison of the distances to scattering regions derived from GRB halos with the 3D dust distribution derived from recently published optical-to-near infrared extinction maps. GRB halos were observed around 7 sources by the Swift XRT and the XMM-Newton EPIC instruments, namely GRB 031203, GRB 050713A, GRB 050724, GRB 061019, GRB 070129, GRB 160623A and GRB 221009A. We used four 3D extinction maps that exploit photometric data from different surveys and apply diverse algorithms for the 3D mapping of extinction, and compared the X-ray halo-derived distances with the local maxima in the 3D extinction density distribution. We found that in all GRBs we can find at least one local maximum in the 3D dust extinction map that is in agreement with the dust distance measured from X-ray rings. For GRBs with multiple X-ray rings, the dust distance measurements coincide with at least 3 maxima in the extinction map for GRB 160623A, and 5 maxima for GRB 221009A. The agreement of these independent distance measurements shows that the methods used to create dust extinction maps may potentially be optimized by the X-ray halo observations from GRBs.

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LOFAR Deep Fields: Probing faint Galactic polarised emission in ELAIS-N1

We present the first deep polarimetric study of Galactic synchrotron emission at low radio frequencies. Our study is based on 21 observations of the European Large Area Infrared Space Observatory Survey-North 1 (ELAIS-N1) field using the Low-Frequency Array (LOFAR) at frequencies from 114.9 to 177.4 MHz. These data are a part of the LOFAR Two-metre Sky Survey Deep Fields Data Release 1. We used very low-resolution ($4.3'$) Stokes QU data cubes of this release. We applied rotation measure (RM) synthesis to decompose the distribution of polarised structures in Faraday depth, and cross-correlation RM synthesis to align different observations in Faraday depth. We stacked images of about 150 hours of the ELAIS-N1 observations to produce the deepest Faraday cube at low radio frequencies to date, tailored to studies of Galactic synchrotron emission and the intervening magneto-ionic interstellar medium. This Faraday cube covers $\sim36~{\rm deg^{2}}$ of the sky and has a noise of $27~{\rm μJy~PSF^{-1}~RMSF^{-1}}$ in polarised intensity. This is an improvement in noise by a factor of approximately the square root of the number of stacked data cubes ($\sim\sqrt{20}$), as expected, compared to the one in a single data cube based on five-to-eight-hour observations. We detect a faint component of diffuse polarised emission in the stacked cube, which was not detected previously. Additionally, we verify the reliability of the ionospheric Faraday rotation corrections estimated from the satellite-based total electron content measurements to be of $~\sim0.05~{\rm rad~m^{-2}}$. We also demonstrate that diffuse polarised emission itself can be used to account for the relative ionospheric Faraday rotation corrections with respect to a reference observation.

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Faraday tomography of LoTSS-DR2 data: I. Faraday moments in the high-latitude outer Galaxy and revealing Loop III in polarisation

Observations of synchrotron emission at low radio frequencies reveal a labyrinth of polarised Galactic structures. However, the explanation for the wealth of structures remains uncertain due to the complex interactions between the interstellar medium and the magnetic field. A multi-tracer approach to the analysis of large sky areas is needed. This paper aims to use polarimetric images from the LOFAR Two metre Sky Survey (LoTSS) to produce the biggest mosaic of polarised emission in the northern sky at low radio frequencies (150 MHz) to date. The large area this mosaic covers allows for detailed morphological and statistical studies of polarised structures in the high-latitude outer Galaxy, including the well-known Loop III region. We produced a 3100 square degree Faraday tomographic cube using a rotation measure synthesis tool. We calculated the statistical moments of Faraday spectra and compared them with data sets at higher frequencies (1.4 GHz) and with a map of a rotation measure derived from extragalactic sources. The mosaic is dominated by polarised emission connected to Loop III. Additionally, the mosaic reveals an abundance of other morphological structures, mainly {narrow and extended} depolarisation canals, which are found to be ubiquitous. We find a correlation between the map of an extragalactic rotation measure and the LoTSS first Faraday moment image. The ratio of the two deviates from a simple model of a Burn slab (Burn 1966) along the line of sight, which highlights the high level of complexity in the magnetoionic medium that can be studied at these frequencies.

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Multi-tracer analysis of straight depolarisation canals in the surroundings of the 3C 196 field

Faraday tomography of a field centred on the extragalactic point source 3C 196 with the LOw Frequency ARray (LOFAR) revealed an intertwined structure of diffuse polarised emission with straight depolarisation canals and tracers of the magnetized and multi-phase interstellar medium (ISM), such as dust and line emission from atomic hydrogen (HI). This study aims at extending the multi-tracer analysis of LOFAR data to three additional fields in the surroundings of the 3C 196 field. For the first time, we study the three-dimensional structure of the LOFAR emission by determining the distance to the depolarisation canals. We use the Rolling Hough Transform to compare the orientation of the depolarisation canals with that of the filamentary structure seen in HI and, based on starlight and dust polarisation data, with that of the plane-of-the-sky magnetic field. Stellar parallaxes from $Gaia$ complement the starlight polarisation with the corresponding distances. Faraday tomography of the three fields shows a rich network of diffuse polarised emission at Faraday depths between $-10~{\rm rad~m^{-2}}$ and $+15~{\rm rad~m^{-2}}$. A complex system of straight depolarisation canals resembles that of the 3C 196 field. The depolarisation canals align both with the HI filaments and with the magnetic field probed by dust. The observed alignment suggests that an ordered magnetic field organises the multiphase ISM over a large area ($\sim$20$^{\circ}$). In one field, two groups of stars at distances below and above 200 pc, respectively, show distinct magnetic-field orientations. These are both comparable with the orientations of the depolarisation canals in the same field. We conclude that the depolarisation canals likely trace the same change of the magnetic field as probed by the stars, which corresponds to the edge of the Local Bubble.

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Spectral index of synchrotron emission: insights from the diffuse and magnetised interstellar medium

The interpretation of Galactic synchrotron observations is complicated by the degeneracy between the strength of the magnetic field perpendicular to the line of sight (LOS), $B_\perp$, and the cosmic-ray electron (CRe) spectrum. Depending on the observing frequency, an energy-independent spectral energy slope $s$ for the CRe spectrum is usually assumed: $s=-2$ at frequencies below $\simeq$400 MHz and $s=-3$ at higher frequencies. Motivated by the high angular and spectral resolution of current facilities such as the LOw Frequency ARray (LOFAR) and future telescopes such as the Square Kilometre Array (SKA), we aim to understand the consequences of taking into account the energy-dependent CRe spectral energy slope on the analysis of the spatial variations of the brightness temperature spectral index, $β$, and on the estimate of the average value of $B_\perp$ along the LOS. We illustrate analytically and numerically the impact that different realisations of the CRe spectrum have on the interpretation of the spatial variation of $β$. We find that the common assumption of an energy-independent $s$ is valid only in special cases. We show that for typical magnetic field strengths of the diffuse interstellar medium ($\simeq$2$-$20 $μ$G), at frequencies of 0.1$-$10 GHz, the electrons that are mainly responsible for the synchrotron emission have energies in the range $\simeq$100 MeV$-$50 GeV. This is the energy range where the spectral slope, $s$, of CRe has its greatest variation. We also show that the polarisation fraction can be much smaller than the maximum value of $\simeq 70\%$ because the orientation of ${\bf B}_\perp$ varies across the telescope's beam and along the LOS. Finally, we present a look-up plot that can be used to estimate the average value of $B_\perp$ along the LOS from a set of values of $β$ measured at centimetre to metre wavelengths, for a given CRe spectrum.

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The multiphase and magnetized neutral hydrogen seen by LOFAR

Faraday tomography of polarimetric observations at low frequency is a unique tool to study the structure of the magneto-ionic interstellar medium (ISM) based on Faraday depth. LOFAR data below 200 MHz revealed a plethora of features in polarization, whose origin remains unknown. Previous studies highlighted the remarkable association of such features to tracers of the magnetized-neutral ISM, as interstellar dust and atomic hydrogen (HI). However, the physical conditions responsible for the correlation between magneto-ionic and neutral media are yet to be clarified. In this letter we investigate further the correlation between LOFAR data and HI observations at 21cm from the Effelsberg-Bonn HI Survey (EBHIS). We focus on the multiphase properties of the HI gas. We present the first statistical study on the morphological correlation between LOFAR tomographic data and the cold (CNM), luke-warm (LNM), and warm (WNM) HI phases, separately. We use the Regularized Optimization for Hyper-Spectral Analysis (ROHSA) approach to decompose the HI phases based on the Gaussian decomposition of the HI spectra. In at least two fields of view -- Fields 3C196 and A -- out of four -- Fields B and C -- we find a significant correlation between LOFAR and EBHIS data using the Histograms of Oriented Gradients (HOG). The absence of correlation in Fields B and C is caused by low signal-to-noise ratio in polarization. The observed HOG correlation in Fields 3C196 and A is associated with all HI phases and it is surprisingly dominant in the CNM and LNM phases. We discuss possible mechanisms that would explain the correlation between CNM, LNM, and WNM, with polarized emission at Faraday depths up to 10 rad m$^{-2}$. Our results show how the complex structure of the ionic medium seen by LOFAR data is tightly related to phase transition in the diffuse and magnetized neutral ISM traced by HI spectroscopic data.

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Foregrounds and their mitigation

The low-frequency radio sky is dominated by the diffuse synchrotron emission of our Galaxy and extragalactic radio sources related to Active Galactic Nuclei and star-forming galaxies. This foreground emission is much brighter than the cosmological 21 cm emission from the Cosmic Dawn and Epoch of Reionization. Studying the physical properties of the foregrounds is therefore of fundamental importance for their mitigation in the cosmological 21 cm experiments. This chapter gives a comprehensive overview of the foregrounds and our current state-of-the-art knowledge about their mitigation.

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Peering into the Dark (Ages) with Low-Frequency Space Interferometers

Neutral hydrogen pervades the infant Universe, and its redshifted 21-cm signal allows one to chart the Universe. This signal allows one to probe astrophysical processes such as the formation of the first stars, galaxies, (super)massive black holes and enrichment of the pristine gas from z~6 to z~30, as well as fundamental physics related to gravity, dark matter, dark energy and particle physics at redshifts beyond that. As one enters the Dark Ages (z>30), the Universe becomes pristine. Ground-based low-frequency radio telescopes aim to detect the spatial fluctuations of the 21-cm signal. Complementary, global 21-cm experiments aim to measure the sky-averaged 21-cm signal. Escaping RFI and the ionosphere has motivated space-based missions, such as the Dutch-Chinese NCLE instrument (currently in lunar L2), the proposed US-driven lunar or space-based instruments DAPPER and FARSIDE, the lunar-orbit interferometer DSL (China), and PRATUSH (India). To push beyond the current z~25 frontier, though, and measure both the global and spatial fluctuations (power-spectra/tomography) of the 21-cm signal, low-frequency (1-100MHz; BW~50MHz; z>13) space-based interferometers with vast scalable collecting areas (1-10-100 km2), large filling factors (~1) and large fields-of-view (4pi sr.) are needed over a mission lifetime of >5 years. In this ESA White Paper, we argue for the development of new technologies enabling interferometers to be deployed, in space (e.g. Earth-Sun L2) or in the lunar vicinity (e.g. surface, orbit or Earth-Moon L2), to target this 21-cm signal. This places them in a stable environment beyond the reach of most RFI from Earth and its ionospheric corruptions, enabling them to probe the Dark Ages as well as the Cosmic Dawn, and allowing one to investigate new (astro)physics that is inaccessible in any other way in the coming decades. [Abridged]

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Magnetically aligned straight depolarisation canals and the rolling Hough transform

Aims. We aim to characterize the properties of the straight depolarization canals detected in the Low Frequency Array (LOFAR) polarimetric observations of a field centered on the extragalactic source 3C 196. We also compare the canal orientations with magnet- ically aligned Hi filaments and the magnetic field probed by polarized dust emission. Methods. We used the rolling Hough transform (RHT) to identify and characterize the orientation of the straight depolarization canals in radio polarimetric data and the filaments in Hi data. Results. The majority of the straight depolarization canals and the Hi filaments are inclined by 10deg with respect to the Galactic plane and are aligned with the plane-of-sky magnetic field orientation probed by the Planck dust polarization data. The other distinct orientation, of 65deg with respect to the Galactic plane, is associated with the orientation of a bar-like structure observed in the 3C 196 field at 350 MHz. Conclusions. An alignment between three distinct tracers of the (local) interstellar medium (ISM) suggests that an ordered magnetic field plays a crucial role in confining different ISM phases. The majority of the straight depolarization canals are a result of a projection of the complicated 3D distribution of the ISM. The RHT analysis is a robust method for identifying and characterizing the straight depolarization canals observed in radio-polarimetric data.

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Systematic biases in low frequency radio interferometric data due to calibration: the LOFAR EoR case

The redshifted 21 cm line of neutral hydrogen is a promising probe of the Epoch of Reionization (EoR). However, its detection requires a thorough understanding and control of the systematic errors. We study two systematic biases observed in the LOFAR EoR residual data after calibration and subtraction of bright discrete foreground sources. The first effect is a suppression in the diffuse foregrounds, which could potentially mean a suppression of the 21 cm signal. The second effect is an excess of noise beyond the thermal noise. The excess noise shows fluctuations on small frequency scales, and hence it can not be easily removed by foreground removal or avoidance methods. Our analysis suggests that sidelobes of residual sources due to the chromatic point spread function and ionospheric scintillation can not be the dominant causes of the excess noise. Rather, both the suppression of diffuse foregrounds and the excess noise can occur due to calibration with an incomplete sky model containing predominantly bright discrete sources. We show that calibrating only on bright sources can cause suppression of other signals and introduce an excess noise in the data. The levels of the suppression and excess noise depend on the relative flux of sources which are not included in the model with respect to the flux of modeled sources. We discuss possible solutions such as using only long baselines to calibrate the interferometric gain solutions as well as simultaneous multi-frequency calibration along with their benefits and shortcomings.

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The Effect of Foreground Mitigation Strategy on EoR Window Recovery

The removal of the Galactic and extragalactic foregrounds remains a major challenge for those wishing to make a detection of the Epoch of Reionization 21-cm signal. Multiple methods of modelling these foregrounds with varying levels of assumption have been trialled and shown promising recoveries on simulated data. Recently however there has been increased discussion of using the expected shape of the foregrounds in Fourier space to define an EoR window free of foreground contamination. By carrying out analysis within this window only, one can avoid the foregrounds and any statistical bias they might introduce by instead removing these foregrounds. In this paper we discuss the advantages and disadvantages of both foreground removal and foreground avoidance. We create a series of simulations with noise levels in line with both current and future experiments and compare the recovered statistical cosmological signal from foreground avoidance and a simplified, frequency independent foreground removal model. We find that while, for current generation experiments, foreground avoidance enables a better recovery at $k_{perp} > 0.6 \mathrm{Mpc}^{-1}$, foreground removal is able to recover significantly more signal at small $k_{los}$ for both current and future experiments. We also relax the assumption that the foregrounds are smooth by introducing a Gaussian random factor along the line-of-sight and then also spatially. We find that both methods perform well for foreground models with line-of-sight and spatial variations around $0.1\%$ however at levels larger than this foregrounds removal shows a greater signal recovery.

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Effects of the sources of reionization on 21-cm redshift-space distortions

The observed 21-cm signal from the epoch of reionization will be distorted along the line-of-sight by the peculiar velocities of matter particles. These redshift-space distortions will affect the contrast in the signal and will also make it anisotropic. This anisotropy contains information about the cross-correlation between the matter density field and the neutral hydrogen field, and could thus potentially be used to extract information about the sources of reionization. In this paper, we study a collection of simulated reionization scenarios assuming different models for the sources of reionization. We show that the 21-cm anisotropy is best measured by the quadrupole moment of the power spectrum. We find that, unless the properties of the reionization sources are extreme in some way, the quadrupole moment evolves very predictably as a function of global neutral fraction. This predictability implies that redshift-space distortions are not a very sensitive tool for distinguishing between reionization sources. However, the quadrupole moment can be used as a model-independent probe for constraining the reionization history. We show that such measurements can be done to some extent by first-generation instruments such as LOFAR, while the SKA should be able to measure the reionization history using the quadrupole moment of the power spectrum to great accuracy.

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Predictions for the 21cm-galaxy cross-power spectrum observable with LOFAR and Subaru

The 21cm-galaxy cross-power spectrum is expected to be one of the promising probes of the Epoch of Reionization (EoR), as it could offer information about the progress of reionization and the typical scale of ionized regions at different redshifts. With upcoming observations of 21cm emission from the EoR with the Low Frequency Array (LOFAR), and of high redshift Lyalpha emitters (LAEs) with Subaru's Hyper Suprime Cam (HSC), we investigate the observability of such cross-power spectrum with these two instruments, which are both planning to observe the ELAIS-N1 field at z=6.6. In this paper we use N-body + radiative transfer (both for continuum and Lyalpha photons) simulations at redshift 6.68, 7.06 and 7.3 to compute the 3D theoretical 21cm-galaxy cross-power spectrum, as well as to predict the 2D 21cm-galaxy cross-power spectrum expected to be observed by LOFAR and HSC. Once noise and projection effects are accounted for, our predictions of the 21cm-galaxy cross-power spectrum show clear anti-correlation on scales larger than ~ 60 h$^{-1}$ Mpc (corresponding to k ~ 0.1 h Mpc$^{-1}$), with levels of significance p=0.04 at z=6.6 and p=0.048 at z=7.3. On smaller scales, instead, the signal is completely contaminated.

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Realistic Simulations of the Galactic Polarized Foreground: Consequences for 21-cm Reionization Detection Experiments

Experiments designed to measure the redshifted 21~cm line from the Epoch of Reionization (EoR) are challenged by strong astrophysical foreground contamination, ionospheric distortions, complex instrumental response and other different types of noise (e.g. radio frequency interference). The astrophysical foregrounds are dominated by diffuse synchrotron emission from our Galaxy. Here we present a simulation of the Galactic emission used as a foreground module for the LOFAR- EoR key science project end-to-end simulations. The simulation produces total and polarized intensity over $10^\circ \times 10^\circ$ maps of the Galactic synchrotron and free-free emission, including all observed characteristics of the emission: spatial fluctuations of amplitude and spectral index of the synchrotron emission, together with Faraday rotation effects. The importance of these simulations arise from the fact that the Galactic polarized emission could behave in a manner similar to the EoR signal along the frequency direction. As a consequence, an improper instrumental calibration will give rise to leakages of the polarized to the total signal and mask the desired EoR signal. In this paper we address this for the first time through realistic simulations.

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Cosmic Dawn and Epoch of Reionization Foreground Removal with the SKA

The exceptional sensitivity of the SKA will allow observations of the Cosmic Dawn and Epoch of Reionization (CD/EoR) in unprecedented detail, both spectrally and spatially. This wealth of information is buried under Galactic and extragalactic foregrounds, which must be removed accurately and precisely in order to reveal the cosmological signal. This problem has been addressed already for the previous generation of radio telescopes, but the application to SKA is different in many aspects. In this chapter we summarise the contributions to the field of foreground removal in the context of high redshift and high sensitivity 21-cm measurements. We use a state-of-the-art simulation of the SKA Phase 1 observations complete with cosmological signal, foregrounds and frequency-dependent instrumental effects to test both parametric and non-parametric foreground removal methods. We compare the recovered cosmological signal using several different statistics and explore one of the most exciting possibilities with the SKA --- imaging of the ionized bubbles. We find that with current methods it is possible to remove the foregrounds with great accuracy and to get impressive power spectra and images of the cosmological signal. The frequency-dependent PSF of the instrument complicates this recovery, so we resort to splitting the observation bandwidth into smaller segments, each of a common resolution. If the foregrounds are allowed a random variation from the smooth power law along the line of sight, methods exploiting the smoothness of foregrounds or a parametrization of their behaviour are challenged much more than non-parametric ones. However, we show that correction techniques can be implemented to restore the performances of parametric approaches, as long as the first-order approximation of a power law stands.

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