Determining the optimum scan map strategy for Herschel-SPIRE using the SPIRE photometer simulator

The forthcoming Herschel space mission will provide an unprecedented view of the far-infrared/submillimetre Universe, with the SPIRE instrument covering the 200–670 μm wavelength range. To obtain the best quality of astronomical data from such an expensive mission the observing modes must be optimized as far as possible. This paper presents the possible scanning strategies that can be utilized by the SPIRE photometer, within the limitations imposed by the Herschel spacecraft. Each strategy is investigated for effectiveness by performing simulated observations, using the SPIRE photometer simulator. By quantifying the data quality using a simple metric, we have been able to select the optimum scanning strategy for SPIRE when it begins taking science data within the next couple of years.
Additionally, this work has led to the development of a specific SPIRE mapmaking algorithm, based on the CMB code MADmap, to be provided as part of the SPIRE data pipeline processing suite. This will allow every SPIRE user to take full advantage of the optimized scan map strategy, which requires the use of maximum likelihood mapmakers such as MADmap.     

Herschel SPIRE FTS relative spectral response calibration

Herschel/SPIRE Fourier transform spectrometer (FTS) observations contain emission from both the Herschel Telescope and the SPIRE Instrument itself, both of which are typically orders of magnitude greater than the emission from the astronomical source, and must be removed in order to recover the source spectrum. The effects of the Herschel Telescope and the SPIRE Instrument are removed during data reduction using relative spectral response calibration curves and emission models. We present the evolution of the methods used to derive the relative spectral response calibration curves for the SPIRE FTS. The relationship between the calibration curves and the ultimate sensitivity of calibrated SPIRE FTS data is discussed and the results from the derivation methods are compared. These comparisons show that the latest derivation methods result in calibration curves that impart a factor of between 2 and 100 less noise to the overall error budget, which results in calibrated spectra for individual observations whose noise is reduced by a factor of 2–3, with a gain in the overall spectral sensitivity of 23 % and 21 % for the two detector bands, respectively.     

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.     

Effects of destriping errors on estimates of the CMB power spectrum

Destriping methods for constructing maps of the cosmic microwave background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates for Planck -like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. Assuming Planck -like low-frequency noise, the noise power spectrum is accurately white at high multipoles  (ℓ≳ 50)  . Destriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis of Planck data and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic '1/ f ' noise.     

asmooth: a simple and efficient algorithm for adaptive kernel smoothing of two-dimensional imaging data

An efficient algorithm for adaptive kernel smoothing (AKS) of two-dimensional imaging data has been developed and implemented using the Interactive Data Language ( idl ). The functional form of the kernel can be varied (top-hat, Gaussian, etc.) to allow different weighting of the event counts registered within the smoothing region. For each individual pixel, the algorithm increases the smoothing scale until the signal-to-noise ratio (S/N) within the kernel reaches a pre-set value. Thus, noise is suppressed very efficiently, while at the same time real structure, that is, signal that is locally significant at the selected S/N level, is preserved on all scales. In particular, extended features in noise-dominated regions are visually enhanced. The asmooth algorithm differs from other AKS routines in that it allows a quantitative assessment of the goodness of the local signal estimation by producing adaptively smoothed images in which all pixel values share the same S/N above the background .
We apply asmooth to both real observational data (an X-ray image of clusters of galaxies obtained with the Chandra X-ray Observatory) and to a simulated data set. We find the asmooth ed images to be fair representations of the input data in the sense that the residuals are consistent with pure noise, that is, they possess Poissonian variance and a near-Gaussian distribution around a mean of zero, and are spatially uncorrelated.     

A high-significance detection of non-Gaussianity in the Wilkinson Microwave Anisotropy Probe 1-yr data using directional spherical wavelets

A directional spherical wavelet analysis is performed to examine the Gaussianity of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 1-yr data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows us to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark, de Oliveira-Costa & Hamilton foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9 per cent significance level is only made at the 95.3 per cent significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of ∼26° and an internal size of ∼3°) at an azimuthal orientation of 72°, are made at the 98.3 per cent significance level, using the same conservative method. The wavelet analysis inherently allows us to localize on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.     

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.     

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.     

Wilkinson Microwave Anisotropy Probe 5-yr constraints on fnl with wavelets

We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f _nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ²  analysis. The  χ²  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f _nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f _nl parameter is constrained to  −8 < f _nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f _nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.     

The EC 14026 stars — IX. KPD 2109+4401

The results of 37 h of high-speed photometry of KPD 2109+4401 are described. At least five periodicities in the range 182–198 s are consistently present in the observations, with amplitudes in the range 1–6 mmag. Results of simultaneous multicolour high-speed photometry with the Stiening photometer are also presented; these data could in principle be used for mode identification of the periodicities. The results of a preliminary study suggest that the pulsations may all be ℓ = 1 and 2 modes. Properties of the star are compared with those of the other EC 14026 stars.     

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.     

Facilities at ARIES for the Nainital-Cape Survey

A collaborative programme searching for mmag pulsations in chemically peculiar stars in the northern hemisphere was initiated in 1997 between Nainital, India, and Cape Town, South Africa. It was therefore named as theNainital-Cape Survey programme. The detection limits imposed by the observing conditions (including atmospheric noise and telescope size) at both Manora Peak and Devasthal sites are described. The scintillation noise on the best photometric nights is≈ 0.1 to 0.2 mmag for these sites. Both places allow one to detect few mmag variation in bright stars(B ≤ 12 mag), and are therefore particularly well-suited for carrying out the proposed survey work. The main characteristics of the three-channel photometer developed at ARIES for carrying out the observations are also presented. This excellent instrument has been used extensively since 1999 at the f/13 Cassegrain focus of ARIES’ 104 cm telescope. In particular, it allowed the survey to result in the discovery of δ Scuti like pulsations in four Am stars, in one rapidly oscillating Ap star, and in a number of probable variables so far. The future prospects are then presented, which regard the acquisition of a high speed time series CCD photometer, a project to build a 3-metre class telescope at Devasthal, and collaborative observations with Indian and foreign astronomical sites.     

The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, ξ and ζ , in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10  h ⁻¹ Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function   Q ₃∼ ζ / ξ ²  . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ≃20 Mpc  h ⁻¹. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading-order PT become important at smaller scales   r ≃10 Mpc  h ^-1  , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.     

A low cosmic microwave background variance in the Wilkinson Microwave Anisotropy Probe data

We have estimated the cosmic microwave background (CMB) variance from the three-year Wilkinson Microwave Anisotropy Probe ( WMAP ) data, finding a value which is significantly lower than the one expected from Gaussian simulations using the WMAP best-fitting cosmological model, at a significance level of 98.7 per cent. This result is even more prominent if we consider only the North ecliptic hemisphere (99.8 per cent). Different analyses have been performed in order to identify a possible origin for this anomaly. In particular, we have studied the behaviour of single-radiometer and single-year data as well as the effect of residual foregrounds and 1/f noise, finding that none of these possibilities can explain the low value of the variance. We have also tested the effect of varying the cosmological parameters, finding that the estimated CMB variance tends to favour higher values of n _s than the one of the WMAP best-fitting model. In addition, we have also tested the consistency between the estimated CMB variance and the actual measured CMB power spectrum of the WMAP data, finding a strong discrepancy. A possible interpretation of this result could be a deviation from Gaussianity and/or isotropy of the CMB.     

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)     

Madam– a map-making method for CMB experiments

We present a new map-making method for cosmic microwave background (CMB) measurements. The method is based on the destriping technique, but it also utilizes information about the noise spectrum. The low-frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum-likelihood analysis, involving the covariance matrix of the amplitudes. We present simulation results with  1/ f   noise and show a reduction in the residual noise with respect to ordinary destriping. This study is related to Planck Low Frequency Instrument (LFI) activities.     

An enlarged cosmic shear survey with the William Herschel Telescope

We report the results of a cosmic shear survey using the 4.2-m William Herschel Telescope on La Palma, to a depth of   R = 25.8 ( z ≈ 0.8)  , over 4 deg². The shear correlation functions are measured on scales from 1 to 15 arcmin, and are used to constrain cosmological parameters. We ensure that our measurements are free from instrumental systematic effects by performing a series of tests, including a decomposition of the signal into E - and B -modes. We also reanalyse the data independently, using the shear measurement pipeline developed for the COMBO-17 survey. This confirms our results and also highlights various effects introduced by different implementations of the basic 'Kaiser–Squires–Broadhurst' shear measurement method. We find that the normalization of the matter power spectrum on 8  h ⁻¹ Mpc scales is  σ₈= (1.02 ± 0.15)(0.3/Ω _m )^1/2  , where the 68 per cent confidence limit error includes noise, sample variance, covariance between angular scales, systematic effects, redshift uncertainty and marginalization over other parameters. We compare these results with other cosmic shear surveys and with recent constraints from the Wilkinson Microwave Anisotropy Probe experiment.     

Observations of flat-spectrum radio sources at λ850 μm from the James Clerk Maxwell Telescope – I. 1997 April to 2000 April

Calibrated data for 65 flat-spectrum extragalactic radio sources are presented at a wavelength of 850 μm, covering a three-year period from 1997 April. The data, obtained from the James Clerk Maxwell Telescope using the SCUBA camera in pointing mode, were analysed using an automated pipeline process based on the Observatory Reduction and Acquisition Control–Data Reduction ( orac–dr ) system. This paper describes the techniques used to analyse and calibrate the data, and presents the data base of results along with a representative sample of the better-sampled light curves.     

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.     

Circular scans for cosmic microwave background anisotropy observation and analysis

A number of experiments for measuring anisotropies of the cosmic microwave background (CMB) use scanning strategies in which temperature fluctuations are measured along circular scans on the sky. It is possible, from a large number of such intersecting circular scans, to build two-dimensional sky maps for subsequent analysis. However, since instrumental effects — especially the excess low-frequency 1/ f noise — project on to such two-dimensional maps in a non-trivial way, we discuss the analysis approach which focuses on information contained in the individual circular scans. This natural way of looking at CMB data from experiments scanning on the circles combines the advantages of elegant simplicity of Fourier series for the computation of statistics useful for constraining cosmological scenarios, and superior efficiency in analysing and quantifying most of the crucial instrumental effects.