Roundoff error sequences in fixed-point arithmetic digital processors

Three assumptions are normally made about roundoff error sequences in fixed-point arithmetic digital processors: all values of error, within the limits set by the roundoff process, have an equal probability of occurrence; they are random; and they are not correlated with any other signal or error sequence. The validity of these assumptions for digital filter realisations employing a signal wordlength in the range of 4 to 3 bits is examined. The investigation begins by using a fast Fourier transform algorithm to perform spectral analysis on roundoff error sequences when the test signal is a quantised sinusoid. It continues by comparing the variance of the error sequence measured at the output of various filter realisations with that theoretically predicted using the normal assumptions; this is done using random test sequences. It is shown that under certain conditions, for the signal wordlengths under consideration, each of the three assumptions can become invalid. In conclusion this work reports attempts to develop more accurate predictive noise models which only incorporate assumptions of greater validity

Functional consequences of Palaeozoic reef collapse

Biogenic reefs have been hotspots of biodiversity and evolutionary novelty throughout the Phanerozoic. The largest reef systems in Earth’s history occurred in the Devonian period, but collapsed during the Late Devonian Mass Extinction. However, the consequences for the functional diversity of Palaeozoic reefs have received little attention. Here, we examine changes in the functional diversity of tabulate coral assemblages over a 35 million year period from the middle Devonian to the Carboniferous, straddling the multiphase extinction event to identify the causes and ecological consequences of the extinction for tabulate corals. By examining five key morphological traits, we show a divergent response of taxonomic and functional diversity to the mass extinction: taxonomic richness peaked during the Givetian (~ 388–383 Ma) and coincided with peak reef building, but functional diversity was only moderate because many species had very similar trait combinations. The collapse of taxonomic diversity and reef building in the late Devonian had minimal impact on functional richness of coral assemblages. However, non-random shifts towards species with larger corallites and lower colony integration suggest a shift from photosymbiotic to asymbiotic taxa associated over the study period. Our results suggest that the collapse of the huge Devonian reef systems was correlated with a breakdown of photosymbiosis and extinction of photosymbiotic tabulate coral taxa. Despite the appearance of new tabulate coral species over the next 35 million years, the extinction of taxa with photosymbiotic traits had long-lasting consequences for reef building and, by extension, shallow marine ecosystems in the Palaeozoic

A blue ring nebula from a stellar merger several thousand years ago

Stellar mergers are a brief but common phase in the evolution of binary star systems. These events have many astrophysical implications; for example, they may lead to the creation of atypical stars (such as magnetic stars, blue stragglers and rapid rotators), they play an important part in our interpretation of stellar populations and they represent formation channels of compact-object mergers. Although a handful of stellar mergers have been observed directly, the central remnants of these events were shrouded by an opaque shell of dust and molecules, making it impossible to observe their final state (for example, as a single merged star or a tighter, surviving binary). Here we report observations of an unusual, ring-shaped ultraviolet (‘blue’) nebula and the star at its centre, TYC 2597-735-1. The nebula has two opposing fronts, suggesting a bipolar outflow of material from TYC 2597-735-1. The spectrum of TYC 2597-735-1 and its proximity to the Galactic plane suggest that it is an old star, yet it has abnormally low surface gravity and a detectable long-term luminosity decay, which is uncharacteristic for its evolutionary stage. TYC 2597-735-1 also exhibits Hα emission, radial-velocity variations, enhanced ultraviolet radiation and excess infrared emission—signatures of dusty circumstellar disks, stellar activity and accretion. Combined with stellar evolution models, the observations suggest that TYC 2597-735-1 merged with a lower-mass companion several thousand years ago. TYC 2597-735-1 provides a look at an unobstructed stellar merger at an evolutionary stage between its dynamic onset and the theorized final equilibrium state, enabling the direct study of the merging process

New Extremely Metal-Poor Stars in the Galactic Halo

We present a detailed abundance analysis based on high resolution and high signal-to-noise spectra of eight extremely metal poor (EMP) stars with [Fe/H] < -3.5$dex, four of which are new. Only stars with 4900 < Teff< 5650 K are included. Two stars of the eight are outliers in each of several abundance ratios. The most metal poor star in this sample, HE1424-0241, has [Fe/H] ~ -4 dex and is thus among the most metal poor stars known in the Galaxy. It has highly anomalous abundance ratios unlike those of any other known EMP giant, with very low Si, Ca and Ti relative to Fe, and enhanced Mn and Co, again relative to Fe. Only (low) upper limits for C and N can be derived from the non-detection of the CH and NH molecular bands. HE0132$-$2429, another sample star, has excesses of N and Sc with respect to Fe. The strong outliers in abundance ratios among the Fe-peak elements in these C-normal stars, not found at somewhat higher metallicities, are definitely real. They suggest that at such low metallicities we are beginning to see the anticipated and long sought stochastic effects of individual supernova events contributing to the Fe-peak material within a single star. A detailed comparison of the results of the analysis procedures adopted by our 0Z project compared to those of the First Stars VLT Large Project finds a systematic difference for [Fe/H] of ~0.3 dex, our values always being higher.Comment: Accepted to the Ap

Evidence for Sub-Chandrasekhar Type Ia Supernovae from Stellar Abundances in Dwarf Galaxies

There is no consensus on the progenitors of Type Ia supernovae (SNe Ia) despite their importance for cosmology and chemical evolution. We address this question using our previously published catalogs of Mg, Si, Ca, Cr, Fe, Co, and Ni abundances in dwarf galaxy satellites of the Milky Way (MW) to constrain the mass at which the white dwarf (WD) explodes during a typical SN Ia. We fit a simple bi-linear model to the evolution of [X/Fe] with [Fe/H], where X represents each of the elements mentioned above. We use the evolution of [Mg/Fe] coupled with theoretical supernova yields to isolate what fraction of the elements originated in SNe Ia. Then, we infer the [X/Fe] yield of SNe Ia for all of the elements except Mg. We compare these observationally inferred yields to recent theoretical predictions for two classes of Chandrasekhar-mass (M_(Ch)) SN Ia as well as sub-M_(Ch) SNe Ia. Most of the inferred SN Ia yields are consistent with all of the theoretical models, but [Ni/Fe] is consistent only with sub-M_(Ch) models. We conclude that the dominant type of SN Ia in ancient dwarf galaxies is the explosion of a sub-M_(Ch) WD. The MW and dwarf galaxies with extended star formation histories have higher [Ni/Fe] abundances, which could indicate that the dominant class of SN Ia is different for galaxies where star formation lasted for at least several Gyr

On the Perils of Hyperfine Splitting: A reanalysis of Mn and Sc Abundance Trends

We investigate the impact of hyperfine splitting on stellar abundance analyses of Mn and Sc, and find that incorrect hfs treatment can lead to spurious abundance trends with metallicity. We estimate corrections to a recent study by Nissen et al. (2000), and find: (1) [Mn/Fe] is described by a bimodal distribution, with [Mn/Fe] ~ -0.3 for stars [Fe/H] < -0.7, and [Mn/Fe] ~ -0.05 for stars at higher metallicity, suggestive of a transition between halo/thick disk and thin disk populations. (2) The large majority of stars show nearly solar [Sc/Fe] ratios; although important deviations cannot be ruled-out.Comment: 5 pages, 2 embedded figures. Uses emulateapj5.sty, onecolfloat.sty. Accepted to ApJ Letters (5/22/00