Polar Faculae Research Articles

Using Polar Faculae to Determine the Sun’s High-latitude Rotation Rate. I. Techniques and Initial Measurements

This paper describes a new way of determining the high-latitude solar rotation rate statistically from simultaneous observations of many polar faculae. In this experiment, I extracted frames from a movie made previously from flat-fielded images obtained in the 6767 Å continuum during 1997–1998 February and used those frames to construct spacetime maps from high-latitude slices of the favorably oriented south polar cap. These maps show an array of slanted tracks whose average slope indicates the east–west speed of faculae at that latitude, λ s . When the slopes are measured and plotted as a function of latitude, they show relatively little scatter ∼ 0.01–02 km s−1 from a straight line whose zero-speed extension passes through the Sun’s south pole. This means that the speed, v(λ s ), and the latitudinal radius, R⊙cosλs , approach 0 at the same rate, so that their ratio gives a nearly constant synodic rotation rate ∼8.°6 day−1 surrounding the Sun’s south pole. A few measurements of the unfavorably oriented north polar cap are consistent with these measurements near the south pole.

Shape of the 11-Year Cycle in the Number of Sunspots and Polar Faculae

Shape of the 11-Year Cycle in the Number of Sunspots and Polar Faculae

Application of historic datasets to understanding open solar flux and the 20th-century grand solar maximum. 2. Solar observations

We study historic observations of solar activity from the 20th-century rise towards the peak of the Modern Grand Solar Maximum (MGSM) and compare with observations of the decline that has occurred since. The major difference in available solar observations of the rise and of the fall are accurate magnetograms from solar magnetographs: we here use synthetic magnetograms to interpret the rise and employ historic observations of Polar Crown Filaments to test them and verify their use. We show that eclipse images at sunspot minimum reveal the long-term variation of open flux deduced from geomagnetic observations in Paper 1 (Lockwood et al., 2022). We also make use of polar coronal hole fluxes derived from historic white light images of polar faculae, but have to consider the implications of the fact that these facular images do not tell us the polarity of the field. Given this caveat, the agreement between the polar coronal hole fluxes and the values derived from open flux continuity modelling based on sunspot numbers is extremely good. This comparison indicates that one possible solution to the “open flux problem” is open flux within the streamer belt that potential-based modelling of coronal fields from photospheric fields is not capturing. We take a detailed look at the solar cycle at the peak of the MGSM, cycle 19, and show the variation of the polar coronal hole fluxes and the inferred poleward flux surges are predictable from the asymmetries in flux emergence in the two hemispheres with implied transequatorial flux transfer and/or “anti-Hale” (or more general “rogue” active region flux) emergence late in the sunspot cycle.

Two New Methods for Counting and Tracking the Evolution of Polar Faculae

Polar faculae are the footpoints of magnetic-field lines near the Sun’s poles that are seen as bright regions along the edges of granules. The time variation in the number of polar faculae has been shown to correlate with the strength of the polar magnetic field and to be a predictor of the subsequent solar cycle. Due to the small size and transient nature of these features, combined with different techniques and observational factors, previous counts of polar faculae differ in magnitude. Further, there were no scalable techniques to measure the statistical properties of the faculae, such as the variation of the facular lifetime with time or solar activity. Using data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), we present two new methods for tracking faculae and measuring their properties. In the first, we calculate the pixel-by-pixel standard deviation of the HMI continuum intensity images over one day, visualizing the faculae as streaks. The lifetime of the facula is found by dividing the angular length of the streaks by the latitude-dependent rotation rate. We apply this method to the more visible pole each day for a week every six months, from September 2010 to March 2021. Combining all of the measured facular lifetimes provides a statistical distribution with a mean of 6.0 hours, a FWHM of 5.4 hours, and a skew towards longer lifetimes, with some faculae lasting up to 1 day. In the second method, we overlay images of the progressive standard deviation with the HMI magnetogram to show the close relationship between the facular candidates and the magnetic field. The results of this method allow us to distinguish between motion due to the Sun’s rotation and “proper motion” due to faculae moving across the Sun’s surface, confirming that faculae participate in convective motions at the poles. Counts of polar faculae using both methods agree with previous counts in their variation with the solar cycle and the polar magnetic field. These methods can be extended to automate the identification and measurement of other properties of polar faculae, which would allow for daily measurements of all faculae since SDO began operation in 2010.

The Polar Precursor Method for Solar Cycle Prediction: Comparison of Predictors and Their Temporal Range

Abstract The polar precursor method is widely considered to be the most robust physically motivated method to predict the amplitude of an upcoming solar cycle. It uses indicators of the magnetic field concentrated near the poles around the sunspot minimum. Here, we present an extensive analysis of the performance of various such predictors, based on both observational data (Wilcox Solar Observatory (WSO) magnetograms, Mount Wilson Observatory polar faculae counts, and Pulkovo A(t) index) and outputs (polar cap magnetic flux and global dipole moment) of various existing flux transport dynamo models. We calculate Pearson correlation coefficients (r) of the predictors with the next cycle amplitude as a function of time measured from several solar cycle landmarks: setting r = 0.8 as a lower limit for acceptable predictions, we find that observations and models alike indicate that the earliest time when the polar predictor can be safely used is 4 yr after the polar field reversal. This is typically 2–3 yr before the solar minimum and about 7 yr before the predicted maximum, considerably extending the usual temporal scope of the polar precursor method. Reevaluating the predictors another 3 yr later, at the time of the solar minimum, further increases the correlation level to r ≳ 0.9. As an illustration of the result, we determine the predicted amplitude of Cycle 25 based on the value of the WSO polar field at the now official minimum date of 2019 December as 126 ± 3. A forecast based on the value in early 2017, 4 yr after the polar reversal would have only differed from this final prediction by 3.1 ± 14.7%.

Prediction of the amplitude of solar cycle 25 using polar faculae observations

Based on the monthly number of polar faculae, a forecast of the amplitude of solar cycle 25 (SC25) is provided, as well as a prediction of the number of solar flares. Faculae near both solar poles have been visually observed using a commercial off-the-shelf 20 cm Schmidt-Cassegrain telescope since 1995. The monthly averages were corrected for varying seeing conditions and the heliographic latitude of the center of the solar diskB0. From the deduced relationship between the smoothed number of monthly polar faculae during the solar cycle minimum, and the subsequent maximum of the monthly sunspot number, a prediction has been made for the amplitude of the next solar cycle. The methodology used can be considered as a precursor technique. The expected number of M- and X-class flares was calculated based on a statistical approach. The maximum of SC25 is predicted to be 118 ± 29, of similar strength than the previous SC24. Also the number of M5 or stronger flares is expected to be comparable to that of the previous solar cycle.

Polar and Low-Latitude Faculae in Activity Cycles 23–24

Polar and low-latitude faculae were identified in daily images based on white-light observations from the MDI (1996–2011) and SOHO (2010–2019) space observatories. The boundaries of the faculae were combined with magnetic field observations at the closest possible instant of observation. The time and latitude distributions, as well as other properties of polar and low-latitude faculae, were analyzed. The resulting data on polar faculae were supplemented with observational data from Mitaka Observatory (Japan) for the period of 1951–1999. Thus, we compiled a summary series of polar activity for the period of 1951–2019. The distributions of polar faculae by area and magnetic field intensity are considered. The maximum distribution of the facula area at latitudes above θ > 55° occurs at values of approximately 6–10 mhs. The magnetic field of polar faculae has a maximum of B ~ 70–100 G. The amplitude of polar activity at the minimum in the 25th cycle approximately matches the amplitude in the 24th cycle. It can be expected that the amplitude of the sunspot activity cycle will be close to that of cycle 24.

The magnetic fine structure of the Sun’s polar region as revealed by Sunrise

Context. Polar magnetic fields play a key role in the solar magnetic cycle and they are the source of a significant portion of the interplanetary magnetic field. However, observations of the poles are challenging and hence our understanding of the polar magnetic environment is incomplete. Aims. We deduce properties of small-scale magnetic features in the polar region using high-resolution data and specifically aim to determine the flux per patch above which one magnetic polarity starts to dominate over the other. Methods. We study the high spatial resolution, seeing-free observations of the north solar polar region, obtained with the IMaX instrument on-board the balloon-borne SUNRISE observatory during June 2009, at the solar activity minimum. We performed inversions of the full Stokes vector recorded by IMaX to retrieve atmospheric parameters of the Sun’s polar region, mainly the temperature stratification and the magnetic field vector. Results. We infer kilo-Gauss (kG) magnetic fields in patches harbouring polar faculae, without resorting to a magnetic filling factor. Within these patches we find the maxima of the magnetic field to be near the dark narrow lanes, which are shifted towards the disc centre side in comparison to the maxima in continuum intensity. In contrast, we did not find any fields parallel to the solar surface with kG strengths. In addition to the kG patches, we found the polar region to be covered in patches of both polarities, which have a range of sizes. We find the field strength of these patches to increase with increasing size and flux, with the smaller patches showing a significant dispersion in field strength. The dominating polarity of the north pole during this phase of the solar cycle is found to be maintained by the larger patches with fluxes above 2.3 × 1017 Mx.

Spatial distribution of quasi-biennial oscillations in high-latitude solar activity

ABSTRACT Quasi-biennial oscillations (QBOs) are considered to be a fundamental mode of solar magnetic activity at low latitudes (≤50°). However, the evolutionary aspect and the hemispheric distribution of solar QBOs at high latitudes (≥60°) are rarely studied. Here, we apply a relatively novel time-frequency analysis technique, called the synchrosqueezed wavelet transform, in order to extract the main components of the polar faculae in the Northern and Southern hemispheres for the time interval from 1951 August to 1998 December. We note the following. (i) Apart from the 22-yr Hale cycle, the 17-yr extended activity cycle and the 11-yr Schwabe cycle, QBOs have been estimated as a prominent time-scale of solar magnetic activity at high latitudes. (ii) The QBOs of the polar faculae are coherent in the two hemispheres, but the temporal (phase) and the spatial (amplitude) variations of solar QBOs occur unevenly on both hemispheres. (iii) For the 11-yr period mode, this begins in the Northern hemisphere three months earlier than in the Southern hemisphere. Moreover, the spatial and temporal distributions of the hemispheric QBOs differ from those of the 11-yr Schwabe cycle mode in the two hemispheres. Our findings could be helpful to improve our knowledge of the physical origin of the spatial distribution of solar QBOs at high latitudes, and could also provide more constraints on solar dynamo models introduced to characterize the different components of the solar magnetic activity cycle.

Characteristic Time Scales of Decadal to Centennial Changes in Global Surface Temperatures Over the Past 150 Years

AbstractWe apply singular spectral analysis (SSA) to series of monthly mean values of surface air temperatures T, International sunspot number (ISSN), and polar faculae PF (1850–2017 for T and ISSN). The efficiency of the SSA algorithm that we use has been regularly improved. For the T, ISSN, and PF series, the SSA eigenvalues and first components are shown with their Fourier spectrum. Components of T, ISSN, or PF share similar periods. Most are found in solar activity. The ~22‐ and ~11‐year components are modulated and drift in phase, reflecting slight differences in spectra. On the shorter‐period side, components at ~9, ~5.5, and ~4.7 years are in good agreement. They have been identified in solar activity. The 60‐year component is prominent in T. It is not immediately apparent in ISSN but can be extracted with an appropriate choice of SSA window. Other types of data allow one to explore longer periods and confirm climatic variations at ~60, ~35, and ~22 years and at 50–150 and 200–500 years. When we consider a longer ISSN series starting in 1700 and recalculate the SSA first component, the trends of solar activity and temperature over the time span from 1850 to 2017 are very similar, with slower rise before 1900 and after the late 1900s, separating a faster rise in much of the twentieth century. These trends, extracted over only 150 years, could be parts of longer, multicentennial changes in solar activity. Much of the variability of surface temperatures could be linked to the Sun.

Singular Spectral Analysis of the aa and Dst Geomagnetic Indices

AbstractWe apply singular spectrum analysis in order to identify trends and quasi‐periodic oscillations in the aa and Dst series of geomagnetic activity. We also analyze the sunspot number International SunSpot Number (ISSN) and the number of polar faculae Polar Faculae (PF). Singular spectrum analysis provides the eigenvalues and therefore trends and oscillatory components of the four series. ISSN is dominated by a trend (the Gleissberg cycle), followed by 10.6, 35.5 years, two ~8‐year components, 21.4 and 5.3 year. aa shows the same trend, a ~47‐year component, then 10.8, 32.3, 21.8, and a series of three close components at 10.6, 12.2, and 9.2 years, followed by a 6 month seasonal component. PF is dominated by the 20.7‐year period, followed by 10.2, 8.3, 41, and 31 years, then a 5.2 year component. Dst is dominated by a trend, then a strong 6‐month component; next are found a 47‐year component, the 10.6 years and a second seasonal line at 1 year. The ~22‐, ~11‐, and ~5.5‐year components are common to the four indices. These “pseudo harmonic” components are evidence of solar activity. Singular spectrum analysis identifies components that vary in frequency and amplitude. The phase relationships of any two components over time can be studied in detail. An illustration is given by the remarkable phase coherency of the 5.3‐year component. But the components are neither truly periodical nor exact multiples of each other. These differences reflect the complex mechanisms that govern solar‐terrestrial relationships.

A Solar Signature in Many Climate Indices

AbstractWe first apply singular spectrum analysis (SSA) to the international sunspot number (1849–2015) and the count of polar faculae (1906–2006). The SSA method finds 22‐, 11‐, and 5.5‐year components as the first eigenvectors of these solar activity proxies. We next apply SSA to the 10 Madden‐Julian oscillation (MJO; 1978–2016) indices. The first, most intense component SSA finds in all MJO indices has either a period of 5.5 or 11 years. The longer‐term modulation of amplitude is on the order of one third of the total variation. The 5.5‐year SSA component 1 of most MJO indices moreover follows the decreasing amplitude of solar cycles. We then apply SSA to climate indices Pacific Decadal Oscillation, El Nino Southern Oscillation precipitation index, Arctic Oscillation, Atlantic Multidecadal oscillation, Tropical Southern Atlantic oscillation, Western Hemisphere Warm Pool, and Brazil and Sahel rainfalls. We find that the first SSA eigenvectors are all combinations of rather pure 11, 5.5, and 3.6‐year pseudo‐cycles. The 5.5‐year component is frequently observed and is particularly important and sharp in the series in which it appears. All these periods have long been attributed to solar activity, and this by itself argues for the existence of a strong link between solar activity and climate. The mechanisms of coupling must be complex and probably nonlinear but they remain to be fully understood (UV radiation, solar wind, and galactic cosmic rays being the most promising candidates). We propose as a first step a Kuramoto model of nonlinear coupling that generates phase variations compatible with the observed ones.

Applications of Information Theory in Solar and Space Physics.

Characterizing and modeling processes at the sun and space plasma in our solar system are difficult because the underlying physics is often complex, nonlinear, and not well understood. The drivers of a system are often nonlinearly correlated with one another, which makes it a challenge to understand the relative effects caused by each driver. However, entropy-based information theory can be a valuable tool that can be used to determine the information flow among various parameters, causalities, untangle the drivers, and provide observational constraints that can help guide the development of the theories and physics-based models. We review two examples of the applications of the information theoretic tools at the Sun and near-Earth space environment. In the first example, the solar wind drivers of radiation belt electrons are investigated using mutual information (MI), conditional mutual information (CMI), and transfer entropy (TE). As previously reported, radiation belt electron flux (Je) is anticorrelated with solar wind density (nsw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed mainly to the Je(t + 2 days) correlation with solar wind velocity (Vsw)(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time <24 h, suggesting that the loss mechanism due to nsw or solar wind dynamic pressure has to start operating in <24 h. Nonstationarity in the system dynamics is investigated using windowed TE. The triangle distribution in Je(t + 2 days) vs. Vsw(t) can be better understood with TE. In the second example, the previously identified causal parameters of the solar cycle in the Babcock–Leighton type model such as the solar polar field, meridional flow, polar faculae (proxy for polar field), and flux emergence are investigated using TE. The transfer of information from the polar field to the sunspot number (SSN) peaks at lag times of 3–4 years. Both the flux emergence and the meridional flow contribute to the polar field, but at different time scales. The polar fields from at least the last 3 cycles contain information about SSN.

Latitude character and evolution of Gnevyshev gap

The time interval, between two highest peaks of the sunspot maximum, during which activity energy substantially absorbed is called Gnevyshev gap. In this study we focus on mysterious evolution of the Gnevyshev gap by analyzing and comparing the integrated (over the whole Sun) characteristics of magnetic field strength of sunspot groups, soft x-ray flares, filaments or prominences and polar faculae. The time latitude distribution of these solar activities from photosphere to coronal height, for the low (\(\leq50^{\circ}\)) and high (\(\geq50^{\circ}\)) latitudes, shows the way Gnevyshev gap is evolved. The presence of double peak structure is noticed in high latitude (\(\geq50^{\circ}\)) activity. During activity maximum the depression (or valley) appearing, in different activity processes, probably due to shifting, spreading, and transfer of energy from higher to lower latitudes with the progress of solar cycle. The morphology of successive lower latitude zones, considering it as a wave pulse, appears to be modified/scattered, by certain degree due to shifting of magnetic energy to empower higher or lower latitudes.

Analysis of spatially deconvolved polar faculae

Polar faculae are bright features that can be detected in solar limb observations and they are related to magnetic field concentrations. Although there is a large number of works studying them, some questions about their nature as their magnetic properties at different heights are still open. Thus, we aim to improve the understanding of solar polar faculae. In that sense, we infer the vertical stratification of the temperature, gas pressure, line of sight velocity and magnetic field vector of polar faculae regions. We performed inversions of the Stokes profiles observed with Hinode/SP after removing the stray light contamination produced by the spatial point spread function of the telescope. Moreover, after solving the azimuth ambiguity, we transform the magnetic field vector to local solar coordinates. The obtained results reveal that the polar faculae are constituted by hot plasma with low line of sight velocities and single polarity magnetic fields in the kilogauss range that are nearly perpendicular to the solar surface. We also found that the spatial location of these magnetic fields is slightly shifted respect to the continuum observations towards the disc centre. We believe that this is due to the hot wall effect that allows detecting photons that come from deeper layers located closer to the solar limb.

Latitudinal Distribution of Photospheric Magnetic Fields of Different Magnitudes

Photospheric magnetic fields are studied using synoptic maps from 1976 to 2003 produced at the National Solar Observatory, Kitt Peak (NSO/KP). Synoptic maps were averaged over the time interval of nearly three solar cycles (Solar Cycles 21 – 23). The change in the latitudinal distribution was considered for the following groups of magnetic field values: $B = 0 \,\mbox{--}\, 5~\mbox{G}$ , $B = 5 \,\mbox{--}\, 15~\mbox{G}$ , $B = 15 \,\mbox{--}\, 50~\mbox{G}$ , and $B > 50~\mbox{G}$ . Magnetic fields in each of the above groups have common latitudinal distribution features, while for different field groups these features are significantly different. Each of the groups is closely related to a certain manifestation of solar activity. Strong magnetic fields are connected with two types of solar activity: active regions (magnetic fields $B>15~\mbox{G}$ ) that are related to sunspot zones, and polar faculae (magnetic fields $50~\mbox{G} > B > 15~\mbox{G}$ ) that occupy latitudes around $65^{\circ}-75^{\circ}$ . Fields from 5 to 15 G occupy the polar regions and are connected with polar coronal holes (the global solar dipole). Fields of $B<5~\mbox{G}$ occupy a) the equatorial region and b) latitudes $40^{\circ}$ – $60^{\circ}$ .

COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

ABSTRACT The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.

Chaos and fractal properties of solar activity phenomena at the high and low latitudes

The solar magnetic activity is produced by a complex dynamo mechanism and exhibits nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar activity phenomena are of great importance for understanding the nonlinear dynamo actions, especially nonlinear dynamo models. To study the chaotic and fractal properties of solar activity phenomena at the high-and low-latitudes, the polar faculae and sunspot numbers in the time interval from 1952 February to 1998 June are used to investigate their nonlinear dynamical behavior by the recurrence analysis method and Grassberger-Procaccia (G-P) algorithm. Firstly, the monthly average value of both polar faculae and sunspot numbers are smoothed to filter the noisy signal by the 13-point smoothing method. This procedure can keep the original dynamical information. Secondly, the correlation coefficient of these two solar activity indicators is analyzed, and the analysis results indicate that there is a negative correlation between polar faculae and sunspot numbers. To obtain more accurate results, the recurrence quantification analysis (RQA) is used to obtain the average value of the rate of DET by selecting four groups of different parameters. And then, we use the G-P algorithm to draw the correlation integral curve graphs and to obtain the correlation dimension of polar faculae and the sunspot numbers. Finally, the analysis results given by RQA and G-P algorithm are analyzed and compared by advanced statistical method. The main conclusions of this paper are as follows. 1) From a statistical point of view, the chaotic and fractal properties of high-and low-latitudes solar activity are different between in the northern hemisphere and in the southern hemisphere, owing to the fact that the temporal variation of solar activity is closely related to the magnetic field evolution. This result is in agreement with the previous results given by the polar faculae. It should be pointed out that this result is not the main goal of this article, we only reinforce this conclusion by the recurrence analysis and G-P algorithm. 2) The chaotic behaviors of solar magnetic activity at high latitude are stronger than at low latitude. Furthermore, the high-latitude solar activity in the northern hemisphere has the most complex fractal structure. Based on the solar nonlinear dynamo theory, the polar magnetic fields are the seed fields of the solar activity. That is to say, the physical meaning of polar faculae is more important than sunspot numbers. We think that our results are useful for understanding the physical nature of the systematic regularity of solar activity phenomena.

Is the new Grand minimum in progress?

AbstractThe sunspot numbers and polar faculae are analyzed to demonstrate that the current solar activity is close to the Grand minimum. Notably protracted Cycle 23 is found to be similar to the cycles on the eve of the Dalton and Gleissberg–Gnevyshev minima. The polar faculae as proxy of the polar field replicate variations of the sunspot cycle amplitude over the last 100 years. The weak sunspot activity of Cycle 24 is assumed to result in the weak polar field.

On mid-term periodicities of high-latitude solar activity

The mid-term periodicities of polar faculae are studied separately for the total disk, northern and southern hemispheres of the Sun for a time interval from 1951 August to 1998 December. Apart from the 11-year Schwabe cycle which is the fundamental period and is found in all of the three time series, the following prominent results are found: (1) the rotational periodicity of solar activity at high latitudes is approximately from 28 to 32days; (2) a large number of quasi-periods appearing in low-latitude solar activity (annual variation, 1.3–1.7years, quasi-biennial oscillation, and 4–5years) also exist in polar faculae; (3) the periodicities on both hemispheres are not identical.