The analysis of indexed astronomical time series V. Fitting sinusoids to high-speed photometry

The estimation of the frequency, amplitude and phase of a sinusoid from observations contaminated by correlated noise is considered. It is assumed that the observations are regularly spaced, but may suffer missing values or long time stretches with no data. The typical astronomical source of such data is high-speed photoelectric photometry of pulsating stars. The study of the observational noise properties of nearly 200 real data sets is reported: noise can almost always be characterized as a random walk with superposed white noise. A scheme for obtaining weighted non-linear least-squares estimates of the parameters of interest, as well as standard errors of these estimates, is described. Simulation results are presented for both complete and incomplete data. It is shown that, in finite data sets, results are sensitive to the initial phase of the sinusoid.     

Photon counting strategies with low-light-level CCDs

Low light level charge-coupled devices (L3CCDs) have recently been developed, incorporating on-chip gain. They may be operated to give an effective readout noise of much less than one electron by implementing an on-chip gain process allowing the detection of individual photons. However, the gain mechanism is stochastic and so introduces significant extra noise into the system. In this paper we examine how best to process the output signal from an L3CCD so as to minimize the contribution of stochastic noise, while still maintaining photometric accuracy.
We achieve this by optimizing a transfer function that translates the digitized output signal levels from the L3CCD into a value approximating the photon input as closely as possible by applying thresholding techniques. We identify several thresholding strategies and quantify their impact on the photon counting accuracy and the effective signal-to-noise ratio.
We find that it is possible to eliminate the noise introduced by the gain process at the lowest light levels. Reduced improvements are achieved as the light level increases up to about 20 photon pixel⁻¹ and above this there is negligible improvement. Operating L3CCDs at very high speeds will keep the photon flux low, giving the best improvements in signal-to-noise ratio.     

Harmonic analysis of cosmic microwave background data – II. From ring-sets to the sky

Despite the fact that the physics of the cosmic microwave background anisotropies is most naturally expressed in Fourier space, pixelized maps are almost always used in the analysis and simulation of microwave data. A complementary approach is investigated here, in which maps are used only in the visualization of the data, and the temperature anisotropies and polarization are only ever expressed in terms of their spherical multipoles. This approach has a number of advantages: there is no information loss (assuming a band-limited observation); deconvolution of asymmetric beam profiles and the temporal response of the instrument are naturally included; correlated noise can easily be taken into account, removing the need for additional 'destriping'; polarization is also analysed in the same framework; and reliable estimates of the spherical multipoles of the sky and their errors are obtained directly for subsequent component separation and power spectrum estimation. The formalism required to analyse experiments which survey the full sky by scanning on circles is derived here, with particular emphasis on the Planck mission. A number of analytical results are obtained in the limit of simple scanning strategies. Although there are non-trivial computational obstacles to be overcome before the techniques described here can be implemented at high resolution, if these can be overcome the method should allow for a more robust return from the next generation of full-sky microwave background experiments.     

On the extraction of extended structure from Herschel-SPIRE scanning observations in the presence of 1/f noise

We present results from a study of the impact of uncorrelated 1/ f noise on the extraction of spatial structure, on a range of scales, from sky mapping observations made using the Herschel-SPIRE (the spectral and photometric imaging receiver) photometer in the scan-map mode. These studies were carried out using a detailed instrument simulator, and the output reduced using the map-making algorithm to be implemented in the SPIRE data pipeline. The influence of source size scale, telescope-scanning rate and 1/ f noise knee frequency is investigated, and operational bounds to the expected losses are presented, using the case of zero 1/ f (white) noise as a benchmark. Both cross-linked and non-cross-linked observing options are studied. The results presented here represent the best current estimate of the sensitivity of the SPIRE photometer to emission on arbitrary scales. The data presented are general and scalable to any SPIRE observation made using the scanning mode.     

Comparing modal noise and FRD of circular and non‐circular cross‐section fibres

Modal noise is a common source of noise introduced to the measurements by optical fibres and is particularly important for fibre‐fed spectroscopic instruments, especially for high‐resolution measurements. This noise source can limit the signal‐to‐noise ratio and jeopardize photon‐noise limited data. The subject of the present work is to compare measurements of modal noise and focal‐ratio degradation (FRD) for several commonly used fibres. We study the influence of a simple mechanical scrambling method (excenter) on both FRD and modal noise. Measurements are performed with circular and octagonal fibres from Polymicro Technology (FBP‐Series) with diameters of 100, 200, and 300μm and for square and rectangular fibres from CeramOptec, among others. FRD measurements for the same sample of fibres are performed as a function of wavelength. Furthermore, we replaced the circular fibre of the STELLA‐échelle‐spectrograph (SES) in Tenerife with an octagonal and found a SNR increase by a factor of 1.6 at 678 nm. It is shown in the laboratory that an excenter with a large amplitude and low frequency will not influence the FRD but will reduce modal noise rather effectively by up to 180%. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Covariance of weak lensing observables

Analytical expressions for covariances of weak lensing statistics related to the aperture mass,   M _ap  , are derived for realistic survey geometries such as the Supernova Acceleration Probe (SNAP) ¹ for a range of smoothing angles and redshift bins. We incorporate the contributions to the noise due to the intrinsic ellipticity distribution and the effects of the finite catalogue size. Extending previous results to the most general case where the overlap of source populations is included in a complete analysis of error estimates, we study how various angular scales in various redshifts are correlated and how the estimation scatter changes with the survey parameters. Dependences on cosmological parameters and source redshift distributions are studied in detail. Numerical simulations are used to test the validity of various ingredients to our calculations. Correlation coefficients are defined in a way that makes them practically independent of cosmology. They can provide important tools to cross-correlate one or more different surveys, as well as various redshift bins within the same survey or various angular scales from the same or different surveys. The dependence of these coefficients on various models of underlying mass correlation hierarchy is also studied. Generalizations of these coefficients at the level of three-point statistics have the potential of probing the complete shape dependence of the underlying bi-spectrum of the matter distribution. A complete error analysis incorporating all sources of errors suggests encouraging results for studies using future space-based weak lensing surveys such as SNAP.     

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.     

On cross-correlating weak lensing surveys

The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal-to-noise ratio, such as the Supernova/Acceleration Probe ( SNAP ). However, removal of any systematics or noise will remain a major cause of concern for any weak lensing survey. One of the best ways of spotting any undetected source of systematic noise is to compare surveys that probe the same part of the sky. In this paper we study various measures that are useful in cross-correlating weak lensing surveys with diverse survey strategies. Using two different statistics – the shear components and the aperture mass – we construct a class of estimators which encode such cross-correlations. These techniques will also be useful in studies where the entire source population from a specific survey can be divided into various redshift bins to study cross-correlations among them. We perform a detailed study of the angular size dependence and redshift dependence of these observables and of their sensitivity to the background cosmology. We find that one-point and two-point statistics provide complementary tools which allow one to constrain cosmological parameters and to obtain a simple estimate of the noise of the survey.     

Revealing of periodicities in the variations of differential rotation of the Sun

It is presumed that a north-southern asymmetry of a solid-body rotation of large spots, depending on even and odd solar activity cycles (Gigolashvili and Khutsishvili 1 1989, 1990) may possibly be explained by the asymmetry of the appearance of large structures with strong magnetic fields in the corresponding hemispheres. Spectral analysis of the observational data shows the presence of cyclic variations of differential rotation of large- and middle-sized spots. Variations of differential rotation of small spots are either absent or overlapped by noise. It is also supposed that the discovered and most frequently realized component of the spectrum of solar differential rotation variations — a four-years periodicity — may be either a real phenomenon or the result of overlapping of multiple quasi bi-annual variations.     

The distribution of microlensed light-curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light-curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.     

黑洞候选体MAXI J1535-571爆发期间的时变现象

利用“慧眼”(Hard X-ray Modulation Telescope, Insight-HXMT)卫星在2017年9月对黑洞候选体MAXI J1535-571的观测数据,研究了该源在爆发期内的时变现象.当源处于不同的爆发谱态时,功率密度谱的谱型存在明显差异.在硬中间态,有明显的限带噪声(band-limited noise)成分和QPO (Quasi-Periodic Oscillation)成分.分析结果表明:低频限带噪声的特征频率随能量的变化呈现正相关,即软能段光子的特征频率小于硬能段光子的特征频率. 0.1–0.5 Hz频率区间的限带噪声RMS (Root Mean Square)谱在硬中间态和软中间态均出现峰值,且在高能端存在差异,可能是主导噪声RMS的能谱成分占比不同.当谱态由硬中间态过渡到软中间态时, C型QPO的RMS谱保持相似趋势,但限带噪声RMS谱存在谱态依赖现象,暗示着噪声和QPO有不同的起源机制.     

Extragalactic source counts and contributions to the anisotropies of the cosmic microwave background: predictions for the Planck Surveyor mission

We present predictions for the counts of extragalactic sources, the contributions to fluctuations and their angular power spectrum in each channel foreseen for the Planck Surveyor (formerly COBRAS/SAMBA ) mission. The contribution to fluctuations owing to clustering of both radio and far-IR sources is found to be generally small in comparison with the Poisson term; however the relative importance of the clustering contribution increases and may eventually become dominant if sources are identified and subtracted down to faint flux limits. The central Planck frequency bands are expected to be 'clean': at high galactic latitude (| b | > 20°), where the reduced galactic noise does not prevent the detection of the extragalactic signal, only a tiny fraction of pixels is found to be contaminated by discrete extragalactic sources. Moreover, the 'flat' angular power spectrum of fluctuations resulting from extragalactic sources substantially differs from that of primordial fluctuations; therefore, the removal of contaminating signals is eased even at frequencies where point sources give a sizeable contribution to the foreground noise.     

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation co-efficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle ei-ther from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.     

Far-infrared detection limits – II. Probing confusion including source confusion

We present a comprehensive analysis for the determination of the confusion levels for the current and the next generation of far-infrared surveys assuming three different cosmological evolutionary scenarios. We include an extensive model for diffuse emission from infrared cirrus in order to derive absolute sensitivity levels taking into account the source confusion noise due to point sources, the sky confusion noise due to the diffuse emission, and instrumental noise. We use our derived sensitivities to suggest best survey strategies for the current and the future far-infrared space missions Spitzer , AKARI ( ASTRO-F ), Herschel and SPICA . We discuss whether the theoretical estimates are realistic and the competing necessities of reliability and completeness. We find the best estimator for the representation of the source confusion and produce predictions for the source confusion using far-infrared source count models. From these confusion limits considering both source and sky confusions, we obtain the optimal, confusion limited redshift distribution for each mission. Finally, we predict the cosmic far-infrared background (CFIRB), which includes information about the number and distribution of the contributing sources.     

Estimating the spectral indices of correlated astrophysical foregrounds by a second-order statistical approach

We present the first tests of a new method, the correlated component analysis (CCA) based on second-order statistics, to estimate the mixing matrix, a key ingredient to separate astrophysical foregrounds superimposed to the Cosmic Microwave Background (CMB). In the present application, the mixing matrix is parametrized in terms of the spectral indices of Galactic synchrotron and thermal dust emissions, while the free–free spectral index is prescribed by basic physics, and is thus assumed to be known. We consider simulated observations of the microwave sky with angular resolution and white stationary noise at the nominal levels for the Planck satellite, and realistic foreground emissions, with a position-dependent synchrotron spectral index. We work with two sets of Planck frequency channels: the low-frequency set, from 30 to 143 GHz, complemented with the Haslam 408 MHz map, and the high-frequency set, from 217 to 545 GHz. The concentration of intense free–free emission on the Galactic plane introduces a steep dependence of the spectral index of the global Galactic emission with Galactic latitude, close to the Galactic equator. This feature makes difficult for the CCA to recover the synchrotron spectral index in this region, given the limited angular resolution of Planck , especially at low frequencies. A cut of a narrow strip around the Galactic equator  (| b | < 3°)  , however, allows us to overcome this problem. We show that, once this strip is removed, the CCA allows an effective foreground subtraction, with residual uncertainties inducing a minor contribution to errors on the recovered CMB power spectrum.     

Detection and extraction of signals from the epoch of reionization using higher-order one-point statistics

Detecting redshifted 21-cm emission from neutral hydrogen in the early Universe promises to give direct constraints on the epoch of reionization (EoR). It will, though, be very challenging to extract the cosmological signal (CS) from foregrounds and noise which are orders of magnitude larger. Fortunately, the signal has some characteristics which differentiate it from the foregrounds and noise, and we suggest that using the correct statistics may tease out signatures of reionization. We generate mock data cubes simulating the output of the Low Frequency Array (LOFAR) EoR experiment. These cubes combine realistic models for Galactic and extragalactic foregrounds and the noise with three different simulations of the CS. We fit out the foregrounds, which are smooth in the frequency direction, to produce residual images in each frequency band. We denoise these images and study the skewness of the one-point distribution in the images as a function of frequency. We find that, under sufficiently optimistic assumptions, we can recover the main features of the redshift evolution of the skewness in the 21-cm signal. We argue that some of these features – such as a dip at the onset of reionization, followed by a rise towards its later stages – may be generic, and give us a promising route to a statistical detection of reionization.     

The broad-band noise characteristics of selected anomalous X-ray pulsars and soft gamma-ray repeaters

We present the broad-band noise structure of selected anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) in the 2–60 keV energy band. We have analysed Rossi X-Ray Timing Explorer Proportional Counter Array archival light curves for four AXPs and one SGR. We detect that the persistent emission of these sources shows band-limited noise at low frequencies in the range 0.005–0.05 Hz varying from 2.5 to 70 per cent integrated rms in times of prolonged quiescence and following outbursts. We discovered band-limited red noise in 1E 2259+586 only for ∼2 yr after its major 2002 outburst. The system shows no broad-band noise otherwise. Although this rise in noise in 1E 2259+586 occurred following an outburst which included a rotational glitch, the other glitching AXPs showed no obvious change in broad-band noise, thus it does not seem that this noise is correlated with glitches. The only source that showed significant variation in broad-band noise was 1E   1048.1−5937  , where the noise gradually rose for 1.95 yr at a rate of ∼3.6 per cent per year. For this source the increases in broad-band noise was not correlated with the large increases in persistent and pulsed flux, or its two short SGR-like bursts. This rise in noise did commence after a long burst, however, given the sparsity of this event, and the possibility that similar bursts went unnoticed the trigger for the rise is noise in 1E   1048.1−5937  is not as clear as for 1E 2259+586. The other three sources indicate a persistent band-limited noise at low levels in comparison.     

Fluctuations in finite-N equilibrium stellar systems

Gravitational amplification of Poisson noise in stellar systems is important on large scales. For example, it increases the dipole noise power by roughly a factor of 6 and the quadrupole noise by 50 per cent for a King model profile. The dipole noise is amplified by a factor of 15 for the core-free Hernquist model. The predictions are computed by summing over the wakes caused by each star in the system — the dressed-particle formalism of Rostoker & Rosenbluth — and are demonstrated by N -body simulation.   This result implies that a collisionless N -body simulation is impossible; the fluctuation noise which causes relaxation is an intrinic part of self-gravity. In other words, eliminating two-body scattering at interparticle scales does not eliminate relaxation altogether.   Applied to dark matter haloes of disc galaxies, particle numbers of at least 10⁶ will be necessary to suppress this noise at a level that does not dominate or significantly affect the disc response. Conversely, haloes are most likely far from phase-mixed equilibrium and the resulting noise spectrum may seed or excite observed structure such as warps, spiral arms and bars. For example, discreteness noise in the halo, similar to that caused by a population of 10⁶-M⊙ black holes, can produce observable warping and possibly excite or seed other disc structure.     

Timeline analysis and wavelet multiscale analysis of the AKARI All-Sky Survey at 90 μm

We present a careful analysis of the point-source detection limit of the AKARI All-Sky Survey in the WIDE-S 90-μm band near the North Ecliptic Pole (NEP). Timeline analysis is used to detect IRAS ( Infrared Astronomy Satellite ) sources and then a conversion factor is derived to transform the peak timeline signal to the interpolated 90-μm flux of a source. Combined with a robust noise measurement, the point-source flux detection limit at signal-to-noise ratio  (S/N) > 5  for a single detector row is  1.1 ± 0.1 Jy  which corresponds to a point-source detection limit of the survey of ∼0.4 Jy.
Wavelet transform offers a multiscale representation of the Time Series Data ( tsd ). We calculate the continuous wavelet transform of the tsd and then search for significant wavelet coefficients considered as potential source detections. To discriminate real sources from spurious or moving objects, only sources with confirmation are selected. In our multiscale analysis, IRAS sources selected above 4σ can be identified as the only real sources at the Point Source Scales. We also investigate the correlation between the non- IRAS sources detected in timeline analysis and cirrus emission using wavelet transform and contour plots of wavelet power spectrum. It is shown that the non- IRAS sources are most likely to be caused by excessive noise over a large range of spatial scales rather than real extended structures such as cirrus clouds.     

Map making in small field modulated CMB polarization experiments: approximating the maximum likelihood method

Map making presents a significant computational challenge to the next generation of kilopixel cosmic microwave background polarization experiments. Years worth of time ordered data (TOD) from thousands of detectors will need to be compressed into maps of the T , Q and U Stokes parameters. Fundamental to the science goal of these experiments, the observation of B modes, is the ability to control noise and systematics. In this paper, we consider an alternative to the maximum likelihood method, called destriping , where the noise is modelled as a set of discrete offset functions and then subtracted from the time stream. We compare our destriping code (Descart: the DEStriping CARTographer) to a full maximum likelihood mapmaker, applying them to 200 Monte Carlo simulations of TOD from a ground-based, partial-sky polarization modulation experiment. In these simulations, the noise is dominated by either detector or atmospheric  1/ f   noise. Using prior information of the power spectrum of this noise, we produce destriped maps of T , Q and U which are negligibly different from optimal. The method does not filter the signal or bias the E- or B-mode power spectra. Depending on the length of the destriping baseline, the method delivers between five and 22 times improvement in computation time over the maximum likelihood algorithm. We find that, for the specific case of single detector maps, it is essential to destripe the atmospheric  1/ f   in order to detect B modes, even though the Q and U signals are modulated by a half-wave plate spinning at 5 Hz.