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1.
The paper is based on the notion that the Nyquist frequency  νN  is a symmetry point of the periodogram of a time series: the power spectrum at frequencies above  νN  is a mirror image of that below  νN  . Koen showed that the sum     (where   tk   and   t ℓ  range over the time points of observation) is zero when the frequency  ν=νN  . This property is used to investigate the Nyquist frequency for data which are almost regularly spaced in time. For some configurations, there are deep minima of SS at frequencies  νP≪νN  ; such  νP  are dubbed 'pseudo-Nyquist' frequencies: the implication is that most of the information about the frequency content of the data is available in the spectrum over  (0, νP)  . Systematic simulation results are presented for two configurations – small random variations in respectively the time points of observation and the lengths of the intervals between successive observations. A few real examples of CCD time series photometry obtained over several hours are also discussed.  相似文献   

2.
We test an analytic model for the two-point correlations of galaxy clusters in redshift space using the Hubble volume N -body simulations. The correlation function of clusters shows no enhancement along the line of sight, owing to the lack of any virialized structures in the cluster distribution. However, the distortion of the clustering pattern arising from coherent bulk motions is clearly visible. The distribution of cluster peculiar motions is well described by a Gaussian, except in the extreme high-velocity tails. The simulations produce a small but significant number of clusters with large peculiar motions. The form of the redshift-space power spectrum is strongly influenced by errors in measured cluster redshifts in extant surveys. When these errors are taken into account, the model reproduces the power spectrum recovered from the simulation to an accuracy of 15 per cent or better over a decade in wavenumber. We compare our analytic predictions with the power spectrum measured from the APM cluster redshift survey. The cluster power spectrum constrains the amplitude of density fluctuations, as measured by the linear rms variance in spheres of radius 8  h −1 Mpc, denoted by σ 8. When combined with the constraints on σ 8 and the density parameter Ω derived from the local abundance of clusters, we find a best-fitting cold dark matter model with     and     , for a power spectrum shape that matches that measured for galaxies. However, for the best-fitting value of Ω and given the value of Hubble's constant from recent measurements, the assumed shape of the power spectrum is incompatible with the most readily motivated predictions from the cold dark matter paradigm.  相似文献   

3.
The quality of helioseismological ground-based data strongly depends on the presence of a gap in the observational window. In order to address that problem in the case of full-disc low-degree p-mode velocity measurements, Fossat et al. proposed a gap-filling method called 'Repetitive music'. The autocorrelation function of the velocity signal shows a correlation of more than 70 per cent at about 4 h because of the quasi-periodicity of p-mode peaks in the Fourier spectrum. The method then consists of filling gaps of the velocity signal with data, when they exist, located 4 h before or after.
By using Monte Carlo simulations, we assess the effects of the gap-filling method on p-mode parameters and their errors. A way to remove the modulation in the power spectrum resulting from the gap-filling method is proposed; its effects on p-mode frequencies, linewidths, amplitudes and asymmetries are discussed as a function of frequency and signal-to-noise ratio.  相似文献   

4.
We present X-ray/ γ -ray spectra of Cyg X-1 observed during the transition from the hard to the soft state and in the soft state by ASCA , RXTE and CGRO /OSSE in 1996 May and June. The spectra consist of a dominant soft component below ∼2 keV and a power-law-like continuum extending to at least ∼800 keV. We interpret them as emission from an optically thick, cold accretion disc and from an optically thin, non-thermal corona above the disc. A fraction f ≳0.5 of total available power is dissipated in the corona.
We model the soft component by multicolour blackbody disc emission taking into account the torque-free inner-boundary condition. If the disc extends down to the minimum stable orbit, the ASCA RXTE data yield the most probable black hole mass of M X≈10 M⊙ and an accretion rate,     , locating Cyg X-1 in the soft state in the upper part of the stable, gas-pressure-dominated, accretion-disc solution branch.
The spectrum of the corona is well modelled by repeated Compton scattering of seed photons from the disc off electrons with a hybrid, thermal/non-thermal distribution. The electron distribution can be characterized by a Maxwellian with an equilibrium temperature of kT e∼30–50 keV, a Thomson optical depth of τ ∼0.3 and a quasi-power-law tail. The compactness of the corona is 2≲ℓh≲7, and a presence of a significant population of electron–positron pairs is ruled out.
We find strong signatures of Compton reflection from a cold and ionized medium, presumably an accretion disc, with an apparent reflector solid angle, Ω/2π∼0.5–0.7. The reflected continuum is accompanied by a broad iron K α line.  相似文献   

5.
With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever-greater precision. However, this increased accuracy also places greater demands on the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two-point statistics of the cosmic shear field. These can be either studied directly using the two-point correlation function or in Fourier space, using the power spectrum. But analysing weak lensing data inevitably involves the masking out of regions, for example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only   N log  N   operations, leading to a new image from which we can compute straightforwardly and with a very good accuracy both the power spectrum and the bispectrum. We then propose a new method to compute the bispectrum with a polar fft algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally, we propose a new method for dark matter mass map reconstruction from shear observations, which integrates this new inpainting concept. A range of examples based on 3D N -body simulations illustrates the results.  相似文献   

6.
We present a calculation of the blazar contribution to the extragalactic diffuse γ -ray background (EGRB) in the EGRET energy range. Our model is based on inverse-Compton scattering as the dominant γ -ray production process in the jets of flat spectrum radio quasars (FSRQs) and BL Lac objects, and on the unification scheme of radio-loud AGN. According to this picture, blazars represent the beamed fraction of the Fanaroff–Riley radio galaxies (FR galaxies).
The observed log  N –log  S distribution and redshift distribution of both FSRQs and BL Lacs constrain our model. Depending slightly on the evolutionary behaviour of blazars, we find that unresolved AGN underproduce the intensity of the extragalactic background radiation. With our model only 20–40 per cent of the extragalactic background emission can be explained by unresolved blazars if we integrate to a maximum redshift of Z max=3. For Z max=5, blazars could account for 40–80 per cent of the EGRB. Roughly 70–90 per cent of the AGN contribution to the EGRB would result from BL Lacs. While the systematic uncertainties in our estimate for the FSRQ contribution appear small, in the case of BL Lacs our model parameters are not consistent with the results from studies in other wavelength regimes, and therefore may have larger systematic uncertainties. Thus we end up with two possibilities, depending on whether we underpredict or overpredict the BL Lac contribution: either unresolved AGN cannot account for the entire EGRB, or unresolved BL Lacs produce the observed background.
We predict a significant flattening of the γ -ray log  N –log  S function in the next two decades of flux below the EGRET threshold.  相似文献   

7.
We implement an independent component analysis (ICA) algorithm to separate signals of different origin in sky maps at several frequencies. Owing to its self-organizing capability, it works without prior assumptions on either the frequency dependence or the angular power spectrum of the various signals; rather, it learns directly from the input data how to identify the statistically independent components, on the assumption that all but, at most, one of the components have non-Gaussian distributions.
We have applied the ICA algorithm to simulated patches of the sky at the four frequencies (30, 44, 70 and 100 GHz) used by the Low Frequency Instrument of the European Space Agency's Planck satellite. Simulations include the cosmic microwave background (CMB), the synchrotron and thermal dust emissions, and extragalactic radio sources. The effects of the angular response functions of the detectors and of instrumental noise have been ignored in this first exploratory study. The ICA algorithm reconstructs the spatial distribution of each component with rms errors of about 1 per cent for the CMB, and 10 per cent for the much weaker Galactic components. Radio sources are almost completely recovered down to a flux limit corresponding to ≃0.7 σ CMB, where σ CMB is the rms level of the CMB fluctuations. The signal recovered has equal quality on all scales larger than the pixel size. In addition, we show that for the strongest components (CMB and radio sources) the frequency scaling is recovered with per cent precision. Thus, algorithms of the type presented here appear to be very promising tools for component separation. On the other hand, we have been dealing here with a highly idealized situation. Work to include instrumental noise, the effect of different resolving powers at different frequencies and a more complete and realistic characterization of astrophysical foregrounds is in progress.  相似文献   

8.
An aliasing effect brought up by mass assignment onto Fast Fourier Transformation (FFT) grids may bias measurement of the power spectrum of large scale structures. In this paper, based on the Beylkin's unequally spaced FFT technique, we propose a new precise method to extract the true power spectrum of a large discrete data set. We compare the traditional mass assignment schemes with the new method using the Daub6 and the 3rd-order B-spline scaling functions. Our measurement of Poisson samples and samples of N-body simulations shows that the B-spline scaling function is an optimal choice for mass assignment in the sense that (1) it has a compact support in real space and thus yields an efficient algorithm (2) without any extra corrections. The Fourier space behavior of the 3rd-order B-spline scaling function enables it to be able to accurately recover the true power spectrum with errors less than 5% up to k ＜ kN. It is expected that such a method can be applied to higher order statistics in Fourier space and will enable us to have a precision capture of the non-Gaussian features in the large scale structure of the universe.  相似文献   

9.
We assess the detectability of baryonic acoustic oscillation (BAO) in the power spectrum of galaxies using ultralarge volume N -body simulations of the hierarchical clustering of dark matter and semi-analytical modelling of galaxy formation. A step-by-step illustration is given of the various effects (non-linear fluctuation growth, peculiar motions, non-linear and scale-dependent bias) which systematically change the form of the galaxy power spectrum on large scales from the simple prediction of linear perturbation theory. Using a new method to extract the scale of the oscillations, we nevertheless find that the BAO approach gives an unbiased estimate of the sound horizon scale. Sampling variance remains the dominant source of error despite the huge volume of our simulation box  (=2.41  h −3 Gpc3)  . We use our results to forecast the accuracy with which forthcoming surveys will be able to measure the sound horizon scale, s , and, hence constrain the dark energy equation of state parameter, w (with simplifying assumptions and without marginalizing over the other cosmological parameters). Pan-STARRS could potentially yield a measurement with an accuracy of  Δ s / s = 0.5–0.7  per cent (corresponding to Δ w ≈ 2–3 per cent), which is competitive with the proposed WFMOS survey (  Δ s / s = 1  per cent Δ w ≈ 4 per cent). Achieving Δ w ≤ 1 per cent using BAO alone is beyond any currently commissioned project and will require an all-sky spectroscopic survey, such as would be undertaken by the SPACE mission concept under proposal to ESA.  相似文献   

10.
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11.
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12.
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   

13.
Particle acceleration by ultrarelativistic shocks: theory and simulations   总被引：1，自引：0，他引：1  
We consider the acceleration of charged particles near ultrarelativistic shocks, with Lorentz factor     . We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultrarelativistic shocks is a power law,     , with a nearly universal value     for the slope of this power law.
We confirm that the ultrarelativistic equivalent of the Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurrence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle     around the shock normal.
We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount:     . This limits the energy change per shock crossing cycle to     , except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor     for those particles that are scattered back across the shock into the upstream region.  相似文献   

14.
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.  相似文献   

15.
We present accurate measurements of the physical conditions in five powerful radio galaxies, as derived from deep, long-slit spectroscopic observations. All five objects show prominent extended line emission, and have X-ray luminosities similar to those of isolated elliptical galaxies. The data are high enough quality that the electron density and temperature can be measured at several positions across the emission-line nebulae.
We subtract a model continuum comprising a combination of a 15-Gyr stellar template, a young stellar template and a power law, so as to be better able to measure faint diagnostic lines. Electron temperatures measured from the [O  iii ](4959+5007)/4363 line ratio are in the range  10 000< T e<20 000 K  , whilst  [S  ii ](6716/6731)  densities fall between  100–500 cm-3.  Using these values, we find pressures within the line-emitting clouds a factor of  10–100  times higher than expected for pressure balance with the hot X-ray haloes of the host galaxies.
Previous studies of sources that show significant evidence of jet–cloud interactions, both in terms of their kinematics and ionization, have concluded that the overpressure is a result of the warm, line-emitting gas being compressed by the radio cocoon; however, there is no evidence that the radio jet is influencing the emission-line regions in four of our five objects.
We suggest that it is plausible that the line-emitting clouds have not yet relaxed into pressure equilibrium from their initial photoionization by the central active galactic nucleus.  相似文献   

16.
It is shown that the energy dependence of the time-lags in Cygnus X-1 excludes any significant contribution of the standard reflected component to the observed lags. The conclusion is valid in the     frequency range where time-lags have been detected with sufficient significance. In fact, the data hint that the reflected component is working in the opposite direction, reducing the lags at energies where the contribution of the reflected component is significant.
We argue that the observed logarithmic dependence of time-lags on energy could be due to the small variations of the spectral index in the frame of a very simple phenomenological model. We assume that an optically thin flow/corona, emitting a power law like spectrum, is present at a range of distances from the compact object. The slope of the locally emitted spectrum is a function of distance, with the hardest spectrum emitted in the innermost region. If perturbations with different time-scales are introduced to the accretion flow at different radii, then X-ray lags naturally appear, caused by the inward propagation of perturbations on the diffusion time-scales.  相似文献   

17.
The two point angular correlation function is an excellent measure of structure in the Universe. To extract from it the three-dimensional power spectrum, one must invert Limber's equation. Here we perform this inversion using a Bayesian prior constraining the smoothness of the power spectrum. Among other virtues, this technique allows for the possibility that the estimates of the angular correlation function are correlated from bin to bin. The outputs of this technique are estimators for the binned power spectrum and a full covariance matrix. Angular correlations mix small and large scales but after the inversion, small-scale data can be trivially eliminated, thereby allowing for realistic constraints on theories of large-scale structure. We analyse the automated plate measurement (APM) catalogue as an example, comparing our results with previous results. As a by-product of these tests, we find – in rough agreement with previous work – that APM places stringent constraints on cold dark matter inspired models, with the shape parameter constrained to be 0.25±0.04 (using data with wavenumber k ≤0.1  h  Mpc−1). This range of allowed values uses the full power spectrum covariance matrix, but assumes negligible covariance in the off-diagonal angular correlation error matrix, which is estimated with a large angular resolution of 0.5° (in the range 0.5° and 20°).  相似文献   

18.
We use very large cosmological N -body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM) cosmogonies, a critical density model ( τ CDM) and a flat low density model with a cosmological constant (ΛCDM). Our simulations each use 109 particles to follow the mass distribution within cubes of side 2  h −1 Gpc ( τ CDM) and 3  h −1 Gpc (ΛCDM) with a force resolution better than 10−4 of the cube side. We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance. Very similar behaviour is found in the two cases. The correlation length increases from     for samples with mean separation     to     for samples with     The lower value here corresponds to τ CDM and the upper to ΛCDM. The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale. Both correlation lengths and power spectrum biases can be predicted to better than 10 per cent using the simple model of Sheth, Mo & Tormen. This prediction requires only the linear mass power spectrum and has no adjustable parameters. We compare our predictions with published results for the automated plate measurement (APM) cluster sample. The observed variation of correlation length with richness agrees well with the models, particularly for ΛCDM. The observed power spectrum (for a cluster sample of mean separation     ) lies significantly above the predictions of both models.  相似文献   

19.
The high resolution laboratory spectrum of hot water vapour has been recorded in the 500–13 000 cm−1 wavenumber range and we report on the analysis of the 4750–13 000 cm−1 (0.769–2.1 μm) portion. The emission spectrum was recorded using an oxy-acetylene welding torch and a Fourier transform spectrometer. Line assignments in the laboratory spectrum as well as in an absorption spectrum of a sunspot umbra were made with the help of the BT2 line-list. Our torch spectrum is the first laboratory observation of the 9300 Å'steam bands' seen in M-stars and brown dwarfs.  相似文献   

20.
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   

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