On the computation of coset leaders with high Hamming weight

AbstractThe Newton radius of a code is the largest weight of a uniquely correctable error. The covering radius is the largest distance between a vector and the code. In this paper, we use the modular representation of a linear code to give an efficient algorithm for computing coset leaders of relatively high Hamming weight. The weights of these coset leaders serve as lower bounds on the Newton radius and the covering radius for linear codes

Magnetic inflation and Stellar Mass. II. On the radii of wingle, rapidly rotating, fully convective M-dwarf stars

Main-sequence, fully convective M dwarfs in eclipsing binaries are observed to be larger than stellar evolutionary models predict by as much as 10%–15%. A proposed explanation for this discrepancy involves effects from strong magnetic fields, induced by rapid rotation via the dynamo process. Although, a handful of single, slowly rotating M dwarfs with radius measurements from interferometry also appear to be larger than models predict, suggesting that rotation or binarity specifically may not be the sole cause of the discrepancy. We test whether single, rapidly rotating, fully convective stars are also larger than expected by measuring their $R\sin i$ distribution. We combine photometric rotation periods from the literature with rotational broadening ($v\sin i$) measurements reported in this work for a sample of 88 rapidly rotating M dwarf stars. Using a Bayesian framework, we find that stellar evolutionary models underestimate the radii by 10 \% \mbox{--}15{ \% }_{-2.5}^{+3}, but that at higher masses (0.18 < M < 0.4 M Sun), the discrepancy is only about 6% and comparable to results from interferometry and eclipsing binaries. At the lowest masses (0.08 < M < 0.18 M Sun), we find that the discrepancy between observations and theory is 13%–18%, and we argue that the discrepancy is unlikely to be due to effects from age. Furthermore, we find no statistically significant radius discrepancy between our sample and the handful of M dwarfs with interferometric radii. We conclude that neither rotation nor binarity are responsible for the inflated radii of fully convective M dwarfs, and that all fully convective M dwarfs are larger than models predict.The authors would like to thank the referee for the thoughtful report, which greatly improved the manuscript. The authors would also like to thank Lisa Prato and Larissa Nofi for IGRINS training, and Heidi Larson, Jason Sanborn, and Andrew Hayslip for operating the DCT during our observations. We would also like to thank Jen Winters, Jonathan Irwin, Paul Dalba, Mark Veyette, Eunkyu Han, and Andrew Vanderburg for useful discussions and helpful comments on this work. Some of this work was supported by the NASA Exoplanet Research Program (XRP) under grant No. NNX15AG08G issued through the Science Mission Directorate.These results made use of the Lowell Observatory's Discovery Channel Telescope, supported by Discovery Communications, Inc., Boston University, the University of Maryland, the University of Toledo and Northern Arizona University; the Immersion Grating Infrared Spectrograph (IGRINS) that was developed under a collaboration between the University of Texas at Austin and the Korea Astronomy and Space Science Institute (KASI) with the financial support of the US National Science Foundation under grant AST-1229522, of the University of Texas at Austin, and of the Korean GMT Project of KASI; data taken at The McDonald Observatory of The University of Texas at Austin; and data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by NASA and the NSF. (NNX15AG08G - NASA Exoplanet Research Program (XRP); Discovery Communications, Inc.; Boston University; University of Maryland; University of Toledo; Northern Arizona University; AST-1229522 - US National Science Foundation; University of Texas at Austin; Korean GMT Project of KASI; NASA; NSF

The effects of metallicity and magnetism on the radii of M dwarf stars

M dwarfs are ubiquitous in the galaxy, yet their fundamental properties are not precisely known. Radii are particularly difficult to determine because M dwarfs are intrinsically small and faint, leading to only a few radius determinations using either long-baseline optical interferometry or eclipses of binary stars. Observations rarely agree with models, and the scatter in M dwarf radius relations is significantly larger and less understood than it is for higher mass stars. I explored the two main hypotheses evoked to explain discrepancies between model radii and observed radii, namely effects from metallicity and strong magnetic fields. I conducted a spectroscopic survey of M dwarfs with a wide range of metallicities and derived radii using the Stefan-Boltzmann law in order to constrain radius relations for the lowest mass and lowest metallicity stars. I found that solar metallicity stars can be up to five times larger than their low-metallicity counterparts for a given effective temperature, but that metallicity has a relatively small effect on mass- or luminosity-to-radius relations. To test the effect of magnetism on radii, I determined a statistical distribution of radii for magnetically active M dwarfs by combining measured rotational broadening values with literature rotation periods. I found that the magnetically active stars were on average 10-15% larger than model predictions and that models and observations were most discrepant for the lowest-mass stars. To deduce whether the 10-15% radius discrepancy could be due entirely to the spotted nature of these stars, I determined the spot temperature and spot filling fraction of one of the most magnetically active stars in my sample. I measured a high spot filling fraction, spot temperatures several hundred Kelvin lower than the photosphere temperature, and I also detected evidence of faculae on the stellar surface. I concluded that spots are the primary cause for models overestimating the sizes of low-mass stars, and that stellar-evolution models should consider the effects of spots to more accurately predict the sizes and temperature of all M dwarfs

The Sun in Time: Age, Rotation, and Magnetic Activity of the Sun and Solar-type Stars and Effects on Hosted Planets

Multi-wavelength studies of solar analogs (G0-5 V stars) with ages from ~50 Myr to 9 Gyr have been carried out as part of the "Sun in Time" program for nearly 20 yrs. From these studies it is inferred that the young (ZAMS) Sun was rotating more than 10x faster than today. As a consequence, young solar-type stars and the early Sun have vigorous magnetohydrodynamic (MHD) dynamos and correspondingly strong coronal X-ray and transition region / chromospheric FUV-UV emissions. To ensure continuity and homogeneity for this program, we use a restricted sample of G0-5 V stars with masses, radii, T(eff), and internal structure (i.e. outer convective zones) closely matching those of the Sun. From these analogs we have determined reliable rotation-age-activity relations and X-ray - UV (XUV) spectral irradiances for the Sun (or any solar-type star) over time. These XUV irradiance measures serve as input data for investigating the photo-ionization and photo-chemical effects of the young, active Sun on the paleo-planetary atmospheres and environments of solar system planets. These measures are also important to study the effects of these high energy emissions on the numerous exoplanets hosted by solar-type stars of different ages. Recently we have extended the study to include lower mass, main-sequence (dwarf) dK and dM stars to determine relationships among their rotation spin-down rates and coronal and chromospheric emissions as a function of mass and age. From rotation-age-activity relations we can determine reliable ages for main-sequence G, K, M field stars and, subsequently, their hosted planets. Also inferred are the present and the past XUV irradiance and plasma flux exposures that these planets have endured and the suitability of the hosted planets to develop and sustain life.Comment: 12 pages, 6 figures; to appear in the proceedings of IAU 258: The Ages of Star

Atomic X-ray Spectroscopy of Accreting Black Holes

Current astrophysical research suggests that the most persistently luminous objects in the Universe are powered by the flow of matter through accretion disks onto black holes. Accretion disk systems are observed to emit copious radiation across the electromagnetic spectrum, each energy band providing access to rather distinct regimes of physical conditions and geometric scale. X-ray emission probes the innermost regions of the accretion disk, where relativistic effects prevail. While this has been known for decades, it also has been acknowledged that inferring physical conditions in the relativistic regime from the behavior of the X-ray continuum is problematic and not satisfactorily constraining. With the discovery in the 1990s of iron X-ray lines bearing signatures of relativistic distortion came the hope that such emission would more firmly constrain models of disk accretion near black holes, as well as provide observational criteria by which to test general relativity in the strong field limit. Here we provide an introduction to this phenomenon. While the presentation is intended to be primarily tutorial in nature, we aim also to acquaint the reader with trends in current research. To achieve these ends, we present the basic applications of general relativity that pertain to X-ray spectroscopic observations of black hole accretion disk systems, focusing on the Schwarzschild and Kerr solutions to the Einstein field equations. To this we add treatments of the fundamental concepts associated with the theoretical and modeling aspects of accretion disks, as well as relevant topics from observational and theoretical X-ray spectroscopy.Comment: 63 pages, 21 figures, Einstein Centennial Review Article, Canadian Journal of Physics, in pres

X-ray Absorption and Reflection in Active Galactic Nuclei

X-ray spectroscopy offers an opportunity to study the complex mixture of emitting and absorbing components in the circumnuclear regions of active galactic nuclei, and to learn about the accretion process that fuels AGN and the feedback of material to their host galaxies. We describe the spectral signatures that may be studied and review the X-ray spectra and spectral variability of active galaxies, concentrating on progress from recent Chandra, XMM-Newton and Suzaku data for local type 1 AGN. We describe the evidence for absorption covering a wide range of column densities, ionization and dynamics, and discuss the growing evidence for partial-covering absorption from data at energies > 10 keV. Such absorption can also explain the observed X-ray spectral curvature and variability in AGN at lower energies and is likely an important factor in shaping the observed properties of this class of source. Consideration of self-consistent models for local AGN indicates that X-ray spectra likely comprise a combination of absorption and reflection effects from material originating within a few light days of the black hole as well as on larger scales. It is likely that AGN X-ray spectra may be strongly affected by the presence of disk-wind outflows that are expected in systems with high accretion rates, and we describe models that attempt to predict the effects of radiative transfer through such winds, and discuss the prospects for new data to test and address these ideas.Comment: Accepted for publication in the Astronomy and Astrophysics Review. 58 pages, 9 figures. V2 has fixed an error in footnote

Eclipsing binaries in open clusters. II. V453 Cyg in NGC 6871

We derive absolute dimensions of the early B-type detached eclipsing binary V453 Cygni (B0.4 IV + B0.7 IV, P=3.89d), a member of the open cluster NGC 6871. From the analysis of new, high-resolution, spectroscopy and the UBV light curves of Cohen (1974) we find the masses to be 14.36 +/- 0.20 and 11.11 +/- 0.13 Msun, the radii to be 8.55 +/- 0.06 and 5.49 +/- 0.06 Rsun, and the effective temperatures to be 26600 +/- 500 and 25 500 +/- 800 K for the primary and secondary stars, respectively. The surface gravities of 3.731 +/- 0.012 and 4.005 +/- 0.015 indicate that V453 Cyg is reaching the end of its main sequence lifetime. We have determined the apsidal motion period of the system to be 66.4 +/- 1.8 yr using the technique of Lacy (1992) extended to include spectroscopic data as well as times of minimum light, giving a density concentration coefficient of log(k_2) = -2.226 +/- 0.024. Contaminating (third) light has been detected for the first time in the light curve of V453 Cyg; previous analyses without this effect systematically underestimate the ratio of the radii of the two stars. The absolute dimensions of the system have been compared to the stellar evolution models of the Granada, Geneva, Padova and Cambridge groups. All model sets fit the data on V453 Cyg for solar helium and metal abundances and an age of 10.0 +/- 0.2 Myr. The Granada models also agree fully with the observed log(k_2) once general relativistic effects have been accounted for. The Cambridge models with convective core overshooting fit V453 Cyg better than those without. Given this success of the theoretical predictions, we briefly discuss which eclipsing binaries should be studied in order to further challenge the models.Comment: Accepted for publication in MNRAS (14 pages, 5 figures, Fig.4 reduced in size

A Photometric Study of the Outer Halo Globular Cluster NGC 5824

Multi-wavelength CCD photometry over 21 years has been used to produce deep color-magnitude diagrams together with light curves for the variables in the Galactic globular cluster NGC 5824. Twenty-one new cluster RR Lyrae stars are identified, bringing the total to 47, of which 42 have reliable periods determined for the first time. The color-magnitude diagram is matched using BaSTI isochrones with age of $13$~Gyr. and reddening is found to be $E(B-V) = 0.15 \pm0.02$; using the period-Wesenheit relation in two colors the distance modulus is $(m-M)_0=17.45 \pm 0.07$ corresponding to a distance of 30.9 Kpc. The observations show no signs of populations that are significantly younger than the $13$~Gyr stars. The width of the red giant branch does not allow for a spread in [Fe/H] greater than $\sigma = 0.05$ dex, and there is no photometric evidence for widened or parallel sequences. The $V, c_{UBI}$ pseudo-color magnitude diagram shows a bifurcation of the red giant branch that by analogy with other clusters is interpreted as being due to differing spectral signatures of the first (75\%) and second (25\%) generations of stars whose age difference is close enough that main sequence turnoffs in the color-magnitude diagram are unresolved. The cluster main sequence is visible against the background out to a radial distance of $\sim17$ arcmin. We conclude that NGC 5824 appears to be a classical Oosterhoff Type II globular cluster, without overt signs of being a remnant of a now-disrupted dwarf galaxy.Comment: 26 pages, 15 figures, 4 tables, accepted for publication in Astronomical Journa