Low heavy-element photospheric abundance: a challenge for solar modeling

Recent spectroscopic data pointing to low heavy-element abundances Z pose a severe problem for solar-structure modeling. The low-Z abundances imply a lower opacity and a relatively shallow convective zone, both of which are in obvious contradiction with the observed helioseismic sound-speed profile. This paper presents a series of solar models with different heavy-element abundances. The SAHA-S equation of state and OPAL opacities properly take into account the respective heavy-element abundances. Diffusion of individual elements is also included in the models. Sound-speed profiles are compared with inversion results and it is shown that the models with low Z are in disagreement with the inversion data. Even combining the effect of diffusion, overshooting and mixing for the sound-speed profile did not lead to a solution of the low-Z problem. Models with varied neon abundance have also been computed. It turned out that a substantial increase of the neon abundance could produce a model in agreement with the sound-speed inversion but the required abundance increase would be unrealistic. The effect of the neon enhancement on the adiabatic exponent profile in the convection zone is also presented.     

Poincaré's méthode nouvelle by skew composition

Poincaré designed the méthode nouvelle in order to build approximate integrals of Hamiltonians developed as series of a small parameter. Due to several critical deficiencies, however, the method has fallen into disuse in favor of techniques based on Lie transformations. The paper shows how to repair these shortcomings in order to give Poincaré’s méthode nouvelle the same functionality as the Lie transformations. This is done notably with two new operations over power series: a skew composition to expand series whose coefficients are themselves series, and a skew reversion to solve implicit vector equations involving power series. These operations generalize both Arbogast’s technique and Lagrange’s inversion formula to the fullest extent possible. This revised version was published online in July 2006 with corrections to the Cover Date.     

Models of a mean granular cell

From inversion of a time series of slit spectra, observed in a quiet region of the solar photosphere, averaged models of a granular cell have been obtained showing the stratification of physical quantities versus optical depth and geometrical height. Furthermore a semi‐empiric dynamic model of a mean granular cell has been derived and the results are presented.     

A chromospheric temperature inversion and its implications on millimeter brightness distribution

The brightness temperature curve of the quiet Sun at millimeter wavelengths suggests a possible inversion in the mid-millimeter range. Interpreting this as a result of an actual inversion in the chromospheric temperature structure, and example of a model chromoshere is presented whose calculated temperature curve exhibits such an inversion. This model is then tested for radial brightness distribution at millimeter wavelengths. Comparing the calculated distributions at 3.2 mm and 6 mm with eclipse measurements made with parabolic cylinders at 3.2 mm and 8.6 mm shows qualitative agreement, allowing for instrumental smoothing. It is conluded that a chromospheric temperature inversion, either actual or effective, could account for the inversion suggested by millimeter data and also the complex brightness distributions measured during eclipses with parabolic cylinders.     

The generalized canonical form of Hori's method for non-canonical systems

Any dynamical system can be put in generalized canonical form through the introduction of a set of auxiliary ‘conjugate’ variables or momenta and solved by perturbation theory based on Lie series. The application of Hori's method for generalized canonical system leads to a new canonical transformation — the Mathieu transformation — defined by the solution of the Hori auxiliary system. This new transformation simplifies the algorithm since the inversion of the solution of the Hori auxiliary system is no longer necessary. In this paper, we wish to show some peculiarities of this technique.     

TEC Compensated Inversion Method of Ionospheric Occultation

For the inversion of ionospheric occultation data, the Abel inversion method of calibrated TEC is usually adopted, but the spherical asymmetry of the real ionosphere will bring errors to the inversion result of electron densities. This paper studies a TEC compensated inversion method. By combining with a background field, this method may eliminate the effect of the horizontal variability of electron density on the TEC, and improve the applicability of the assumption of spherical symmetry as well as the inversion accuracy. Applying this method to the inversion of simulative occultation events, the result demonstrates that compared with the traditional Abel transform inversion, the TEC compensated inversion method can reduce the inversion error. Comparing the various background fields obtained in different ways, it is shown that the higher the coincidence level between the background field and the real field, the better the inversion result.     

GPS/LEO掩星技术中超折射效应的修正

在GPS掩星探测地球大气技术中，Abel积分变换要求大气折射指数n是折射半径a的单值函数，当大气折射率的垂直梯度达到小于一个极限值dN／dr≈-0．16N-unit m^-1上述单值性不成立，称其为超折射，此时Abel积分变换不再适用,如果还是在形式上应用经典的Abel变换，在反演结果中就会产生负大气折射率偏差．描述了低对流层中超折射现象的物理特性和数学表示；在广义Abel积分变换的基础上，讨论了超折射层内和超折射层下的大气剖面反演算法；选择了一个简单的采样间隔内等大气折射率垂直梯度假设，对英国高分辨率无线电探空观测资料进行模拟计算，验证了负超折射与大气折射率偏差的关系，并提出的广义Abel变换的合理性.     

Site-testing at Muztagh-ata site Ⅲ:temperature inversion in surface-layer atmosphere

In this article,we present detailed seasonal,monthly and daily statistics of temperature difference in the surface layer at the Muztagh-ata site based on the temperature measurements at two heights of 2 m and6 m.We find that temperature inversion occurs frequently at our site during nighttime,especially during the cold season.Strong temperature inversion always represents stable atmospheric turbulence,which is crucial for an optical observatory.By analyzing the behavior of temperature inversion and its correlation with wind and cloud amount,one conclusion can be made that radiation inversion is the main reason for the existence of temperature inversion in the surface-layer at the Muztagh-ata site.     

Evidence of climatic warming in the southern Urals region derived from borehole temperatures and meteorological data

Thirty borehole temperature–depth profiles in the central and southern Urals, Russia were scrutinized for evidence of ground surface temperature histories. We explored two inversion schemes: a simple ramp inversion in which solutions are parameterized in terms of an onset time and magnitude of change and a more sophisticated functional space inverse algorithm in which the functional form of the solution is left unspecified. To enhance and potentially identify latitudinal differences in the ground surface temperature signal, we subdivided the data into three groups based on geographic proximity and simultaneously inverted the borehole temperature–depth logs. The simultaneous inversions highlighted 13 temperature–depth logs that could not both fit a common ground surface temperature history and a priori models within reasonable bounds. Our results confirm that this is an effective way to reduce site-specific noise from an ensemble of boreholes. Each inversion scheme gives comparable results indicating locally variable warming on the order of 1°C starting between 1800 and 1900 AD. Similarly surface air temperature records from 12 nearby meteorological stations exhibit locally variable warming also on the order of 1°C of warming during the 20th century. To explore the degree to which borehole temperatures and surface air temperature (SAT) time series are responding to the same signal, we average the SAT data into the same three groups and used these averages as a forcing function at the Earth's surface to generate synthetic transient temperature profiles. Root mean square (RMS) misfits between these synthetic temperature profiles and averaged temperature–depth profiles are low, suggesting that first-order curvature in borehole temperatures and variations in SAT records are correlated.     

Analysis of stellar occultation data: Effects of photon noise and initial conditions

A new inversion technique for obtaining temperature, pressure, and number density profiles of a planetary atmosphere from an occultation light curve is described. This technique employs an improved boundary condition to begin the numerical inversion and permits the computation of errors in the profiles caused by photon noise in the light curve. We present our assumptions about the atmosphere, optics, and noise and develop the equations for temperature, pressure, and number density and their associated errors. By inverting in equal increments of altitude, Δh, rather than in equal increments of time, Δt, the inversion need not be halted at the first negative point on the light curve as required by previous methods. The importance of the boundary condition is stressed, and a new initial condition is given. Numerical results are presented for the special case of inversion of a noisy isothermal light curve. From these results, simple relations are developed which can be used to predict the noise quality of an occultation. It is found that fractional errors in temperature profiles are comparable to those of pressure and number density profiles. An example of the inversion method is shown. Finally, we discuss the validity of our assumptions. In an appendix we demonstrate that minimum fractional errors in scale height determined from the inversion are comparable to those from an isothermal fit to a noisy isothermal light curve.     

Tomography of stellar non‐radial pulsations

The stellar surface imaging technique is used for studying stellar non‐radial pulsations on the basis of inversions of time series of variable line profiles without making assumptions on the specific shape of the pulsations. The inversion results in an image of the stellar surface in which sectoral and tesseral modes can be distinguished in many cases and the pulsational degree and the azimuthal order can be determined. The capability of the technique is studied with simulated data. Then, the surface imaging technique is applied to high‐resolution spectra of the rapidly rotating Beta Cep‐type star ω¹ Sco, which shows strong line‐profile variations. Stellar surface imaging is concluded to be a useful technique for pulsation‐mode identification. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inversion of Zeeman polarization for solar magnetic field diagnostics

The topic of magnetic field diagnostics with the Zeeman effect is currently vividly discussed. There are some testable inversion codes available to the spectropolarimetry community and their application allowed for a better understanding of the magnetism of the solar atmosphere. In this context, we propose an inversion technique associated with a new numerical code. The inversion procedure is promising and particularly successful for interpreting the Stokes profiles in quick and sufficiently precise way. In our inversion, we fit a part of each Stokes profile around a target wavelength, and then determine the magnetic field as a function of the wavelength which is equivalent to get the magnetic field as a function of the height of line formation.To test the performance of the new numerical code, we employed “hare and hound” approach by comparing an exact solution (called input) with the solution obtained by the code (called output). The precision of the code is also checked by comparing our results to the ones obtained with the HAO MERLIN code. The inversion code has been applied to synthetic Stokes profiles of the Na D₁ line available in the literature. We investigated the limitations in recovering the input field in case of noisy data. As an application, we applied our inversion code to the polarization profiles of the Fe i λ 6302.5 Å observed at IRSOL in Locarno.     

A fast Stokes inversion technique based on quadratic regression

Stokes inversion calculation is a key process in resolving polarization information on radiation from the Sun and obtaining the associated vector magnetic fields. Even in the cases of simple local thermodynamic equilibrium(LTE) and where the Milne-Eddington approximation is valid, the inversion problem may not be easy to solve. The initial values for the iterations are important in handling the case with multiple minima. In this paper, we develop a fast inversion technique without iterations. The time taken for computation is only 1/100 the time that the iterative algorithm takes. In addition, it can provide available initial values even in cases with lower spectral resolutions. This strategy is useful for a filter-type Stokes spectrograph, such as SDO/HMI and the developed two-dimensional real-time spectrograph(2DS).     

Maximum Entropy Regularization Method of Ionospheric Occultation

With the increasing of applications of Global Positioning System (GPS), the research on the factors affecting the radio signals is becoming more and more important. One of the most significant effects on ionosphere monitoring is the ionospheric radio occultation (IRO), and the IRO data is now serving as one of the most important monitoring sources for the ionospheric measurements. Meanwhile the inversion of the occultation data is a popular topic. The traditional Abel inversion process through compensated total electron content (TEC) is a linear inversion method, thus it would transfer the measurement errors directly to the inversion results. In order to improve the occultation results, we introduce in this paper two nonlinear methods, namely the regularization method and the maximum entropy regularization method. Through designed simulative experiments, we verify and compare these three methods, and conclude that the maximum entropy regularization method can reduce significantly the influence of measurement errors.     

Comparison of different instantaneous models of electron concentration height profiles at single location

Three different models of electron concentration height profile have been compared to profiles obtained from ionograms at the Warsaw station. The electron density profiles are obtained from ionograms by inversion methods. These models use as an input the standard ionospheric characteristics. Some of the models are intended to compute monthly median profiles. To obtain the instantaneous profile the values of needed parameters are taken from the simultaneously constructed instantaneous maps of ionospheric parameters. For instantaneous maps construction, two techniques are used: the kriging technique with modifications concerning ionospheric behaviour, where deviations of measurements from monthly median maps are used, and a fitting method where median maps are updated with measurements. The comparison is done for the COST 238 PRIME height profile model, a local model based on a modified Rush model, and a model where an artificial neural network technique is aaplied to time series of profiles. The usefulness of the average representative height profile constructed from a set of instantaneous profiles is discussed.     

Inversion of synchrotron spectra

The problem of synchrotron radiation spectra is treated from the viewpoint of deconvolving the spectrum of ultrarelativistic source electrons from the observed photon spectrum. It is shown that for homogeneous sources the problem amounts to inversion of a Meijer transform with a modified Bessel finction kernel. A precise analytic inversion is only possible in the complex plane but Meijer transform tables are available for a wide range of functions. More convenient inversion formulae prove possible by use of a Laplace transform approximation or by analysing the spectra in terms of their integral moments. The filtering property of the transform is also established showing that the contribution to the synchrotron spectrum of high frequency components in the electron spectrum declines exponentially with their frequency. Thus, as with other Laplace-like transforms, only a few terms in an electron spectrum expansion can be deconvolved for any plausible noise level in the synchrotron spectrum.     

Filaments and large-scale magnetic fields

We have used Stanford magnetic field maps to construct distributions of longitudinal magnetic field gradients in the neighbourhood of polarity inversion lines. The distributions were constructed with proper account of the type of the polarity inversion lines and of the existence or absence of dark filaments above them. It is shown that for polarity inversion lines that pass inside active regions or on their boundary, grad B_II distributions for portions of the lines with persisting filament are shifted toward lower values of gradient as compared with grad B_II distributions for portions of the lines without filaments. The influence of the spatial resolution of the magnetograms upon polarity inversion line characteristics is discussed.     

电离层掩星反演的正则最大熵法

电离层掩星数据现已成为电离层观测数据的重要来源,对掩星数据的反演研究一直是掩星研究的热点.传统采用的改正TEC(1btal Electron Content)的Abel变换反演法为线性反演法,它会把测量误差带入反演结果中.为改善反演效果受测量误差的影响,引入两种非线性的反演方法一正则化和正则最大熵反演法.随后设计模拟试验,对3种方法进行验证、比较,得到正则最大熵反演法可以很好地减小测量误差的影响.     

Non-parametric reconstruction of distribution functions from observed galactic discs

A general inversion technique for the recovery of the underlying distribution function for observed galactic discs is presented and illustrated. Under the assumption that these discs are axisymmetric and thin, the proposed method yields a unique distribution compatible with all the observables available. The derivation may be carried out from the measurement of the azimuthal velocity distribution arising from positioning the slit of a spectrograph along the major axis of the galaxy. More generally, it may account for the simultaneous measurements of velocity distributions corresponding to slits presenting arbitrary orientations with respect to the major axis. The approach is non-parametric, i.e. it does not rely on a particular algebraic model for the distribution function. Special care is taken to account for the fraction of counter-rotating stars, which strongly affects the stability of the disc. An optimization algorithm is devised — generalizing the work of Skilling &38; Bryan — to carry this truly two-dimensional ill-conditioned inversion efficiently. The performance of the overall inversion technique with respect to the noise level and truncation in the data set is investigated with simulated data. Reliable results are obtained up to a mean signal-to-noise ratio of 5, and when measurements are available up to 4  R _e. A discussion of the residual biases involved in non-parametric inversions is presented. The prospects of application of the algorithm to observed galaxies and other inversion problems are discussed.     

Inversion of relief on Mars

Relief inversion has been invoked to explain a number of geomorphic features of the martian surface. Terrestrial relief inversion occurs when former depressions become elevated because their fill is more resistant to erosion than the surrounding terrain. It is a common product of long-term landscape evolution on Earth, especially in relatively stable intra-cratonic settings and flat, or near flat lying successions. The inverted relief will preserve relicts of former land surfaces and is therefore older than the surrounding terrain. Relief inversion can occur by a range of processes, including infill of depressions by intrinsically resistant material, selective secondary cementation via diagenesis and weathering, or surface armouring. We examine a number of possible cases of inverted relief on Mars that appear to have formed by these three processes. We suggest that the most likely cementing agents for surface induration are iron oxides, silica, and sulfates. Possible cementation mechanisms include fluid mixing during regional groundwater flow, cooling of hydrothermal or basinal fluids as they near the surface, and evaporation and sublimation of near surface water. Wind action appears the most common erosive process on Mars capable of the regional landscape lowering necessary for relief inversion to occur, unlike on Earth where both deflation and runoff are important. Preliminary crater densities of selected features show that the tops of the proposed inverted relief have considerably more craters than the surrounding plains, as is predicted by the inversion hypothesis. More accurate dating of inverted surfaces and the adjacent areas may provide a simple way of measuring the degree of erosion over time in at least some areas of Mars.