Study of Solar Coronal Rotation using Nobeyama Radio Heliograph (NoRH) at 17 GHz

Study of Solar Coronal Rotation using Nobeyama Radio Heliograph (NoRH) at 17 GHz | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Study of Solar Coronal Rotation using Nobeyama Radio Heliograph (NoRH) at 17 GHz Ved Prakash Gupta, Vivek Kumar Singh, Rishabh Gupta, Satish Chandra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8422228/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The solar activity cycle is closely linked to the solar rotation, making rotation one of the Sun’s most fundamental properties. The Sun does not rotate uniformly; its rotation rate varies with both altitude and latitude. However, the available information on solar rotation remains insufficient for fully predicting solar activity and, consequently, space weather. Solar rotation can be studied using several approaches, including tracer tracking on the solar surface, spectral analysis and flux modulation. In this study, solar rotation is determined through flux modulation, while Lomb–Scargle periodogram (LSP) is employed to identify periodicities in the data. In the flux modulation method, radio features crossing the solar disc are monitored, and statistical analysis of daily radioheliograph images (spanning 1992–2020) provides rotation periods as a function of latitude. Periodic components within these time series are extracted using statistical techniques such as LSP. The analysis is conducted on latitude bins, each representing equally spaced regions, seperated by 5°, across the solar full-disc (SFD) images from the Nobeyama Radioheliograph (NoRH) at 17 GHz, covering latitudes from 45°S to 45°N. A least-squares polynomial fit is applied to the rotational profiles of the northern and southern hemispheres. The resulting differential coefficients are found to vary with the sunspot cycle. The findings reveal both rigid and differential rotation across different epochs, specifically from the declining phase of SC 22 through the conclusion of SC 24. Solar rotation differential rotation solar activity corona chromosphere Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction The study of solar differential rotation is crucial to understanding the dynamic behaviour of the Sun. Differential rotation, the variation of angular velocity with latitude and altitude, is a key driver of the solar dynamo mechanism that generates and sustains the Sun’s magnetic field (Charbonneau 2010 ; Cameron & Schüssler 2015 ). This rotational shear redistributes magnetic flux across the solar surface and corona, influencing the emergence of sunspots, the evolution of active regions, and the modulation of solar irradiance (Howard 1984 ; Hathaway & Wilson 1990 ). Consequently, variations in differential rotation are intimately connected to the solar cycle and play a crucial role in shaping space weather phenomena that affect Earth’s magnetosphere and technological systems (Jiang et al. 2014 ; Cameron et al. 2016 ). Over the past century, differential rotation has been estimated using diverse observational techniques. Classical approaches include tracking sunspot groups (Balthasar et al. 1986 ; Snodgrass 1983 ), Doppler velocity measurements of the photosphere (Ulrich et al. 1988 ; Snodgrass 1984 ), and helioseismology, which probes the solar interior through p-mode oscillations (Howe et al. 2000 ; Schou et al. 2002 ; Zhao 2013 ). In the corona, tracers such as X-ray bright points (Kariyappa 2008 ; Chandra et al. 2010 , 2018 ), EUV coronal bright points (Brajša et al. 2002 , 2004 ; Wöhl et al. 2010 ), and radio emissions (Vats et al. 2001 ; Chandra & Vats 2011 ; Singh et al. 2021a , b ) have been employed to derive latitudinal rotation profiles. Among these, the flux modulation method has proven particularly effective for radio data. This technique relies on the modulation of radio flux as coronal features rotate across the solar disc. By constructing time series of flux variations at different latitudes and applying spectral analysis methods such as autocorrelation, Fast Fourier Transform, or Lomb–Scargle periodogram (Lomb 1976 ; Scargle 1982 ; Vander-Plas 2018), the rotation period can be extracted with high precision. The flux modulation method is advantageous because it does not depend on the identification of individual tracers, but instead utilizes statistical properties of radio brightness variations across latitude bins (Chandra, Vats & Iyer 2009 ; Bhatt et al. 2017 ). The Nobeyama Radioheliograph (NoRH), operational since 1992 at the Nobeyama Radio Observatory in Japan, provides daily full-disc solar images at 17 GHz ( https://solar.nro.nao.ac.jp/norh/html/daily/ ). The 17 GHz emission originates primarily from the upper chromosphere and lower corona, where gyro-resonance and free–free emission mechanisms dominate (Vats et al. 2001 ; Chandra & Vats 2011 ). These emissions are sensitive to both thermal plasma conditions and magnetic field structures, making NoRH data a valuable diagnostic of coronal dynamics. The long-term, continuous coverage of NoRH offers a unique opportunity to study solar rotation across multiple cycles with consistent instrumentation. Previous research has extensively utilized NoRH 17 GHz data to investigate coronal rotation and its variability. Chandra, Vats & Iyer ( 2009 , 2010 ) applied flux modulation analysis to NoRH images to derive latitudinal rotation profiles and reported significant north–south asymmetry. Routh et al. ( 2024 ) extended the analysis to multiwavelength comparisons, confirming the consistency of NoRH-derived rotation rates with EUV observations. Singh et al. ( 2021a , b ) employed NoRH data in combination with multi-frequency radio flux to explore radial differential rotation and its relationship with solar cycles. These studies collectively demonstrate that NoRH 17 GHz observations provide robust insights into coronal rotation, complementing results from X-ray, EUV, and helioseismic methods. In the present work, we build upon these foundations by analyzing nearly three decades (1992–2020) of NoRH data using the flux modulation method. Our aim is to quantify equatorial rotation rates and differential coefficients across solar cycles 22–24, examine hemispheric asymmetries, and assess correlations with sunspot numbers. This long-term dataset allows us to explore how coronal rotation evolves with solar cycle phases and magnetic polarity reversals, thereby contributing to a deeper understanding of solar dynamo processes and space weather drivers. The present study makes use of daily full-disc solar images observed at 17 GHz by the Nobeyama Radioheliograph (NoRH), which has been in continuous operation since 1992 at the Nobeyama Radio Observatory in Japan. These data span nearly three decades, from 1992 to 2020, thereby covering solar cycles 22, 23, and 24. Because of this, NoRH data provide a unique diagnostic of coronal dynamics and are especially well-suited for long-term studies of solar rotation. But in year 2019 and 2020, siginificant modulation could not beobserved in the time series of solar radio flux. Hence, periodic component could not be computed through flux modulation method. The flux modulation method is employed to estimate rotation rates from these images. This technique does not rely on tracking individual features but instead analyzes the modulation of radio flux as coronal structures rotate across the solar disc. Each full-disc image is divided into latitude strips, and the average pixel intensity in each strip is computed daily to generate time series of radio flux variations. The periodic components of these time series are extracted using the Lomb–Scargle periodogram, which is particularly effective for unevenly spaced data (Lomb 1976 ; Scargle 1982 ; Vander-Plas 2018). This approach has been successfully applied in earlier studies (Chandra, Vats & Iyer 2009 ) using NoRH data, where Vats & Chandra ( 2011 ) reported significant north–south asymmetry in coronal rotation, and Singh et al. ( 2021a , b ) extended the analysis to multi-frequency radio flux to explore radial differential rotation and its relationship with solar cycles. More recently, Routh et al. ( 2024 ) confirmed the consistency of NoRH-derived rotation rates with EUV observations, demonstrating the robustness of this method. By building upon these foundations, the present work aims to provide a comprehensive long-term analysis of equatorial rotation rates, differential coefficients, and their correlation with solar cycle phases, thereby contributing to a deeper understanding of solar dynamo processes and space weather drivers. 2. Data Analysis and Outcomes Using the flux modulation method, synodic rotation periods were derived from daily solar full-disc images captured by the Nobeyama Radioheliograph (NoRH) at 17 GHz. These synodic periods were then converted into sidereal rotation periods following the standard transformation outlined by Snodgrass ( 1983 , 1984 ). The angular rotation rate at each latitude was computed, and its latitudinal dependence was modeled using the classical solar differential rotation law: $$\:{\Omega\:}\left(\psi\:\right)=A+B{\text{sin}}^{2}\psi\:$$ where: \(\:{\Omega\:}\left(\psi\:\right)\) is the sidereal rotation rate at latitude \(\:\psi\:\) , A is the equatorial rotation rate, B is the differential rotation coefficient. \(\:{\Omega\:}\left(\psi\:\right)=A+B{\text{sin}}^{2}\psi\:\) , for northern and southern solar hemisphere for the year 2015. The Fig. 2 illustrates the sidereal rotation rate plotted against \(\:{\text{sin}}^{2}\psi\:\) for both hemispheres for year 2015. Regression analysis yields the following empirical relations: \(\:{\Omega\:}\left(\psi\:\right)=15.36-2.01{\text{sin}}^{2}\psi\:\) , for northen hemisphere and \(\:{\Omega\:}\left(\psi\:\right)=14.69-2.17{\text{sin}}^{2}\psi\:\) , for the southern hemisphere. These results confirm the presence of differential rotation, with both hemispheres exhibiting a decrease in rotation rate with increasing latitude. Notably, in the year 2015 the northern hemisphere shows a slightly higher equatorial rotation rate, while the southern hemisphere displays a stronger latitudinal gradient. 2.1. Cycle-Dependent Variations and Hemispheric Asymmetry in Solar Differential Rotation (1992–2020) Annual values of coefficients A and B from the year 1992 to 2020 were extracted in the same way and compared, in Fig. 3 , with sunspot numbers obtained from WDC-SILSO. The study period (1992–2020) was segmented according to the progression of solar cycles 22, 23, and 24 using NOAA/SWPC data. The analysis reveals temporal variations in differential rotation characteristics, with evidence of both rigid and differential rotation regimes across different phases of solar activity. These variations correlate with the sunspot cycle, suggesting a dynamic coupling between solar magnetic activity and rotational behavior. The Figure also reveals a clear hemispheric asymmetry and solar cycle dependence in both equatorial rotation rate ( A ) and differential rotation coefficient ( B ), consistent with and extending earlier chromospheric-coronal studies. The top panel illustrates the annual variation in equatorial rotation rate ( A ) from 1992 to 2018, showing that the northern hemisphere (red) consistently rotates faster than the southern hemisphere (blue), with both exhibiting temporal modulation that broadly tracks the solar sunspot number (SSN). Peaks in A often coincide with solar maxima, particularly around 2000 and 2014, suggesting a dynamic coupling between equatorial rotation and magnetic activity. The bottom panel shows the variation in the differential rotation coefficient ( B ), where both hemispheres display negative values indicative of classical solar differential rotation. Notably, the southern hemisphere (blue) exhibits a steeper gradient (larger magnitude of B ), implying stronger latitudinal shear compared to the north. These variations in B also correlate with SSN, with flatter gradients (smaller B ) during solar minima and steeper gradients during active phases, reflecting a transition between rigid and differential rotation regimes. These findings align with and extend earlier studies. Snodgrass ( 1983 , 1984 ) first quantified solar differential rotation using Doppler and magnetic tracers, reporting equatorial rates near 14.5–15.0°/day and latitudinal gradients around − 2.5°/day. Beck (1999) and helioseismic investigations confirmed these values and noted temporal modulation linked to solar cycles. More recently, Javaraiah ( 2020 ) analyzed sunspot group data from 1874–2017 and found systematic variations in A and B across cycles, with hemispheric asymmetries becoming more pronounced during cycle maxima. Sharma et al. ( 2020 ) reported a statistically significant correlation between hemispheric asymmetry in coronal rotation and solar activity during cycle 24, reinforcing the view that rotation dynamics are magnetically modulated. Kumar et al. (2024) extended this to the transition region and corona using EUV irradiance and radio flux, showing sidereal rotation periods varying from 19.4 to 28.1 days, with cycle-dependent shifts. Compared to these earlier works, the present NoRH-based analysis offers a unique long-term radio perspective across cycles 22–24, confirming the persistence of hemispheric asymmetry and the modulation of rotation parameters with solar activity. The correlation between A and SSN supports the idea that equatorial rotation accelerates during active phases, while the variation in B suggests that differential rotation strengthens with magnetic complexity. These results contribute to a growing body of evidence that solar rotation is not static but dynamically linked to the solar dynamo and magnetic field evolution. 2.2. Phase-Wise Modulation of Solar Rotation Parameters and Hemispheric Asymmetry Across Cycles 22–24 Figure 4 illustrates the phase-wise variation in the equatorial rotation rate ( A ) and differential rotation coefficient ( B ) for the northern and southern hemispheres, plotted alongside annual sunspot numbers during the declining phase of SC 22 and throughout SC 23 and 24. Across the declining phase of Cycle 22 and through Cycles 23 and 24, the Fig. 4 shows a persistent hemispheric asymmetry and clear solar-cycle modulation in both coefficients: the equatorial rotation rate A (top) and the lower-latitudinal differential rotation coefficient B (bottom). A in the north remains systematically higher than in the south, with both tracking the annual sunspot number (SSN). A rises toward activity maxima and diminishes near minima, with the modulation amplitude strongest in Cycle 23 and visibly muted in the weaker Cycle 24. In B , both hemispheres maintain negative values consistent with differential rotation, but the southern hemisphere generally exhibits a larger magnitude (steeper latitudinal shear), especially near Cycle 23’s peak, while shear relaxes ( B decreases) around minima—an alternating tendency toward more rigid rotation in quiet phases and enhanced differential rotation during active phases. Phase-wise, the declining tail of Cycle 22 already displays the north–south split that intensifies through Cycle 23; Cycle 24 preserves the asymmetry but with reduced dynamical range, echoing its subdued magnetic activity. These behaviors are consistent with earlier chromospheric and coronal studies: sunspot-group tracer analyses and Doppler/helioseismic results reported equatorial rates near 14.5–15.0°/day and gradients around − 2.0 to − 2.9°/day with cycle-linked modulation; Ca II K and He I 10830 Å synoptic maps likewise show stronger shear during active phases and hemispheric differences that wax and wane with SSN; coronal EUV/radio proxies further corroborate the weakening of rotational modulation in the comparatively low-amplitude Cycle 24. Taken together, the NoRH phase-wise analysis strengthens the picture that solar rotation parameters are dynamically coupled to the magnetic cycle, with asymmetry and shear responding to the evolving distribution and complexity of active-region fields. 3. Latitudinal and Temporal Variations in Solar Rotation The contour plot (Fig. 5 ) derived from Nobeyama 17 GHz microwave observations spanning 1992 to 2018 reveals significant latitudinal and temporal variations in the solar rotation period between ± 45° latitude. This interval encompasses the declining phase of Solar Cycle 22 and the entirety of Solar Cycles 23 and 24. The rotation period exhibits a clear differential pattern, with shorter periods (~ 16–20 days) concentrated near the equator and progressively longer periods (~ 28–32 days) observed toward higher latitudes. This latitudinal gradient confirms the well-established solar differential rotation, wherein equatorial regions rotate faster than mid-latitudes. Notably, the contour lines display phase-wise modulation in rotation rates, with discernible shifts corresponding to solar cycle transitions. During solar maxima, particularly in Cycles 23 and 24, the rotation period contours appear more compressed and irregular, suggesting enhanced magnetic activity and the influence of migrating active regions. Conversely, solar minima are marked by smoother gradients and more stable rotation profiles. These findings underscore the dynamic coupling between solar magnetic activity and rotational behavior, and they align with torsional oscillation patterns and zonal flow migrations reported in helioseismic studies. The Nobeyama 17 GHz data, sensitive to chromospheric and low-coronal magnetic structures, thus provide a valuable proxy for tracking rotational dynamics and their evolution across solar cycles. 4. A Comparative Study from Sunspots to Coronal Emissions The comparative analysis of solar rotation profiles derived from various observational datasets reveals significant insights into the latitudinal dependence of solar angular velocity and its variation across different atmospheric layers and observational techniques. The present study, based on Nobeyama Radioheliograph (NoRH) microwave observations, exhibits a robust differential rotation pattern characterized by a maximum equatorial rotation rate of approximately 14.9° day⁻¹, gradually decreasing toward higher latitudes up to ± 45°. This profile, represented by the bold red solid line, aligns closely with earlier NoRH-based studies such as Chandra et al. ( 2009 , 2011) and Routh et al. ( 2025 ), indicating temporal consistency and methodological reliability in microwave coronal measurements. When compared with X-ray observations from Yohkoh/SXT (Chandra et al. 2010 ) and Hinode/XRT (Chandra et al. 2018 ), the present work shows a slightly steeper latitudinal gradient, suggesting enhanced sensitivity to coronal features in the microwave regime. EUV-based studies using SOHO/EIT (Brajsa et al. 2004; Krachik et al. 2006) and SDO/AIA 30.4 nm (Routh et al. 2024 ) also exhibit strong differential rotation, though with marginally lower equatorial rates, possibly due to differences in feature tracking and emission heights. Chromospheric measurements using Ca II K data from KoSO (Mishra et al. 2024 ) present intermediate rotation rates, bridging the photospheric and coronal regimes. Sunspot-based analyses from KSO, GPR/USF, and KoSO (Poljncic et al. 2017; Ruzdjak et al. 2017; Jha et al. 2021 ) consistently yield lower rotation rates, particularly beyond ± 30°, reflecting the deeper anchoring of sunspot features and reduced latitudinal shear in the photosphere. These profiles exhibit flatter gradients, contrasting with the sharper decline observed in coronal datasets. The convergence of results across instruments and wavelengths underscores the multi-layered nature of solar rotation and validates the differential rotation paradigm. The present work contributes a high-fidelity microwave coronal profile that complements and extends existing rotational diagnostics, offering a valuable benchmark for solar dynamo modeling and cycle-dependent rotational studies. 5. Discussion The long-term analysis of solar coronal rotation using Nobeyama Radioheliograph (NoRH) 17 GHz observations provides critical insights into the dynamics of solar rotation and its coupling with magnetic activity. The derived equatorial rotation rates ( A ) and differential rotation coefficients ( B ) exhibit clear temporal modulation across Solar Cycles 22–24, with persistent hemispheric asymmetry. The northern hemisphere consistently demonstrates higher equatorial rotation rates compared to the southern hemisphere, while the southern hemisphere shows stronger latitudinal shear, as reflected in larger magnitudes of B . This asymmetry is consistent with earlier reports based on sunspot tracers (Snodgrass 1983 , 1984 ; Javaraiah 2020 ) and coronal proxies (Chandra et al. 2010 , 2018 ; Sharma et al. 2020 ), reinforcing the view that solar rotation is magnetically modulated. The physics underlying these variations can be understood in terms of the solar dynamo mechanism. Differential rotation acts as a key driver of the Ω-effect, stretching poloidal magnetic fields into toroidal components (Charbonneau 2010 ; Cameron & Schüssler 2015 ). The observed modulation of A and B with sunspot number (SSN) suggests that rotational shear responds dynamically to the evolving distribution of active-region magnetic fields. During solar maxima, enhanced magnetic complexity leads to stronger latitudinal gradients, while minima correspond to more rigid rotation regimes. This behavior is consistent with torsional oscillations and zonal flows detected in helioseismic studies (Howe et al. 2000 ; Zhao 2013 ), which reveal migrating bands of faster and slower rotation linked to magnetic activity belts. The contour plots of rotation period further highlight the latitudinal dependence of rotation, with shorter periods (~ 16–20 days) near the equator and longer periods (~ 28–32 days) at higher latitudes. This gradient confirms the classical paradigm of solar differential rotation, wherein equatorial plasma rotates faster than mid-latitudes (Beck 2000 ; Schou et al. 2002 ). The compression and irregularity of contours during solar maxima reflect the influence of magnetic fields and migrating active regions, while smoother gradients during minima indicate reduced magnetic interference. These findings underscore the coupling between magnetic activity and rotational dynamics, with NoRH data providing a unique radio perspective that complements EUV and X-ray observations (Brajsa et al. 2004; Routh et al. 2024 ). The comparative analysis across observational techniques – from sunspot tracers to chromospheric Ca II K and coronal EUV/X-ray proxies – demonstrates the multi-layered nature of solar rotation. Sunspot-based studies consistently yield lower equatorial rates and flatter gradients, reflecting deeper anchoring in the photosphere (Beljan et al. 2017 ; Ruzdjak et al. 2017; Jha et al. 2021 ). In contrast, coronal datasets, including NoRH microwave observations, show higher equatorial rates and steeper gradients, indicative of enhanced shear in the upper atmosphere. This stratification highlights the importance of multi-wavelength approaches in capturing the full complexity of solar rotation. 6. Conclusion The present study, based on nearly three decades of NoRH 17 GHz observations, confirms the persistence of solar differential rotation and its modulation by magnetic activity across Solar Cycles 22–24. The equatorial rotation rate ( A ) accelerates during active phases, while the differential rotation coefficient ( B ) steepens, reflecting stronger latitudinal shear. Hemispheric asymmetry is a robust feature, with the northern hemisphere rotating faster and the southern hemisphere exhibiting stronger shear. These results extend earlier findings from sunspot, chromospheric, and coronal studies, providing a unique long-term radio perspective on coronal rotation. Physically, the modulation of rotation parameters with solar cycle progression underscores the dynamic coupling between rotation and the solar dynamo. The observed variations in A and B are consistent with the Ω-effect, torsional oscillations, and zonal flow migrations, all of which highlight the role of rotation in shaping magnetic field evolution. The NoRH dataset, sensitive to upper chromospheric and low-coronal structures, thus serves as a valuable diagnostic for understanding the interplay between rotation and magnetism. In conclusion, solar rotation is not a static property but a dynamic phenomenon intimately linked to solar magnetic activity. The long-term NoRH analysis strengthens the evidence that rotational dynamics evolve with solar cycles, hemispheric asymmetry persists across epochs, and differential rotation responds to magnetic complexity. These findings contribute to the broader effort of constraining solar dynamo models and improving predictive capabilities for solar activity and space weather. Declarations Competing interests: The authors declare no competing interests. Ethics, Consent to Participate, and Consent to Publish declarations Not applicable. Funding Declaration No funding. Author Contribution VPG and VKS involved in the analysis of the data; SC and RG developed programming code for analysis; VKS initially drafted the paper. SC observed all the research work and finalise the manuscript. All authors are carefully proofread the text and references. Acknowledgement Authors are thankful to Physicists implicate in whole Nobeyama Radio Heliograph mission and data archive for NoRH data. We are also thankful to SILSO-SIDC for SSN data used in the present work. Data Availability The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. References H. Balthasar, M. Vázquez, H. Wöhl, Differential Rotation of Sunspot groups in the period from 1874 through 1976 and changes of the rotation velocity within the solar cycle. Astron. Astrophys. 155 , 87 (1986) J.G. 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Astrophys. 520 , A29 (2010) J. Zhao, Helioseismic measurements of differential rotation and meridional flow, Solar and Astrophysical Dynamos and Magnetic Activity, Proceedings of the International Astronomical Union, IAU Symposium, 294, 3–12(2013) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8422228","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":575831947,"identity":"f7d13320-3512-4ba8-97b0-3ae3b65b3433","order_by":0,"name":"Ved Prakash Gupta","email":"","orcid":"","institution":"Sam Higginbottom University of Agriculture, Technology and Sciences","correspondingAuthor":false,"prefix":"","firstName":"Ved","middleName":"Prakash","lastName":"Gupta","suffix":""},{"id":575831948,"identity":"afbe647d-71f9-4fcb-9749-ec10b30d9df4","order_by":1,"name":"Vivek Kumar Singh","email":"","orcid":"","institution":"Sam Higginbottom University of Agriculture, Technology and Sciences","correspondingAuthor":false,"prefix":"","firstName":"Vivek","middleName":"Kumar","lastName":"Singh","suffix":""},{"id":575831949,"identity":"549d1a1e-d472-4e51-89a8-909895128ca3","order_by":2,"name":"Rishabh Gupta","email":"","orcid":"","institution":"Pt. Prithi Nath (PG) College","correspondingAuthor":false,"prefix":"","firstName":"Rishabh","middleName":"","lastName":"Gupta","suffix":""},{"id":575831950,"identity":"e17a8848-a7f5-4472-8a83-f1a1f217e188","order_by":3,"name":"Satish Chandra","email":"data:image/png;base64,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","orcid":"","institution":"Pt. 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01:17:51","extension":"xml","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":83431,"visible":true,"origin":"","legend":"","description":"","filename":"54341cd6edba4fbfad2260a8fe0dd8f71structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/eb60200ea73141ff354c71cf.xml"},{"id":101099605,"identity":"29f1e6ec-3fd3-4de3-9056-12049b0cce14","added_by":"auto","created_at":"2026-01-26 01:17:51","extension":"html","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":90896,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/8df844caced6df3b7d95f17f.html"},{"id":101205682,"identity":"d9743982-b4df-493d-9d7a-629f1d7924f0","added_by":"auto","created_at":"2026-01-27 09:50:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":153929,"visible":true,"origin":"","legend":"\u003cp\u003eA sample Nobeyama Radioheliograph (NoRH) 17 GHz solar full-disk (SFD) image, overlaid with latitude lines spaced at 5° intervals, extending from 45°N to 45°S across the solar disk from west limb to east limb.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/3830edbaf83fafe402082acf.png"},{"id":101099587,"identity":"c5102aeb-d28b-42f0-8267-6cae09fc65b3","added_by":"auto","created_at":"2026-01-26 01:17:51","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":211819,"visible":true,"origin":"","legend":"\u003cp\u003eAnnual rotation rate profile fitted with differential rotation formula Ω(ψ)=A+B sin\u003csup\u003e2\u003c/sup\u003e⁡ψ, for northern and southern solar hemisphere for the year 2015.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/9bf17b1764aa81a35fd17fd9.png"},{"id":101099591,"identity":"43b70fe0-3ce9-413d-aa45-4a7367df549b","added_by":"auto","created_at":"2026-01-26 01:17:51","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":619345,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTop Panel \u003c/strong\u003eAnnual\u003cstrong\u003e \u003c/strong\u003evariation in equatorial rotation rate \u003cem\u003eA\u003c/em\u003e\u003cstrong\u003e \u003c/strong\u003ewith SSN in northern hemisphere(red color) and southern hemisphere(blue color). \u003cstrong\u003eBottom Panel\u003c/strong\u003e Annual\u003cstrong\u003e \u003c/strong\u003evariation in lower latitudinal differential rotation rate \u003cem\u003eB\u003c/em\u003e\u003cstrong\u003e \u003c/strong\u003ewith SSN in northern hemisphere(red color) and southern hemisphere(blue color).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/d2fc93ca0e1fd17059aa9f6e.png"},{"id":101099595,"identity":"b4acff66-3612-47b6-9db4-641b4f975a3f","added_by":"auto","created_at":"2026-01-26 01:17:51","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":513491,"visible":true,"origin":"","legend":"\u003cp\u003ePhase wise variation in northern and southern hemispheric coefficients A and B with annual sunspot numbers for declining phase of cycle 22, cycle 23 and cycle 24.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/1bd8489e72fd203b95e630f0.png"},{"id":101099603,"identity":"e15ac9f0-d85f-472a-8bcd-90a989a44191","added_by":"auto","created_at":"2026-01-26 01:17:51","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":271459,"visible":true,"origin":"","legend":"\u003cp\u003eA contour plot of phasewise solar rotation period deduce from NoRH 17 GHz SFD images observed duing 1992 – 2018.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/79624bcaf4c544efa33b71be.png"},{"id":101206103,"identity":"3220c08d-984c-42e6-a625-7093f6739c21","added_by":"auto","created_at":"2026-01-27 09:54:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":307706,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of solar rotation rate profiles as a function of latitude derived from multiple observational datasets across different instruments and spectral regimes.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/36e804e146576882bff20e94.png"},{"id":107515381,"identity":"e25c657b-5ed5-4d95-b042-af6b392c42b4","added_by":"auto","created_at":"2026-04-22 08:28:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2034087,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8422228/v1/14a69f5a-ead5-4e0b-84af-ae88c1296270.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Study of Solar Coronal Rotation using Nobeyama Radio Heliograph (NoRH) at 17 GHz","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe study of solar differential rotation is crucial to understanding the dynamic behaviour of the Sun. Differential rotation, the variation of angular velocity with latitude and altitude, is a key driver of the solar dynamo mechanism that generates and sustains the Sun\u0026rsquo;s magnetic field (Charbonneau \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Cameron \u0026amp; Sch\u0026uuml;ssler \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). This rotational shear redistributes magnetic flux across the solar surface and corona, influencing the emergence of sunspots, the evolution of active regions, and the modulation of solar irradiance (Howard \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Hathaway \u0026amp; Wilson \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1990\u003c/span\u003e). Consequently, variations in differential rotation are intimately connected to the solar cycle and play a crucial role in shaping space weather phenomena that affect Earth\u0026rsquo;s magnetosphere and technological systems (Jiang et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Cameron et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOver the past century, differential rotation has been estimated using diverse observational techniques. Classical approaches include tracking sunspot groups (Balthasar et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1986\u003c/span\u003e; Snodgrass \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1983\u003c/span\u003e), Doppler velocity measurements of the photosphere (Ulrich et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Snodgrass \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1984\u003c/span\u003e), and helioseismology, which probes the solar interior through p-mode oscillations (Howe et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Schou et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Zhao \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). In the corona, tracers such as X-ray bright points (Kariyappa \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Chandra et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), EUV coronal bright points (Brajša et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; W\u0026ouml;hl et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), and radio emissions (Vats et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Chandra \u0026amp; Vats \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Singh et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003eb\u003c/span\u003e) have been employed to derive latitudinal rotation profiles. Among these, the flux modulation method has proven particularly effective for radio data. This technique relies on the modulation of radio flux as coronal features rotate across the solar disc. By constructing time series of flux variations at different latitudes and applying spectral analysis methods such as autocorrelation, Fast Fourier Transform, or Lomb\u0026ndash;Scargle periodogram (Lomb \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Scargle \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1982\u003c/span\u003e; Vander-Plas 2018), the rotation period can be extracted with high precision. The flux modulation method is advantageous because it does not depend on the identification of individual tracers, but instead utilizes statistical properties of radio brightness variations across latitude bins (Chandra, Vats \u0026amp; Iyer \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Bhatt et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe Nobeyama Radioheliograph (NoRH), operational since 1992 at the Nobeyama Radio Observatory in Japan, provides daily full-disc solar images at 17 GHz (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://solar.nro.nao.ac.jp/norh/html/daily/\u003c/span\u003e\u003cspan address=\"https://solar.nro.nao.ac.jp/norh/html/daily/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The 17 GHz emission originates primarily from the upper chromosphere and lower corona, where gyro-resonance and free\u0026ndash;free emission mechanisms dominate (Vats et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Chandra \u0026amp; Vats \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). These emissions are sensitive to both thermal plasma conditions and magnetic field structures, making NoRH data a valuable diagnostic of coronal dynamics. The long-term, continuous coverage of NoRH offers a unique opportunity to study solar rotation across multiple cycles with consistent instrumentation.\u003c/p\u003e \u003cp\u003ePrevious research has extensively utilized NoRH 17 GHz data to investigate coronal rotation and its variability. Chandra, Vats \u0026amp; Iyer (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) applied flux modulation analysis to NoRH images to derive latitudinal rotation profiles and reported significant north\u0026ndash;south asymmetry. Routh et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) extended the analysis to multiwavelength comparisons, confirming the consistency of NoRH-derived rotation rates with EUV observations. Singh et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003eb\u003c/span\u003e) employed NoRH data in combination with multi-frequency radio flux to explore radial differential rotation and its relationship with solar cycles. These studies collectively demonstrate that NoRH 17 GHz observations provide robust insights into coronal rotation, complementing results from X-ray, EUV, and helioseismic methods.\u003c/p\u003e \u003cp\u003eIn the present work, we build upon these foundations by analyzing nearly three decades (1992\u0026ndash;2020) of NoRH data using the flux modulation method. Our aim is to quantify equatorial rotation rates and differential coefficients across solar cycles 22\u0026ndash;24, examine hemispheric asymmetries, and assess correlations with sunspot numbers. This long-term dataset allows us to explore how coronal rotation evolves with solar cycle phases and magnetic polarity reversals, thereby contributing to a deeper understanding of solar dynamo processes and space weather drivers.\u003c/p\u003e \u003cp\u003eThe present study makes use of daily full-disc solar images observed at 17 GHz by the Nobeyama Radioheliograph (NoRH), which has been in continuous operation since 1992 at the Nobeyama Radio Observatory in Japan. These data span nearly three decades, from 1992 to 2020, thereby covering solar cycles 22, 23, and 24. Because of this, NoRH data provide a unique diagnostic of coronal dynamics and are especially well-suited for long-term studies of solar rotation. But in year 2019 and 2020, siginificant modulation could not beobserved in the time series of solar radio flux. Hence, periodic component could not be computed through flux modulation method.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe flux modulation method is employed to estimate rotation rates from these images. This technique does not rely on tracking individual features but instead analyzes the modulation of radio flux as coronal structures rotate across the solar disc. Each full-disc image is divided into latitude strips, and the average pixel intensity in each strip is computed daily to generate time series of radio flux variations. The periodic components of these time series are extracted using the Lomb\u0026ndash;Scargle periodogram, which is particularly effective for unevenly spaced data (Lomb \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Scargle \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1982\u003c/span\u003e; Vander-Plas 2018).\u003c/p\u003e \u003cp\u003eThis approach has been successfully applied in earlier studies (Chandra, Vats \u0026amp; Iyer \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) using NoRH data, where Vats \u0026amp; Chandra (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) reported significant north\u0026ndash;south asymmetry in coronal rotation, and Singh et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003eb\u003c/span\u003e) extended the analysis to multi-frequency radio flux to explore radial differential rotation and its relationship with solar cycles. More recently, Routh et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) confirmed the consistency of NoRH-derived rotation rates with EUV observations, demonstrating the robustness of this method. By building upon these foundations, the present work aims to provide a comprehensive long-term analysis of equatorial rotation rates, differential coefficients, and their correlation with solar cycle phases, thereby contributing to a deeper understanding of solar dynamo processes and space weather drivers.\u003c/p\u003e"},{"header":"2. Data Analysis and Outcomes","content":"\u003cp\u003eUsing the flux modulation method, synodic rotation periods were derived from daily solar full-disc images captured by the Nobeyama Radioheliograph (NoRH) at 17 GHz. These synodic periods were then converted into sidereal rotation periods following the standard transformation outlined by Snodgrass (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1983\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). The angular rotation rate at each latitude was computed, and its latitudinal dependence was modeled using the classical solar differential rotation law:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\Omega\\:}\\left(\\psi\\:\\right)=A+B{\\text{sin}}^{2}\\psi\\:$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\Omega\\:}\\left(\\psi\\:\\right)\\)\u003c/span\u003e \u003c/span\u003e is the sidereal rotation rate at latitude \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\psi\\:\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cem\u003eA\u003c/em\u003e is the equatorial rotation rate,\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cem\u003eB\u003c/em\u003e is the differential rotation coefficient.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\Omega\\:}\\left(\\psi\\:\\right)=A+B{\\text{sin}}^{2}\\psi\\:\\)\u003c/span\u003e \u003c/span\u003e, for northern and southern solar hemisphere for the year 2015.\u003c/p\u003e \u003cp\u003eThe Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the sidereal rotation rate plotted against \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{sin}}^{2}\\psi\\:\\)\u003c/span\u003e\u003c/span\u003e for both hemispheres for year 2015. Regression analysis yields the following empirical relations: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Omega\\:}\\left(\\psi\\:\\right)=15.36-2.01{\\text{sin}}^{2}\\psi\\:\\)\u003c/span\u003e\u003c/span\u003e, for northen hemisphere and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Omega\\:}\\left(\\psi\\:\\right)=14.69-2.17{\\text{sin}}^{2}\\psi\\:\\)\u003c/span\u003e\u003c/span\u003e, for the southern hemisphere. These results confirm the presence of differential rotation, with both hemispheres exhibiting a decrease in rotation rate with increasing latitude. Notably, in the year 2015 the northern hemisphere shows a slightly higher equatorial rotation rate, while the southern hemisphere displays a stronger latitudinal gradient.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Cycle-Dependent Variations and Hemispheric Asymmetry in Solar Differential Rotation (1992\u0026ndash;2020)\u003c/h2\u003e \u003cp\u003eAnnual values of coefficients \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e from the year 1992 to 2020 were extracted in the same way and compared, in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, with sunspot numbers obtained from WDC-SILSO. The study period (1992\u0026ndash;2020) was segmented according to the progression of solar cycles 22, 23, and 24 using NOAA/SWPC data. The analysis reveals temporal variations in differential rotation characteristics, with evidence of both rigid and differential rotation regimes across different phases of solar activity. These variations correlate with the sunspot cycle, suggesting a dynamic coupling between solar magnetic activity and rotational behavior. The Figure also reveals a clear hemispheric asymmetry and solar cycle dependence in both equatorial rotation rate (\u003cem\u003eA\u003c/em\u003e) and differential rotation coefficient (\u003cem\u003eB\u003c/em\u003e), consistent with and extending earlier chromospheric-coronal studies.\u003c/p\u003e \u003cp\u003eThe top panel illustrates the annual variation in equatorial rotation rate (\u003cem\u003eA\u003c/em\u003e) from 1992 to 2018, showing that the northern hemisphere (red) consistently rotates faster than the southern hemisphere (blue), with both exhibiting temporal modulation that broadly tracks the solar sunspot number (SSN). Peaks in \u003cem\u003eA\u003c/em\u003e often coincide with solar maxima, particularly around 2000 and 2014, suggesting a dynamic coupling between equatorial rotation and magnetic activity. The bottom panel shows the variation in the differential rotation coefficient (\u003cem\u003eB\u003c/em\u003e), where both hemispheres display negative values indicative of classical solar differential rotation. Notably, the southern hemisphere (blue) exhibits a steeper gradient (larger magnitude of \u003cem\u003eB\u003c/em\u003e), implying stronger latitudinal shear compared to the north. These variations in \u003cem\u003eB\u003c/em\u003e also correlate with SSN, with flatter gradients (smaller \u003cem\u003eB\u003c/em\u003e) during solar minima and steeper gradients during active phases, reflecting a transition between rigid and differential rotation regimes.\u003c/p\u003e \u003cp\u003eThese findings align with and extend earlier studies. Snodgrass (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1983\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1984\u003c/span\u003e) first quantified solar differential rotation using Doppler and magnetic tracers, reporting equatorial rates near 14.5\u0026ndash;15.0\u0026deg;/day and latitudinal gradients around \u0026minus;\u0026thinsp;2.5\u0026deg;/day. Beck (1999) and helioseismic investigations confirmed these values and noted temporal modulation linked to solar cycles. More recently, Javaraiah (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) analyzed sunspot group data from 1874\u0026ndash;2017 and found systematic variations in \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e across cycles, with hemispheric asymmetries becoming more pronounced during cycle maxima. Sharma et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) reported a statistically significant correlation between hemispheric asymmetry in coronal rotation and solar activity during cycle 24, reinforcing the view that rotation dynamics are magnetically modulated. Kumar et al. (2024) extended this to the transition region and corona using EUV irradiance and radio flux, showing sidereal rotation periods varying from 19.4 to 28.1 days, with cycle-dependent shifts.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCompared to these earlier works, the present NoRH-based analysis offers a unique long-term radio perspective across cycles 22\u0026ndash;24, confirming the persistence of hemispheric asymmetry and the modulation of rotation parameters with solar activity. The correlation between \u003cem\u003eA\u003c/em\u003e and SSN supports the idea that equatorial rotation accelerates during active phases, while the variation in \u003cem\u003eB\u003c/em\u003e suggests that differential rotation strengthens with magnetic complexity. These results contribute to a growing body of evidence that solar rotation is not static but dynamically linked to the solar dynamo and magnetic field evolution.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Phase-Wise Modulation of Solar Rotation Parameters and Hemispheric Asymmetry Across Cycles 22\u0026ndash;24\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the phase-wise variation in the equatorial rotation rate (\u003cem\u003eA\u003c/em\u003e) and differential rotation coefficient (\u003cem\u003eB\u003c/em\u003e) for the northern and southern hemispheres, plotted alongside annual sunspot numbers during the declining phase of SC 22 and throughout SC 23 and 24.\u003c/p\u003e \u003cp\u003eAcross the declining phase of Cycle 22 and through Cycles 23 and 24, the Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows a persistent hemispheric asymmetry and clear solar-cycle modulation in both coefficients: the equatorial rotation rate \u003cem\u003eA\u003c/em\u003e (top) and the lower-latitudinal differential rotation coefficient \u003cem\u003eB\u003c/em\u003e (bottom). \u003cem\u003eA\u003c/em\u003e in the north remains systematically higher than in the south, with both tracking the annual sunspot number (SSN). \u003cem\u003eA\u003c/em\u003e rises toward activity maxima and diminishes near minima, with the modulation amplitude strongest in Cycle 23 and visibly muted in the weaker Cycle 24. In \u003cem\u003eB\u003c/em\u003e, both hemispheres maintain negative values consistent with differential rotation, but the southern hemisphere generally exhibits a larger magnitude (steeper latitudinal shear), especially near Cycle 23\u0026rsquo;s peak, while shear relaxes (\u003cem\u003eB\u003c/em\u003e decreases) around minima\u0026mdash;an alternating tendency toward more rigid rotation in quiet phases and enhanced differential rotation during active phases. Phase-wise, the declining tail of Cycle 22 already displays the north\u0026ndash;south split that intensifies through Cycle 23; Cycle 24 preserves the asymmetry but with reduced dynamical range, echoing its subdued magnetic activity.\u003c/p\u003e \u003cp\u003eThese behaviors are consistent with earlier chromospheric and coronal studies: sunspot-group tracer analyses and Doppler/helioseismic results reported equatorial rates near 14.5\u0026ndash;15.0\u0026deg;/day and gradients around \u0026minus;\u0026thinsp;2.0 to \u0026minus;\u0026thinsp;2.9\u0026deg;/day with cycle-linked modulation; Ca II K and He I 10830 \u0026Aring; synoptic maps likewise show stronger shear during active phases and hemispheric differences that wax and wane with SSN; coronal EUV/radio proxies further corroborate the weakening of rotational modulation in the comparatively low-amplitude Cycle 24. Taken together, the NoRH phase-wise analysis strengthens the picture that solar rotation parameters are dynamically coupled to the magnetic cycle, with asymmetry and shear responding to the evolving distribution and complexity of active-region fields.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Latitudinal and Temporal Variations in Solar Rotation","content":"\u003cp\u003eThe contour plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) derived from Nobeyama 17 GHz microwave observations spanning 1992 to 2018 reveals significant latitudinal and temporal variations in the solar rotation period between \u0026plusmn;\u0026thinsp;45\u0026deg; latitude. This interval encompasses the declining phase of Solar Cycle 22 and the entirety of Solar Cycles 23 and 24. The rotation period exhibits a clear differential pattern, with shorter periods (~\u0026thinsp;16\u0026ndash;20 days) concentrated near the equator and progressively longer periods (~\u0026thinsp;28\u0026ndash;32 days) observed toward higher latitudes. This latitudinal gradient confirms the well-established solar differential rotation, wherein equatorial regions rotate faster than mid-latitudes. Notably, the contour lines display phase-wise modulation in rotation rates, with discernible shifts corresponding to solar cycle transitions. During solar maxima, particularly in Cycles 23 and 24, the rotation period contours appear more compressed and irregular, suggesting enhanced magnetic activity and the influence of migrating active regions. Conversely, solar minima are marked by smoother gradients and more stable rotation profiles. These findings underscore the dynamic coupling between solar magnetic activity and rotational behavior, and they align with torsional oscillation patterns and zonal flow migrations reported in helioseismic studies. The Nobeyama 17 GHz data, sensitive to chromospheric and low-coronal magnetic structures, thus provide a valuable proxy for tracking rotational dynamics and their evolution across solar cycles.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. A Comparative Study from Sunspots to Coronal Emissions","content":"\u003cp\u003eThe comparative analysis of solar rotation profiles derived from various observational datasets reveals significant insights into the latitudinal dependence of solar angular velocity and its variation across different atmospheric layers and observational techniques. The present study, based on Nobeyama Radioheliograph (NoRH) microwave observations, exhibits a robust differential rotation pattern characterized by a maximum equatorial rotation rate of approximately 14.9\u0026deg; day⁻\u0026sup1;, gradually decreasing toward higher latitudes up to \u0026plusmn;\u0026thinsp;45\u0026deg;. This profile, represented by the bold red solid line, aligns closely with earlier NoRH-based studies such as Chandra et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, 2011) and Routh et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), indicating temporal consistency and methodological reliability in microwave coronal measurements.\u003c/p\u003e \u003cp\u003eWhen compared with X-ray observations from Yohkoh/SXT (Chandra et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) and Hinode/XRT (Chandra et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), the present work shows a slightly steeper latitudinal gradient, suggesting enhanced sensitivity to coronal features in the microwave regime. EUV-based studies using SOHO/EIT (Brajsa et al. 2004; Krachik et al. 2006) and SDO/AIA 30.4 nm (Routh et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) also exhibit strong differential rotation, though with marginally lower equatorial rates, possibly due to differences in feature tracking and emission heights. Chromospheric measurements using Ca II K data from KoSO (Mishra et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) present intermediate rotation rates, bridging the photospheric and coronal regimes.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSunspot-based analyses from KSO, GPR/USF, and KoSO (Poljncic et al. 2017; Ruzdjak et al. 2017; Jha et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) consistently yield lower rotation rates, particularly beyond \u0026plusmn;\u0026thinsp;30\u0026deg;, reflecting the deeper anchoring of sunspot features and reduced latitudinal shear in the photosphere. These profiles exhibit flatter gradients, contrasting with the sharper decline observed in coronal datasets. The convergence of results across instruments and wavelengths underscores the multi-layered nature of solar rotation and validates the differential rotation paradigm. The present work contributes a high-fidelity microwave coronal profile that complements and extends existing rotational diagnostics, offering a valuable benchmark for solar dynamo modeling and cycle-dependent rotational studies.\u003c/p\u003e"},{"header":"5. Discussion","content":"\u003cp\u003eThe long-term analysis of solar coronal rotation using Nobeyama Radioheliograph (NoRH) 17 GHz observations provides critical insights into the dynamics of solar rotation and its coupling with magnetic activity. The derived equatorial rotation rates (\u003cem\u003eA\u003c/em\u003e) and differential rotation coefficients (\u003cem\u003eB\u003c/em\u003e) exhibit clear temporal modulation across Solar Cycles 22\u0026ndash;24, with persistent hemispheric asymmetry. The northern hemisphere consistently demonstrates higher equatorial rotation rates compared to the southern hemisphere, while the southern hemisphere shows stronger latitudinal shear, as reflected in larger magnitudes of \u003cem\u003eB\u003c/em\u003e. This asymmetry is consistent with earlier reports based on sunspot tracers (Snodgrass \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1983\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Javaraiah \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and coronal proxies (Chandra et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Sharma et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), reinforcing the view that solar rotation is magnetically modulated.\u003c/p\u003e \u003cp\u003eThe physics underlying these variations can be understood in terms of the solar dynamo mechanism. Differential rotation acts as a key driver of the Ω-effect, stretching poloidal magnetic fields into toroidal components (Charbonneau \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Cameron \u0026amp; Sch\u0026uuml;ssler \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The observed modulation of \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e with sunspot number (SSN) suggests that rotational shear responds dynamically to the evolving distribution of active-region magnetic fields. During solar maxima, enhanced magnetic complexity leads to stronger latitudinal gradients, while minima correspond to more rigid rotation regimes. This behavior is consistent with torsional oscillations and zonal flows detected in helioseismic studies (Howe et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Zhao \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), which reveal migrating bands of faster and slower rotation linked to magnetic activity belts.\u003c/p\u003e \u003cp\u003eThe contour plots of rotation period further highlight the latitudinal dependence of rotation, with shorter periods (~\u0026thinsp;16\u0026ndash;20 days) near the equator and longer periods (~\u0026thinsp;28\u0026ndash;32 days) at higher latitudes. This gradient confirms the classical paradigm of solar differential rotation, wherein equatorial plasma rotates faster than mid-latitudes (Beck \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Schou et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). The compression and irregularity of contours during solar maxima reflect the influence of magnetic fields and migrating active regions, while smoother gradients during minima indicate reduced magnetic interference. These findings underscore the coupling between magnetic activity and rotational dynamics, with NoRH data providing a unique radio perspective that complements EUV and X-ray observations (Brajsa et al. 2004; Routh et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe comparative analysis across observational techniques \u0026ndash; from sunspot tracers to chromospheric Ca II K and coronal EUV/X-ray proxies \u0026ndash; demonstrates the multi-layered nature of solar rotation. Sunspot-based studies consistently yield lower equatorial rates and flatter gradients, reflecting deeper anchoring in the photosphere (Beljan et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Ruzdjak et al. 2017; Jha et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In contrast, coronal datasets, including NoRH microwave observations, show higher equatorial rates and steeper gradients, indicative of enhanced shear in the upper atmosphere. This stratification highlights the importance of multi-wavelength approaches in capturing the full complexity of solar rotation.\u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThe present study, based on nearly three decades of NoRH 17 GHz observations, confirms the persistence of solar differential rotation and its modulation by magnetic activity across Solar Cycles 22\u0026ndash;24. The equatorial rotation rate (\u003cem\u003eA\u003c/em\u003e) accelerates during active phases, while the differential rotation coefficient (\u003cem\u003eB\u003c/em\u003e) steepens, reflecting stronger latitudinal shear. Hemispheric asymmetry is a robust feature, with the northern hemisphere rotating faster and the southern hemisphere exhibiting stronger shear. These results extend earlier findings from sunspot, chromospheric, and coronal studies, providing a unique long-term radio perspective on coronal rotation.\u003c/p\u003e \u003cp\u003ePhysically, the modulation of rotation parameters with solar cycle progression underscores the dynamic coupling between rotation and the solar dynamo. The observed variations in \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e are consistent with the Ω-effect, torsional oscillations, and zonal flow migrations, all of which highlight the role of rotation in shaping magnetic field evolution. The NoRH dataset, sensitive to upper chromospheric and low-coronal structures, thus serves as a valuable diagnostic for understanding the interplay between rotation and magnetism.\u003c/p\u003e \u003cp\u003eIn conclusion, solar rotation is not a static property but a dynamic phenomenon intimately linked to solar magnetic activity. The long-term NoRH analysis strengthens the evidence that rotational dynamics evolve with solar cycles, hemispheric asymmetry persists across epochs, and differential rotation responds to magnetic complexity. These findings contribute to the broader effort of constraining solar dynamo models and improving predictive capabilities for solar activity and space weather.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests:\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eEthics, Consent to Participate, and Consent to Publish declarations\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eFunding Declaration\u003c/strong\u003e \u003cp\u003eNo funding.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eVPG and VKS involved in the analysis of the data; SC and RG developed programming code for analysis; VKS initially drafted the paper. SC observed all the research work and finalise the manuscript. All authors are carefully proofread the text and references.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eAuthors are thankful to Physicists implicate in whole Nobeyama Radio Heliograph mission and data archive for NoRH data. We are also thankful to SILSO-SIDC for SSN data used in the present work.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eH. Balthasar, M. V\u0026aacute;zquez, H. W\u0026ouml;hl, Differential Rotation of Sunspot groups in the period from 1874 through 1976 and changes of the rotation velocity within the solar cycle. Astron. Astrophys. \u003cb\u003e155\u003c/b\u003e, 87 (1986)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJ.G. 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The Sun does not rotate uniformly; its rotation rate varies with both altitude and latitude. However, the available information on solar rotation remains insufficient for fully predicting solar activity and, consequently, space weather. Solar rotation can be studied using several approaches, including tracer tracking on the solar surface, spectral analysis and flux modulation. In this study, solar rotation is determined through flux modulation, while Lomb\u0026ndash;Scargle periodogram (LSP) is employed to identify periodicities in the data. In the flux modulation method, radio features crossing the solar disc are monitored, and statistical analysis of daily radioheliograph images (spanning 1992\u0026ndash;2020) provides rotation periods as a function of latitude. Periodic components within these time series are extracted using statistical techniques such as LSP. The analysis is conducted on latitude bins, each representing equally spaced regions, seperated by 5\u0026deg;, across the solar full-disc (SFD) images from the Nobeyama Radioheliograph (NoRH) at 17 GHz, covering latitudes from 45\u0026deg;S to 45\u0026deg;N. A least-squares polynomial fit is applied to the rotational profiles of the northern and southern hemispheres. The resulting differential coefficients are found to vary with the sunspot cycle. The findings reveal both rigid and differential rotation across different epochs, specifically from the declining phase of SC 22 through the conclusion of SC 24.\u003c/p\u003e","manuscriptTitle":"Study of Solar Coronal Rotation using Nobeyama Radio Heliograph (NoRH) at 17 GHz","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-26 01:17:46","doi":"10.21203/rs.3.rs-8422228/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"421eb961-cfae-4ad3-8ab7-b79db91b253f","owner":[],"postedDate":"January 26th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-22T08:27:00+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-26 01:17:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8422228","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8422228","identity":"rs-8422228","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}