Sunspot Magnetic Fields Research Articles

Reconciliating the Vertical and Horizontal Gradients of the Sunspot Magnetic Field

In the literature, we found 15 references showing that the sunspot photospheric magnetic field vertical gradient is on the order of 3-4 G/km, with field strength decreasing with height, whereas the horizontal gradient is nine times weaker on the order of 0.4-0.5 G/km. This is confirmed by our recent THEMIS observations. As a consequence, the vanishing of divB→ is not realized. In other words, a loss of magnetic flux is observed with increasing height, which is not compensated for by an increase of the horizontal flux. We show that the lack of spatial resolution, vertical as well as horizontal, cannot be held responsible for the nonvanishing observed divB→. The present paper is devoted to the investigation of this problem. We investigate how the magnetic field is influenced by the plasma anisotropy due to the stratification, which is responsible for an “aspect ratio” between horizontal and vertical typical lengths. On the example of our THEMIS observations, made of two spectral lines formed at two different depths, which enables the retrieval of the three components entering divB→, it is shown that once this aspect ratio is applied, the rescaled divB→ vanishes, which suggests a new methodology for MHD modeling in the photosphere.

Long-period oscillations of sunspots according to simultaneous ground-based and space observations

An analysis of oscillatory processes with periods not shorter than several tens of minutes in three isolated sunspots, which were observed during identical periods in the optical and radio bands, is illustrated. SDO/HMI magnetograms at an interval of 45 s and radio maps at a wavelength of 1.76 cm, obtained using a Nobeyama radioheliograph (NoRH), have been used. The time profiles, which were constructed based on the NoRH and SDO/HMI data, indicate that the oscillations of the radioemission correlate with those of the sunspot magnetic field. The wavelet spectra and cross-wavelet transform reveal common oscillation periods of 30–40, 70–100, and 150–200 min. The identical oscillation periods, found using fundamentally different methods from ground-based and space observations, confirm the solar nature of these oscillations, which can be interpreted as oscillations of a sunspot as a whole.

Long-term variations of solar magnetic fields derived from geomagnetic data

Sunspots are dark spots on the solar surface associated with strong magnetic fields. The number, area, and brightness of sunspots are supposed to reflect the intensity of the solar magnetic fields and are often used as proxies for their long-term variations. However, the correlations between the sunspot parameters and solar magnetic fields are not constant, and the causes and the time profiles of the variations in these correlations are not quite clear. Therefore, the sunspot data alone cannot be used as proxy for deriving the variations of the sunspot magnetic fields for periods when no instrumental measurements are available. But the Earth is a sort of a probe reacting to interplanetary disturbances which are manifestation of the solar magnetic fields, so records of the geomagnetic activity can be used as diagnostic tools for reconstructing past solar magnetic fields evolution. In the present study we combine sunspot and geomagnetic data to estimate the long-term variations of sunspot magnetic fields.

Helioseismology of sunspots: how sensitive are travel times to the Wilson depression and to the subsurface magnetic field?

In order to assess the ability of helioseismology to probe the subsurface structure and magnetic field of sunspots, we need to determine how helioseismic travel times depend on perturbations to sunspot models. Here we numerically simulate the propagation of f, p1, and p2 wave packets through magnetic sunspot models. Among the models we considered, a ~50 km change in the height of the Wilson depression and a change in the subsurface magnetic field geometry can both be detected above the observational noise level. We also find that the travel-time shifts due to changes in a sunspot model must be modeled by computing the effects of changing the reference sunspot model, and not by computing the effects of changing the subsurface structure in the quiet-Sun model. For p1 modes the latter is wrong by a factor of four. In conclusion, numerical modeling of MHD wave propagation is an essential tool for the interpretation of the effects of sunspots on seismic waveforms.

Evidence for partial Taylor relaxation from changes in magnetic geometry and energy during a solar flare

Solar flares are powered by energy stored in the coronal magnetic field, a portion of which is released when the field reconfigures into a lower energy state. Investigation of sunspot magnetic field topology during flare activity is useful to improve our understanding of flaring processes. Here we investigate the deviation of the non-linear field configuration from that of the linear and potential configurations, and study the free energy available leading up to and after a flare. The evolution of the magnetic field in NOAA region 10953 was examined using data from Hinode/SOT-SP, over a period of 12 hours leading up to and after a GOES B1.0 flare. Previous work on this region found pre- and post-flare changes in photospheric vector magnetic field parameters of flux elements outside the primary sunspot. 3D geometry was thus investigated using potential, linear force-free, and non-linear force-free field extrapolations in order to fully understand the evolution of the field lines. Traced field line geometrical and footpoint orientation differences show that the field does not completely relax to a fully potential or linear force-free state after the flare. Magnetic and free magnetic energies increase significantly ~ 6.5-2.5 hours before the flare by ~ 10^31 erg. After the flare, the non-linear force-free magnetic energy and free magnetic energies decrease but do not return to pre-flare 'quiet' values. The post-flare non-linear force-free field configuration is closer (but not equal) to that of the linear force-free field configuration than a potential one. However, the small degree of similarity suggests that partial Taylor relaxation has occurred over a time scale of ~ 3-4 hours.

Cyclic and Long-Term Variation of Sunspot Magnetic Fields

Measurements from the Mount Wilson Observatory (MWO) were used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that presented in Pevtsov et al. (Astrophys. J. Lett. 742, L36, 2011), we selected the sunspot with the strongest measured field strength for each observing week and computed monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500 – 700 gauss (G), but no statistically significant long-term trends. Next, we used the sunspot observations from the Royal Greenwich Observatory (RGO) to establish a relationship between the sunspot areas and the sunspot field strengths for cycles 15 – 19. This relationship was used to create a proxy of the peak magnetic field strength based on sunspot areas from the RGO and the USAF/NOAA network for the period from 1874 to early 2012. Over this interval, the magnetic field proxy shows a clear solar cycle variation with an amplitude of 500 – 700 G and a weaker long-term trend. From 1874 to around 1920, the mean value of magnetic field proxy increases by about 300 – 350 G, and, following a broad maximum in 1920 – 1960, it decreases by about 300 G. Using the proxy for the magnetic field strength as the reference, we scaled the MWO field measurements to the measurements of the magnetic fields in Pevtsov et al. (2011) to construct a combined data set of maximum sunspot field strengths extending from 1920 to early 2012. This combined data set shows strong solar cycle variations and no significant long-term trend (the linear fit to the data yields a slope of − 0.2±0.8 G year−1). On the other hand, the peak sunspot field strengths observed at the minimum of the solar cycle show a gradual decline over the last three minima (corresponding to cycles 21 – 23) with a mean downward trend of ≈ 15 G year−1.

Magnetic field variations and spatial configurations of long-period sunspot oscillations according to the SOHO data

The phenomenon of long-period sunspot oscillations with periods from several tens to a thousand minutes is studied using data on the magnetic field strength and sunspot coordinates obtained based on the SOHO MDI data. It has been indicated that oscillations of the sunspot magnetic field strength are related to relative and absolute horizontal oscillation modes, as a result of which certain limitations are imposed on the interpretation of the phenomenon.

Synchronism of long-period oscillations of the magnetic field in sunspots

It is shown that long-period (T = 10–20 h) oscillations of the magnetic field in sunspots, combined in bipolar groups, are excited synchronously in the main and tail spots of a group. At the same time, there is no correlation between long-period oscillations of the field of sunspots which are in different active regions, i.e., spaced sunspots oscillate independently. This fact eliminates the question about the apparatus nature of the oscillations of interest (if there is an artifact, oscillations of all sunspots on the visible solar hemisphere would be synchronous!). High-resolution (0.5 angular seconds per pixel) MDI(SOHO) data show a high correlation between long-period oscillations of the magnetic field at isolated points of the sunspot shadow. This points to the fact that the sunspot shadow participates in long-period oscillations as a quite integral physical formation.

THE COSMIC-RAY INTENSITY NEAR THE ARCHEAN EARTH

We employ three-dimensional state of the art magnetohydrodynamic models of the early solar wind and heliosphere and a two-dimensional model for cosmic ray transport to investigate the cosmic ray spectrum and flux near the Archean Earth. We assess how sensitive the cosmic ray spectrum is to changes in the sunspot placement and magnetic field strength, the large scale dipole magnetic field strength, the wind ram pressure, and the Sun's rotation period. Overall, our results confirm earlier work that suggested the Archean Earth would have experienced a greatly reduced cosmic ray flux than is the case today. The cosmic ray reduction for the early Sun is mainly due to the shorter solar rotation period and tighter winding of the Parker spiral, and to the different surface distribution of the more active solar magnetic field. These effects lead to a global reduction of the cosmic ray flux at 1AU by up to two orders of magnitude or more. Variations in the sunspot magnetic field have more effect on the flux than variations in the dipole field component. The wind ram pressure affects the cosmic ray flux through its influence on the size of the heliosphere via the pressure balance with the ambient interstellar medium. Variations in the interstellar medium pressure experienced by the solar system in orbit through Galaxy could lead to order of magnitude changes in the cosmic ray flux at Earth on timescales of a few million years.

Turbulent effects of sunspot magnetic field reconstruction

We study the effects of two-dimensional turbulence generated in sunspot umbra due to strong magnetic fields and Alfven oscillations excited in sunspots due to relatively weak magnetic fields on the evolution of sunspots. Two phases of sunspot magnetic field decaying are shown to exist. The initial rapid phase of magnetic field dissipation is due to two-dimensional turbulence. The subsequent slow phase of magnetic field decaying is associated with Alfven oscillations. Our results correspond to observed data that provide evidence for two types of sunspot evolution. The effect of macroscopic diamagnetic expulsion of magnetic field from the convective zone or photosphere toward sunspots is essential in supporting the long-term stability and equilibrium of vertical magnetic flux tubes in sunspots.

DECREASING SUNSPOT MAGNETIC FIELDS EXPLAIN UNIQUE 10.7 cm RADIO FLUX

Infrared spectral observations of sunspots from 1998 to 2011 have shown that on average sunspots changed, the magnetic fields weakened, and the temperatures rose. The data also show that sunspots or dark pores can only form at the solar surface if the magnetic field strength exceeds about 1500 G. Sunspots appear at the solar surface with a variety of field strengths, and during the period from 1998 to 2002 a histogram of the sunspot magnetic fields shows a normal distribution with a mean of 2436 ± 26 G and a width of 323 ± 20 G. During this observing period the mean of the magnetic field distribution decreased by 46 ± 6 G per year, and we assume that as the 1500 G threshold was approached, magnetic fields appeared at the solar surface which could not form dark sunspots or pores. With this assumption we propose a quantity called the sunspot formation fraction and give an analytical form derived from the magnetic field distribution. We show that this fraction can quantitatively explain the changing relationship between sunspot number and solar radio flux measured at 10.7 cm wavelengths.

Magnetic network elements in solar cycle 23

AbstractIn this report, we present our recent effort to understand the cyclic behavior of network magnetic elements based on the unique database from full-disk observations provided by Michelson Doppler Imager on board the Solar and Heliospheric Observatory in the interval including the entire cycle 23. The following results are unclosed. (1) The quiet regions dominate the solar magnetic flux for about 8 years in solar cycle 23, and from the solar minimum to maximum they contribute (0.94-1.44)×1023Mx flux to the solar photosphere. In the entire cycle 23, the magnetic flux of the quiet regions is 1.12 times that of active regions. The occupation ratio of quiet region flux equally characterizes the course of a solar cycle. (2) With the increasing magnetic flux per element, the variations of numbers and total flux of the network elements show three-fold scenario: no-correlation, anti-correlation, and correlation with sunspots, respectively. The anti-correlated elements covering the range of (3-32)×1018Mx occupy 77% of total element number and 37% of quiet Sun flux. (3) The time-latitude distribution of anti-correlated magnetic elements is out of phase with that of sunspots, while the correlated elements display the similar butterfly diagram of sunspots but with wider latitude distribution. These results imply that the correlated elements are the debris of decayed sunspots, and the source of anti-correlated elements is modulated by sunspot magnetic field.

Principal component analysis of background and sunspot magnetic field variations during solar cycles 21-23

The aim of this paper is to derive the principal components (PCs) in variations of (i) the solar background magnetic field (SBMF), measured by the Wilcox Solar Observatory with low spatial resolution for solar cycles 21–23, and (ii) the sunspot magnetic field (SMF) in cycle 23, obtained by SOHO/MDI. For reduction of the component dimensions, principal component analysis (PCA) is carried out to identify global patterns in the data and to detect pairs of PCs and corresponding empirical orthogonal functions (EOFs). PCA reveals two main temporal PCs in the SBMF of opposite polarities originating in opposite hemispheres and running noticeably off-phase (with a delay of about 2.5 yr), with their maxima overlapping in the most active hemisphere for a given cycle. Their maximum magnitudes are reduced by a factor of 3 from cycle 21 to 23, and overlap in the Northern hemisphere for cycle 21, in the Southern one in cycle 22 and in the Northern one again in cycle 23. The reduction of magnitudes and slopes of the maxima of the SBMF waves from cycle 21 to cycle 23 leads us to expect lower magnitudes of the SBMF wave in cycle 24. In addition, PCA allowed us to detect four pairs of EOFs in the SBMF latitudinal components: the two main latitudinal EOFs attributed to symmetric types and another three pairs of EOFs assigned to asymmetric types of meridional flows. The results allow us to postulate the existence of dipole and quadruple (or triple-dipole) magnetic structures in the SBMF, which vary from cycle to cycle and take the form of two waves travelling off-phase, with a phase shift of one-quarter of the 11 yr period. Similar PC and EOF components were found in temporal and latitudinal distributions of the SMF for cycle 23, revealing polarities opposite to the SBMF polarities, and a double maximum in time or maxima in latitude corresponding to the maxima of the SBMF PC residuals or minima in the SBMF EOFs, respectively. This suggests that the SBMF waves modulate the occurrence and magnitude of the SMF in time and latitude.

CORRELATION BETWEEN THE 22-YEAR SOLAR MAGNETIC CYCLE AND THE 22-YEAR QUASICYCLE IN THE EARTH'S ATMOSPHERIC TEMPERATURE

According to the variation pattern of the solar magnetic field polarity and its relation to the relative sunspot number, we established the time series of the sunspot magnetic field polarity index and analyzed the strength and polarity cycle characteristics of the solar magnetic field. The analysis showed the existence of a cycle with about a 22-year periodicity in the strength and polarity of the solar magnetic field, which proved the Hale proposition that the 11-year sunspot cycle is one-half of the 22-year solar magnetic cycle. By analyzing the atmospheric temperature field, we found that the troposphere and the stratosphere in the middle latitude of both the northern and southern hemispheres exhibited a common 22-year quasicycle in the atmospheric temperature, which is believed to be attributable to the 22-year solar magnetic cycle.

Sunspot oscillations as derived from the SOHO/MDI magnetograms

As a result of processing long (up to 144 h) series of sunspot magnetograms obtained on the SOHO (Solar and Heliospheric Observatory) spacecraft with the MDI (Michelson Doppler Imager) instrument it is shown that the mode with a period of 800–1300 min is a limiting low-frequency oscillation mode of the magnetic field of a sunspot as a whole. Its period is essentially and nonlinearly depends on the sunspot magnetic field strength. In addition to this mode, higher harmonics are also revealed in the sunspot oscillation spectra in the bands 40–45, 60–80, 135–170, 220–250, and 480–520 min. The oscillation power in these bands monotonically and rapidly decreases with increasing frequency, which is characteristic for overtones arising due to the nonlinear nature of oscillations. The limiting oscillation mode stably exists in sunspots for 1.5–2 days, which coincides with the average lifetime of a supergranular cell. The mode with the period of 35–48 h observed in the power spectrum is not an eigen mode of sunspots, because its period is independent of its magnetic field strength. Probably, it occurs as a quasiperiod of an external exciting force caused by disturbances from supergranular cells surrounding the sunspot.

ON MOLECULAR HYDROGEN FORMATION AND THE MAGNETOHYDROSTATIC EQUILIBRIUM OF SUNSPOTS

We have investigated the problem of sunspot magnetohydrostatic equilibrium with comprehensive IR sunspot magnetic field survey observations of the highly sensitive Fe I lines at 15650 \AA\ and nearby OH lines. We have found that some sunspots show isothermal increases in umbral magnetic field strength which cannot be explained by the simplified sunspot model with a single-component ideal gas atmosphere assumed in previous investigations. Large sunspots universally display non-linear increases in magnetic pressure over temperature, while small sunspots and pores display linear behavior. The formation of molecules provides a mechanism for isothermal concentration of the umbral magnetic field, and we propose that this may explain the observed rapid increase in umbral magnetic field strength relative to temperature. Existing multi-component sunspot atmospheric models predict that a significant amount of molecular hydrogen (H2) exists in the sunspot umbra. The formation of H2 can significantly alter the thermodynamic properties of the sunspot atmosphere and may play a significant role in sunspot evolution. In addition to the survey observations, we have performed detailed chemical equilibrium calculations with full consideration of radiative transfer effects to establish OH as a proxy for H2, and demonstrate that a significant population of H2 exists in the coolest regions of large sunspots.

Laboratory determination of Landé factors for the molecular radical FeH

We report laboratory measurements of the Zeeman response of lines in the 0-0 Wing-Ford band of the F-X system ( λ ~ 1 μ m) of FeH, measured in magnetic fields 0.3 – 0.5 Tesla. New Lande factors are used to deduce the magnetic field in sunspots from Stokes V profiles recorded at the solar telescope THEMIS. The magnetic field deduced from atomic lines (Ti, Fe) is slightly higher than that found from FeH.

THE LATITUDE DISTRIBUTION OF SMALL-SCALE MAGNETIC ELEMENTS IN SOLAR CYCLE 23

With the unique data set from full-disk observations provided by Michelson Doppler Imager on board the Solar and Heliospheric Observatory in the interval embodying solar cycle 23, we have found that the cyclic variations of numbers and total flux of these small-scale magnetic elements covering fluxes of (2.9-32.0) Multiplication-Sign 10{sup 18} Mx and (4.27-38.01) Multiplication-Sign 10{sup 19} Mx show anticorrelation and correlation with sunspots, respectively. In this study, the time-latitude distributions of these anticorrelated and correlated elements are analyzed. The following results are disclosed: (1) for the correlated elements, the cyclic variations of the total flux in low-latitude and middle-latitude regions show a longer duration of cyclic maximum phase than that of an active region (AR) in the corresponding latitude region; the total flux of these elements shows the accordant south-north asymmetry with that of AR; the time-latitude distribution of their number displays a similar butterfly diagram but with a latitude distribution that is twice as wide as that of sunspots. (2) For the anticorrelated elements, the time-latitude distribution of number shows a solar cycle variation different from the sunspot butterfly diagram; in each latitude, the distribution of anticorrelated elements always shows the anticorrelated variation with that of sunspots; duringmore » solar cycle 23, the average speed of the peak latitudinal migration for anticorrelated elements reaches 7.5 deg year{sup -1}, almost three times that for sunspots. These results seem to imply that the correlated elements are the debris of decayed sunspots, and the anticorrelated elements have a different source but are affected or modulated by sunspot magnetic field.« less

ON THE FORCE-FREE NATURE OF PHOTOSPHERIC SUNSPOT MAGNETIC FIELDS AS OBSERVED FROMHINODE(SOT/SP)

A magnetic field is force-free if there is no interaction between the magnetic field and plasma in surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. Computation of various magnetic parameters such as magnetic energy, gradient of twist of sunspot fields and any kind of extrapolations, heavily hinge on the force-free approximation of the photospheric sunspot magnetic fields. Thus it is important to inspect the force-freeness of sunspot fields. The force-freeness of sunspot magnetic fields has been examined earlier by some researchers ending with incoherent results. Accurate photospheric vector field measurements with high spatial resolution are required to inspect the force-free nature of sunspots. We use several such vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter aboard the Hinode. Both necessary and sufficient conditions for force-freeness are examined by checking global and local nature of magnetic forces over sunspots. We find that the sunspot magnetic fields are not much away from force-free configuration, although they are not completely force-free on the photosphere. The umbral and inner penumbral fields are more force-free than the middle and the outer penumbral fields. During their evolution, sunspot magnetic fields are found to maintain their proximity to force-free behaviour. Although a dependence of net Lorentz force components is seen on the evolutionary stages of the sunspots, we don't find a systematic relationship between the nature of sunspot fields and associated flare activity. Further, we examine whether the fields at photosphere follow linear or non-linear force free conditions. After examining this in various complex and simple sunspots we conclude that,in either case,the photospheric sunspot fields are closer to satisfy non linear force-free field approximation.

LONG-TERM TRENDS IN SUNSPOT MAGNETIC FIELDS

Recent studies indicate that a maximum field strength in sunspots shows a gradual decrease over the last several years. By extrapolating this trend, Penn & Livingston proposed that sunspots may completely disappear in the not-so-distant future. To verify these recent findings, we employ historic synoptic data sets from seven observatories in the former USSR covering the period from 1957 to 2011 (from 1998 to 2011, observations were taken at only one observatory). Our results indicate that while sunspot field strengths rise and wane with solar cycle, there is not a long-term trend that would suggest a gradual decrease in sunspot magnetic fields over the four and a half solar cycles covered by these observations.