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1.
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.  相似文献   

2.
Given a set of images, whose pixel values can be considered as the components of a vector, it is interesting to estimate the modulus of such a vector in some localized areas corresponding to a compact signal. For instance, the detection/estimation of a polarized signal in compact sources immersed in a background is relevant in some fields like astrophysics. We develop two different techniques, one based on the Neyman–Pearson lemma, the Neyman–Pearson filter (NPF), and another based on pre-filtering before fusion, the filtered fusion (FF), to deal with the problem of detection of the source and estimation of the polarization given two or three images corresponding to the different components of polarization (two for linear polarization, three including circular polarization). For the case of linear polarization, we have performed numerical simulations on two-dimensional patches to test these filters following two different approaches (a blind and a non-blind detection), considering extragalactic point sources immersed in cosmic microwave background (CMB) and non-stationary noise with the conditions of the 70 GHz Planck channel. The FF outperforms the NPF, especially for low fluxes. We can detect with the FF extragalactic sources in a high noise zone with fluxes      Jy for (blind/non-blind) detection and in a low noise zone with fluxes      Jy for (blind/non-blind) detection with low errors in the estimated flux and position.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
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.  相似文献   

6.
Polarization is the next frontier of cosmic microwave background analysis, but its signal is dominated over much of the sky by foregrounds which must be carefully removed. To determine the efficacy of this cleaning, it is necessary to have sensitive tests for residual foreground contamination in polarization sky maps. The dominant Galactic foregrounds introduce a large-scale anisotropy on to the sky, so it makes sense to use a statistic sensitive to overall directionality for this purpose. Here, we adapt the rapidly computable     statistic of Bunn and Scott to polarization data, and demonstrate its utility as a foreground monitor by applying it to the low-resolution Wilkinson Microwave Anisotropy Probe 3-yr sky maps. With a thorough simulation of the maps' noise properties, we find no evidence for contamination in the foreground cleaned sky maps.  相似文献   

7.
Recently, a symmetry-based method to test for statistical isotropy of the cosmic microwave background was developed. We apply the method to template-cleaned 3- and 5-years Wilkinson Microwave Anisotropy Probe - Differencing Assembly maps. We examine a wide range of angular multipoles from  2 < l < 300  . The analysis detects statistically significant signals of anisotropy inconsistent with an isotropic cosmic microwave background in some of the foreground-cleaned maps. We are unable to resolve whether the anomalies have a cosmological, local astrophysical or instrumental origin. Assuming the anisotropy arises due to residual foreground contamination, we estimate the residual foreground power in the maps. For the W -band maps, we also find a highly improbable degree of isotropy we cannot explain. We speculate that excess isotropy may be caused by faulty modelling of detector noise.  相似文献   

8.
We address the problem of encoding and compressing data dominated by noise. Information is decomposed into 'reference' sequences plus arrays containing noisy differences susceptible to being described by a known probability distribution. One can then give reliable estimates of the optimal compression rates by estimating the corresponding Shannon entropy. As a working example, this idea is applied to an idealized model of the cosmic microwave background (CMB) data on board the Planck satellite. Data reduction is a critical issue in space missions because the total information that can be downloaded to Earth is sometimes limited by telemetry allocation. Similar limitations might arise in remotely operated ground based telescopes. This download-rate limitation could reduce the amount of diagnostics sent on the stability of the instruments and, as a consequence, curb the final sensitivity of the scientific signal. Our proposal for Planck consists of taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences could be made independent of the external signal, so that they are dominated by thermal (white) instrumental noise, which is simpler to model than the sky signal. Similar approaches can be found in other individual applications. Generic simulations and analytical predictions show that high compression rates,     can be obtained with minor or zero loss of sensitivity. Possible effects of digital distortion are also analysed. The proposed scheme is flexible and reliable enough to be optimized in relation to other critical aspects of the corresponding application. For Planck , this study constitutes an important step towards a more realistic modelling of the final sensitivity of the CMB temperature anisotropy maps.  相似文献   

9.
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.  相似文献   

10.
We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.  相似文献   

11.
Foreground subtraction is the biggest challenge for future redshifted 21-cm observations to probe reionization. We use a short Giant Meter Wave Radio Telescope (GMRT) observation at 153 MHz to characterize the statistical properties of the background radiation across ∼1° to subarcmin angular scales, and across a frequency band of 5 MHz with 62.5 kHz resolution. The statistic we use is the visibility correlation function, or equivalently the angular power spectrum   C l   . We present the results obtained from using relatively unsophisticated, conventional data calibration procedures. We find that even fairly simple-minded calibration allows one to estimate the visibility correlation function at a given frequency   V 2( U , 0)  . From our observations, we find that   V 2( U , 0)  is consistent with foreground model predictions at all angular scales except the largest ones probed by our observations where the model predictions are somewhat in excess. On the other hand, the visibility correlation between different frequencies  κ( U , Δν)  seems to be much more sensitive to calibration errors. We find a rapid decline in  κ( U , Δν)  , in contrast with the prediction of less than 1 per cent variation across 2.5 MHz. In this case, however, it seems likely that a substantial part of the discrepancy may be due to limitations of data reduction procedures.  相似文献   

12.
We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang, using a technique based on the discrete wavelet transform. Their analysis was performed on the two DMR faces centred on the North and South Galactic poles, respectively, using the Daubechies 4 wavelet basis. We show that these results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations of the data, we calculate estimates of the skewness, kurtosis and scale–scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity in the DMR-DSMB map at greater than the 99 per cent confidence level, but most of these occur on pixel–pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond ℓ=40 from the COBE maps, only one robust detection remains. Moreover, using Monte Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. We repeat the analysis for the 53+90 GHz coadded COBE map. In this case, after removing ℓ>40 multipoles, two non-Gaussian detections at the 99 per cent level remain. Nevertheless, again using Monte Carlo simulations, we find that the probability of obtaining two such detections by chance is 0.28. Thus, we conclude the wavelet technique does not yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE data.  相似文献   

13.
It is the aim of this paper to introduce the use of isotropic wavelets to detect and determine the flux of point sources appearing in cosmic microwave background (CMB) maps. The most suitable wavelet to detect point sources filtered with a Gaussian beam is the 'Mexican Hat'. An analytical expression of the wavelet coefficient obtained in the presence of a point source is provided and used in the detection and flux estimation methods presented. For illustration the method is applied to two simulations (assuming Planck mission characteristics) dominated by CMB (100 GHz) and dust (857 GHz), as these will be the two signals dominating at low and high frequencies respectively in the Planck channels. We are able to detect bright sources above 1.58 Jy at 857 GHz (82 per cent of all sources) and above 0.36 Jy at 100 GHz (100 per cent of all), with errors in the flux estimation below 25 per cent. The main advantage of this method is that nothing has to be assumed about the underlying field, i.e. about the nature and properties of the signal plus noise present in the maps. This is not the case in the detection method presented by Tegmark & Oliveira-Costa. Both methods are compared, producing similar results.  相似文献   

14.
We have studied the problem of an all-sky search in reference to a continuous gravitational wave particularly for such sources whose wave-form are known in advance. We have made an analysis of the number of templates required for matched-filter analysis as applicable to these sources. We have employed the concept of fitting factor (FF); treating the source location as the parameters of the signal manifold and have studied the matching of the signal with templates corresponding to different source locations. We have investigated the variation of FF with source location and have noticed a symmetry in template parameters,  θT  and  φT  . It has been found that the two different template values in source location, each in  θT  and  φT  , have the same FF. We have also computed the number of templates required assuming the noise power spectral density   S n ( f )  to be flat. It is observed that higher FF requires an exponentially increasing, large number of templates.  相似文献   

15.
We examine the ability of the future Planck mission to provide a catalogue of galaxy clusters observed via their Sunyaev–Zel'dovich (SZ) distortion in the cosmic microwave background (CMB). For this purpose we produce full-sky SZ maps based on N -body simulations and scaling relations between cluster properties for several cosmological models. We extrapolate the N -body simulations by a mass function to high redshifts in order to obtain a realistic SZ background. The simulated Planck observations include, besides the thermal and kinematic SZ effects, contributions from the primordial CMB, extragalactic point sources as well as Galactic dust, free–free and synchrotron emission. A harmonic-space maximum-entropy method is used to separate the SZ signal from contaminating components in combination with a cluster detection algorithm based on thresholding and flux integration to identify clusters and to obtain their fluxes. We estimate a survey sensitivity limit (depending on the quality of the recovered cluster flux) and provide cluster survey completeness and purity estimates. We find that, given our modelling and detection algorithm, Planck will reliably detect at least several thousands of clusters over the full sky. The exact number depends on the particular cosmological model (up to 10 000 cluster detections in a concordance ΛCDM model with  σ8= 0.9  ). We show that the Galaxy does not significantly affect the cluster detection. Furthermore, the dependence of the thermal SZ power spectrum on the matter variance on scales of  8 h −1  Mpc and the quality of its reconstruction by the employed method are investigated. Our simulations suggest that the Planck cluster sample will not only be useful as a basis for follow-up observations, but also will have the ability to provide constraints on cosmological parameters.  相似文献   

16.
This paper presents the results from the Jodrell BankInstituto de Astrofisicia de Canarias (IAC) two-element 33-GHz interferometer operated with an element separation of 32.9 wavelengths and hence sensitive to 1°-scale structure on the sky. The level of cosmic microwave background (CMB) fluctuations, assuming a flat CMB spatial power spectrum over the range of multipoles =208±18, was found using a likelihood analysis to be at the 68 per cent confidence level, after the subtraction of the contribution of monitored point sources. Other possible foreground contributions have been assessed and are expected to have negligible impact on this result.  相似文献   

17.
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.  相似文献   

18.
One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free‐free and thermal dust emission. The feasibility of using simple neural networks to extract CMB has been demonstrated on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto‐correlation and cross‐correlation power spectra within a mask covering about 63 % of the sky have been used together with a “high pass filter” in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron neural networks. This spectrum contains a bright feature with signal to noise ratios 4.5 within 200 ≪ l ≪ 250. The spectrum is significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour quite different from the “canonical” models (weak lensing plus B‐modes spectra with different tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

19.
We investigate which practical constraints are imposed by foregrounds on the detection of the B-mode polarization generated by gravitational waves, in the case of experiments of the type currently being planned. As the B-mode signal is probably dominated by foregrounds at all frequencies, the detection of the cosmological component depends drastically on our ability to remove foregrounds. We provide an analytical expression with which to estimate the level of the residual polarization for Galactic foregrounds, according to the method employed for their subtraction. We interpret this result in terms of the lower limit of the tensor-to-scalar ratio r that allows us to disentangle the cosmological B-mode polarization from the foreground contribution. Polarized emission from extragalactic radio sources and gravitational lensing is also taken into account. As a first approach, we consider the ideal limit of an instrumental noise-free experiment: for full-sky coverage and a resolution of 1°, we obtain a limit of   r ∼ 10−4  . This value can be improved by high-resolution experiments and, in principle, there is no clear fundamental limit on the detectability of the polarization of gravitational waves. Our analysis is also applied to planned or hypothetical future polarization experiments, taking into account expected noise levels.  相似文献   

20.
The Sunyaev–Zel'dovich (SZ) effect and the Faraday rotation from haloes are examined over a wide mass range, including gas condensation and magnetic field evolution. Contributions to the cosmic microwave background (CMB) angular power spectrum are evaluated for galaxy clusters, galaxy groups and galaxies. Smaller mass haloes are found to play a more important role than massive haloes for the B -mode polarization associated with the SZ CMB anisotropies. The B modes from the Faraday rotation dominate the secondary B modes caused by gravitational lensing at  ℓ > 3000  . Measurement of B -mode polarization in combination with the SZ power spectrum can potentially provide important constraints on intracluster magnetic field and gas evolution at early epochs.  相似文献   

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