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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

STATISTICAL ANALYSIS OF TANK 5 FLOOR SAMPLE RESULTS

Sampling has been completed for the characterization of the residual material on the floor of Tank 5 in the F-Area Tank Farm at the Savannah River Site (SRS), near Aiken, SC. The sampling was performed by Savannah River Remediation (SRR) LLC using a stratified random sampling plan with volume-proportional compositing. The plan consisted of partitioning the residual material on the floor of Tank 5 into three non-overlapping strata: two strata enclosed accumulations, and a third stratum consisted of a thin layer of material outside the regions of the two accumulations. Each of three composite samples was constructed from five primary sample locations of residual material on the floor of Tank 5. Three of the primary samples were obtained from the stratum containing the thin layer of material, and one primary sample was obtained from each of the two strata containing an accumulation. This report documents the statistical analyses of the analytical results for the composite samples. The objective of the analysis is to determine the mean concentrations and upper 95% confidence (UCL95) bounds for the mean concentrations for a set of analytes in the tank residuals. The statistical procedures employed in the analyses were consistent with the Environmental Protection Agency (EPA) technical guidance by Singh and others [2010]. Savannah River National Laboratory (SRNL) measured the sample bulk density, nonvolatile beta, gross alpha, radionuclide, inorganic, and anion concentrations three times for each of the composite samples. The analyte concentration data were partitioned into three separate groups for further analysis: analytes with every measurement above their minimum detectable concentrations (MDCs), analytes with no measurements above their MDCs, and analytes with a mixture of some measurement results above and below their MDCs. The means, standard deviations, and UCL95s were computed for the analytes in the two groups that had at least some measurements above their MDCs. The identification of distributions and the selection of UCL95 procedures generally followed the protocol in Singh, Armbya, and Singh [2010]. When all of an analyte's measurements lie below their MDCs, only a summary of the MDCs can be provided. The measurement results reported by SRNL are listed in Appendix A, and the results of this analysis are reported in Appendix B. The data were generally found to follow a normal distribution, and to be homogeneous across composite samples.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2013

Statistical Analysis of Tank 5 Floor Sample Results (U)

Sampling has been completed for the characterization of the residual material on the floor of Tank 5 in the F-Area Tank Farm at the Savannah River Site (SRS), near Aiken, SC. The sampling was performed by Savannah River Remediation (SRR) LLC using a stratified random sampling plan with volume-proportional compositing. The plan consisted of partitioning the residual material on the floor of Tank 5 into three non-overlapping strata: two strata enclosed accumulations, and a third stratum consisted of a thin layer of material outside the regions of the two accumulations. Each of three composite samples was constructed from five primary sample locations of residual material on the floor of Tank 5. Three of the primary samples were obtained from the stratum containing the thin layer of material, and one primary sample was obtained from each of the two strata containing an accumulation. This report documents the statistical analyses of the analytical results for the composite samples. The objective of the analysis is to determine the mean concentrations and upper 95% confidence (UCL95) bounds for the mean concentrations for a set of analytes in the tank residuals. The statistical procedures employed in the analyses were consistent with the Environmental Protection Agency (EPA) technical guidance by Singh and others [2010]. Savannah River National Laboratory (SRNL) measured the sample bulk density, nonvolatile beta, gross alpha, and the radionuclide1, elemental, and chemical concentrations three times for each of the composite samples. The analyte concentration data were partitioned into three separate groups for further analysis: analytes with every measurement above their minimum detectable concentrations (MDCs), analytes with no measurements above their MDCs, and analytes with a mixture of some measurement results above and below their MDCs. The means, standard deviations, and UCL95s were computed for the analytes in the two groups that had at least some measurements above their MDCs. The identification of distributions and the selection of UCL95 procedures generally followed the protocol in Singh, Armbya, and Singh [2010]. When all of an analyte's measurements lie below their MDCs, only a summary of the MDCs can be provided. The measurement results reported by SRNL are listed, and the results of this analysis are reported. The data were generally found to follow a normal distribution, and to be homogenous across composite samples.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Convergence of statistical moments of particle density time series in scrape-off layer plasmas

Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a fixed shape, an exponential distribution of waiting times, and amplitudes represents the radial motion of blob-like structures. With an analytic formulation of the process at hand, we derive expressions for the mean squared error on estimators of sample mean and sample variance as a function of sample length, sampling frequency, and the parameters of the stochastic process. Employing that the probability distribution function of a particularly relevant stochastic process is given by the gamma distribution, we derive estimators for sample skewness and kurtosis and expressions for the mean squared error on these estimators. Numerically, generated synthetic time series are used to verify the proposed estimators, the sample length dependency of their mean squared errors, and their performance. We find that estimators for sample skewness and kurtosis based on the gamma distribution are more precise and more accurate than common estimators based on the method of moments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2002

Experimental Investigations of Non-Stationary Properties In Radiometer Receivers Using Measurements of Multiple Calibration References

Radiometers must be periodically calibrated because the receiver response fluctuates. Many techniques exist to correct for the time varying response of a radiometer receiver. An analytical technique has been developed that uses generalized least squares regression (LSR) to predict the performance of a wide variety of calibration algorithms. The total measurement uncertainty including the uncertainty of the calibration can be computed using LSR. The uncertainties of the calibration samples used in the regression are based upon treating the receiver fluctuations as non-stationary processes. Signals originating from the different sources of emission are treated as simultaneously existing random processes. Thus, the radiometer output is a series of samples obtained from these random processes. The samples are treated as random variables but because the underlying processes are non-stationary the statistics of the samples are treated as non-stationary. The statistics of the calibration samples depend upon the time for which the samples are to be applied. The statistics of the random variables are equated to the mean statistics of the non-stationary processes over the interval defined by the time of calibration sample and when it is applied. This analysis opens the opportunity for experimental investigation into the underlying properties of receiver non stationarity through the use of multiple calibration references. In this presentation we will discuss the application of LSR to the analysis of various calibration algorithms, requirements for experimental verification of the theory, and preliminary results from analyzing experiment measurements.

Racette, Paul↗
DOE OSTI2019

Inorganic Element Concentrations in Passerine Eggs Collected at Technical Areas 36, 39, and 16 at Los Alamos National Laboratory

In 2018, nonviable avian eggs were opportunistically collected at Los Alamos National Laboratory near open detonation sites at Technical Area (TA) 36 and TA-39 and near the TA-16 burning grounds and were evaluated for inorganic elements (mostly metals). A total of eight western bluebird Sialia mexicana ) and ash-throated flycatcher ( Myiarchus cinerascens ) egg samples were collected among the three locations of interest. Due to the small sample size, statistical comparisons could not be made. However, concentrations of inorganic elements observed in this study were compared with the upper-level bounds of background concentrations (mean + three standard deviations = 99% confidence interval; regional statistical reference level [RSRL]). Several inorganic elements were not detected in avian eggs and the majority of inorganic elements detected were below the RSRL. The few elements that exceeded the RSRL were below the lowest observable adverse effect level (LOAEL), when available. These data suggest that inorganic element concentrations in eggs observed here are not of ecological concern. As these data are preliminary, more data are needed to make a robust assessment, including additional background samples.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Constant pressure and temperature discrete-time Langevin molecular dynamics

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Development of physics-consistent conditional diffusion model to overcome data scarcity in critical heat flux

Deep generative modeling provides a powerful pathway to overcome data scarcity in energy-related applications where experimental data are often limited. By learning the underlying probability distribution of the training dataset, deep generative models, such as the diffusion model, can generate high-fidelity synthetic samples that statistically resemble the training data. Such synthetic data generation can significantly enrich the size and diversity of the available training data, and more importantly, improve the robustness of downstream machine learning models in predictive tasks. The objective of this paper is to investigate the effectiveness of diffusion models for overcoming data scarcity in nuclear energy applications. By leveraging a public dataset on critical heat flux which covers a wide range of commercial nuclear reactor operational conditions, we developed a diffusion model that can generate an arbitrary amount of synthetic samples. Since a vanilla diffusion model can only generate samples randomly, we also developed a conditional diffusion model capable of generating targeted critical heat flux data under user-specified thermal-hydraulic conditions. The performance of the diffusion model was evaluated based on its ability to capture empirical feature distributions and pair-wise correlations, as well as to maintain physical consistency. The results showed that both the diffusion model and conditional diffusion model can successfully generate realistic and physics-consistent critical heat flux data. Furthermore, uncertainty quantification results demonstrate that the conditional diffusion model is highly effective in augmenting critical heat flux data while maintaining acceptable levels of uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1989

On optimizing a constellation of altimetric satellites for measuring global oceanic mesoscale

The orbital configuration of the Eos polar-platform constellation is examined to determine if baseline orbital parameters are appropriately specified to meet the mission goal of measuring global oceanic mesoscale variability. Using the Nyquist sampling theorem, spatial and temporal measurement requirements are first established for the constellation. Based upon these requirements, the optimum solution indicates that a total of five spacecraft are required to meet the mesoscale mapping task. Additional analyses are performed on both a two-platform configuration as well as the complete four-platform Eos constellation. The results of these calculations show that an optimized configuration of four properly-phased Eos platforms, placed into identical 835-km sun-synchronous orbits with 13-day repeat periods, can very nearly meet statistically significant sampling criteria for mapping global oceanic mesoscale variability.

Chase, Robert↗
NASA NTRS1961

Application of Monte Carlo Technique for Determining Maneuvering Loads from Statistical Information on Airplane Motions

Results of a statistical analysis of horizontal-tail loads on a fighter airplane are presented. The data were obtained from a number of operational training missions with flight at altitudes up to about 50,000 feet and at Mach numbers up to 1.22. The analysis was performed to determine the feasibility of calculating horizontal-tail load from data on the flight conditions and airplane motions. In the analysis the calculated loads are compared with the measured loads for the different types of missions performed. The loads were calculated by two methods: a direct approach and a Monte Carlo technique. The procedures used and some of the problems associated with the data analysis are discussed. frequencies of occurrence of tail loads of given magnitudes are derived from statistical information on the flight quantities. In the direct method, a time history of tail load is calculated from time-history measurements of the flight quantities. The Monte Carlo method could be useful for extending loads information for design of prospective airplanes . For the Monte Carlo method, the The results indicate that the accuracy of loads, regardless of the method used for calculation, is largely dependent on the knowledge of the pertinent airplane aerodynamic characteristics and center-of-gravity location. In addition, reliable Monte Carlo results require an adequate sample of statistical data and a knowledge of the more important statistical dependencies between the various flight conditions and airplane motions.

Hamer, Harold A.↗
DOE OSTI2012

Statistical uncertainty analysis applied to the DRAGONv4 code lattice calculations and based on JENDL-4 covariance data

In this paper, multi-group microscopic cross-section uncertainty is propagated through the DRAGON (Version 4) lattice code, in order to perform uncertainty analysis on k{infinity} and 2-group homogenized macroscopic cross-sections predictions. A statistical methodology is employed for such purposes, where cross-sections of certain isotopes of various elements belonging to the 172 groups DRAGLIB library format, are considered as normal random variables. This library is based on JENDL-4 data, because JENDL-4 contains the largest amount of isotopic covariance matrixes among the different major nuclear data libraries. The aim is to propagate multi-group nuclide uncertainty by running the DRAGONv4 code 500 times, and to assess the output uncertainty of a test case corresponding to a 17 x 17 PWR fuel assembly segment without poison. The chosen sampling strategy for the current study is Latin Hypercube Sampling (LHS). The quasi-random LHS allows a much better coverage of the input uncertainties than simple random sampling (SRS) because it densely stratifies across the range of each input probability distribution. Output uncertainty assessment is based on the tolerance limits concept, where the sample formed by the code calculations infers to cover 95% of the output population with at least a 95% of confidence. This analysis is the first attempt to propagate parameter uncertainties of modern multi-group libraries, which are used to feed advanced lattice codes that perform state of the art resonant self-shielding calculations such as DRAGONv4. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Planck intermediate results: XXVII. High-redshift infrared galaxy overdensity candidates and lensed sources discovered by Planck and confirmed by Herschel -SPIRE

We have used the Planck all-sky submillimetre and millimetre maps to search for rare sources distinguished by extreme brightness, a few hundred millijanskies, and their potential for being situated at high redshift. These “cold” Planck sources, selected using the High Frequency Instrument (HFI) directly from the maps and from the Planck Catalogue of Compact Sources (PCCS), all satisfy the criterion of having their rest-frame far-infrared peak redshifted to the frequency range 353–857 GHz. This colour-selection favours galaxies in the redshift range z = 2–4, which we consider as cold peaks in the cosmic infrared background. With a 4'.5 beam at the four highest frequencies, our sample is expected to include overdensities of galaxies in groups or clusters, lensed galaxies, and chance line-of-sight projections. In this paper, we perform a dedicated Herschel-SPIRE follow-up of 234 such Planck targets, finding a significant excess of red 350 and 500μm sources, in comparison to reference SPIRE fields. About 94% of the SPIRE sources in the Planck fields are consistent with being overdensities of galaxies peaking at 350μm, with 3% peaking at 500μm, and none peaking at 250μm. About 3% are candidate lensed systems, all 12 of which have secure spectroscopic confirmations, placing them at redshifts z> 2.2. Only four targets are Galactic cirrus, yielding a success rate in our search strategy for identifying extragalactic sources within the Planck beam of better than 98%. The galaxy overdensities are detected with high significance, half of the sample showing statistical significance above 10σ. The SPIRE photometric redshifts of galaxies in overdensities suggest a peak at z ≃ 2, assuming a single common dust temperature for the sources of T d = 35 K. Under this assumption, we derive an infrared (IR) luminosity for each SPIRE source of about 4 × 10 12 L ⊙ , yielding star formation rates of typically 700 M ⊙ yr -1 . If the observed overdensities are actual gravitationally-bound structures, the total IR luminosity of all their SPIRE-detected sources peaks at 4 × 10 13 L ⊙ , leading to total star formation rates of perhaps 7 × 10 3 M ⊙ yr -1 per overdensity. Taken together, these sources show the signatures of high-z (z> 2) protoclusters of intensively star-forming galaxies. Finally, all these observations confirm the uniqueness of our sample compared to reference samples and demonstrate the ability of the all-skyPlanck-HFI cold sources to select populations of cosmological and astrophysical interest for structure formation studies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Radial structure and formation of the Milky Way disc

The formation of the Galactic disc is an enthusiastically debated issue. Numerous studies and models seek to identify the dominant physical process(es) that shaped its observed properties; for example, satellite accretion, starburst, quenching, gas infall, and stellar radial migration. Taking advantage of the improved coverage of the inner Milky Way provided by the SDSS DR16 APOGEE catalogue and of the ages published in the APOGEE-AstroNN Value Added Catalogue (VAC), we examined the radial evolution of the chemical and age properties of the Galactic stellar disc with the aim of better constraining its formation. Using a sample of 199 307 giant stars with precise APOGEE abundances and APOGEE-AstroNN ages, selected in a ±2 kpc layer around the galactic plane, we assessed the dependency as a function of guiding radius of (i) the median metallicity, (ii) the ridge lines of the [Fe/H] – [Mg/Fe] and age–[Mg/Fe] distributions, and (iii) the age distribution function (ADF). The giant star sample allows us to probe the radial behaviour of the Galactic disc from R g = 0 to 14–16 kpc. The thick disc [Fe/H] – [Mg/Fe] ridge lines follow closely grouped parallel paths, supporting the idea that the thick disc did form from a well-mixed medium. However, the ridge lines present a small drift in [Mg/Fe], which decreases with increasing guiding radius. At sub-solar metallicity, the intermediate and outer thin disc [Fe/H] – [Mg/Fe] ridge lines follow parallel sequences shifted to lower metallicity as the guiding radius increases. We interpret this pattern as the signature of a dilution of the interstellar medium from R g ~ 6 kpc to the outskirts of the disc, which occurred before the onset of the thin disc formation. The APOGEE-AstroNN VAC provides stellar ages for statistically significant samples of thin disc stars from the Galactic centre up to R g ~ 14 kpc. An important result provided by this dataset is that the thin disc presents evidence of an inside-out formation up to R g ~ 10 – 12 kpc. Moreover, about ~7 Gyr ago, the [Mg/Fe] ratio in the outer thin disc (R g > 10 kpc) was higher by about ~0.03–0.05 dex than in the more internal regions of the thin disc. This could be the fossil record of a pollution of the outer disc gas reservoir by the thick disc during its starburst phase.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

RELICS: Strong Lens Models for Five Galaxy Clusters from the Reionization Lensing Cluster Survey

Strong gravitational lensing by galaxy clusters magnifies background galaxies, enhancing our ability to discover statistically significant samples of galaxies at ${\boldsymbol{z}}\gt 6$, in order to constrain the high-redshift galaxy luminosity functions. In this study, we present the first five lens models out of the Reionization Lensing Cluster Survey (RELICS) Hubble Treasury Program, based on new HST WFC3/IR and ACS imaging of the clusters RXC J0142.9+4438, Abell 2537, Abell 2163, RXC J2211.7–0349, and ACT-CLJ0102–49151. The derived lensing magnification is essential for estimating the intrinsic properties of high-redshift galaxy candidates, and properly accounting for the survey volume. We report on new spectroscopic redshifts of multiply imaged lensed galaxies behind these clusters, which are used as constraints, and detail our strategy to reduce systematic uncertainties due to lack of spectroscopic information. In addition, we quantify the uncertainty on the lensing magnification due to statistical and systematic errors related to the lens modeling process, and find that in all but one cluster, the magnification is constrained to better than 20% in at least 80% of the field of view, including statistical and systematic uncertainties. The five clusters presented in this paper span the range of masses and redshifts of the clusters in the RELICS program. We find that they exhibit similar strong lensing efficiencies to the clusters targeted by the Hubble Frontier Fields within the WFC3/IR field of view. Outputs of the lens models are made available to the community through the Mikulski Archive for Space Telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2011

Quantitative Examination of a Large Sample of Supra-Arcade Downflows in Eruptive Solar Flares

Sunward-flowing voids above post-coronal mass ejection flare arcades were first discovered using the soft X-ray telescope aboard Yohkoh and have since been observed with TRACE (extreme ultraviolet (EUV)), SOHO/LASCO (white light), SOHO/SUMER (EUV spectra), and Hinode/XRT (soft X-rays). Supra-arcade downflow (SAD) observations suggest that they are the cross-sections of thin flux tubes retracting from a reconnection site high in the corona. Supra-arcade downflowing loops (SADLs) have also been observed under similar circumstances and are theorized to be SADs viewed from a perpendicular angle. Although previous studies have focused on dark flows because they are easier to detect and complementary spectral data analysis reveals their magnetic nature, the signal intensity of the flows actually ranges from dark to bright. This implies that newly reconnected coronal loops can contain a range of hot plasma density. Previous studies have presented detailed SAD observations for a small number of flares. In this paper, we present a substantial SADs and SADLs flare catalog. We have applied semiautomatic detection software to several of these events to detect and track individual downflows thereby providing statistically significant samples of parameters such as velocity, acceleration, area, magnetic flux, shrinkage energy, and reconnection rate. We discuss these measurements (particularly the unexpected result of the speeds being an order of magnitude slower than the assumed Alfven speed), how they were obtained, and potential impact on reconnection models.

Savage, Sabrina L.↗
DOE OSTI2017

Economic consequences of aviation system disruptions: A reduced-form computable general equilibrium analysis

The state of the art approach to economic consequence analysis (ECA) is computable general equilibrium (CGE) modeling. However, such models contain thousands of equations and cannot readily be incorporated into computerized systems used by policy analysts to yield estimates of economic impacts of various types of transportation system failures due to natural hazards, human related attacks or technological accidents. This paper presents a reduced-form approach to simplify the analytical content of CGE models to make them more transparent and enhance their utilization potential. The reduced-form CGE analysis is conducted by first running simulations one hundred times, varying key parameters, such as magnitude of the initial shock, duration, location, remediation, and resilience, according to a Latin Hypercube sampling procedure. Statistical analysis is then applied to the “synthetic data” results in the form of both ordinary least squares and quantile regression. The analysis yields linear equations that are incorporated into a computerized system and utilized along with Monte Carlo simulation methods for propagating uncertainties in economic consequences. Although our demonstration and discussion focuses on aviation system disruptions caused by terrorist attacks, the approach can be applied to a broad range of threat scenarios.

Aviation System Disruptions↗
DOE OSTI2013

Project of a Super Charm-Tau factory at the Budker Institute of Nuclear Physics in Novosibirsk

A project of a Super Charm-Tau factory is being developed at the Budker Institute of Nuclear Physics (Siberian Branch, Russian Academy of Sciences) in Novosibirsk. The electron-positron collider to be employed will operate at c.m. energies in the range between 2 and 5 GeV at an unprecedentedly high luminosity of 10{sup 35} cm{sup -2} s{sup -1} with a longitudinal electron polarization at the beam-interaction point. The main objective of experiments at the Super Charm-Tau factory is to study processes involving the production and properties of charmed quarks and tau leptons. A high luminosity of this setup will make it possible to obtain a statistical data sample that will be three to four orders of magnitude vaster than that from any other experiment performed thus far. Experiments at this setup are assumed to be sensitive to effects of new physics beyond the Standard Model. Investigations to be carried out at the Super-Charm-Tau factory will supplement future experiments at Super-B factories under construction in Italy and in Japan.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

The information content of stellar halos: stellar population gradients and accretion histories in early-type illustris galaxies

Long dynamical timescales in the outskirts of galaxies preserve the information content of their accretion histories, for example in the form of stellar population gradients. We present a detailed analysis of the stellar halo properties of a statistically representative sample of early-type galaxies from the Illustris simulation, and show that stellar population gradients at large radii can indeed be used to infer basic properties of galactic accretion histories. We measure metallicity, age, and surface-brightness profiles in quiescent Illustris galaxies ranging from M{sub ⋆} = 10{sup 10}–2 × 10{sup 12} M{sub ⊙} and show that they are in reasonable agreement with observations. At fixed mass, galaxies that accreted little of their stellar halo material tend to have steeper metallicity and surface-brightness profiles, between 2–4 effective radii (R{sub e}), than those with larger accreted fractions. Profiles of metallicity and surface-brightness in the stellar halo typically flatten from z = 1 to the present. This suggests that the accretion of stars into the stellar halo tends to flatten metallicity and surface-brightness profiles, a picture which is supported by the tight correlation between the two gradients in the stellar halo. We find no statistical evidence of additional information content related to accretion histories in stellar halo metallicity profiles, beyond what is contained in surface-brightness profiles. Age gradients in the stellar halo do not appear to be sensitive to galactic accretion histories, and none of the stellar population gradients studied are strongly correlated with the mean merger mass-ratio. Our findings relate specifically to regions of the stellar halo within 4 R{sub e}, but suggest that future observations that reach large radii outside galaxies (including to 10 R{sub e} and beyond) will have the best potential to constrain galactic accretion histories.

79 ASTRONOMY AND ASTROPHYSICS↗