Combined Power Spectrum Research Articles

Probing the physics of star formation (ProPStar)

Context. Turbulence is a key component of molecular cloud structure. It is usually described by a cascade of energy down to the dissipation scale. The power spectrum for subsonic incompressible turbulence is ∝k−5/3, while for supersonic turbulence it is ∝k−2. Aims. We determine the power spectrum in an actively star-forming molecular cloud, from parsec scales down to the expected magnetohydrodynamic (MHD) wave cutoff (dissipation scale). Methods. We analyzed observations of the nearby NGC 1333 star-forming region in three different tracers to cover the different scales from ∼10 pc down to 20 mpc. The largest scales are covered with the low-density gas tracer 13CO (1–0) obtained with a single dish, the intermediate scales are covered with single-dish observations of the C18O (3–2) line, while the smallest scales are covered in H13CO+ (1–0) and HNC (1–0) with a combination of NOEMA interferometer and IRAM 30m single-dish observations. The complementarity of these observations enables us to generate a combined power spectrum covering more than two orders of magnitude in spatial scale. Results. We derive the power spectrum in an active star-forming region spanning more than 2 decades of spatial scales. The power spectrum of the intensity maps shows a single power-law behavior, with an exponent of 2.9 ± 0.1 and no evidence of dissipation. Moreover, there is evidence that the power spectrum of the ions to have more power at smaller scales than the neutrals, which is opposite to the theoretical expectations. Conclusions. We show new possibilities for studying the dissipation of energy at small scales in star-forming regions provided by interferometric observations.

Solar-like oscillations inγCephei A as seen through SONG and TESS

Context.Fundamental stellar parameters such as mass and radius are some of the most important building blocks in astronomy, both when it comes to understanding the star itself and when deriving the properties of any exoplanet(s) they may host. Asteroseismology of solar-like oscillations allows us to determine these parameters with high precision.Aims.We investigate the solar-like oscillations of the red-giant-branch starγCep A, which harbours a giant planet on a wide orbit.Methods.We did this by utilising both ground-based radial velocities from the SONG network and space-borne photometry from the NASA TESS mission.Results.From the radial velocities and photometric observations, we created a combined power spectrum, which we used in an asteroseismic analysis to extract individual frequencies. We clearly identify several radial and quadrupole modes as well as multiple mixed, dipole modes. We used these frequencies along with spectroscopic and astrometric constraints to model the star, and we find a mass of 1.27−0.07+0.05M⊙, a radius of 4.74−0.08+0.07R⊙, and an age of 5.7−0.9+0.8Gyr. We then used the mass ofγCep A and our SONG radial velocities to derive masses forγCep B andγCep Ab of 0.328−0.012+0.009M⊙and 6.6−2.8+2.3 MJup, respectively.

Deep Neural Network for EEG Signal-Based Subject-Independent Imaginary Mental Task Classification.

Mental task identification using electroencephalography (EEG) signals is required for patients with limited or no motor movements. A subject-independent mental task classification framework can be applied to identify the mental task of a subject with no available training statistics. Deep learning frameworks are popular among researchers for analyzing both spatial and time series data, making them well-suited for classifying EEG signals. In this paper, a deep neural network model is proposed for mental task classification for an imagined task from EEG signal data. Pre-computed features of EEG signals were obtained after raw EEG signals acquired from the subjects were spatially filtered by applying the Laplacian surface. To handle high-dimensional data, principal component analysis (PCA) was performed which helps in the extraction of most discriminating features from input vectors. The proposed model is non-invasive and aims to extract mental task-specific features from EEG data acquired from a particular subject. The training was performed on the average combined Power Spectrum Density (PSD) values of all but one subject. The performance of the proposed model based on a deep neural network (DNN) was evaluated using a benchmark dataset. We achieved 77.62% accuracy. The performance and comparison analysis with the related existing works validated that the proposed cross-subject classification framework outperforms the state-of-the-art algorithm in terms of performing an accurate mental task from EEG signals.

Quijote-PNG: The Information Content of the Halo Power Spectrum and Bispectrum

We investigate how much can be learnt about four types of primordial non-Gaussianity (PNG) from small-scale measurements of the halo field. Using the quijote-png simulations, we quantify the information content accessible with measurements of the halo power spectrum monopole and quadrupole, the matter power spectrum, the halo–matter cross spectrum, and the halo bispectrum monopole. This analysis is the first to include small, nonlinear scales, up to , and to explore whether these scales can break degeneracies with cosmological and nuisance parameters making use of thousands of N-body simulations. We perform all the halo measurements in redshift space with a single sample comprised of all halos with mass >3.2 × 1013 h −1 M ⊙. For local PNG, measurements of the scale-dependent bias effect from the power spectrum using sample variance cancellation provide significantly tighter constraints than measurements of the halo bispectrum. In this case measurements of the small scales add minimal additional constraining power. In contrast, the information on equilateral and orthogonal PNG is primarily accessible through the bispectrum. For these shapes, small-scale measurements increase the constraining power of the halo bispectrum by up to 4×, though the addition of scales beyond k ≈ 0.3 h Mpc−1 improves constraints largely through reducing degeneracies between PNG and the other parameters. These degeneracies are even more powerfully mitigated through combining power spectrum and bispectrum measurements. However, even with combined measurements and small-scale information, equilateral non-Gaussianity remains highly degenerate with σ 8 and our bias model.

Primordial non-Gaussianity from biased tracers: likelihood analysis of real-space power spectrum and bispectrum

Upcoming galaxy redshift surveys promise to significantly improve current limits on primordial non-Gaussianity (PNG) through measurements of 2- and 3-point correlation functions in Fourier space. However, realizing the full potential of this dataset is contingent upon having both accurate theoretical models and optimized analysis methods. Focusing on the local model of PNG, parameterized by f NL, we perform a Monte-Carlo Markov Chain analysis to confront perturbation theory predictions of the halo power spectrum and bispectrum in real space against a suite of N-body simulations. We model the halo bispectrum at tree-level, including all contributions linear and quadratic in f NL, and the halo power spectrum at 1-loop, including tree-level terms up to quadratic order in f NL, and all loops induced by local PNG linear in f NL. Keeping the cosmological parameters fixed, we examine the effect of informative priors on the linear non-Gaussian bias parameter on the statistical inference of f NL. A conservative analysis of the combined power spectrum and bispectrum, in which only loose priors are imposed and all parameters are marginalized over, can improve the constraint on by more than a factor of 5 relative to the power spectrum-only measurement. Imposing a strong prior on b ϕ, or assuming bias relations for both b ϕ and b ϕδ (motivated by a universal mass function assumption), improves the constraints further by a factor of few. In this case, however, we find a significant systematic shift in the inferred value of f NL if the same range of wavenumber is used. Likewise, a Poisson noise assumption can lead to significant systematics, and it is thus essential to leave all the stochastic amplitudes free.

Probing primordial non-Gaussianity with the power spectrum and bispectrum of future 21 cm intensity maps

After reionisation, the 21cm emission line of neutral hydrogen within galaxies provides a tracer of dark matter. Next-generation intensity mapping surveys, with the SKA and other radio telescopes, will cover large sky areas and a wide range of redshifts, facilitating their use as probes of primordial non-Gaussianity. {Previous works have shown that the bispectrum can achieve tight constraints on primordial non-Gaussianity with future surveys that are purposely designed for intensity mapping in interferometer mode}. Here we investigate the constraints attainable from surveys operating in single-dish mode, \rev{using the combined power spectrum and bispectrum signal}. In the case of the power spectrum, single-dish surveys typically outperform interferometer surveys. We find that the reverse holds for the bispectrum: single-dish surveys are not competitive with surveys designed for interferometer mode.

Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

ABSTRACT We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering, and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from stage IV weak lensing surveys.

Inferring the properties of the sources of reionization using the morphological spectra of the ionized regions

ABSTRACT High-redshift 21-cm observations will provide crucial insights into the physical processes of the Epoch of Reionization. Next-generation interferometers such as the Square Kilometer Array will have enough sensitivity to directly image the 21-cm fluctuations and trace the evolution of the ionizing fronts. In this work, we develop an inferential approach to recover the sources and IGM properties of the process of reionization using the number and, in particular, the morphological pattern spectra of the ionized regions extracted from realistic mock observations. To do so, we extend the Markov Chain Monte Carlo analysis tool 21cmmc by including these 21-cm tomographic statistics and compare this method to only using the power spectrum. We demonstrate that the evolution of the number-count and morphology of the ionized regions as a function of redshift provides independent information to disentangle multiple reionization scenarios because it probes the average ionizing budget per baryon. Although less precise, we find that constraints inferred using 21-cm tomographic statistics are more robust to the presence of contaminants such as foreground residuals. This work highlights that combining power spectrum and tomographic analyses more accurately recovers the astrophysics of reionization.

Principal component analysis of the primordial tensor power spectrum

We study how the shape of the spectrum of primordial gravitational waves can be constrained by future experiments looking at the B-mode of the Cosmic Microwave Background (CMB) polarization. We implement a Principal Component Analysis (PCA) including the effects of diffuse foreground residuals, following component separation, in the uncertainty of CMB angular power spectra, and taking into account the gravitational lensing by Large Scale Structure. We perform our study by considering the capabilities of future B-mode CMB experiments such as LiteBIRD, the Simons Observatory (SO) and Stage-IV (CMB-S4), in particular in detecting deviations of the primordial tensor spectrum from the scale-invariant behavior. We find that diffuse foreground residuals impact substantially both the derivation of the PCA basis and the corresponding constraining power, in all cases. In particular, depending on which experimental specifications and which value r of tensor-to-scalar ratio for cosmological perturbations are considered, adding foregrounds residuals can determine an increase as large as a factor ∼ 4 both on the uncertainty on r and on the recovery of the PCA modes. We study the limitations of the methodology, including the effect of physicality priors on the PCA, which we quantify via a Monte Carlo Markov chain (MCMC) analysis of the combined cosmological and PCA power spectrum parameter space.

All-sky Measurement of the Anisotropy of Cosmic Rays at 10 TeV and Mapping of the Local Interstellar Magnetic Field

Abstract We present the first full-sky analysis of the cosmic ray arrival direction distribution with data collected by the High-Altitude Water Cherenkov and IceCube observatories in the northern and southern hemispheres at the same median primary particle energy of 10 TeV. The combined sky map and angular power spectrum largely eliminate biases that result from partial sky coverage and present a key to probe into the propagation properties of TeV cosmic rays through our local interstellar medium and the interaction between the interstellar and heliospheric magnetic fields. From the map, we determine the horizontal dipole components of the anisotropy δ 0h = 9.16 × 10−4 and δ 6h = 7.25 × 10−4 (±0.04 × 10−4). In addition, we infer the direction (229.°2 ± 3.°5 R.A., 11.°4 ± 3.°0 decl.) of the interstellar magnetic field from the boundary between large-scale excess and deficit regions from which we estimate the missing corresponding vertical dipole component of the large-scale anisotropy to be .

The gravitational and lensing-ISW bispectrum of 21 cm radiation

Cosmic Microwave Background experiments from COBE to Planck, have launched cosmology into an era of precision science, where many cosmological parameters are now determined to the percent level. Next generation telescopes, focussing on the cosmological 21cm signal from neutral hydrogen, will probe enormous volumes in the low-redshift Universe, and have the potential to determine dark energy properties and test modifications of Einstein's gravity. We study the 21cm bispectrum due to gravitational collapse as well as the contribution by line of sight perturbations in the form of the lensing-ISW bispectrum at low-redshifts ($z \sim 0.35-3$), targeted by upcoming neutral hydrogen intensity mapping experiments. We compute the expected bispectrum amplitudes and use a Fisher forecast model to compare power spectrum and bispectrum observations of intensity mapping surveys by CHIME, MeerKAT and SKA-mid. We find that combined power spectrum and bispectrum observations have the potential to decrease errors on the cosmological parameters by an order of magnitude compared to Planck. Finally, we compute the contribution of the lensing-ISW bispectrum, and find that, unlike for the cosmic microwave background analyses, it can safely be ignored for 21cm bispectrum observations.

Power spectrum entropy based detection and mitigation of low-rate DoS attacks

Low-Rate DoS (LDoS) attacks send periodical packet bursts to the bottleneck routers which can throttle the bandwidth of TCP flows. They are difficult to detect while severely degrading the Quality of Service (QoS) of TCP applications. By combining Power Spectrum Analysis with Information Entropy, we introduce two novel information metrics to detect the LDoS attacks: Fourier Power Spectrum Entropy (FPSE) and Wavelet Power Spectrum Entropy (WPSE). As the energy of LDoS attack signal is mostly concentrated in the low-frequency range, FPSE and WPSE of LDoS attacks both exhibit lower values compared to those of normal flows. Therefore, these two metrics can be applied here to detect LDoS attacks efficiently. By evaluating on NS-3 simulations and real network traces, the results validate the effectiveness of these two metrics to differentiate LDoS attacks from normal flows. They can detect the LDoS attacks efficiently with fewer false alarms compared to the other detection mechanisms. Based on these two metrics, we also propose a Power Spectrum Entropy-based Robust-RED (PRRED) queuing algorithm to mitigate LDoS attacks. The evaluation results in NS-3 demonstrate that the proposed algorithm is able to effectively preserve the TCP bandwidth while countering the different LDoS attacks.

Accurate initial conditions in mixed dark matter–baryon simulations

We quantify the error in the results of mixed baryon--dark-matter hydrodynamic simulations, stemming from outdated approximations for the generation of initial conditions. The error at redshift 0 in contemporary large simulations, is of the order of few to ten percent in the power spectra of baryons and dark matter, and their combined total-matter power spectrum. After describing how to properly assign initial displacements and peculiar velocities to multiple species, we review several approximations: (1) {using the total-matter power spectrum to compute displacements and peculiar velocities of both fluids}, (2) scaling the linear redshift-zero power spectrum back to the initial power spectrum using the Newtonian growth factor ignoring homogeneous radiation, (3) using longitudinal-gauge velocities with synchronous-gauge densities, and (4) ignoring the phase-difference in the Fourier modes for the offset baryon grid, relative to the dark-matter grid. Three of these approximations do not take into account that dark matter and baryons experience a scale-dependent growth after photon decoupling, which results in directions of velocity which are not the same as their direction of displacement. We compare the outcome of hydrodynamic simulations with these four approximations to our reference simulation, all setup with the same random seed and simulated using Gadget-III.

Joint resonant CMB power spectrum and bispectrum estimation

We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multi-variate Gaussian where the covariance is determined by the Fisher matrix of the sine and cosine terms, we can efficiently produce spectra that are statistically close to those derived from full simulations. By drawing a large number of spectra from this PDF, both for the power spectrum and the bispectrum, we can quickly determine the statistical significance of candidate signatures in the CMB, considering both single frequency and multi-frequency estimators. We show that for resonance models, cosmology and foreground parameters have little influence on the estimated amplitude, which allows to simplify the analysis considerably. A more precise likelihood treatment can then be applied to candidate signatures only. We also discuss a modal expansion approach for the power spectrum, aimed at quickly scanning through large families of oscillating models.

ON THE GEOMETRIC NATURE OF LOW-FREQUENCY QUASI-PERIODIC OSCILLATIONS IN NEUTRON-STAR LOW-MASS X-RAY BINARIES

We report on a detailed analysis of the so-called ~1 Hz quasi-periodic oscillation (QPO) in the eclipsing and dipping neutron-star low-mass X-ray binary EXO 0748-676. This type of QPO has previously been shown to have a geometric origin. Our study focuses on the evolution of the QPO as the source moves through the color-color diagram, in which it traces out an atoll-source-like track. The QPO frequency increases from ~0.4 Hz in the hard state to ~25 Hz as the source approaches the soft state. Combining power spectra based on QPO frequency reveals additional features that strongly resemble those seen in non-dipping/eclipsing atoll sources. We show that the low-frequency QPOs in atoll sources and the ~1 Hz QPO in EXO 0748-676 follow similar relations with respect to the noise components in their power spectra. We conclude that the frequencies of both types of QPOs are likely set by (the same) precession of a misaligned inner accretion disk. For high-inclination systems, like EXO 0748-676, this results in modulations of the neutron-star emission due to obscuration or scattering, while for lower-inclination systems the modulations likely arise from relativistic Doppler boosting and light-bending effects.

Polyspectra searches for sharp oscillatory features in cosmic microwave sky data

We undertake a thorough search for signatures of sharp oscillatory features in the WMAP9 power spectrum and bispectrum as well as in the Planck power spectrum. For the first time, we carry out searches in both the power spectrum and bispectrum simultaneously, employing well-defined look-elsewhere statistics to assess significances in a rigorous manner. Developing efficient methods to scan power spectrum likelihoods for oscillatory features, we present results for the phenomenological bare sine and cosine modulations, allowing validation against existing Planck Likelihood surveys, as well as templates that include the correct sharp feature scaling. In particular, we study degeneracies between feature and cosmological parameters. For frequencies beyond the scale set by the acoustic peaks, the dependencies are realised through uninteresting adjustments of the comoving distance to last scattering. Hence, it is sufficient to keep cosmological parameters fixed and employ fast Gaussian approximations to the likelihood as a function of the feature model amplitude. In cases where results can be compared to the literature, our method shows excellent agreement. We supplement results from the Planck Likelihood with an analysis based on the Planck SMICA component separation map that, working on the assumption that the component separation algorithm is reliable, allows for the inclusion of a larger sky fraction. In principle, this allows us to place the most stringent constraints to date on the amplitudes of feature models in the temperature power spectrum. Invoking the WMAP bispectrum, we perform a combined power spectrum and bispectrum survey. We use and slightly generalise statistics developed in previous work to reliably judge the significance of large feature model amplitude estimates. We conclude that our results are entirely consistent with a featureless realisation of a Gaussian CMB.

Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck

Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the ΛCDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit ΛCDM angular power spectrum to remove foreground contributions from the data at multipoles ℓ ⩾50. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to ℓ ∼1850 in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the 95% confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit ΛCDM model to be at 36% confidence distance from the center of the nonparametric confidence set—this is considerably larger than the confidence distance (9%) derived earlier from a similar analysis of the WMAP 7-year data. Another interesting result of our analysis is that at low multipoles, the Planck data do not suggest any upturn, contrary to the expectation based on the integrated Sachs-Wolfe contribution in the best-fit ΛCDM cosmology.

Combining power spectrum and bispectrum measurements to detect oscillatory features

The simplest inflationary models present us with few observable parameters to discriminate between them. A detection of features in the spectra of primordial density perturbations could provide valuable insights and lead to stringent tests of models of the early Universe. So far, searches for oscillatory features have not produced statistically significant results. In this work we consider a combined search for features in the power spectrum and bispectrum. We show that possible dependencies between the estimates of feature model amplitudes based on the two- and three-point correlators are largely statistically independent under the assumption of the null hypothesis of a nearly Gaussian featureless cosmic microwave background. Building on this conclusion we propose an optimal amplitude estimator for a combined search and study the look-elsewhere effect in feature model surveys. In particular we construct analytic models for the distribution of amplitude estimates that allow for a reliable assessment of the significance of potential findings. We also propose a well-behaved integrated statistic that is designed to detect evidence for models exhibiting features at multiple frequencies.

Planck2013 results. XXII. Constraints on inflation

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to $n_s = 0.9603 \pm 0.0073$, ruling out exact scale invariance at over 5 $\sigma$. Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V" < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n > 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining $d n_s/d ln k = -0.0134 \pm 0.0090$. Several analyses dropping the slow-roll approximation are carried out, including detailed model comparison and inflationary potential reconstruction. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit $\chi^2$ by ~ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with bounds on $f_\mathrm{NL}$ measured by Planck. The fractional primordial contribution of CDM isocurvature modes in the curvaton and axion scenarios has upper bounds of 0.25% or 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelation can improve $\chi^2$ by approximatively 4 as a result of slightly lowering the theoretical prediction for the $\ell<40$ multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.

Influence of Dynamic Characteristics of Wheels between Vehicle with Traditional and Articulated Bogie

The wheel-rail combined power spectrum densities are transformed into time domain samples by IFFT method, and add abnormal corrugation samples. The samples were taken as the inputting disturbances of a vehicle-track vertical coupling dynamics model, and the interaction force of wheel/rail is calculated by the models of vehicle with traditional bogie frame and articulated frame of vehicle/track coupling system. Dynamic responses of wheels on corrugation track can be calculated. The results show that wheels vibration intensity of vehicle with articulated bogie is lower.