Measuring the Solar Rotation Period Through the Analysis of Sunspots
ABSTRACT
Understanding how the Sun rotates across different latitudes has been central to solar physics for more than a century, and modern observations continue to refine that picture. In this work, we revisit the problem using a full year of Solar and Heliospheric Observatory (SOHO) observations, focusing on the motions of identified active regions rather than individual sunspots. Over the course of the year, 377 regions were tracked between 36°S and 29°N, and their positions were converted into heliographic coordinates to allow a consistent comparison across the disk. By following their longitudinal drift, we derived rotation periods for three latitude intervals: 0°–±10°, ±10°–±20°, and ±20°–±35°. The resulting rotation periods 25.62, 26.02, and 26.16 days, respectively show the familiar pattern of increasingly slow rotation toward higher latitudes. This gradient is a hallmark of differential rotation and agrees closely with long-established measurements, despite our use of a relatively modest dataset. The tight consistency across latitude bands suggests that even simple daily cadence observations can yield reliable constraints when the data are carefully filtered and transformed into an appropriate coordinate system. Beyond confirming earlier results, the analysis highlights the value of systematic data cleaning and uniform tracking procedures in solar rotation studies. Although the data underlying this work are by no means exotic, they nonetheless provide a clear view of how the Sun’s rotational behavior changes with latitude. These findings reinforce the connection between surface rotation, the structure of the solar interior, and the long-term evolution of the solar magnetic cyclerelationships that remain central to ongoing efforts to understand the dynamics of our star. The main difference between this article and other articles is that it examines and analyzes a larger volume of data and provides accurate results.
INTRODUCTION.
Since the beginning of astronomy researchers have been fascinated by the unusual patterns visible on the Sun’s surface. In the 1600s Christoph Scheiner emerged as one of the pioneering scientists to create a detailed and systematic log of these phenomena. His significant publication Rosa Ursina (1630) effectively proved that sunspots were solar formations and not flaws, in vision the telescope or atmospheric conditions. Scheiner’s findings were crucial in demonstrating that the Sun was not a fixed ball but a variable and active entity. Years prior to Scheiner Johannes Fabricius released, in 1611 what is regarded as the initial scientific account detailing the regular motion of sunspots. He observed that the spots traveled across the surface and deduced that they had to rotate along, with the Sun itself. Fabricius’s observations offered some of the direct proof that the Sun rotatesan understanding that influenced the subsequent generations of research. [1,2]
As solar studies progressed into the century efforts to comprehend the Suns rotation grew more advanced. In 1918 John St. John evaluated the understanding astronomers had about rotation during his era and highlighted that significant uncertainties persisted despite numerous observations. He proposed that the Sun could not act as an object and that its various layers had to rotate at distinct speeds. His research was among the significant efforts to distinguish the activity of the solar surface, from that of the inner layers and it contributed to emphasizing the intricate nature of the Sun’s inner composition. [3]
Towards the end of the century innovative theoretical methods offered a profound understanding of the Sun’s internal structure. A key contribution was made by Michael J. Thompson, whose 2003 review combined data to create a comprehensive depiction of the Sun’s rotational behavior beneath its surface. Thompson demonstrated that the convective zone, the zone and the tachocline all displayed distinct rotation characteristics. His research prompted scientists to consider rotation not as a singular straightforward movement but, as a complex, layered and three-dimensional structure. [4]
Advancement in comprehending the Sun’s magnetic dynamics advanced the discipline significantly. Chitre and Choudhuri investigated the dynamo and demonstrated that the creation of the Sun’s magnetic field was strongly influenced by its internal rotational behavior. They described how the interplay between rotation, meridional circulations and convective turbulence could generate the Sun’s characteristic 11-year activity cycle. Their work established a link, between the investigation of rotation and magnetism. [5]
Building on this progress, Gilman explored the links among convection, rotation, and magnetic fields in greater depth. He showed that the solar dynamo could only be understood by considering the full complexity of the internal flows, the Sun’s asymmetric rotation, and the large-scale turbulent motions that shape its subsurface layers. His work became an important theoretical foundation for modern models of the Sun’s rotational and magnetic behavior. [6]
Data Collection of Sunspot Regions.
To obtain precise and reliable information about the motion of sunspot-bearing regions, it was essential to use stable, high-quality solar observations. In this study, daily full-disk images from the SOHO spacecraft were examined, as they provided continuous, evenly spaced coverage suitable for tracking solar features over extended intervals. Verification of the retrieved features was further supported by the BASS 2000 solar database, which supplied positional and physical metadata helpful for confirming region identities and their day-to-day evolution. Since individual sunspots often appeared or disappeared within short intervals, the analysis focused instead on Active Regions (ARs). Statistical studies indicated that sunspots occurred inside ARs with a probability close to 98%, making ARs significantly more reliable tracers of large-scale solar rotation. These regions, being magnetically enhanced structures on the photosphere, hosted sunspots, flares, and other forms of magnetic activity, which rendered their positions stable enough to follow across several days. The initial dataset consisted of 3,039 daily records corresponding to 408 distinct Active Regions observed throughout 2024. All images were taken at 00:00 UTC to ensure uniform cadence. The regions occupied latitudes extending from 36° south to 29° north, and their lifetimes varied between 1 and 14 days. After removing corrupted, incomplete, or inconsistent entries, a refined dataset of 377 Active Regions remained for analysis. Table 1 provides information about the data collected. And Table 2 is an example of the collected data (Data related for the same AR).
| Table 1. Information containedin the data (from 2024/1/1 to 2024/12/27) | |
| Date of sunspot | Example: 2024/5/1 |
| Number of sunspot | 377 |
| Center longitude | Example: 23° |
| Center latitude | Example: 30° |
| 3039 data of active regions from | -36° to +29° |
| Table 2. Example of data for spot number 3027 | ||
| Date | Center longitude (°) | Center latitude (°) |
| 2024-12-27 | 187 | -8 |
| 2024-12-26 | 186 | -8 |
| 2024-12-25 | 185 | -8 |
| 2024-12-24 | 185 | -8 |
| 2024-12-23 | 185 | -8 |
| 2024-12-22 | 184 | -8 |
| 2024-12-21 | 183 | -8 |
| 2024-12-21 | 183 | -8 |
| 2024-12-20 | 178 | -11 |
| 2024-12-19 | 178 | -10 |
| 2024-12-18 | 179 | -8 |
Data Cleaning.
Before any calculation of rotation periods, the dataset underwent an extensive cleaning process designed to remove outliers and inconsistencies. Outliers were defined as data points displaying abrupt, nonphysical shifts in heliographic longitude. For example, AR 3534 exhibited a smooth longitudinal evolution from one day to the next, but a single entry deviated sharply from the trend before returning to the expected pattern the following day. This anomalous measurement was removed because such a deviation could not reasonably be attributed to true solar motion. Similar checks were applied throughout the dataset, and entries with missing coordinates, conflicting NOAA identifiers, or timing inconsistencies were excluded. These steps ensured that the final longitudinal time series reflected coherent physical behavior rather than observational noise. The basis for detecting outliers is that the geographical longitude of the spot decreases uniformly over the observable range, and if data is observed that disrupts this trend, it should be considered outliers and removed. Table 3 shows the difference in the center longitudinal of this spot in row 6. In other words, Table 3 is an example of outliers that need to be removed from the data.
| Table 3. An example of outlier data where the longitude of the spot suddenly decreased instead of increasing. The disruption of the decreasing pattern in this interval can be seen in row 6. | ||
| Date | Center longitude (°) | Center latitude (°) |
| 2024-01-07 | 220 | -12 |
| 2024-01-06 | 223 | -15 |
| 2024-01-05 | 223 | -15 |
| 2024-01-04 | 226 | -15 |
| 2024-01-03 | 225 | -14 |
| 2024-01-02 | 222 | -12 |
| 2024-01-01 | 225 | -14 |
Rotation Period Calculation.
The rotation period for each latitude was determined by analyzing the longitudinal drift of each AR over the duration of its visibility. Since observations were recorded every 24 hours, the Sun’s average rotational advance of about 13.2° per day provided the scaling necessary for interpreting the measured drift. For a given region, the number of observing days was multiplied by 13.2°, and the measured change in longitude between the first and last day was added to this value to determine the total longitudinal shift.
The method can be illustrated using Active Region 3761. This region, located near a latitude of approximately 10° south, was observed for six consecutive days. Over this interval, the baseline rotational contribution was six times 13.2°, giving 79.2°. The observed longitudinal difference between the first and last days was 5°, which brought the total displacement to 84.2°. Because a full solar rotation corresponds to 360°, the rotation period was obtained through proportional scaling. In plain form, the calculation yielded a rotation period of 25.65 days for this region.
This procedure was applied to all 377 Active Regions. After rotation periods were calculated individually, they were grouped and averaged within specific latitude bands. The resulting mean periods were 25.62 days for regions between 0° and ±10°, 26.02 days for those between ±10° and ±20°, and 26.16 days for regions between ±20° and ±35°. These values, drawn directly from the numerical analysis, formed the basis for the regression study used to examine the dependence of rotation period on heliographic latitude. A scatter plot confirmed that rotation periods increased systematically with distance from the equator, consistent with the classical pattern of differential rotation.
RESULT.
The rotation periods obtained in this work were closely aligned with long-established measurements of solar differential rotation. Classical analyses reported an equatorial rotation period of about 25.4 days, with values near 26.1 and 27.0 days at latitudes of roughly 20° and 30°. Later studies based on long-term sunspot observations found a similar pattern, with an equatorial value near 25.38 days and corresponding mid-latitude periods around 26.24 and 27.12 days. Table 4 shows the average solar rotation periods at different latitude ranges from which the data was collected. Figure 1 also shows the period of the solar rotation at each latitude. The R2 number has a small percentage error due to the dispersion of the data and the relatively small number of them, but consistent with further calculations, this conclusion can still be reached. [7]
| Table 4. The average period of the Sun’s rotation in different orbits | |
| Latitude range (degrees) | Period (days) |
| ±0° until ±10° | 25.62 |
| ±10° until ±20° | 26.02 |
| ±20° until ±35° | 26.16 |
DISCUSSION.
In the latitude range from 0° to ±10°, earlier studies had reported rotation periods of roughly 25.4 days, while our analysis produced a slightly larger value of 25.62 days. The difference between the two corresponded to only about 0.86%, which indicated very close agreement. A similar pattern appeared in the next band, between ±10° and ±20°, where previous measurements suggested about 26.1 days and our result was 26.02 days, giving a deviation of approximately 0.84%. These small differences suggested that the present method was successfully reproducing the commonly accepted values for solar rotation [7].
At higher latitudes, between ±20° and ±35°, the difference became more noticeable. Earlier works typically reported periods close to 27.0 days, whereas our average was 26.16 days, corresponding to a deviation of about 3.5%. This larger discrepancy was expected because measurements become less precise farther from the solar equator. Features located near the edge of the solar disk often referred to as the solar limb are observed at an angle rather than directly from above. As a result, their shapes appear compressed, a geometric effect known as foreshortening, which makes their exact positions harder to determine. In addition, projection effects arise when the curved surface of the Sun is represented on a flat image, causing small distortions in the apparent longitude of surface features. Figure 2 show near the solar limb, due to projection effects and geometric foreshortening, the solar meridians appear compressed and converge toward each other. In contrast, near the center of the solar disk, where the observer’s line of sight is approximately perpendicular to the photospheric surface, the heliographic coordinate grid is observed with minimal geometric distortion, and the angular separation of the meridians appears more uniform and expanded. Consequently, the determination of the positions of active regions, as well as the estimation of their dimensions and surface areas, is geometrically more accurate near the disk center than near the solar limb. This projection effect is clearly evident in active regions numbered 3848, 3849, and 3850 in Figure 2.
Active Regions themselves also evolved over time as their magnetic structures strengthened, fragmented, or decayed. Because of these internal changes, the apparent center of a region could shift slightly from one day to the next, introducing small uncertainties that were later amplified in the rotation calculation. Furthermore, since the observations were taken only once per day, short-term variations in motion could not be fully resolved. Despite these limitations, the overall agreement with the literature remained strong, demonstrating that carefully cleaned daily SOHO data were still capable of reproducing the well-established pattern of solar differential rotation with good quantitative accuracy [8].
ACKNOWLEDGMENTS.
I thank my supervisor, Dr. Koorosh Rokni, for his invaluable guidance and continuous support throughout this research. His expertise and encouragement were essential in shaping this study and in strengthening my development as a researcher.
REFERENCES.
- C. Scheiner, Rosa Ursina sive Solis (Apud Andream Phaeum, 1630), book 4, part 2, pp. 145–150.
- J. Fabricius, De Maculis in Sole Observatis, et Apparente earum cum Sole Conversione, Narratio (Wesselius, 1611).
- J. St. John, The present condition of the problem of solar rotation. Astrophys. J. 48, 219–239 (1918).
- M. J. Thompson, The internal rotation of the Sun. Annu. Rev. Astron. Astrophys. 41, 599–643 (2003).
- S. M. Chitre, A. R. Choudhuri, The solar dynamo. Scholarpedia 2, 3145 (2007).
- P. A. Gilman, The solar dynamo: Observations and theories of solar convection, global circulation, and magnetic fields. Phys. Earth Planet. Inter. 30, 152–167 (1982).
- H. B. Snodgrass, Synoptic observations of differential rotation. Solar Phys. 82, 189–199 (1983).
- R. Howard, J. Harvey, Rotation rate of the solar photosphere. Solar Phys. 12, 23–51 (1970).
Posted by buchanle on Friday, June 12, 2026 in May 2026.
Tags: active regions, differential motion, eclipse period, Sun, sunspot