One-dimensional Power Spectrum Research Articles

Particle initialization effects on Lyman-α forest statistics in cosmological SPH simulations

ABSTRACT Confronting measurements of the Lyman-α forest with cosmological hydrodynamical simulations has produced stringent constraints on models of particle dark matter and the thermal and ionization state of the intergalactic medium. We investigate the robustness of such models of the Lyman-α forest, focusing on the effect of particle initial conditions on the Lyman-α forest statistics in cosmological SPH simulations. We study multiple particle initialization algorithms in simulations that are designed to be identical in other respects. In agreement with the literature, we find that the correct linear theory evolution is obtained when a glass-like configuration is used for initial unperturbed gas particle positions alongside a regular grid configuration for dark matter particles and the use of non-identical initial density perturbations for gas and dark matter. However, we report that this introduces a large scale-dependent distortion in the 1D Lyman-α transmission power spectrum at small scales (k > 0.05 s km−1). The effect is close to 50 per cent at k ∼ 0.1 s km−1, and persists at higher resolution. This can severely bias inferences in parameters such as the dark matter particle mass. By considering multiple initial conditions codes and their variations, we also study the impact of a variety of other assumptions and algorithmic choices, such as adaptive softening, background radiation density, particle staggering, and perturbation theory accuracy, on the matter power spectrum, the Lyman-α flux power spectrum, and the Lyman-α flux PDF. This work reveals possible pathways towards more accurate theoretical models of the Lyman-α forest to match the quality of upcoming measurements.

Optimal 1D Ly α forest power spectrum estimation – III. DESI early data

ABSTRACT The 1D power spectrum P1D of the Ly α forest provides important information about cosmological and astrophysical parameters, including constraints on warm dark matter models, the sum of the masses of the three neutrino species, and the thermal state of the intergalactic medium. We present the first measurement of P1D with the quadratic maximum likelihood estimator (QMLE) from the Dark Energy Spectroscopic Instrument (DESI) survey early data sample. This early sample of 54 600 quasars is already comparable in size to the largest previous studies, and we conduct a thorough investigation of numerous instrumental and analysis systematic errors to evaluate their impact on DESI data with QMLE. We demonstrate the excellent performance of the spectroscopic pipeline noise estimation and the impressive accuracy of the spectrograph resolution matrix with 2D image simulations of raw DESI images that we processed with the DESI spectroscopic pipeline. We also study metal line contamination and noise calibration systematics with quasar spectra on the red side of the Ly α emission line. In a companion paper, we present a similar analysis based on the Fast Fourier Transform estimate of the power spectrum. We conclude with a comparison of these two approaches and discuss the key sources of systematic error that we need to address with the upcoming DESI Year 1 analysis.

Accurate, automatic determination of astigmatism and phase with Ctfplotter in IMOD

Ctfplotter in the IMOD software package is a flexible program for determination of CTF parameters in tilt series images. It uses a novel approach to find astigmatism by measuring defocus in one-dimensional power spectra rotationally averaged over a series of restricted angular ranges. Comparisons with Ctffind, Gctf, and Warp show that Ctfplotter’s estimated astigmatism is generally more reliable than that found by these programs that fit CTF parameters to two-dimensional power spectra, especially at higher tilt angles. In addition to that intrinsic advantage, Ctfplotter can reduce the variability in astigmatism estimates further by summing results over multiple tilt angles (typically 5), while still finding defocus for each individual image. Its fitting strategy also produces better phase estimates. The program now includes features for tuning the sampling of the power spectrum so that it is well-represented for analysis, and for determining an appropriate fitting range that can vary with tilt angle. It can thus be used automatically in a variety of situations, not just for fitting tilt series, and has been integrated into the SerialEM acquisition software for real-time determination of focus and astigmatism.

Canonical Hubble-Tension-Resolving Early Dark Energy Cosmologies Are Inconsistent with the Lyman-α Forest.

Current cosmological data exhibit discordance between indirect and some direct inferences of the present-day expansion rate H_{0}. Early dark energy (EDE), which briefly increases the cosmic expansion rate prior to recombination, is a leading scenario for resolving this "Hubble tension" while preserving a good fit to cosmic microwave background (CMB) data. However, this comes at the cost of changes in parameters that affect structure formation in the late-time universe, including the spectral index of scalar perturbations n_{s}. Here, we present the first constraints on axionlike EDE using data from the Lyman-α forest, i.e., absorption lines imprinted in background quasar spectra by neutral hydrogen gas along the line of sight. We consider two independent measurements of the one-dimensional Lyα forest flux power spectrum from the Sloan Digital Sky Survey (SDSS eBOSS) and from the MIKE/HIRES and X-Shooter spectrographs. We combine these with a baseline dataset comprised of Planck CMB data and baryon acoustic oscillation (BAO) measurements. Combining the eBOSS Lyα data with the CMB and BAO dataset reduces the 95% confidence level (C.L.) upper bound on the maximum fractional contribution of EDE to the cosmic energy budget f_{EDE} from 0.07 to 0.03 and constrains H_{0}=67.9_{-0.4}^{+0.4} km/s/Mpc (68% C.L.), with maximum aposteriori value H_{0}=67.9 km/s/Mpc. Similar results are obtained for the MIKE/HIRES and X-Shooter Lyα data. Our Lyα-based EDE constraints yield H_{0} values that are in >4σ tension with the SH0ES distance-ladder measurement and are driven by the preference of the Lyα forest data for n_{s} values lower than those required by EDE cosmologies that fit Planck CMB data. Taken at face value, the Lyα forest severely constrains canonical EDE models that could resolve the Hubble tension.

The Dark Energy Spectroscopic Instrument: one-dimensional power spectrum from first Ly α forest samples with Fast Fourier Transform

ABSTRACTWe present the one-dimensional Ly α forest power spectrum measurement using the first data provided by the Dark Energy Spectroscopic Instrument (DESI). The data sample comprises 26 330 quasar spectra, at redshift z > 2.1, contained in the DESI Early Data Release and the first 2 months of the main survey. We employ a Fast Fourier Transform (FFT) estimator and compare the resulting power spectrum to an alternative likelihood-based method in a companion paper. We investigate methodological and instrumental contaminants associated with the new DESI instrument, applying techniques similar to previous Sloan Digital Sky Survey (SDSS) measurements. We use synthetic data based on lognormal approximation to validate and correct our measurement. We compare our resulting power spectrum with previous SDSS and high-resolution measurements. With relatively small number statistics, we successfully perform the FFT measurement, which is already competitive in terms of the scale range. At the end of the DESI survey, we expect a five times larger Ly α forest sample than SDSS, providing an unprecedented precise one-dimensional power spectrum measurement.

Decaying Dark Matter and Lyman-α forest constraints

Decaying Cold Dark Matter (DCDM) is a model that is currently under investigation regarding primarily the S 8 tension between cosmic microwave background (CMB) and certain large-scale structure measurements. The decay into one massive and one (or more) massless daughter particle(s) leads to a suppression of the power spectrum in the late universe that depends on the relative mass splitting ϵ = (1 - m 2/M 2)/2 between the mother and massive daughter particle as well as the lifetime τ. In this work we investigate the impact of the BOSS DR14 one-dimensional Lyman-α forest flux power spectrum on the DCDM model using a conservative effective model approach to account for astrophysical uncertainties. Since the suppression of the power spectrum due to decay builds up at low redshift, we find that regions in parameter space that address the S 8 tension can be well compatible with the Lyman-α forest. Nevertheless, for values of the degeneracy parameter ϵ ∼ 0.1-0.5%, for which the power suppression occurs within the scales probed by BOSS Lyman-α data, we find improved constraints compared to previous CMB and galaxy clustering analyses, obtaining τ ≳ 18 Gyrs for small mass splitting. Furthermore, our analysis of the BOSS Lyman-α flux power spectrum allows for values τ ∼ 102 Gyrs, ϵ ∼ 1%, that have been found to be preferred by a combination of Planck and galaxy clustering data with a KiDS prior on S 8, and we even find a hint for a marginal preference within this regime.

A neural network emulator for the Lyman-α forest 1D flux power spectrum

ABSTRACT The Lyman-α forest offers a unique avenue for studying the distribution of matter in the high redshift universe and extracting precise constraints on the nature of dark matter, neutrino masses, and other ΛCDM extensions. However, interpreting this observable requires accurate modelling of the thermal and ionization state of the intergalactic medium, and therefore resorting to computationally expensive hydrodynamical simulations. In this work, we build a neural network that serves as a surrogate model for rapid predictions of the one-dimensional Lyman-α flux power spectrum (P1D), thereby making Bayesian inference feasible for this observable. Our emulation technique is based on modelling P1D as a function of the slope and amplitude of the linear matter power spectrum rather than as a function of cosmological parameters. We show that our emulator achieves sub-percent precision across the full range of scales (k∥ = 0.1 – $4\, \mathrm{Mpc}^{-1}$) and redshifts (z = 2 – 4.5) considered, and also for three ΛCDM extensions not included in the training set: massive neutrinos, running of the spectral index, and curvature. Furthermore, we show that it performs at the 1 per cent level for ionization and thermal histories not present in the training set and performs at the percent level when emulating down to $k_{\parallel }=8\, \mathrm{Mpc}^{-1}$. These results affirm the efficacy of our emulation strategy in providing accurate predictions even for cosmologies and reionization histories that were not explicitly incorporated during the training phase, and we expect it to play a critical role in the cosmological analysis of the DESI survey.

Compressing the Cosmological Information in One-dimensional Correlations of the Lyman-α Forest

Observations of the Lyman-α forest from spectroscopic surveys such as the Baryon Oscillation Spectroscopic Survey or its extension, eBOSS, or the ongoing Dark Energy Spectroscopic Instrument (DESI) survey offer a unique window to study the growth of structure on megaparsec scales. Interpretation of these measurements is a complicated task, requiring hydrodynamical simulations to model and marginalize over the thermal and ionization state of the intergalactic medium. This complexity has limited the use of Lyα clustering measurements in joint cosmological analyses. In this work we show that the cosmological information content of the one-dimensional power spectrum (P 1D) of the Lyman-α forest can be compressed into a simple two-parameter likelihood without any significant loss of constraining power. We simulate P 1D measurements from DESI using hydrodynamical simulations and show that the compressed likelihood is model independent and lossless, recovering unbiased results even in the presence of massive neutrinos or running of the primordial power spectrum.

Fourier formalism for relativistic axion-photon conversion with astrophysical applications

We study the weak mixing of photons and relativistic axionlike particles (axions) in plasmas with background magnetic fields, $\mathbf{B}$. We show that, to leading order in the axion-photon coupling, the conversion probability, ${P}_{\ensuremath{\gamma}\ensuremath{\rightarrow}a}$, is given by the one-dimensional power spectrum of the magnetic field components perpendicular to the particle trajectory. Equivalently, we express ${P}_{\ensuremath{\gamma}\ensuremath{\rightarrow}a}$ as the Fourier transform of the magnetic field autocorrelation function, and establish a dictionary between properties of the real-space magnetic field and the energy-dependent conversion probability. For axions more massive than the plasma frequency, (${m}_{a}>{\ensuremath{\omega}}_{\mathrm{pl}}$), we use this formalism to analytically solve the problem of perturbative axion-photon mixing in a general magnetic field. In the general case where ${\ensuremath{\omega}}_{\mathrm{pl}}/{m}_{a}$ varies arbitrarily along the trajectory, we show that a naive application of the standard formalism for ``resonant'' conversion can give highly inaccurate results, and that a careful calculation generically gives nonresonant contributions at least as large as the resonant contribution. Furthermore, we demonstrate how techniques based on the Fast Fourier Transform provide a new, highly efficient numerical method for calculating axion-photon mixing. We briefly discuss magnetic field modeling in galaxy clusters in the light of our results and argue, in particular, that a recently proposed ``regular'' model used for studying axion-photon mixing (specifically applied to the Perseus cluster) is inconsistent with observations. Our formalism suggests new methods to search for imprints of axions, and will be important for spectrographs with percent level sensitivity, which includes existing X-ray observations by Chandra as well as the upcoming Athena mission.

Simulating intergalactic gas for DESI-like small scale Lymanα forest observations

Measurements of the Lyα forest based on large numbers of quasar spectra from sky surveys such as SDSS/eBOSS accurately probe the distribution of matter on small scales and thus provide important constraints on several ingredients of the cosmological model. A main summary statistic derived from those measurements is the one-dimensional power spectrum, P1D, of the Lyα absorption. However, model predictions for P1D rely on expensive hydrodynamical simulations of the intergalactic medium, which was the limiting factor in previous analyses. Datasets from upcoming surveys such as DESI will push observational accuracy near the 1%-level and probe even smaller scales. This observational push mandates even more accurate simulations as well as more careful exploration of parameter space. In this work we evaluate the robustness and accuracy of simulations and the statistical framework used to constrain cosmological parameters. We present a comparison between the grid-based simulation code Nyx and SPH-based code Gadget in the context of P1D. In addition, we perform resolution and box-size convergence tests using Nyx code.We use a Gaussian process emulation scheme to reduce the number of simulations required for exploration of parameter space without sacrificing the model accuracy. We demonstrate the ability to produce unbiased parameter constraints in an end-to-end inference test using mock eBOSS- and DESI-like data, and we advocate for the usage of adaptive sampling schemes as opposed to using a fixed Latin hypercube design.

Neutrino mass bounds from confronting an effective model with BOSS Lyman-α data

We present an effective model for the one-dimensional Lyman-α flux power spectrum far above the baryonic Jeans scale. The main new ingredient is constituted by a set of two parameters that encode the impact of small, highly non-linear scales on the one-dimensional power spectrum on large scales, where it is measured by BOSS. We show that, by marginalizing over the model parameters that capture the impact of the intergalactic medium, the flux power spectrum from both simulations and observations can be described with high precision. The model displays a degeneracy between the neutrino masses and the (unknown, in our formalism) normalization of the flux power spectrum. This degeneracy can be lifted by calibrating one of the model parameters with simulation data, and using input from Planck CMB data. We demonstrate that this approach can be used to extract bounds on the sum of neutrino masses with comparably low numerical effort, while allowing for a conservative treatment of uncertainties from the dynamics of the intergalactic medium. An explorative analysis yields an upper bound of 0.16eV at 95% C.L. when applied to BOSS data at 3 ≤ z ≤ 4.2. We also forecast that if the systematic and statistical errors will be reduced by a factor two the upper bound will become 0.1eV at 95% C.L, and 0.056eV when assuming a 1% error.

Central Slice Theorem-based Relationship between 1D-NPS Obtained by the Slit Method and 2D-NPS for CT Images

The method using a numerical slit (slit method) is used commonly to obtain the one-dimensional (1D) noise power spectrum (NPS) in computed tomography. However, the relationship between the 1D-NPS obtained by the slit method and the original two-dimensional (2D) NPS derived by the 2D Fourier transformation has not been elucidated clearly. The purpose of this study was to clarify their relationship based on the well-known central slice theorem (projection slice theorem) and validate it using computer simulation analysis. With the application of the central slice theorem, we described that the 1D-NPS obtained by the slit method was equal to the central slice (profile) in the 2D-NPS when we set the slit length to the maximum (i.e. the matrix size of the noise image). To verify this, we generated computer-simulated noise images with the known 2D-NPS (true 2D-NPS). From those images, we obtained the 1D-NPS that was obtained by the slit method and compared it with the central slice in the true 2D-NPS. When we set the slit length to the maximum, the 1D-NPS obtained by the slit method showed good agreement with the central slice in the true 2D-NPS. We clarified the relationship between the 1D-NPS obtained by the slit method and the 2D-NPS using a theoretical approach and the computer simulation. We had to maximize the slit length to achieve the accurate measurement of the 1D-NPS using the slit method.

Statistical Detection of IGM Structures during Cosmic Reionization Using Absorption of the Redshifted 21 cm line by H i against Compact Background Radio Sources

Abstract Detecting neutral hydrogen structures in the intergalactic medium (IGM) during cosmic reionization via absorption (21 cm forest) against a background radiation is considered independent and complementary to the three-dimensional tomography and power spectrum techniques. The direct detection of this absorption requires very bright (≳10–100 mJy) background sources at high redshifts (z ≳ 8), which are evidently rare; very long times of integration; or instruments of very high sensitivity. This motivates a statistical one-dimensional (1D) power spectrum approach along narrow sightlines but with fainter background objects (∼1–10 mJy), which are likely to be more abundant and significant contributors at high redshifts. The 1D power spectrum reduces cosmic variance and improves sensitivity especially on small spatial scales. Using standard radiative transfer and fiducial models for the instrument, the background sources, and the evolution of IGM structures during cosmic reionization, the potential of the 1D power spectrum along selected narrow directions is investigated against uncertainties from thermal noise and the chromatic synthesized point spread function (PSF) response. Minimum requirements on the number of high-redshift background sources, the telescope sensitivity, and the PSF quality are estimated for a range of instrumental, background source, and reionization model parameters. The 1D power spectrum is intrinsically stronger at higher redshifts. A ∼1000 hr observing campaign targeting ∼100 narrow sightlines to radio-faint, high-redshift background objects with modern radio telescopes, especially the Square Kilometre Array, can detect the 1D power spectrum on a range of spatial scales and redshifts, and potentially discriminate between models of cosmic reionization.

A Monte Carlo Implementation of Galactic Free–Free Emission for the EoR Foreground Models

Abstract The overwhelming foreground causes severe contamination on the detection of 21 cm signal during the Epoch of Reionization (EoR). Among various foreground components, the Galactic free–free emission is less studied, so that its impact on the EoR observation remains unclear. To better constrain this emission, we perform Monte Carlo simulation of Hα emission, which comprises direct and scattered Hα radiation from H ii regions and warm ionized medium (WIM). The positions and radii of H ii regions are quoted from the Wide-Field Infrared Survey Explorer H ii catalog, and the WIM is described by an axisymmetric model. The scattering is off dust and free electrons that are realized by applying an exponential fitting to the HI4PI H i map and an exponential disk model, respectively. The simulated Hα intensity, the Simfast21 software, and the latest SKA1-Low layout configuration are employed to simulate the SKA “observed” images of Galactic free–free emission and the EoR signal. By analyzing the one-dimensional power spectra, we find that the Galactic free–free emission can be about 105.4–102.1, 105.0–101.7, and 104.3–101.1 times more luminous than the EoR signal on scales of in the 116–124, 146–154, and 186–194 MHz frequency bands, respectively. We further calculate the two-dimensional power spectra inside the EoR window and show that the power leaked by Galactic free–free emission can still be significant, as the power ratios can reach about 110%–8000%, 30%–2400%, and 10%–250% on scales of in three frequency bands. Therefore, we indicate that the Galactic free–free emission should be carefully treated in future EoR detections.

Turbulence statistics in a negatively buoyant multiphase plume

We investigate the turbulence statistics in a {multiphase plume made of heavy particles (particle Reynolds number at terminal velocity is 450)}. Using refractive-index-matched stereoscopic particle image velocimetry, we measure the locations of particles {whose buoyancy drives the formation of a multiphase plume,} {together with the local velocity of the induced flow in the ambient salt-water}. {Measurements in the plume centerplane exhibit self-similarity in mean flow characteristics consistent with classic integral plume theories.} The turbulence characteristics resemble those measured in a bubble plume, {including strong anisotropy in the normal Reynolds stresses. However, we observe structural differences between the two multiphase plumes. First, the skewness of the probability density function (PDF) of the axial velocity fluctuations is not that which would be predicted by simply reversing the direction of a bubble plume. Second, in contrast to a bubble plume, the particle plume has a non-negligible fluid-shear production term in the turbulent kinetic energy (TKE) budget. Third, the radial decay of all measured terms in the TKE budget is slower than those in a bubble plume.} Despite these dissimilarities, a bigger picture emerges that applies to both flows. The TKE production by particles (or bubbles) roughly balances the viscous dissipation, except near the plume centerline. The one-dimensional power-spectra of the velocity fluctuations show a -3 power-law that puts both the particle and bubble plume in a category different from single-phase shear-flow turbulence.

Turbulence versus Fire-hose Instabilities: 3D Hybrid Expanding Box Simulations

Abstract The relationship between a decaying plasma turbulence and proton fire hose instabilities in a slowly expanding plasma is investigated using three-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field along the radial direction, and we start with an isotropic spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations with zero cross-helicity. A turbulent cascade rapidly develops and leads to a weak proton heating that is not sufficient to overcome the expansion-driven perpendicular cooling. The plasma system eventually drives the parallel and oblique fire hose instabilities that generate quasi-monochromatic wave packets that reduce the proton temperature anisotropy. The fire hose wave activity has a low amplitude with wave vectors quasi-parallel/oblique with respect to the ambient magnetic field outside of the region dominated by the turbulent cascade and is discernible in one-dimensional power spectra taken only in the direction quasi-parallel/oblique with respect to the ambient magnetic field; at quasi-perpendicular angles the wave activity is hidden by the turbulent background. These waves are partly reabsorbed by protons and partly couple to and participate in the turbulent cascade. Their presence reduces kurtosis, a measure of intermittency, and the Shannon entropy, but increases the Jensen–Shannon complexity of magnetic fluctuations; these changes are weak and anisotropic with respect to the ambient magnetic field and it is not clear if they can be used to indirectly discern the presence of instability-driven waves.

An Origin for the Angular Momentum of Molecular Cloud Cores: A Prediction from Filament Fragmentation

Abstract The angular momentum of a molecular cloud core plays a key role in star formation, as it is directly related to the outflow and the jet emanating from the newborn star, and it eventually results in the formation of the protoplanetary disk. However, the origin of the core rotation and its time evolution are not well understood. Recent observations reveal that molecular clouds exhibit a ubiquity of filamentary structures and that star-forming cores are associated with the densest filaments. As these results suggest that dense cores form primarily in filaments, the mechanism of core formation from filament fragmentation should explain the distribution of the angular momentum of these cores. In this paper we analyze the relation between velocity fluctuations along the filament close to equilibrium, and the angular momentum of the cores formed along its crest. We first find that an isotropic velocity fluctuation that follows the three-dimensional Kolmogorov spectrum does not reproduce the observed angular momentum of molecular cloud cores. We then identify the need for a large power at small scales and study the effect of three power spectrum models. We show that the one-dimensional Kolmogorov power spectrum with a slope of −5/3 and an anisotropic model with reasonable parameters are compatible with the observations. Our results stress the importance of more detailed and systematic observations of both the velocity structure along filaments, and the angular momentum distribution of molecular cloud cores, to determine the validity of the mechanism of core formation from filamentary molecular clouds.

Contribution of Radio Halos to the Foreground for SKA EoR Experiments

The overwhelming foreground contamination is one of the primary impediments to probing the Epoch of Reionization (EoR) through measuring the redshifted 21 cm signal. Among various foreground components, radio halos are less studied and their impacts on the EoR observations are still poorly understood. In this work, we employ the Press-Schechter formalism, merger-induced turbulent re-acceleration model, and the latest SKA1-Low layout configuration to simulate the SKA "observed" images of radio halos. We calculate the one-dimensional power spectra from simulated images and find that radio halos can be about $10^4$, $10^3$ and $10^{2.5}$ times more luminous than the EoR signal on scales of $0.1\,\text{Mpc}^{-1} < k < 2\,\text{Mpc}^{-1}$ in the 120-128, 154-162, and 192-200 MHz bands, respectively. By examining the two-dimensional power spectra inside properly defined EoR windows, we find that the power leaked by radio halos can still be significant, as the power ratios of radio halos to the EoR signal on scales of $0.5\,\text{Mpc}^{-1} \lesssim k \lesssim 1\,\text{Mpc}^{-1}$ can be up to about 230-800%, 18-95%, and 7-40% in the three bands, when the 68% uncertainties caused by the variation of the number density of bright radio halos are considered. Furthermore, we find that radio halos located inside the far side-lobes of the station beam can also impose strong contamination within the EoR window. In conclusion, we argue that radio halos are severe foreground sources and need serious treatments in future EoR experiments.

The one-dimensional power spectrum from the SDSS DR14 Lyα forests

We present a measurement of the 1D Lyα forest flux power spectrum, using the complete Baryon Oscillation Spectroscopic Survey (BOSS) and first extended-BOSS (eBOSS) quasars at zqso > 2.1, corresponding to the fourteenth data release (DR14) of the Sloan Digital Sky Survey (SDSS). Our results cover thirteen bins in redshift from zLyα = 2.2 to 4.6, and scales up to k = 0.02 (km/s)−1. From a parent sample of 180,413 visually inspected spectra, we selected the 43,751 quasars with the best quality; this data set improves the previous result from the ninth data release (DR9), both in statistical precision (achieving a reduction by a factor of two) and in redshift coverage. We also present a thorough investigation of identified sources of systematic uncertainties that affect the measurement. The resulting 1D power spectrum of this work is in excellent agreement with the one from the BOSS DR9 data.

Generalized early warning signals in multivariate and gridded data with an application to tropical cyclones.

Tipping events in dynamical systems have been studied across many applications, often by measuring changes in variance or autocorrelation in a one-dimensional time series. In this paper, methods for detecting early warning signals of tipping events in multidimensional systems are reviewed and expanded. An analytical justification of the use of dimension-reduction by empirical orthogonal functions, in the context of early warning signals, is provided and the one-dimensional techniques are also extended to spatially separated time series over a 2D field. The challenge of predicting an approaching tropical cyclone by a tipping-point analysis of the sea-level pressure series is used as the primary example, and an analytical model of a moving cyclone is also developed in order to test predictions. We show that the one-dimensional power spectrum indicator may be used following dimension-reduction or over a 2D field. We also show the validity of our moving cyclone model with respect to tipping-point indicators.