Enigmas in measurements of solar magnetic field

The mean magnetic field (MMF) of the photosphere of the Sun as a star was measured in 2001?C2010 at the Crimean Astrophysical Observatory using two Fe I absorption lines with ?? = 524.7 nm and ?? = 525.0 nm. The regression coefficient b for 1054 pairs of daily values measured simultaneously on both lines equals 0.82 (a correlation coefficient is 0.94; magnetic field strengths determined by the line with ?? = 525.0 nm are lower than those for the line with ?? = 524.7 nm). However, the b value varied significantly along with phases of the 11-year cycle from 0.88 in 2003 to 0.49 in 2009. It is difficult to ascribe these variations to purely instrumental or solar causes. Moreover, the semiannual value of b decreased with the decrease in the absolute strength of the MMF, which contradicts the model of thin magnetic flux ropes of the photosphere. Similar behavior of b was also observed in the comparison of MMF measured at the Crimean Astrophysical Observatory and Stanford by the line with ?? = 525.0 nm. The inconsistency of the results obtained by these two iron lines on different instruments has been noted. It has been concluded that the variance in and odd behavior of b are predetermined not only by the instrument and the Sun (by the so-called fine structure of the photosphere field), but also by the act of measuring. When recording solar (and stellar) magnetic fields and modeling atmospheric processes, quantum effects have to be taken into account, such as nonlocality, indistinguishability, and the entanglement of photons, as well as that a photon only acquires its properties at the exact moment of its detection. The best approximation to reality can be achieved by averaging the MMF measurements carried out with different magnetographs and in different spectral lines.     

On Multi-Line Spectro-Polarimetric Diagnostics of the Quiet Sun’s Magnetic Fields

On the long way to establish reliable physical properties of the solar atmosphere from different kinds of magnetic field measurement, significant progress has been achieved, but many important issues are still waiting for solution. This is essential for the investigation of weak magnetic fields of the quiet Sun, which usually cover most of the solar surface. Weak magnetic fields significantly contribute to the formation of the interplanetary magnetic field. The problem of reliable diagnostics of such fields hardly ever has a simple solution using only single spectral line observations. A better chance is given by multi-spectral line spectro-polarimetric observations, especially with lines having very different properties. In the present study, we use simultaneous high-precision Stokes-meter measurements of the quiet solar magnetic fields in 15 lines in the vicinity of Fe?i?525.0?nm. These measurements cover the whole range of heliocentric distances. Magnetic field strength ratios of different spectral lines with respect to Fe?i 525.0?nm vary between 1.07 and 2.12. This ratio depends also on the heliocentric position, moving closer to the limb it decreases and approaches values of about unity in most cases. To interpret the observations, different model approaches are compared. SIR-inversions (Stokes Inversion based on Response functions) with a two-component atmospheric model approach reproduce the basic observables much better than with one-component atmospheres. Our best fits are connected with field strengths of 1?–?2?kG and filling factors of less than five percent. To check the justification for the recent re-calibration of the data from the Michelson Doppler Imager (MDI) onboard SOHO, we carried out a numerical experiment, and we confirm our former conclusion that there is no need for such a re-calibration.     

SIR: An Inversion Technique of Spectral Lines

During the last years, inversion techniques have become one of the most powerful tools to obtain, from spectropolarimetric data, the stratification of physical quantities (temperature, pressure, velocity fields, magnetic field, etc.) describing different structures in the solar atmosphere. The SIR code (Stokes Inversion based on Response functions), developed at the Instituto de Astrofísica de Canarias (IAC), is internationally acknowledged nowadays at the most sophisticated and accurate inversion method. The main results derived from its application to the study of the solar photosphere, are presented. Two recent extensions are reported as well: inversion under NLTE conditions, and the MISS code (Multiline Inversion of Stellar Spectra). This revised version was published online in July 2006 with corrections to the Cover Date.     

Night‐time science with large solar telescopes: The magnetic Sun through time

Today the Sun has a regular magnetic cycle driven by a dynamo action. But how did this regular cycle develop? How do basic parameters such as rotation rate, age, and differential rotation affect the generation of magnetic fields? Zeeman Doppler imaging (ZDI) is a technique that uses high‐resolution observations in circularly polarised light to map the surface magnetic topology on stars. Utilising the spectropolarimetric capabilities of future large solar telescopes it will be possible to study the evolution and morphology of the magnetic fields on a range of Sun‐like stars from solar twins through to rapidly‐rotating active young Suns and thus study the solar magnetic dynamo through time. In this article I discuss recent results from ZDI of Sun‐like stars and how we can use night‐time observations from future solar telescopes to solve unanswered questions about the origin and evolution of the Sun's magnetic dynamo (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Richard Christopher Carrington: Briefly Among the Great Scientists of His Time

We recount the life and career of Richard Christopher Carrington (1826??C?1875) and explore his pivotal relationship with Astronomer Royal George Biddell Airy. Carrington was the pre-eminent solar astronomer of the 19th century. During a ten year span, he determined the position of the Sun??s rotation axis and made the following discoveries: i)?the latitude variation of sunspots over the solar cycle, ii)?the Sun??s differential rotation, and iii)?the first solar flare (with Hodgson). Due to the combined effects of family responsibilities, failure to secure a funded position in astronomy (reflecting Airy??s influence), and ill health, Carrington??s productive period ended when he was at the peak of his powers.     

Large-Scale Magnetic Field of the Sun and Evolution of Sunspot Activity

The evolution of the large-scale magnetic field of the Sun has been studied using an algorithm of tomographic inversion. By analyzing line-of-sight magnetograms, we mapped the radial and toroidal components of the Sun??s large-scale magnetic field. The evolution of the radial and toroidal magnetic field components in the 11-year solar cycle has been studied in a time?Clatitude aspect. It is shown that the toroidal magnetic field of the Sun is causally related to sunspot activity; i.e., the sunspot formation zones drift in latitude and follow the toroidal magnetic fields. The results of our analysis support the idea that the high-latitude toroidal magnetic fields can serve as precursors of sunspot activity. The toroidal fields in the current cycle are anomalously weak and also show a barely noticeable equatorward drift. This behavior of the toroidal magnetic field suggests low activity levels in the current cycle and in the foreseeable future.     

The Whole Heliosphere Interval in the Context of a Long and Structured Solar Minimum: An Overview from Sun to Earth

Throughout months of extremely low solar activity during the recent extended solar-cycle minimum, structural evolution continued to be observed from the Sun through the solar wind and to the Earth. In 2008, the presence of long-lived and large low-latitude coronal holes meant that geospace was periodically impacted by high-speed streams, even though solar irradiance, activity, and interplanetary magnetic fields had reached levels as low as, or lower than, observed in past minima. This time period, which includes the first Whole Heliosphere Interval (WHI 1: Carrington Rotation (CR) 2068), illustrates the effects of fast solar-wind streams on the Earth in an otherwise quiet heliosphere. By the end of 2008, sunspots and solar irradiance had reached their lowest levels for this minimum (e.g., WHI 2: CR 2078), and continued solar magnetic-flux evolution had led to a flattening of the heliospheric current sheet and the decay of the low-latitude coronal holes and associated Earth-intersecting high-speed solar-wind streams. As the new solar cycle slowly began, solar-wind and geospace observables stayed low or continued to decline, reaching very low levels by June??C?July 2009. At this point (e.g., WHI 3: CR 2085) the Sun?CEarth system, taken as a whole, was at its quietest. In this article we present an overview of observations that span the period 2008??C?2009, with highlighted discussion of CRs 2068, 2078, and 2085. We show side-by-side observables from the Sun??s interior through its surface and atmosphere, through the solar wind and heliosphere and to the Earth??s space environment and upper atmosphere, and reference detailed studies of these various regimes within this topical issue and elsewhere.     

What do the solar activity indices represent?

Sunspot number, sunspot area, and radio flux at 10.7 cm are the indices which are most frequently used to describe the long‐term solar activity. The data of the daily solar full‐disk magnetograms measured at Mount Wilson Observatory from 19 January 1970 to 31 December 2012 are utilized together with the daily observations of the three indices to probe the relationship of the full‐disk magnetic activity respectively with the indices. Cross correlation analyses of the daily magnetic field measurements at Mount Wilson observatory are taken with the daily observations of the three indices, and the statistical significance of the difference of the obtained correlation coefficients is investigated. The following results are obtained: (1) The sunspot number should be preferred to represent/reflect the full‐disk magnetic activity of the Sun to which the weak magnetic fields (outside of sunspots) mainly contribute, the sunspot area should be recommended to represent the strong magnetic activity of the Sun (in sunspots), and the 10.7 cm radio flux should be preferred to represent the full‐disk magnetic activity of the Sun (both the weak and strong magnetic fields) to which the weak magnetic fields mainly contribute. (2) On the other hand, the most recommendable index that could be used to represent/reflect the weak magnetic activity is the 10.7 cm radio flux, the most recommendable index that could be used to represent the strong magnetic activity is the sunspot area, and the most recommendable index that could be used to represent the full‐disk magnetic activity of the Sun is the 10.7cm radio flux. Additionally, the cycle characteristics of the magnetic field strengths on the solar disk are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Global Context of Solar Activity During the Whole Heliosphere Interval Campaign

The Whole Heliosphere Interval (WHI) was an international observing and modeling effort to characterize the 3-D interconnected ??heliophysical?? system during this solar minimum, centered on Carrington Rotation 2068, March 20??C?April 16, 2008. During the latter half of the WHI period, the Sun presented a sunspot-free, deep solar minimum type face. But during the first half of CR 2068 three solar active regions flanked by two opposite-polarity, low-latitude coronal holes were present. These departures from the quiet Sun led to both eruptive activity and solar wind structure. Most of the eruptive activity, i.e., flares, filament eruptions and coronal mass ejections (CMEs), occurred during this first, active half of the interval. We determined the source locations of the CMEs and the type of associated region, such as active region, or quiet sun or active region prominence. To analyze the evolution of the events in the context of the global solar magnetic field and its evolution during the three rotations centered on CR 2068, we plotted the CME source locations onto synoptic maps of the photospheric magnetic field, of the magnetic and chromospheric structure, of the white light corona, and of helioseismological subsurface flows. Most of the CME sources were associated with the three dominant active regions on CR 2068, particularly AR 10989. Most of the other sources on all three CRs appear to have been associated with either isolated filaments or filaments in the north polar crown filament channel. Although calculations of the flux balance and helicity of the surface magnetic features did not clearly identify a dominance of one region over the others, helioseismological subsurface flows beneath these active regions did reveal a pronounced difference among them. These preliminary results suggest that the ??twistedness?? (i.e., vorticity and helicity) of subsurface flows and its temporal variation might be related to the CME productivity of active regions, similar to the relationship between flares and subsurface flows.     

Mirror Mode Waves Downstream of a Stream Interaction Region Forward Shock near 1 AU

Mirror mode waves in the solar wind are typically observed not as quasi-periodic sinusoidal signatures, but as trains of nonperiodic structures of two types: magnetic ??peaks?? and magnetic ??dips.?? Some trains of long durations have been called mirror mode storms. In this work we report mirror mode waves downstream of a stream interaction region (SIR) forward shock observed near 1?AU on 7?May 2007 with Solar Terrestrial Relations Observatory (STEREO) and Time History of Events and Macroscale Interactions during Substorms (THEMIS) data. The high-resolution magnetic-field data (0.125-second resolution) from STEREO are scanned to search for magnetic dips and peaks (or upgoing magnetic ??mesas??) in the solar wind. STEREO-A observes a mirror mode storm: the appearance of mirror mode waves (mainly magnetic peaks and upgoing mesas) is simultaneous with the entry into a high-density, high-temperature, and high plasma ?? accompanied by a depressed field region; the magnetic dips survive in the lower plasma-?? region. STEREO-B observes mirror mode waves (mainly magnetic peaks) with different amplitudes and asymmetric forms, which can survive in a low plasma ?? region. THEMIS-D, which was located in the solar wind, also observes mirror mode waves (mainly magnetic peaks and upgoing mesas) as well as an enhanced ion temperature anisotropy (T _????3T _??). The enhanced ion temperature anisotropy and high plasma ?? satisfy the mirror-instability criterion. These observations of STEREO and THEMIS-D show that mirror mode waves can be excited downstream of a SIR forward shock near 1?AU.     

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.     

Inversion of Stokes vector profiles in terms of a 3-component model

Various spectropolarimetric observations show peculiar Stokes profiles that reveal the coexistence of at least two magnetic components in the same resolution element. An example is given by observations of the full Stokes vector in a complex active region performed with the ZIMPOL I Stokes polarimeter. In order to deduce the physical parameters of the observed regions from such measured profiles, we have extended an existing inversion code, so that it can now fit the data with models composed of up to three different atmospheric components. Two of these components are magnetic and may possess different field strengths, field geometries, temperature stratifications, and velocity fields. The third component describes the field free atmosphere surrounding the magnetic features.The so extended inversion code has then been applied to the ZIMPOL I data. In this paper we present and discuss sample fits. The code is able to reproduce the observed complex Stokes profiles with good accuracy and provides physical parameters for both of the coexisting magnetic atmospheres. Inversion tests with a 2-component model (with one magnetic and one non-magnetic component) applied to the same profiles do not reproduce the measurements sufficiently well.     

The Evolution of Barbs of a Polar Crown Filament Observed by SDO

From 16 to 21 August 2010, a northern (???N60) polar crown filament was observed by Solar Dynamics Observatory (SDO). Employing the six-day SDO/AIA data, we identify 69 barbs, and select 58 of them, which appeared away from the western solar limb (???W60), as our sample. We systematically investigate the evolution of filament barbs. Three different types of apparent formation of barbs are detected, including i)?the convergence of surrounding moving plasma condensations, comprised 55.2?% of our sample, ii)?the flows of plasma condensations from the filament, comprised 37.9?%, and iii)?the plasma injections from the neighboring brightening regions, comprised 6.9?%. We also find three different ways that barb disappear, involving: i)?bi-lateral movements (44.8?%), and ii)?outflowing of barb plasma (27.6?%) results in the disappearance of a barb, as well as iii)?disappearance of a barb is associated with a neighboring brightening (27.6?%). The evolution of the magnetic fields, e.g. emergence and cancellation of magnetic flux, may cause the formation or disappearance of the barb magnetic structures. Barbs exchange plasma condensations with the surrounding atmosphere, filament, and nearby brightenings, leading to the increase or drainage of barb material. Furthermore, we find that all the barbs undergo oscillations. The average oscillation period, amplitude, and velocity are 30?min, 2.4?Mm, and 5.7?km?s^?1, respectively. Besides the oscillations, 21 (36?%) barbs manifested sideward motions having an average speed of 0.45?km?s^?1. Small-scale wave-like propagating disturbances caused by small-scale brightenings are detected, and the barb oscillations associated with these disturbances are also found. We propose that the kinematics of barbs are influenced or even caused by the evolution of the neighboring photospheric magnetic fields.     

Simulation of the Unusual Solar Minimum with 3D SIP-CESE MHD Model by Comparison with Multi-Satellite Observations

The observations both near the Sun and in the heliosphere during the activity minimum between solar cycles 23 and 24 exhibit different phenomena from those typical of the previous solar minima. In this paper, we have chosen Carrington rotation 2070 in 2008 to investigate the properties of the background solar wind by using the three-dimensional (3D) Solar?CInterPlanetary Conservation Element/Solution Element Magnetohydrodynamic (MHD) model. We also study the effects of polar magnetic fields on the characteristics of the solar corona and the solar wind by conducting simulations with an axisymmetric polar flux added to the observed magnetic field. The numerical results are compared with the observations from multiple satellites, such as the Solar and Heliospheric Observatory (SOHO), Ulysses, Solar Terrestrial Relations Observatory (STEREO), Wind and the Advanced Composition Explorer (ACE). The comparison demonstrates that the first simulation with the observed magnetic fields reproduces some observed peculiarities near the Sun, such as relatively small polar coronal holes, the presence of mid- and low-latitude holes, a tilted and warped current sheet, and the broad multiple streamers. The numerical results also capture the inconsistency between the locus of the minimum wind speed and the location of the heliospheric current sheet, and predict slightly slower and cooler polar streams with a relatively smaller latitudinal width, broad low-latitude intermediate-speed streams, and globally weak magnetic field and low density in the heliosphere. The second simulation with strengthened polar fields indicates that the weak polar fields in the current minimum play a crucial role in determining the states of the corona and the solar wind.     

Small-scale background magnetic field on the sun in solar cycle 23

Based on SOHO/MDI data (an archive of magnetic maps with a resolution of ～2″), we have investigated the dynamics of the small-scale background magnetic field on the Sun in solar cycle 23. The cyclic variations and surface structure of the background magnetic field have been analyzed using the mean estimates of 〈B〉 and 〈B ²〉 of the observed magnetic field strength B for various solar surface areas and at various B levels. We have established that the cyclic variations of 〈2〉 at latitudes below 30° are essentially similar to those of the total radio flux F _10.7. A significant difference between the background magnetic fields in the northern and southern solar hemispheres persisting throughout the solar cycle has been detected. We have found the effect of background magnetic field growth toward the solar limb and concluded that the transversal component in the background magnetic field is significant. The relatively weak small-scale background magnetic fields are shown to form a special population with its own special laws of cyclic variation.     

Photosphere model of 2N/2M solar flare: July 18, 2000

We investigate the photosphere parameters of a 2N/M2 solar flare that occurred in the NOAA 9077 active area on 18 July, 2000 before its maximum. We use Echelle Zeeman spectrograms obtained in orthogonal circular polarizations by means of a solar spectrograph of the astronomical observatory of Kiev National University, Ukraine (Kurochka, E.V., et. al, 1980). The photosphere is simulated by SIR software (Ruiz Cobo, B. and del Toro Inesta, J.C., 1992). The model of the flare??s photosphere is characterized by a two-component structure, including a magnetic flux tube and its nonmagnetic environment. For both components, we obtain the height distribution of the following parameters: temperature, magnetic field density and line-of-sight velocity. The temperature in the magnetic flux tube increases to approximately 5100 K in the upper photosphere layer of 250?C400 km. The magnetic field intensity decreases sharply from 2600 G (lower photosphere) to 100 G (middle photosphere) with a gradient of about 12 G/km. The model of the nonmagnetic environment differs slightly from the model of undisturbed photosphere.     

Imbalance of magnetic fields on the Sun

Differences of magnetic field flows of “+” and “?” polarities, i.e. the imbalance of magnetic fields for 26 years—from January 1, 1977, to September 30, 2003—are investigated,. The synoptic maps of the longitudinal vector of Sun’s magnetic field strength obtained at the Kitt Peak National Observatory (United States) and kindly given to us by Dr. J. Harvey have served as the initial material. The imbalance of magnetic fields’ cyclicity features and the deviations from the dipole structure of Sun’s magnetic field are determined. The contribution of latitude zones and fields of various strength into the general magnetic flux from the Sun is found. The latter characteristic was compared with the Sun’s mean magnetic field (MMF) obtained from the observations of the Sun as a star (Kotov et al., 2002; Kotov, 2008). The obtained results testify that the imbalance is one of physical characteristics of the Sun. The confirmations of this conclusion are the strict regularities of the Sun’s dipole structure changing; the complicated character of the imbalance cyclicity, i.e., the multiplicity of cycles; the solar nature of MMF changing; and the distinction between two classes of magnetic fields in the imbalance characteristics.     

Investigation of Quasi-periodic Solar Oscillations in Sunspots Based on SOHO/MDI Magnetograms

In this work we study quasi-periodic solar oscillations in sunspots, based on the variation of the amplitude of the magnetic field strength and the variation of the sunspot area. We investigate long-period oscillations between three minutes and ten hours. The magnetic field synoptic maps were obtained from the SOHO/MDI. Wavelet (Morlet), global wavelet spectrum (GWS) and fast Fourier transform (FFT) methods are used in the periodicity analysis at the 95?% significance level. Additionally, the quiet Sun area (QSA) signal and an instrumental effect are discussed. We find several oscillation periods in the sunspots above the 95?% significance level: 3??C?5, 10??C?23, 220??C?240, 340 and 470 minutes, and we also find common oscillation periods (10??C?23 minutes) between the sunspot area variation and that of the magnetic field strength. We discuss possible mechanisms for the obtained results, based on the existing models for sunspot oscillations.     

Probing the Role of Magnetic-Field Variations in NOAA AR 8038 in Producing a Solar Flare and CME on 12 May 1997

We carried out a multi-wavelength study of a Coronal Mass Ejection (CME) and an associated flare, occurring on 12 May 1997. We present a detailed investigation of magnetic-field variations in NOAA Active Region 8038 which was observed on the Sun during 7??C?16 May 1997. This region was quiet and decaying and produced only a very small flare activity during its disk passage. However, on 12 May 1997 it produced a CME and associated medium-size 1B/C1.3 flare. Detailed analyses of H?? filtergrams and SOHO/MDI magnetograms revealed continual but discrete surge activity, and emergence and cancellation of flux in this active region. The movie of these magnetograms revealed the two important results that the major opposite polarities of pre-existing region as well as in the emerging-flux region were approaching towards each other and moving magnetic features (MMF) were ejected from the major north polarity at a quasi-periodicity of about ten hours during 10??C?13 May 1997. These activities were probably caused by magnetic reconnection in the lower atmosphere driven by photospheric convergence motions, which were evident in magnetograms. The quantitative measurements of magnetic-field variations such as magnetic flux, gradient, and sunspot rotation revealed that in this active region, free energy was slowly being stored in the corona. Slow low-layer magnetic reconnection may be responsible for the storage of magnetic free energy in the corona and the formation of a sigmoidal core field or a flux rope leading to the eventual eruption. The occurrence of EUV brightenings in the sigmoidal core field prior to the rise of a flux rope suggests that the eruption was triggered by the inner tether-cutting reconnection, but not the external breakout reconnection. An impulsive acceleration, revealed from fast separation of the H?? ribbons of the first 150 seconds, suggests that the CME accelerated in the inner corona, which is also consistent with the temporal profile of the reconnection electric field. Based on observations and analysis we propose a qualitative model, and we conclude that the mass ejections, filament eruption, CME, and subsequent flare were connected with one another and should be regarded within the framework of a solar eruption.     

磁塌缩不稳定与自生间歇磁流

太阳和天体物理吸积盘中的场是一种空间间歇的磁流。在整个太阳上都可发现这种间歇磁流片，其中光球上90%以上的磁流呈现为强场形态，其强度为0.1-0.2T，大小为50-300km；在吸积盘中，已知脉动磁场比宏观磁场强几个数量级。磁场的重联湮灭，导致在薄电流片区形成小尺度的磁环胞以及同涨的横等离激元。磁流和等离激元之间的非线性相互作用引起自类似塌缩，形成更为空间间歇的塌缩的磁环元胞。而横等离激元诱发的自生磁场具有调制不稳定性，导致磁场塌缩，形成高度间歇的磁流。分别在磁流力学和等离子体动力论两种情况下，分析了这种磁塌缩不稳定性，并用于解释太阳上的间歇磁流以及寻求天体物理吸积盘中的反常粘滞。