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NASA NTRS1993

Cluster evolution as a probe of primordial density fluctuations

Although COBE's detection of large angle microwave background anisotropies fixes the amplitude of density fluctuations on length scales k exp -1 approximately = (300-6000) h(exp -1)Mpc, what is crucial for the level of large scale clustering is the amplitude of density fluctuations on scales (5-50) h(exp -1)Mpc. The level of dynamical clustering is usually parameterized by the size of the mass fluctuations in 8 h exp -1 Mpc spheres, sigma sub 8. For the cold dark matter model, COBE gives sigma sub 8 approximately = 1, while models with extra large scale power give sigma sub 8 approximately = 1/2. The most massive clusters of galaxies (greater than or approximately = 10 exp 15 solar mass) form from rare 'peak patches' found in the initial mass density distribution. Their abundance as a function of redshift is a sensitive probe of the wave number band k(exp -1) approx. (3-8) h(exp -1)Mpc, hence of sigma sub 8, and so cluster evolution can discriminate among models allowed by the COBE results. We use our Hierarchical Peaks Method, which accurately reproduces the results of P3M N-body simulations, to calculate the evolution of cluster x-ray flux counts, luminosity, and temperature functions as a function of sigma sub 8 for CDM models and those with more large scale power. We find that the EMSS and Edge et al. cluster samples support sigma sub 8 in the range from approx. 0.6-0.9, and that models with more large scale power (and hence flatter fluctuation spectra in the cluster regime) fit the x-ray bright end better.

Bond, J. Richard↗
NASA NTRS2003

Constraints on the Energy Content of the Universe from a Combination of Galaxy Cluster Observables

We demonstrate that constraints on cosmological parameters from the distribution of clusters as a function of redshift (dN/dz) are complementary to accurate angular diameter distance (D(sub A)) measurements to clusters, and their combination significantly tightens constraints on the energy density content of the Universe. The number counts can be obtained from X-ray and/or SZ (Sunyaev-Ze'dovich effect) surveys, and the angular diameter distances can be determined from deep observations of the intra-cluster gas using their thermal bremsstrahlung X-ray emission and the SZ effect. We combine constraints from simulated cluster number counts expected from a 12 deg(sup 2) SZ cluster survey and constraints from simulated angular diameter distance measurements based on the X-ray/SZ method assuming a statistical accuracy of 10% in the angular diameter distance determination of 100 clusters with redshifts less than 1.5. We find that Omega(sub m), can be determined within about 25%, Omega(sub lambda) within 20% and w within 16%. We show that combined dN/dz+(sub lambda) constraints can be used to constrain the different energy densities in the Universe even in the presence of a few percent redshift dependent systematic error in D(sub lambda). We also address the question of how best to select clusters of galaxies for accurate diameter distance determinations. We show that the joint dN/dz+ D(lambda) constraints on cosmological parameters for a fixed target accuracy in the energy density parameters are optimized by selecting clusters with redshift upper cut-offs in the range 0.55 approx. less than 1. Subject headings: cosmological parameters - cosmology: theory - galaxies:clusters: general

Molnar, Sandor M.↗
NASA NTRS2019

The X-Ray Halo Scaling Relations of Supermassive Black Holes

We carry out a comprehensive Bayesian correlation analysis between hot halos and direct masses of supermassive black holes (SMBHs), by retrieving the X-ray plasma properties (temperature, luminosity, density, pressure, and masses) over galactic to cluster scales for 85 diverse systems. We find new key scalings, with the tightest relation being −, followed by −. The tighter scatter (down to 0.2 dex) and stronger correlation coefficient of all the X-ray halo scalings compared with the optical counterparts (as the −) suggest that plasma halos play a more central role than stars in tracing and growing SMBHs (especially those that are ultramassive). Moreover, correlates better with the gas mass than dark matter mass. We show the important role of the environment, morphology, and relic galaxies/coronae, as well as the main departures from virialization/self-similarity via the optical/X-ray fundamental planes. We test the three major channels for SMBH growth: hot/Bondi-like models have inconsistent anticorrelation with X-ray halos and too low feeding; cosmological simulations find SMBH mergers as subdominant over most of cosmic time and too rare to induce a central-limit-theorem effect; the scalings are consistent with chaotic cold accretion, the rain of matter condensing out of the turbulent X-ray halos that sustains a long-term self-regulated feedback loop. The new correlations are major observational constraints for models of SMBH feeding/feedback in galaxies, groups, and clusters (e.g., to test cosmological hydrodynamical simulations), and enable the study of SMBHs not only through X-rays, but also via the Sunyaev–Zel'dovich effect (Compton parameter), lensing (total masses), and cosmology (gas fractions).

Supermassive black holes↗
NASA NTRS2015

NASA Software Cost Estimation Model: An Analogy Based Estimation Model

The cost estimation of software development activities is increasingly critical for large scale integrated projects such as those at DOD and NASA especially as the software systems become larger and more complex. As an example MSL (Mars Scientific Laboratory) developed at the Jet Propulsion Laboratory launched with over 2 million lines of code making it the largest robotic spacecraft ever flown (Based on the size of the software). Software development activities are also notorious for their cost growth, with NASA flight software averaging over 50% cost growth. All across the agency, estimators and analysts are increasingly being tasked to develop reliable cost estimates in support of program planning and execution. While there has been extensive work on improving parametric methods there is very little focus on the use of models based on analogy and clustering algorithms. In this paper we summarize our findings on effort/cost model estimation and model development based on ten years of software effort estimation research using data mining and machine learning methods to develop estimation models based on analogy and clustering. The NASA Software Cost Model performance is evaluated by comparing it to COCOMO II, linear regression, and K-­ nearest neighbor prediction model performance on the same data set.

Hihn, Jairus↗
NASA NTRS2006

Spatial Correlation Function of the Chandra Selected Active Galactic Nuclei

We present the spatial correlation function analysis of non-stellar X-ray point sources in the Chandra Large Area Synoptic X-ray Survey of Lockman Hole Northwest (CLASXS). Our 9 ACIS-I fields cover a contiguous solid angle of 0.4 deg(exp 2) and reach a depth of 3 x 10(exp -15) erg/square cm/s in the 2-8 keV band. We supplement our analysis with data from the Chandra Deep Field North (CDFN). The addition of this field allows better probe of the correlation function at small scales. A total of 233 and 252 sources with spectroscopic information are used in the study of the CLASXS and CDFN fields respectively. We calculate both redshift-space and projected correlation functions in co-moving coordinates, averaged over the redshift range of 0.1 < z < 3.0, for both CLASXS and CDFN fields for a standard cosmology with Omega(sub Lambda) = 0.73,Omega(sub M) = 0.27, and h = 0.71 (H(sub 0) = 100h km/s Mpc(exp -1). The correlation function for the CLASXS field over scales of 3 Mpc< s < 200 Mpc can be modeled as a power-law of the form xi(s) = (S/SO)(exp - gamma), with gamma = 1.6(sup +0.4 sub -0.3) and S(sub o) = 8.0(sup +.14 sub -1.5) Mpc. The redshift-space correlation function for CDFN on scales of 1 Mpc< s < 100 Mpc is found to have a similar correlation length so = 8.55(sup +0.74 sub -0.74) Mpc, but a shallower slope (gamma = 1.3 +/- 0.1). The real-space correlation functions derived from the projected correlation functions, are found to be tau(sub 0 = 8.1(sup +1.2 sub -2.2) Mpc, and gamma = 2.1 +/- 0.5 for the CLASXS field, and tau(sub 0) = 5.8(sup +.1.0 sub -1.5) Mpc, gamma = 1.38(sup +0.12 sub -0.14 for the CDFN field. By comparing the real- and redshift-space correlation functions in the combined CLASXS and CDFN samples, we are able to estimate the redshift distortion parameter Beta = 0.4 +/- 0.2 at an effective redshift z = 0.94. We compare the correlation functions for hard and soft spectra sources in the CLASXS field and find no significant difference between the two groups. We have also found that the correlation between X-ray luminosity and clustering amplitude is weak, which, however, is fully consistent with the expectation using the simplest relations between X-ray luminosity, black hole mass, and dark halo mass. We study the evolution of the AGN clustering by dividing the samples into 4 redshift bins over 0.1 Mpc< z <3.0 Mpc. We find a very mild evolution in the clustering amplitude, which show the same evolution trend found in optically selected quasars in the 2dF survey. We estimate the evolution of the bias, and find that the bias increases rapidly with redshift (b(z = 0.45) = 0.95 +/- 0.15 and b(z = 2.07) = 3.03 +/- 0.83): The typical mass of the dark matter halo derived from the bias estimates show little change with redshift. The average halo mass is found to be log (M(sub halo)/M(sun))approximates 12.1. Subject headings: cosmology: observations - large-scale structure of the universe - x-rays: diffuse background - galaxies: nuclei

Yang, Y.↗
NASA NTRS1995

The orbital eccentricities of binary millisecond pulsars in globular clusters

Low-mass binary millisecond pulsars (LMBPs) are born with very small orbital eccentricities, typically of order e(sub i) approximately 10(exp -6) to 10(exp -3). In globular clusters, however, higher eccentricities e(sub f) much greater than e(sub i) can be induced by dynamical interactions with passing stars. Here we show that the cross section for this process is much larger than previously estimated. This is becuse, even for initially circular binaries, the induced eccentricity e(sub f) for an encounter with pericenter separation r(sub p) beyond a few times the binary semimajor axis a declines only as a power law (e(sub f) varies as (r(sub p)/a)(exp -5/2), and not as an exponential. We find that all currently known LMBPs in clusters were probably affected by interactions, with their current eccentricities typically greater than at birth by an order of magnitude or more.

Rasio, Frederic A.↗
NASA NTRS2000

Coronal Activity in Low-Mass Pre-Main Sequence Stars: NGC 2264

We present the preliminary results of an analysis of ROSAT images in the region of the populous young (age approx. 3 Myr) star-forming region NGC 2264. The cluster was imaged with the ROSAT HRI in two sets of pointings -- one set near the central region of the cluster, centered on the star LW Mon, and the other set in the southern part of the cluster, centered near the star V428 Mon, just south of the Cone Nebula. In total 113 unique X-ray sources have been identified in the ROSAT images with signal-to-noise ratios greater than 3. The limiting luminosities (log Lx(ergs/sec)) for 3-sigma detections are estimated to be 30.18, 30.23, and 30.08 for the northern field, southern field, and overlap region between the two fields respectively. Extensive optical photometry, classification spectroscopy, and proper motions, obtained from recent ground-based surveys of this region, were used to identify the most likely optical counterpart to each X-ray source. Although most of our X-ray selected sample appears to be associated with NGC 2264 members, we find that the vast majority of the cluster membership was undetected in the ROSAT HRI survey. The X-ray cumulative luminosity function for solar-mass stars in NGC 2264 shows that most of the low-mass members probably have X-ray luminosities similar to those seen for the X-ray brightest members of older clusters such as IC 2391/IC 2602 (age approx. 50 Myr) and the Pleiades (age approx. 100 Myr). This research was funded in part by the SAO Summer Intern Program and NASA grant NAG5-8120.

Tebbe, H. J.↗
NASA NTRS1997

Sulfur in Cometary Dust

The computer-intensive project consisted of the analysis and synthesis of existing data on composition of comet Halley dust particles. The main objective was to obtain a complete inventory of sulfur containing compounds in the comet Halley dust by building upon the existing classification of organic and inorganic compounds and applying a variety of statistical techniques for cluster and cross-correlational analyses. A student hired for this project wrote and tested the software to perform cluster analysis. The following tasks were carried out: (1) selecting the data from existing database for the proposed project; (2) finding access to a standard library of statistical routines for cluster analysis; (3) reformatting the data as necessary for input into the library routines; (4) performing cluster analysis and constructing hierarchical cluster trees using three methods to define the proximity of clusters; (5) presenting the output results in different formats to facilitate the interpretation of the obtained cluster trees; (6) selecting groups of data points common for all three trees as stable clusters. We have also considered the chemistry of sulfur in inorganic compounds.

Fomenkova, M. N.↗
NASA NTRS2014

Comparison of Nickel XANES Spectra and Elemental Maps from a Ureilite, a LL3.8 Ordinary Chondrite, Two Carbonaceous Chondrites and Two Large Cluster IDPs

Nickel in the extraterrestrial world is commonly found in both Fe-Ni sulfide and Fe-Ni met-al forms [1] and in the pure metal state in the interior of iron meteorites where it is not easily oxidized. Ni is also found in olivine, pyroxene and glasses and in some melts the partitioning of Ni between the olivines and glass is controlled by the amount of S in the melt [2]. Its most common valence state is Ni(2+) but Ni also occurs as Ni(0), Ni(+), and Ni(3+) and rarely as Ni(2-), Ni(1-) and Ni(4+) [3]. It's valence state in olivines is Ni(2+) in octa-hedral coordination on the M1 site and rarely on the M2 site.[4]. The chemical sensitivity of X-ray absorp-tion near-edge structure (XANES) spectroscopy is well established and can be used to determine not only va-lence states but also coordination sites [5]. We report here Ni XANES spectroscopy and elemental maps collected from 2 carbonaceous chondrites, 2 large clus-ter IDPs, 1 ureilite and 1 LL3 orginary chondrite.Using XANES it may be possible to find a common trait in the large cluster IDPs that will also be found in mete-orite samples.

Wirick, S.↗
NASA NTRS2019

The Seismic Signatures of Recently Formed Impact Craters on Mars

We investigated the seismic signatures of recent impact crater clusters on Mars that would be recorded by the Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight)seismometers. We used a database of 77 measured and dated impact sites, with craters with diameters between 2.1 and 33.8 m, along with inferred impact angle, bolide trajectory, and varying target material properties to empirically scale for the momentum, expected seismic source function, and radiation pattern of impacts. The impact source is simulated in a local 3‐Dfinite difference wave propagation code and coupled to teleseismic distances by scaling the spectra of 1‐D global synthetic seismograms. We use the InSight seismometer noise floors to estimate detectability of impact(s) across azimuth and distance. Our experiments reveal that impact clusters have a higher peak corner frequency resulting from energy contributed by smaller craters to the power spectrum. We also find that the time separation between individual impacts in a cluster is small (<10–15 ms) and requires a seismometer closely situated to the source (<10 km) and a high sampling rate (>100 Hz) to resolve individual impacts within the cluster. Two of the clusters in our database(>20‐m effective diameter) would have been detectable by InSight, with the assumptions that the Martian background noise and seismic attenuation are both low. Joint detection of surface changes from newly formed crater(s) in images and by InSight will provide precise source locations that are crucial for constraining the internal structure of Mars

N. C. Schmerra↗
NASA NTRS1989

Alternative models of cooling flows

Two cooling flow models that differ from the standard models in clusters of galaxies are examined. The goal is to find a model in which the observations are reproduced without appealing to an unusual initial mass function for star formation. In one model, drag heating by galaxies reheats the cluster gas and also suppresses thermal instabilities in certain temperature regimes. In another model, the gas cools and begins to form stars, which lead to supernovae that reheat the cooled gas to the ambient cluster tmeperature. This model is viable only if high-mass stars are formed and if the supernovae are subluminous.

Bregman, Joel N.↗
NASA NTRS2000

Sunyaev - Zel'dovich Effect Imaging of Massive Clusters of Galaxies at Redshift > 0.8

We present Sunyaev-Zel'dovich Effect (SZE) imaging observations of three distant (z greater than 0.8) and highly X-ray luminous clusters of galaxies, C1J1226+33, C1J0152-13 and MS1054-03. Two of the clusters, C1J1226+33 and C1J0152-13, were recently discovered in the WARPS X-ray survey. Their high X-ray luminosity suggests they are massive systems and, if confirmed, would provide strong constraints on the cosmological parameters of structure formation models. Our Sunyaev-Zel'dovich Effect data provide confirmation that they are massive clusters similar to the well studied cluster MS1054-03. Assuming the clusters have the same gas mass fraction derived from SZE measurements of eighteen known massive clusters, we are able to infer their mass and electron temperatures from the SZE data. The derived electron temperatures are 10.0, 8.5, and 10.3 KeV, respectively, and we infer total masses of approximately 2 x 10(circumflex) 14 h(circumflex) -l M - sun within a radius of 65" for all three clusters. For C1J0152-13 and MS1054-03 we find good agreement between our SZE derived temperatures and those derived from X-ray spectroscopic measurements. No X-ray derived temperatures are available for C1J1226+33, and thus the SZE data provide the first confirmation that it is indeed a massive system. The demonstrated ability to determine cluster temperatures and masses from SZE observations without access to X-ray data illustrates the power of using deep SZE surveys to probe the distant universe.

Joy, Marshall↗
NASA NTRS2014

Type Ia Supernova Rate Measurements to Redshift 2.5 from Candles: Searching for Prompt Explosions in the Early Universe

The Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) was a multi-cycle treasury program on the Hubble Space Telescope(HST) that surveyed a total area of approx. 0.25 deg(sup 2) with approx.900 HST orbits spread across five fields over three years. Within these survey images we discovered 65 supernovae (SNe) of all types, out to z approx. 2.5. We classify approx. 24 of these as Type Ia SNe (SNe Ia) based on host galaxy redshifts and SN photometry (supplemented by grism spectroscopy of six SNe). Here we present a measurement of the volumetric SN Ia rate as a function of redshift, reaching for the first time beyond z = 2 and putting new constraints on SN Ia progenitor models. Our highest redshift bin includes detections of SNe that exploded when the universe was only approx. 3 Gyr old and near the peak of the cosmic star formation history. This gives the CANDELS high redshift sample unique leverage for evaluating the fraction of SNe Ia that explode promptly after formation (500 Myr). Combining the CANDELS rates with all available SN Ia rate measurements in the literature we find that this prompt SN Ia fraction isfP0.530.09stat0.100.10sys0.26, consistent with a delay time distribution that follows a simplet1power law for all timest40 Myr. However, mild tension is apparent between ground-based low-z surveys and space-based high-z surveys. In both CANDELS and the sister HST program CLASH (Cluster Lensing And Supernova Survey with Hubble), we find a low rate of SNe Ia at z > 1. This could be a hint that prompt progenitors are in fact relatively rare, accounting for only 20 of all SN Ia explosions though further analysis and larger samples will be needed to examine that suggestion.

Ia↗
NASA NTRS1991

A search for clustering among the meteoroid impacts detected by the Apollo lunar seismic network

A difference is noted between meteoroids whose masses lie above and below 1 kg in temporal meteoroid-impact clusterings detected by the Apollo lunar seismic network; while the former exhibit little temporal clustering, small ones show strong clusterings identifiable with terrestrial meteor showers. This finding suggests a different type and origin for the two meteoroid sizes; the small may be primarily cometary, while the large may derive from near-earth asteroids and short-period comets. It is speculated that the June, 1975, and January, 1977 swarms of large meteoroids may contain high-density meteoritic objects interpretable as meteorite streams.

Oberst, Juergen↗
NASA NTRS1994

Nuclear Star Formation in the Hot-Spot Galaxy NGC 2903

We present high-resolution near-infrared imaging obtained using adaptive optics and HST/NICMOS and ground-based spectroscopy of the hot-spot galaxy NGC 2903. Our near-infrared resolution imaging enables us to resolve the infrared hot spots into individual young stellar clusters or groups of these. The spatial distribution of the stellar clusters is not coincident with that of the bright H II regions, as revealed by the HST/NICMOS Pace image. Overall, the circumnuclear star formation in NGC 2903 shows a ring-like morphology with an approximate diameter of 625 pc. The SF properties of the stellar clusters and H II regions have been studied using the photometric and spectroscopic information in conjunction with evolutionary synthesis models. The population of bright stellar clusters shows a very narrow range of ages, 4 to 7 x 10(exp 6) yr after the peak of star formation, or absolute ages 6.5 to 9.5 x 10(exp 6) yr (for the assumed short-duration Gaussian bursts), and luminosities similar to the clusters found in the Antennae interacting galaxy. This population of young stellar clusters accounts for some 7 - 12% of the total stellar mass in the central 625 pc of NGC 2903. The H II regions in the ring of star formation have luminosities close to that of the super-giant H II region 30 Doradus, they are younger than the stellar clusters, and will probably evolve into bright infrared stellar clusters similar to those observed today. We find that the star formation efficiency in the central regions of NGC 2903 is higher than in normal galaxies, approaching the lower end of infrared luminous galaxies.

Alonso-Herrero, A.↗
NASA NTRS2001

Search for the Identification of 3EG J1835+5918: Evidence for a New Type of High-Energy Gamma-Ray Source

The EGRET source 3EG J1835+5918 is the brightest and most accurately positioned of the as-yet unidentified high-energy gamma-ray sources at high Galactic latitude (l, b = 89 deg, 25 deg). We present a multiwavelength study of the region around it, including X-ray, radio, and optical imaging surveys, as well as optical spectroscopic classification of most of the active objects in this area. Identifications are made of all but one of the ROSAT and ASCA sources in this region to a flux limit of approximately 5 x 10(exp -14) erg/sq cm s, which is 10(exp -4) of the gamma-ray flux. The identified X-ray sources in or near the EGRET error ellipse are radio-quiet QSOs, a galaxy cluster, and coronal emitting stars. We also find eight quasars using purely optical color selection, and we have monitored the entire field for variable optical objects on short and long time scales without any notable discoveries. The radio sources inside the error ellipse are all fainter than 4 mJy at 1.4 GHz. There are no flat-spectrum radio sources in the vicinity; the brightest neighboring radio sources are steep-spectrum radio galaxies or quasars. Since no blazar-like or pulsar-like candidate has been found as a result of these searches, 3EG J1835+5918 must be lacking one or more of the physically essential attributes of these known classes of gamma-ray emitters. If it is an AGN it lacks the beamed emission radio of blazars by at least a factor of 100 relative to identified EGRET blazars. If it is an isolated neutron star, it lacks the steady thermal X-rays from a cooling surface and the magnetospheric non-thermal X-ray emission that is characteristic of all EGRET pulsars. If a pulsar, 3EG J1835+5918 must be either older or more distant than Geminga, and probably an even more efficient or beamed gamma-ray engine. One intermittent ROSA T source falls on a blank optical field to a limit of B greater than 23.4, V greater than 23.3, and R greater than 22.5. In view of this conspicuous absence, RX J1836-2+5925 should be examined further as a candidate for identification with 3EG J1835+5918 and possibly the prototype of a new class of high-energy gamma-ray source.

Mirabal, N.↗
NASA NTRS2020

Properties and Astrophysical Implications of the 150 M Binary Black Hole Merger GW190521

The gravitational-wave signal GW190521 is consistent with a binary black hole (BBH) merger source at redshift 0.8 with unusually high component masses, 85 (+21,-14) Mꙩ and 66 (+17,-18) Mꙩ, compared to previously reported events, and shows mild evidence for spin-induced orbital precession. The primary falls in the mass gap predicted by (pulsational) pair-instability supernova theory, in the approximate range 65–120 Mꙩ. The probability that at least one of the black holes in GW190521 is in that range is 99.0%. The final mass of the merger (142 (+28,-16) Mꙩ) classifies it as an intermediate-mass black hole. Under the assumption of a quasi-circular BBH coalescence, we detail the physical properties of GW190521’s source binary and its post-merger remnant, including component masses and spin vectors. Three different waveform models, as well as direct comparison to numerical solutions of general relativity, yield consistent estimates of these properties. Tests of strong-field general relativity targeting the merger-ringdown stages of the coalescence indicate consistency of the observed signal with theoretical predictions. We estimate the merger rate of similar systems to be 0.13 (+0.30,-0.11)Gp/cu.c yr. We discuss the astrophysical implications of GW190521 for stellar collapse and for the possible formation of black holes in the pair-instability mass gap through various channels: via (multiple) stellar coalescences, or via hierarchical mergers of lower-mass black holes in star clusters or in active galactic nuclei. We find it to be unlikely that GW190521 is a strongly lensed signal of a lower-mass black hole binary merger. We also discuss more exotic possible sources for GW190521, including a highly eccentric black hole binary, or a primordial black hole binary.

R. Abbott↗
NASA NTRS2000

Hot HB Stars in Globular Clusters: Physical Parameters and Consequences for Theory: Radiative Levitation Versus Helium Mixing - 5

Atmospheric parameters (T(sub eff), log g), masses and helium abundances are derived for 42 hot horizontal branch (HB) stars in the globular cluster NGC6752. For 19 stars we derive magnesium and iron abundances as well and find that iron is enriched by a factor of 50 on average with respect to the cluster abundance whereas the magnesium abundances are consistent with the cluster abundance. Radiation pressure may levitate heavy elements like iron to the surface of the star in a diffusive process. Taking into account the enrichment of heavy elements in our spectroscopic analyses we find that high iron abundances can explain part, but not all, of the problem of anomalously low gravities along the blue HB. The blue HB stars cooler than about 15,100 K and the sdB stars (T(sub eff) greater than or = 20,000 K) agree well with canonical theory when analysed with metal-rich ([M/H] = +0.5) model atmospheres, but the stars in between these two groups remain offset towards lower gravities and masses. Deep Mixing in the red giant progenitor phase is discussed as another mechanism that may influence the position of the blue HB stars in the (T(sub eff), log g)-plane but not their masses.

Moehler, S.↗