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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Understanding the Hydronium Cation in the Solid State: A Study in Synthetic Hydronium Uranyl Phosphate and Arsenate Mineral Systems and Their Irradiation Stability

Here, we present neutron diffraction, electronic structure calculations, and optical vibrational spectroscopic characterization of hydronium uranyl phosphate (HUP), the synthetic analog of chernikovite ((H 3 O)(UO 2 )(PO 4 )·3H 2 O) to gain insight into structural features of the hydronium cation in the solid state. HUP crystallizes in P2 1 /c instead of previously reported P4/ncc 1 at room temperature and Pccn below 302 K. Lower symmetry was required due to hydronium and interstitial water positions within the structure. Crystallographic positions of hydronium cations determined from powder neutron diffraction data are bolstered by Raman and attenuated total reflectance infrared spectroscopic measurements and are further informed by density functional theory with phonon eigenvector analysis for spectral assignments. Finally, HUP and its arsenate analog (trogerite, (H 3 O)(UO 2 )(AsO 4 )·3H 2 O), (HUAs) were studied using He 2+ irradiation as an analog for α radiolysis to investigate the irradiation stability of these phases and the stability of hydronium cations in the solid state. Dose studies were employed wherein each sample was irradiated to 5, 10, 15, 25, and 50 MGy. Structural insight regarding irradiated materials is gained using optical vibrational spectroscopy and powder X-ray diffraction. Surprising irradiation stability of HUAs was found up to 50 MGy of dose, which may have important implications for understanding and modeling the geologic stability of legacy U.

actinides↗
DOE OSTI2021

Davis Computational Spectroscopy Workflow—From Structure to Spectra

Here, we describe an automated workflow that connects a series of atomic simulation tools to investigate the relationship between atomic structure, lattice dynamics, materials properties, and inelastic neutron scattering (INS) spectra. Starting from the atomic simulation environment (ASE) as an interface, we demonstrate the use of a selection of calculators, including density functional theory (DFT) and density functional tight binding (DFTB), to optimize the structures and calculate interatomic force constants. We present the use of our workflow to compute the phonon frequencies and eigenvectors, which are required to accurately simulate the INS spectra in crystalline solids like diamond and graphite as well as molecular solids like rubrene. We have also implemented a machine-learning force field based on Chebyshev polynomials called the Chebyshev interaction model for efficient simulation (ChIMES) to improve the accuracy of the DFTB simulations. We then explore the transferability of our DFTB/ChIMES models by comparing simulations derived from different training sets. We show that DFTB/ChIMES demonstrates ~100× reduction in computational expense while retaining most of the accuracy of DFT as well as yielding high accuracy for different materials outside of our training sets. The DFTB/ChIMES method within the workflow expands the possibilities to use simulations to accurately predict materials properties of increasingly complex structures that would be unfeasible with ab initio methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

GPU-Accelerated Solution of the Bethe–Salpeter Equation for Large and Heterogeneous Systems

We present a massively parallel GPU-accelerated implementation of the Bethe–Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting from single-particle eigenvalues and eigenvectors obtained with density functional theory. The algorithms adopted here circumvent the slowly converging sums over empty and occupied states and the inversion of large dielectric matrices through a density matrix perturbation theory approach and a low-rank decomposition of the screened Coulomb interaction, respectively. Further computational savings are achieved by exploiting the nearsightedness of the density matrix of semiconductors and insulators to reduce the number of screened Coulomb integrals. We scale our calculations to thousands of GPUs with a hierarchical loop and data distribution strategy. The efficacy of our method is demonstrated by computing the VEEs of several spin defects in wide-band-gap materials, showing that supercells with up to 1000 atoms are necessary to obtain converged results. We discuss the validity of the common approximation that solves the BSE with truncated sums over empty and occupied states. In conclusion, we then apply our GW-BSE implementation to a diamond lattice with 1727 atoms to study the symmetry breaking of triplet states caused by the interaction of a point defect with an extended line defect.

Absorption spectra↗
DOE OSTI2022

Computational Aspects of Single-Molecule Kinetics for Coupled Catalytic Cycles: A Spectral Analysis

Catalysis from single active sites is analyzed using methods developed from single molecule kinetics. Using a stochastic Markov state description, the observable properties of general catalytic networks of reactions are expressed using an eigenvalue decomposition of the transition matrix for the Markov process. By the use of a sensitivity analysis, the necessary eigenvalues and eigenvectors are related to the energies of controlling barriers and wells located along the reaction routes. A generalization of the energetic span theory allows the eigenvalues to be computed from several activation energies corresponding to distinct barrier-well pairings. The formalism is demonstrated accurately for model problems for a physically realistic mechanism for an alkene hydrogenation reaction on a single atom catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Estimation of the Kelvin–Helmholtz Unstable Boundary

The Kelvin–Helmholtz (KH) instability is one of the most important mechanisms of the viscous-like interaction between the solar wind and the magnetosphere (MSP), which transport the mass, energy, momentum, and magnetic flux. Thus, it is important to examine whether the magnetopause boundary is KH unstable or not. Based on the KH onset conditions, this report proposes to use a matrix to identify the most KH unstable direction based on the in situ measurements of the density, velocity, and magnetic field in the MSP and magnetosheath. The range of the KH unstable direction can be easily estimated based on the eigenvalues of the matrix. The eigenvectors of the matrix provide a new boundary normal coordinate system, which could be useful for 2-D KH instability simulation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Atomic-scale imaging of frequency-dependent phonon anisotropy

Directly visualizing vibrational anisotropy in individual phonon modes is essential for understanding a wide range of intriguing optical, thermal and elastic phenomena in materials. Although conventional optical and diffraction techniques have been used to estimate vibrational anisotropies, they fall short in achieving the spatial and energy resolution necessary to provide detailed information. Here, we introduce a new form of momentum-selective electron energy-loss spectroscopy, which enables the element-resolved imaging of frequency- and symmetry-dependent vibrational anisotropies with atomic resolution. Vibrational anisotropies manifest in different norms of orthogonal atomic displacements, known as thermal ellipsoids. Using the centrosymmetric strontium titanate as a model system, we observed two distinct types of oxygen vibrations with contrasting anisotropies: oblate thermal ellipsoids below 60 meV and prolate ones above 60 meV. In non-centrosymmetric barium titanate, our approach can detect subtle distortions of the oxygen octahedra by observing the unexpected modulation of q-selective signals between apical and equatorial oxygen sites near 55 meV, which originates from reduced crystal symmetry and may also be linked to ferroelectric polarization. These observations are quantitatively supported by theoretical modelling, which demonstrates the reliability of our approach. The measured frequency-dependent vibrational anisotropies shed new light on the dielectric and thermal behaviours governed by acoustic and optical phonons. Furthermore, the ability to visualize phonon eigenvectors at specific crystallographic sites with unprecedented spatial and energy resolution opens new avenues for exploring dielectric, optical, thermal and superconducting properties.

Ferroelectrics and multiferroics↗
DOE OSTI2020

Electronic structure with direct diagonalization on a D-wave quantum annealer

Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A universal variational quantum eigensolver for non-Hermitian systems

Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional $$O(log_{2}{N})$$ O ( l o g 2 N ) quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High-redshift quasars along the main sequence

The 4D Eigenvector 1 empirical formalism (4DE1) and its main sequence (MS) for quasars has emerged as a powerful tool for organising the diversity among quasar populations, as several key observational measures and physical parameters are systematically changing along it. Trends revealed by 4DE1 are very well established to explain all the diverse characteristics seen in low-redshift quasar samples. Nevertheless, the situation is far less clear when dealing with high-luminosity and high-redshift sources. Here, we aim to evaluate the behaviour of our sample of 22 quasars at high redshift (2.2 ≤ z ≤ 3.7) and high luminosity (47.39 ≤ L bol ≤ 48.36) in the context of the 4DE1. Our approach involves studying quasar physics through a spectroscopic exploration of UV and optical emission line diagnostics. We used new observations from the ISAAC instrument at ESO-VLT and primarily from the SDSS to cover the optical and the UV rest-frames, respectively. The emission lines were characterised both via a quantitative parametrisation of the line profiles and a decomposition of the emission line profiles using multicomponent fitting routines. We provide spectrophotometric properties and line profile measurements for Hβ+[O III]λλ4959,5007, as well as Si IVλ1397+O IV]λ1402, C IVλ1549+He IIλ1640, and the 1900 Å blend (including Al IIIλ1860, Si III]λ1892, and C III]λ1909). For six out of the 22 objects, a significantly blueshifted component on the Hβ profile is present. In 14 out of 22 cases, an Hβ outflowing component associated with [O III] is detected. The majority of [O III]λλ4959,5007 emission line profiles show blueshifted velocities higher than 250 km s -1 . We find extremely broad [O III]λλ4959,5007 emission that is comparable to the width of Hβ broad profile in some highly accreting quasars. The [O III]λλ4959,5007 and C IVλ1549 blueshifts show very high amplitudes and a high degree of correlation. The line widths and shifts are correlated for both [O III]λλ4959,5007 and C IVλ1549, suggesting that emission from outflowing gas is providing a substantial broadening effect to both lines. Otherwise, the links between C IVλ1549 centroid velocity at half intensity (c(1/2)), Eddington ratio (L/L Edd ), and bolometric luminosity are found to be in agreement with previous studies of high-luminosity quasars. Our analysis suggests that the behaviour of quasars of very high luminosity all along the main sequence is strongly affected by powerful outflows involving a broad range of spatial scales. The main sequence correlations remain valid at high redshift and high luminosity even if a systematic increase in line width is observed. Scaling laws based on UV Al IIIλ1860 and Hβ emission lines are equally reliable estimators of M BH .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Mapping Critical Vulnerabilities in Natural Gas Pipeline Systems through Network Centrality and GIS Analytics

Natural gas plays a central role in the US energy landscape, providing 43% of electricity generation in 2023. Its exclusive recovery ability on pipelines for transmission underscores the importance of understanding the disruption recovery ability of this infrastructure. This study employs a network-based analytical framework integrating geographic information systems (GIS) with multiple centrality measures—betweenness, closeness, degree, and eigenvector—to pinpoint key segments and evaluate the structural robustness of the national pipeline network. Pipelines are grouped by System ID and Operator ID to capture variations across organizational and physical structures. The analysis reveals uneven patterns of network influence, where certain pipelines function as critical connectors or dominant hubs. Spatial mapping highlights geographic dependencies and potential chokepoints, offering a clear view of where targeted risk prevention measures would be most effective. The findings provide practical guidance for prioritizing maintenance, enhancing system robustness, and mitigating risks to ensure a stable and secure energy supply. Future research will expand the framework to incorporate dynamic operational data and real-time network behavior.

Peterson, Steven [ORNL] (ORCID:0000000287672998)↗
DOE OSTI2022

The role of breakup and coalescence in fine-scale bubble-induced turbulence. II. Kinematics

This second part of our research explores the kinematic aspect of fine-scale bubble-induced turbulence (BIT) to (i) present the effect of bubble breakup and coalescence and (ii) compare it against the universal kinematic fine-scale turbulence characteristics reported in the literature. To this end, we simulate a dilute bubbly system of 0.5% void fraction using two distinct numerical simulations. In the volume-of-fluid (VoF) simulation, bubbles undergo breakup and coalescence. In the immersed boundary method (IBM) simulation, however, they act as rigid spheres. We also perform a simulation of classical homogeneous isotropic turbulence (HIT). The first important outcome of this study is that BIT is radically different from HIT in terms of its kinematic fine-scale characteristics. In the vorticity-dominating regions, BIT exhibits a weak vortex stretching. This weak vortex stretching is due to (a) the intermediate strain-rate eigenvalues skewed weakly to positive and (b) the extensive strain-rate eigenvector aligning perpendicular to the vorticity vector. The BIT has, on average, not only a weak enstrophy production but also a weak strain production in strain-dominating regions. The weak strain production is due to (a) the presence of vortex stretching in highly strained fluid elements and (b) the absolute magnitude of compressive strain-rate eigenvalue being as close to the extensive strain-rate eigenvalue. Thus, none of the kinematic fine-scale HIT characteristics is noted for BIT. The second important conclusion is that bubble breakup and coalescence play little to no influence on the kinematics of fine-scale BIT as VoF and IBM simulations produce similar results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Quantum mechanical calculations for material modeling using Kohn–Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. Here, these calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn–Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh–Ritz projection step of the discretized Kohn–Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Including the parallel mass flow in calculating the steady-state solutions and stability of the momentum balance equations for a quasisymmetric stellarator

The Helically Symmetric Experiment (HSX) is a quasisymmetric stellarator with minimal parallel viscous damping in a helical direction. The parallel flow (Vǁ) along the magnetic field is similarly weakly damped by viscosity. In this paper, the self-consistent steady-state parallel and poloidal momentum balance equations are used to show that a large Vǁ on the order of the ion thermal velocity can increase the ion resonant radial electric field (Er) beyond the value calculated using the typical approximation that Vǁ is zero. By altering the damping of Vǁ, either by degrading the quasisymmetry or varying the neutral density, the ion resonant Er can shift in a controllable fashion. It is shown explicitly that there exist stable and unstable steady-state solutions in the two-dimensional space of Vǁ and Er. A stability analysis of each solution is performed by calculating the eigenvalues and eigenvectors of the Jacobian. The unstable solution corresponds to a saddle point in which the eigenvalues have opposite signs. The analysis leads to the conclusion that unstable solutions occur when the derivative of the total poloidal damping with respect to Er is positive. A hysteresis in Er and Vǁ is observed when the radial current density is linearly increased to a maximum and then decreased back to zero. Jumps in the radial electric field and the parallel flow are observed as the radial current density drives the evolution from one stable point to the next. This result is similar to experimental data observed on several devices.

Physics↗
DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗
DOE OSTI2024

Superconductor to exciton condensate transition in a model copper-oxide material

Abstract Superconductivity and exciton condensation are fundamental phenomena in condensed matter physics, associated with the condensation of electron–electron and electron–hole pairs, respectively, into coherent quantum states. In this study, we present evidence of a superconductor to exciton condensate transition within the context of the three-band Hubbard model of copper-oxide-like materials. As the electron–electron repulsion increases, the superconducting phase is superseded by exciton condensation. In support of theoretical predictions—not yet realized experimentally—we observe the coexistence of the two condensates in the vicinity of the transition where the quantum states become a superposition of electron–electron and electron–hole condensates. Coexistence is rigorously computed from large eigenvalues and their eigenvectors in both the two-electron reduced density matrix (2-RDM) and the particle-hole RDM, which we obtain from a direct variational ground-state energy minimization with respect to the 2-RDM by semidefinite programming. We further discern that adjacent d orbitals and intervening p orbitals facilitate electron–electron pairing between copper orbitals, thereby supporting the superexchange mechanism for superconductivity. These observations suggest the feasibility of witnessing a superconductor to exciton condensate transition in copper-oxide analogs, bearing significant implications for identifying materials conducive to efficient transport processes.

Schouten, Anna O. (ORCID:0000000264255219)↗
DOE OSTI2024

Computation of the expectation value of the spin operator S^ 2 for the spin-flip Bethe–Salpeter equation

Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator S^ 2 . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of S^ 2 may be found to differ from 2.00; this difference is called 'spin contamination'. The expectation values S^ 2 must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Here, our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for S^ 2 as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating S^ 2 , we present the derivation for the general equation for computing S^ 2 with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The parameter-level performance of covariance matrix conditioning in cosmic microwave background data analyses

Empirical estimates of the band power covariance matrix are commonly used in cosmic microwave background (CMB) power spectrum analyses. While this approach easily captures correlations in the data, noise in the resulting covariance estimate can systematically bias the parameter fitting. Conditioning the estimated covariance matrix, by applying prior information on the shape of the eigenvectors, can reduce these biases and ensure the recovery of robust parameter constraints. In this work, we use simulations to benchmark the performance of four different conditioning schemes, motivated by contemporary CMB analyses. The simulated surveys measure the TT, TE, and EE power spectra over the angular multipole range 300 ≤ ℓ ≤ 3500 in Δℓ = 50 wide bins, for temperature map-noise levels of 10, 6.4, and $2\, \mu$K arcmin. We divide the survey data into N real = 30, 50, or 100 uniform subsets. We show the results of different conditioning schemes on the errors in the covariance estimate, and how these uncertainties on the covariance matrix propagate to the best-fitting parameters and parameter uncertainties. The most significant effect we find is an additional scatter in the best-fitting point, beyond what is expected from the data likelihood. For a minimal conditioning strategy, N real = 30, and a temperature map-noise level of 10$\, \mu$K arcmin, we find the uncertainty on the recovered best-fitting parameter to be ×1.3 larger than the apparent posterior width from the likelihood (×1.2 larger than the uncertainty when the true covariance is used). Stronger priors on the covariance matrix reduce the misestimation of parameter uncertainties to $\lt 1{{\ \rm per\ cent}}$. As expected, empirical estimates perform better with higher N real , ameliorating the adverse effects on parameter constraints.

79 ASTRONOMY AND ASTROPHYSICS↗