Robust Radio Interferometric Calibration Using the t-Distribution

A major stage of radio interferometric data processing is calibration or the estimation of systematic errors in the data and the correction for such errors. A stochastic error (noise) model is assumed, and in most cases, this underlying model is assumed to be Gaussian. However, outliers in the data due to interference or due to errors in the sky model would have adverse effects on processing based on a Gaussian noise model. Most of the shortcomings of calibration such as the loss in flux or coherence, and the appearance of spurious sources, could be attributed to the deviations of the underlying noise model. In this paper, we propose to improve the robustness of calibration by using a noise model based on Student's t distribution. Student's t noise is a special case of Gaussian noise when the variance is unknown. Unlike Gaussian noise model based calibration, traditional least squares minimization would not directly extend to a case when we have a Student's t noise model. Therefore, we use a variant of the Expectation Maximization (EM) algorithm, called the Expectation-Conditional Maximization Either (ECME) algorithm when we have a Student's t noise model and use the Levenberg-Marquardt algorithm in the maximization step. We give simulation results to show the robustness of the proposed calibration method as opposed to traditional Gaussian noise model based calibration, especially in preserving the flux of weaker sources that are not included in the calibration model.Comment: MNRAS accepte

Reduced Ambiguity Calibration for LOFAR

Interferometric calibration always yields non unique solutions. It is therefore essential to remove these ambiguities before the solutions could be used in any further modeling of the sky, the instrument or propagation effects such as the ionosphere. We present a method for LOFAR calibration which does not yield a unitary ambiguity, especially under ionospheric distortions. We also present exact ambiguities we get in our solutions, in closed form. Casting this as an optimization problem, we also present conditions for this approach to work. The proposed method enables us to use the solutions obtained via calibration for further modeling of instrumental and propagation effects. We provide extensive simulation results on the performance of our method. Moreover, we also give cases where due to degeneracy, this method fails to perform as expected and in such cases, we suggest exploiting diversity in time, space and frequency.Comment: Draft version. Final version published on 10 April 201

Wide-field LOFAR-LBA power-spectra analyses: Impact of calibration, polarization leakage and ionosphere

Contamination due to foregrounds (Galactic and Extra-galactic), calibration errors and ionospheric effects pose major challenges in detection of the cosmic 21 cm signal in various Epoch of Reionization (EoR) experiments. We present the results of a pilot study of a field centered on 3C196 using LOFAR Low Band (56-70 MHz) observations, where we quantify various wide field and calibration effects such as gain errors, polarized foregrounds, and ionospheric effects. We observe a `pitchfork' structure in the 2D power spectrum of the polarized intensity in delay-baseline space, which leaks into the modes beyond the instrumental horizon (EoR/CD window). We show that this structure largely arises due to strong instrumental polarization leakage ($\sim30\%$) towards {Cas\,A} ($\sim21$ kJy at 81 MHz, brightest source in northern sky), which is far away from primary field of view. We measure an extremely small ionospheric diffractive scale ($r_{\text{diff}} \approx 430$ m at 60 MHz) towards {Cas\,A} resembling pure Kolmogorov turbulence compared to $r_{\text{diff}} \sim3 - 20$ km towards zenith at 150 MHz for typical ionospheric conditions. This is one of the smallest diffractive scales ever measured at these frequencies. Our work provides insights in understanding the nature of aforementioned effects and mitigating them in future Cosmic Dawn observations (e.g. with SKA-low and HERA) in the same frequency window.Comment: 20 pages, 11 figures, accepted for publication in MNRA

Foregrounds for observations of the cosmological 21 cm line: II. Westerbork observations of the fields around 3C196 and the North Celestial Pole

In the coming years a new insight into galaxy formation and the thermal history of the Universe is expected to come from the detection of the highly redshifted cosmological 21 cm line. The cosmological 21 cm line signal is buried under Galactic and extragalactic foregrounds which are likely to be a few orders of magnitude brighter. Strategies and techniques for effective subtraction of these foreground sources require a detailed knowledge of their structure in both intensity and polarization on the relevant angular scales of 1-30 arcmin. We present results from observations conducted with the Westerbork telescope in the 140-160 MHz range with 2 arcmin resolution in two fields located at intermediate Galactic latitude, centred around the bright quasar 3C196 and the North Celestial Pole. They were observed with the purpose of characterizing the foreground properties in sky areas where actual observations of the cosmological 21 cm line could be carried out. The polarization data were analysed through the rotation measure synthesis technique. We have computed total intensity and polarization angular power spectra. Total intensity maps were carefully calibrated, reaching a high dynamic range, 150000:1 in the case of the 3C196 field. [abridged]Comment: 20 pages, 22 figures, accepted for publication in A&A. A version with full resolution figures is available at http://www.astro.rug.nl/~bernardi/NCP_3C196/bernardi.pd

Radio Interferometric Calibration Using The SAGE Algorithm

The aim of the new generation of radio synthesis arrays such as LOFAR and SKA is to achieve much higher sensitivity, resolution and frequency coverage than what is available now, especially at low frequencies. To accomplish this goal, the accuracy of the calibration techniques used is of considerable importance. Moreover, since these telescopes produce huge amounts of data, speed of convergence of calibration is a major bottleneck. The errors in calibration are due to system noise (sky and instrumental) as well as the estimation errors introduced by the calibration technique itself, which we call solver noise. We define solver noise as the distance between the optimal solution (the true value of the unknowns, uncorrupted by the system noise) and the solution obtained by calibration. We present the Space Alternating Generalized Expectation Maximization (SAGE) calibration technique, which is a modification of the Expectation Maximization algorithm, and compare its performance with the traditional Least Squares calibration based on the level of solver noise introduced by each technique. For this purpose, we develop statistical methods that use the calibrated solutions to estimate the level of solver noise. The SAGE calibration algorithm yields very promising results both in terms of accuracy and speed of convergence. The comparison approaches we adopt introduce a new framework for assessing the performance of different calibration schemes.Comment: 12 pages, 10 figures, Accepted for publication in MNRA

Prospects for detecting the 21cm forest from the diffuse intergalactic medium with LOFAR

We discuss the feasibility of the detection of the 21cm forest in the diffuse IGM with the radio telescope LOFAR. The optical depth to the 21cm line has been derived using simulations of reionization which include detailed radiative transfer of ionizing photons. We find that the spectra from reionization models with similar total comoving hydrogen ionizing emissivity but different frequency distribution look remarkably similar. Thus, unless the reionization histories are very different from each other (e.g. a predominance of UV vs. x-ray heating) we do not expect to distinguish them by means of observations of the 21cm forest. Because the presence of a strong x-ray background would make the detection of 21cm line absorption impossible, the lack of absorption could be used as a probe of the presence/intensity of the x-ray background and the thermal history of the universe. Along a random line of sight LOFAR could detect a global suppression of the spectrum from z>12, when the IGM is still mostly neutral and cold, in contrast with the more well-defined, albeit broad, absorption features visible at lower redshift. Sharp, strong absorption features associated with rare, high density pockets of gas could be detected also at z~7 along preferential lines of sight.Comment: 12 pages, 13 figures. MNRAS, in pres

Reionization and high-redshift galaxies: the view from quasar absorption lines

Determining when and how the first galaxies reionised the intergalactic medium promises to shed light on both the nature of the first objects and the cosmic history of baryons. Towards this goal, quasar absorption lines play a unique role by probing the properties of diffuse gas on galactic and intergalactic scales. In this review, we examine the multiple ways in which absorption lines trace the connection between galaxies and the intergalactic medium near the reionisation epoch. We first describe how the Ly α forest is used to determine the intensity of the ionising ultraviolet background and the global ionising emissivity budget. Critically, these measurements reflect the escaping ionising radiation from all galaxies, including those too faint to detect directly. We then discuss insights from metal absorption lines into reionisation-era galaxies and their surroundings. Current observations suggest a buildup of metals in the circumgalactic environments of galaxies over z ~ 6 to 5, although changes in ionisation will also affect the evolution of metal line properties. A substantial fraction of metal absorbers at these redshifts may trace relatively low-mass galaxies. Finally, we review constraints from the Ly α forest and quasar near zones on the timing of reionisation. Along with other probes of the high-redshift Universe, absorption line data are consistent with a relatively late end to reionisation (5.5 ≲ z ≲ 7); however, the constraints are still fairly week. Significant progress is expected to come through improved analysis techniques, increases in the number of known high-redshift quasars from optical and infrared sky surveys, large gains in sensitivity from next-generation observing facilities, and synergies with other probes of the reionisation era

Foregrounds for observations of the cosmological 21 cm line: I. First Westerbork measurements of Galactic emission at 150 MHz in a low latitude field

We present the first results from a series of observations conducted with the Westerbork telescope in the 140--160 MHz range with a 2 arcmin resolution aimed at characterizing the properties of the foregrounds for epoch of reionization experiments. For the first time we have detected fluctuations in the Galactic diffuse emission on scales greater than 13 arcmin at 150 MHz, in the low Galactic latitude area known as Fan region. Those fluctuations have an $rms$ of 14 K. The total intensity power spectrum shows a power--law behaviour down to $\ell \sim 900$ with slope $\beta^I_\ell = -2.2 \pm 0.3$. The detection of diffuse emission at smaller angular scales is limited by residual point sources. We measured an $rms$ confusion noise of $\sim$3 mJy beam$^{-1}$. Diffuse polarized emission was also detected for the first time at this frequency. The polarized signal shows complex structure both spatially and along the line of sight. The polarization power spectrum shows a power--law behaviour down to $\ell \sim 2700$ with slope $\beta^P_\ell = -1.65 \pm 0.15$. The $rms$ of polarization fluctuations is 7.2 K on 4 arcmin scales. By extrapolating the measured spectrum of total intensity emission, we find a contamination on the cosmological signal of $\delta T= \sqrt{\ell (\ell+1) C^I_\ell / 2\pi} \sim 5.7$ K on 5 arcmin scales and a corresponding $rms$ value of $\sim$18.3 K at the same angular scale. The level of the polarization power spectrum is $\delta T \sim 3.3$ K on 5 arcmin scales. Given its exceptionally bright polarized signal, the Fan region is likely to represent an upper limit on the sky brightness at moderate and high Galactic latitude.Comment: Minor corrections made to match the final version printed on A&A. A version with high resolution figures is available at http://www.astro.rug.nl/~bernardi/FAN/fan.pd