Solar Rotation Research Articles

Modeling and analysis of solar Doppler difference bias with arbitrary rotation axis

The solar rotation causes the solar Doppler difference bias, which leads to the decline of the velocity measurement accuracy. Modeling and compensation are an effective solution. The limited model with specific geometric direction, where the solar rotation axis is perpendicular to the plane through the Sun, the Earth and Mars, was established. However, in fact, the geometric relationship among the Sun, Mars and the spacecraft is not fully in line with the hypothesis of the model due to the spacecraft orbital angle and the solar rotation axis drift. Thus, this model is not consistent with the fact. In order to solve this problem, a universal solar Doppler difference bias model, which provides the expression with arbitrary rotation axis, is established in this paper. In this method, for any point at the solar surface, four variables including the direction of the solar rotation linear velocity at this point, the distance from this point to the rotation axis, the vector from this point to Mars, and the vector from this point to the spacecraft are calculated. Based on these four variables, the solar Doppler difference bias corresponding to this point is obtained. The theoretical analysis and simulation results demonstrate that the solar Doppler difference bias model with the actual rotation axis is different from that with one of the specific rotation axes. Therefore, it is indispensable to build the proposed model for compensation. Besides, the direction of the solar rotation axis, the spacecraft-Mars-Sun angle and the spacecraft-to-Mars distance are important impact factors for the proposed model.

Connecting measurements of solar and stellar brightness variations

Context. A comparison of solar and stellar brightness variations is hampered by the difference in spectral passbands that are used in observations, and also by the possible difference in the inclination of the solar and stellar rotation axes from the line of sight. Aims. We calculate the rotational variability of the Sun as it would be measured in passbands used for stellar observations. In particular, we consider the filter systems used by the CoRoT, Kepler, TESS, and Gaia space missions. We also quantify the effect of the inclination of the rotation axis on the solar rotational variability. Methods. We employed the spectral and total irradiance reconstruction (SATIRE) model to calculate solar brightness variations in different filter systems as observed from the ecliptic plane. We then combined the simulations of the surface distribution of the magnetic features at different inclinations using a surface flux transport model with the SATIRE calculations to compute the dependence of the variability on the inclination. Results. For an ecliptic-bound observer, the amplitude of the solar rotational variability, as observed in the total solar irradiance (TSI), is 0.68 mmag (averaged over solar cycles 21–24). We obtained corresponding amplitudes in the Kepler (0.74 mmag), CoRoT (0.73 mmag), TESS (0.62 mmag), Gaia G (0.74 mmag), Gaia GRP (0.62 mmag), and Gaia GBP (0.86 mmag) passbands. Decreasing the inclination of the rotation axis decreases the rotational variability. For a sample of randomly inclined stars, the variability is on average 15% lower in all filter systems we considered. This almost compensates for the difference in amplitudes of the variability in TSI and Kepler passbands, making the amplitudes derived from the TSI records an ideal representation of the solar rotational variability for comparison to Kepler stars with unknown inclinations. Conclusions. The TSI appears to be a relatively good measure of solar variability for comparisons with stellar measurements in the CoRoT, Kepler, TESS Gaia G, and Gaia GRP filters. Whereas the correction factors can be used to convert the variability amplitude from solar measurements into the values expected for stellar missions, the inclination affects the shapes of the light curves so that a much more sophisticated correction than simple scaling is needed to obtain light curves out of the ecliptic for the Sun.

Study of the Periodicities of the Solar Differential Rotation

Data on solar hydrogen filaments obtained at the Abastumani Astrophysical Observatory during solar activity cycles 19-22 are used to study the characteristic periods of the solar differential rotation. In addition to the known 11-year period of solar activity, a quasi-biennial periodicity was revealed for the rotation rates of hydrogen filaments and a quasi-five-year periodicity was also found for the number of hydrogen filaments.

Long- and Short-Term Evolutions of Magnetic Field Fluctuations in High-Speed Streams

High-speed streams (HSSs) are believed to be only slightly affected by different interactions on their path from the Sun to Earth and thus the analysis of their observations can provide information on the structure and temporal variations of the magnetic field and plasma parameters at the source region. We have chosen three coronal holes supplying 14 HSSs recorded by Wind in 2008. For each HSS, we have calculated the average magnetic field and plasma parameters as well as power spectral densities (PSDs) of magnetic field fluctuations in the MHD and kinetic ranges to investigate their long- and short-term variations. We suggest that long-term variations are connected with a time evolution of the source region on the time scale of solar rotations. On the other hand, the short-term variations would reflect a longitudinal structure of the coronal hole. Our study reveals that coronal holes are very stable source of HSSs and their temporal evolution on short- and long-time scales is negligible. This is true for the average parameters as well as for the fluctuation power and PSDs. Observed correlations between bulk and/or thermal velocity and PSD parameters are consistent with already published results. We suggest that they do not originate in the source region but they can be mostly attributed to interaction with the ambient slow wind that affects even the HSS core.

The mean tilt of sunspot bipolar regions: theory, simulations and comparison with observations

ABSTRACT A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of the Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the solar differential rotation affects the mean tilt, which can explain deviations from Joy’s law for the sunspot bipolar regions at high latitudes. The theoretical results obtained and the results from numerical simulations based on the non-linear mean-field dynamo theory, which takes into account conservation of the total magnetic helicity and the budget equation for the evolution of the Wolf number density, are in agreement with observational data of the mean tilt of sunspot bipolar regions over individual solar cycles 15–24.

The Hidden Cycle of the Solar Tesseral-Quadrupole Magnetic Field

Based on the Stanford harmonic coefficients of the solar magnetic fields and on the results of Shannon entropy transfer technique applied to magnetic mode intensities (Mikhaylutsa in J. Astrophys. Astron.40, 22, 2019), we have found that most of the medium and small-scale solar magnetic modes (order $l > 3$; degree $m > 0$) must be interdependent. The features and physical sense of these dependencies are analyzed and suggest that an unknown process in the Sun may control clusters of dependent magnetic modes according to some underlying physical scenario. The scenario may be revealed by studying the spatial distribution of the global surface magnetic field. We find that the tesseral-quadrupole ($l = 2$; $m = 1$) polarity distribution reappears periodically over four solar cycles. The periodicity (${T}\approx 72$ solar rotations) is synchronized with the phases of modulation of the Shannon entropy transfer from the tesseral-quadrupole mode. An unknown process (twice per sunspot cycle) organizes a recurring cluster of interconnected magnetic modes that restore the global structure of the tesseral-quadrupole polarity, as a kind of “template.” This cycle is hidden in traditional methods of analysis, but its spatial-phase origin is made clear by the Shannon entropy transfer technique. Investigation of the “template” rotation rate suggests a probable coincidence with the 27-day Bartels rotation period.

Magnetic Field Geometry and Composition Variation in Slow Solar Winds: The Case of Sulfur.

We present an examination of the first ionization potential (FIP) fractionation scenario, invoking the ponderomotive force in the chromosphere and its implications for the source(s) of slow-speed solar winds by using observations from The Advanced Composition Explorer (ACE). Following a recent conjecture that the abundance enhancements of intermediate FIP elements, S, P, and C, in slow solar winds can be explained by the release of plasma fractionated on open fields, though from regions of stronger magnetic field than usually associated with fast solar wind source regions, we identify a period in 2008 containing four solar rotation cycles that show repeated pattern of sulfur abundance enhancement corresponding to a decrease in solar wind speed. We identify the source regions of these slow winds in global magnetic field models, and find that they lie at the boundaries between a coronal hole and its adjacent active region, with origins in both closed and open initial field configurations. Based on magnetic field extrapolations, we model the fractionation and compare our results with element abundances measured by ACE to estimate the solar wind contributions from open and closed fields, and to highlight potentially useful directions for further work.

갈릴레오의 흑점 연구와 태양 자전 논증

This paper examines how Galileo Galilei (1564-1642), a mathematician and philosopher from Florence, proved the solar rotation. By analyzing his works Letters on the Sunspots and Discourse on Bodies in Water, this paper argues that Galileo could reach his conclusion by introducing substantial evidence from natural philosophy as well as from the mixed mathematical sciences. This contradicts previous researches that suggest that Galileo supported his argument on solar rotation only through observations of sunspots and mathematical reasoning based on them. The natural philosophical elements Galileo introduced were the analogy between the Earth and the Sun that he drew using the then popular idea of fluid heaven, his idea of a fluid-like solar “atmosphere” that included sunspots, and his theory of matter. In making the argument for solar rotation, Galileo blurred the strict disciplinary boundary that had existed between mixed mathematics and natural philosophy. Galileo’s solar rotation was the product of his hybrid practice, by which he crisscrossed the boundaries between the two disciplines, combining elements of mixed mathematics with those of natural philosophy.

Signature of the 27-day oscillation in the MLT tides and its relation with solar radiation at low latitudes

The modulation of the dominant atmospheric tides (i.e. diurnal, semidiurnal and terdiurnal) in the mesosphere and lower thermosphere (MLT) is investigated using long-term meteor wind database from three Southern hemispheric low-latitude locations, São João do Cariri (7.4° S, 36.5° W), Cachoeira Paulista (22.7° S, 45° W) and Santa Maria (29.7° S, 53.7° W). The spectral analysis reveals an evident and intermittent signature of a 27-day oscillation in the tidal amplitudes. Relationship between the 27-day tidal modulation in the MLT and solar rotation is looked into utilizing solar UV flux (Lyman-α) that indicates a conspicuous linkage of the tides with the solar short-term variability. The strong correlation between the solar variability and tidal modulation in the concerned period with positive lags at certain intervals may indicate predominate solar influence on the MLT tides. Potential involvement of the lower, middle and upper atmospheric dynamics and chemistry to support the observed oscillation feature is deemed plausible.

Power spectra of solar brightness variations at various inclinations

Context. Magnetic features on the surfaces of cool stars lead to variations in their brightness. Such variations on the surface of the Sun have been studied extensively. Recent planet-hunting space telescopes have made it possible to measure brightness variations in hundred thousands of other stars. The new data may undermine the validity of setting the sun as a typical example of a variable star. Putting solar variability into the stellar context suffers, however, from a bias resulting from solar observations being carried out from its near-equatorial plane, whereas stars are generally observed at all possible inclinations. Aims. We model solar brightness variations at timescales from days to years as they would be observed at different inclinations. In particular, we consider the effect of the inclination on the power spectrum of solar brightness variations. The variations are calculated in several passbands that are routinely used for stellar measurements. Methods. We employ the surface flux transport model to simulate the time-dependent spatial distribution of magnetic features on both the near and far sides of the Sun. This distribution is then used to calculate solar brightness variations following the Spectral And Total Irradiance REconstruction approach. Results. We have quantified the effect of the inclination on solar brightness variability at timescales down to a single day. Thus, our results allow for solar brightness records to be made directly comparable to those obtained by planet-hunting space telescopes. Furthermore, we decompose solar brightness variations into components originating from the solar rotation and from the evolution of magnetic features.

Inflection point in the power spectrum of stellar brightness variations

Context. Young and active stars generally have regular, almost sinusoidal, patterns of variability attributed to their rotation, while the majority of older and less active stars, including the Sun, have more complex and non-regular light curves, which do not have clear rotational-modulation signals. Consequently, the rotation periods have been successfully determined only for a small fraction of the Sun-like stars (mainly the active ones) observed by transit-based planet-hunting missions, such as CoRoT, Kepler, and TESS. This suggests that only a small fraction of such systems have been properly identified as solar-like analogues. Aims. We aim to apply a new method of determining rotation periods of low-activity stars, such as the Sun. The method is based on calculating the gradient of the power spectrum (GPS) of stellar brightness variations and identifying a tell-tale inflection point in the spectrum. The rotation frequency is then proportional to the frequency of that inflection point. In this paper, we compare this GPS method to already-available photometric records of the Sun. Methods. We applied GPS, auto-correlation functions, Lomb-Scargle periodograms, and wavelet analyses to the total solar irradiance (TSI) time series obtained from the Total Irradiance Monitor on the Solar Radiation and Climate Experiment and the Variability of solar IRradiance and Gravity Oscillations experiment on the SOlar and Heliospheric Observatory missions. We analysed the performance of all methods at various levels of solar activity. Results. We show that the GPS method returns accurate values of solar rotation independently of the level of solar activity. In particular, it performs well during periods of high solar activity, when TSI variability displays an irregular pattern, and other methods fail. Furthermore, we show that the GPS and light curve skewness can give constraints on facular and spot contributions to brightness variability. Conclusions. Our results suggest that the GPS method can successfully determine the rotational periods of stars with both regular and non-regular light curves.

Nearly Century-scale Variation of the Sun’s Radius

Abstract The Kodaikanal Archive Program (India) is now available to the scientific community in digital form as daily digitized solar white light pictures, from 1923 to 2011. We present here the solar radius data, obtained after a painstaking effort to remove all effects that contribute to the error in their measurements (limb darkening, distortion of the objective lens, refraction, other instrumental effects, etc.). These data were analyzed to reveal any significant periodic variations, after applying a multi-taper method with red noise approximation and the Morlet wavelet transform analysis. After removing obvious periodic variations (such as solar rotation and Earth annual rotation), we found a possible cycle variation at 11.4 yr, quasi biennial oscillations at 1.5 and 3.8 yr, and Rieger-type periodicity at ≈159, 91, and 63 days. Another yr periodicity (as a mean) resulting from two other main periodicities detected at 6.3–7.8 yr can be identified as an atmospheric component. The detrending data show, over a mean radius of , a residual of less than ≈(−)1 mas over the time period of analysis: if not spurious, this estimate indicates a faint decline, but probably confirms more the constancy of the solar diameter during the considered ranging time, within instrumental and methodological limits. The Kodaikanal long quality observations contribute to international efforts to bring past solar data measurements to the community to further explore issues, for instance, those of the luminosity/radius properties that could be used to pinpoint the “seat of the solar cycle.”

De-noising SDO/HMI Solar Magnetograms by Image Translation Method Based on Deep Learning

Abstract In astronomy, long-exposure observations are one of the important ways to improve signal-to-noise ratios (S/Ns). In this Letter, we apply a deep-learning model to de-noise solar magnetograms. This model is based on a deep convolutional generative adversarial network with a conditional loss for image-to-image translation from a single magnetogram (input) to a stacked magnetogram (target). For the input magnetogram, we use Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) line-of-sight magnetograms at the center of the solar disk. For the target magnetogram, we make 21-frame-stacked magnetograms, taking into account solar rotation at the same position. We train a model using 7004 pairs of the input and target magnetograms from 2013 January to 2013 October. We then validate the model using 707 pairs from 2013 November and test the model using 736 pairs from 2013 December. Our results from this study are as follows. First, our model successfully de-noises SDO/HMI magnetograms, and the de-noised magnetograms from our model are mostly consistent with the target magnetograms. Second, the average noise level of the de-noised magnetograms is greatly reduced from 8.66 to 3.21 G, and it is consistent with that of the target magnetograms, 3.21 G. Third, the average pixel-to-pixel correlation coefficient value increases from 0.88 (input) to 0.94 (de-noised), which means that the de-noised magnetograms are more consistent with the target ones than the input ones. Our results can be applied to many scientific fields in which the integration of many frames (or long-exposure observations) are used to improve the S/N.

Inference of Solar Rotation from Perturbations of Acoustic Mode Eigenfunctions

Abstract Today’s picture of the internal solar rotation rate profile results essentially from helioseismic analyses of frequency splittings of resonant acoustic waves. Here we present another, complementary estimation of the internal solar rotation rate using the perturbation of the shape of the acoustic waves. For this purpose, we extend a global helioseismic approach developed previously for the investigation of the meridional flow to work on the components of the differential rotation. We discuss the effect of rotation on mode eigenfunctions and the observables based thereon. Based on a numerical study using a simulated rotation rate profile, we tailor an inversion approach and also consider the case of the presence of an additional meridional flow. This inversion approach is then applied to data from the Michelson Doppler Imager (MDI) on board the Solar Heliospheric Observatory and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory. In the end, rotation rate profiles estimated from eigenfunction perturbation and frequency splittings are compared. The rotation rate profiles from the two different approaches are qualitatively in good agreement, especially for the MDI data. Significant differences are obtained at high latitudes >50° and near the subsurface. The result from HMI data shows larger discrepancies between the different methods. We find that the two global helioseismic approaches provide complementary methods for measuring the solar rotation. Comparing the results from different methods may help to reveal systematic influences that affect analyses based on eigenfunction perturbations, like meridional flow measurements.

Timing Terminators: Forecasting Sunspot Cycle 25 Onset

Recent research has demonstrated the existence of a new type of solar event, the "terminator." Unlike the Sun's signature events, flares and Coronal Mass Ejections, the terminator most likely originates in the solar interior, at or near the tachocline. The terminator signals the end of a magnetic activity cycle at the Sun's equator and the start of a sunspot cycle at mid latitudes. Observations indicate that the time difference between these events is very short, less than a solar rotation, in the context of the sunspot cycle. As the (definitive) start and end point of solar activity cycles the precise timing of terminators should permit new investigations into the meteorology of our star's atmosphere. In this letter we use a standard method in signal processing, the Hilbert transform, to identify a mathematically robust signature of terminators in sunspot records and in radiative proxies. Using a linear extrapolation of the Hilbert phase of the sunspot number and F10.7 solar radio flux time series we can achieve higher fidelity historical terminator timing than previous estimates have permitted. Further, this method presents a unique opportunity to project, from analysis of sunspot data, when the next terminator will occur, May 2020 ($+4$, $-1.5$ months), and trigger the growth of sunspot cycle 25.

Determination of the solar rotation parameters via orthogonal polynomials

Accurate measurements of the solar differential rotation parameters are necessary for understanding the solar dynamo mechanism. We use the orthogonalization process to estimate these parameters. The advantage of the orthogonalization of the data in the tracer motion statistical analysis is outlined. The differential rotation is represented in terms of various types of polynomials. We compare the quality of a set of models of the solar differential rotation using the Akaike information criterion and choose the best one. Applying the proposed method, we studied the solar differential rotation and its North-South asymmetry using observations of coronal holes. A statistical analysis of observations from the Atmospheric Imaging Assembly (AIA) on Solar Dynamics Observatory (SDO) reveals the differential rotation pattern of coronal holes and its North-South asymmetry.

Toward the 1-cm Galileo orbits: challenges in modeling of perturbing forces

Precise orbit determination demands knowledge of perturbing forces acting on the satellites of the Global Navigation Satellite Systems (GNSS). The metadata published by the European GNSS Agency for the Galileo satellites allow for the composition of the analytical box-wing model dedicated for coping with the direct solar radiation pressure (SRP), albedo, and infrared radiation (IR). Based on the box-wing model, we evaluated both the magnitude and the characteristic periods of accelerations caused by all the aforementioned forces. We assess which perturbations can be absorbed by the extended Empirical CODE Orbit Model (ECOM2) and what are the consequences of neglecting higher-order ECOM2 coefficients. In order to evaluate the impact of SRP, albedo, IR, and the navigation antenna thrust, we perform a series of precise Galileo orbit determination strategies for Galileo In-Orbit-Validation (IOV), Full Operational Capability (FOC), and two FOC satellites launched into eccentric orbits. The proposed box-wing model is capable of absorbing approximately 97% of the SRP in the Sun-satellite direction, whereas the rest can be mitigated by an additionally estimated small set of empirical parameters. The purely physical box-wing model does not fully handle satellite misorientation and re-radiation effects, such as Y-bias, solar panel rotation lag, that is the misalignment causing a constant acceleration perpendicular to the solar panel axis and the direction to the Sun. However, the box-wing model is especially crucial in terms of the absorption of the higher-order terms of SRP and stabilizes the orbit solutions during the eclipsing periods. Based on the SLR residual analysis, we found a systematic effect at the level up to 50 mm resulting from the omission of the high-order empirical orbit coefficients. We also found that the impact of the albedo, IR, and transmitter antenna thrust on the Galileo orbits reach the level of 5, 14, and 20 mm, respectively. Eventually, we obtain the overall accuracy of the Galileo-FOC orbits at the level of 22.5 mm, even for the eclipsing period for the solution which considers the box-wing model with the estimation of the constant empirical accelerations.

Quasi-6-day waves in the mesosphere and lower thermosphere region and their possible coupling with the QBO and solar 27-day rotation

By using atmospheric wind data in the mesopause and lower thermosphere (MLT) region, features of seasonal variations in the quasi-6-day wave (6DW) at different latitudes are analyzed, and modulation of the 6DW by the diurnal tide and solar 27-day period is discussed. The data used in the analysis are extracted from a wind dataset collected by a meteor radar chain from December 2008 to November 2017. The meteor radar chain includes four stations, in Mohe, Beijing, Wuhan, and Sanya. Features of seasonal variations in the 6DW indicate that in summer the 6DW is usually strongest during July and August, followed by stronger variations in January and April. At certain altitudes over Wuhan and Sanya, the 6DW is slightly different in different years and altitudes. In our analysis of seasonal variations in the 6DW, we find that it is generally affected by annual oscillations and semiannual oscillations. The annual oscillations of the 6DW in the mid-low latitudes are modulated by the quasibiennial oscillation in the diurnal tide, resulting in seasonal features that are different from those at other latitudes. In addition, the 6DW amplitude at mid-high latitudes has a significant 27-day solar rotation variation, which was prominent in 2016.

Empirical Patterns of High-Energy Particle Dynamics of the Van Allen Radiation Belts

The Van Allen radiation belts consist of megaelectron volt particles trapped in the Earth’s magnetic field mainly with protons at low altitudes and electrons at high altitudes. These concentric, donut-shaped radiation belts are constantly changing due to a variety of physical processes caused by specific types of heliospheric structure. The radiation poses risks for astronauts and spacecraft systems. The understanding of these processes that operate across the universe can help with designs of future space missions as well as the understanding of the universe. The data gathered from the last three months of the Radiation Belt Storm Probes mission (RBSP mission) is examined for patterns and trends in the dynamics of the radiation belts and their relationships with solar activities. From the data, it is shown that the patterns of the high-energy particle dynamics in the belts follow the changes in solar activity. When the Sun’s magnetic field weakens, cosmic rays from deep space are able to carry an increased flux of energetic particles into the solar system. The outer belt exhibits a pattern of electron energization during cycles lasting an average of 27 days, corresponding to the time taken for one solar rotation. The sudden outward shift of the belts on July 19th, 2019 was most likely caused by the shutdown of one of the two Van Allen probes, as the relative position of the probe to the belts changed. Two solar wind streams that arrived from August 27th to the 28th caused the “dropout” event on August 28th, as the contact between the solar wind streams and magnetosphere pushed the magnetosphere’s boundary and enabled the particles outside the shifted boundary to escape into space. A positive polarity coronal hole high speed stream (CH HSS) contributed to the intense September electron re-energization process in the radiation belts starting on September 1st.

Grand Minima in a spherical non-kinematicα2Ω mean-field dynamo model

We present a non-kinematic axisymetricα2Ω mean-field dynamo model in which the completeα-tensor and mean differential rotation profile are both extracted from a global magnetohydrodynamical simulation of solar convection producing cycling large-scale magnetic fields. The nonlinear backreaction of the Lorentz force on differential rotation is the only amplitude-limiting mechanism introduced in the mean-field model. We compare and contrast the amplitude modulation patterns characterizing this mean-field dynamo, to those already well-studied in the context of non-kinematicαΩ models using a scalarα-effect. As in the latter, we find that large quasi-periodic modulation of the primary cycle are produced at low magnetic Prandtl number (Pm), with the ratio of modulation period to the primary cycle period scaling inversely with Pm. The variations of differential rotation remain well within the bounds set by observed solar torsional oscillations. In this low-Pm regime, moderately supercritical solutions can also exhibit aperiodic Maunder Minimum-like periods of strongly reduced cycle amplitude. The inter-event waiting time distribution is approximately exponential, in agreement with solar activity reconstructions based on cosmogenic radioisotopes. Secular variations in low-latitude surface differential rotation during Grand Minima, as compared to epochs of normal cyclic behavior, are commensurate in amplitude with historical inferences based on sunspot drawings. Our modeling results suggest that the low levels of observed variations in the solar differential rotation in the course of the activity cycle may nonetheless contribute to, or perhaps even dominate, the regulation of the magnetic cycle amplitude.