Large Error Bars Research Articles

The advantages of logarithmically scaled data for electromagnetic inversion

Non-linear inversion algorithms traverse a data misfit space over multiple iterations of trial models in search of either a global minimum or some target misfit contour. The success of the algorithm in reaching that objective depends upon the smoothness and predictability of the misfit space. For any given observation, there is no absolute form a datum must take, and therefore no absolute definition for the misfit space; in fact, there are many alternatives. However, not all misfit spaces are equal in terms of promoting the success of inversion. In this work, we appraise three common forms that complex data take in electromagnetic geophysical methods: real and imaginary components, a power of amplitude and phase, and logarithmic amplitude and phase. We find that the optimal form is logarithmic amplitude and phase. Single-parameter misfit curves of log-amplitude and phase data for both magnetotelluric and controlled-source electromagnetic methods are the smoothest of the three data forms and do not exhibit flattening at low model resistivities. Synthetic, multiparameter, 2-D inversions illustrate that log-amplitude and phase is the most robust data form, converging to the target misfit contour in the fewest steps regardless of starting model and the amount of noise added to the data; inversions using the other two data forms run slower or fail under various starting models and proportions of noise. It is observed that inversion with log-amplitude and phase data is nearly two times faster in converging to a solution than with other data types. We also assess the statistical consequences of transforming data in the ways discussed in this paper. With the exception of real and imaginary components, which are assumed to be Gaussian, all other data types do not produce an expected mean-squared misfit value of 1.00 at the true model (a common assumption) as the errors in the complex data become large. We recommend that real and imaginary data with errors larger than 10 per cent of the complex amplitude be withheld from a log-amplitude and phase inversion rather than retaining them with large error-bars.

Variances in r-process predictions from uncertain nuclear rates

Rapid neutron capture or ‘r-process’ nucleosynthesisis a critical process for creating approximately half of heavy elements above iron in the Universe. Simulations of the r- process require theoretical calculations of neutron capture and, β-decay rates for thousands of short-lived nuclei for which no experimental data exists. We explore the impact of uncertainties in theoretical nuclear rates by performing global monte carlo simulations. We show that randomly varying neutron capture and β-decay rates within current theoretical model uncertainties results in large error bars for r-process predictions. We conclude that the reduction of rate uncertainties either by new measurements or by improved nuclear models will allow for more robust r-process predictions.

ALMA observations ofαCentauri

The precise mechanisms that provide the non-radiative energy for heating the chromosphere and the corona of the Sun and those of other stars constitute an active field of research. By studying stellar chromospheres one aims at identifying the relevant physical processes. Defining the permittable extent of the parameter space can also serve as a template for the Sun-as-a-star. Earlier observations with Herschel and APEX have revealed the temperature minimum of alpha Cen, but these were unable to spatially resolve the binary into individual components. With the data reported here, we aim at remedying this shortcoming. Furthermore, these earlier data were limited to the wavelength region between 100 and 870mu. In the present context, we intend to extend the spectral mapping to longer wavelengths, where the contrast between stellar photospheric and chromospheric emission becomes increasingly evident. ALMA is particularly suited to point sources, such as unresolved stars. ALMA provides the means to achieve our objectives with both its high sensitivity of the collecting area for the detection of weak signals and the high spatial resolving power of its adaptable interferometer for imaging close multiple stars. This is the first detection of main-sequence stars at a wavelength of 3mm. Furthermore, the individual components of the binary alpha CenAB are clearly detected and spatially well resolved at all ALMA wavelengths. The high S/N of these data permit accurate determination of their relative flux ratios. The previously obtained flux ratio of 0.44, which was based on measurements in the optical and at 70mu, is consistent with the present ALMA results, albeit with a large error bar. Given the distinct difference in their cyclic activity, the similarity of their submm SEDs appears surprising.

Direct constraints on diffusion models from cosmic-ray positron data: Excluding the minimal model for dark matter searches

Galactic Cosmic-ray (CR) transport parameters are usually constrained by the boron-to-carbon ratio. This procedure is generically plagued with degeneracies between the diffusion coefficient and the vertical extent of the Galactic magnetic halo. The latter is of paramount importance for indirect dark matter (DM) searches, because it fixes the amount of DM annihilation or decay that contributes to the local antimatter CR flux. These degeneracies could be broken by using secondary radioactive species, but the current data still have large error bars, and this method is extremely sensitive to the very local interstellar medium (ISM) properties. Here, we propose to use the low-energy CR positrons in the GeV range as another direct constraint on diffusion models. We show that the PAMELA data disfavor small diffusion halo ($L\lesssim 3$ kpc) and large diffusion slope models, and exclude the minimal ({\em min}) configuration (Maurin et al. 2001, Donato et al. 2004) widely used in the literature to bracket the uncertainties in the DM signal predictions. This is complementary to indirect constraints (diffuse radio and gamma-ray emissions) and has strong impact on DM searches. Indeed this makes the antiproton constraints more robust while enhancing the discovery/exclusion potential of current and future experiments, like AMS-02 and GAPS, especially in the antiproton and antideuteron channels.

The extended ROSAT-ESO Flux Limited X-ray Galaxy Cluster Survey (REFLEX II)

The X-ray luminosity function that is closely related to the cluster mass function is an important statistic of the census of galaxy clusters in our Universe. It is also an important means to probe the cosmological model of our Universe. Based on our recently completed REFLEX II cluster sample comprising 910 galaxy clusters with redshifts we construct the X-ray luminosity function of galaxy clusters for the nearby Universe and discuss its implications. We derived the X-ray luminosity function of the REFLEX II clusters on the basis of a precisely constructed selection function for the full sample and for several redshift slices from z = 0 to z = 0.4. In this redshift interval we find no significant signature of redshift evolution of the luminosity function. We provide the results of fits of a parameterized Schechter function and extensions of it which provide a reasonable characterization of the data. We also use a model for structure formation and galaxy cluster evolution to compare the observed X-ray luminosity function with the theoretical predictions for different cosmological models. The most interesting constraints can be derived for the cosmological parameters Ωm and σ8. We explore the influence of several model assumptions on which our analysis is based. We find that the scaling relation of X-ray luminosity and mass introduces the largest systematic uncertainty. From the statistical uncertainty alone we can constrain the matter density parameter, Ωm ~ 0.27 ± 0.03 and the amplitude parameter of the matter density fluctuations, σ8 ~ 0.80 ± 0.03. Marginalizing over the most important uncertainties, the normalisation and slope of the LX − M scaling relation, we have larger error bars and a result of Ωm ~ 0.29 ± 0.04 and σ8 ~ 0.77 ± 0.07 (1σ confidence limits). We compare our results with those of the SZ-cluster survey provided by the Planck mission and we find very good agreement with the results using Planck clusters as cosmological probes, but there is some tension with Planck cosmological results from the microwave background anisotropies, which we discuss in the paper. We also make a comparison with results from the SDSS cluster survey, several cosmological X-ray cluster surveys, and recent Sunyaev-Zel’dovich effect surveys. We find good agreement with these previous results and show that the REFLEX II survey provides a significant reduction in the uncertainties compared to earlier measurements.

Indirect determination of the electric field in plasma discharges using laser-induced fluorescence spectroscopy

The evaluation of electric fields is of prime interest for the description of plasma characteristics. In this work, different methods for determining the electric field profile in low-pressure discharges using one- and two-dimensional Laser-Induced Fluorescence (LIF) measurements are presented and discussed. The energy conservation, fluid, and kinetic approaches appear to be well-suited for the electric field evaluation in this region of the plasma flow. However, the numerical complexity of a two-dimensional kinetic model is penalizing due to the limited signal-to-noise ratio that can be achieved, making the computation of the electric field subject to large error bars. The ionization contribution which appears in the fluid model makes it unattractive on an experimental viewpoint. The energy conservation and 1D1V kinetic approaches should therefore be preferred for the determination of the electric field when LIF data are used.

THE OPTICAL, ULTRAVIOLET, AND X-RAY STRUCTURE OF THE QUASAR HE 0435–1223

Microlensing has proven an effective probe of the structure of the innermost regions of quasars, and an important test of accretion disk models. We present light curves of the lensed quasar HE 0435-1223 in the R band and in the ultraviolet, and consider them together with X-ray light curves in two energy bands that are presented in a companion paper. Using a Bayesian Monte Carlo method, we constrain the size of the accretion disk in the rest-frame near- and far-UV, and constrain for the first time the size of the X-ray emission regions in two X-ray energy bands. The R-band scale size of the accretion disk is about 10^15.23 cm (~23 r_g), slightly smaller than previous estimates, but larger than would be predicted from the quasar flux. In the UV, the source size is weakly constrained, with a strong prior dependence. The UV to R-band size ratio is consistent with the thin disk model prediction, with large error bars. In soft and hard X-rays, the source size is smaller than ~10^14.8 cm (~10 r_g) at 95% confidence. We do not find evidence of structure in the X-ray emission region, as the most likely value for the ratio of the hard X-ray size to the soft X-ray size is unity. Finally, we find that the most likely value for the mean mass of stars in the lens galaxy is ~0.3 M_sun, consistent with other studies.

A NEW LOOK ATSPITZERPRIMARY TRANSIT OBSERVATIONS OF THE EXOPLANET HD 189733b

Blind source separation techniques are used to reanalyse two exoplanetary transit lightcurves of the exoplanet HD189733b recorded with the IR camera IRAC on board the Spitzer Space Telescope at 3.6$\mu$m during the "cold" era. These observations, together with observations at other IR wavelengths, are crucial to characterise the atmosphere of the planet HD189733b. Previous analyses of the same datasets reported discrepant results, hence the necessity of the reanalyses. The method we used here is based on the Independent Component Analysis (ICA) statistical technique, which ensures a high degree of objectivity. The use of ICA to detrend single photometric observations in a self-consistent way is novel in the literature. The advantage of our reanalyses over previous work is that we do not have to make any assumptions on the structure of the unknown instrumental systematics. Such "admission of ignorance" may result in larger error bars than reported in the literature, up to a factor $1.6$. This is a worthwhile trade-off for much higher objectivity, necessary for trustworthy claims. Our main results are (1) improved and robust values of orbital and stellar parameters, (2) new measurements of the transit depths at 3.6$\mu$m, (3) consistency between the parameters estimated from the two observations, (4) repeatability of the measurement within the photometric level of $\sim 2 \times 10^{-4}$ in the IR, (5) no evidence of stellar variability at the same photometric level within 1 year.

Ambiguities in the rate of oxygen formation during stellar helium burning in the12C(α,γ) reaction

The rate of oxygen formation determines the C/O ratio during stellar helium burning. It is the single most important nuclear input of stellar evolution theory including the evolution of Type II and Type Ia supernova. Yet the low energy cross section of the fusion of 4He + 12C denoted as the 12C(a,g)16O reaction still remains uncertain after forty years of extensive work. We analyze and critically review the most recent measurements of complete angular distributions of the outgoing gamma-rays at very low energies (Ecm > 1.0 MeV). Our analysis of the angular distribution measured with the EUROGAM/GANDI arrays lead us to conclude considerably larger error bars than published hence they are excluded from the current sample of "world data". We show that the current sample of "world data" of the measured E2 cross section factors below 1.7 MeV cluster to two distinct groups that lead to two distinct extrapolations of SE2(300) ~ 60 or ~ 154 keVb. We point to a much neglected discrepancy between the measured E1-E2 phase difference (phi_12) and unitarity as required by the Watson theorem, suggesting systematic problem(s) of some of the measured gamma-ray angular distributions. The ambiguity of the extrapolated SE2(300) together with a previously observed ambiguity of SE1(300) represent the current state of the art of the field and they must be resolved by future measurements of complete and detailed angular distributions of the 12C(a,g) reaction at very low energies (Ecm < 1.0 MeV).

A large population of red supergiants in the super star cluster NGC 1705-1

We present near-infrared integral field observations of the super star cluster in the amorphous galaxy NGC1705. Data have been collected with SINFONI mounted on the VLT. Adaptive optics was used under good seeing conditions. Mosaics of the cluster and its immediate surrounding have been constructed. The cluster is not spatially resolved. Its radius is smaller than 2.85 ± 0.50pc. The K-band spectrum of the cluster is dominated by strong CO absorption bandheads. It is typical of a Galactic K 4–5 supergiant. Its age is estimated to be 12 ± 6Myr. The large error bar is rooted in the uncertainties of the input physics and ingredients of different evolutionary models.

WHAT DO WE REALLY KNOW ABOUT URANUS AND NEPTUNE?

The internal structures and compositions of Uranus and Neptune are not well constrained due to the uncertainty in rotation period and flattening, as well as the relatively large error bars on the gravitational coefficients. While Uranus and Neptune are similar in mass and radius, they differ in other physical properties such as thermal emission, obliquity, and inferred atmospheric enrichment. In this letter we consider the uncertainty in the planetary rotation periods, show that rotation periods more consistent with the measured oblateness imply that Uranus and Neptune have different internal structures, and speculate on the source of that difference. We conclude that Uranus and Neptune might have very different structures and/or compositions despite their similar masses and radii. We point out that understanding these differences can have important implications for our view of the formation and evolution of Uranus and Neptune as well as intermediate-mass extra-solar planets in general.

The Galactic Cepheid period–luminosity relation revisited using bona fide cluster Cepheids

AbstractClassical Cepheids in Galactic open clusters (cluster Cepheids: CCs) have been studied extensively for multiple decades, thanks to their importance as calibrators of the Galactic Cepheid period–luminosity relation (PLR). Here we revisit the calibration of the Galactic PLR using a new sample of CCs, since even recent calibrations show significant discrepancies. The CC sample employed for the calibration is based on the preliminary results of a self-consistent, eight-dimensional all-sky census. This census is based mostly on literature data, supplemented with high-precision radial-velocity observations from both hemispheres. New CCs are identified from our census and the degree of confidence in membership is quantified for known candidates. Using only bona fide CCs, we obtain MV = (−3.08 ± 0.50) log P + (−0.94 ± 0.42) mag, which is in perfect agreement with the results by Sandage, Tammann, and Reindl, albeit with larger error bars and an rms of 0.21 mag. The key to obtaining a meaningful calibration is to employ accurate cluster distance moduli and space reddening values. A homogeneous study of all bona fide host clusters would be desirable to increase precision and confidence in the calibration.

Relative dispersion observations and trajectory modeling in the Santa Barbara Channel

Relative dispersion statistics and related Lagrangian parameters, not well observed in coastal regions, are obtained from in situ surface drifter observations and presented in the context of Lagrangian stochastic models. Clusters of GPS tracked surface drifters, with initial horizontal spacing of 5–10 m, were repetitively deployed in the Santa Barbara Channel from July 2004 to June 2005. The drifters sampled their position every 10 min for 1–2 days. Mean square pair separation distance, or relative dispersion, increases approximately exponentially in time during the first ∼5 h of sampling (e‐folding time of 0.9 h). Thereafter, the dispersion increase is approximately quadratic in time. Large error bars on the observed mean dispersion, and higher‐order Lagrangian statistics that are not clearly supportive of the aforementioned dispersion curves, indicate uncertainty. The mean square relative (separation) velocity shows near‐linear growth with pair separation distance, extending from 0.3 to 85 cm2 s−2over length scales from ∼8 m to 2.2 km. The observed length scale dependency in square relative velocity is investigated in a Lagrangian stochastic model (LSM) for a cloud of particles. Modeled dispersion agrees with observations only when the velocity scale for the sub‐grid scale random normal deviate in the LSM (typically a constant) is length scale dependent, and takes into consideration the observed scaling. Occasional large (&gt;25 cm s−1) discrepancies in grid‐scale velocities between drifters and HF radar cause general disagreement in distributions of ending positions of LSM trajectories when compared with Lagrangian observations.

Seismic detection of acoustic sharp features in the CoRoT target HD 49933

The technique of determining the acoustic location of layers of sharp changes in the sound speed inside a star from the oscillatory signal in its frequencies is applied on a solar-type star, the CoRoT target, HD49933. We are able to determine the acoustic depth of the second helium ionisation zone of HD49933 to be 794 +55/-68 seconds. The acoustic depth of the base of the convective zone is found to be 1855 +173/-412 seconds where the large error bars reflect the ambiguity in the result, which is difficult to determine with present precision on the frequencies because of the intrinsically weak nature of the signal. The positions of both these layers are consistent with those in a representative stellar model of HD49933.

First results on the neutron-induced fission cross-section of 231Pa for incident neutron energies En > 17 MeV

First results on the neutron-induced fission cross-section of 231Pa for incident neutron energies En>17MeV are presented. The experiments were carried out with quasi mono-energetic neutrons produced in the reaction T(d, n)4He. Corrections for low-energy neutron background produced in this reaction at incident deuteron energies Ed>2MeV are taken into account and based on experimental data obtained by two different techniques. Despite the relatively large error bars at the higher neutron energies, the new cross-section values meet the accuracy requirements set by the IAEA and will allow to remove the hitherto existing large spread between different previously published data. Recent cross-section calculations describe well the new experimental results, which are in consistency with cross-section values obtained in a particle-transfer reaction at excitation energies corresponding to neutron energies En<10MeV.

AnXMM-Newtonspatially-resolved study of metal abundance evolution in distant galaxy clusters

We present an XMM-Newton analysis of the X-ray spectra of 39 clusters of galaxies at 0.4<z<1.4, covering a temperature range of 1.5<=kT<=11 keV. We performed a spatially resolved spectral analysis to study how the abundance evolves with redshift not only through a single emission measure performed on the whole cluster but also spatially resolving the cluster emission. We do not observe a statistically significant (>2sigma) abundance evolution with redshift. The most significant deviation from no evolution (90% c.l.) is observed in the emission from the whole cluster (r<0.6r500), that could be parametrized as Z=A*(1+z)^(-0.8+/-0.5). Dividing the emission in 3 radial bins, no significant evidence of abundance evolution could be observed fitting the data with a power-law. A substantial agreement with measures presented in previous works is found. The error-weighted mean of the spatially resolved abundances in 3 redshift bins is consistent to be constant with z. Although the large error bars in the measure of the weighted-mean abundance prevent us from claiming any significant spatially resolved evolution, the trend with z in the 0.15-0.4r500 radial bin complements nicely the measures of Maughan et al., and broadly agrees with theoretical predictions. We also found that the data points derived from the spatially resolved analysis are well fitted by the relation Z(r,z)=Z0*(1+(r/0.15r500)^2)^(-a)*((1+z)/1.6)^(-gamma), showing a significant negative trend of Z with the radius and no significant evolution with the redshift. The present study is the first attempt made to spatially resolve the evolution of abundance with redshift. However, the sample size and the low statistics associated with most of the clusters in the sample prevents us to draw any statistically significant conclusion on the different evolutionary path that the different regions of the clusters may have traversed.

Shear moduli of two dimensional binary glasses

The shear moduli of two-component glasses in two dimensions are studied within mode coupling theory. Varying the concentration, strong mixing effects are observed along the glass transition lines for two interaction potentials. Nonoverlapping disks with size ratios between 0.3 and 0.9, and point particles interacting with (magnetic) dipoles of strength ratio between 0.1 and 0.6 are considered. Equilibrium structure factors (partially obtained from Monte Carlo simulations) and glass form factors, and perturbative calculations show that a softening of the elastic shear constant of glass upon adding another component arises from a dilution effect of the majority component. For very disparate mixtures, an anomalous elastic strenghtening results from what we interpret as clustering of the smaller particles in the voids between the larger ones. This might point to a glass–glass transition. We include simulation data on hard disk mixtures which show that the theory underestimates the moduli by around 50%, but otherwise captures the qualitative trends (within the rather large simulational error bars).

Correction to “Late 20th century warming and freshening in the central tropical Pacific”

[1] We present corrections to uncertainty estimates of late 20th century (1972-1998) coral-based sea-surface temperature (SST) and salinity (SSS) trends from Palmyra, Fanning and Christmas Islands of the central tropical Pacific reported in Nurhati et al. [2009] (Geophysical Research Letters, 36, L21606, doi:10.1029/2009GL040270). In our original paper we had assigned relatively large error bars to coral Sr/Ca-based warming trends observed at all three islands, rendering those trends statistically insignificant with respect to the large errors. However, those large uncertainties originate from large errors associated with quantifying absolute SST at any given point, whereas the uncertainties for SST trends should reflect errors in quantifying relative changes, which are much lower. Late 20th century warming trends of 0.94–1.65°C at the three islands are statistically significant with the corrected error ranges of ±0.19–0.37°C (1σ; originally ±5.73–6.57°C). Freshening trends inferred from coral-based oxygen isotopic composition of seawater (δ18OSW) of −0.32‰ and −0.12‰ (1σ) at Palmyra and Fanning, respectively, are associated with corrected error ranges of ±0.07‰ and ±0.08‰ (1σ; originally ±0.08‰ for both), respectively. Christmas experienced an insignificant +0.03 ± 0.11‰ (1σ; originally also ±0.11‰) trend in δ18OSWover this period. With the new, lower uncertainty estimates, the coral-based SST and SSS trends are statistically significant, thereby strengthening Nurhati et al.'s (2009) conclusions that robust warming and freshening have occurred in the central tropical Pacific over the late 20th century. Our detailed uncertainty calculations presented below will be of value to the paleoclimate community, as the correct calculation of absolute errors and relative errors represents a key component of paleoclimatic reconstruction.

Health damages from air pollution in China

This study evaluates air pollution-related health impacts on the Chinese economy by using an expanded version of the Emissions Prediction and Policy Analysis model. We estimated that marginal welfare impact to the Chinese economy of ozone and particulate-matter concentrations above background levels increased from 1997 US$22 billion in 1975 to 1997 US$112 billion in 2005, despite improvements in overall air quality. This increase is a result of the growing urban population and rising wages that thus increased the value of lost labor and leisure. In relative terms, however, welfare losses from air pollution decreased from 14% of the historical welfare level to 5% during the same period because the total size of the economy grew much faster than the absolute air pollution damages. In addition, we estimated that particulate-matter pollution alone led to a gross domestic product loss of 1997 US$64 billion in 1995. Given that the World Bank's comparable estimate drawn from a static approach was only 1997 US$34 billion, this result suggests that conventional static methods neglecting the cumulative impact of pollution-caused welfare damage are likely to underestimate pollution-health costs substantially. However, our analysis of uncertainty involved in exposure–response functions suggests that our central estimates are susceptible to significantly large error bars of around ±80%.

OBSERVATIONAL SELECTION EFFECTS AND THEM-σ RELATION

We examine the possibility that the observed relation between black-hole mass and host-galaxy stellar velocity dispersion (the M-sigma relation) is biased by an observational selection effect, the difficulty of detecting a black hole whose sphere of influence is smaller than the telescope resolution. In particular, we critically investigate recent claims that the M-sigma relation only represents the upper limit to a broad distribution of black-hole masses in galaxies of a given velocity dispersion. We find that this hypothesis can be rejected at a high confidence level, at least for the early-type galaxies with relatively high velocity dispersions (median 268 km/s) that comprise most of our sample. We also describe a general procedure for incorporating observational selection effects in estimates of the properties of the M-sigma relation. Applying this procedure we find results that are consistent with earlier estimates that did not account for selection effects, although with larger error bars. In particular, (i) the width of the M-sigma relation is not significantly increased; (ii) the slope and normalization of the M-sigma relation are not significantly changed; (iii) most or all luminous early-type galaxies contain central black holes at zero redshift. Our results may not apply to late-type or small galaxies, which are not well-represented in our sample.