Principal Components and Independent Component Analysis of Solar and Space Data

Principal components analysis (PCA) and independent component analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It permits the identification of structures that remain coherent and correlated or that recur throughout a time series. ICA seeks for maximally independent modes and takes into account all order correlations of the data. We apply PCA to the interplanetary magnetic field polarity near 1 AU and to the 3.25R _⊙ source-surface fields in the solar corona. The rotations of the two-sector structures of these systems vary together to high accuracy during the active interval of solar cycle 23. We then use PCA and ICA to hunt for preferred longitudes in northern hemisphere Carrington maps of magnetic fields.     

Rigid rotation of the solar core? On the reliable extraction of low-ℓ rotational p-mode splittings from full-disc observations of the Sun

We present low-ℓ rotational p-mode splittings from the analysis of 8 yr of observations made by the Birmingham Solar-Oscillations Network (BiSON) of the full solar disc. These data are presented in the light of a thorough investigation of the fitting techniques used to extract them. Particular attention is paid to both the origin and magnitude of bias present in these estimates. An extensive Monte Carlo strategy has been adopted to facilitate this study – in all, several thousand complete, artificial proxies of the 96-month data set have been generated to test the analysis of real 'full-disc' data. These simulations allow for an assessment of any complications in the analysis which might arise from variations in the properties of the p modes over the 11-yr solar activity cycle.
The use of such an extended data set affords greater precision in the splittings, and by implication the rotation rate inferred from these data, and reduces bias inherent in the analysis, thereby giving a more accurate determination of the rotation. The grand, weighted sidereal average of the BiSON set is     , a value consistent with that expected were the deep radiative interior     to rotate at the same frequency, and in the same 'rigid' manner, as the more precisely and accurately studied outer part of the radiative zone.     

Rotation of the solar core from BiSON and LOWL frequency observations

Determination of the rotation of the solar core requires very accurate data on splittings for the low-degree modes which penetrate to the core, as well as for modes of higher degree to suppress the contributions from the rest of the Sun to the splittings of the low-degree modes. Here we combine low-degree data based on 32 months of observations with the BiSON network and data from the LOWL instrument. The data are analysed with a technique that specifically aims at obtaining an inference of rotation that is localized to the core. Our analysis provides what we believe is the most stringent constraint to date on the rotation of the deep solar interior.     

Seismic view of the solar interior

The interior of the Sun is not directly observable to us. Nevertheless, it is possible to infer the physical conditions prevailing in the solar interior with the help of theoretical models coupled with observational input provided by measured frequencies of solar oscillations. The frequencies of these solar oscillations depend on the internal structure and dynamics of the Sun and from the knowledge of these frequencies it is possible to infer the internal structure as well as the large scale flows inside the Sun, in the same way as the observations of seismic waves on the surface of Earth help us in the study of its interior. With the accumulation of seismic data over the last six years it has also become possible to study temporal variations in the solar interior. Some of these seismic inferences would be described.     

Automated classification of stellar spectra — II. Two-dimensional classification with neural networks and principal components analysis

We investigate the application of neural networks to the automation of MK spectral classification. The data set for this project consists of a set of over 5000 optical (3800–5200 Å) spectra obtained from objective prism plates from the Michigan Spectral Survey. These spectra, along with their two-dimensional MK classifications listed in the Michigan Henry Draper Catalogue, were used to develop supervised neural network classifiers. We show that neural networks can give accurate spectral type classifications (σ₆₈= 0.82 subtypes, σ_rms= 1.09 subtypes) across the full range of spectral types present in the data set (B2–M7). We show also that the networks yield correct luminosity classes for over 95 per cent of both dwarfs and giants with a high degree of confidence.   Stellar spectra generally contain a large amount of redundant information. We investigate the application of principal components analysis (PCA) to the optimal compression of spectra. We show that PCA can compress the spectra by a factor of over 30 while retaining essentially all of the useful information in the data set. Furthermore, it is shown that this compression optimally removes noise and can be used to identify unusual spectra.   This paper is a continuation of the work carried out by von Hippel et al. (Paper I).     

Effects of errors in the solar radius on helioseismic inferences

Frequencies of intermediate-degree f modes of the Sun seem to indicate that the solar radius is smaller than what is normally used in constructing solar models. We investigate the possible consequences of an error in radius on results for solar structure obtained using helioseismic inversions. It is shown that solar sound speed will be overestimated if oscillation frequencies are inverted using reference models with a larger radius. Using solar models with a radius of 695.78 Mm and new data sets, the base of the solar convection zone is estimated to be at a radial distance of 0.7135 ± 0.0005 of the solar radius. The helium abundance in the convection zone as determined using models with an OPAL equation of state is 0.248 ± 0.001, where the errors reflect the estimated systematic errors in the calculation, the statistical errors being much smaller. Assuming that the OPAL opacities used in the construction of the solar models are correct, the surface Z / X is estimated to be 0.0245 ± 0.0006.     

Perspectives on the interior of the Sun

The interior of the Sun is not directly accessible to observations. Nonetheless, it is possible to infer the physical conditions inside the Sun with the help of structure equations governing its equilibrium and with the powerful observational tools provided by the neutrino fluxes and oscillation frequencies. The helioseismic data show that the internal constitution of the Sun can be adequately represented by a standard solar model. It turns out that a cooler solar core is not a viable solution for the measured deficit of neutrino fluxes, and the resolution of the solar neutrino puzzle should be sought in the realm of particle physics.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Helioseismology

The sun being the nearest star, seismic observations with high spatial resolution are possible, thus providing accurate measurement of frequencies of about half million modes of solar oscillations covering a wide range of degree. With these data helioseismology has enabled us to study the solar interior in sufficient detail to infer the large-scale structure and rotation of the solar interior. With the availability of high quality helioseismic data over a good fraction of a solar cycle it is also possible to study temporal variations in solar structure and dynamics. Some of these problems and recent results will be discussed.     

ASO-S/HXI太阳指向镜算法研究

硬X射线成像是研究太阳耀斑等爆发现象的重要手段.由于采用调制成像而非直接成像的原因, X射线图像在日面上的位置需要借助太阳指向镜提供的仪器指向的日面坐标来确定.因此,指向信息对于耀斑定位实现多波段研究,理解太阳耀斑的物理过程具有重要的科学意义.在此对两种太阳指向镜指向信息的获取算法进行了测试.结合太阳指向镜的设计方案,首先利用SDO (Solar Dynamics Observatory)/AIA (Atmospheric Imaging Assembly) 4500?的数据产生测试图像,其次对其进行二值化处理,分别提取日面轮廓和4个边角指定区域面积;最后分别利用最小二乘法和四象限法对太阳中心坐标进行反演.初步结果显示最小二乘法受随机噪声影响小,定位精度相对稳定约为0.25′′,并可提供四象限法解算的初值;后者的精度可以优于0.14′′,但受随机噪声影响较大.两种算法的精度都显著优于硬X射线成像仪(Hard X-ray Imager, HXI)太阳指向镜的设计要求,可为指向数据在将来科学分析中的实际应用提供参考.     

Effect of Coulomb collisions on time variations of the solar neutrino flux

We consider the processes that might suppress the time variations in the solar neutrino flux produced by the radial motion of the Earth through the neutrino interference pattern. We calculate these time variations and the extent to which they are suppressed by Coulomb collisions of the neutrino-emitting nuclei. This is done for both the 0.862-MeV ⁷Be neutrino line and the continuous neutrino spectrum, assuming a Gaussian energy response function of the neutrino detector. We find that the collisional decoherence averages out the time variations for neutrino masses A simple and clear physical picture of the time-dependent solar neutrino problem is presented and qualitative coherence criteria are discussed.     

Formation of buoyant magnetic structures by a localized velocity shear

Motivated by considerations of the solar tachocline, we study the generation of strong buoyant magnetic structures by a sheared velocity field localized in a convectively stable background, using non-linear three-dimensional (3D) magnetohydrodynamic (MHD) simulations. The shear flow can spontaneously create strong tube-like toroidal (streamwise) magnetic structures from an imposed weak uniform poloidal (cross-stream) magnetic field. The structures are magnetically buoyant and therefore rise, and may evolve further to a rich variety of geometries, including kinked or arched shapes. The emergence process can repeat indefinitely with a characteristic period. These mechanisms may be relevant to the MHD processes in the solar tachocline and the creation and emergence of solar active regions.     

Forecast daily indices of solar activity, F10.7, using support vector regression method

The 10.7cm solar radio flux (F10.7), the value of the solar radio emission flux density at a wavelength of 10.7cm, is a useful index of solar activity as a proxy for solar extreme ultraviolet radiation. It is meaningful and important to predict F10.7 values accurately for both long-term (months-years) and short-term (days) forecasting, which are often used as inputs in space weather models. This study applies a novel neural network technique, support vector regression (SVR), to forecasting daily values of F10.7. The aim of this study is to examine the feasibility of SVR in short-term F10.7 forecasting. The approach, based on SVR, reduces the dimension of feature space in the training process by using a kernel-based learning algorithm. Thus, the complexity of the calculation becomes lower and a small amount of training data will be sufficient. The time series of F10.7 from 2002 to 2006 are employed as the data sets. The performance of the approach is estimated by calculating the norm mean square error and mean absolute percentage error. It is shown that our approach can perform well by using fewer training data points than the traditional neural network.     

Study of the Diurnal Variation of Cosmic Rays during Different Phases of Solar Activity

The pressure-corrected hourly counting rate data of ground-based super neutron monitor stations, situated in different latitudes, have been employed to study the characteristics of the long-term variation of cosmic-ray diurnal anisotropy for a long (44-year) period (1965?–?2008). Some of these super neutron monitors are situated in low latitudes with high cutoff rigidity. Annual averages of the diurnal amplitudes and phases have been obtained for each station. It is found that the amplitude of the diurnal anisotropy varies with a period of one solar activity cycle (11 years), whereas the diurnal phase varies with a period of 22 years (one solar magnetic cycle). The average diurnal amplitudes and phases have also been calculated by grouping the days on the basis of ascending and descending periods of each solar cycle (Cycles 20, 21, 22, and 23). Systematic and significant differences are observed in the characteristics of the diurnal variation between the descending periods of the odd and even solar cycles. The overall vector averages of the descending periods of the even solar cycles (20 and 22) show significantly smaller diurnal amplitudes compared to the vector averages of the descending periods of the odd solar cycles (21 and 23). In contrast, we find a large diurnal phase shift to earlier hours only during the descending periods of even solar cycles (20 and 22), as compared to almost no shift in the diurnal phase during the descending periods of odd solar cycles. Further, the overall vector average diurnal amplitudes of the ascending period of odd and even solar cycles remain invariant from one ascending period to the other, or even between the even and odd solar cycles. However, we do find a significant diurnal phase shift to earlier hours during the ascending periods of odd solar cycles (21 and 23) in comparison to the diurnal phase in the ascending periods of even solar cycles (20 and 22).     

A new inversion of solar rotational splitting data

The fine structure of the solar p-mode spectrum is used to obtain an estimate of the Sun's internal rotation rate, as a function of both latitude and depth, for fractional radii in the range 0.55 < r/R < 0.85. Because each piece of data is a weighted average of the rotation rate over an extended region of the solar interior and because the number of such measurements is finite, such an inversion unavoidably has limited resolution and suffers from other systematic errors. Accordingly, the results of the inversion presented here and other published inversions should be interpreted with this in mind. These problems are discussed in detail for the present inversion.Such systematic errors can be avoided by seeking not a functional form of the rotation rate but rather the values of suitably weighted averages of the rotation rate (or of functions derivable from it). Here it is shown that the value of a broad average over depth of the radial gradient of the solar rotation rate, concentrated in the convection zone, is consistent with the gradient being zero in this region but is apparently inconsistent with the picture of constant rotation on cylindrical surfaces aligned with the rotation axis. This result, which confirms the inference from the former type of inversion, is of importance for modelling the dynamics of the convection zone and also for dynamo models of the Sun's magnetic field.The National Center for Atmospheric Research is supported by the National Science Foundation.     

Self-similar pressure oscillations in neutron star envelopes as probes of neutron star structure

We study eigenmodes of acoustic oscillations of high multipolarity l ∼ 100–1000 and high frequency (∼100 kHz), localized in neutron star envelopes. We show that the oscillation problem is self-similar. Once the oscillation spectrum is calculated for a given equation of state (EOS) in the envelope and given stellar mass M and radius R , it can be rescaled to a star with any M and R (but the same EOS in the envelope). For l ≳ 300, the modes can be subdivided into the outer and inner ones. The outer modes are mainly localized in the outer envelope. The inner modes are mostly localized near the neutron drip point, being associated with the softening of the EOS after the neutron drip. We calculate oscillation spectra for the EOSs of cold-catalyzed and accreted matter and show that the spectra of the inner modes are essentially different. A detection and identification of high-frequency pressure modes would allow one to infer M and R and determine also the EOS in the envelope (accreted or ground state) providing a new, potentially powerful method to explore the main parameters and internal structure of neutron stars.     

Intermediate‐term variations in solar radius during solar cycle 23

In this study, we look for the mid‐term variations in the daily average data of solar radius measurements made at the Solar Astrolabe Station of TUBITAK National Observatory (TUG) during solar cycle 23 for a time interval from 2000 February 26 to 2006 November 15. Due to the weather conditions and seasonal effect dependent on the latitude, the data series has the temporal gaps. For spectral analysis of the data series, thus, we use the Date Compensated Discrete Fourier Transform (DCDFT) and the CLEANest algorithm, which are powerful methods for irregularly spaced data. The CLEANest spectra of the solar radius data exhibit several significant mid‐term periodicities at 393.2, 338.9, 206.5, 195.2, 172.3 and 125.4 days which are consistent with periods detected in several solar time series by several authors during different solar cycles. The knowledge relating to the origin of solar radius variations is not yet present. To see whether these variations will repeat in next cycles and to understand how the amplitudes of such variations change with different phases of the solar cycles, we need more systematic efforts and the long‐term homogeneous data. Since most of the periodicities detected in the present study are frequently seen in solar activity indicators, it is thought that the physical mechanisms driving the periodicities of solar activity may also be effective in solar radius variations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Can Asymmetry of Solar Activity be Extended into Extended Cycle？

With the use of the Royal Greenwich Observatory data set of sunspot groups,an attempt is made to examine the north-south asymmetry of solar activity in the “extended” solar cycles. It is inferred that the asymmetry established for individual solar cycles does not extend to the “extended” cycles.     

Testing turbulent convection theory in solar models – I. Structure of the solar convection zone

Turbulent convection models (TCMs) based on hydrodynamic moment equations are compared with the classical mixing-length theory (MLT) in solar models. The aim is to test the effects of some physical processes on the structure of the solar convection zone, such as the dissipation, diffusion and anisotropy of turbulence that have been ignored in the MLT. Free parameters introduced by the TCMs are also tested in order to find appropriate values for astrophysical applications. It is found that the TCMs usually give larger convective heat fluxes than the MLT does, and the heat transport efficiency is sensitively related to the dissipation parameters used in the TCMs. As a result of calibrating to the present solar values, our solar models usually have rather smaller values of the mixing length to local pressure scaleheight ratio than the standard solar model. The turbulent diffusion is found to have important effects on the structure of the solar convection zone. It leads to significantly lowered and expanded profiles for the Reynolds correlations, and a larger temperature gradient in the central part of the superadiabatic convection region but a smaller one near the boundaries of the convection zone. It is interesting to note that, due to a careful treatment of turbulence developing towards isotropic state, our non-local TCM results in radially dominated motion in the central part and horizontally dominated motion near the boundaries of the convection zone, just as what has been observed in many 3D numerical simulations. Our solar models with the TCMs give small but meaningful differences in the temperature and sound speed profiles compared with the standard solar model using the MLT.