Large-scale 21-cm Cosmology with LOFAR and AARTFAAC Gehlot, Bharat Kumar
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Large-scale 21-cm Cosmology with LOFAR and AARTFAAC
PhD thesis
to obtain the degree of PhD at the University of Groningen
on the authority of the
Rector Magnificus prof. dr. E. Sterken and in accordance with the decision by the College of Deans.
This thesis will be defended in public on Friday 08 February 2019 at 12:45 hours
by
Bharat Kumar Gehlot
born on 10 August 1991
in New Delhi, India
Prof. L.V.E. Koopmans Prof. R.A.M.J. Wijers
Assessment Committee Prof. M.A.W. Verheijen Prof. P. Zarka
Prof. R. Subrahmanyan
To my parents.
the Northern Sky (in Hammer-Aitoff projection) produced with 6 hours of AARTFAAC data overlaid on a sky-map using the HiPS option in Stellarium software. LOFAR “Superterp” is shown in the landscape part. Background:
An artist’s impression of a starry sky.
ISBN: 978-94-034-1431-7 (printed version) ISBN: 978-94-034-1430-0 (electronic version)
Printed by: IPSKAMP Printing, Enschede, Netherlands.
v
Contents
Table of Contents v
1 Introduction 1
1.1 An overview . . . . 2
1.2 A Short Chronology of the Universe . . . . 3
1.3 Current status of affairs . . . . 5
1.3.1 Thompson scattering of CMB photons . . . . 6
1.3.2 High redshift quasar and GRB absorption spectra . . . 7
1.3.3 High redshift galaxy surveys . . . . 9
1.4 A new probe: the redshifted 21-cm line . . . . 9
1.4.1 Current and planned 21-cm experiments . . . . 11
1.4.2 The LOw-Frequency ARray (LOFAR) . . . . 14
1.4.3 The AARTFAAC Cosmic Explorer . . . . 17
1.5 Observational challenges in 21-cm experiments . . . . 19
1.5.1 Foreground emission . . . . 19
1.5.2 Ionospheric effects . . . . 20
1.5.3 Calibration . . . . 21
1.6 This thesis . . . . 21
2 Wide-field LOFAR-LBA power-spectra analyses 25 2.1 Introduction . . . . 27
2.2 Observations and Data processing . . . . 29
2.2.1 LOFAR-LBA system . . . . 30
2.2.2 Observations . . . . 31
2.2.3 Flagging and averaging . . . . 31
2.2.4 Calibration . . . . 32
2.2.5 Imaging . . . . 36
2.2.6 Source modeling . . . . 37
2.3 Differential power Spectrum . . . . 38
2.3.1 Excess Noise . . . . 40
2.3.2 Effect of calibration cut . . . . 41
2.4 Delay Spectrum of gridded visibilities . . . . 42
2.5 Ionospheric Scintillation . . . . 53
2.6 Conclusions and summary . . . . 58
Appendix 2.A Rotation Measure synthesis . . . . 61
3 Cosmic Dawn power spectrum limit with LOFAR 65 3.1 Introduction . . . . 67
3.2 Observations and preprocessing . . . . 69
3.2.1 LOFAR-Low Band Array . . . . 69
3.2.2 Observations . . . . 70
3.2.3 Data selection and preprocessing . . . . 71
3.3 Calibration Scheme . . . . 71
3.3.1 Calibrating the 3C220 field . . . . 73
3.3.2 Calibrating the NCP field . . . . 75
3.4 Noise statistics in LOFAR-LBA . . . . 77
3.4.1 Physical Excess Noise . . . . 77
3.4.2 Comparison with sub-band level noise . . . . 81
3.5 Gaussian Process Regression . . . . 82
3.5.1 Methodology . . . . 82
3.5.2 Application of GPR to the LOFAR-LBA data . . . . 83
3.6 Power Spectra Results . . . . 86
3.6.1 The 3C220 field: cylindrical power spectra . . . . 87
3.6.2 The NCP field: cylindrical power spectra . . . . 89
3.6.3 Comparison with noise power spectra . . . . 90
3.6.4 Spherically averaged power spectra . . . . 92
3.7 Summary and Outlook . . . . 94
3.7.1 Outlook . . . . 96
4 AARTFAAC Cosmic Explorer 97 4.1 Introduction . . . . 99
4.2 Observations and preprocessing . . . 102
4.2.1 The LOFAR AARTFAAC wide-field imager . . . 102
4.2.2 ACE observational setup and status . . . 104
4.2.3 Data preprocessing . . . 105
4.3 Calibration and Imaging . . . 105
4.3.1 Direction Independent calibration . . . 106
4.3.2 Direction Dependent calibration . . . 106
4.3.3 Imaging . . . 108
4.4 Thermal noise statistics . . . 108
4.5 Power Spectrum Analysis . . . 111
4.5.1 Cylindrically averaged power spectrum estimation . . . 112
4.5.2 Foreground Subtraction with GPR . . . 117
4.5.3 Spherically averaged power spectrum estimation . . . . 119
4.6 Summary and future work . . . 123
4.6.1 Future outlook and forecast . . . 123
5 Modelling Degree-Scale foregrounds 125 5.1 Introduction . . . 127
5.2 Observations and preprocessing . . . 129
5.2.1 The AARTFAAC wide-field Imager . . . 129
5.2.2 Observational setup . . . 131
5.2.3 Data preprocessing . . . 132
5.3 Calibration and imaging scheme . . . 133
5.4 Modelling the Diffuse Galactic Emission . . . 135
5.4.1 Removing compact sources . . . 135
5.4.2 Modeling with multiscale CLEAN . . . 137
5.4.3 Modelling with Shapelets . . . 139
5.4.4 Comparing the two diffuse emission modelling methods 139 5.5 The Angular power spectrum . . . 140
5.5.1 Power spectra from diffuse foreground modelling methods142 5.6 Summary and Future work . . . 143
5.6.1 Future Work . . . 144
6 Conclusions and future outlook 145 6.1 Main results . . . 146
6.1.1 A wide-field LOFAR-LBA power-spectrum analysis . . . 146
6.1.2 A first Cosmic-Dawn 21-cm signal power spectrum limit 148 6.1.3 The AARTFAAC Cosmic Explorer . . . 149
6.1.4 Modelling foregrounds on degree scales . . . 150
6.2 Future outlook and concluding remarks . . . 150
Bibliography 153
English summary 159
Nederlandse Samenvatting 165
हदी सारांश 171
Acknowledgments 177
1
1
1
Introduction
1
1.1 An overview
Understanding the formation and evolution of structures during different phases in the history of the Universe is one of the major frontiers in present-day as- tronomy and cosmology. Around 400,000 years after the Big Bang, matter decoupled from radiation, leaving a relic signature called the Cosmic Mi- crowave Background (CMB) radiation. Observations of the CMB radiation by the WMAP (Wilkinson Microwave Anisotropy Probe) and Planck missions have shed light on the formation of the Universe in the Big-Bang cosmology paradigm (Hinshaw et al. 2013; Planck Collaboration et al. 2016b). These observations provide a plethora of information about the major constituents of the Universe: baryonic (visible) matter, dark matter, and dark energy, as well as provide constraints on the structure formation in the infant Universe.
After matter decoupled from radiation, tiny matter density fluctuations grew under gravitational instability to form the first structures of dark and bary- onic matter, which are thought to have evolved into a cosmic web of sheets, filaments, and clusters as we observe them today (Springel et al. 2005). On the other hand, observations of galaxies and clusters of galaxies in the local uni- verse also provide a wealth of information, improving our understanding of the astrophysics of galaxies and structure formation in the local Universe (Cole et al. 2005). A combination of these observations generates a paradigm of structure formation in the Universe. Complex objects such as stars, galaxies, and clusters of galaxies that surround us today, are formed inside the over- dense regions that grew out of tiny fluctuations in the otherwise very smooth matter density that emerged from the Big Bang.
However, a substantial hiatus still exists in our current knowledge of the Uni-
verse. In particular, the cosmic Dark Ages which started after matter decou-
pled from radiation, the Cosmic Dawn (CD) when the first luminous objects
appeared and heated the Inter-Galactic Medium (IGM), and the Epoch of
Reionization (EoR) during which ionizing radiation from the first generation
of stars and galaxies started to ionize the IGM, are all poorly explored. The
CD and EoR are pivotal periods in the history of the Universe as they bear the
imprint of structure formation and evolution in the early stages of evolution of
the Universe. Apart from the CMB, so far no direct detection of the emission
of the IGM exist for these intervening epochs when the first stars and galax-
ies are thought to have formed. Our current knowledge of star and galaxy
formation is based on nearby objects which evolve in a completely different
environment, compared to theses first-generation luminous objects. Hence it
is crucial to study the properties of these first stars and galaxies during the CD
and EoR. Several experiments aim to study these cosmic epochs via the 21-cm
line of neutral hydrogen, using, or planning to use, a wide range of current
1
1.2: A Short Chronology of the Universe 3
and next-generation radio telescopes. This thesis presents various techniques to study and mitigate the challenges in observing these periods and explores the possibility of observing the Cosmic Dawn with the LOFAR and AART- FAAC radio telescopes, and present results obtained from these experiments.
In this chapter, we first go through different transitional periods in the IGM history of the Universe and place the CD and EoR on this cosmic timeline (section 1.2). We briefly summarise the current observational constraints on the CD and EoR in section 1.3. In section 1.4, we present the redshifted 21-cm line of neutral hydrogen as a new observational probe of the CD and EoR and provide a brief overview of experiments aiming to detect its signal.
We provide a brief description of the LOFAR-EoR key science project and the AARTFAAC Cosmic Explorer, and a brief technical overview of the radio telescopes used by these projects, in sections 1.4.2 and 1.4.3. Section 1.5 presents an overview of the key challenges faced by these 21-cm experiments.
Finally, this introductory chapter concludes with a brief overview and the major objectives of the chapters in this thesis (section 1.6).
1.2 A Short Chronology of the Universe
The Big Bang (BB) model of the origin and evolution of the Universe is broadly accepted. According to this model, the Universe started 13.8 billion years ago, likely from a quantum-gravity singularity. Roughly 10
−43seconds after the BB, the Universe was homogeneous to an extremely high level, isotropic and in a hot, dense and quantum state. The Universe is thought to have gone through a rapid expansion at an exponential rate via a process called infla- tion, and its size grew by a factor of about 10
26. This expansion also inflated inhomogeneities in the matter density, caused by quantum fluctuations (Kolb
& Turner 1990), by a large factor. Soon after this, matter annihilated with antimatter, and because of a minute asymmetry between the two, left an ex- cess of baryons. After this, the Universe continued to expand and cool down.
One second after the BB, the Universe was filled with a hot soup of neutrons, protons, electrons, positrons, photons, and neutrinos with a temperature of around 10
10K. Three minutes after the BB, the Universe cooled down suffi- ciently for neutrons and protons to combine via fusion and form light nuclei such as deuterium, helium and their isotopes. This process of the formation of light elements, via fusion, is called primordial nucleosynthesis.
The universe at this stage was still hot, dense and full of subatomic particles and light nuclei. The Universe was opaque and acted similarly to a blackbody due to the very high scattering cross-section between photons and electrons.
As the universe expanded further, it cooled down, decreasing its density. This
decrease, in turn, reduced scattering. Finally, after ∼ 380, 000 years, the Uni-
4 chapter 1: In tro duction
Figure 1.1 – Cartoon depicting a timeline of the Universe as per current understanding of the structure formation in the Universe.
Image credit: Roen Kelly/Discover magazine.
1
1.3: Current status of affairs 5
verse cooled below 3000 K, which allowed ions and electrons to recombine and form neutral hydrogen and helium via the process of recombination. At this point (z ∼ 1100), photons decoupled from baryons and the Universe became largely transparent. The relic radiation from this last scattering surface has a blackbody spectrum and is known as the Cosmic Microwave Background (CMB) radiation. Today, the peak of the blackbody spectrum is redshifted and into the microwave part of the electromagnetic spectrum, observed e.g., by the WMAP and Planck space missions.
Recombination ushered the universe into the cosmic Dark Ages (1100 ≳ z ≳ 30), during which the Universe was mostly dark, neutral and devoid of any luminous objects other than the fading CMB radiation. During this period, small perturbations in the matter density left over from inflation, grew fur- ther under the influence of gravitational instability to form first non-linear structures of dark and baryonic matter (dark matter ‘halos’ and stars and galaxies inside of them). The neutral gas falling into these halos is thought to have formed the first generation of stars and have accreted onto black holes, which together later formed the first galaxies. Formation of the first stars around 400 Myr after the BB, ended the dark ages and marked the beginning of the Cosmic Dawn (CD; 30 ≳ z ≳ 12). The ultraviolet and X-ray radia- tion from these stars and black holes heated the cold neutral hydrogen in the surrounding IGM, and during the transitional Epoch of Reionization (EoR;
12 ≳ z ≳ 6), radiation ionised most of the IGM. The EoR lasted for about 600 Myr until the hydrogen in the IGM phase transitioned nearly fully from being neutral to ionized. For a detailed theoretical overview of the astrophysics during these epochs, the reader is referred to Furlanetto, Oh & Briggs (2006);
Zaroubi (2013)
1.3 Current status of affairs
Although the narrative presented above provides a fiducial model of the struc- ture formation in the Universe in the first 1 Gyr after the BB, several key questions remain unanswered: e.g. What was the timing and duration of CD and EoR? Exactly when did these first stars form and what were their prop- erties (e.g., mass, luminosity function)? What sources were responsible for heating and ionizing the IGM? What were the properties of the first galaxies, e.g. their type, size, mass, luminosity, morphology, etc?
Direct observations of the IGM in these epochs are expected to answer these
questions. So far there have been only indirect observations, apart from detec-
tions of some rare objects (e.g., galaxies, quasars and GRBs). The following
subsections briefly describe the currently available observational constraints.
1
Figure 1.2 – Constraints on the ionization fraction x
e(z) during the EoR from CMB data for three different models. The dark and light blue regions represent the 68%
and 95% confidence intervals. Left: x
e(z) as a redshift-symmetric hyperbolic tan- gent function. Centre: x
e(z) as a redshift-asymmetric power law function. Right:
redshift-symmetric parameterization of x
e(z) with additional constraints from the ki- netic Sunyaev-Zeldovich effect. Image reproduced from Planck Collaboration et al.
(2016a)
1.3.1 Thompson scattering of CMB photons
The primordial CMB radiation is linearly polarized as a result of Thompson scattering between the CMB photons and free electrons before the epoch of recombination. However, the number density of electrons increases due to reionization and causes re-scattering of CMB photons during the EoR. The probability of an interaction between CMB photons and free electrons is re- lated to the Thomson scattering optical depth τ of CMB photons given by:
τ =
∫
t0t(z)
n
eσ
Tc dt, (1.1)
where n
eis the number density of free electrons at time t, σ
Tis the Thompson scattering cross-section, t
0is the present time and t(z) is the time at redshift z. The value of n
edepends on the evolution of the neutral hydrogen fraction of the IGM with redshift, or, in other words, on the reionization history.
Thompson scattering of the quadrupole component of the CMB radiation field by the free electrons during EoR causes linear-polarization anisotropy in the CMB at large angular scales. The amplitude of the polarization anisotropy is related to the size of the horizon at the redshift when the scattering occurred, and also depends on the scattering optical depth τ . Planck Collaboration et al. (2016a), from the analysis of the CMB temperature and polarization power spectra, found the optical depth for Thompson scattering to be τ = 0.058 ±0.012, which can be translated to a model-dependent ionization fraction x
e(z) = n
e(z)/n
H(z), where n
H(z) is the number density of hydrogen atoms.
However, this constraint is only sensitive to the line-of-sight integral of n
e(z).
Therefore, the reionization history cannot be determined uniquely from the
1
1.3: Current status of affairs 7
measurements of the Thompson scattering optical depth alone. Figure 1.2 shows constraints on x
e(z) for three different ionisation models determined using Planck CMB data. Constraints on x
e(z) are currently not very secure and are heavily model dependent.
1.3.2 High redshift quasar and GRB absorption spectra
Absorption spectra of high-redshift quasars can also be used to place con- straints on reionization using the Gunn-Peterson effect (Gunn & Peterson 1965). Consider radiation blue-ward of the Ly-α transition, emitted by a back- ground source at a particular redshift. In an expanding universe, the spectrum of the radiation is redshifted and eventually is absorbed by intervening neutral hydrogen clouds along the line of sight at intermediate redshifts. The absorp- tion feature occurs at the frequency corresponding to the rest-frame frequency of Ly-α in the redshifted spectra. After reionization largely completed, the neutral hydrogen density in the IGM is extremely low, and quasar spectra show discrete Ly-α absorption lines due to these (still rare) intervening neu- tral hydrogen clouds along the sight-line at different redshifts. This collection of absorption lines in a quasar spectrum is called the Ly-α forest.
However, as the IGM becomes more neutral toward higher redshifts (i.e., dur- ing the EoR), it absorbs a more significant fraction of the Ly-α emission, developing a ‘trough’ blue-wards of the Ly-α line in the observed spectra of high redshift quasars. This feature is called the Gunn-Peterson trough and was first observed by Becker et al. (2001) in the high redshift quasar spectra shown in figure 1.3. After this discovery, many optical quasar spectra have been observed to infer the neutral hydrogen fraction in the IGM as a function of redshift (Fan et al. 2003, 2006). A comparison between the optical spectra shown in figure 1.3 suggests that most of the hydrogen in post-reionization Universe (z < 6) is ionized and there is a sudden increase in the fraction of neutral hydrogen at z ≳ 6, suggesting that the EoR ended around z ≈ 6.
However, due to the large scattering cross-section of Ly-α photons with neu- tral hydrogen, even a minuscule neutral hydrogen fraction (10
−4.5) can cause the optical depth to saturate (Becker, Bolton & Lidz 2015). Furthermore, the absorption spectra only probe the line of sight evolution of the neutral hydrogen fraction in the IGM and require several observations along different sight-lines to infer its global state. Hence, this method can only be used to place weak lower limits on the IGM neutral fraction.
Similar to quasar absorption spectroscopy, optical spectra of high redshift
Gamma-Ray Bursts (GRBs) exhibit Ly-α absorption due to neutral hydrogen
in the IGM. The advantage of GRB absorption spectroscopy is that GRBs are
very luminous objects and can be detected at even higher redshifts. The first
1
Figure 1.3 – The optical quasar spectra of four high-redshift quasars observed with
the Keck telescope. The wavelengths are denoted in the quasar rest frame. The Gunn-
Peterson trough becomes more prominent at higher redshifts. Figure reproduced from
Becker et al. (2001).
1
1.4: A new probe: the redshifted 21-cm line 9
upper limit on neutral hydrogen fraction of x
HI< 0.17 at z = 6.3 was placed by Totani et al. (2006).
1.3.3 High redshift galaxy surveys
Near-infrared observations of high redshift galaxies are instrumental in search- ing for the sources responsible for reionization. Current and upcoming high- redshift galaxy surveys with the Hubble Space Telescope (Bouwens et al. 2011) and the planned James Webb Space Telescope can and will provide a wealth of information on the nature of these sources. The ultraviolet luminosity func- tions determined from these surveys can be used to infer the star formation rates at high redshifts. Similarly, observations of GRBs at high redshifts are another tracer of the formation rates of massive stars, and a sufficient num- ber of detections may provide constraints on star formation during the EoR (Wang 2013).
However, inferring the reionization history with galaxy surveys at high red- shifts require several assumptions based on models. For example, inferring the star formation rate density from luminosity functions requires assump- tions about the initial mass function of stars, which is poorly constrained at high redshifts. Similarly, estimation of the ionization fraction from the star- formation rate density requires information about the escape fraction of Ly-α photons and the IGM recombination rate in the clumpy gas which are again highly uncertain. The lack of knowledge about the parameters mentioned above makes studies of these early phases of the Universe extremely difficult.
1.4 A new probe: the redshifted 21-cm line
Given the limitations of the probes described in section 1.3, only a direct and independent probe of the thermal and ionization history of the IGM during the cosmic dawn reionization can provide a more comprehensive picture of these eras. In recent years, largely thanks to enormous strides forward in low- frequency radio telescope technology and computing, the 21-cm line of neutral hydrogen has become as a promising probe of neutral hydrogen in the IGM during the CD and EoR.
A neutral hydrogen atom, in its ground-state, consists of a single proton and
an electron in 1s orbital. The electron and proton spins are coupled and can
exist in a parallel or anti-parallel spin state, depending on the alignment of
the electron and proton spins. These spin-states have an energy difference
of about 5.87 µeV (with the parallel spin state being at higher energy). A
(hyperfine) transition between these spin-states can be mediated by absorption
or emission of a photon, with a frequency of 1420 MHz (wavelength of about
1
Figure 1.4 – Results of simulations of the expected 21-cm signal as a function of red- shift adopted from Pritchard & Loeb (2010a).Top panel: evolution of 21-cm brightness temperature fluctuations during different epochs. Bottom panel: The sky averaged differential brightness as a function of redshift.
21 cm). However, the transition is forbidden, with a transition probability of 2.9×10
−15s
−1with a lifetime for spontaneous emission of 11 million years. The large abundance of neutral hydrogen (about 75% of all baryonic matter) in the Universe makes the 21-cm transition an excellent tracer of neutral hydrogen in the Universe. Unlike Ly-α photons, 21-cm photons have a smaller chance of getting absorbed by intervening gas in the IGM along the sight-line between the source and the observer. This absorption, in principle, enables three- dimensional tomographic mapping of the Universe during the CD and EoR.
The brightness temperature of the 21-cm line is used to measure the 21-cm signal. The brightness temperature of radiation is equivalent to the tempera- ture of a blackbody in thermal equilibrium with its surroundings. According to Planck’s law, the specific intensity I
ν(energy emitted per unit area per unit frequency per unit solid angle) of the radiation emitted by a blackbody, at a temperature T and as a function of frequency, is:
I
ν= 2hν
3c
21 e
hν
kB T
− 1 , (1.2)
where h is Planck’s constant, k
Bis Boltzmann’s constant, c is the speed of
light and ν is frequency. The rest frame frequency of the 21-cm transition is
1420 MHz. The redshifted 21-cm emission from the CD and EoR (30 ≳ z ≳ 6)
lies in the wide frequency range of 50-200 MHz. In the limit of very high
temperatures or low frequencies (Rayleigh-Jeans approximation), i.e., hν <<
1
1.4: A new probe: the redshifted 21-cm line 11
k
BT , Planck’s law modifies to:
I
ν= 2ν
2c
2k
BT = 2k
BT
λ
2. (1.3)
The brightness temperature T
b(ν) can then be expressed in terms of a specific intensity as:
T
b(ν) = λ
22k
BI
ν. (1.4)
The 21-cm transition of neutral hydrogen in the IGM can be observed in absorption or emission against the CMB radiation (Field 1957, 1959). The differential brightness temperature δT
bof the redshifted 21-cm radiation from the CD and EoR depends on several factors such as the brightness temperature of the CMB radiaton (T
CM B), the neutral hydrogen fraction x
HI, the matter density contrast (δ), and the cosmological parameters. δT
bcan be written as (Madau, Meiksin & Rees 1997):
δT
b≈ 27 x
HI(1 + δ)
( 1 + z 10
)
12
(
1 − T
CM B(z) T
S) ( Ω
b0.044 h 0.7
)
× ( Ω
m0.27 )
12
(
1 − Y
p1 − 0.248 ) (
1 + 1 H(z)
dv
∥dr
∥)
−1mK, (1.5) where T
Sis the spin (or excitation) temperature of the 21-cm transition, Ω
band Ω
mare the baryonic and total matter density parameters, respectively, Y
pis the primordial helium abundance by mass, h is the normalised Hubble parameter, H(z) is the redshift dependent Hubble parameter and dv
∥/dr
∥is the proper gradient of the peculiar velocity along the line of sight.
Figure 1.4 shows a simulation of the evolution of the 21-cm brightness temper- ature fluctuations and sky-averaged brightness temperature with time. The first astrophysical sources appear around z ∼ 30 and start to ionize the neutral hydrogen in their surroundings. The regions with δT
b= 0 are the bubbles of ionized gas in the neutral IGM which grow with time and merge to form larger ionized regions. Eventually, the entire IGM gets ionized by z ∼ 6. The figure also shows the sky-averaged brightness temperature of the 21-cm signal. The evolution profile of the latter shows different time periods when the 21-cm signal is seen in absorption or emission.
1.4.1 Current and planned 21-cm experiments
Several current and next generation interfermoeters, such as the LOw Fre- quency ARray
1(LOFAR; van Haarlem et al. 2013), the Giant Meterwave Radio
1
http://www.lofar.org/
1
Telescope
2(GMRT; Paciga et al. 2011), the Murchison Widefield Array
3(MWA;
Tingay et al. 2013; Bowman et al. 2013), the Precision Array for Probing the Epoch of Reionization
4(PAPER; Parsons et al. 2010), the Hydrogen Epoch of Reionization Array
5(HERA; DeBoer et al. 2017), NENUFAR
6(New Exten- sion in Nançay Upgrading loFAR; Zarka et al. 2012), and the planned Square Kilometre Array
7(SKA; Mellema et al. 2013; Koopmans et al. 2015) are seek- ing to statistically detect the power spectrum of the brightness temperature fluctuations in the cosmological 21-cm signal during the EoR and CD.
Complementary to these experiments, single element radiometers such as the Experiment to Detect the Global Epoch of Reionization Signature (EDGES;
Bowman et al. 2018), the Large-aperture Experiment to Detect the Dark Ages (LEDA; Bernardi et al. 2016), the Shaped Antenna measurement of the back- ground RAdio Spectrum 2 (SARAS 2; Singh et al. 2017), the Sonda Cosmológ- ica de las Islas para la Detección de Hidrógeno Neutro (SCI-HI; Voytek et al.
2014), the Probing Radio Intensity at high z from Marion (PRIZM; Philip et al. 2018), and the Netherlands-China Low frequency Explorer
8(NCLE) are aiming to measure the sky-averaged 21-cm signal as a function of redshift.
Although detection of the power spectrum of 21-cm brightness temperature fluctuations remains elusive, several experiments have already placed inter- esting upper limits on the power spectrum of the 21-cm signal at differ- ent redshifts during the EoR. The tightest upper limit has been provided by the LOFAR-EoR Key Science Project (KSP) of ∆
221< (79.6 mK)
2at k ≈ 0.053 h cMpc
−1in the redshift range z = 9.6 − 10.6 (Patil et al. 2017).
Only Ewall-Wice et al. (2016) and Gehlot et al. (2018b) have provided upper limits on the 21-cm signal during the CD using the MWA and LOFAR-Low Band Antenna array, respectively.
Recently, the EDGES collaboration (Bowman et al. 2018) reported a deep spectral feature centred at 78 MHz. This feature was presented as a tenta- tive detection of the long sought-after 21-cm absorption feature seen against the CMB around the redshift z ∼ 17. Figure 1.5 shows the best-fit absorp- tion profiles obtained with different hardware configurations in the EDGES experiment. The location of this potential absorption trough (z ∼ 17) is consistent with the simulations and theoretical models of the CD (Pritchard
2
http://gmrt.ncra.tifr.res.in/
3
http://www.mwatelescope.org/
4
http://eor.berkeley.edu/
5
http://reionization.org/
6
https://nenufar.obs-nancay.fr/
7
http://skatelescope.org/
8
https://www.ru.nl/astrophysics/research/radboud-radio-lab-0/projects/
netherlands-china-low-frequency-explorerncle/
1
1.4: A new probe: the redshifted 21-cm line 13
Figure 1.5 – The best-fit 21-cm absorption profiles for different hardware configu- rations (H1 - H8) of the EDGES experiment in 60-100 MHz frequency range. The black line corresponds to the hardware configuration with the highest signal to noise ratio. The dotted line (P8) corresponds to the same analysis as H2 but with a dif- ferent foreground model and a wider frequency range. This figure is reproduced from Bowman et al. (2018).
& Loeb 2010a; Mesinger, Ferrara & Spiegel 2013; Cohen et al. 2017). How- ever, the depth (∆T
21∼ 0.5 K within 99% confidence interval) and width (∆ν ∼ 19 MHz) of the feature is considerably deeper and wider than the pre- dictions by the most optimistic models (Pritchard & Loeb 2010b; Fialkov &
Barkana 2014; Fialkov & Loeb 2016; Cohen et al. 2017). Although, Hills et al.
(2018) raised concerns about this claimed detection, if the detection is verified
and confirmed by other ongoing experiments, it might unveil exotic astrophys-
ical phenomena (Barkana 2018; Fialkov, Barkana & Cohen 2018; Ewall-Wice
et al. 2018; Feng & Holder 2018; Dowell & Taylor 2018).
1
Figure 1.6 – The LBA dipoles (left panel) and the HBA tiles (right panel). Image reproduced from van Haarlem et al. (2013).
1.4.2 The LOw-Frequency ARray (LOFAR)
LOFAR is a state of the art radio interferometer constructed in the north- ern part of the Netherlands. It operates in the low-frequency range from 10 − 240 MHz, corresponding to a wavelength range 1.2 − 30 m, which spans the lowest end of the electromagnetic spectrum observable from Earth. The international LOFAR telescope consists of 51 stations
9, 38 of which are spread across the north-eastern part of the Netherlands and remaining 13 stations are distributed across six countries in Europe, providing baseline lengths rang- ing from 70 m to 2000 km. Unlike traditional radio telescopes, LOFAR does not have any moving components, the pointing and tracking are achieved by electronically combining the signals from different receiver elements within a station in real-time.
LOFAR design and layout
Each LOFAR station has two distinct types of receivers: Low Band Antenna (LBA) which are designed to operate within 10 −90 MHz frequency range, and High Band Antennas (HBA) which are sensitive in 110 − 240 MHz frequency range. LBAs are low-band dual polarisation droop dipoles having an arm length of 1.38 m placed above a conducting ground plane at an angle of 45
◦with respect to the ground (left panel of figure 1.6). An LBA dipole has a full-sky Field of View with Full Width Half Maximum (FWHM) of 120
◦. The HBAs are a group (referred to as a ‘tile’) of 16 bow-tie shaped dual-polarisation antennas arranged in a 4 × 4 grid of size 5 × 5 m (right panel of figure 1.6).
The 16 dipoles in an HBA tile are analogue beam-formed to produce a single tile beam with an FWHM of ∼ 25
◦at 150 MHz. The 48 High-Band Antenna
9
A LOFAR station is akin to a dish in conventional radio telescopes.
1
1.4: A new probe: the redshifted 21-cm line 15
Figure 1.7 – Station layout of Core, Remote and International stations. The big circles represent the LBA dipoles and regular grids of squares represent HBA tiles.
Image reproduced from van Haarlem et al. (2013).
tiles of the 24 core stations are split into two independently operating fields.
The LOFAR stations are divided into three categories based on their distance from the centre of the array and receiver layout. Out of 51 LOFAR stations, 24 stations also referred to as the Core Stations, are spread within a dense core of 2 km radius located near Exloo in the Netherlands; 14 stations, also referred to as Remote Stations, are spread across the 40 × 80 km area in the northeastern part of the Netherlands. The remaining 13 stations called International Stations are distributed across six countries in Europe. The central region of the LOFAR core is called “superterp”, and it houses 6 Core Stations within a 300 m diameter. Figure 1.8 shows an aerial photograph of the superterp. The dense core of LOFAR provides unparalleled sensitivity, and the long baselines provide high-resolution imaging at low frequencies.
The main difference between the Core, Remote and International Stations is the number of LBA and HBA dipoles and their layout within the stations.
Each Core Station or Remote Station consists of 96 LBA dipoles randomly spread within an area of 81 m diameter and 48 HBA tiles arranged in a regular pattern. However, HBA tile arrangement is different for Core and Remote Stations. The International Stations have 96 LBA dipoles and 96 HBA tiles.
The LBA dipole and HBA tile layout for the three stations are shown in
figure 1.7.
1
Figure 1.8 – An aerial of the superterp, located near Exloo (Netherlands). Image reproduced from van Haarlem et al. (2013).
LOFAR signal processing chain
The voltages measured by the receiver elements are digitised using a 12-bit A/D converter with a sampling clock of 200 MHz housed in a receiver unit (RCU). At any given time, the RCUs can only process the signal from 48 out of 96 LBA dipoles or 48 HBA tiles. This setup allows the user to choose from different station configurations, depending on the requirements. The digitised data are then split into 488 sub-bands of 195.3 kHz width by a polyphase filter, providing a total bandwidth of 96 MHz. The digitised signals from the receivers are combined in a beam-former to produce a digitally steerable station beam.
The total bandwidth of the system can be traded against the number of beams (pointings) in the sky, e.g., for two pointings, effective bandwidth per pointing is reduced to 48 MHz.
The beam-formed data are transported over a dedicated fibre-optics Wide Area
Network (WAN) to the central processing facility (CEP) located at the Center
of Information and Technology (CIT; University of Groningen) in Groningen,
the Netherlands. The GPU correlator (COBALT) located at the CIT gener-
ates correlations (XX, XY, YX, YY) at 1 s integration and 3 kHz frequency
resolution (64 channels per sub-band) and stores them in Measurement Set
(MS) format on CEP storage clusters. We refer the readers to van Haarlem
1
1.4: A new probe: the redshifted 21-cm line 17
et al. (2013) for detailed information of the sensitivity and observing capabil- ities of the LOFAR international telescope.
1.4.3 The AARTFAAC Cosmic Explorer
If the claimed detection of the 21-cm absorption feature by the EDGES col- laboration is validated, the strength of the 21-cm absorption feature will also lead to a substantial increase in the 21-cm brightness temperature fluctua- tions in the redshift range z = 16 − 19 corresponding to the deepest part of the absorption trough (Barkana 2018; Fialkov, Barkana & Cohen 2018).
Such large signals make it possible to statistically detect the 21-cm brightness temperature fluctuations in this redshift range on angular scales of about a degree within a ∼ 50 times shorter integration time as compared to previous predictions.
This opportunity has motivated us to commence a long-term program called the “AARTFAAC Cosmic Explorer” (ACE) programme, which aims to mea- sure, or set stringent limits on, the power spectrum of the brightness tem- perature fluctuations of the 21-cm signal from redshift z ∼ 18 using the Amsterdam-ASTRON Radio Transient Facility And Analysis Centre (AART- FAAC) system (Prasad et al. 2016). AARTFAAC is a wide-field imager based on LOFAR and cross-correlates up to 576 individual receiver elements (LBA dipoles or HBA tiles) from the twelve innermost stations in the LOFAR core, providing a much larger field of view and increased sensitivity on large angu- lar scales compared to the LOFAR beam-formed array. The ACE programme aims for a 1000 h deep integration of a large section of the northern sky to mea- sure or set firm upper limits on the power spectrum of the 21-cm signal. The LOFAR-EoR research group has provisionally been awarded 1000 h of obser- vations with LOFAR-AARTFAAC by the LOFAR time allocation committee to carry out the ACE programme (proposal code: LT10_006). The Principal Investigators of the program are L.V.E. Koopmans and B.K. Gehlot. A brief overview of the LOFAR-AARTFAAC wide-field imager is provided below.
LOFAR-AARTFAAC wide-field imager
AARTFAAC is a LOFAR based all-sky radio transient monitor (Prasad et al.
2016; Kuiack et al. 2018). It piggybacks on currently ongoing LOFAR obser- vations by tapping the digital signal streams from individual receiver elements of a subset of the LOFAR stations and independently processes these signal streams. The choice of the subset of LOFAR stations is defined primarily by sensitivity and image quality. AARTFAAC operates in two modes viz.
A6 where the six innermost stations (the superterp) of the LOFAR core are
used, and A12 where the twelve innermost stations of the LOFAR core are
1
Figure 1.9 – The layout of AARTFAAC stations. The A6 mode utilises stations within the white circle. The A12 mode utilises the A6 plus six other stations high- lighted by white polygons. The white patches represent LBAs and the red patches represent HBAs. This image is adapted from LOFAR interactive map
10.
used. Figure 1.9 shows the stations that are included in AARTFAAC. The A6 mode consists of 288 receiver elements (LBA dipoles or HBA tiles from six su- perterp stations) within a 300 m diameter circle and forms a densely sampled uv-plane (almost fully filled uv-coverage within 0 − 300 m after a 12-hr track).
A6 is co-planar at the centimetre level, which is optimal for wide-field imaging.
The A12 consists of 576 receiver elements (from 12 central stations of LOFAR core) which provide higher sensitivity and improved resolution imaging over A6. The stations utilised in A12 are chosen such that they provide a uniform uv-coverage while maintaining a reasonably small w-component. For opera- tions in the LBA band, the dipoles in the LBA_OUTER station configuration are selected for AARTFAAC observations. In the LBA_OUTER configuration, the 48 outermost dipoles are selected from 96 randomly spread dipoles (see van Haarlem et al. (2013) for more information about LOFAR station configura- tions).
10
http://astron.nl/lofartools/lofarmap.html
1
1.5: Observational challenges in 21-cm experiments 19 The digitised signals from the receiver elements are tapped before digital beam- forming and transported to the AARTFAAC GPU correlator located at the CIT in Groningen, the Netherlands. Currently, due to limited network capac- ity, only 16 sub-bands can be correlated in the 16-bit mode. Each sub-band is 195.3 kHz wide and consists of up to 64 channels, providing a maximum frequency resolution of 3 kHz and a maximum instantaneous bandwidth of 3.1 MHz. The output XX, XY, YX, YY correlations are either dumped on the AARTFAAC storage/compute cluster or routed to the AARTFAAC real-time calibration and the imaging pipeline for transient detection. AARTFAAC can only observe in a drift-scan mode. However, phase-tracking can be applied to the raw data during or after preprocessing. The raw data from the AART- FAAC storage/compute cluster can be streamed via a fast network (1 Gbit/s) to LOFAR processing cluster at the CIT. The raw data can be converted to standard Measurement Set (MS) format using custom software packages.
Readers may refer to Prasad et al. (2016) for further information about AART- FAAC system design and capabilities.
1.5 Observational challenges in 21-cm experiments
The 21-cm experiments seeking to measure the faint 21-cm signal from the EoR and CD are limited by real-world challenges, which contaminate and distort this faint signal. The key challenges in 21-cm experiments are contamination due to bright astrophysical foregrounds, distortions of the incoming signals by the ionosphere which is the uppermost ionised part of the Earth’s atmosphere, artefacts due to the complex instrumental response, and Radio Frequency Interference (RFI). Overcoming these challenges is the most crucial part of all 21-cm signal experiments, and it is imperative to mitigate or remove these effects in order to detect the faint 21-cm signal.
1.5.1 Foreground emission
The 21-cm signal from the early Universe is extremely faint. According to current theoretical predictions, the brightness temperature of the 21-cm signal ranges from several milli-Kelvin to several tens of milli-Kelvins depending upon the redshift and the spatial scale of the emission. At low frequencies (< 200 MHz), the Galactic foreground emission and extra-galactic sources, such as radio galaxies and clusters, dominate the sky. The intensity of this foreground emission is 4-5 orders of magnitude higher than the expected 21- cm signal. Even the fluctuations on the brightness of these foregrounds are around three orders of magnitude higher than the 21-cm signal.
The foreground emission has two dominant components: (1) diffuse emis-
1
Figure 1.10 – A cartoon depicting the different foreground components that con- taminate the 21-cm signal. Image credit: Vibor Jelić
sion comprising Galactic synchrotron emission, Galactic free-free emission and extra-galactic synchrotron emission. The other dominant component is the emission of extra-galactic sources, such as radio galaxies and clusters. Syn- chrotron emission from supernova remnants (usually within our Galaxy) is another source of foreground emission. Figure 1.10 shows a sketch depict- ing various foreground components at low frequencies. These foregrounds are mostly a result of continuum emission processes involving the interaction be- tween relativistic charged particles and a magnetic field and have very smooth spectral behaviour which can be modelled using power-laws or higher order log-polynomial models. On the contrary, the 21-cm signal is expected to have a non-smooth spectral structure. All foreground removal techniques exploit these distinct spectral behaviours to remove the foregrounds from the observed data.
1.5.2 Ionospheric effects
Gases in the uppermost part of the Earth’s atmosphere are photo-ionised by
UV and X-ray radiation from the sun, giving rise to a permanent layer of
plasma called the ionosphere. Low-frequency electromagnetic waves propa-
1
1.6: This thesis 21
gating through the ionosphere are distorted by fluctuations in the density of the ionospheric plasma. This ‘turbulence’ induces spatially varying phase- shifts in the propagating wave-front causing refractive and diffractive effects on various spatial scales. These phase-shifts result in refraction and diffraction (e.g., scintillation) of observed sources.
1.5.3 Calibration
Instrumental imperfections, such as complex receiver gains, global band-pass errors, direction-dependent antenna response errors, and ionospheric propaga- tion effects corrupt the sky observed by a radio telescope. These effects must be ‘calibrated’ in order to achieve a sufficiently high dynamic range while maintaining high image fidelity. Achieving a high level of accuracy in the cali- bration of the instrument in order to detect the 21-cm signal is one of the most critical challenges in all 21-cm experiments. Self-calibration is the most com- monly employed strategy to calibrate the instrument. Self-calibration is an iterative scheme where the difference between the real sky and a ‘sky-model’
is minimised in order to obtain the instrumental gains and eventually the sky emission. In addition to this, direction-dependent calibration accounts for mul- tiple direction dependent corruption effects during calibration and subtraction of sources.
Nonetheless, there are numerous challenges which limit the accuracy of the calibration desired in 21-cm experiments. For example, the sky-model used during calibration is based on other observations and is often erroneous itself which causes imperfect calibration and subtraction of sources. Furthermore, it is almost impossible to include all sources of foreground emission in the sky- model. Using an incomplete and inaccurate sky-model in calibration leads to biases in the residual data which makes it difficult to obtain the weak 21-cm signal.
Even if the calibration process is perfect and foregrounds are removed with high accuracy, there is the additional thermal-noise uncertainty in the data due to receiver noise and the stochastic nature of the sky emission. This thermal noise is uncorrelated in time and frequency and averages down by integrating over more extended time and larger frequency range. Notwithstanding, several hundred or even thousands of hours of observations are required to reduce the thermal noise and achieve adequate sensitivity to detect the 21-cm signal.
1.6 This thesis
From the previous sections, the reader may have discerned the importance
of exploring the Cosmic Dawn and Epoch of Reionization using the 21-cm
1
signal of neutral hydrogen, to fill the hiatus in our current understanding of the formation and evolution of structure in the Universe. Many ongoing and upcoming efforts aim to probe these eras using low-frequency radio interfer- ometers. These experiments need to overcome significant challenges such as foreground emission, ionospheric distortions, complex instrumental responses, as well as biases generated during the signal processing stage, which all corrupt the weak 21-cm signal.
This thesis presents a range of investigations of essential aspects of these detec- tion challenges and also presents the first 21-cm signal power-spectrum limits at the highest redshifts currently reachable by low-frequency radio telescopes.
In particular, the thesis focusses on understanding the consequences of these complex challenges for current and future 21-cm experiments that probe the CD and EoR and developing innovative techniques to overcome, or bypass, these challenges in current and future CD and EoR 21-cm signal experiments.
• Chapter 2 focuses on quantifying (polarised) foregrounds, polarisation leakage, systematic biases and ionospheric effects and their impact on Cosmic Dawn experiments using LOFAR-LBA. Various statistical meth- ods are employed to quantify these effects and discuss methods to miti- gate and remove them. The lessons learned from this analysis are valu- able in planned experiments with AARTFAAC, NENUFAR, HERA and SKA-Low which all aim to probe the CD.
• Chapter 3 illustrates a novel multi-beam calibration strategy for LOFAR- LBA. It also illustrates the application of the entire LOFAR-EoR pro- cessing pipeline on this unique dataset. The lessons learned in chapter 2 help refine the LOFAR-EoR data processing pipeline, which is then used to determine, for the very first time, a 21-cm power spectrum limit in very high redshift range of z = 19 − 25, from 14 h of dual-pointing data observed with LOFAR-LBA.
• Chapter 4 provides an overview of the AARTFAAC Cosmic Explorer (ACE) programme, which we have started in order to probe the 21-cm signal brightness temperature fluctuations at redshift z ∼ 18 correspond- ing to the location of the alleged 21-cm absorption feature reported by the EDGES collaboration. This chapter also presents the first 21-cm sig- nal power-spectrum results from 6 h of ACE data obtained in a unique
“semi drift-scan” mode and processed with the LOFAR-EoR processing pipeline.
• Chapter 5 addresses another critical challenge in 21-cm signal experi-
ments, being the of modelling the diffuse foreground emission and in-
cluding it in the gain-calibration step. Wide-field observations of a field
1
1.6: This thesis 23
around North Celestial Pole with the AARTFAAC-HBA are used to ob- tain such a model for the first time. The resulting wide-field images are the first-ever images produced with the AARTFAAC-HBA system. Two different methods are demonstrated to model the diffuse emission in the field and compare the results. Finally, an angular power spectrum is pre- sented to quantify the strength of the foreground emission as a function of angular scale.
• Chapter 6 summarises the thesis research and presents a number of con-
cluding remarks, ending with a discussion on future work and follow up
research of the presented results.
1
2
25
2
Wide-field LOFAR-LBA power-spectra analyses:
Impact of calibration, polarization leakage and ionosphere
B. K. Gehlot, L. V. E. Koopmans, A. G. de Bruyn, S. Zaroubi, M. A. Brentjens, K. M. B. Asad, M. Hatef, V. Jelić, M.
Mevius, A. R. Offringa, V. N. Pandey, S. Yatawatta
Monthly Notices of Royal Astronomical Society, 478, 1484 (2018)
2
Abstract
Contamination due to foregrounds (Galactic and Extra-galactic), calibration
errors and ionospheric effects pose major challenges in the detection of the
cosmic 21 cm signal in various Epoch of Reionization and Cosmic Dawn ex-
periments. We present the results of a pilot study of a field centred on 3C196
using LOFAR Low Band (56-70 MHz) observations, where we quantify various
wide field and calibration effects such as gain errors, polarised foregrounds, and
ionospheric effects. We observe a ‘pitchfork’ structure in the 2D power spec-
trum of the polarised 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
( ∼ 30%) towards Cas A (∼ 21 kJy at 81 MHz, the brightest source in north-
ern sky), which is far away from the primary field of view. We measure an
extremely small ionospheric diffractive scale (r
diff≈ 430 m at 60 MHz) towards
Cas A resembling pure Kolmogorov turbulence compared to r
diff∼ 3 − 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 the aforementioned effects
and mitigating them in future Cosmic Dawn observations (e.g. with SKA-low
and HERA) in the same frequency window.
2
2.1: Introduction 27
2.1 Introduction
The first stars and galaxies formed during the so-called Cosmic Dawn (CD) spanning redshifts 30 ≳ z ≳ 15 (Pritchard & Furlanetto 2007). The ultraviolet and X-ray radiation from these first stars started to heat and ionize the neutral Hydrogen (HI hereafter) in the surrounding Inter-Galactic Medium (IGM), continuing until hydrogen gas in the universe transitioned from being fully neutral to become fully ionized (Madau, Meiksin & Rees 1997). Substantial ionization of the IGM only occurred at z ≲ 15 and this process completed around z ∼ 6. This era in the history of the universe is known as the Epoch of Reionization (EoR).
Current constraints on the redshift range of the reionization are inferred from indirect probes such as high-redshift quasar spectra (Becker et al. 2001; Fan et al. 2003, 2006), the optical depth for Thomson scattering from Cosmic Microwave Background (CMB) polarization anisotropy (Page et al. 2007; Ko- matsu et al. 2011; Hinshaw et al. 2013; Planck Collaboration et al. 2016a), IGM temperature measurements (Theuns et al. 2002; Bolton et al. 2010), Ly- man break galaxies (Pentericci et al. 2011; Ono et al. 2012; Schenker et al.
2012), the kinetic Sunyaev-Zel’dovich effect (Zahn et al. 2012) and high red- shift gamma ray bursts (Wang 2013). The most recent constraint on the upper limit of reionization redshifts comes from Planck Collaboration et al. (2016a) suggesting that the universe is ionized at ≲ 10% level for z ≳ 10 and substan- tial reionization happened during redshifts between z = 7.8 and 8.8. Although these probes shed some light on the timing and duration of the reionization, there is very little known about the evolution of IGM during reionization, nature of sources of the ionizing radiation and their evolution.
Observations of 21 cm hyperfine transition of HI at high redshifts promises to be an excellent probe of the HI distribution in IGM during EoR (Madau, Meiksin & Rees 1997; Shaver et al. 1999; Furlanetto, Oh & Briggs 2006;
Pritchard & Loeb 2012; Zaroubi 2013). Several ongoing and upcoming ex- periments such as the LOw Frequency ARray
1(LOFAR; van Haarlem et al.
2013), the Giant Meterwave Radio Telescope
2(GMRT; Paciga et al. 2011), the Murchison Widefield Array
3(MWA; Tingay et al. 2013; Bowman et al. 2013), the Precision Array for Probing the Epoch of Reionization
4(PAPER; Parsons et al. 2010), the 21 Centimeter Array (21CMA; Zheng et al. 2016), the Hydro- gen Epoch of Reionization Array
5(HERA; DeBoer et al. 2017), and the Square
1
http://www.lofar.org/
2
http://gmrt.ncra.tifr.res.in/
3
http://www.mwatelescope.org/
4
http://eor.berkeley.edu/
5
http://reionization.org/
2
Kilometre Array
6(SKA; Mellema et al. 2013; Koopmans et al. 2015) aim to detect the redshifted 21 cm emission from the EoR. Although the above instru- ments focus largely on detecting the EoR, LOFAR-LBA, and the upcoming HERA, SKA-low, LEDA
7(Large-aperture Experiment to detect Dark Ages;
Price et al. 2017) and NENUFAR
8(New Extension in Nançay Upgrading lo- FAR; Zarka et al. 2012) also observe at frequency range 50-80 MHz which corresponds to a part of the redshift range of the Cosmic Dawn (30 ≳ z ≳ 15).
In this chapter, we focus on challenges for observing the Cosmic Dawn (CD) with LOFAR, and the future SKA-Low which will largely have a similar layout.
Since these telescopes operate at a lower frequency range (50-80 MHz), they will face challenges (foregrounds and ionosphere) similar to EoR experiments but more severe in strength.
The expected 21 cm signal from z = 30 to 15 is extremely faint with ∆
221∼ (5 −6 mK)
2(Furlanetto, Oh & Briggs 2006; Pritchard & Loeb 2012). This sig- nal is buried deep below galactic and extra-galactic foreground emission which dominate the sky at these low frequencies (50-80 MHz). The foreground emis- sion is ∼ 4 orders of magnitude larger in strength than the 21 cm signal and has a brightness temperature of several Kelvins (Bernardi et al. 2010) (on rel- evant angular scales) at high Galactic latitudes where LOFAR-EoR observing fields are located. Even if the foregrounds are removed with great accuracy, the noise per voxel (or volume element) in the images cubes after hundreds of hours of integration will still be orders of magnitude higher than the expected signal. Therefore, the current experiments (both EoR and CD) are aiming for a statistical detection of the signal instead of directly mapping out HI in IGM at high redshifts. The LOFAR EoR Key Science Project (KSP) currently predominantly focuses on a statistical detection of the redshifted 21 cm signal from z = 7 to 12 (110-180 MHz) using LOFAR-High Band Antenna (HBA) observations and measure its power spectrum as a function of redshift (Patil et al. 2017). Contamination due to the (polarised) foregrounds, ionospheric propagation effects and systematic biases (e.g. station-beam errors) pose con- siderable challenges in the detection of this signal. It is crucial to remove these bright foregrounds and mitigate other effects accurately in order to obtain a reliable (accurate and precise) estimate of the 21 cm power spectrum. This requires a detailed understanding of the nature of these effects and the errors associated with these effects. Several contamination effects in LOFAR EoR observations (High Band Antenna, 110-180 MHz) have been studied in great detail, such as polarization leakage (see Asad et al. 2015, 2016, 2018), sys- tematic biases (see Patil et al. 2016), ionospheric effects (see Vedantham &
6
http://skatelescope.org/
7
http://www.tauceti.caltech.edu/leda/
8
https://nenufar.obs-nancay.fr/
2
2.2: Observations and Data processing 29
Koopmans 2015, 2016; Mevius et al. 2016), LOFAR Radio Frequency Inter- ference (RFI) environment (Offringa et al. 2010; Offringa, van de Gronde &
Roerdink 2012; Offringa et al. 2013a,b), calibration and effects of beam errors (Kazemi et al. 2011; Kazemi, Yatawatta & Zaroubi 2013; Kazemi & Yatawatta 2013; Yatawatta 2013, 2015, 2016).
In this work, we study some of the aforementioned effects at low frequencies using LOFAR Low Band Antenna (LBA) observations of a field centred on 3C196 (3C196 field hereafter) at lower frequency (56-70 MHz), covering part of the CD, where both the foregrounds and ionospheric effects are known to be even stronger. LOFAR-HBA observations of the 3C196 field show bright polarised emission of ∼ few Kelvins with complicated and rich morphology (Jelić et al. 2015). We address the broadband nature of the excess noise due to systematic biases, polarised foregrounds and ionospheric effects. A similar analysis has been done by Ewall-Wice et al. 2016 using low-frequency MWA observations (75-112 MHz), which addresses the MWA RFI environment, in- strumental, and ionospheric effects at these frequencies. Our analysis provides improved insight on the spectral behaviour of the associated errors as well as the level of these contamination effects in ongoing and upcoming experiments to detect the HI signal from the CD era at low frequencies (50-80 MHz).
The chapter is organised as follows: in section 2, we briefly describe the data processing steps. In section 3, we discuss the differential Stokes power spec- trum method to study excess noise and its behaviour for different calibration strategies. In section 4, we discuss the delay power spectrum method to study the polarised foregrounds and polarization leakage. We also discuss the effect of different calibration strategies and source subtraction on polarization leak- age. In section 5, we discuss the ionospheric effects at low frequencies using cross coherence method. In section 6, we provide conclusions and a summary of the analysis in this work.
2.2 Observations and Data processing
We have used LOFAR-LBA observations of the 3C196 field for our analy- sis, it being one of the two primary observation windows of the LOFAR EoR KSP. 3C196 is a relatively compact (4 arcsec) bright radio source placed at the centre of the field and serves as a band-pass calibrator. Observed data was processed using the standard LOFAR software pipeline (see e.g. LOFAR imaging cookbook
9). The observational setup and the steps for data process- ing are briefly described in the following subsections. Figure 2.1 shows a flow chart of the data processing steps.
9
