The statistical study of quasi‐periodic oscillations of the radio emission in solar quiet regions

In this study we discuss variations of the radio emission from the Quiet Sun Areas (QSA) at centimeter wavelength (1.76 cm). Data were obtained from Nobeyama Radioheliograph (NoRH). Oscillations of selected areas were studied carefully from data taken over one week. We try to find quasi‐periodic solar oscillations from the QSA. We used the traditional Fast Fourier Transform (FFT), Global Wavelet Spectrum (GWS) and Wavelet (Morlet) for studying signals in the frequency/time‐frequency domain. We used the Fisher randomization test to verify the significance of the observed signal. Instrumental and sky noises were studied using a cross‐correlation analysis. Additionally, a single pixel analysis were done. Wide ranges of solar oscillation periods were found from the Quiet Sun Area (QSA): 3–15, 35–70, and 90 minutes. Some physical explanations are suggested for these oscillations. However, it is not possible to give a conclusive statement about the origin of the long quasi‐periodic (>60 min) oscillations from the QSA (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian approach for g‐mode detection,or how to restrict our imagination

Nowadays, g‐mode detection is based upon a priori theoretical knowledge. By doing so, detection becomes more restricted to what we can imagine. De facto, the universe of possibilities ismade narrower. Such an approach is pertinent for Bayesian statisticians. Examples of how Bayesian inferences can be applied to spectral analysis and helioseismic power spectra are given. Our intention is not to give the full statistical framework (much too ambitious) but to provide an appetizer for going further in the direction of a proper Bayesian inference, especially for detecting gravity modes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detrending time series for astronomical variability surveys

We present a detrending algorithm for the removal of trends in time series. Trends in time series could be caused by various systematic and random noise sources such as cloud passages, changes of airmass, telescope vibration, CCD noise or defects of photometry. Those trends undermine the intrinsic signals of stars and should be removed. We determine the trends from subsets of stars that are highly correlated among themselves. These subsets are selected based on a hierarchical tree clustering algorithm. A bottom-up merging algorithm based on the departure from normal distribution in the correlation is developed to identify subsets, which we call clusters. After identification of clusters, we determine a trend per cluster by weighted sum of normalized light curves. We then use quadratic programming to detrend all individual light curves based on these determined trends. Experimental results with synthetic light curves containing artificial trends and events are presented. Results from other detrending methods are also compared. The developed algorithm can be applied to time series for trend removal in both narrow and wide field astronomy.     

Low‐frequency heliographic observations of the quiet Sun corona

We present new results of heliographic observations of quiet‐Sun radio emission fulfilled by the UTR‐2 radio telescope. The solar corona investigations have been made close to the last solar minimum (Cycle 23) in the late August and early September of 2010 by means of the two‐dimensional heliograph within 16.5–33 MHz. Moreover, the UTR‐2 radio telescope was used also as an 1‐D heliograph for one‐dimensional scanning of the Sun at the beginning of September 2010 as well as in short‐time observational campaigns in April and August of 2012. The average values of integral flux density of the undisturbed Sun continuum emission at different frequencies have been found. Using the data, we have determined the spectral index of quiet‐Sun radio emission in the range 16.5–200 MHz. It is equal to –2.1±0.1. The brightness distribution maps of outer solar corona at frequencies 20.0 MHz and 26.0 MHz have been obtained. The angular sizes of radio Sun were estimated. It is found that the solar corona at these frequencies is stretched‐out along equatorial direction. The coefficient of corona ellipticity varies slightly during above period. Its mean magnitudes are equal to ≈ 0.75 and ≈ 0.73 at 20.0 MHz and 26.0 MHz, respectively. The presented results for continuum emission of solar corona conform with being ones at higher frequencies. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi‐frequency solar observations at Metsähovi Radio Observatory and KAIRA

We describe solar observations carried out for the first time jointly with Kilpisjärvi Atmospheric Imaging Receiver Array (KAIRA) and Aalto University Metshovi Radio Observatory (MRO). KAIRA is new radio antenna array observing the decimeter and meter wavelength range. It is located near Kilpisjärvi, Finland, and operated by the SodankyläGeophysical Observatory, University of Oulu. We investigate the feasibility of KAIRA for solar observations, and the additional benefits of carrying out multi‐instrument solar observations with KAIRA and the MRO facilities, which are already used for regular solar observations. The data measured with three instruments at MRO, and with KAIRA during time period 2014 April–October were analyzed. One solar radio event, measured on 2014 April 18, was studied in detail. Seven solar flares were recorded with at least two of the three instruments at MRO, and with KAIRA during the chosen time period. KAIRA is a great versatile asset as a new Finnish instrument that can also be used for solar observations. Collaboration observations with MRO instruments and KAIRA enable detailed multi‐frequency solar flare analysis. Flare pulsations, flare statistics and radio spectra of single flares can be investigated due to the broad frequency range observations. The Northern locations of both MRO and KAIRA make as long as 15‐hour unique solar observations possible during summer time. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Peak asymmetry of solar p modes: a framework to explain the effects of the correlated noise from the acoustic source

It is well known that in the power spectrum solar p modes have asymmetric profiles, which depart from a Lorentzian shape. We present a framework to explain the contribution of correlated background noise, from the acoustic source, to this asymmetry. An important prediction is that observed peak asymmetry may differ depending on the way the p-mode observations are made, and on how the data are prepared. Furthermore, if valid, the proposed framework may provide the basis for separating the contribution of the correlated noise from that of the source location and properties.     

A new method for determining the sensitivity of X-ray imaging observations and the X-ray number counts

We present a new method for determining the sensitivity of X-ray imaging observations, which correctly accounts for the observational biases that affect the probability of detecting a source of a given X-ray flux, without the need to perform a large number of time-consuming simulations. We use this new technique to estimate the X-ray source counts in different spectral bands (0.5–2, 0.5–10, 2–10 and 5–10 keV) by combining deep pencil-beam and shallow wide-area Chandra observations. The sample has a total of 6295 unique sources over an area of  11.8 deg²  and is the largest used to date to determine the X-ray number counts. We determine, for the first time, the break flux in the 5–10 keV band, in the case of a double power-law source count distribution. We also find an upturn in the 0.5–2 keV counts at fluxes below about  6 × 10⁻¹⁷ erg s⁻¹ cm⁻²  . We show that this can be explained by the emergence of normal star-forming galaxies which dominate the X-ray population at faint fluxes. The fraction of the diffuse X-ray background resolved into point sources at different spectral bands is also estimated. It is argued that a single population of Compton thick active galactic nuclei (AGN) cannot be responsible for the entire unresolved X-ray background in the energy range 2–10 keV.     

On measuring low-degree p-mode frequency splitting with full-disc integrated data

The standard method of measuring rotational splitting from solar full-disc oscillation data, based on maximum-likelihood fitting of multi-Lorentzian profiles to oscillation power spectra, systematically overestimates the splitting. One of the reasons is that the maximum likelihood estimators (MLE) become unbiased only asymptotically as the number of data tends to infinity; for a finite data set they are often biased, inducing a systematic error. In this paper we assess by Monte Carlo simulations the amount of systematic error in the splitting measurement, using artificially generated power spectra. The simulations are carried out for multiplets of degree     2 and 3 with various signal-to-noise ratios, linewidths and observing times. We address the possible use of non-MLE estimators that could provide a smaller or negligible systematic error. The implication for asteroseismology is also discussed.     

On the measurement precision of solar p-mode eigenfrequencies

We make use of 3456 d of observations of the low-ℓ p-mode oscillations of the Sun in order to study the evolution over time of the measurement precision of the radial eigenfrequencies. These data were collected by the ground-based Birmingham Solar-Oscillations Network (BiSON) between 1991 January and 2000 June. When the power spectrum of the complete time series is fitted, the analysis yields frequency uncertainties that are close to those expected from the returned coherence times of the modes. The slightly elevated levels compared with the prediction appear to be consistent with a degradation of the signal-to-noise ratio in the spectrum that is the result of the influence of the window function of the observations (duty cycle 71 per cent). The fractional frequency precision reaches levels of a several parts in 10⁶ for many of the modes. The corresponding errors reported from observations made by the GOLF instrument on board the ESA/NASA SOHO satellite, when extrapolated to the length of the BiSON data set, are shown to be (on average) about ∼25 per cent smaller than their BiSON counterparts owing to the uninterrupted nature of the data from which they were derived.
An analysis of the BiSON data in contiguous segments of different lengths, T , demonstrates that the frequency uncertainties scale as T ^−1/2. This is to be expected in the regime where the coherence (life) times of the modes, τ _{n ℓ}, are smaller than the observing time T (the 'oversampled' regime). We show that mode detections are only now beginning to encroach on the 'undersampled' regime (where   T < τ _{n ℓ})  .     

Use of genetic algorithms to determine low-l rotational p-mode splittings at high frequencies

We present a comparative study of genetic and standard fitting routines applied to the task of extracting reliable estimates of the rotational splitting of full-disc, low-angular-degree (low- l ) solar p-mode data at high frequencies. 100 artificial proxies of a 10-yr data base of observations made by the Birmingham Solar-Oscillations Network (BiSON) were used to test the two approaches. All sets were analysed over the frequency range from 3000 to 4000 μHz.
Previous work, based on non-linear 'hill-climbing' fitting techniques, has demonstrated the unfortunate tendency for full-disc estimates of the splitting to overestimate the true, underlying values at high frequencies. Here, we show that the resulting bias is less severe when a genetic-fitting approach is adopted. This is largely the result of the number of erroneous 'null-valued' estimates of the splitting being considerably reduced: these estimates are, in effect, re-introduced into the expected normal distribution of fitted splittings. We also illustrate the diverse control one has when using a genetic algorithm as a fitting routine; this diversity is shown to allow further refinement in the estimate of the rotational splitting.
Finally, we address the issue of the reliability of the formal splitting uncertainties returned by the mode fitting, and find that complications arising from the strong anticorrelation between the splittings and their error estimates are not alleviated by the use of the genetic technique.     

New aspects of Doppler imaging in Sun-as-a-star observations

Birmingham Solar Oscillations Network (BiSON) instruments use resonant scattering spectrometers to make unresolved Doppler velocity observations of the Sun. Unresolved measurements are not homogenous across the solar disc and so the observed data do not represent a uniform average over the entire surface. The influence on the inhomogeneity of the solar rotation and limb darkening has been considered previously and is well understood. Here, we consider a further effect that originates from the instrumentation itself. The intensity of light observed from a particular region on the solar disc is dependent on the distance between that region on the image of the solar disc formed in the instrument and the detector. The majority of BiSON instruments have two detectors positioned on opposite sides of the image of the solar disc and the observations made by each detector are weighted towards differing regions of the disc. Therefore, the visibility and amplitudes of the solar oscillations and the realization of the solar noise observed by each detector will differ. We find that the modelled bias is sensitive to many different parameters such as the width of solar absorption lines, the strength of the magnetic field in the resonant scattering spectrometer, the orientation of the Sun's rotation axis, the size of the image observed by the instrument and the optical depth in the vapour cell. We find that the modelled results best match the observations when the optical depth at the centre of the vapour cell is 0.55. The inhomogeneous weighting means that a 'velocity offset' is introduced into unresolved Doppler velocity observations of the Sun, which varies with time, and so has an impact on the long-term stability of the observations.     

太阳活动与太阳自转速率变化关系的分析

研究发现,太阳自转速率的变化与太阳活动之间存在一定的联系,但是不同学者的研究结论存在着矛盾:有的认为两者为正相关,而有的却认为是负相关.究竟两者之间是什么关系,需要做进一步深入的分析.利用EEMD (Ensemble Empirical Mode Decomposition)等方法对太阳自转速率和太阳黑子数据序列进行相关关系以及相位关系的计算和分析,以探讨太阳自转速率变化与太阳活动之间的关系.研究发现:两者的长期趋势项分量呈显著负相关;在11 yr左右周期分量上,观测到的太阳自转速率滞后太阳黑子的变化约2 yr时,呈显著负相关关系,超前3 yr时呈现次显著的正相关;对太阳活动第12–23周各周内部太阳黑子与太阳自转速率的相关分析表明,两者的关系比较复杂,但负相关关系更为显著.这为进一步理解太阳活动变化与太阳自转速率变化之间的成因联系提供了新的依据.     

The visibility of low‐frequency solar acoustic modes

We make predictions of the detectability of low‐frequency p modes. Estimates of the powers and damping times of these low‐frequency modes are found by extrapolating the observed powers and widths of higher‐frequency modes with large observed signal‐to‐noise ratios. The extrapolations predict that the low‐frequency modes will have small signal‐to‐noise ratios and narrow widths in a frequency‐power spectrum. Monte Carlo simulations were then performed where timeseries containing mode signals and normally distributed Gaussian noise were produced. The mode signals were simulated to have the powers and damping times predicted by the extrapolations. Various statistical tests were then performed on the frequency‐amplitude spectra formed from these timeseries to investigate the fraction of spectra in which the modes could be detected. The results of these simulations were then compared to the number of p‐modes candidates observed in real Sun‐as‐a‐star data at low frequencies. The fraction of simulated spectra in which modes were detected decreases rapidly as the frequency of modes decreases and so the fraction of simulations in which the low‐frequency modes were detected was very small. However, increasing the signal‐to‐noise (S/N) ratio of the low‐frequency modes by a factor of 2 above the extrapolated values led to significantly more detections. Therefore efforts should continue to further improve the quality of solar data that is currently available. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Significance of periodogram peaks and a pulsation mode analysis of the Beta Cephei star V403 Car

We discuss some commonly used methods for determining the significance of peaks in the periodograms of time series. We review methods for constructing the classical significance tests, their corresponding false alarm probability functions and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We discuss the concepts of independent frequencies and oversampling in periodogram analysis. We then compare the results of new Monte Carlo simulations for evenly spaced time series with results obtained previously by other authors, and present the results of Monte Carlo simulations for a specific unevenly spaced time series obtained for V403 Car.