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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Astron. Space Sci.</journal-id>
<journal-title>Frontiers in Astronomy and Space Sciences</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Astron. Space Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-987X</issn>
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<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-id pub-id-type="publisher-id">1666743</article-id>
<article-id pub-id-type="doi">10.3389/fspas.2025.1666743</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Astronomy and Space Sciences</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Solar observation with MeerKAT: demonstration of technical readiness and initial science highlights</article-title>
<alt-title alt-title-type="left-running-head">Kansabanik et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fspas.2025.1666743">10.3389/fspas.2025.1666743</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Kansabanik</surname>
<given-names>Devojyoti</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<contrib contrib-type="author">
<name>
<surname>Gouws</surname>
<given-names>Marcel</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Patra</surname>
<given-names>Deepan</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Vourlidas</surname>
<given-names>Angelos</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/579416/overview"/>
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<contrib contrib-type="author">
<name>
<surname>Kotz&#xe9;</surname>
<given-names>Pieter</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Oberoi</surname>
<given-names>Divya</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/170449/overview"/>
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<contrib contrib-type="author">
<name>
<surname>Shaik</surname>
<given-names>Shaheda Begum</given-names>
</name>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1351701/overview"/>
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<contrib contrib-type="author">
<name>
<surname>Buchner</surname>
<given-names>Sarah</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
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<contrib contrib-type="author">
<name>
<surname>Camilo</surname>
<given-names>Fernando</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
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<aff id="aff1">
<sup>1</sup>
<institution>NASA Jack Eddy Fellow, University Corporation for Atmospheric Research</institution>, <addr-line>Boulder</addr-line>, <addr-line>CO</addr-line>, <country>United States</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>The Johns Hopkins University Applied Physics Laboratory</institution>, <addr-line>Laurel</addr-line>, <addr-line>MD</addr-line>, <country>United States</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>South African Radio Astronomy Observatory, Liesbeek House</institution>, <addr-line>Cape Town</addr-line>, <country>South Africa</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, S. P. Pune University Campus</institution>, <addr-line>Pune</addr-line>, <country>India</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>National Radio Astronomy Observatory</institution>, <addr-line>Charlottesville</addr-line>, <addr-line>VA</addr-line>, <country>United States</country>
</aff>
<aff id="aff6">
<sup>6</sup>
<institution>George Mason University</institution>, <addr-line>Fairfax</addr-line>, <addr-line>VA</addr-line>, <country>United States</country>
</aff>
<aff id="aff7">
<sup>7</sup>
<institution>U.S. Naval Research Laboratory</institution>, <addr-line>Washington</addr-line>, <addr-line>DC</addr-line>, <country>United States</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/295223/overview">Patrick Antolin</ext-link>, Northumbria University, United Kingdom</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/617991/overview">Sven Wedemeyer</ext-link>, University of Oslo, Norway</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1408582/overview">Masumi Shimojo</ext-link>, National Astronomical Observatory of Japan (NAOJ), Japan</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Devojyoti Kansabanik, <email>devojyoti96@gmail.com</email>, <email>dkansabanik@ucar.edu</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>19</day>
<month>09</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>12</volume>
<elocation-id>1666743</elocation-id>
<history>
<date date-type="received">
<day>16</day>
<month>07</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>25</day>
<month>08</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Kansabanik, Gouws, Patra, Vourlidas, Kotz&#xe9;, Oberoi, Shaik, Buchner and Camilo.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Kansabanik, Gouws, Patra, Vourlidas, Kotz&#xe9;, Oberoi, Shaik, Buchner and Camilo</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Solar radio emissions offer unique diagnostic insights into the solar corona. However, their dynamic and multiscale nature, along with several orders of magnitude variations in intensity, pose significant observational challenges. To date, at gigahertz frequencies, MeerKAT stands out globally with high potential of producing high-fidelity, spectroscopic snapshot images of the Sun, enabled by its dense core, high sensitivity, and broad frequency coverage. Yet, as a telescope originally designed for observing faint galactic and extragalactic sources, observing the Sun at the boresight of the telescope requires customized observing strategies and calibration methods. This work demonstrates the technical readiness of MeerKAT for solar observations at the boresight of the telescope in the UHF (580&#x2013;1015 MHz) and L-band (900&#x2013;1670 MHz) frequency ranges, including optimized modes, a dedicated calibration scheme, and a tailored, entirely automated calibration and imaging pipeline. The quality of solar images is validated through morphological comparisons with the solar images at other wavelengths. Several unique early science results showcase the potential of this new capability of MeerKAT. Once fully commissioned and operational, this will unlock novel solar studies, significantly expand the scientific portfolio of MeerKAT, and lay the groundwork for solar observations with the mid-frequency telescope of the upcoming Square Kilometre Array Observatory, for which MeerKAT serves as a precursor.</p>
</abstract>
<kwd-group>
<kwd>solar radio emissions</kwd>
<kwd>solar corona</kwd>
<kwd>spectroscopic snapshot images</kwd>
<kwd>calibration methods</kwd>
<kwd>solar observations</kwd>
<kwd>automated calibration</kwd>
<kwd>imaging pipeline</kwd>
<kwd>solar images</kwd>
</kwd-group>
<contract-num rid="cn001">80NSSC22M0097 80NSSC21K1860 80NSSC22K0970</contract-num>
<contract-num rid="cn002">12-R&#x26;D-TFR-5.02-0700</contract-num>
<contract-sponsor id="cn001">Science Mission Directorate<named-content content-type="fundref-id">10.13039/100016465</named-content>
</contract-sponsor>
<contract-sponsor id="cn002">Department of Atomic Energy, Government of India<named-content content-type="fundref-id">10.13039/501100001502</named-content>
</contract-sponsor>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Stellar and Solar Physics</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The solar atmosphere consists of hot, magnetized plasma, with thermal and non-thermal electrons producing radio emissions across a broad frequency range (kHz to GHz) through processes like thermal bremsstrahlung, plasma emission, gyro-resonance, gyro-synchrotron, and electron-cyclotron maser emission. Solar radio emissions have been studied extensively from a few kHz to hundreds of GHz (e.g., <xref ref-type="bibr" rid="B78">Pick and Vilmer, 2008</xref>; <xref ref-type="bibr" rid="B34">Gary, 2023</xref>). Most observations rely on spectrograms, which provide spectrotemporal data but lack spatial information. Solar imaging at radio wavelengths has been carried out for decades by a small number of dedicated interferometers, including the Nan&#xe7;ay Radio Heliograph (NRH; <xref ref-type="bibr" rid="B10">Bonmartin et al., 1983</xref>) and Gauribidanur Radio Heliographs (GRAPH; <xref ref-type="bibr" rid="B90">Sundaram and Subramanian, 2004</xref>), both still operational, and the Nobeyama Radioheliograph (NoRH; <xref ref-type="bibr" rid="B69">Nakajima et al., 1994</xref>), which is no longer active. This has changed with new-generation radio interferometers such as the Murchison Widefield Array (MWA; <xref ref-type="bibr" rid="B52">Lonsdale et al., 2009</xref>; <xref ref-type="bibr" rid="B92">Tingay et al., 2013</xref>), LOw Frequency ARray (LOFAR; <xref ref-type="bibr" rid="B94">van Haarlem et al., 2013</xref>), upgraded Giant Metrewave Radio Telescope (uGMRT; <xref ref-type="bibr" rid="B40">Gupta et al., 2017</xref>), Jansky Very Large Array(JVLA; <xref ref-type="bibr" rid="B76">Perley et al., 2009</xref>), the Expanded Owens Valley Solar Array (EOVSA; <xref ref-type="bibr" rid="B36">Gary et al., 2012</xref>), and Atacama large millimeter-submillimeter array (ALMA; <xref ref-type="bibr" rid="B8">Bastian et al., 2022</xref>; <xref ref-type="bibr" rid="B88">Shimojo et al., 2024</xref>). Although not all of them focus solely on solar observations, they have been instrumental in advancing our understanding of solar physics.</p>
<p>MeerKAT, a new-generation radio interferometric telescope in South Africa (<xref ref-type="bibr" rid="B42">Jonas and MeerKAT Team, 2016</xref>) and a precursor to the mid-frequency telescope of the upcoming Square Kilometre Array Observatory (SKAO, <xref ref-type="bibr" rid="B27">Dewdney et al., 2009</xref>; <xref ref-type="bibr" rid="B84">Santander-Vela et al., 2021</xref>), comprises 64 cryogenically cooled 13.5 m dishes with excellent sensitivity. It operates across UHF (580&#x2013;1015 MHz), L (900&#x2013;1670 MHz), and S (1750&#x2013;3500 MHz) bands. Its dense core, 39 dishes within 1 km, and extended baselines up to 8 km provide superb surface brightness sensitivity and a well-sampled Fourier coverage, enabling high-fidelity spectroscopic snapshot imaging, even off-boresight (<xref ref-type="bibr" rid="B46">Kansabanik et al., 2024</xref>). These characteristics make MeerKAT an ideal instrument for studying the dynamic Sun at GHz frequencies, including active emissions, coronal mass ejection (CME) magnetometry (e.g., <xref ref-type="bibr" rid="B44">Kansabanik et al., 2023</xref>; <xref ref-type="bibr" rid="B46">Kansabanik et al., 2024</xref>), and faint transient detections. Although significant advances have been made at meter wavelengths with SKA-Low precursor (MWA) (<xref ref-type="bibr" rid="B71">Oberoi et al., 2023</xref>, and references therein) and pathfinders (LOFAR, uGMRT) (e.g., <xref ref-type="bibr" rid="B53">Magdaleni&#x107; et al., 2020</xref>; <xref ref-type="bibr" rid="B100">Zhang et al., 2024</xref>; <xref ref-type="bibr" rid="B65">Mondal et al., 2024</xref>), solar studies using precursor and pathfinders at mid-frequency of SKAO remain in early stages.</p>
<p>The first MeerKAT application to solar science was conducted by <xref ref-type="bibr" rid="B46">Kansabanik et al. (2024)</xref>, showcasing its potential for high-fidelity solar imaging. These observations placed the Sun in a sidelobe of the primary beam of the telescope, rather than at boresight, to sufficiently attenuate the intense solar emission and enable stable operation of the signal chain. However, the large angular size of the Sun and the chromaticity of the primary beam sidelobes posed significant challenges, necessitating attenuation that reduced sensitivity by a factor of <inline-formula id="inf1">
<mml:math id="m1">
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<mml:mo>&#x223c;</mml:mo>
<mml:mn>1000</mml:mn>
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</inline-formula>. The complex, evolving structures of the Sun that span arcseconds [smallest detectable scale is often set by coronal scattering (<xref ref-type="bibr" rid="B5">Bastian, 1994</xref>)] to full-disk scales at GHz frequencies pose substantial calibration challenges. Successfully addressing these requires a two-step approach: (1) optimizing telescope configuration for solar observations and (2) calibrating data to match this new configuration.</p>
<p>This paper demonstrates the technical readiness of MeerKAT for solar observations with the Sun positioned at the boresight of the telescope, including a dedicated pipeline for calibrating these non-standard observations. The structure of the paper is as follows: <xref ref-type="sec" rid="s2">Section 2</xref> details system optimization and observing procedures. <xref ref-type="sec" rid="s3">Section 3</xref> addresses the effects of the motion of the Sun on the sky, followed by a description of the data processing pipeline, including calibration, imaging, and mitigation strategies for the effects of non-sidereal solar motions in <xref ref-type="sec" rid="s4">Section 4</xref>. <xref ref-type="sec" rid="s6">Section 6</xref> verifies system performance and demonstrates the technical readiness. We highlight several preliminary interesting science results in <xref ref-type="sec" rid="s7">Section 7</xref>. <xref ref-type="sec" rid="s8">Section 8</xref> concludes the paper with a discussion about future works.</p>
</sec>
<sec id="s2">
<title>2 Configuring MeerKAT for solar observations</title>
<sec id="s2-1">
<title>2.1 Challenges in observing the sun with MeerKAT</title>
<p>The Sun is the source with the highest flux density at GHz frequencies and has a large angular size <inline-formula id="inf2">
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<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
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<mml:mrow>
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<mml:mo stretchy="false">)</mml:mo>
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</inline-formula>. The full-width half-maximum of the primary beam of MeerKAT is about 2<inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
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</inline-formula> at the central frequency of UHF- and L-band, respectively (<xref ref-type="bibr" rid="B22">de Villiers, 2023</xref>). Hence, the Sun fills a significant portion of the primary beam of MeerKAT at UHF and L-band. The Sun fills the entire beam at the higher frequency part of S-bands. This results in a significantly higher beam-integrated power compared to typical astronomical sources, necessitating strong attenuation to ensure that the signal chain of the telescope remains within its optimal regime. However, this creates a calibration challenge. The quiet Sun has a flux density of a few hundred Solar Flux Unit (sfu) [1 sfu &#x3d; <inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:mn>1</mml:mn>
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</inline-formula> Jansky (Jy)], increasing with frequency due to its thermal nature and reaching several thousand sfu due to non-thermal emissions during the presence of solar activity. In contrast, all bright astronomical calibrators (<xref ref-type="bibr" rid="B75">Perley and Butler, 2017</xref>) as well as the A-team sources (<xref ref-type="bibr" rid="B21">de Gasperin et al., 2020</xref>) have negative spectral indices, with flux densities that decrease with frequency. As a result, they cannot be observed with the same attenuation settings as the Sun. This makes traditional flux density calibration using astronomical calibrators infeasible for solar observations with MeerKAT, necessitating an independent method to characterize the spectral response of the attenuators. To prepare MeerKAT for solar observations, we have performed several engineering tests between late 2022 and late 2023 under the project ID: EXT-20221114-PK-01.</p>
</sec>
<sec id="s2-2">
<title>2.2 Description of signal power management at MeerKAT for solar observations</title>
<p>In general, the low-noise amplifier (LNA) &#x2013; the first component in the signal chain of a radio telescope&#x2013;is designed to have a linear response over a wide dynamic range, enabling it to accommodate strong signals such as those from the Sun. However, downstream sub-systems, including those of MeerKAT, have more limited dynamic ranges, and the default configuration is optimized for observing faint astronomical sources. To manage strong solar signals, MeerKAT employs attenuators within the Radio Frequency Conditioning Unit (RFCU). This is a room-temperature subsystem located just before the analog-to-digital converter (ADC) in the signal chain. These attenuators offer 0&#x2013;63 dB attenuation in 1 dB steps. To calibrate this attenuation, we have used a built-in noise diode. The built-in noise diode injects noise with a temperature approximately equal to system temperature on cold sky, leading to an increase in power by approximately 3 dB. Hence, measuring the change corresponding to the power injected by the noise diode when using attenuators allows us to measure the effective attenuation.</p>
<p>We estimated the additional signal attenuation required for MeerKAT solar observations to maintain the input power to the ADCs near the nominal level, based on source flux density and the band-averaged System Equivalent Flux Density (SEFD). Under cold-sky conditions, MeerKAT sets attenuation to align ADC input power to the nominal <inline-formula id="inf6">
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</inline-formula>&#x2009;dBFS (dBFS: Decibels relative to full scale; 0 dBFS is the digital maximum), with <inline-formula id="inf7">
<mml:math id="m7">
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</inline-formula>&#x2009;dBFS as the upper operational limit. Using a band-averaged SEFD (<ext-link ext-link-type="uri" xlink:href="https://skaafrica.atlassian.net/wiki/spaces/ESDKB/pages/277315585/MeerKAT&#x2b;specifications#System-Equivalent-Flux-Density-(SEFD)">MeerKAT SEFD specifications</ext-link>) and typical mean solar flux densities of 100&#x2009;sfu (UHF) and 200&#x2009;sfu (L-band), the required additional attenuation is given by<disp-formula id="e1">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
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<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
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<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:mo>&#x2061;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>log</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mi mathvariant="normal">F</mml:mi>
<mml:mi mathvariant="normal">D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mi mathvariant="normal">F</mml:mi>
<mml:mi mathvariant="normal">D</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>yielding <inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>32 dB and <inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>35 dB for UHF- and L-bands, respectively. These estimates were validated with solar test observations on 11 November 2022 (UHF) and 11 January 2023 (L-band).</p>
<p>These estimates are based on quiet solar flux density and are designed to set the ADC power to the <italic>nominal power level</italic>, which is the minimum input power level required for optimal operation of the ADC. Hence, this value of <inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> provides the maximum possible headroom needed to accommodate the increased flux density during solar flares. While the estimates of solar flux density mentioned above are representative, the disc-integrated quiet Sun solar flux density can vary on timescales of a day. To account for this time variability, we developed a flexible system that automatically obtains the quiet solar flux density <inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> from the previous day measurements from the Learmonth Solar Radio Observatory; alternatively, this information can also be provided by the user. This system estimates and applies the required additional attenuation <inline-formula id="inf12">
<mml:math id="m13">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> following <xref ref-type="disp-formula" rid="e1">Equation 1</xref>.</p>
</sec>
<sec id="s2-3">
<title>2.3 Characterization of the attenuators</title>
<p>Since attenuators introduce an additional element into the signal path, it is essential to assess their impact on spectral properties, as well as their influence on visibility amplitudes and phases. To achieve this, we analyze the variations in visibility amplitudes and phases for various attenuation levels, while ensuring that the ADC power stays within its optimal operating range. The latter is needed to ensure that the signal-to-noise ratio (SNR) of visibility does not change significantly.</p>
<sec id="s2-3-1">
<title>2.3.1 Phase and amplitude distortion</title>
<p>To understand the phase response of attenuators, we compared visibility phases on the baseline between antennas m000 and m001 (baseline length of 37 m) across multiple scans on the Sun with varying attenuation levels <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>. As shown in the top panels of <xref ref-type="fig" rid="F1">Figure 1</xref>, the phases for X-polarization (similar for Y-polarization) remain consistent within <inline-formula id="inf14">
<mml:math id="m15">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> degrees. Although the attenuation change <inline-formula id="inf15">
<mml:math id="m16">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is similar across antennas, these changes happen with respect to different initial attenuation settings. Initial attenuation values are different across antennas needed to arrive at <italic>nominal power level</italic> on the cold sky. As a result, the phase shifts introduced in different antennas may differ. The small differences in phases seen in the top panel of <xref ref-type="fig" rid="F1">Figure 1</xref> may arise from this or from the variations in solar emission itself. However, these small changes can conveniently be calibrated out during self-calibration.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>
<italic>Top panels:</italic> Visibility phases for X-polarization for baseline between antennas m000 and m001 (baseline length of 37 m) for different values of <inline-formula id="inf16">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. <italic>Bottom panels:</italic> Spectral variation of auto-correlation power for 3 dB changes in <inline-formula id="inf17">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> between 29 and 32 dB. The solid black line shows the power level change averaged over all antennas, while the blue shaded region indicates the standard deviation about the mean. The red dashed line marks the expected 3 dB attenuation. The left and right panels represent UHF and L-bands, respectively. Y-polarization shows a similar behavior.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g001.tif">
<alt-text content-type="machine-generated"> Four plots show changes in visibility phase and auto-correlation power over frequency range 0.6 to 1.7 GHz with attenuation levels. The top plots depict visibility phase with varying attenuation levels,. revealing negligible phase variations The bottom plots illustrate changes in auto-correlation power with a baseline around 3 dB.</alt-text>
</graphic>
</fig>
<p>To assess the spectral behavior of the amplitude response of attenuators, we analyzed the auto-correlation power of all antennas in both UHF and L-bands, with <inline-formula id="inf18">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> varied in 3 dB steps. The bottom panels of <xref ref-type="fig" rid="F1">Figure 1</xref> show that while power changes closely match the expected 3 dB increments in L-band, in the UHF-band changes show a small frequency-dependent variation. Self-calibration can correct for antenna-to-antenna phase variations due to an additional attenuator. However, due to reasons mentioned in <xref ref-type="sec" rid="s2-1">Section 2.1</xref>, the spectral response of the amplitude of the attenuators can not be calibrated using astronomical sources. Hence, we calibrated this absolute flux scaling and spectral response of attenuators using built-in noise diodes.</p>
</sec>
<sec id="s2-3-2">
<title>2.3.2 Antenna-to-antenna variation</title>
<p>While <inline-formula id="inf19">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is used uniformly in all antennas, actual adjustments in power level can vary between antennas due to the distinct physical nature of their attenuators. <xref ref-type="fig" rid="F2">Figure 2</xref> illustrates the percentage deviation from the mean spectral change across all antennas to highlight the extent of these variations. The antenna-to-antenna attenuation variations are sufficiently small, within <inline-formula id="inf20">
<mml:math id="m21">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. Hence, one can average over multiple antennas to build up the SNR for estimating the attenuation value using the noise diodes.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The relative variation in power level across different antennas, resulting from a 3 dB change in <inline-formula id="inf21">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, is shown as a percentage deviation from the mean change for X-polarization. The same is true for Y-polarization.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g002.tif">
<alt-text content-type="machine-generated">Line graph showing the percentage deviation of the power level with attenuation changes from the mean over frequency from 0.6 to 1.7 GHz for multiple antennas. The color-coded legend indicates antenna indices from 0 to 52.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec id="s2-4">
<title>2.4 Observing strategy with noise diode for flux density calibration</title>
<p>As discussed in <xref ref-type="sec" rid="s2-1">Sections 2.1</xref>, <xref ref-type="sec" rid="s2-3">2.3</xref>, standard calibrators including the A-team sources cannot be observed with the same attenuation as used for the Sun, and the applied <inline-formula id="inf22">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> exhibits a non-flat spectral response that must be characterized for absolute flux calibration. This is achieved using the built-in noise diode. Located after the LNA and before the attenuator in the signal chain, they inject a power of known strength, similar to the system temperature, <inline-formula id="inf23">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sys</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, in both UHF and L-band receivers. During calibrator scans without the additional attenuation, the noise diode-induced power change is <inline-formula id="inf24">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cal</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cal,on</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cal,off</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf25">
<mml:math id="m26">
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the frequency and the subscripts on and off refer to the observed power with the noise diode switched on and off, respectively. During solar scans with additional attenuation, it is <inline-formula id="inf26">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun,on</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun,off</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. Hence, the ratio <inline-formula id="inf27">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cal</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> captures the spectral variation in the attenuation, enabling calibration of the attenuator response and determination of the absolute flux density of the solar observations. The presence of additional attenuation <inline-formula id="inf28">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> reduces the effective noise diode power during solar observations, making it difficult to achieve sufficient SNR, even when the noise power is similar to the <inline-formula id="inf29">
<mml:math id="m30">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sys</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. As discussed in <xref ref-type="sec" rid="s4-2">Section 4.2</xref>, this necessitates longer integration over time and/or frequency. The value of the noise diode being used for MeerKAT is close to the minimum needed for calibrating the attenuator response for solar observations. Reducing them below their current levels will require too long integrations, which is likely to make their use for solar flux density calibration impractical.</p>
</sec>
<sec id="s2-5">
<title>2.5 Standard observing procedure of solar observation with MeerKAT</title>
<p>In preparation for solar observations with MeerKAT, we conducted tests in the engineering mode and arrived at the following observing procedure for routine solar observations.<list list-type="simple">
<list-item>
<p>1. Flux calibrator scan: Observe a standard MeerKAT flux/bandpass calibrator (e.g., J1939-6342 or J0408-6545 (MeerKAT flux and bandpass calibrators) with nominal attenuation.</p>
</list-item>
<list-item>
<p>2. Calibrator observation with noise diode: Perform a 3&#x2013;5 min scan on the same calibrator, switching the noise diode on and off for every successive correlator integration, so that consecutive data records alternate between noise-on and noise-off states. (Currently implemented via engineering mode).</p>
</list-item>
<list-item>
<p>3. Phase and polarization calibrator: Observe suitable phase and polarization calibrators with nominal attenuation settings.</p>
</list-item>
<list-item>
<p>4. Point to the Sun: Slew to the Sun with nominal attenuation still active. Switching on solar attenuation before the Sun is in the primary beam may cause system issues.</p>
</list-item>
<list-item>
<p>5. Enable solar attenuation: Once on the Sun, activate the additional solar attenuation <inline-formula id="inf30">
<mml:math id="m31">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</list-item>
<list-item>
<p>6. Solar scan with noise diode: Conduct solar scans with the noise diode toggled on alternate correlator dumps. It is recommended to limit the scan duration to 30 min for phase calibrator observations.</p>
</list-item>
<list-item>
<p>7. Disable attenuation: After the solar scan, disable <inline-formula id="inf31">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att,dB</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> before slewing away from the Sun.</p>
</list-item>
<list-item>
<p>8. Post-scan calibrator: Re-observe the phase calibrator with standard attenuation.</p>
</list-item>
<list-item>
<p>9. Repeat cycle: Repeat steps 4-8 for the remaining observing time.</p>
</list-item>
</list>
</p>
<p>We note that once the functionality required for inserting appropriate attenuation in the signal path and for toggling the noise diode on alternate correlator dumps is implemented in the MeerKAT Observation Planning Tool, all essential requirements for enabling a solar observing mode will have been met.</p>
</sec>
<sec id="s2-6">
<title>2.6 Minimum pointing distance of calibrators from the sun</title>
<p>When the telescope points near the Sun, the system temperature can increase significantly. For the MeerKAT beam, this minimum angular distance, <inline-formula id="inf32">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun,min</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, is approximately <inline-formula id="inf33">
<mml:math id="m34">
<mml:mrow>
<mml:mn>7</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> in UHF and <inline-formula id="inf34">
<mml:math id="m35">
<mml:mrow>
<mml:mn>4.5</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> in L-bands (<ext-link ext-link-type="uri" xlink:href="https://archive-gw-1.kat.ac.za/public/meerkat/Solar-avoidance-radius.jpg">MeerKAT Solar Avoidance Zone</ext-link>). Therefore, calibrators or astronomical targets should be observed at angular distances greater than <inline-formula id="inf35">
<mml:math id="m36">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun,min</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Additionally, solar wind turbulence can introduce phase errors and scatter broadening in calibrator observations near the Sun. The phase error due to such turbulence can be estimated using (VLA Test Memo 236, <xref ref-type="bibr" rid="B101">Butler 2005</xref>; <ext-link ext-link-type="uri" xlink:href="https://library.nrao.edu/public/memos/vla/test/VLAT_236.pdf">NRAO</ext-link>):<disp-formula id="e2">
<mml:math id="m37">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>degree</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x223c;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>7</mml:mn>
<mml:mspace width="0.3333em"/>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cm</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mspace width="0.3333em"/>
<mml:msubsup>
<mml:mrow>
<mml:mi>B</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>km</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>0.29</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3d5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mn>0.71</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <inline-formula id="inf36">
<mml:math id="m38">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the minimum angular distance from the Sun (in degrees), <inline-formula id="inf37">
<mml:math id="m39">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cm</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> the wavelength (in cm), <inline-formula id="inf38">
<mml:math id="m40">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>B</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>km</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> the baseline (in km), and <inline-formula id="inf39">
<mml:math id="m41">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3d5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> the allowable phase error (in degrees). For MeerKAT, assuming <inline-formula id="inf40">
<mml:math id="m42">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3d5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>degree</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, <xref ref-type="disp-formula" rid="e2">Equation 2</xref> yields <inline-formula id="inf41">
<mml:math id="m43">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>degree</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>15</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> (UHF) and <inline-formula id="inf42">
<mml:math id="m44">
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> (L-band), as detailed in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Minimum angular distance of the calibrators from the Sun for specified expected phase errors.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Band</th>
<th align="center">
<inline-formula id="inf43">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3d5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mtext>,degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">
<inline-formula id="inf44">
<mml:math id="m46">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mtext>,degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="left">
<inline-formula id="inf45">
<mml:math id="m47">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3d5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mtext>,degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="left">
<inline-formula id="inf46">
<mml:math id="m48">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mtext>,degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="left">
<inline-formula id="inf47">
<mml:math id="m49">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3d5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mtext>,degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="left">
<inline-formula id="inf48">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mtext>,degree</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">UHF-band (37 cm)</td>
<td align="center">1.0</td>
<td align="center">79.0</td>
<td align="left">5.0</td>
<td align="left">25.0</td>
<td align="left">10.0</td>
<td align="left">15.0</td>
</tr>
<tr>
<td align="left">L-band (21 cm)</td>
<td align="center">1.0</td>
<td align="center">53.0</td>
<td align="left">5.0</td>
<td align="left">16.0</td>
<td align="left">10.0</td>
<td align="left">10.0</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s3">
<title>3 Effects of motion of the sun</title>
<p>The apparent motion of the Sun in the sky is unlike that of most astronomical sources. It is governed by two key components: the non-sidereal motion of the Sun on the sky, and the movement of solar features on the solar disc due to differential solar rotation. Both these effects must be considered when observing and analyzing solar data.</p>
<sec id="s3-1">
<title>3.1 Sidereal motion</title>
<p>The Sun, being a non-sidereal source, its Equatorial coordinates (RA-Decl.) drift across the sky at an average rate of <inline-formula id="inf49">
<mml:math id="m51">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> per day (<inline-formula id="inf50">
<mml:math id="m52">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>.</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2032;</mml:mo>
<mml:mo>&#x2032;</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> per minute), giving rise to a uniform shift in the coordinates of solar features. In radio interferometry, <italic>delay-tracking</italic> at the correlator compensates for geometric delays between received signals at different antennas as the source moves. While sidereal sources are tracked at a fixed equatorial coordinate, solar observations with a telescope require tracking the solar center. At MeerKAT, the correlator delay center is continuously updated at a kHz rate using a linear model, with model parameters&#x2013;delay and delay-rate&#x2013;estimated and refreshed every 5 s. This approach ensures accurate correlation and prevents decorrelation due to the solar apparent motion.</p>
</sec>
<sec id="s3-2">
<title>3.2 Differential rotation</title>
<p>In addition to the non-sidereal motion, the Sun also exhibits differential rotation&#x2013;the rotation period at its equator is <inline-formula id="inf51">
<mml:math id="m53">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>25 days and that at polar regions is <inline-formula id="inf52">
<mml:math id="m54">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>34 days (<xref ref-type="bibr" rid="B54">Mancuso et al., 2020</xref>). This causes solar features at different latitudes to move in the plane of the sky at varying rates, with the maximum projected motion occurring near the solar disk center. The maximum differential motion is, <inline-formula id="inf53">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>diff,rot</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2248;</mml:mo>
<mml:mn>5</mml:mn>
<mml:mo>.</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2032;</mml:mo>
<mml:mo>&#x2032;</mml:mo>
</mml:mrow>
</mml:msup>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. To limit smearing arising due to differential rotation, even after correcting for the overall non-sidereal motion of the Sun, integration times should not exceed <inline-formula id="inf54">
<mml:math id="m56">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>130 min in the UHF band and <inline-formula id="inf55">
<mml:math id="m57">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>50 min in the L-band.</p>
<p>We note that differential solar rotation breaks the &#x201c;rigid-sky&#x201d; assumption of radio interferometric imaging, making corrections in the visibility domain or during the imaging and deconvolution non-trivial. Current tools like Common Astronomy Software Application (CASA; <xref ref-type="bibr" rid="B91">The CASA Team et al., 2022</xref>) and W-Stacking CLEAN (WSClean; <xref ref-type="bibr" rid="B73">Offringa et al., 2014</xref>) do not support such corrections. This limitation will become more critical for the SKAO, with its higher spatial resolution, where uncorrected differential rotation may smear fine-scale features even when integrating over short times. For example, maximum integration time should be less than <inline-formula id="inf56">
<mml:math id="m58">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>5 min at 1 GHz to avoid smearing due to differential rotation. A dedicated imaging algorithm to address this is under development and will be presented in a forthcoming publication.</p>
</sec>
</sec>
<sec id="s4">
<title>4 Description of the calibration and imaging pipeline</title>
<p>Boresight solar observations with MeerKAT are non-standard and demand specialized calibration and imaging strategies. Existing tools such as <sans-serif>SolarKAT</sans-serif> (<xref ref-type="bibr" rid="B83">Samboco et al., 2024</xref>), designed to mitigate solar contamination in standard astronomical data, are not suitable for this purpose. To automate this process, we developed a dedicated pipeline inspired by <sans-serif>IDIA-processMeerKAT</sans-serif> (<xref ref-type="bibr" rid="B16">Collier et al., 2021</xref>). This pipeline is fully automated, user-friendly, and deployable in both standard single-node workstations as well as high-performance cluster environments. It is distributed through PyPI <ext-link ext-link-type="uri" xlink:href="https://pypi.org/project/meersolar/">https://pypi.org/project/meersolar/</ext-link>. All images presented in this work are produced from observations automatically calibrated and imaged using this pipeline.</p>
<p>Its key features include:<list list-type="simple">
<list-item>
<p>1. Support for both Full-Stokes (polarization) calibration and imaging of solar observations.</p>
</list-item>
<list-item>
<p>2. Process-based parallelization using <sans-serif>Dask</sans-serif> (<xref ref-type="bibr" rid="B82">Rocklin, 2015</xref>), enabling cross-platform execution from clusters to single-node systems, unlike the MPI-based parallelism in <sans-serif>IDIA-processMeerKAT</sans-serif>.</p>
</list-item>
<list-item>
<p>3. Efficient operation on memory-constrained machines, allowing large dataset processing where traditional tools may fail.</p>
</list-item>
<list-item>
<p>4. Remote monitoring of pipeline progress.</p>
</list-item>
</list>
</p>
<p>The pipeline uses <sans-serif>CASA</sans-serif> for calibration and <sans-serif>WSClean</sans-serif> for imaging. While examples of Stokes I imaging are presented here, full polar imaging will be presented in a forthcoming publication describing the imaging pipeline (Patra et al., in prep.). <xref ref-type="fig" rid="F3">Figure 3</xref> illustrates the pipeline flowchart. A master controller manages modular blocks, with independent tasks (e.g., attenuation calibration, data partitioning) running in parallel, while sequential tasks (e.g., calibration, self-calibration, imaging) are executed in order. Internal parallelism within blocks, such as per-scan calibration steps and time-chunked self-calibration, maximizes computational efficiency.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>A flowchart of the pipeline for calibration and imaging of solar observations with MeerKAT. The master controller controls the workflow of the pipeline. Tasks inside individual rectangular blocks are executed in parallel and controlled by the master controller.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g003.tif">
<alt-text content-type="machine-generated">Flowchart depicting the process of MeerKAT solar radio observation data processing, starting with &#x22;Measurement Set&#x22;. Steps include "Solar Attenuation Calibration," &#x22;Partitioning,&#x22; &#x22;Basic Flagging,&#x22; &#x22;Model Import for Calibrators,&#x22; &#x22;Basic Calibration,&#x22; and &#x22;Apply Solutions and Self-cal.&#x22; The final stage includes &#x22;Correct primary beam response&#x22; and &#x22;Spectro-polarimetric Snapshot Imaging.&#x22; Arrows indicate the sequence of operations. Each section includes detailed tasks such as calibration, flagging, and imaging techniques.</alt-text>
</graphic>
</fig>
<sec id="s4-1">
<title>4.1 Data partitioning, flagging and calibration</title>
<p>The Measurement Set (MS) is partitioned by scans and converted into multi-MS format for parallel processing using <sans-serif>Dask</sans-serif>. Flagging, calibration, and application of gain solutions are performed in parallel across scans. Persistent RFI and faulty antennas are flagged in all calibrator and solar scans. Automated RFI flagging using <sans-serif>flagdata task of CASA</sans-serif> in <sans-serif>tfcrop</sans-serif> mode is applied to flux and phase calibrators but skipped for solar scans due to the intrinsic variability of solar emission. Bandpass calibrator models (<ext-link ext-link-type="uri" xlink:href="https://skaafrica.atlassian.net/wiki/spaces/ESDKB/pages/1481408634/Flux&#x2b;and&#x2b;bandpass&#x2b;calibration#Applying-a-full-sky-model-to-a-CASA-measurement-set">MeerKAT flux density and bandpass calibrator models</ext-link>) are used, and only scans without noise-diode firings are selected to derive delay, bandpass, and gain solutions using <sans-serif>gaincal</sans-serif> and <sans-serif>bandpass</sans-serif>, limited to baselines <inline-formula id="inf57">
<mml:math id="m59">
<mml:mrow>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>200</mml:mn>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> to avoid contamination from large angular scale quiet Sun emission. Post-calibration flagging is applied to residuals using <sans-serif>rflag</sans-serif>, followed by a final calibration round. However, bright compact solar features may still contaminate the longer baselines used. To assess this, we shift the phase center of the calibrator scans to the Sun and generate a dirty image using baselines <inline-formula id="inf58">
<mml:math id="m60">
<mml:mrow>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>200</mml:mn>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. If the resulting contamination level, quantified as <inline-formula id="inf59">
<mml:math id="m61">
<mml:mrow>
<mml:mi mathvariant="normal">&#x394;</mml:mi>
<mml:mi>I</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, exceeds 2% (corresponding to a tolerable gain error of 1%), we perform direction-dependent calibration to subtract the solar contribution and repeat the calibration iteration.</p>
</sec>
<sec id="s4-2">
<title>4.2 Flux density calibration using noise diodes</title>
<p>Absolute flux density calibration of solar observations is performed in two steps. First, the instrumental bandpass is calibrated without applying <inline-formula id="inf60">
<mml:math id="m62">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, using bandpass calibrator scans as described in <xref ref-type="sec" rid="s4-1">Section 4.1</xref>. Next, the spectral response of <inline-formula id="inf61">
<mml:math id="m63">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is calibrated using the noise diode by measuring the change in auto-correlation power between the diode-on and diode-off states in both calibrator <inline-formula id="inf62">
<mml:math id="m64">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cal</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> and solar <inline-formula id="inf63">
<mml:math id="m65">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> scans. For calibrator scans without <inline-formula id="inf64">
<mml:math id="m66">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, the diode induces a significant power increase, leading to an estimated <inline-formula id="inf65">
<mml:math id="m67">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>2% variation in gain due to the departure of the system from linearity. In contrast, the effect is negligible for solar scans with <inline-formula id="inf66">
<mml:math id="m68">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> due to the fractionally much smaller power increase. To allow us to correct for this non-linearity, bandpass solutions are derived separately for the diode-on and diode-off states using the calibrator scans and applied accordingly.</p>
<p>While power variations due to the noise diode are easily detectable in calibrator scans without averaging, this is not the case for solar scans due to the suppression by <inline-formula id="inf67">
<mml:math id="m69">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Individual <inline-formula id="inf68">
<mml:math id="m70">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> estimates are noisy, but their SNR improves with integration time, until they get limited by intrinsic solar variability. To determine the optimal averaging time, we evaluated the standard deviation of the <inline-formula id="inf69">
<mml:math id="m71">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> spectrum as a function of integration time. As shown in the left panel of <xref ref-type="fig" rid="F4">Figure 4</xref>, the standard deviation saturates beyond 15 min. Therefore, we adopt 15 min as the optimal integration interval for estimating <inline-formula id="inf70">
<mml:math id="m72">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from solar scans. The middle and right panels of <xref ref-type="fig" rid="F4">Figure 4</xref> show the estimated <inline-formula id="inf71">
<mml:math id="m73">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> spectra for a UHF-band observation with 32 dB attenuation in both polarizations. The spectra exhibit intrinsic frequency dependence but no significant scan-to-scan variation beyond noise. To avoid using noisy per-channel estimates and increasing SNR, we fit a cubic spline to the scan-averaged spectra and use it to scale the bandpass solutions applied to the solar scans. The fitted spectra are shown by the solid black lines in the middle and right panels of <xref ref-type="fig" rid="F4">Figure 4</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Left panel: Variation of band-averaged standard deviation of <inline-formula id="inf72">
<mml:math id="m74">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for different temporal integrations. It is evident, beyond 15 min of averaging, that the standard deviation <inline-formula id="inf73">
<mml:math id="m75">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sun</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> does not drop further. Right panel: Spectrum of the estimated <inline-formula id="inf74">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> across different scans. The blue dashed line represents the fixed <inline-formula id="inf75">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> value applied during all scans. It is evident that the observed <inline-formula id="inf76">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>att</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> fluctuates within <inline-formula id="inf77">
<mml:math id="m79">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> dB of the set value across scans. Solid black lines in the middle and right panels show the fitted response on the scan-averaged spectrum.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g004.tif">
<alt-text content-type="machine-generated">Three graphs are displayed. The first graph shows the standard deviation of \(d_{\text{sun}}\) decreasing over time, with red data points and a black curve. The second and third graphs depict polarization X and Y, respectively, illustrating variations in \(S_{\text{att}}\) over frequency with multiple overlapping scans. The solid black line represents average measurements, and the dashed blue line indicates a reference level at \(-32\) decibels.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s4-3">
<title>4.3 Spectroscopic snapshot self-calibration</title>
<p>Solar radio emission exhibits strong spectral and temporal variability, making the solar sky model inherently time-dependent. The time and frequency scale of the variation depends on solar activity and can range from a few seconds to several minutes and a few kHz to several MHz. To address this dynamic temporal and spectral variability scale, the spectral and temporal axes are adaptively divided into chunks such that deviations from the mean remain below certain thresholds (default is 10% for frequency, 1% for time). This ensures that variability is preserved while enabling computationally efficient self-calibration. A spectral chunk from the lower part of the band is selected to maximize surface brightness sensitivity and improve modeling on shorter baselines. The self-calibration procedure follows the convergence criteria in <xref ref-type="bibr" rid="B43">Kansabanik et al. (2022)</xref>, <xref ref-type="bibr" rid="B44">Kansabanik et al. (2023)</xref>, starting with phase-only calibration and advancing to joint amplitude-phase calibration upon convergence. CLEAN thresholding is progressively reduced, and the process is stopped when no further improvement in image dynamic range is observed. Convergence is defined as a relative change in dynamic range below a user-defined threshold <inline-formula id="inf78">
<mml:math id="m80">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> over three iterations, with a maximum iteration cap to prevent oscillatory behavior for small <inline-formula id="inf79">
<mml:math id="m81">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</sec>
<sec id="s4-4">
<title>4.4 Spectroscopic snapshot imaging</title>
<p>At GHz frequencies, solar radio emission exhibits structure across a broad range of angular scales&#x2014;from arcseconds to the full solar disc&#x2014;often with significant complexity. The imaging pipeline supports user-defined baseline selection and weighting strategies, and by default adopts Briggs weighting (<xref ref-type="bibr" rid="B11">Briggs, 1995</xref>) with a robust parameter of 0.0 to achieve a balance between resolution and sensitivity. Multiscale deconvolution is employed with frequency-dependent multiscale parameters. These choices, detailed in <xref ref-type="sec" rid="s15">Supplementary Appendix S9.1</xref>, are made to avoid deconvolution artifacts.</p>
</sec>
<sec id="s4-5">
<title>4.5 Primary beam correction</title>
<p>As the Sun is an extended source, its observed emission must be corrected for the direction-dependent primary beam response. We apply image-based primary beam correction using the array-averaged MeerKAT beam model from holography measurements (<xref ref-type="bibr" rid="B23">de Villiers and Cotton, 2022</xref>; <xref ref-type="bibr" rid="B22">de Villiers, 2023</xref>). The beam is described by the Jones matrix <inline-formula id="inf80">
<mml:math id="m82">
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> in direction cosines <inline-formula id="inf81">
<mml:math id="m83">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mo>,</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> from the boresight of the telescope. At MeerKAT, <inline-formula id="inf82">
<mml:math id="m84">
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf83">
<mml:math id="m85">
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> correspond to <inline-formula id="inf84">
<mml:math id="m86">
<mml:mrow>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf85">
<mml:math id="m87">
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> polarizations (<ext-link ext-link-type="uri" xlink:href="https://katdal.readthedocs.io/en/latest/signs.html#polarisation">MeerKAT polarization convention</ext-link>) as per IAU convention (<xref ref-type="bibr" rid="B17">Commission 40: Radio astronomy, 1973</xref>) used in common softwares like with <sans-serif>CASA</sans-serif> and <sans-serif>WSClean</sans-serif>. <inline-formula id="inf86">
<mml:math id="m88">
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf87">
<mml:math id="m89">
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> polarizations are appropriately labeled in the IAU convention in the measurement set using katdal software package. Hence, appropriate changes are also made in <inline-formula id="inf88">
<mml:math id="m90">
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> to be consistent with the IAU convention.</p>
<p>To apply correction, the beam is first mapped from <inline-formula id="inf89">
<mml:math id="m91">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> to equatorial coordinates of the image, then rotated by the parallactic angle <inline-formula id="inf90">
<mml:math id="m92">
<mml:mrow>
<mml:mi>&#x3c7;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. The sky-frame beam matrix is:<disp-formula id="e3">
<mml:math id="m93">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sky</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>P</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mspace width="0.3333em"/>
<mml:mi>R</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c7;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where the parallactic rotation matrix is:<disp-formula id="e4">
<mml:math id="m94">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c7;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mtable class="matrix">
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi>&#x3c7;</mml:mi>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi>&#x3c7;</mml:mi>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi>&#x3c7;</mml:mi>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi>&#x3c7;</mml:mi>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>The frequency-averaged Stokes I beam is computed as:<disp-formula id="e5">
<mml:math id="m95">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msubsup>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>sky</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">&#x7c;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>where <inline-formula id="inf91">
<mml:math id="m96">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf92">
<mml:math id="m97">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represent the start and end frequencies of the image. The Stokes I image corrected for the primary beam is obtained by dividing by <inline-formula id="inf93">
<mml:math id="m98">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> obtained using <xref ref-type="disp-formula" rid="e3">Equations 3</xref>&#x2013;<xref ref-type="disp-formula" rid="e5">5</xref>. We note that while UHF and L-band have overlapping frequencies, the primary beam should be derived from the appropriate band, as they use different feeds, resulting in distinct beam responses even at the same frequency.</p>
</sec>
</sec>
<sec id="s5">
<title>5 Observation details</title>
<p>MeerKAT, with its field of view of roughly <inline-formula id="inf94">
<mml:math id="m99">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B22">de Villiers, 2023</xref>), enables full-disk observations of low-altitude solar atmosphere in a single pointing at the solar center, eliminating the need for mosaicking. In the standard solar observing mode, visibilities are recorded with 4096 spectral channels and a temporal resolution of 2 s. The excellent spectroscopic and snapshot <italic>uv</italic>-coverage supports high-quality imaging at these native resolutions, while the final choice of spectral and temporal averaging can be tailored by the user based on scientific requirements and available computing resources.</p>
<p>We have used data taken as part of engineering tests (project ID: EXT-20221114-PK-01) and the SARAO (South African Radio Astronomy Observatory) Science Verification (SSV) observations (project ID: SSV-20240609-DK-01). Engineering tests are performed in both UHF- and L-band, while SSV observations were taken only in the UHF-band. Results from observations performed on 04 December 2023 and 10 June 2024 are presented in this paper. All spectroscopic snapshot images presented in this paper are generated using a 50 MHz bandwidth and 15 min of temporal averaging for the ease of data analysis.</p>
</sec>
<sec id="s6">
<title>6 System verification</title>
<p>To evaluate the accuracy of calibration and image reconstruction in the presence of attenuators, we compare radio images with co-temporal extreme ultraviolet (EUV) observations. <xref ref-type="fig" rid="F5">Figure 5</xref> shows this comparison using EUV images from Atmospheric Imaging Assembly (AIA, <xref ref-type="bibr" rid="B51">Lemen et al., 2012</xref>) onboard Solar Dynamics Observatory (SDO; <xref ref-type="bibr" rid="B77">Pesnell et al., 2012</xref>), closest in time to the radio image. The MeerKAT image centered at 942.11 MHz is produced using 50 MHz and 15 min of data. Key features are highlighted with colored arrows, which are identical across all panels. The large coronal hole (region 7) appears with similar morphology in both bands. An additional, smaller coronal hole is also marked (region 10). On-disk active regions (regions 8 and 9) and eastern limb active regions (regions 1 and 6) are identifiable. Additional filamentary structures are indicated by regions 2, 3, 4, and 5.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Morphological comparison between MeerKAT UHF band image with 211&#xc5; EUV image from SDO/AIA. The top panel shows the radio image from MeerKAT (averaged data over 50 MHz spectral and 15 min of temporal chunk) showing emissions at more than <inline-formula id="inf95">
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</inline-formula> significance. The bottom left is the AIA image at its original spatial resolution <inline-formula id="inf96">
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</inline-formula>. Several features have been marked by numbered arrows in all three images for visual guidance.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g005.tif">
<alt-text content-type="machine-generated">Three panels display solar observations. The top panel shows a solar map at 942.11 MHz with a brightness temperature scale from five hundred thousand to two million Kelvin. Colored arrows indicate various points labeled one to ten. The bottom two panels feature solar images at 211 Angstroms, each with similar arrow indicators. The scale on the right measures brightness in data numbers from zero to two thousand.</alt-text>
</graphic>
</fig>
<p>Despite the high surface brightness sensitivity of MeerKAT, its shortest baseline is not short enough to detect structures comparable in size to the solar disc at the upper end of the L-band, the minimum baseline length of approximately <inline-formula id="inf98">
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</inline-formula>29 m) of MeerKAT is capable of capturing emission at an angular scale <inline-formula id="inf102">
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</inline-formula>. Hence, at the UHF band, we do not expect significant missing flux, as already demonstrated by <xref ref-type="bibr" rid="B46">Kansabanik et al. (2024)</xref>. <xref ref-type="fig" rid="F6">Figure 6</xref> presents spectroscopic images from UHF and L-band observations taken on 2024 December 04. The UHF-band images (left panels) capture extended diffuse emission, whereas the L-band images (right panels) show a loss of large-scale structure toward the higher end of the frequency range. All of these images have spectral and temporal integrations of 50 MHz and 15 min, respectively. The observed brightness temperatures reach values on the order of a million Kelvin, consistent with typical coronal temperatures. Notably, the near-overlapping frequency images from the UHF and L-band (top right and bottom left) exhibit similar morphology and peak brightness temperatures, indicating consistency in both flux density calibration and primary beam correction across the two bands.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Spectroscopic radio images from MeerKAT observations on 4 December 2023 are shown (50 MHz and 15 min integrations). The left and right panels display images from the UHF and L-band observations, respectively, above <inline-formula id="inf103">
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</inline-formula> detection significance at three representative frequencies. The white circles indicate the optical solar disc. Synthesized beams are shown at the bottom left of each image, which varies between <inline-formula id="inf104">
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</caption>
<graphic xlink:href="fspas-12-1666743-g006.tif">
<alt-text content-type="machine-generated">Six-panel image of the Sun observed at different frequencies, each showing brightness temperature in Kelvin. Top left is 629.2 MHz, top right 997.17 MHz; middle left 825.76 MHz, middle right 1240.43 MHz; bottom left 942.11 MHz, bottom right 1522.97 MHz. Color scales range from dark purple/blue for cooler areas to bright yellow/green for hotter regions. Each panel has a central circle denoting the Sun&#x2019;s optical disk with varying patterns of light intensity indicating temperature differences.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s7">
<title>7 Glimpses of early science results</title>
<p>At metre wavelengths, high-quality spectro-polarimetric snapshot imaging with SKA-low precursors like the MWA and pathfinders such as LOFAR and uGMRT has already demonstrated the ability to observe a wide range of solar phenomena (<xref ref-type="bibr" rid="B71">Oberoi et al., 2023</xref>)&#x2014; from the quiet Sun (e.g., <xref ref-type="bibr" rid="B95">Vocks et al., 2018</xref>; <xref ref-type="bibr" rid="B85">Sharma and Oberoi, 2020</xref>; <xref ref-type="bibr" rid="B99">Zhang et al., 2022</xref>), coronal holes (<xref ref-type="bibr" rid="B57">McCauley et al., 2019</xref>; <xref ref-type="bibr" rid="B80">Rahman et al., 2019</xref>) and weak transient events (<xref ref-type="bibr" rid="B86">Sharma et al., 2018</xref>; <xref ref-type="bibr" rid="B63">Mondal et al., 2020a</xref>; <xref ref-type="bibr" rid="B62">Mondal, 2021</xref>), to faint emissions from CME plasma (<xref ref-type="bibr" rid="B64">Mondal et al., 2020b</xref>; <xref ref-type="bibr" rid="B44">Kansabanik et al., 2023</xref>; <xref ref-type="bibr" rid="B46">Kansabanik et al., 2024</xref>), high-resolution imaging of solar noise storms (<xref ref-type="bibr" rid="B65">Mondal et al., 2024</xref>; <xref ref-type="bibr" rid="B66">Mondal et al., 2025</xref>), intense active emissions from high energy particles (e.g., <xref ref-type="bibr" rid="B61">Mohan et al., 2019</xref>; <xref ref-type="bibr" rid="B58">Mohan, 2021</xref>; <xref ref-type="bibr" rid="B59">Mohan, 2021</xref>), CME shocks (e.g., <xref ref-type="bibr" rid="B9">Bhunia et al., 2023</xref>; <xref ref-type="bibr" rid="B100">Zhang et al., 2024</xref>; <xref ref-type="bibr" rid="B49">Kumari et al., 2025</xref>). Recent high-fidelity polarimetric studies (e.g., <xref ref-type="bibr" rid="B57">McCauley et al., 2019</xref>; <xref ref-type="bibr" rid="B80">Rahman et al., 2019</xref>; <xref ref-type="bibr" rid="B67">Morosan et al., 2022</xref>; <xref ref-type="bibr" rid="B28">Dey et al., 2025</xref>) also started providing new insights on the radio emission from the solar corona, <inline-formula id="inf106">
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<p>MeerKAT solar observations enable unprecedented spectroscopic snapshot imaging of the Sun at centimeter wavelengths. The high image fidelity, as demonstrated through comparisons with EUV images from AIA, will advance the study of the solar corona and eruptive events and open up discovery potential. This section provides glimpses of a range of new science objectives that can potentially be achieved using MeerKAT solar observations already available. Detailed analyses and discussion of individual science targets with higher spectro-temporal resolution are deferred to forthcoming publications.</p>
<sec id="s7-1">
<title>7.1 A complementary diagnostic of multi-thermal solar atmospheric plasma</title>
<p>EUV spectral lines (<xref ref-type="bibr" rid="B48">Khan and Nagaraju, 2022</xref>) and soft X-ray observations are widely used to probe the thermal structure of the solar atmosphere. Slit-based spectrographs like EUV Imaging Spectrometer onboard Hinode (Hinode/EIS; <xref ref-type="bibr" rid="B19">Culhane et al., 2007</xref>) and Coronal Diagnostic Spectrometer onboard Solar and Heliospheric Observatory (SOHO/CDS; <xref ref-type="bibr" rid="B25">Del Zanna et al., 2001</xref>) offer good spectral resolution and broad temperature coverage (log <inline-formula id="inf107">
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<p>In contrast, full-disk EUV imagers such as SDO/AIA, Solar Ultraviolet Imager onboard Geostationary Operational Environmental Satellite (GOES/SUVI; <xref ref-type="bibr" rid="B20">Darnel et al., 2022</xref>) and mid- and near-UV imagers like the Solar Ultraviolet Imaging Telescope onboard Aditya-L1 (SUIT/Aditya-L1; <xref ref-type="bibr" rid="B93">Tripathi et al., 2025</xref>), provide high-cadence observations in multiple broad UV channels. While EUV-imagers nominally span log <inline-formula id="inf108">
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</inline-formula>, their temperature sensitivity for chromospheric and TR plasma is limited, and DEMs can be reliably estimated primarily in the log <inline-formula id="inf109">
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<p>Radio observations directly measure the free&#x2013;free continuum emission from all of the plasma along the line of sight (LoS), providing sensitivity to the total emission measure across a broad temperature range. Hence, high-fidelity spectroscopic and snapshot imaging observation using MeerKAT offers a complementary tool to probe the full-disk TR and coronal plasma dynamics, filling the gap between slit-based spectrographs and EUV imagers.</p>
<sec id="s7-1-1">
<title>7.1.1 Study of quiescent sun plasma above the chromosphere</title>
<p>Radio waves cannot escape from regions where the local plasma frequency exceeds the emission frequency. Since the local plasma frequency is inversely related to local electron density and electron density varies with altitude above the solar surface, each frequency probes down to a specific atmospheric depth. Resolving the height structure of the solar atmosphere with spectroscopic radio imaging requires high spectral resolution and a broad frequency coverage across the characteristic plasma frequencies <inline-formula id="inf110">
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</inline-formula> of the different layers. The highest frequency of MeerKAT UHF band in general lies at the bottom of the TR, as shown in the right panel of <xref ref-type="fig" rid="F7">Figure 7</xref>, determined using the electron density distribution of the solar atmosphere obtained from <xref ref-type="bibr" rid="B4">Aschwanden (2005)</xref>. Hence, using MeerKAT UHF-band, which can capture diffuse quiescent emission well, probes emission above the chromosphere&#x2014;from the TR and corona.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>The left panel shows an image from MeerKAT at 942 MHz on 2023 December 04. The PSF is shown at the bottom left of the image. The contour levels are at <inline-formula id="inf111">
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</inline-formula> of the peak brightness temperature. White contours represent positive values, and cyan contours represent negative values. A green circle marks the optical disk of the Sun. Different PSF-sized regions for which spectra are shown in <xref ref-type="fig" rid="F8">Figure 8</xref> are marked. The right panel shows plasma frequency <inline-formula id="inf113">
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</inline-formula> as a function of height above the solar surface. Emission at MeerKAT UHF-band (580&#x2013;1015 MHz) probes the atmospheric heights above the chromosphere.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g007.tif">
<alt-text content-type="machine-generated">A two-part image consists of a heliographic plot and a graph. The left side is a heliographic image of the sun at 942.11 MHz, dated 2023-12-04, showing regions labeled LR1, LR2, LR3, DR1, DR2, DR3, CH1, CH2, CH3. A color bar indicates brightness temperature in Kelvin. The right side is a graph plotting height above the solar surface where plasma frequency is equal to observing frequency. It features lines for different frequencies (580 MHz, 1015 MHz) and a transition region highlight.</alt-text>
</graphic>
</fig>
<p>High-frequency (<inline-formula id="inf114">
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</inline-formula> GHz; JVLA, EOVSA, NoRH) and low-frequency (<inline-formula id="inf115">
<mml:math id="m120">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
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</inline-formula>150&#x2013;432 MHz; NRH) instruments have long been used to study solar atmospheric layers (<xref ref-type="bibr" rid="B1">Alissandrakis, 2020</xref>), but their sparse <italic>uv</italic> coverage and limited surface brightness sensitivity hinder imaging of faint, extended quiescent structures. Consequently, spatially resolved studies have focused on bright sources like active regions and flares (e.g., <xref ref-type="bibr" rid="B96">Vourlidas and Bastian, 1996</xref>; <xref ref-type="bibr" rid="B6">Bastian et al., 1998</xref>; <xref ref-type="bibr" rid="B37">Gary et al., 2018</xref>), while quiet Sun analyses rely mostly on disk-integrated or spectrally averaged observations (e.g., <xref ref-type="bibr" rid="B98">Zhang et al., 2001</xref>; <xref ref-type="bibr" rid="B50">Landi and Chiuderi Drago, 2008</xref>).</p>
<p>
<xref ref-type="fig" rid="F8">Figure 8</xref> shows spatially resolved radio spectra from the quiescent Sun regions. Each of these has been extracted from PSF-sized regions marked in the left panel of <xref ref-type="fig" rid="F7">Figure 7</xref>. The observed spectra (red points) are fitted with a power law, <inline-formula id="inf116">
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</inline-formula> (solid green line), while simulated coronal spectra considering only free-free emission based on SDO/AIA-derived DEMs (<xref ref-type="bibr" rid="B46">Kansabanik et al., 2024</xref>) are shown as solid black lines. The first row of <xref ref-type="fig" rid="F8">Figure 8</xref> shows spectra from limb regions (LR1&#x2013;LR3), located at <inline-formula id="inf117">
<mml:math id="m122">
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</inline-formula> above the solar surface, where emission originates purely from coronal plasma, resulting in good agreement between observed and simulated spectra. The second row presents on-disk spectra (DR1&#x2013;DR3), which come from plasma above the chromosphere and may include contributions from low-temperature TR plasma. Considering the TR optical depth model from <xref ref-type="bibr" rid="B3">Alissandrakis et al. (1980)</xref>; <xref ref-type="bibr" rid="B1">Alissandrakis (2020)</xref>, we have found that while free-free optical depth is close to unity in active regions <xref ref-type="bibr" rid="B35">Gary and Hurford (1989)</xref>; <xref ref-type="bibr" rid="B4">Aschwanden (2005)</xref>, for quiescent solar regions, it could be smaller than one. Hence, TR cooler plasma may contribute to on-disk decimetric MeerKAT emission in addition to coronal emission. As low-temperature plasma contributes more at lower frequencies (<xref ref-type="bibr" rid="B70">Nindos, 2020</xref>; <xref ref-type="bibr" rid="B1">Alissandrakis, 2020</xref>), spectra appear steeper than coronal-only simulations, providing a hint of the contribution from TR cool plasma not captured by EUV-based DEMs.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Spatially resolved spectra from the marked PSF-sized regions in <xref ref-type="fig" rid="F7">Figure 7</xref>. Only spectral points with more than 3<inline-formula id="inf118">
<mml:math id="m123">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
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</inline-formula> detection significance are shown. The first row shows the spectra for limb regions, LR1, LR2, and LR3. The second row shows the spectra for on-disk regions, DR1, DR2, and DR3. The third row shows the spectra for coronal hole regions, CH1, CH2, and CH3. The fourth row shows the spectra from filament regions FL1 and FL2 and a coronal cavity region, CV1, associated with that filament.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g008.tif">
<alt-text content-type="machine-generated">Twelve graphs show brightness temperature versus frequency for different regions, labeled LR1, LR2, LR3, DR1, DR2, DR3, CH1, CH2, CH3, FL1, FL2, and CV1. Each graph includes simulated and fitted spectra, with observed spectrum points marked by red circles. Spectral indices with uncertainties are noted for each region. Trends vary across graphs.</alt-text>
</graphic>
</fig>
<p>Slit-based EUV spectrograph observations have shown that there is a temperature minimum of EM at log <inline-formula id="inf119">
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<mml:mrow>
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<mml:mo>&#x2273;</mml:mo>
<mml:mn>5.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> are routinely available from EUV observations from SDO/AIA, similar maps below log <inline-formula id="inf121">
<mml:math id="m126">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>5.2</mml:mn>
</mml:mrow>
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</inline-formula> are rare. We anticipate that MeerKAT observations can provide these full-disk EM maps, including plasma at lower temperatures. However, that requires careful modeling of the TR (<xref ref-type="bibr" rid="B3">Alissandrakis et al., 1980</xref>; <xref ref-type="bibr" rid="B1">Alissandrakis, 2020</xref>) and multi-thermal free-free radiative transfer (<xref ref-type="bibr" rid="B31">Fleishman et al., 2021</xref>), which is beyond the scope of this paper.</p>
</sec>
<sec id="s7-1-2">
<title>7.1.2 Study of coronal holes, filaments and coronal cavities</title>
<p>Coronal holes (CHs), characterized by open magnetic fields and reduced density and temperature (<xref ref-type="bibr" rid="B18">Cranmer, 2009</xref>), appear as dark regions in EUV and are key sources of fast solar wind. A prominent CH, labeled as region 7 in <xref ref-type="fig" rid="F5">Figure 5</xref>, shows spectra from three PSF-sized regions (CH1&#x2013;CH3) in the third row of <xref ref-type="fig" rid="F8">Figure 8</xref>. Unlike other regions, CH spectra flatten below <inline-formula id="inf122">
<mml:math id="m127">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>700</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> MHz, saturate at <inline-formula id="inf123">
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<mml:mtext>B</mml:mtext>
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<mml:mn>0.25</mml:mn>
</mml:mrow>
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</inline-formula> MK, and can not be fit by a single power-law. This suggests emission from a cool, optically thick plasma layer unique to CHs. Further detailed modeling is needed to interpret these observations in detail and is beyond the scope of this work.</p>
<p>Coronal filaments and prominences (<xref ref-type="bibr" rid="B74">Parenti, 2014</xref>) are cool, dense, elongated structures suspended in the corona along polarity inversion lines and supported by sheared magnetic fields, typically observed in H<inline-formula id="inf124">
<mml:math id="m129">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and EUV absorption. Surrounding them are coronal cavities, low-density, magnetically structured voids seen as dark, circular or elliptical regions in EUV and soft X-rays, especially at the limb (<xref ref-type="bibr" rid="B39">Gibson and Fan, 2006</xref>; <xref ref-type="bibr" rid="B33">Fuller and Gibson, 2009</xref>). Often associated with magnetic flux ropes and potential CME precursors, these cavities provide key pre-eruptive diagnostics (<xref ref-type="bibr" rid="B32">Forland et al., 2013</xref>; <xref ref-type="bibr" rid="B38">Gibson, 2015</xref>). Past radio observations using NRH (<xref ref-type="bibr" rid="B55">Marqu&#xe9;, 2004</xref>) detected such cavities and estimated densities under isothermal assumptions, but were limited by narrow spectral coverage, which is now overcome by MeerKAT. Spectra from two filament regions (FL1 and FL2) and the coronal cavity (CV1) are shown in the bottom row of <xref ref-type="fig" rid="F8">Figure 8</xref>. The presence of cool plasma can be inferred based on a reason along the same lines as presented in <xref ref-type="sec" rid="s7-1-1">Section 7.1.1</xref>. Although CV1 is at the limb, when compared to the other limb spectra (LR1-LR2), the spectrum in the CV1 region shows significant steepening compared to the simulated spectrum. A forthcoming study investigating filaments and coronal cavities will explore the capability of MeerKAT for probing pre-eruptive solar phenomena.</p>
</sec>
</sec>
<sec id="s7-2">
<title>7.2 Study of solar eruptions and non-thermal energy release: flares, CMEs and associated radio bursts</title>
<p>Solar eruptions are explosive phenomena that occur in the solar atmosphere, involving the sudden release of vast amounts of energy stored in the magnetic field due to coronal dynamics. These events include solar flares, CMEs, and eruptive prominences, and are manifestations of magnetic reconnection and plasma instabilities in the solar corona. They can accelerate particles to high energies and expel large amounts of magnetized plasma in the form of CMEs into the heliosphere. These energetic particles and CMEs play a crucial role in driving space weather. Understanding the evolution of magnetic fields during their initiation, evolution, and propagation is essential for a deeper understanding of these phenomena. Spectroscopic radio imaging plays a crucial role in providing the magnetic field measurements remotely during these eruptions (<xref ref-type="bibr" rid="B97">Vourlidas et al., 2020</xref>; <xref ref-type="bibr" rid="B2">Alissandrakis and Gary, 2021</xref>; <xref ref-type="bibr" rid="B13">Carley et al., 2021</xref>) as well as providing an estimation of non-thermal particles associated with these processes. Both high-frequency (<inline-formula id="inf125">
<mml:math id="m130">
<mml:mrow>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> GHz) (<xref ref-type="bibr" rid="B14">Chen et al., 2020</xref>; <xref ref-type="bibr" rid="B30">Fleishman et al., 2020</xref>) and low-frequency (meter-wavelength) (<xref ref-type="bibr" rid="B7">Bastian et al., 2001</xref>; <xref ref-type="bibr" rid="B64">Mondal et al., 2020b</xref>; <xref ref-type="bibr" rid="B44">Kansabanik et al., 2023</xref>; <xref ref-type="bibr" rid="B46">Kansabanik et al., 2024</xref>) observations have demonstrated their capabilities for probing non-thermal particles and measuring magnetic fields at the flare site and CME plasma at higher coronal heights, respectively. However, these eruptions lack observational probes in a crucial region in the lower corona, both in white-light, EUV, and radio wavelengths. Recently, new-generation visible light instruments, PROBA-3 (<xref ref-type="bibr" rid="B87">Shestov, S. V. et al., 2021</xref>) and Aditya-L1/VELC (<xref ref-type="bibr" rid="B89">Singh et al., 2025</xref>), and SunCET (<xref ref-type="bibr" rid="B56">Mason et al., 2021</xref>) in the EUV, have been designed to observe this coronal region (at heliocentric distances <inline-formula id="inf126">
<mml:math id="m131">
<mml:mrow>
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<mml:mn>2</mml:mn>
<mml:mspace width="0.3333em"/>
<mml:msub>
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<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2299;</mml:mo>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>). The frequency range and high fidelity spectroscopic snapshot imaging capability of MeerKAT make it highly suitable for observing these eruptions between heliocentric distances of <inline-formula id="inf127">
<mml:math id="m132">
<mml:mrow>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>1</mml:mn>
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<mml:mn>2</mml:mn>
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</inline-formula>.</p>
<p>We observed the Sun with MeerKAT from 2024 June 9&#x2013;11 as part of SSV observations, targeting the active region (AR) NOAA (National Oceanic and Atmospheric Administration) AR 13711 and the reappearance of AR 13664, which was responsible for the May 2024 geomagnetic storm, anticipating continued activity. The top left panel of <xref ref-type="fig" rid="F9">Figure 9</xref> shows a composite image of a CME event which erupted from the western limb on 10 June 2024, at 09:40 UTC, as generated using JHelioviewer (<xref ref-type="bibr" rid="B68">M&#xfc;ller et al., 2017</xref>), with the central image showing GOES/SUVI 195 &#xc5; EUV image, and the outer panel showing SOHO/LASCO (<xref ref-type="bibr" rid="B12">Brueckner et al., 1995</xref>; <xref ref-type="bibr" rid="B29">Domingo et al., 1995</xref>) C2 base-difference coronagraph image. The top right panel shows an image from MeerKAT at 629 MHz with contours overlaid on the SUVI image, with the eruption site marked by the red box. During this observing window, a long-duration X-class flare peaking at 11:07 UTC (blue line in the bottom panel of <xref ref-type="fig" rid="F9">Figure 9</xref>) occurred and remained above M-class level for a large period, from approximately 09:48 to 12:22 UTC (blue shaded region).</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Flare and CME eruption on 2024 June 10. The top left panel shows base-difference composite images of the western limb eruption, with SUVI 195 &#xc5; EUV images at the center and LASCO C2 coronagraph images around. In the top-right panel, MeerKAT 629 MHz radio contours at 5%, 10%, 20%, 40%, 60%, and 80% of the peak are overlaid on SUVI, with the red box marking the eruption site. The bottom panel shows the GOES X-ray light curve; the shaded region (09:48&#x2013;12:22 UTC) indicates M-class flux levels. Red dashed lines mark the MeerKAT observation window.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g009.tif">
<alt-text content-type="machine-generated">Composite image showing three elements: Top left, a grayscale image of the solar corona with intense bright spots and a timestamp. Top right, a colored solar map with contour lines and a red box highlighting an area. Bottom, a line graph plotting solar X-ray flux over time, with red and blue lines representing different wavelengths. Time markers and color-coded areas are visible.</alt-text>
</graphic>
</fig>
<p>Several intense solar radio bursts were observed during this period in MeerKAT total power normalized dynamic spectrum, as shown in the top panel of <xref ref-type="fig" rid="F10">Figure 10</xref>. A prominent, broadband burst around 10:46 UTC is highlighted in the bottom left panel, while several reverse-drifting bursts, typically associated with sunward-traveling electrons, are seen in the bottom right panel. Since dynamic spectra provide only spatially integrated information, distinguishing overlapping emissions requires spatially resolved dynamic spectra (SPREDS; <xref ref-type="bibr" rid="B60">Mohan and Oberoi, 2017</xref>). Previously demonstrated at meter wavelengths using the MWA, the high-dynamic-range spectroscopic snapshot capability of MeerKAT at GHz frequencies offers similar potential. A detailed SPREDS-based analysis of these radio bursts is beyond the scope of this work.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>The top panel displays the complete duration of solar observations with MeerKAT on 2024 June 10. The bottom panels provide a zoomed-in view of the second and fourth scans. In all figures, the upper subpanels show MeerKAT total power dynamic spectrum, the middle subpanels present the band-averaged time series, and the lower subpanels plot the corresponding GOES X-ray light curve.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g010.tif">
<alt-text content-type="machine-generated">The image displays two dynamic spectrum plots, light curves, and graphs from MeerKAT and GOES observations on June 10, 2024. The top dynamic spectrum shows frequency versus time with varying flux density, highlighted by color from dark purple to yellow. A MeerKAT light curve below shows mean flux density over time, with noticeable peaks. The GOES light curve features flux in different wavelengths (0.5-4.0 and 1.0-8.0 Angstroms), indicated by blue and red lines, showing fluctuations over the same time period. The repeated layout is presented for consistency and comparison.</alt-text>
</graphic>
</fig>
<p>Three snapshot radio images at 629 MHz overlaid on SUVI images during the CME eruption are shown in the top panels of <xref ref-type="fig" rid="F11">Figure 11</xref>. The bottom left panel highlights the eruption site. The region from where the spectra have been extracted at multiple timestamps is marked and the spectra are shown in the bottom right panel. A progressive steepening of the spectra with time is observed, suggesting a non-thermal origin of the emission. Spectroscopic snapshot imaging at high spectral and temporal cadence can offer valuable insights into the evolving physical conditions at the eruption site, from pre-eruption to post-eruption. A detailed analysis will be presented in a future study.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>The top panels display overlays of MeerKAT 629 MHz radio images (in a reddish-yellow colormap) on SUVI 195 &#xc5; images. The bottom left panel shows the brightness temperature map at 629 MHz during the CME, highlighting a PSF-sized region. The corresponding spectra at various timestamps from this region are shown in the bottom right panel. Timestamps and spectral indices for each of the spectra are shown in the legend.</p>
</caption>
<graphic xlink:href="fspas-12-1666743-g011.tif">
<alt-text content-type="machine-generated">Three solar images display an eruption region over time, marked by vivid colors. The top row shows progress at SUVI times: 10:12:40, 10:27:41, and 10:48:08, with corresponding MeerKAT times slightly later. Below, a purple-toned plot at 629.2 MHz indicates the eruption's location with a bright spot and includes a brightness temperature scale. A chart on the right correlates frequency with brightness temperature, using different colors and symbols for varying time intervals on June 10, 2024. Labels indicate temperature in Kelvin and frequencies in MHz.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec id="s8">
<title>8 Conclusion and future works</title>
<p>This study has demonstrated the technical readiness of MeerKAT for carrying out well-calibrated solar observations with the telescope pointed directly at the Sun. Despite being originally designed for the observations of faint and distant galactic and extragalactic sources, MeerKAT can now be effectively utilized for solar science, enabled by the development of a specialized observing mode and a tailored calibration and imaging pipeline. Several technical challenges associated with solar observations&#x2013;such as the need to attenuate the intense solar flux density to get the signal to lie within the linear range of the receivers, perform reliable flux density calibration using internal noise diodes, and account for the sidereal drift of the Sun during the observation&#x2013;have been addressed. The resulting calibrated images show strong morphological agreement with EUV observations and expectations based on simulations, validating the viability of using MeerKAT for solar radio imaging and also demonstrating the robustness of the interferometric calibration and imaging pipeline. We note that MeerKAT solar observations at the upper end of the L-band and the S-band will be affected by missing flux density issues due to the limited availability of sufficiently short baselines. Potential solutions to this issue will involve incorporating single-dish total power measurements from MeerKAT itself, or from other instruments, into the interferometric imaging process.</p>
<p>Nonetheless, these developments offer access to a previously underexplored observational regime, enabling high spatial and spectro-temporal resolution studies of the solar atmosphere. Even the limited observations obtained during this work highlight the valuable novel insights that can be gained into the structure and dynamics of the quiet corona, weak transient events, and large-scale eruptive phenomena such as flares and CMEs. Additionally, the polarimetric capabilities of MeerKAT hold promise for coronal magnetic field studies when combined with multi-wavelength space-based and <italic>in-situ</italic> data. Ongoing efforts to characterize and validate its polarization response for solar observations aim to support such advancements and pave the way for future breakthroughs. We hope that the work presented here will also provide motivation and guidance for commissioning the solar observing mode alongside other observing modes for the upcoming next-generation instruments like the SKA-mid (<xref ref-type="bibr" rid="B79">Plunkett et al., 2023</xref>).</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s9">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="sec" rid="s15">Supplementary Material</xref>, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s10">
<title>Author contributions</title>
<p>DK: Conceptualization, Formal Analysis, Investigation, Methodology, Software, Visualization, Writing &#x2013; original draft, Writing &#x2013; review and editing. MG: Conceptualization, Data curation, Methodology, Project administration, Validation, Writing &#x2013; original draft, Writing &#x2013; review and editing. DP: Writing &#x2013; original draft, Writing &#x2013; review and editing. AV: Conceptualization, Supervision, Visualization, Writing &#x2013; original draft, Writing &#x2013; review and editing. PK: Writing &#x2013; original draft, Writing &#x2013; review and editing, Conceptualization. DO: Writing &#x2013; original draft, Writing &#x2013; review and editing. SS: Writing &#x2013; original draft, Writing &#x2013; review and editing. SB: Data curation, Project administration, Writing &#x2013; original draft, Writing &#x2013; review and editing. FC: Project administration, Writing &#x2013; original draft, Writing &#x2013; review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s11">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. This work uses observations from MeerKAT radio telescope. MeerKAT telescope is operated by the South African Radio Astronomy Observatory, which is a facility of the National Research Foundation, an agency of the Department of Science, Technology, and Innovation. The authors acknowledge the contribution of all those who designed and built MeerKAT instrument. DK acknowledges support for this research by the NASA Living with a Star Jack Eddy Postdoctoral Fellowship Program, administered by UCAR&#x2019;s Cooperative Programs for the Advancement of Earth System Science (CPAESS) under award 80NSSC22M0097. DP and DO acknowledge support from the Department of Atomic Energy, Government of India, under the project no. 12-R&#x26;D-TFR-5.02-0700. AV was supported by NASA grants 80NSSC21K1860 and 80NSSC22K0970. MG, PK, SB, and FC was supported by South African Radio Astronomy Observatory. DK gratefully acknowledges Justin Jonas and Thomas Abbott (SARAO) for their valuable feedback on the early draft of the manuscript. DK gratefully acknowledges Surajit Mondal (NJIT, USA) for useful discussions and suggestions.</p>
</sec>
<sec sec-type="COI-statement" id="s12">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s13">
<title>Generative AI statement</title>
<p>The author(s) declare that Generative AI was used in the creation of this manuscript. Generative AI is used to typo and grammer corrections and verified all the changes by the authors.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="s14">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec sec-type="supplementary-material" id="s15">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fspas.2025.1666743/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fspas.2025.1666743/full&#x23;supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="Presentation1.pdf" id="SM1" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
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