Observed Power Spectrum Research Articles

Depth to Curie temperature across the central Red Sea from magnetic data using the de-fractal method

Abstract The central Red Sea rift is considered to be an embryonic ocean. It is characterised by high heat flow, with more than 90% of the heat flow measurements exceeding the world mean and high values extending to the coasts — providing good prospects for geothermal energy resources. In this study, we aim to map the depth to the Curie isotherm (580 °C) in the central Red Sea based on magnetic data. A modified spectral analysis technique, the “de-fractal spectral depth method” is developed and used to estimate the top and bottom boundaries of the magnetised layer. We use a mathematical relationship between the observed power spectrum due to fractal magnetisation and an equivalent random magnetisation power spectrum. The de-fractal approach removes the effect of fractal magnetisation from the observed power spectrum and estimates the parameters of depth to top and depth to bottom of the magnetised layer using iterative forward modelling of the power spectrum. We applied the de-fractal approach to 12 windows of magnetic data along a profile across the central Red Sea from onshore Sudan to onshore Saudi Arabia. The results indicate variable magnetic bottom depths ranging from 8.4 km in the rift axis to about 18.9 km in the marginal areas. Comparison of these depths with published Moho depths, based on seismic refraction constrained 3D inversion of gravity data, showed that the magnetic bottom in the rift area corresponds closely to the Moho, whereas in the margins it is considerably shallower than the Moho. Forward modelling of heat flow data suggests that depth to the Curie isotherm in the centre of the rift is also close to the Moho depth. Thus Curie isotherm depths estimated from magnetic data may well be imaging the depth to the Curie temperature along the whole profile. Geotherms constrained by the interpreted Curie isotherm depths have subsequently been calculated at three points across the rift — indicating the variation in the likely temperature profile with depth.

Irregularity and decadal variation in ENSO: a simplified model based on Principal Oscillation Patterns

A new method of estimating the decay time, mean period and forcing statistics of El Nino-Southern Oscillation (ENSO) has been found. It uses a two-dimensional stochastically forced damped linear oscillator model with the model parameters estimated from a Principal Oscillation Pattern (POP) analysis and associated observed power spectra. It makes use of extended observational time series of 150 years of sea surface temperature (SST) and sea level pressure (SLP) as well as climate model output. This approach is motivated by clear physical relationships that SST and SLP POP patterns have to the ENSO cycle, as well as to each other, indicating that they represent actual physical modes of the climate system. Moreover, the leading POP mode accounts for 20–50 % of the variance on interannual time scales. The POP real part is highly correlated with several Nino indices near zero lag while the imaginary part exhibits a 6–9 month lead time and thus is a precursor. The observed POP power spectra show markedly different behavior for the peak and precursor, the former having more power at ENSO frequencies and the latter dominating at low frequencies. The results realistically suggest a period of oscillation of 4–6 years and a decay time of 8 months, which corresponds to the practical ENSO prediction limit. A fundamental finding of this approach is that the difference between the observed peak and precursor spectra at low frequencies can be related to the forcing statistics using the simple model, as well as to the difference between patterns of decadal and interannual variability in the Pacific.

Perturbations in loop quantum cosmology

The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible, we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, quantum gravity phase of the universe. Here, we have described how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB.

The power spectrum of solar convection flows from high-resolution observations and 3D simulations

We compare Fourier spectra of photospheric velocity fields from very high resolution IMaX observations to those from recent 3D numerical magnetoconvection models. We carry out a proper comparison by synthesizing spectral lines from the numerical models and then applying to them the adequate residual instrumental degradation that affects the observational data. Also, the validity of the usual observational proxies is tested by obtaining synthetic observations from the numerical boxes and comparing the velocity proxies to the actual velocity values from the numerical grid. For the observations, data from the SUNRISE/IMaX instrument with about 120 km spatial resolution are used, thus allowing the calculation of observational Fourier spectra well into the subgranular range. For the simulations, we use four series of runs obtained with the STAGGER code and synthesize the IMaX spectral line (FeI 5250.2 A) from them. Proxies for the velocity field are obtained via Dopplergrams (vertical component) and local correlation tracking (horizontal component). A very good match between observational and simulated Fourier power spectra is obtained for the vertical velocity data for scales between 200 km and 6 Mm. Instead, a clear vertical shift is obtained when the synthetic observations are not degraded. The match for the horizontal velocity data is much less impressive because of the inaccuracies of the LCT procedure. Concerning the internal comparison of the direct velocity values of the numerical boxes with those from the synthetic observations, a high correlation (0.96) is obtained for the vertical component when using the velocity values on the log($tau_{500}$) = -1 surface in the box. The corresponding Fourier spectra are near each other. A lower maximum correlation (0.5) is reached (at $tau_{500}$ = 1) for the horizontal velocities as a result of the coarseness of the LCT procedure.

Anomalous Anisotropies of Cosmic Rays from Turbulent Magnetic Fields

The propagation of cosmic rays (CRs) in turbulent interstellar magnetic fields is typically described as a spatial diffusion process. This formalism predicts only a small deviation from an isotropic CR distribution in the form of a dipole in the direction of the CR density gradient or relative background flow. We show that the existence of a global CR dipole moment necessarily generates a spectrum of higher multipole moments in the local CR distribution. These anomalous anisotropies are a direct consequence of Liouville's theorem in the presence of a local turbulent magnetic field. We show that the predictions of this model are in excellent agreement with the observed power spectrum of multi-TeV CRs.

Improved Representation of Tropical Pacific Ocean–Atmosphere Dynamics in an Intermediate Complexity Climate Model

Abstract A new anomaly coupling technique is introduced into a coarse-resolution dynamic climate model [the Liège Ocean Carbon Heteronomous model (LOCH)–Vegetation Continuous Description model (VECODE)–Earth System Models of Intermediate Complexity Climate deBilt (ECBILT)–Coupled Large-Scale Ice–Ocean model (CLIO)–Antarctic and Greenland Ice Sheet Model (AGISM) ensemble (LOVECLIM)], improving the model’s representation of eastern equatorial Pacific surface temperature variability. The anomaly coupling amplifies the surface diabatic atmospheric forcing within a Gaussian-shaped patch applied in the tropical Pacific Ocean. It is implemented with an improved predictive cloud scheme based on empirical relationships between cloud cover and key state variables. Results are presented from a perturbed physics ensemble systematically varying the parameters controlling the anomaly coupling patch size, location, and amplitude. The model’s optimal parameter combination is chosen through calibration against the observed power spectrum of monthly-mean surface temperature anomalies in the Niño-3 region. The calibrated model exhibits substantial improvement in equatorial Pacific interannual surface temperature variability and robustly reproduces El Niño–Southern Oscillation (ENSO)-like variability. The authors diagnose some of the key atmospheric and oceanic feedbacks in the model important for simulating ENSO-like variability, such as the positive Bjerknes feedback and the negative heat flux feedback, and analyze the recharge–discharge of the equatorial Pacific ocean heat content. They find LOVECLIM robustly captures important ocean dynamics related to thermocline adjustment and equatorial Kelvin waves. The calibrated model demonstrates some improvement in simulating atmospheric feedbacks, but the coupling between ocean and atmosphere is relatively weak. Because of the tractability of LOVECLIM and its consequent utility in exploring long-term climate variability and large ensemble perturbed physics experiments, improved representation of tropical Pacific ocean–atmosphere dynamics in the model may more readily allow for the investigation of the role of tropical Pacific ocean–atmosphere dynamics in past climate changes.

MODELING SOLAR OSCILLATION POWER SPECTRA. II. PARAMETRIC MODEL OF SPECTRAL LINES OBSERVED IN DOPPLER-VELOCITY MEASUREMENTS

We describe a global parametric model for the observed power spectra of solar oscillations of intermediate and low degree. A physically motivated parameterization is used as a substitute for a direct description of mode excitation and damping as these mechanisms remain poorly understood. The model is targeted at the accurate fitting of power spectra coming from Doppler velocity measurements and uses an adaptive response function that accounts for both the vertical and horizontal components of the velocity field on the solar surface and for possible instrumental and observational distortions. The model is continuous in frequency, can easily be adapted to intensity measurements and extends naturally to the analysis of high-frequency pseudo modes (interference peaks at frequencies above the atmospheric acoustic cutoff).

Anisotropic imprint of long-wavelength tensor perturbations on cosmic structure

Inflationary models predict a correlation between primordial density perturbations (scalar metric perturbations) and gravitational waves (tensor metric perturbations) in the form of a scalar-scalar-tensor three-point correlation, or bispectrum in Fourier space. The squeezed limit of this bispectrum implies a quadrupolar asymmetry in the observed local power spectrum for matter and galaxies. Here we show (like others before) that an infrared divergence in the amplitude of this power asymmetry predicted in single-field slow-roll models is canceled by projection effects when considering the observed power spectrum. We then further evaluate the nonzero, but finite, residual quadrupolar power asymmetry that remains after the divergences are canceled. While the quadrupolar power asymmetry is small, it is conceptually important. Our calculation moreover clarifies how the predictions for this power asymmetry may change in models with different scalar-scalar-tensor bispectra, and shows that convincing detection of the quadrupolar power asymmetry would rule out the single-field slow-roll models of inflation.

Non-Gaussianity from excited initial inflationary states

We study squeezed limit $f_{NL}$ generation by excited initial inflationary states in a model independent way. We restrict "excited" to mean a Bogoliubov transformation of the Bunch Davies state. We simultaneously impose the constraints that the observable power spectrum is nearly scale invariant over at least three decades and that the observable modes today be subhorizon at the beginning of inflation while not causing significant backreaction. We show that most excited initial inflationary states for single field inflationary models with negligible superhorizon evolution do not produce an observable squeezed limit $f_{NL}$. The case in which one mode is in the Bunch Davies state while the other two modes are in an excited state with $0.01<|\beta_k|\leq0.1$ may generate a squeezed limit $f_{NL}$ which is detectable with future experiments.

Variation in the escape fraction of ionizing photons from galaxies and the redshifted 21-cm power spectrum during reionization

The observed power spectrum of redshifted 21cm fluctuations is known to be sensitive to the astrophysical properties of the galaxies that drove reionization. Thus, detailed measurements of the 21cm power spectrum and its evolution could lead to measurements of the properties of early galaxies that are otherwise inaccessible. In this paper, we study the effect of mass and redshift dependent escape fractions of ionizing radiation on the ability of forthcoming experiments to constrain galaxy formation via the redshifted 21cm power spectrum. We use a model for reionization which combines the hierarchical galaxy formation model GALFORM implemented within the Millennium-II dark matter simulation, with a semi-numerical scheme to describe the resulting ionization structure. Using this model we show that the structure and distribution of ionised regions at fixed neutral fraction, and hence the slope and amplitude of the 21 cm power spectrum, is dependent on the variation of ionising photon escape fraction with galaxy mass and redshift. However, we find that the influence of the unknown escape fraction and its evolution is smaller than the dominant astrophysical effect provided by SNe feedback strength in high redshift galaxies. The unknown escape fraction of ionizing radiation from galaxies is therefore unlikely to prevent measurement of the properties of high redshift star formation using observations of the 21cm power spectrum.

Towards modeling quasi-periodic oscillations of microquasars with oscillating slender tori

Context. One of the often discussed models for X-ray binaries high-frequency quasi-periodic oscillations is the oscillating torus model that considers oscillation modes of slender accretion tori. Aims. Here, we aim at developing this model by considering the observable signature of an optically thick slender accretion torus subject to simple periodic deformations. Methods. We compute light curves and power spectra of a slender accretion torus subject to simple periodic deformations: vertical or radial translation, rotation, expansion and shear. Results. We show that different types of deformations lead to very different Fourier power spectra and therefore could be observationally distinguished. Conclusions. This work is a first step in a longer-term study of the observable characteristics of the oscillating torus model. It gives promising perspectives on the possibility to constrain this model by studying the observed power spectra of quasi-periodic oscillations.

Calibration errors unleashed: effects on cosmological parameters and requirements for large-scale structure surveys

Imperfect photometric calibration of galaxy surveys due to either astrophysical or instrumental effects leads to biases in measuring galaxy clustering and in the resulting cosmological parameter measurements. More interestingly (and disturbingly), the spatially varying calibration also generically leads to violations of statistical isotropy of the galaxy clustering signal. Here we develop, for the first time, a formalism to propagate the effects of photometric calibration variations with arbitrary spatial dependence across the sky to the observed power spectra and to the cosmological parameter constraints. We develop an end-to-end pipeline to study the effects of calibration, and illustrate our results using specific examples including Galactic dust extinction and survey-dependent magnitude limits as a function of zenith angle of the telescope. We establish requirements on the control of calibration so that it doesn't significantly bias constraints on dark energy and primordial non-Gaussianity. Two principal findings are: 1) largest-angle photometric calibration variations (dipole, quadrupole and a few more modes, though not the monopole) are the most damaging, and 2) calibration will need to be understood at the 0.1%-1% level (i.e. rms variations mapped out to accuracy between 0.001 and 0.01 mag), though the precise requirement strongly depends on the faint-end slope of the luminosity function and the redshift distribution of galaxies in the survey.

A new method to detect solar-like oscillations at very low S/N using statistical significance testing

We introduce a new method to detect solar-like oscillations in frequency power spectra of stellar observations, under conditions of very low signal to noise. The Moving-Windowed-Power-Search, or MWPS, searches the power spectrum for signatures of excess power, over and above slowly varying (in frequency) background contributions from stellar granulation and shot or instrumental noise. We adopt a false-alarm approach (Chaplin et al. 2011) to ascertain whether flagged excess power, which is consistent with the excess expected from solar-like oscillations, is hard to explain by chance alone (and hence a candidate detection). We apply the method to solar photometry data, whose quality was systematically degraded to test the performance of the MWPS at low signal-to-noise ratios. We also compare the performance of the MWPS against the frequently applied power-spectrum-of-power-spectrum (PSxPS) detection method. The MWPS is found to outperform the PSxPS method.

The structure of reionization in hierarchical galaxy formation models

Understanding the epoch of reionization and the properties of the first galaxies represents an important goal for modern cosmology. The structure of reionization and hence the observed power spectrum of redshifted 21-cm fluctuations are known to be sensitive to the astrophysical properties of the galaxies that drove reionization. Thus, detailed measurements of the 21-cm power spectrum and its evolution could lead to measurements of the properties of early galaxies that are otherwise inaccessible. In this paper, we make predictions for the ionized structure during reionization and the 21-cm power spectrum based on detailed models of galaxy formation. We combine the semi-analytic galform model implemented within the Millennium-II dark matter simulation, with a semi-numerical scheme to describe the resulting ionization structure. Semi-analytic models based on the Millennium-II Simulation follow the properties of galaxies within haloes of mass greater than ∼1.4 × 108 M⊙ at z > 6, corresponding to the faint sources thought to dominate reionization. Using these models we show that the details of supernovae (SNe) and radiative feedback affect the structure and distribution of ionized regions, and hence the slope and amplitude of the 21-cm power spectrum. These results indicate that forthcoming measurements of the 21-cm power spectrum could be used to uncover details of early galaxy formation. We find that the strength of SN feedback is the dominant effect governing the evolution of structure during reionization. In particular, we show SN feedback to be more important than radiative feedback, the presence of which we find does not influence either the total stellar mass or overall ionizing photon budget. Thus, if SN feedback is effective at suppressing star formation in high-redshift galaxies, we find that photoionization feedback does not lead to self-regulation of the reionization process as has been thought.

Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and whichneed additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects,which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into thedetailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the termsat a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of μ, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of μ and multipole momentswhich dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion. This is similar to the situation in real space, but predicting power spectrum in redshift spaceis more difficult because of the explicit influence of small scale dispersion type effects in RSD, which extend to very large scales.

Synoptic-scale disturbances over the northern South China Sea and their responses to El Niño

Using surface and aerological meteorological observations obtained at the Xisha Automatic Weather Station and three moored buoys along the continental slope, characteristics of the synoptic-scale disturbances over the northern South China Sea (NSCS) are extensively studied. The power spectra of surface and aerological observations suggest a synoptic feature with a pronounced energy peak at a period of 5–8 d and a weak peak at 3–4 d. The standard deviation of the synoptic temperature component derived at Xisha Station from 1976 to 2011 indicates that the strongest variability normally exists in August all through the whole troposphere. At the interannual scale, it is found that El Nino plays an important role in regulating the synoptic disturbances of atmosphere. The vertical synoptic disturbances have a double active peak following El Nino condition. The first peak usually occurs during the mature phase of El Nino, and the second one occurs in the summer of decay year. Comparing with the summer of developing years, the summer of the decaying year of El Nino has more active and stronger synoptic disturbances, especially for the 5–8 d period variations.

Scale dependence of the halo bias in general local-type non-Gaussian models I: analytical predictions and consistency relations

The large-scale clustering pattern of biased tracers is known to be a powerful probe of the non-Gaussianities in the primordial fluctuations. The so-called scale-dependent bias has been reported in various type of models of primordial non-Gaussianities. We focus on local-type non-Gaussianities, and unify the derivations in the literature of the scale-dependent bias in the presence of multiple Gaussian source fields as well as higher-order coupling to cover the models described by frequently-discussed fNL, gNL and tNL parameterization. We find that the resultant power spectrum is characterized by two parameters responsible for the shape and the amplitude of the scale-dependent bias in addition to the Gaussian bias factor. We show how (a generalized version of) Suyama-Yamaguchi inequality between fNL and tNL can directly be accessible from the observed power spectrum through the dependence on our new parameter which controls the shape of the scale-dependent bias. The other parameter for the amplitude of the scale-dependent bias is shown to be useful to distinguish the simplest quadratic non-Gaussianities (i.e., fNL-type) from higher-order ones (gNL and higher), if one measures it from multiple species of galaxies or clusters of galaxies. We discuss the validity and limitations of our analytic results by comparison with numerical simulations in an accompanying paper.

Redshift-space distortion of the 21-cm background from the epoch of reionization - I. Methodology re-examined

The peculiar velocity of the intergalactic gas responsible for the cosmic 21cm background from the epoch of reionization and beyond introduces an anisotropy in the three-dimensional power spectrum of brightness temperature fluctuations. Measurement of this anisotropy by future 21cm surveys is a promising tool for separating cosmology from 21cm astrophysics. However, previous attempts to model the signal have often neglected peculiar velocity or only approximated it crudely. This paper re-examines the effects of peculiar velocity on the 21cm signal in detail, improving upon past treatment and addressing several issues for the first time. (1) We show that properly accounting for finite optical depth eliminates the unphysical divergence of 21cm brightness temperature in overdense regions of the IGM found by previous work that employed the usual optically-thin approximation. (2) The approximation made previously to circumvent the diverging brightness temperature problem by capping velocity gradient can misestimate the power spectrum on all scales. (3) The observed power spectrum in redshift-space remains finite even in the optically-thin approximation if one properly accounts for the redshift-space distortion. However, results that take full account of finite optical depth show that this approximation is only accurate in the limit of high spin temperature. (4) The linear theory for redshift-space distortion results in ~30% error in the observationally relevant wavenumber range, at the 50% ionized epoch. (5) We describe and test two numerical schemes to calculate the 21cm signal from reionization simulations to incorporate peculiar velocity effects in the optically-thin approximation accurately. One is particle-based, the other grid-based, and while the former is most accurate, we demonstrate that the latter is computationally more efficient and can achieve sufficient accuracy. [Abridged]

Disentangling non-Gaussianity, bias, and general relativistic effects in the galaxy distribution

Local non-Gaussianity, parametrized by $f_{\rm NL}$, introduces a scale-dependent bias that is strongest at large scales, precisely where General Relativistic (GR) effects also become significant. With future data, it should be possible to constrain $f_{\rm NL} = {\cal O}(1)$ with high redshift surveys. GR corrections to the power spectrum and ambiguities in the gauge used to define bias introduce effects similar to $f_{\rm NL}= {\cal O}(1)$, so it is essential to disentangle these effects. For the first time in studies of primordial non-Gaussianity, we include the consistent GR calculation of galaxy power spectra, highlighting the importance of a proper definition of bias. We present observable power spectra with and without GR corrections, showing that an incorrect definition of bias can mimic non-Gaussianity. However, these effects can be distinguished by their different redshift and scale dependence, so as to extract the true primordial non-Gaussianity.

Inflation with general initial conditions for scalar perturbations

We explore the possibility of a single field quasi-de Sitter inflationary model with general initial state for primordial fluctuations. In this paper, first we compute the power spectrum and the bispectrum of scalar perturbations with coherent state as the initial state. We find that a large class of coherent states are indistinguishable from the Bunch-Davies vacuum state and hence consistent with the current observations. In case of a more general initial state built over Bunch-Davies vacuum state, we show that the constraints on the initial state from observed power spectrum and local bispectrum are relatively weak and for quasi-de Sitter inflation a large number of initial states are consistent with the current observations. However, renormalizability of the energy-momentum tensor of the fluctuations constraints the initial state further.