1 National Centre for Radio Astrophysics, Tata Institute of Fundamental
Research, S.P. Pune University Campus, Ganeshkhind, Pune 411007, India.
2 Department of Physics and Astronomy, National Institute of Technology,
Rourkela 769008, India.
3 Indian Institute of Astrophysics, II Block, Koramangala, Bangalore-560 034,
India.
4 Rosseland Centre for Solar Physics, University of Oslo, Postboks 1029
Blindern, N-0315 Oslo, Norway.
5 Institute of Theoretical Astrophysics, University of Oslo, Postboks 1029
Blindern, N-0315 Oslo, Norway.
6 Center for Solar-Terrestrial Research, New Jersey Institute of Technology,
323 M L King Jr Boulevard, Newark, NJ 07102-1982, USA.
7 Fachhochschule Nordwestschweiz, Bahnhofstrasse 6, 5210 Windisch,
Switzerland.

# Preparing for Solar and Heliospheric Science with the SKAO: An Indian
Perspective

Divya Oberoi1,* Susanta Kumar Bisoi2 K. Sasikumar Raja3 Devojyoti Kansabanik1
Atul Mohan4,5 Surajit Mondal6 and Rohit Sharma7

###### Abstract

The Square Kilometre Array Observatory (SKAO) is perhaps the most ambitious
radio telescope envisaged yet. It will enable unprecedented studies of the
Sun, the corona and the heliosphere and help to answer many of the outstanding
questions in these areas. Its ability to make a vast previously unexplored
phase space accessible, also promises a large discovery potential. The Indian
solar and heliospheric physics community have been preparing for this science
opportunity. A significant part of this effort has been towards playing a
leading role in pursuing science with SKAO precursor instruments. This article
briefly summarises the current status of the various aspects of work done as a
part of this enterprise and our future goals.

###### keywords:

keyword1—keyword2—keyword3.

<EMAIL_ADDRESS>
1 January 20151 January 2015

12.3456/s78910-011-012-3 #### 000 0000 1– 1

##  1 Introduction

As in practically all other areas of astrophysics, the Square Kilometer Array
Observatory (SKAO) is envisaged to be a powerful tool to dramatically enhance
our understanding in the field of solar and heliospheric physics. Both within
India and internationally, the scientific community pursuing this area of
research at radio wavelengths, has historically been comparatively small, and
that continues to be the case even today. Nonetheless, there has been a
significant international effort to pursue this science opportunity with the
SKAO which Indian researchers have also been a part of (Nakariakov $et~{}al$.,
2015; Nindos $et~{}al$., 2019). In fact, the SKAO Science Working Group for
Solar, Heliospheric, and Ionospheric (SHI) was set up at the Indian
initiative.

Indian solar and heliospheric science community is particularly well poised
for playing a leading role in this area. Being home to the Ooty Radio
Telescope (ORT; Swarup $et~{}al$., 1971) and the set of instruments at the
Gauribidanur Radio Observatory (GRO; Ramesh $et~{}al$., 1998, 2011) which have
been carrying out dedicated observations in this field and the Giant Metrewave
Radio Telescope (GMRT; Swarup, 1991; Gupta $et~{}al$., 2017) which has also
been used for solar studies (e.g. Mercier $et~{}al$., 2006, 2015; Bisoi
$et~{}al$., 2018), India has had a rich and long tradition of solar and
heliospheric studies. At metrewave bands, the Murchison Widefield Array (MWA;
Lonsdale $et~{}al$., 2009; Tingay $et~{}al$., 2013; Wayth $et~{}al$., 2018) is
currently perhaps the best-suited radio interferometer for providing high
dynamic range and high-fidelity spectroscopic snapshot imaging required for
meeting the science needs of solar and heliospheric science. Ever since its
inception, Indian scientists have been playing a leading role in establishing
solar and heliospheric science as one of the key science objectives of the MWA
and continue to lead it (Oberoi & Kasper, 2004; Oberoi & Benkevitch, 2010;
Bowman $et~{}al$., 2013; Beardsley $et~{}al$., 2020). Though the bulk of the
work by the Indian community has been at frequencies overlapping with the
SKAO-Low, the future plans involve making use of the SKAO-Mid frequencies as
well.

The MWA is a precursor for the SKAO, especially the SKAO-Low. Not only is it
located at the site chosen for the SKAO-Low the MWA also shares many design
features and hence also the challenges with the SKAO-Low. The MWA was also
among the first aperture array interferometers to be built and marks a big
step in both engineering and science. The data from the MWA are sufficiently
different in their character and data volumes from most other existing
instruments and their analysis represents a significant challenge in its own
right. Building reliable and precise tools and techniques for analyzing the
MWA data lie directly on the path to doing the same for the SKAO. As will be
substantiated later, the confluence of these data and our specialized tools
are already enabling explorations of previously inaccessible phase space.
These science explorations serve many different purposes, from academic to
societal. From a purely academic perspective, they deliver exciting science
and help us sharpen our science questions for the SKAO. They also provide us
with very useful experience in preparing for solar and heliospheric science in
the SKAO era even as we make good progress with the available instrumentation.
From an Indian perspective, they play a crucial role in developing the
academic human resource needed in the country, not only to be able to pursue
science with the SKAO once it becomes available but hopefully play a defining
role in this science area. By demonstrating cutting-edge science, these works
also serve the purpose of attracting young talent to the field of solar and
heliospheric radio physics.

This work gives an overview of our journey thus far, it summarises the current
status and our plans for the near future. The paper is organised broadly into
sections on solar and heliospheric physics, followed by a concluding section.

##  2 Solar Physics

The Sun is a particularly challenging radio source to be imaged. The
challenges stem from the wide range of variations seen in solar emissions –
time scales spanning solar cycles to sub-second; spectral scales from smooth
thermal emission to $\sim$100 kHz; brightness temperatures from $10^{4}$K for
gyrosynchrotron (GS) emission from coronal mass ejection (CME) plasma to
$10^{13}$K for bright type-III solar bursts; fractional polarisation ranging
from $\leq$1% to nearly 100%; and angular scales small enough to be unresolved
by most earlier solar interferometers to the degree scale quiet solar disc and
even larger CMEs (e.g. McLean & Labrum, 1985; Sastry, 2009; Nindos, 2020,
etc.). This made it infeasible for most radio interferometers to gather the
information needed to make high dynamic range high-fidelity images over the
short time and narrow spectral scales necessary to track the evolution of
solar emission in detail. Fortunately, however, for the active emissions from
the well-known solar type-I through type V bursts, which can outshine the
quiescent Sun by orders of magnitude, much of the physics can be learned from
the characteristics of the emission seen in their dynamic spectra (DS) and
imaging was not strictly necessary (McLean & Labrum, 1985; Saint-Hilaire
$et~{}al$., 2013; Reid & Ratcliffe, 2014). Hence much of what we have learned
thus far about the various solar type bursts comes from a large body of
literature based on non-imaging DS-based studies. The majority of these
studies have been limited to Stokes I measurements, though a small fraction
has also included measurements of Stokes V emissions. Certain information can,
however, only be obtained using imaging studies – estimates of brightness
temperatures ($T_{B}$); disentangling the multiple sources of emission
simultaneously present on the Sun; gathering morphological information of the
emission features and their relationships with features observed in other
wavebands, etc., Ideally, the imaging needs to be done with spectral and
temporal resolutions finer than the frequency and time scales of the intrinsic
solar variability, provide the sufficient dynamic range to simultaneously
observe sources with vastly different intrinsic $T_{B}$s and also provide full
Stokes information with leakages much smaller than the lowest expected
fractional polarization.

While science-rich, interferometric imaging is very compute-intensive and
spectro-polarimetric snapshot imaging pushes the demands on computational
requirements by multiple orders of magnitude. At meter wavelengths, there are
additional challenges to be overcome for solar imaging, especially when using
aperture array instruments like the MWA (and the future SKAO-Low), which add
to its algorithmic complexity and computational demands (Mondal $et~{}al$.,
2019; Kansabanik $et~{}al$., 2022c; Kansabanik, 2022; Kansabanik $et~{}al$.,
2022a). These factors severely limit the volumes of data that can be studied
in detail using spectroscopic snapshot imaging. The use of DS is, on the other
hand, much more straightforward. Its computationally light and data volumes
friendly nature allows it to be easily scaled to large data volumes. Both
imaging and non-imaging studies, hence, have their importance and
complementary roles to play in solar physics. Enabling imaging studies with
the new generation instruments necessarily requires the availability of a
robust and capable polarimetric imaging pipeline.

The earliest work from the 32-tile prototype for the MWA already reported
evidence for numerous weak and short-lived nonthermal emissions, even during
comparatively quiet solar conditions (Oberoi $et~{}al$., 2011). Working
towards characterizing their observational features and building an
understanding of these physical systems has been an enduring theme of our
work. This section describes the major aspects of our work towards non-imaging
studies, the development of interferometric imaging pipelines tailored to the
needs of solar radio imaging, and the imaging studies enabled by them.

###  2.1 Non-imaging Studies

As discussed earlier, non-imaging studies are technically much simpler as
compared to imaging studies, and form the natural place to start when pursuing
science with any new instrument. We also took the same approach with the MWA.

####  2.1.1 Flux Density Calibration

Reliable flux density calibration has always been a non-trivial issue for
solar radio observations, especially at low radio frequencies. For dedicated
solar instruments, there are only a handful of sources in the sky, which have
sufficient flux density to be used as flux density calibrators. Additional
complications arise due to the confluence of the bright Galactic background
and the typical large fields of view (FoV) of low-frequency instruments. For
instruments designed for usual astronomical observations, the vast difference
in the flux densities of the Sun and the typical calibrator sources usually
pose a challenge for the linearity range of the electronic signal chain and
need special attention.

For the MWA, we developed a novel approach to provide accurate solar flux
density calibration. The use of the Galactic background for calibrating an
array of active elements had already been demonstrated (Rogers $et~{}al$.,
2004), and we extended this work to the case of a two-element interferometer
(Oberoi $et~{}al$., 2017). The necessary ingredients for this technique are –
a reliable model for the Galactic background over the MWA band; an accurate
model for the MWA primary beams; a robust characterization of the MWA
receiver; and baselines lengths long enough to resolve out the bulk of the
Galactic emission, but short enough to view the Sun as an unresolved source.
These were all available from prior work and/ or the MWA design.

This computationally lean technique uses $<0.1$% of the MWA data and can
provide absolute flux density calibration with an accuracy of 10$-$60%. The
accuracy of relative flux density calibration is $\sim 1$%. This technique is
equally applicable to quiet and active times and can provide calibration at
the native time and frequency resolution of the data. It played a key role in
establishing flux densities of many weak solar radio bursts (e.g. Suresh
$et~{}al$., 2017; Sharma $et~{}al$., 2018, etc.) and a prescription was
successfully developed and implemented to translate this flux density to MWA
radio images (Mohan & Oberoi, 2017). This combination has since been used
successfully in many of the studies described in Secs. 2.3 and 2.4.

####  2.1.2 Wavelet-based Identification and Characterization of Features in
Dynamic-spectrum

Early MWA observations led to an appreciation of the presence of numerous
short-lived and narrow-band emission features even during periods of
comparatively low solar activity. The strengths of these features were much
weaker than those typically associated with the well-known solar bursts
(Oberoi $et~{}al$., 2011). The natural next step was to characterize these
emissions in terms of the various parameters which could be discerned using
the DS from MWA observations. Their high observed rate, of thousands of
emission features per hour in the 30.72 MHz of MWA bandwidth, necessarily
required an automated but robust approach for accurately identifying and
parameterizing these features. Suresh $et~{}al$. (2017) developed a wavelet-
based automated technique to reliably identify and parameterize these emission
features under weak to moderate solar activity conditions. Though the
implementation presented was tuned to MWA data, the technique itself is
general and can be used on DS from other instruments, including the future
SKAO-Low.

Some pre-processing of the raw MWA DS was needed to prepare the data for
wavelet-based feature detection. After removing the known instrumental
artifacts, a mean background continuum level was estimated and subtracted from
each of the 4-minute chunks of data. A Gaussian Mixtures Model (GMM) approach
was used for background estimation. GMM provides a probabilistic framework
based on the assumption that the data come from a parent distribution
consisting of a superposition of a finite numbers of Gaussian and uses the
data to estimate the parameters of these constituent Gaussians (McLachlan &
Peel, 2000; Pedregosa $et~{}al$., 2012). The DS data were modeled as a
collection of Gaussians and, because of the low to medium levels of solar
activity prevailing during these observations, the Gaussian component with the
lowest mean and largest weight was assumed to represent the thermal background
continuum. A suitable low-degree polynomial was fit to the smooth spectral
trends observed and subtracted from the observed data leaving behind residuals
in the 3–4% range. A 2D Ricker wavelet, also known as a Mexican hat, was used
as the mother wavelet in the Continuous Wavelet Transform (CWT) framework to
first identify the locations of these features and then also estimate their
spectral and temporal extents.

This technique detected about 14,200 impulsive emission features in about 4.5
hours of observations with flux densities in the range from 0.6–$\sim$300 SFU
(1 SFU = 104 Jy), making these perhaps the weakest nonthermal emissions
reported till then. A power law fit over the 12–155 SFU range yielded a power
law index, $\alpha=-2.2$ for peak flux densities. Their energies were
estimated to lie in the range $10^{15}$–$10^{18}$ ergs, much lower than
typical ranges for solar type-I and type-III radio bursts, and described well
by a power slope of $-1.98$. The distributions of their bandwidths and
durations were found to be smooth and unimodal with peaks around 4–5 MHz and
1–2 seconds respectively. These emission features seemed to be fairly
uniformly distributed across the spectral range probed by these observations.
While the spectral profiles were usually found to be symmetric about the peak,
the temporal profiles showed no such symmetry. Interestingly, the background
flux densities at the location in DS of these features are found to vary by a
factor of $\sim$2, as shown in Fig. 1. These large variations are not likely
to arise due to changes in the thermal emission from the coronal plasma. The
authors interpret this as evidence for the presence of multiple instances of
nonthermal emission which remained unresolved in the observations.

Figure 1: Variation of the background solar flux density. The 2D histogram
highlights the variation in the background solar flux density seen at the
frequency and time, where an emission feature was identified in DS using the
wavelet based analysis. The colour axis is on a log scale. (Reproduced from
Suresh $et~{}al$. (2017))

####  2.1.3 Gaussian Mixture based Characterization of Weak Nonthermal
Impulsive Emissions

It is reasonable to regard the emission seen in the solar DS as a
superposition of a slowly varying (order minutes and longer) and impulsive
nonthermal emission (order seconds and smaller). The slowly varying emission
is expected to be dominated by the coronal thermal bremsstrahlung, while the
impulsive emissions must arise from nonthermal processes in the corona. The
widespread presence of the nonthermal impulsive features was obvious even in
the science commissioning data from the MWA (2013). Estimating their flux
densities and coming up with metrics to quantify their presence, therefore,
became one of the first natural questions to answer and was addressed by
Sharma $et~{}al$. (2018). A dataset with a medium level of activity was chosen
for this exercise. The flux density calibration of a DS from a short baseline
was done as described in Sec. 2.1.1. To separate the impulsive emissions from
the slowly varying component a robust median filter over a 120 s window was
used and the median so computed was subtracted from the observed DS. As the
impulsive nonthermal emissions are superposed on the background thermal
emission, they must always appear as a positive tail in the histogram of the
resulting DS of impulsive emission. An example histogram of impulsive emission
is shown in Fig. 2 along with the various component Gaussians determined using
GMM analysis. The Gaussian with zero mean represents the slowly varying
thermal emission and, for periods of medium solar activity, also has the
largest weight amongst all Gaussian components. The most interesting aspect of
this work was that it provided a way for quantifying both the prevalence and
the flux density of impulsive nonthermal emissions. In, what was a surprising
result at the time, we found that the prevalence (fractional occupancy) of the
nonthermal emissions ranged between 17 and 45 % and that the energy emitted in
the impulsive emissions is very comparable to that emitted in the slowly
varying component even during periods of medium levels of solar activity. The
density of impulsive emissions was also found to correlate with the strength
of the slowly varying emission, similar to what is seen for Type-I bursts. The
authors suggested that the observed increase likely arises due to impulsive
emissions too fine to be resolved by these observations.

Figure 2: Gaussian mixture modeling of solar emission. The observed
distribution of solar ﬂux density at 180 MHz for 70 minutes of observation is
shown by black dots in units of SFU. The component Gaussians are shown by
dashed lines and their sum by the solid orange line. Note that the y-axis is
in log scale and spans four orders of magnitude. For this dataset, the GMM
found 7 Gaussians components, the means ($\mu$), widths ($\sigma$), and
weights ($w$) are listed. (Reproduced from Sharma $et~{}al$. (2018))

###  2.2 Development of Calibration and Imaging Pipelines

Solar radio images are a rich source of information, going well beyond what DS
can offer. However, for reasons enumerated at the start of Sec. 2, it is an
intrinsically hard problem. In addition, especially during periods of solar
activity, very faint emissions co-exist (e.g. GS and thermal emissions from
the CME plasma) with very bright active emissions (e.g. type-II, type-IV
bursts, and noise storms). To understand the overall coronal dynamics and
magnetic field topology, these emissions, spanning a huge range of
$\mathrm{T_{B}}$, need to be detected in the same image. This requires high
imaging dynamic range high fidelity spectro-polarimetric snapshot imaging.

The unique array layout of the MWA, with a large number of antenna elements
distributed over a small footprint, makes it exceptionally well suited for
high dynamic range spectroscopic snapshot imaging of the Sun. Due to its large
number of antenna elements, the MWA data is already very voluminous, about a
TB of raw data every hour, and this number will increase many-fold with the
availability of the SKAO. The need for spectroscopic snapshot imaging
translates to making a very large number (tens to hundreds of thousands) of
images at high time and spectral resolutions, rendering the traditional manual
data analysis approach impractical. While several groups across the world are
working towards automating interferometric imaging procedures in the run-up to
the SKAO, the unique requirements of the solar observations make it hard to
adapt the generic techniques developed primarily for astronomical observations
for the solar use case. The Indian Solar Physics community has been putting in
a concerted effort over the past few years toward building robust calibration
and imaging pipelines optimized for low-frequency solar observations. Not only
can these pipelines operate in an unsupervised manner, but the images from
these pipelines also show improvements by multiple orders of magnitude in
dynamic range over earlier attempts and achieve polarimeteric leakages on par
with high quality imaging of other astronomical objects. They now represent
the state-of-the-art in low radio frequency solar imaging.

While the current implementation of these pipelines has been optimized for the
MWA, due to similarities in array architecture with the SKAO, especially the
SKAO-Low, it will be possible to easily adapt these pipelines for solar
imaging with the SKAO. Key design considerations for these pipelines were to,
on the one hand, hide the bulk of the complexity by providing well-chosen
defaults for the numerous parameters which need to be specified and thus make
high-quality solar radio imaging accessible to the uninitiated, and on the
other, provide all of the flexibility to the expert user to tune the
calibration and imaging parameters as desired. Successive incarnations of
these pipelines are described in the following text and have met the stated
objectives to a large extent. Our ultimate objective is to provide the
community of solar scientists with the tools which would enable them to
generate science ready solar images at meter wavelengths like the current
practice for visible, extreme ultra-violet (EUV), and X-ray band data from the
Solar Dynamics Observatory (SDO; Pesnell $et~{}al$., 2012), Solar and
Heliospheric Observatory (SOHO; Domingo $et~{}al$., 1995) etc.

####  2.2.1 Total Intensity Calibration and Imaging Pipeline

The first incarnation of this pipeline was named “Automated Imaging Routine
for Compact Arrays for Radio Sun” (AIRCARS; Mondal $et~{}al$., 2019). Most of
the early MWA solar work was based on non-imaging studies (Sec. 2.1). While
these studies were interesting in their own right, they were only scraping the
surface in terms of making use of the information content of the MWA data,
both in terms of using its imaging capability and sensitivity. The fact that
interferometric imaging is intrinsically an iterative process and the
traditional analysis methods are very human effort intensive, made it
infeasible to generate the very large number of images needed for
spectroscopic snapshot studies. Additionally, early efforts to adapt the
existing generic astronomical imaging tools to solar imaging led to imaging
dynamic ranges much lower than those expected from the MWA data.

A key reason behind this was the deficiencies in the calibration. At the MWA,
calibrator observations were generally done when the Sun was below the horizon
to avoid contamination from the solar emission. Although the antenna
themselves have a very stable instrumental response (Sokolowski $et~{}al$.,
2020), the ionospheric phase usually changed significantly between the
calibrator and target (Sun) observations and rendered the calibration
solutions obtained from night-time observations sub-optimal for solar
observations. While a similar issue is regularly tackled in radio imaging
using a technique called self-calibration, solar observations are generally
not amenable to it due to the lack of good initial calibration solutions
available for solar observation and the highly non-linear nature of the self-
calibration process. AIRCARS overcomes this by using the large number of MWA
antennas and its centrally condensed architecture cleverly by generating a
sufficiently precise though low-resolution solar model for initializing the
self-calibration process. For any given time slice, AIRCARS starts with
calibration of only the phases of antenna gains using all baselines with at
least one of their antennas from the dense central MWA core. Antennas outside
the core are progressively added. The antennas from the compact MWA core look
through essentially the same ionosphere and provide a certain level of
coherency of the array (Kansabanik, 2022). This allows AIRCARS to initiate the
self-calibration process with a reasonable solar model. AIRCARS also
incorporates additional heuristics to tune the entire process so that the
calibration solutions converge to their true values.

AIRCARS has been extensively used with data from a wide variety of solar and
ionospheric conditions (Mohan $et~{}al$., 2019b, a; Mondal $et~{}al$., 2020b,
a; Mondal, 2021; Mondal & Oberoi, 2021; Mohan, 2021b, a; Kansabanik
$et~{}al$., 2022b) and has produced some of the highest dynamic range images
at these frequencies. It routinely produces images with dynamic ranges
$\gtrsim 300$ for the quiet featureless Sun and $\gtrsim 10^{5}$ in presence
of bright and compact active solar emissions. A sample image demonstrating the
imaging quality of AIRCARS is shown in Fig. 3. The image shows a type-II solar
radio burst in progress with peak $\mathrm{T_{B}}$ $\sim 10^{9}\ \mathrm{K}$.
The thermal emission from the solar disc is at $\mathrm{T_{B}}\approx 10^{5}\
\mathrm{K}$ and is detected with high significance. For this image, the
imaging dynamic range is $\sim 10^{5}$.

Figure 3: A sample image from AIRCARS. Solar image during a type-II radio
burst is shown. The image is made over 40 $\mathrm{kHz}$ and 0.5 $\mathrm{s}$.
Peak $T_{B}$ is $\sim 10^{9}\ \mathrm{K}$. Dynamic range of the image is
100,000. Contour levels are at 0.02, 0.03, 0.1, 0.3, 1, 3, 10, 30, 80, and 90
% of the peak $T_{B}$. Dotted yellow circle represents the optical disc of the
Sun (Reproduced from Mondal $et~{}al$. (2019))

.

####  2.2.2 Polarimetric Calibration and Imaging Pipeline :

Having established the ability of MWA solar observations to deliver high
dynamic range high fidelity Stokes I images using AIRCARS, we have recently
developed the second incarnation of AIRCARS. Referred to as “Polarimetry using
Automated Imaging Routine for Compact Arrays for Radio Sun” (P-AIRCARS,
Kansabanik $et~{}al$., 2022c; Kansabanik, 2022; Kansabanik $et~{}al$., 2022a),
it is designed for robust polarisation calibration and imaging of the solar
observations with the MWA.

Full Stokes polarisation calibration is more challenging than working only
with Stokes I. These challenges are even greater for the low-radio frequency
full Stokes solar imaging. Solar emissions can span a very large range of
intrinsic polarisations ($\leq 1\%$ to $\sim 100\%$) which can also vary
rapidly across time and frequency. Additionally, the wide field-of-view (FoV)
aperture arrays tend to have large direction-dependent instrumental
polarization. Due to these reasons, some of the assumptions made for routine
polarimetric calibration for small FoV instruments are no longer valid in this
regime (Lenc $et~{}al$., 2017).

Polarimetric solar observations with the MWA have been carried out
successfully earlier, though only for the brighter active emissions, and using
an ad-hoc approach of mitigating instrumental polarisation (McCauley
$et~{}al$., 2019; Rahman $et~{}al$., 2020). The limited imaging dynamic range
and polarimetric fidelity it can deliver make this method unsuitable for weak
emissions and those with a low degree of fractional polarisation. P-AIRCARS
overcomes these limitations by implementing a robust polarisation calibration.
For low radio frequency solar observations with aperture arrays, it is not
feasible to obtain calibrator observations at nearby times with the same
primary beam pointing as used for target (Sun). P-AIRCARS is, hence, designed
to work with any calibrator observation. It builds on three pillars – i) self-
calibration; ii) availability of a reliable instrumental beam model
(Sokolowski $et~{}al$., 2017); and iii) some well-established properties of
low-frequency solar radio emission. Conventional polarisation calibration
algorithms available in standard radio interferometric packages (e.g. CASA and
AIPS) assume the instrumental leakages to be small and are hence not suitable
for polarisation self-calibration of the MWA solar observations. P-AIRCARS
uses a full Jones matrix calibration formalism implemented in CubiCal (Kenyon
$et~{}al$., 2018). In addition to polarisation calibration, P-AIRCARS also
incorporates several improvements beyond AIRCARS. These include bandpass self-
calibration, a more flexible framework, and optimizations based on learnings
from the AIRCARS experience. These have led to improvements in Stokes I
imaging quality over AIRCARS. P-AIRCARS is the state-of-the-art polarisation
calibration and imaging algorithm for low-frequency solar observations. Though
it is currently optimized for MWA solar observations, P-AIRCARS will be
equally suitable for the future SKAO, especially the SKAO-Low.

Figure 4: A sample image from P-AIRCARS. A circular polarisation image of a
type-I noise storm at 159 MHz is shown by the color map. The image is made
over 40 $\mathrm{kHz}$ and 0.5 $\mathrm{s}$. The dynamic range of Stokes I and
Stokes V images are $\sim 600$ and $300$ respectively. The Peak degree of
circular polarisation is approximately $-88\%$. Green contours show the Stokes
I emission. Contour levels are at 5, 10, 20, 40, 60, and 80 % of the peak of
the Stokes I emission.

An example P-AIRCARS image is shown in Fig. 4, which comes from a time when a
type-I noise storm was in progress. P-AIRCARS routinely achieves residual
instrumental leakages $\leq|2|\%$ from Stokes I to other Stokes parameters.
For this particular example, residual leakage from Stokes I to Stokes V is
$<|1.8|\%$. These values of residual leakages are comparable to what is
generally achieved for high-quality astronomical observations with the MWA
(Lenc $et~{}al$., 2017, 2018; Riseley $et~{}al$., 2018, 2020) and represent a
significant improvement over what has been reported earlier for solar
observations (McCauley $et~{}al$., 2019; Rahman $et~{}al$., 2020). The Stokes
images delivered by P-AIRCARS are limited primarily by the thermal noise of
the data. The precise polarisation calibration provided by P-AIRCARS will make
it possible to routinely detect and estimate the plasma parameters of the CMEs
using the polarisation images of the gyrosynchrotron (e.g. Bastian $et~{}al$.,
2001; Mondal $et~{}al$., 2020b, etc,) or thermal emission (e.g. Gopalswamy &
Kundu, 1993; Ramesh $et~{}al$., 2021, etc.) from the CME plasma, and measure
the very low level of circular polarisation ($\leq|1|\%$) (Sastry, 2009) from
the quiet Sun thermal emissions, which remains a standing challenge. With the
SKAO sensitivity, it should become feasible to detect the low level of
circular polarisation and measure the global coronal magnetic field routinely,
even during the quiescent periods.

####  2.2.3 Image-based Flux Density Calibration

Absolute flux density calibration of the low-frequency solar observations has
several challenges, as already discussed in Sec. 2.1.1. The same section also
presented a non-imaging absolute flux density calibration technique developed
for the MWA (Oberoi $et~{}al$., 2017), which has been used in several studies.
Though successful, this technique relied crucially on the availability of
multiple very short baselines ($\lesssim 10\lambda$) to obtain the total solar
flux density, which restricts the adaptability of this approach for the
extended configuration of the MWA Phase-II (Wayth $et~{}al$., 2018). AIRCARS
and P-AIRCARS can provide high dynamic range images without requiring any
dedicated calibrator observations. But due to the intrinsic limitation of the
self-calibration based approach used in AIRCARS and P-AIRCARS, they cannot
provide an absolute flux density calibration.

With the precise calibration and high dynamic range imaging capability using
AIRCARS and P-AIRCARS, it is possible to detect numerous background galactic
and extra-galactic radio sources even in the presence of the Sun in the FoV
(Fig. 15). This presents the opportunity to arrive at an image-based absolute
flux density calibration by comparing the observed flux densities of these
sources with their catalog flux densities obtained from the GLEAM survey
(Wayth $et~{}al$., 2015; Hurley-Walker $et~{}al$., 2017). This approach is
demonstrated convincingly by Kansabanik $et~{}al$. (2022b). This work also
used the well-established stability of the MWA bandpass shapes (Sokolowski
$et~{}al$., 2020) to establish the robustness of the image-based absolute flux
density calibration. The key achievement of this work is that it provides the
framework to arrive at absolute flux density calibration for any MWA solar
observation, irrespective of the array configuration used. It delivers an
uncertainty of $\sim$10% on the estimated flux density, which arises mostly
due to the intrinsic uncertainty of the GLEAM flux density measurements. This
method also demonstrates the usefulness of a well-characterized and the stable
instrumental response for precise flux density calibration, a useful lesson
for the design of the SKAO-Low.

The state-of-the-art full Stokes calibration and imaging pipeline, P-AIRCARS,
and the robust absolute flux density calibration open a new window of high
fidelity spectro-polarimetric snapshot imaging studies of the meter wavelength
Sun. The success of these techniques and tools can be measured by the
unprecedented quality of imaging they deliver. They have been developed with
the future needs of the SKAO in mind and can potentially form the backbone of
the standard full Stokes solar imaging with the SKAO.

###  2.3 Studies of Solar Radio Bursts

Solar radio bursts are among the brightest observable radio transients -
lasting from a few seconds to several hours, with $T_{B}$ ranging from $\sim
10^{7}$ – $10^{13}\ \mathrm{K}$ (McLean & Labrum, 1985; Saint-Hilaire
$et~{}al$., 2013). They have been studied extensively using both imaging and
non-imaging techniques over several decades (see Reid & Ratcliffe, 2014, for a
review). Based on the emission morphology in the frequency-time plane (DS),
solar radio bursts are classified into several types starting from types I
through V (Wild, 1950). Though the early classification has stood the test of
time for some seventy years, every significant advancement in instrumentation
capabilities has brought about discoveries of previously unappreciated aspects
of emissions at finer scales, often leading to elaborate sub-classification of
each burst type. The most recent wave of such discoveries is in progress today
owing to instruments like the MWA and LOFAR. (e.g. Suresh $et~{}al$., 2017;
Kontar $et~{}al$., 2017; Sharykin $et~{}al$., 2018; Mohan $et~{}al$., 2019b,
a; Magdalenić $et~{}al$., 2020; Mohan, 2021a; Mondal & Oberoi, 2021). Of the
various solar burst types, we focus on the ones which had garnered a lot of
attention in the recent past primarily owing to some notable discoveries.

####  2.3.1 Type-III Solar Radio Bursts

Type-III bursts are caused by supra-thermal electron beams produced at
particle acceleration sites in the corona. These beams traverse across open
magnetic field lines threaded across coronal iso-density layers. Along their
path, they excite the two-stream instability which leads to a series of wave-
wave and wave-particle interactions that give rise to coherent plasma emission
from the iso-density layers at the local plasma frequency ($\nu_{p}$) and its
harmonic frequency($2\nu_{p}$) (e.g. Ginzburg & Zhelezniakov, 1958; Melrose,
1970; Robinson & Cairns, 1994). Since $\nu_{p}$ relates to local density, by
analyzing the mean type-III source locations in spectroscopic images, the
radial density profile of the solar corona can be inferred (e.g. Morosan
$et~{}al$., 2014; McCauley $et~{}al$., 2018, etc.).

Type-III bursts are known to demonstrate fine-scale spectro-temporal
variability in the image plane and intensity. Though an individual burst lasts
for only a few seconds in a metrewave band, often groups of type-III bursts
lasting for minutes to $\sim$ an hour are observed. The spectro-temporal
intensity maps of these bursts demonstrate a variety of characteristics like
quasi-periodic pulsations (QPPs), scattered striae like emission confined in
frequency and time, skewed temporal profiles, etc. The rise and decay
timescales of burst pulses follow power-law trends with observation frequency,
with spectral indices close to -1 (e.g. Reid & Ratcliffe, 2014; Kontar
$et~{}al$., 2019). Besides these features in the DS, the type-III burst
sources also show interesting morphological characteristics in the image
plane. These include variations in source sizes and centroid locations across
frequency and time. Some of these are related to the radio-wave propagation
effects, while others are linked to the properties of particle acceleration
processes in the corona. To disentangle these two effects, high-fidelity
imaging at sub-second sub-MHz resolutions is necessary.

Limited imaging capabilities forced earlier studies exploring sub-second, sub-
MHz spectro-temporal evolution of these bursts to rely purely on DS data.
These studies had no choice but to tacitly attribute the observed variability
in flux density to a single source of emission. While this would usually be
true for strongest events, this need not be the case for relatively weaker
bursts with $T_{B}\sim 10^{8}$–$10^{10}\mathrm{K}$. In fact, weak type-IIIs in
this $T_{B}$ range are well known to be associated with micro- or mini- flares
(e.g. Benz $et~{}al$., 2005; Reid & Vilmer, 2017), which are in turn known to
be very common especially during active periods (e.g. Aschwanden & Freeland,
2012). This suggests that the temporal overlap of multiple independent weak
flares is a likely occurrence and limits the usefulness of DS studies for
weaker events.

Figure 5: Left panel: Sample image from MWA with two active regions A1 and A2
(top) and the whole sun integrated dynamic spectrum for a minute-long
observation (bottom). The black circle in the top image shows the optical disk
of the Sun and the ellipse to the bottom left the resolution of the
observation. Contours mark 10, 30, 50, 70 and 90% of the peak $T_{B}$. Right
panel: SPREDS for A1 and A2 revealing the localized emission features.
(Adapted from Mohan & Oberoi (2017))

There have been several imaging studies of type-IIIs as well from earlier
generations of instruments, though most of them also focused on strong type-
III events which out-shined any co-temporal events by several orders of
magnitude. These images were often made with integration times of few to many
seconds and yielded dynamic ranges of only a few tens (e.g. Kundu $et~{}al$.,
1983; Saint-Hilaire $et~{}al$., 2013). The burst source regions undergo flux
enhancements over several orders of magnitude during their short burst span
($T_{B}\sim 10^{7}-10^{12}\ \mathrm{K}$) as revealed by dynamic spectral
studies (e.g. Saint-Hilaire $et~{}al$., 2013).

It is hence evident that to study weaker bursts which tend to overlap in time,
and show rapid variability spanning multiple orders of magnitude in $T_{B}$
over fine spectro-temporal scales one necessarily needs high fidelity snapshot
spectroscopic imaging with dynamic ranges of order 103. The new generation
interferometric arrays like the MWA now make it possible. The set of images
spanning a range in time (observing duration) and frequency (bandwidth) with
fine spectro-temporal resolution would generate a 4D data cube with
information spread across frequency, time, and angular sky coordinates. To
provide a convenient framework for studying such a datacube, in analogy with
the usual DS, we defined SPatially REsolved Dynamic Spectra (SPREDS), which
shows the time-frequency structure of emission arising from a given resolution
element on the Sun. Figure 5 shows a sample image of the Sun along with SPREDS
for the two active regions A1 and A2. The whole sun dynamic spectra are also
shown. The differences between the emissions from A1 and A2 are self-evident
and there is no way to discern this from the usual DS.

Figure 6: QPPs discovered in source area, flux density and orientation. The
anti-correlation in time series of area of the type-III source and its
integrated flux density, as derived from the best fit Gaussian parameters, is
visually evident. (Adapted from Mohan $et~{}al$. (2019b))

Mohan $et~{}al$. (2019b) presented the first high dynamic range snapshot
spectroscopic ($\delta t\sim 0.5\,s$; $\delta\nu\sim 160\,kHz$) imaging study
of a group of weak type-IIIs using MWA images generated with AIRCARS. This
group of bursts lasted only for a few minutes and was associated with a GOES
B6 class flare. A type-I source was also present, the $T_{B}$ of which was
occasionally comparable to the type-III bursts. The morphology of the type-III
burst emission was always found to be described well by a 2D Gaussian
function. The best fit 2D Gaussian parameters to type-III emission provided a
detailed characterization of the spectro-temporal variability of the intensity
and morphology of the type-III source during the event. The availability of
such fine-grained characterization enabled the authors to disentangle the
intrinsic dynamics of the source from propagation effects through the
inhomogeneous coronal medium. This and other aspects related to propagation
effects are discussed in Section 2.6.2.

This study conclusively demonstrated the existence of a new type of QPP where
the source sizes showed an anti-correlated pulsation with intensity, akin to a
sausage mode at timescales of $\sim$ 2 s. They also discovered similar
timescale QPPs in source orientation. Figure 6(a) shows these QPPs for one of
the episodes from this group of bursts. While QPPs in the intensity of type-
III sources were already known and three degenerate classes of models had been
proposed to explain this phenomena (Aschwanden, 1987). Establishing the
presence of QPPs along the area and orientation axes had to wait for high-
fidelity imaging to become available. The most important aspect of this work
was that the additional information available from imaging enabled the authors
to break the degeneracy in favor of the lone model where QPPs arise as a
result of dynamics close to the particle acceleration site, possibly due to
coupling with a local magnetohydrodynamic (MHD) wave mode (Aschwanden
$et~{}al$., 1994). The other two relied on phenomena relating to emission
mechanism along the path of the electron beam and were ruled out as they
required physical motion of magnetic flux tubes at speeds about two orders of
magnitude larger than the estimated local Alfvén speeds.

We have also used imaging studies of type-III events to derive the scales of
coronal flux tubes across a heliocentric height range of 1.4 - 1.8 $R_{\odot}$
using MWA data in 80 – 200 MHz range (Mohan $et~{}al$., 2019b; Mohan, 2021a).
The sizes derived were consistent with the empirical model proposed by
Aschwanden (2003). Type-III emissions are circularly polarised, there have
been few imaging studies exploring this. The first such attempt has been made
using the MWA data as well (Rahman $et~{}al$., 2020), though it relied on a
heuristic approach for polarimetric calibration (McCauley $et~{}al$., 2019).
This work was already able to demonstrate previously unappreciated aspects,
like significant polarisation fluctuations happening across different stages
of a single event from its onset to decay.

These results demonstrate the scientific potential of snapshot spectroscopic
imaging and the new phase space of research it has opened up. With the
availability of our high fidelity polarimetric imaging pipeline (Sec. 2.2.2),
a whole new axis of this phase space will become accessible for exploration.
We intend to make good use of this opportunity by continuing to identify and
study interesting events and work towards building a general physical picture.

####  2.3.2 Type-I Solar Radio Bursts

Type-I bursts or the solar noise storms are another form of coherent plasma
emission sources associated with active regions. Unlike the type III bursts,
these events are not associated with any obvious particle acceleration events
or flares. They can be associated with non-flaring active regions undergoing
magnetic field reconfiguration (Smith & McIntosh, 1962; Iwai $et~{}al$.,
2012).

Figure 7: (a): SPREDS for the type-I source during the microflare. White lines
marked at 30 s intervals reveal the periodic bunching of the burst-like
emission features. (b): Frequency averaged SPREDS data (red). The black curve
shows the same data processed by a 10 s running window to reveal the 30 s
QPPs. Thermal energy evolution derived from EUV data is shown in blue. The
inset shows a EUV 94Å image of the braided ARTB loop region.(Adapted from
Mohan $et~{}al$. (2019a))

Type-I bursts, unlike type IIIs, can last for hours and appear intermittently
above active regions during different phases of their existence. They also
show QPPs occasionally, the origins of which and the existence of their high
energy counterparts are not well understood yet. These QPPs have longer
periods, ranging from several seconds to minutes, unlike type IIIs, hinting at
a different physical origin. Using SPREDS based studies Mohan $et~{}al$.
(2019a) studied the spectro-temporal characteristics of a weak type I storm
associated with an Active Region Transient Brightening (ARTB) event.

Figure 8: (a-c): Normalized cross-correlation functions for source flux versus
area (left) and position angle versus area (right) for every observation
frequency. Dominant correlated variation mode shifts from ‘T’ to ‘S’ during
the event. (d): Correlated 30 s QPPs in the band averaged SPREDS data which is
processed by a 30 s running mean filter. Vertical lines are marked every 30 s.
(e): Schematic of the ‘T’ mode. (Adapted from Mohan (2021b) and Mohan (2021a))

The ARTB was associated with a weak microflare. The study incorporated EUV and
X-ray imaging analysis of the associated active region, which provided the
thermal energy evolution. Magnetic field extrapolation studies using the Non-
Linear Force Free technique (Wheatland, 2007) were carried out to understand
the free energy content in the local magnetic field, which powered the
microflare. This was the first detailed multiwavelength study of a type
I–ARTB– microflare system, from pre-flare to post-flare phase. The radio
source was present in all three phases. It revealed many interesting aspects
including the presence of 30 s QPPs in the radio data. QPPs were present
before, during, and after the microflare, but the intensity and the regularity
of the pulsations were enhanced during the flare (Fig. 7(b)) with $T_{B}$
approaching $10^{9}\,K$. The analysis showed that the QPPs resulted from a
systematic release of magnetic free energy across the braided coronal loops at
local Alfvén timescales in the radio source heights. The lower coronal EUV
source images revealed the presence of braiding in the region at the scales
required to explain the QPPs (Fig. 7(b)). The magnetic free energy released
during the QPPs produced numerous accelerated particle beams, signatures of
which could be found in the SPREDS as type-III like strands of emission
(Fig.7(a)). These beams were subsequently damped by collisions in the ambient
medium.

In an independent study, the structural evolution of the type I source was
studied for the first time by Mohan $et~{}al$. (2019a). The sources were found
to be well described by 2D Gaussians. This work led to the discovery of
correlated modes of variability, often seen as pulsations, in the integrated
flux density, area, and position angle of the source across all observational
bands centered around 200 MHz. The correlated evolutionary modes can be
classified into a sausage-like ‘S’ mode in which the area evolves in an anti-
phased manner with integrated flux density; and a wind-unwind-like ‘T’ mode in
which the area evolves in a correlated manner with position angle (schematic -
Fig. 8(e)). Figure 8(d) shows the correlated QPPs in the flare phase. In the
pre-flare data, the presence of ‘T’ mode was found but not ‘S’, whereas it was
the contrary in the post-flare phase. The flare phase marked the rise of the
‘S’ mode alongside the existing ‘T’ mode. This transition is seen in the
normalized cross-correlation functions evaluated for the integrated flux
density and position angle with respect to the area during the event in pre-
to post-flare phases (Fig. 8 (a-c)). The ‘T’ mode could be related to the
presence of excess free energy in torsional modes in the excessively strained
pre-flare magnetic loops driven by footpoint motions. Such a scenario has been
long predicted by coronal loop simulations and this excess energy is expected
to be released in the form of heating and in reorganizing of the local
magnetic field structure. This can explain the observed microflare and the
rise of ‘S’ mode during the flare, releasing the excess ‘T’ mode energy. As a
result mode conversion happens via the flare from ‘T’ to ‘S’ mode (Fig. 8
a-c).

Though the magnetic field evolution of internally twisted loops has been
addressed by simulations (e.g. Gordovskyy & Browning, 2012; Threlfall
$et~{}al$., 2018), these could not be studied in the case of weak events. This
is because the observations were primarily focused on the high energy and
microwave bands, which are sensitive to only relatively strong flares which
cause major changes in the local magnetic field structure (e.g. Gordovskyy
$et~{}al$., 2012, 2020). This implies that the meterwave type-I source
structural evolution studies, like the one presented, are a unique and
powerful technique to track the dynamics of internally twisted loops with
minimal thermal and nonthermal energy flux using the evolution of the coherent
flux density from the high energy electron beams produced in the region. More
such studies need to be done for a variety of active regions varying in
magnetic field strengths, configurations, and other physical characteristics.
This will help improve the understanding of the prevalence and characteristics
of correlated QPPs, and their links to physical dynamics.

###  2.4 Gyrosynchroton Emission from CMEs

Figure 9: Radio emission from GS emission from CME plasma. a.  Radio emission
averaged over 108–145 $\mathrm{MHz}$ from the CME on 2015 November 4 is shown
by the cyan contours and overlaid on a LASCO C2 difference image. Regions,
where spectra have been extracted, are marked in blue circles. The green
circles are drawn at 3 and 4 $\mathrm{R_{\odot}}$, respectively. b. Radio
emission from the CME on 2014 May 04 at 80 MHz is shown by the green contours
overlaid on LASCO C2 and C3 white light images. Radio emissions from two CMEs
are marked by yellow and purple boxes. The red circles are drawn at 4 and 8.5
$R_{\odot}$. c. Observed spectrum from region 13 of the CME on 2015 November 4
at 03:04 UT is shown by the red points. The fitted GS spectrum is shown by the
black solid line. d. A comparison of the spectra from present works with the
previous works is shown. Flux densities from the CMEs in the present work are
much lower than detected earlier. (Panels (a) and (c) adapted from Mondal
$et~{}al$. (2020b))

Coronal Mass Ejections (CMEs) are large eruptions of magnetized plasma from
the solar atmosphere into the solar corona. These are the largest explosions
in the Solar System and are the main drivers of space weather. Under the right
conditions, CMEs can cause massive damage to satellites, lead to large-scale
disruptions in power grids, and impact flight paths and GPS-based navigation
systems among many other impacts on our technology-reliant society. Hence
understanding and predicting the effectiveness of a CME for causing space
weather is globally a very active area of research. The extent to which a CME
affects the Earth, or its geo-effectiveness, is primarily determined by the
orientation of its magnetic field and measuring/ predicting this has been a
challenge. While several techniques have been used to estimate the magnetic
field of CMEs, none of these are suitable for routine applications. Some of
these well-known techniques are based on observations of – splitting of type-
II radio bursts observed in the dynamic spectra (e.g. Kumari $et~{}al$.,
2017a; Mahrous $et~{}al$., 2018), circular polarisation of moving type-IV
bursts (e.g. Sasikumar Raja $et~{}al$., 2014; Kumari $et~{}al$., 2017b), and
the standoff distance technique using EUV and white light images (e.g.
Gopalswamy $et~{}al$., 2011; Schmidt $et~{}al$., 2016). Most of these methods
are sensitive only to the average CME magnetic field, although, under some
conditions, spatially resolved information about the magnetic field can also
be obtained.

A promising approach for routinely measuring the CME magnetic fields is by
modeling the GS emission from a CME. Measurements of GS emission can also be
used to infer the distribution of nonthermal particles, another important
contributor to space weather. This technique was first demonstrated by Bastian
$et~{}al$. (2001). Since CMEs are efficient particle accelerators, it is
natural to expect that this emission should be there for all CMEs.
Additionally, since this emission is expected to peak at the metric and
decimetric wavelengths, low-frequency radio observations are very well suited
for these measurements. Despite significant effort being devoted towards it,
this emission has been detected in only a handful of instances (Bastian
$et~{}al$., 2001; Maia $et~{}al$., 2007; Tun & Vourlidas, 2013; Bain
$et~{}al$., 2014; Mondal $et~{}al$., 2020b).

With the availability of high dynamic range images from AIRCARS and P-AIRCARS,
it is now possible to detect much fainter GS emissions from CMEs. Figure 9d
shows a comparison of all of the published gyronsynchrotron spectra with our
work (Mondal $et~{}al$., 2020b, and Kansabanik et al., 2022, in preparation).
The flux densities detected in AIRCARS and P-AIRCARS images are much lower
than those detected earlier. The radio emission from the CME analyzed by
Mondal $et~{}al$. (2020b) is shown by the cyan contours overlaid on the LASCO
C2 difference image of Fig. 9a. This was a rather slow and unremarkable CME
and still, the authors were able to detect radio emission out to $\sim 4.73\
\mathrm{R_{\odot}}$. For another event much fainter radio emission from two
CMEs are detected simultaneously using P-AIRCARS (Fig. 9b). Here the CME GS
emission is detected out to $8.3\ \mathrm{R_{\odot}}$, the largest
heliocentric distance to date to which such emission has been detected. This
was also a slow CME. The recent detections using AIRCARS/P-AIRCARS imaging of
MWA data suggest that the main reason behind the low historic success rate in
the detection of CME GS emission has been the limitations imposed by the
imaging quality available.

The MWA and AIRCARS/P-AIRCARS combination not only enables the detection of
faint radio emissions from CMEs at large coronal heights, but the MWA data
also provide a very good spectral sampling. This makes the fitting of the GS
model to the observed spectra for estimating plasma parameters of the CMEs
more robust. Mondal $et~{}al$. (2020b) extracted spatially resolved spectra
from the multi-frequency observations covering $100-220\ \mathrm{MHz}$ at
several PSF sized regions shown by the blue circles in the Fig. 9a. A sample
spectra from Region 13 at 03:04 UT is shown in the Fig. 9c. Spectra are fitted
using the numerical code for GS modeling by Fleishman & Kuznetsov (2010). The
quality of the fit is self-evident. The estimated magnetic field strengths at
different regions vary between $\sim 7-13\ \mathrm{G}$, which are similar to
those obtained by earlier studies.

Although this method has proven to be a useful tool for remote estimating
magnetic field and nonthermal electron distribution, the GS model has some
degeneracies when used to estimate plasma parameters over a narrow frequency
range. The most notable of these is between the estimated magnetic field
strength and the angle it makes with the line of sight (LOS). The same
spectral peak flux density can be achieved by multiple combinations of
increasingly larger magnetic field strengths and smaller angles with the LOS.

A circular polarisation spectrum, if available, can break this degeneracy and
this is a possibility we plan to explore using P-AIRCARS images. Very recently
our efforts have been rewarded by the very first detection of circularly
polarised emission from a CME (Kansabanik et al. 2022, in preparation). With a
larger number of constraints on the GS model, enabled by polarimetric imaging,
we can expect a more robust GS modeling of the spectra and a more accurate
estimation of the physical parameters of CME plasma. Our work provides
evidence that the further increase in imaging quality and spectral coverage
brought about by the availability of SKAO-Low will enable the GS modeling
technique to be used for routine measurement of CME magnetic fields. We
envisage that this can turn SKAO-Low radio observations into a routine
workhorse for space weather, much like the coronagraph measurements today.

###  2.5 Understanding Coronal Heating

The resolution of the so-called coronal heating problem is now generally
understood to come from one or both of the following two processes: a) Alfvén
wave heating b) Nanoflare based heating (e.g. De Moortel & Browning, 2015;
Klimchuk, 2015, etc.). In the Alfvén wave heating scenario, Alfvén waves are
generated in the convective zone and the photosphere due to the convective
fluid motions, which then propagate to the corona where they eventually get
dissipated through various pathways, depositing their heat into the corona.
This scenario is believed to be efficient if the convective timescales are
smaller than the Alfvén timescale. When the Alfvén timescale is larger than
the convective timescale, the magnetic field lines get tangled and twisted,
which later release this energy via magnetic reconnection processes, giving
rise to small flares generally referred to as ”nanoflares”. Though
individually each nanoflare deposits a very small amount of energy, due to
their large numbers, due to their large numbers they are believed to be able
to deposit the energy at a rate sufficient to maintain the coronal temperature
at an MK (Parker, 1988). As the convective deposition of energy into the
coronal magnetic fields is active all over the Sun, Parker hypothesized that
these small reconnection events must give rise to tiny flares, referred to as
“nanoflares”, which must occur throughout the corona.

Nanoflares can accelerate electrons to supra-thermal energies, and when this
beam of energetic electrons interacts with the thermal plasma it is passing
through, it gives rise to coherent emission via plasma resonance processes
(e.g. Che, 2018). The coherent nature of this radio emission implies that for
a flare of the same energy the observational signature at radio wavelengths is
much stronger than the thermal emission signatures seen at EUV and X-ray
bands.

This motivated some studies to detect the radio signatures of these
nanoflares, but they were focused primarily on Type-I noise storms, which are
generally associated with active regions (Mercier & Trottet, 1997; Ramesh
$et~{}al$., 2013a). However, for the nanoflare hypothesis to be true, such
radio transients must also exist in the quiet corona. While this has been
appreciated for a while, the available imaging quality has been insufficient
to detect these low-contrast, rapid, narrow-band radio flashes. Mondal
$et~{}al$. (2020a) presented the very first evidence for the presence of
ubiquitous impulsive narrow-band emissions from the quiet solar corona with
flux densities of the order of a few mSFU, temporal widths generally smaller
than 1s, and bandwidths smaller than 12 MHz. Based on their narrow-band and
impulsive nature, they concluded that these emissions are nonthermal in origin
and have been given the name of Weak Impulsive Narrowband Quiet Sun Emissions
(WINQSEs). As the observed properties of WINQSEs meet all of the expectations
for them to be the radio counterparts of nanoflares, this hypothesis was put
forth by Mondal $et~{}al$. (2020a). Confirmation of this hypothesis requires
significant additional evidence.

The first evidence towards testing this hypothesis comes from Mondal (2021),
who identified the counterpart of a group of WINQSEs in the EUV band and then
used it to estimate the energy associated with the WINQSEs group using the
standard differential emission measure techniques. They found the energy
associated with the WINQSEs group to be $\approx 3\times 10^{25}$ergs,
suggesting that the energy associated with individual WINQSEs may likely lie
in the nanoflare regime ($\sim 10^{24}$ ergs). A key necessary condition for
this hypothesis to be true is that WINQSEs should always be present
irrespective of the state of activity of the Sun. To investigate this, data
from an extremely quiet solar condition were analyzed and WINQSEs have been
detected in this dataset as well (Mondal et al. 2022, submitted).
Additionally, since Mondal $et~{}al$. (2020a), we have also improved our
imaging and detection technique, and also fixed some issues which are
generally unimportant for routine solar imaging, but need attention when
dealing with flux densities of order a percent of the background. This
forthcoming work will provide the first conclusive evidence for the ubiquity
of WINQSEs during extremely quiet solar conditions. Due to the significance of
WINQSEs from a coronal heating perspective and also from the perspective of
characterizing and understanding a new class of solar radio transients, work
is ongoing on various fronts ranging from understanding their spectral and
temporal characteristics. These include the use of machine learning algorithms
for detection of WINQSEs and characterizing their morphologies (Bawaji et al.
2022, submitted), attempts to estimate the bandwidth of individual WINQSEs,
exploration of their temporal profiles using high time resolution data,
detection of EUV counterparts of WINQSEs to determine energies associated with
these. The use of an independent imaging technique and pipeline using the so-
called residual visibilities to look for WINQSEs-like features in the MWA data
has also yielded consistent results (Sharma $et~{}al$., 2022).

It is useful to emphasize that with noise statistics of AIRCARS/P-AIRCARS
images approaching thermal noise, we are already pushing the MWA data to its
limits, especially in WINQSEs-related work. While incremental technical
improvements will continue for some more time, they are not expected to lead
to a large improvement in the imaging sensitivity or dynamic range of MWA
images. We expect the SKAO-Low to be the instrument that will enable the next
big step in this field and, hopefully, revolutionizes our understanding of
this new class of radio transients called WINQSEs.

###  2.6 Coronal Propagation Effects

|
---|---
Figure 10: (a): Evolution of the observed type-III source area. it (b):
$\delta N/N$ derived using MWA data in 80 – 200 MHz. The theoretical
saturation limit ($\delta N/N_{sat}$) above which the medium is supposed to be
in strong scattering regime is shown. (c) Variation of $\epsilon\sim\delta
N/N$ at meterwave frequencies for the quiet Sun.

With the typical inner coronal densities (heliocentric height $\lesssim$
2$R_{\odot}$) varying in the range 109 – 108 $cm^{-3}$, the local plasma
frequency ($\nu_{p}$=8.98$\sqrt{{n_{e}}}\,kHz$, where $n_{e}$ is the electron
density in $cm^{-3}$) lies in the metrewave band. The refractive index in the
medium, $n$, for radiation of frequency $\nu$ is given by

$n=\sqrt{1-\left(\frac{\nu_{p}}{\nu}\right)^{2}}.$ (1)

Being close to the local $\nu_{p}$, metrewaves are heavily influenced by the
local density variations. These include the stochastic density fluctuations
arising due to local turbulence as well as the spatial inhomogeneities in the
density profile caused by plasma flows and magnetic field structures. The
effects of all these can be described under a common framework introduced by
Arzner & Magun (1999). This was later revisited and improved and a publicly
available modeling framework was developed by Kontar $et~{}al$. (2019).

While analyzing the impact of the propagation effects at a frequency $\nu$, it
is important to consider the variation in $\nu_{p}/\nu$ along the wave
trajectory from the source to the observer. In the case of solar radio bursts
involving coherent emission, like type Is and types IIIs, the emission
originates in regions where $\nu\sim$ 1 – 2$\nu_{p}$. Scattering is the
dominant propagation effect that significantly alters the apparent location as
well as the morphology of the source.

####  2.6.1 Propagation Effects under Quiet Sun conditions

Figure 11: Quiet Sun morphology as a function frequency (Sharma & Oberoi,
2020). $T_{B}$ maps for 8 frequency bands from 109 MHz to 240 MHz. The
frequency and time averaging are 2 MHz and 4 min respectively. The six contour
levels corresponds to 10%, 20%, 40%, 60%, 80% and 90% w.r.t maximum $T_{B}$.
(Reproduced from Sharma & Oberoi (2020))

High-fidelity studies of the quiet Sun at meter wavelengths are challenging
due to a variety of reasons – the presence of complex coronal magnetic field
topologies; weak variations in the emission features superposed on the much
brighter large angular scale emission, which is intrinsically harder to image.
Till recently, it was common practice to make synthesis observations over many
hours to get reasonable quiet Sun images at meter wavelengths (e.g. Kundu
$et~{}al$., 1987; Mercier & Chambe, 2009; Vocks $et~{}al$., 2018). These
studies established a relationship between optical, UV, and X-ray and
meterwave emission features. For example in synoptic maps, optical wavelengths
show large-scale counterparts in meterwaves (e.g. Kundu $et~{}al$., 1987).
Features like coronal helmets and active streamers brighten meterwave thermal
emission (e.g. Axisa $et~{}al$., 1971). Propagation effects like refraction
and scattering induce an apparent shift in the observed locations of compact
radio sources (Steinberg $et~{}al$., 1971; Arzner & Magun, 1999; Gordovskyy
$et~{}al$., 2019; Kontar $et~{}al$., 2019, e.g.). Scattering lowers the
apparent coronal brightness temperature, especially at meterwaves (Thejappa &
Kundu, 1994; Thejappa & MacDowall, 2008).

The Figure 11 from Sharma & Oberoi (2020) presents a stack of $T_{B}$ maps as
a function of frequency and provides a convenient way to track the evolution
of the radio morphology of thermal bremsstrahlung emission with coronal
height. They observed a gradual and systematic change in the single dominant
compact emission feature in the western hemisphere, splitting into two
segments at higher coronal elevations. A key focus of this work was to
quantify propagation effects using the novel approach based on a comparison of
the simulated maps from a data-driven empirical model for thermal
bremsstrahlung emission (FORWARD; Gibson $et~{}al$., 2016), which does not
include the impact of propagation effects, with the observed solar maps made
using MWA data. At frequencies above 200 MHz, they found an excellent
agreement in the modeled and observed solar flux densities integrated all over
the solar disc (and hence independent of propagation effects like scattering),
inspiring confidence in this approach. At lower frequencies, however, they
found the observer flux density to be systematically lower than that from the
FORWARD model. Non-radial shifts as large as 8’-11’ were found in the location
of the peak of a bright active region, a clear indication of the presence of
non-radial coronal structures. The angular size of the Sun was found to be
35–40% larger in the MWA images. They find scattering to play a dominant role
in determining the observed $T_{B}$. As considerable radiation is scattered in
and out of the lines of sight, the observed $T_{B}$ depends on both the
intrinsic $T_{B}$ of the region from where the radiation is originating and
the $T_{B}$ of the neighboring regions. Their estimates of the level of
density inhomogeneities lie in the range from 1–10% and are consistent with
earlier estimates.

####  2.6.2 Propagation Effects on Burst Emissions

The metrewave bursts, especially the type IIIs are excellent probes for
studying the dynamics in the local coronal density structures. With the advent
of modern interferometric arrays and snapshot spectroscopic imaging studies at
sub-second and sub-MHz resolutions, investigations of stochastic properties of
the coronal medium have now become tractable. The presence of stochastic
electron density fluctuations ($\delta N/N$, where $N$ represents the mean
electron density and $\delta N$, the local departure from the mean) causes the
radio waves from the burst source to undergo a diffusive transport resulting
in a systematic growth in the apparent source size and broadening of the
observed burst pulse. By tracking these effects systematically and modeling
the source diffusion, Mohan $et~{}al$. (2019b) derived $\delta N/N$ in the
inner corona below a heliocentric height of 2$R_{\odot}$. Fig. 10(a) clearly
shows the linear growth in the apparent source size.

Mohan (2021a) extended the analysis to a much larger height range using MWA
data spanning 80 – 200 MHz, and compared the results with other independent
estimates of $\delta N/N$ from LOFAR in the 30 – 80 MHz band. Figure 10(b)
shows the variation of $\delta N/N$ with height derived by Mohan (2021a) with
dots and the best fit powerlaw function with spectral index,
$\beta\sim$2.2$\pm$0.73. Similar to Mohan $et~{}al$. (2019b), this study also
found the $\delta N/N$ values to be higher than the saturation limit, $\delta
N/N_{sat}$, estimated using the model by Arzner & Magun (1999), or that one is
in the so-called strong scattering regime where wave propagation is well
described by a pure diffusion framework. This implies that the other sources
of propagation effects like refraction, radio wave ducting due to randomly
oriented fibrillar over-dense structures (Robinson, 1983) and radio echos
(Kuznetsov $et~{}al$., 2020) from random over dense pockets in the medium,
which could give rise to non-diffusive effects in the observed evolutionary
profiles, can safely be ignored. The study revealed that the variation in
$\delta N/N$ across the inner corona height range of 1.4 – 2.2 $R_{\odot}$ is
within a factor of few. Since weak type-III bursts are associated with weak
solar flares which are quite frequent and associated with active regions with
widely varying physical conditions, more studies along these lines can help
develop a more detailed picture of the characteristics and evolution of
density fluctuations in the inner corona.

###  2.7 Polarisation Studies of Solar Radio Emissions

Polarisation studies of the radio emissions (both thermal and nonthermal) from
the solar corona are sensitive probes of the emission mechanisms involved and
the coronal magnetic fields - the hard-to-measure driver of coronal dynamics
and space weather. In broad terms, the anisotropies in the coronal medium due
to the all-pervading coronal magnetic field leave their imprint on the
polarisation properties of the radiation originating from this medium. While
their scientific merits have been appreciated for a while, high-fidelity
polarimetric radio imaging poses significant technical challenges. For this
reason, most of the polarimetric studies of the solar corona thus far have
relied on non-imaging dynamic spectrum measurements. Some instruments have
also used simultaneous Stokes I imaging with Stokes V dynamic spectra to help
with the localization of the source of polarised emission (Sasikumar Raja,
2014).

As discussed in Sec. 2.2.2, we have recently developed a full Stokes snapshot
spectroscopic imaging pipeline optimized for solar imaging with the MWA
(Kansabanik $et~{}al$., 2022c; Kansabanik, 2022; Kansabanik $et~{}al$.,
2022a). It offers polarimetric calibration on par with usual interferometric
imaging and we expected it to enable multiple new avenues for exploration with
the MWA and the future SKAO when it becomes available. A limited but
illustrative set of examples of the kinds of studies polarimetric imaging
capability will enable include the following – It has been reported that
thermal emission (for instance from the coronal streamers) split into two
modes o-mode and x-mode due to radio wave propagation in the solar corona
(Ramesh $et~{}al$., 2010b). It is known that o-mode and x-mode are circularly
polarized with opposite senses of polarisation. Polarimetric imaging
capability will enable measurements of the degree and sense of circular
polarisations and their energy budgets (Ramesh $et~{}al$., 2010a, 2013b).
Detailed polarimetric studies of well-known solar bursts, including
identifying if the emission comes from Fundamental or Harmonic based on their
degree of polarisation (e.g. Ramesh $et~{}al$., 2011; Sasikumar Raja & Ramesh,
2013). Routine well-constrained modeling of gyrosynchrotron emission from CMEs
(Sec. 2.4). Examining and understanding the polarimetric properties of the
newly discovered WINQSEs (Sec. 2.5). Estimation of mean coronal magnetic field
for the quiet Sun regions using the low level ($<$1%) circular polarisation
arising due to the birefringence of the coronal medium (Sastry, 2009). In
addition, as this would be the first exploration of this phase of space, it
also offers considerable discovery potential.

##  3 Heliospheric Physics

Heliospheric physics deals with exploring and understanding the plasma of
solar origin permeating the entire solar system. This medium carries the
influence of the Sun to the Earth (and all other planets) and this is where
Space Weather develops and takes place. The vastness of this medium implies
that space-based probes which provide local measurements can only offer a very
limited and insufficient sampling. The tenuousness of this medium makes it
exceptionally hard to study, though in the past few decades there have been
some heliospheric imagers that have extended the idea of coronagraphs to the
entire heliosphere with remarkably success (Jackson $et~{}al$., 2004; Eyles
$et~{}al$., 2009). Well before these instruments became available, radio
observations in the metrewave band had already established themselves as
efficient remote sensing probes of the interplanetary medium by studying the
propagation effects on emissions from celestial sources and spacecraft radio
beacons. These include angular and spectral broadening (Woo $et~{}al$., 1995),
Faraday rotation (Bird $et~{}al$., 1985) and phase and amplitude
scintillations due to the interplanetary medium (Hewish $et~{}al$., 1964;
Kojima & Kakinuma, 1990). The following sections discuss the various
investigations of the heliosphere enabled by radio observations using existing
and the future SKAO-Low.

###  3.1 Interplanetary Scintillation

The outermost layer of the Sun, the so-called corona, has a very high
temperature ($\sim{10^{6}}\,$K) causing a huge pressure difference between the
corona and the interplanetary medium. The high-pressure gradient, despite the
restoring influence of solar gravity, causes the coronal plasma to escape out
into the interplanetary medium (IPM), and eventually form the solar wind. The
solar wind due to its expansion through the interplanetary space develops
fluctuations (Parker, 1958, 1963) or turbulence (Bruno & Carbone, 2005) in
velocity, magnetic field, and density. The scale sizes of such fluctuations
often show a wide range of spatial scales. The large-scale sizes in the solar
wind, above 104 km, generally, follow a power-law spectrum (Intriligator &
Wolfe, 1970). Fluctuations of scale size greater than 107 km also occur in the
solar wind. These develop principally due to stream structures in the solar
wind, and cannot be explained by the turbulence spectrum. Unlike velocity and
magnetic field fluctuations, density fluctuations are ubiquitous in the solar
wind. Further, density fluctuations are also believed to be a better tracer of
solar wind flows as compared to the background solar wind density, N
(Ananthakrishnan $et~{}al$., 1980; Woo $et~{}al$., 1995; Huddleston
$et~{}al$., 1995). Hence, knowing how density fluctuations ($\Delta$N) or
relative density fluctuations ($\frac{\Delta{N}}{N}$) vary in time and with
distance from the Sun is crucially important for a variety of applications
ranging from understanding turbulent dissipation to the consequent local
heating in the solar wind.

The variations in solar wind density fluctuations can be measured through a
phenomenon known as “Interplanetary scintillation (IPS)”, which was first
reported by Hewish $et~{}al$. (1964). IPS is the radio analog of the optical
twinkling of stars which is caused by turbulent density fluctuations in
Earth’s atmosphere. In IPS the radio waves from distant point-like extra-
galactic radio sources are scattered by density fluctuations in the solar wind
and give rise to amplitude fluctuations in the radiation incident on ground-
based radio telescopes. The typical geometry during IPS observation is shown
in Fig. 12. The angle $\epsilon$ is the solar elongation while ‘r’ is the
heliocentric distance of the radio source, in AU, and is given by r =
sin($\epsilon$). The scintillation measured at 327 MHz at the Earth are
modulated by a Fresnel filter function $\mathsf{Sin^{2}(\frac{q^{2}\lambda
z}{4\pi})}$, where q is the wave number of the density irregularities, z is
the distance from E to P, and $\lambda$ is the observing wavelength. It must
be noted that IPS at 327 MHz are caused primarily by solar wind density
fluctuations with scale sizes $\leq$103 km. (Pramesh Rao $et~{}al$., 1974;
Coles & Filice, 1985; Yamauchi $et~{}al$., 1998; Fallows $et~{}al$., 2008). On
the other hand, due to the action of the Fresnel filter, scale sizes $\geq$
$10^{3}$ km result in scintillation only at distances $>$ 1 AU. In other
words, the Earth is well within the Fresnel or the near zone for these scale
sizes. The IPS phenomena thus acts as an in-built filter that doesn’t allow
contributions to the measured scintillation at the Earth from large-scale size
density fluctuations.

IPS observations have been used to study the fine scales structures in
cometary ion tails as they occult well known IPS sources. (Ananthakrishnan
$et~{}al$., 1975; Slee $et~{}al$., 1987; Janardhan $et~{}al$., 1991; Janardhan
& Alurkar, 1992; Janardhan $et~{}al$., 1992). It is found that a regime
dominated by high values of density fluctuations at small spatial scales exist
along and close to the axis of cometary plasma tails, which is usually an
order of magnitude greater than that in solar wind. On the other hand, a fine
scale regime, similar to that of the solar wind plasma, also exists close to
the edge in cometary tail plasma. Both the regimes have the ability to produce
enhanced scintillation as observed through IPS observations for Comets Austin
and Halley (Janardhan $et~{}al$., 1992).

IPS measurements along the line of sight to the radio source can be quantified
using the scintillation index (m), which is defined as the ratio of the
scintillating flux ${\Delta}S$ to the mean source flux $<$S$>$,
$\mathsf{m=\frac{{\Delta}S}{<S>}}$. Thus, an ideal point source, for which the
scintillating flux is equal to the mean source flux, will have a $m$, of unity
at some fixed distance from the Sun. In fact $m$ increases with decreasing $r$
or $\epsilon$, until a certain $\epsilon$. This region is known as the weak
scattering region. Beyond this point, $m$ falls off sharply as it approaches
the near-Sun region known as the strong scattering region. The $\epsilon$ at
which $m$ turns over is dependent on frequency. At 327 MHz it lies between 10∘
and 14∘ or $\sim$40 R⊙, where, R⊙ is the solar radius. In the weak scattering
region, the approximation of scattering by a thin screen is valid (Salpeter,
1967), which means that most of the contribution to the scintillation will
come from the point “P” on the LOS that is closest to the Sun. Plane waves
from distant, compact extragalactic radio sources on passing through the thin
screen of density fluctuations will develop rms phase deviation,
$\phi{{}_{rms}}$, given by

$\centering\phi_{rms}=(2\pi)^{\frac{1}{4}}{\lambda}r_{e}(aL)^{\frac{1}{2}}[<{{\Delta}N}^{2}>]^{\frac{1}{2}},\@add@centering$
(2)

where $r_{e}$ is the classical electron radius, $\lambda$ is the observing
wavelength, and $a$ is the typical scale size in the thin screen of thickness
$L$. In the weak scattering regime, $m=\sqrt{2}{\phi{{}_{rms}}}$, and thus
using the variations in $m$, the changes in solar wind density fluctuations
can be inferred. The measurements of $m$ have been made possible through
ground-based IPS observations of a single station facility at Ooty Radio
Telescope (ORT) in India since the 1970s and a three-station facility at the
Institute for Space-Earth Environmental Research (ISEE) in Japan since the
1980s. There are other ground-based IPS facilities such as MEXART in Mexico
(Mejia-Ambriz $et~{}al$., 2010; Chang $et~{}al$., 2016) and Pushchino in
Russia, providing daily routine measurements for $m$. The IPS studies reported
here use observations from the ORT and ISEE facilities.

In the past few decades increasingly sophisticated algorithms, using IPS
observations as their primary observables, have been developed for 3D
reconstruction of global heliospheric parameters – density and velocity (e.g.
Jackson $et~{}al$., 1997, 1998). More recently these reconstructions have been
extended to include data IPS stations from across the world, from Thompson
scattering based heliospheric imagers and also incorporate MHD models. These
models can now also provide a reconstruction of the heliospheric magnetic
fields (Jackson $et~{}al$., 2020) and have recently been used for a detailed
modeling exercise for a CME (Iwai $et~{}al$., 2022).

In the past few years, the wide FoV imaging capability of the MWA has also
been put to use for IPS observations (Morgan $et~{}al$., 2018). A novel aspect
of these studies is that they use high time resolution imaging to
simultaneously observe a large number of IPS sources distributed across the
large MWA FoV and represents a significant advance in the field. Other
interesting aspects of these studies are that, in addition to be being used
for heliospheric physics, these observations are also being used to address
other science objectives ranging from understanding the properties of these
very compact sources at low radio frequencies (Chhetri $et~{}al$., 2018b, a)
to carrying out an all sky survey of compact radio sources (Morgan $et~{}al$.,
2019). Very recently IPS observations have also been demonstrated using the
Australian Square Kilometre Array Pathfinder (ASKAP; Chhetri $et~{}al$., 2022)
– another wide FoV imaging instrument, but operating at frequencies much
higher than the MWA and other instruments used for IPS. While limited in
scope, this is a very interesting development. The higher observing
frequencies of ASKAP allow one to use IPS to probe regions of the heliosphere
at much smaller elongations than possible with most IPS instruments.

Figure 12: A schematic of the IPS observing geometry. A schematic of the IPS
observing geometry. The Earth, the Sun, the point of closest approach of the
LOS to the Sun (P), and the foot point of a perpendicular from P to the
ecliptic plane are shown by points E, S, P, and A respectively, while the
angles $\epsilon$ and $\gamma$ are the solar elongations and the heliographic
latitude of the observed source. The radial distance from the Sun, ’r’ of the
LOS to the radio source is generally given by sin($\epsilon$). (reproduced
from Bisoi $et~{}al$. (2014))

###  3.2 Determining Angular Diameter of Radio Sources

IPS has been demonstrated to be a very efficient way to detect and
characterize sub-arcsecond structures in radio sources (Little & Hewish, 1966,
1968) and a recent example is Chhetri $et~{}al$. (2018b). Assuming a Gaussian
brightness distribution for the compact component of the radio source, the
systematic variation of $m$ with $\epsilon$ in the weak scattering region can
be used as an indicator of angular source size of scintillating radio source
(Janardhan & Alurkar, 1993). An independent method of estimating angular
diameter is based on fitting the observed IPS power spectra with solar wind
parameters including the radial speeds, the strength of scintillation, inner
and outer scales, power law index of density fluctuations along with the
angular size of a scintillating component of the radio sources (Manoharan &
Ananthakrishnan, 1990).

###  3.3 Variations in Large-scale Structure of Solar Wind

Since IPS observations are primarily sensitive to density fluctuations of
scale sizes less than 1000 km (typically at a frequency of 327 MHz), they can
probe a large region of the inner heliosphere, covering from 0.2 to 0.8 AU,
and have been successfully used to study the large-scale structure of solar
wind (of scale sizes $\approx$ 100–1000 km) as a function of helio-latitudes
and heliocentric distances over several solar cycles (Ananthakrishnan
$et~{}al$., 1980; Janardhan $et~{}al$., 1996; Manoharan, 2012).

###  3.4 Probing Density Fluctuations in Interplanetary Medium

It is important to note that IPS measures only the fluctuations, and not the
bulk density itself. However, any enhancement or decrease in IPS level in the
solar wind is associated with corresponding variations in density. Thus,
whenever interplanetary disturbances travel in the IPM, containing either
enhanced or depleted rms density fluctuations as compared to the background
solar wind, they exhibit themselves as changes in the level of scintillation.
It implies that whenever solar wind turbulence levels change, they will be
reflected in IPS measurements as changes in $m$. It is worth mentioning here
that IPS is sufficiently sensitive to changes in $\Delta{N}$ that it has been
used to probe density fluctuations in tenuous cometary ion tails (Janardhan
$et~{}al$., 1992) and to study solar wind disappearance events wherein average
densities at 1 AU drop to values below 0.1 $cm^{-3}$ (Janardhan $et~{}al$.,
2005). On the other hand, IPS measurements have also been useful to study the
propagation of large-scale disturbances like CME (e.g. Manoharan, 2006). The
CME while propagating in the IPM causes an increase in density and turbulence
in its sheath region, which can be mapped by obtaining the enhancement in the
g-index (g = ${\Delta}S/{\overline{\Delta{S}}}$) for each observation of all
the radio sources obscured by the CME. The g-maps, thus produced, show
enhanced regions of density and turbulence where g $>$1\. Further, using time
series of IPS g-index and velocity and time-dependent computer-assisted
tomographic technique, the three-dimensional heliospheric reconstruction of
solar wind velocity and density have also been obtained, which help in
tracking the traveling interplanetary disturbances associated with CMEs (e.g.
Manoharan, 2010).

###  3.5 Probing Long-term Variations of Solar Cycle Magnetic Activity

The study by Janardhan $et~{}al$. (2010) of solar cycle changes of solar
photospheric fields using ground-based magnetograms has shown that there has
been a steady decline in their strength at high latitudes ($>$45∘) since
$\sim$mid-1990’s. Since solar high-latitude magnetic fields supply most of the
heliospheric magnetic flux during solar minimum conditions (Svalgaard
$et~{}al$., 2005), the long-term decline in solar field strength implies that
it would affect the heliospheric open flux and, in turn, the magnetic field
fluctuations or the solar wind turbulence in the fast solar wind at high-
latitudes. A steady decline in coronal magnetic field strength correlated with
the reduction in photospheric field strength has also been noticed (Sasikumar
Raja $et~{}al$., 2019a). Using IPS measurements of $m$ at 327 MHz obtained
from the ISEE facility between 1983 and 2009, Janardhan $et~{}al$. (2011)
reported the temporal variations in $m$ during solar cycles 22–23. For the 27
selected IPS sources, including a point source 1148-001, which had at least
400 individual observations over this period of 27 years, the values of $m$
were made distance independent by normalizing every individual observation for
each source by the value of $m$ for the source 1148-001 at the corresponding
$\epsilon$. The temporal variations obtained thus for the normalized $m$ for
all of the 27 sources, as shown in Fig. 13 that depicts the annual means of
$m$ for each source in blue open circles as a function of time, unambiguously
showed a steady decline in $m$ starting from around mid-1990s. The reduction
in $m$ implies a global reduction in solar wind turbulence levels as expected.
It has been further noticed (Ingale $et~{}al$., 2019) that the steady decline
of solar wind turbulence levels has been continuing until the conclusion of
the solar cycle 24, in sync with the continuing decline in high-latitude
photospheric field strength.

Figure 13: Annual variation of scintillation index level. Shows the annual
means of $m$ as a function of time, covering the period between 1983 – 2009,
for a total of 27 IPS radio sources (reproduced from Janardhan $et~{}al$.
(2011)).

###  3.6 Locating Signatures of Unusual Polar Reversal

The polarity of the Sun’s magnetic field in each solar hemisphere reverses
around the maximum of each 11-year solar cycle, the well known polar reversal.
The occurrence of the reversal process ultimately decides the strength of the
polar field at the end of a solar cycle, which acts as a precursor for
predicting the amplitude of the upcoming solar cycle. The signatures of the
polar reversal can be identified in the solar wind as polar coronal holes.
These coronal holes are the source regions of high-speed solar wind that begin
to develop in both solar hemispheres after the field reversal takes place
(Krieger $et~{}al$., 1973; Nolte $et~{}al$., 1976; Zirker, 1977). Further, it
is known that polar coronal holes usually fully developed $\sim$2 years after
the field reversal (Fujiki $et~{}al$., 2016). In cycle 24, the polar reversal
showed an unusual pattern in the photospheric synoptic magnetic maps, wherein
the southern hemisphere underwent a single and clean polar reversal in Nov
2013 while the polar reversal in the northern hemisphere started in Jun 2012
and was completed after more than a year, in Nov 2014 (Janardhan $et~{}al$.,
2018). Signatures of this unusual field reversal pattern were identifiable in
the solar wind velocity maps, produced using a tomographic technique applied
to multi-station IPS observations at 327 MHz obtained from the ISEE facility,
which showed well-defined polar coronal holes in the southern hemisphere just
around 2 years after the field reversal while the polar coronal holes were not
fully developed in the northern hemisphere. A difference in time of appearance
of fully developed polar coronal holes in the two hemispheres thus clearly
indicates the completion of reversal occurred at different times in the two
hemispheres.

###  3.7 Probing Solar Wind Turbulence and Magnetic Field Fluctuations

In another study of the inner heliospheric solar wind during the solar cycle
23 and covering heliocentric distances of 0.26 - 0.82 AU, the variations in
relative density fluctuations or solar wind density modulation index defined
as, ${\epsilon}_{N}$ = $\frac{{\Delta}N}{N}$, were computed (Bisoi $et~{}al$.,
2014). The values of ${\Delta}N$ at a particular heliocentric distance were
directly computed using measurements of $m$ from ISEE at that distance, while
values of $N$ at 1 AU were extrapolated using a solar wind density model to
determine the value of $N$ at the heliocentric distance where the ${\Delta}N$
values were estimated. Also, the values of $m$ were made source size
independent before computation of ${\Delta}N$. It was found that the variation
of ${\epsilon}_{N}$ both for the ecliptic and non-ecliptic radio sources was
roughly constant with heliocentric distance as depicted in Fig. 14. It is
shown that the length scales probed by the IPS observations at 327 MHz are in
the inertial range of the turbulence spectrum. Thus, it is reasonable to
presume that the magnetic field is frozen in the solar wind plasma and the
density fluctuations can be taken as a proxy for magnetic field fluctuations
(e.g. Spangler, 2002). Furthermore, it is found that the temporal variation of
${\epsilon}_{N}$, after making the ${\Delta}N$ values distance independent,
showed a decline of around 8% during the period 1998–2008. Presuming a linear
relationship between the relative density fluctuations and the magnetic field
fluctuations (Spangler & Spitler, 2004), it appears reasonable that the
magnetic field fluctuations have also been declining steadily over the same
period. The decline in solar wind density fluctuations as inferred by IPS
observations is, therefore, claimed to be linked to the steady decline of
solar photospheric magnetic activity.

Figure 14: Spatial variation of the density modulation index,
${\epsilon}_{N}$, of all 27 selected sources in the period from 1998 to 2008.
While the blue and red solid dots are the actual measurements of normalized
modulation indices for ecliptic sources and non-ecliptic sources,
respectively, the large open circles in black represent averages of all
observation at intervals of 0.1 AU. The solid line is a fit to these average
values (reproduced from Bisoi $et~{}al$., 2014).

###  3.8 Tracking Source Region of Geomagnetic Events

Over the years, it has been established that when the interplanetary magnetic
field (IMF-$B_{z}$) becomes southward, it produces a strong coupling between
the solar wind and the Earth’s magnetosphere through magnetic reconnection of
the IMF-$B_{z}$ and the terrestrial magnetic field, leading to geomagnetic
storm events (Dungey, 1961). Further, it is known that the long-duration
southward IMF-$B_{z}$ events (magnitudes greater than -10 nT and lasting for
over 3 h) play a significant role in triggering magnetic storms (Gonzalez &
Tsurutani, 1987; Tsurutani $et~{}al$., 1992). Tracking back the source regions
of such geomagnetic events, which are, often, associated with well-defined
solar eruptive phenomena such as CMEs is crucial as their interplanetary
counterparts preferentially result in southward IMF-$B_{z}$ condition at 1 AU.
The synoptic velocity maps, those produced using IPS observations via
tomographic technique and then projected back to the source surface, at 2.5
R⊙, can be used to track the source region of the southward IMF-$B_{z}$
events. From the tomographic velocity map, the velocity of solar wind flow in
the traceback region can be identified and can be linked to the source region.
Bisoi $et~{}al$. (2016), using the IPS tomographic maps, tracked the source
region of a prolonged southward IMF-$B_{z}$ that produced severe geomagnetic
storm conditions, and were able to locate the high-velocity solar wind flows
in the traceback region, which had occurred because of the eruption of a CME
on the Sun.

###  3.9 IPS with the SKAO

The high sensitivity observations of a large number of IPS radio sources per
day can be carried out using the SKAO at different frequencies as compared to
the current dedicated ground-based IPS facilities such as ORT and ISEE etc. as
well as radio interferometers such as LOFAR and MWA etc., which can provide
IPS observations between $\sim$ 200–1000 IPS radio sources per day. Through
IPS observations of a large number of radio sources along the multiple LOS,
complete distribution of solar wind plasma properties such as density and
velocity variations those sensitive to IPS, can be obtained. This, in turn,
can be employed to estimate the systematic variation in the scintillation
index as a function of heliocentric distance and heliolatitudes. In addition,
they can be used to produce a three-dimensional heliospheric reconstruction of
traveling disturbances in the solar wind such as CME and so on, providing a
more robust estimation of solar wind density and velocity, as compared to the
other IPS observations mentioned earlier. The high sensitivity IPS
observations thus obtained from the SKAO shall be used

  1. 1.

for studying variations in solar wind plasma, especially those of density
fluctuations, as discussed earlier.

  2. 2.

for studying large-scale structure of solar wind and its variation as a
function of heliocentric distance and heliolatitudes.

  3. 3.

for studying long-term solar wind variations such as solar cycle changes of
solar wind associated with photospheric magnetic activity changes.

  4. 4.

for tracking CME propagation as well as tracking solar wind disturbances
traveling in IPM along with coronal white-light images obtained from other
spacecraft such as ADITYA-L1, Parker’s Solar Probe and Solar Orbiter etc.

  5. 5.

for the heliospheric reconstruction of solar wind density, velocity, and
IMF-$B_{z}$ at 1 AU to make IPS-based prediction of space weather events using
the aforementioned parameters.

  6. 6.

building a robust IPS-based estimated system for predicting the arrival of CME
at 1 AU using global MHD simulations along with white-light coronal
observations.

###  3.10 Heliospheric Faraday Rotation

Figure 15: Stokes I emissions from the background radio sources and galactic
plane in the presence of the Sun in the FoV. Left panel:  Image centered at 80
$\mathrm{MHz}$, $\sim 60^{\circ}$ on each side, obtained over 2 minutes and
2.28 $\mathrm{MHz}$ after subtraction of modeled solar visibilities from the
data. The image is from the observation on 2014 May 04 using the MWA, and the
red circle with radius 2 $\mathrm{R_{\odot}}$ is the region where the Sun was
present. (reproduced from Kansabanik $et~{}al$. (2022b)). Right panel:  The
Sun is present at the center of the image. The extended emission at the bottom
left of the figure is the galactic diffuse emission from the galactic plane.
(Left panel reproduced from Kansabanik $et~{}al$. (2022b))

It is well established that solar magnetic fields are a key driver of all
kinds of space weather phenomena. Their routine measurements are only
available at the solar photosphere and from in-situ spacecraft measurements
usually near the Earth or at certain vantage points in the heliosphere. There
are other techniques available to measure magnetic fields up to few tens of
solar radii using observations at different wavebands (e.g. Gopalswamy
$et~{}al$., 2011; Kumari $et~{}al$., 2017a; Ramesh $et~{}al$., 2021; Sasikumar
Raja & Ramesh, 2013; Bastian $et~{}al$., 2001; Mondal $et~{}al$., 2020b;
Sasikumar Raja $et~{}al$., 2022a, etc.). Measurements of the magnetic fields
in the solar wind and CMEs over the entire heliosphere remain a challenge and
are only rarely possible.

When linearly polarised radiation passes through a magnetized plasma, its
plane of polarisation rotates. The magnitude of Faraday rotation (FR)
experienced depends on the three quantities; i) electron density
($\mathrm{n_{e}}(\vec{r})$), ii) magnetic field ($\mathrm{\vec{B}}(\vec{r})$)
and the wavelength of the emission ($\lambda$), and is given by

$\begin{split}\mathrm{FR}&=\lambda^{2}\times\mathrm{\frac{e^{3}}{8\pi\epsilon
m_{e}^{2}c^{3}}\int_{obs}^{src}\mathrm{n_{e}}(\vec{r})\mathrm{\vec{B}}(\vec{r})\
.\ d\vec{s}}=\lambda^{2}\times\mathrm{RM},\end{split}$ (3)

where, $\mathrm{e}$ is the charge of an electron; $\mathrm{m_{e}}$ is the mass
of an electron; $\mathrm{c}$ is the speed of light; $\epsilon$ is the
permittivity of the medium; $\vec{r}$ is the coordinates of a point in three-
dimensional space; $\vec{s}$ is a vector coordinate along the LoS through the
plasma, and $\mathrm{RM}$ is called “Rotation Measure” (Brentjens, M. A. & de
Bruyn, A. G., 2005). Measuring FR due to the heliospheric and/or CME plasma
along the lines of sight to background linearly polarised sources can be a
powerful remote sensing tool for measuring these magnetic fields (see Oberoi &
Lonsdale (2012) for a review). This technique has been successfully used in
past; using spacecraft radio beacons (e.g. Bird & Edenhofer, 1990; Jensen
$et~{}al$., 2013; Wexler $et~{}al$., 2019, etc.) and more interestingly also
using astronomical sources (Mancuso & Spangler, 2000; Kooi $et~{}al$., 2017,
2021). Most of these observations were carried out at higher frequencies and
using small FoV instruments, and thus can sample only a small part of the
heliosphere at any given time. Moreover, the $\lambda^{2}$ dependence of FR
implies that at high frequencies small change in $\mathrm{RM}$ due to a small
change in $\mathrm{\vec{B}}(\vec{r})$ may not produce detectable changes in
$\mathrm{FR}$.

Wide FoV instruments like the MWA can sample large parts of the sky at any
given time and can track CMEs as they make their way across the heliosphere.
Measurements of FR simultaneously for a large number of pierce points across
the CME/heliosphere, open the very exciting possibility of constraining the
models for CME/heliospheric magnetic fields using these data (Bowman
$et~{}al$., 2013; Nakariakov $et~{}al$., 2015). Though scientifically very
rewarding and exciting, the following challenges need to be overcome before we
can measure the Heliospheric FR using wide FoV instruments:

  1. 1.

The Sun is by far the strongest source in the low radio frequency sky and
always makes the dominant contribution to the visibilities measured by large
FoV instruments. For daytime measurements of the heliospheric magnetic fields,
one needs to do high fidelity full Stokes imaging of astronomical sources with
polarised flux densities of at most a few $\mathrm{Jy}$ in the presence of the
Sun, the flux density of which is four or more orders of magnitude larger.

  2. 2.

The instrumental polarisation for wide FoV aperture array instruments is
direction-dependent. This instrumental artifact needs to be corrected with
high accuracy to get to the heliospheric RM signal (e.g. Lenc $et~{}al$.,
2017).

  3. 3.

At the meter wavelengths, ionospheric RM is of a similar order of magnitude or
larger as compared to the RM due to a CME far away from the Sun (see Fig. 2 of
Oberoi & Lonsdale (2012)). Precise correction of ionospheric RM variation is,
hence, essential for heliospheric FR measurements.

With the availability of P-AIRCARS (Kansabanik $et~{}al$., 2022c; Kansabanik,
2022; Kansabanik $et~{}al$., 2022a), the first of these challenges has now
been met (Sec. 2.2.2). High dynamic range imaging provided by P-AIRCARS allows
Kansabanik $et~{}al$. (2022b) to detect numerous background galactic and
extra-galactic sources in Stokes I down to flux density of 4.6 $\mathrm{Jy}$
in the presence of the $10^{4}\ \mathrm{Jy}$ Sun. The white dots in Fig. 15
(left panel) are the astronomical sources and the location of the Sun is shown
by the red circle. The most promising source of linearly polarised emission at
these frequencies is however the large angular scale Galactic background (Lenc
$et~{}al$., 2017). We demonstrate that galactic diffuse emission can also be
detected in the presence of the Sun (Fig. 15 (right panel)). The bright source
at the center of the image is the Sun and the extended emission towards the
lower left corner is the diffuse emission from the Galactic plane. Being able
to detect these sources during the daytime marks significant progress toward
measuring heliospheric FR during the daytime. P-AIRCARS delivers precise
polarisation calibration and produces a high dynamic range of full Stokes
images. We are pursuing the objective of demonstrating making similar full
Stokes maps of background sources and enabling these heliospheric FR
measurements. With the much-improved sensitivity of the SKAO, it should become
possible to routinely perform these observations.

###  3.11 Radio Occultation Observations to Probe Solar corona and the Solar
Wind

Radio occultation observations of point sources are an excellent probe of the
solar corona and the solar wind. Such observations help in understanding
density structure-function, the amplitude of density turbulence, density
modulation index, heating rates in the solar wind, dissipation scales among
other things. When a compact radio source is observed through the foreground
solar wind, it can lead to one or more of the following observable
consequences : (i) the apparent size of the radio source increase due to the
scattering of the radio waves in the turbulent medium (referred to as angular
broadening or scatter broadening); (ii) this angular broadening is accompanied
by a drop in the apparent peak flux density while conserving the flux density
integrated over the entire source; (iii) the observed anisotropy in angular
broadening (typically observed below $10\ R_{\odot}$) carries an imprint of
the anisotropies in the coronal and solar wind medium giving rise to the
scattering; and (iv) the position angle (PA; measured from the north through
the east) of the measured anisotropies can help constrain the orientation of
the magnetic field in the corona.

Currently, the biggest limitations of this technique come from the limited
ability of existing instruments to make sensitive measurements in the
proximity of the Sun. There are few ecliptic sources with flux density large
enough to be comfortably imaged as they are occulted by the corona. The
ability to image a large number of background sources in the same field of
view as the Sun has already been demonstrated by SKAO precursors like the MWA
(Kansabanik $et~{}al$., 2022b). Both SKAO-Mid and SKAO-Low promise all of the
essential ingredients to extract the numerous scientific benefits from such
studies – higher sensitivity and imaging dynamic ranges and much better
angular resolutions. In the interim significant progress can already be made
using observations from precursor facilities like MWA, MeerKAT, and ASKAP.

The favorite source used for such studies thus far has been the Crab Nebula,
whose distance of closest approach to the Sun is $\sim 5R_{\odot}$. The
angular broadening of the Crab Nebula was first reported by Machin & Smith
(1952). After that many authors have reported such observations at different
frequencies (ranging from radio and microwave) and using interferometers with
varying baseline lengths (Hewish, 1957, 1958; Slee, 1959; Hewish & Wyndham,
1963; Erickson, 1964; Sastry & Subramanian, 1974; Ramesh $et~{}al$., 2001;
Sasikumar Raja $et~{}al$., 2016, 2017, 2019b, 2021). The following text
showcases the learnings thus far from occultation studies and the expectations
from the SKAO.

####  3.11.1 Occultation Observations of Crab Nebula

The parameters discussed above vary with heliocentric distance and phase of
the solar cycle. Such observable quantities provide clues to estimating the
various turbulence parameters of the solar corona and solar wind. For example,
Figure 16 shows the observations carried out at GRO in the years 2011 and
2013. It is evident that as the Crab Nebula approaches the sun (ingress), the
peak flux density decreases until 11 June. Crab is not detected from 12–18
June as its flux density drops below the instrument sensitivity threshold. The
flux density increases from 19 June onwards as the Crab Nebula egresses. Note
that at its closest, the Crab Nebula is about 5 $R_{\odot}$from the Sun.

Figure 16: A solar disk view of the Crab Nebula occultation is shown in the
upper panel. The red circle indicates the Sun, and the green circles represent
the location of the Crab Nebula with respect to the Sun on different days in
June. $\Delta$ R.A. and $\Delta$dec. are the offset distances of Crab Nebula
from the Sun in right ascension and declination, respectively. The closest
dotted concentric circle around the Sun has a radius of $\approx
5~{}R_{\odot}$. The radii of the circles increase in steps of $5~{}R_{\odot}$.
The lower panel shows the observed flux density of the Crab Nebula on
different days during its occultation by the solar corona. The periods before
and after June 16th correspond to the ingress and egress, respectively. The
symbols ‘*’ and square indicate the observations carried out in 2011 and 2013
June, respectively. The minimum detectable flux density of the Gauribidanur
Radioheliograph $\approx 100$ Jy is used as an error bar.

Using the Very Large Array observations in A configuration (baselines up to 35
km) Anantharamaiah $et~{}al$. (1994) observed multiple sources with flux
densities in the range 0.5–0.9 Jy at 1.3, 2, 3.5, 6, 20, and 90 cm. The solar
elongation of these sources ranges between 2–20 $R_{\odot}$. These
observations show that angular broadening is evident at microwave frequencies.

####  3.11.2 Density Structure Function

By measuring the peak flux density (V(s)) and zero-baseline flux density
(V(0)) or the radio source is observed far from the Sun $\gtrsim 50R_{\odot}$)
one can measure the mutual coherence function ($\Gamma(s)$) and then the
density structure function $D_{\phi}(s)$ using (Prokhorov $et~{}al$., 1975)

$D_{\phi}(s)=-2ln[\Gamma(s)]=-2ln[V(s)/V(0)]$ (4)

####  3.11.3 Amplitude of Turbulence

By knowing $D_{\phi}(s)$, it is possible to measure the amplitude of the
turbulence ($C_{N}^{2}$) using the General Structure Function (GSF) (Ingale
$et~{}al$., 2015) defined as,

$\displaystyle{D_{\phi}(s)}=\frac{8\pi^{2}r_{e}^{2}\lambda^{2}\Delta
L}{\rho~{}2^{\alpha-2}(\alpha-2)}{\Gamma\bigg{(}1-{\frac{\alpha-2}{2}}\bigg{)}}{\frac{C_{N}^{2}(R)l_{i}^{\alpha-2}(R)}{(1-f_{p}^{2}(R)/f^{2})}}$
$\displaystyle{\times\bigg{\\{}{{}_{1}F_{1}}{\bigg{[}-{\frac{\alpha-2}{2}},~{}1,~{}-\bigg{(}{\frac{s}{l_{i}(R)}}\bigg{)}^{2}\bigg{]}}-1\bigg{\\}}}\,\,\,\,{\rm
rad}^{2},$ (5)

where ${{}_{1}F_{1}}$ is the confluent hypergeometric function, $\lambda$ is
the observing wavelength, $R$ is the heliocentric distance (in $R_{\odot}$),
$r_{e}$ is the classical electron radius, $\Delta L$ is the thickness of the
scattering medium, $\rho$ is the anisotropy of the source, $s$ is the baseline
length of the interferometer, $\alpha$ is the slope of the turbulent spectrum
($\approx 3$ or $\approx 11/3$), $f_{p}$ and f are the plasma and observing
frequencies, respectively and $l_{i}$ is the inner scale.

####  3.11.4 Density Modulation Index

By knowing the $C_{N}^{2}$, it is possible to measure the density fluctuations
$\delta N_{k_{i}}$ at the inner scales using (Chandran $et~{}al$., 2009)

${\delta}N_{k_{i}}^{2}(R)=4\pi C_{N}^{2}(R)k_{i}^{3-\alpha}e^{-1}\,,$ (6)

where $k_{i}=2\pi/l_{i}$.

Further, by knowing the ${\delta}N_{k_{i}}$ and the background electron
density ($N_{e}$), the density modulation index ($\epsilon_{N_{e}}$) can be
measured using,

$\epsilon_{N_{e}}(R)\equiv{\frac{\delta N_{k_{i}}(R)}{N_{e}(R)}}.$ (7)

####  3.11.5 Proton Heating Rates

By making use of $\epsilon_{N_{e}}$, it is possible to measure the proton
heating rates in the solar wind. Chandran $et~{}al$. (2009) suggested that
density fluctuations at small scales are manifestations of low frequency,
oblique ($k_{\perp}\gg k_{\parallel}$), $\rm Alfv\acute{e}n$ wave turbulence
and are often referred to kinetic $\rm Alfv\acute{e}n$ waves. Note that the
quantities $k_{\perp}$ and $k_{\parallel}$ are the components of the wave
vector k in perpendicular and parallel directions to the background large-
scale magnetic field, respectively.

Chandran $et~{}al$. (2009); Sasikumar Raja $et~{}al$. (2017, 2021) envisage a
situation where the “balanced” counter-propagating $\rm Alfv\acute{e}n$ waves
cascade and resonantly damp on the protons at the inner scale and thus heat
the solar wind. The proton heating rate (i.e. the turbulent energy cascade
rate) at inner scales is,

$\epsilon_{k_{i}}(R)=c_{0}\rho_{p}k_{i}(R)\delta v_{k_{i}}^{3}(R)~{}\rm
erg~{}cm^{-3}~{}s^{-1}\,,$ (8)

where, $\rho_{p}=m_{p}N_{e}(R)~{}\rm g~{}cm^{-3}$ with $m_{p}$ is the proton
mass, $k_{i}=2\pi/l_{i}$ and $\delta v_{k_{i}}$ are the wavenumber and
magnitude of turbulent velocity fluctuations at inner scales. The dimensional
less quantity $c_{0}$ is assumed to be 0.25.

By knowing the $\epsilon_{N_{e}}$, one can derive $\delta v_{k_{i}}$ using the
kinetic $\rm Alfv\acute{e}n$ wave dispersion relation

$\displaystyle\delta
v_{k_{i}}(R)=\Bigg{(}\frac{1+\gamma_{i}k_{i}^{2}(R)\rho_{i}^{2}(R)}{k_{i}(R)l_{i}(R)}\Bigg{)}$
$\displaystyle\epsilon_{N_{e}}(R,k_{i})v_{A}(R)\,$ (9)

where the adiabatic index $\gamma_{i}$ is taken to be 1 and $v_{A}$ is the
$\rm Alfv\acute{e}n$ speed in the solar wind.

####  3.11.6 Observations Through CMEs and Coronal Streamers

There were attempts to observe the Crab Nebula through CMEs and streamers. The
Crab Nebula, when observed through a CME at a distance of 41 $R_{\odot}$on 04
June 1997 (Ramesh $et~{}al$., 2001) is shown a left panel of Fig. 17. The
right panel of the same Fig. shows the Crab Nebula, as observed through a
streamer on 16 June 2016 (10.2 $R_{\odot}$) (Sasikumar Raja $et~{}al$., 2017).
The Figure clearly shows that isotropic angular broadening is observed when
the Crab nebula is observed through a CME. In contrast, a clear anisotropic
angular broadening is observed in the case of streamers.

Figure 17: Imaging observations of the Crab Nebula by Gauribidanur
Radioheliograph. The left panel shows the observations through a Coronal Mass
Ejection on 04 June 1997 (Ramesh $et~{}al$., 2001). The right panel shows the
observations through a streamer on 17 June 2016 (Sasikumar Raja $et~{}al$.,
2017). The arrows point in the sun-ward direction.

####  3.11.7 Dissipation Scales

Using multi-baseline observations of radio point sources through the solar
corona or solar wind can measure the dissipation scales. Recently Sasikumar
Raja $et~{}al$. (2019b) reported the dissipation scales using radio
occultation observations from the Gauribindanur Radioheliograph (GRAPH) and
the VLA. The calibrated visibilities are averaged over the observation
duration and plotted as a function of baseline length (Fig. 18, left panel).
These visibilities are fitted with a GSF model shown in Eq. 3.11.3 for
different $l_{i}$ values. The value of $l_{i}$ which shows the least deviation
between the observed and model values is regarded as the dissipation scale for
that heliocentric distance. In the right panel of Figure 18, the red circles
indicate the observations, and solid, dashed, and dot-dashed lines are the
models for dissipation scales. This study suggests that short baseline
observations are crucial in measuring the dissipation scales of the solar
corona and solar wind.

Figure 18: In the left panel, blue circles show the structure-function
measured from the visibilities vs. the baseline length of the interferometer,
and the red curve indicates the GSF model shown in equation 3.11.3. In the
right panel, red circles show the observationally derived dissipation scales.
The solid line indicates the prediction of the proton inertial length model.
The dashed line indicates the proton gyroradius computed using a temperature
of $10^{5}$ K and the Parker spiral magnetic field model and the dash-dotted
line indicates the proton gyroradius using a temperature of $10^{6}$ K and the
magnetic field model Venzmer & Bothmer (2018).

####  3.11.8 Variation of the Turbulent Plasma Parameters with Heliocentric
Distance and Solar cycle

The parameters discussed so far in this section, like $C_{N}^{2}$, density
modulation index ($\epsilon_{N_{e}}$), proton heating rate
($\epsilon_{k_{i}}$), dissipation scales, etc., all vary with heliocentric
distance and the phase of the solar cycle (Sasikumar Raja $et~{}al$., 2016,
2019b, 2021). A sensitive radio facility like the SKAO, will be able to
regularly measure these parameters and establish their dependence on the
heliocentric distance and phase of the solar cycle.

####  3.11.9 Magnetic Topology of Solar Wind

In Figure 17, the arrow is pointing towards the Sun. The right panel shows
that the coronal streamer was in the direction opposite the arrow. Also, we
know that beyond 10 $R_{\odot}$, the direction of the streamer will be
radially outward direction but the major axis of the Crab Nebula was
perpendicular to the direction of the magnetic field direction. Similar
behaviour was also reported by Anantharamaiah $et~{}al$. (1994). This has the
remarkable implication that the knowledge of the position angle can help
ascertain the magnetic topology up to 50 $R_{\odot}$. Since the SKAO will
provide a much higher sensitivity, resolution and imaging dynamic range than
the current instrumentation, we can expect to observe many such sources and
obtain valuable information on the magnetic topology of the solar wind.

####  3.11.10 Role of the SKAO on Occultation Observation

As just mentioned, the SKAO is expected to provide a significant improvement
over the capabilities of the existing instrumentation and the SKAO precursors
and pathfinders. By providing the sensitivity and imaging quality to enable
observations of a large number of ecliptic sources in the solar vicinity at
any given time, these studies will add yet another set of observables to
heliospheric studies and space weather. These will complement the information
obtained from the observations of IPS (Sec. 3.1) and heliospheric FR (Sec.
3.10), under quiescent conditions and also very interestingly through
structures like streamers, interaction regions, and CMEs. These observations
will provide an unprecedented opportunity to characterize the turbulent
coronal and solar wind plasma and magnetic fields and potentially play a
crucial role in the understanding of solar wind heating and acceleration. This
solar wind is a rich test bed for understanding the properties of
magnetohydrodynamic (MHD) turbulence. Using radio occultation observations, we
can study and investigate the following aspects.

  * •

Understanding the compressibility of solar wind turbulence.

  * •

Quantifying the role of radio wave scattering that leads to depressed quiet
Sun brightness temperatures at low radio frequencies.

  * •

Investigating the impact of solar wind turbulence on the origin, coronal
propagation, and the apparent sizes of solar radio burst sources. Being able
to disentangle the propagation effects from intrinsic ones will, in-turn, help
in building a more detailed understanding of the emission mechanisms involved.

  * •

Understanding the range of inner scales/dissipation scales present in the
solar wind.

  * •

Understanding the role of turbulence in the propagation of Solar Energetic
Particles (SEP) through the heliosphere (e.g. Reid & Kontar, 2010).

  * •

Carrying out a detailed comparison the various turbulence parameters measured
using independent remote sensing methods like occultation studies and in-situ
measurements by future instruments similar to Parker Solar Probe, Solar
Orbiter, etc.

##  4 Conclusion

Indian researchers have been systematically preparing for solar and
heliospheric science which will be enabled by the upcoming SKAO. On the solar
physics front, we have been leading the global solar science effort with the
only SKAO-Low precursor, the MWA. We have successfully met the challenge of
building unsupervised automated imaging pipelines for full Stokes snapshot
spectroscopic imaging with aperture array instruments like the SKAO-Low. The
outputs from these pipelines represent the state-of-the-art in metrewave solar
imaging, marking improvements of one or more orders of magnitude in dynamic
range, polarisation purity, and fidelity. Our explorations of the novel phase
space made accessible by these images have led to multiple interesting
studies. These science projects have carefully been chosen to match the
advantages provided by our high-quality spectroscopic snapshot imaging
capability and highlight previously unappreciated or unknown aspects of well-
known active emissions or tackle challenging problems like detection of
expected but weak gyrosynchrotron emission from CMEs and the discovery of the
weakest impulsive nonthermal emissions from the quiet Sun reported yet. On the
heliospheric physics front, we not only have a rich legacy to build on, but
recent developments are also promising to provide the necessary stepping
stones to SKAO science. We are actively engaged in pursuing the science
opportunities already made available by the SKAO precursors at SKAO-Low
frequencies and plan to increase our engagement with work related to SKAO-Mid
frequencies. Alongside advancing the frontiers of scientific knowledge, we
are, on the hand working to develop the human resource with the necessary
scientific and technical skills to make the most of the SKAO when it becomes
available, and on the other developing state-of-the-art imaging pipelines
which will make high quality radio imaging analysis more accessible to the
larger solar physics community.

## Acknowledgements

This scientific work makes use of the Murchison Radio-astronomy Observatory,
operated by CSIRO. We acknowledge the Wajarri Yamatji people as the
traditional owners of the Observatory site. Support for the operation of the
MWA is provided by the Australian Government (NCRIS), under a contract to
Curtin University administered by Astronomy Australia Limited. We acknowledge
the Pawsey Supercomputing Centre which is supported by the Western Australian
and Australian Governments. DO and DK acknowledges the support of the
Department of Atomic Energy, Government of India, under project no.
12-R&D-TFR-5.02-0700. This work is supported by the Research Council of Norway
through its Centres of Excellence scheme, project number 262622 (“Rosseland
Centre for Solar Physics”). AM acknowledges support from the EMISSA project
funded by the Research Council of Norway (project number 286853) We thank the
developers of Python 3 (Van Rossum & Drake Jr, 1995; Van Rossum & Drake, 2009)
and the various associated packages, especially Matplotlib (Hunter, 2007),
Astropy (Price-Whelan $et~{}al$., 2018), NumPy (Harris $et~{}al$., 2020) and
SciPy (Virtanen $et~{}al$., 2020). KSR acknowledges the useful discussions
that he had with R. Ramesh, Indian Institute of Astrophysics, Bangalore,
India, and Prasad Subramanian, IISER-Pune, India. SM acknowledges partial
support by USA NSF grant AGS-1654382 to the New Jersey Institute of
Technology.

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