A note on the error analysis of classical Gram-Schmidt

An error analysis result is given for classical Gram--Schmidt factorization of a full rank matrix $A$ into $A=QR$ where $Q$ is left orthogonal (has orthonormal columns) and $R$ is upper triangular. The work presented here shows that the computed $R$ satisfies \normal{R}=\normal{A}+E where $E$ is an appropriately small backward error, but only if the diagonals of $R$ are computed in a manner similar to Cholesky factorization of the normal equations matrix. A similar result is stated in [Giraud at al, Numer. Math. 101(1):87--100,2005]. However, for that result to hold, the diagonals of $R$ must be computed in the manner recommended in this work.Comment: 12 pages This v2. v1 (from 2006) has not the biliographical reference set (at all). This is the only modification between v1 and v2. If you want to quote this paper, please quote the version published in Numerische Mathemati

The population of white dwarf binaries with hot subdwarf companions

Hot subdwarfs (sdBs) are core helium-burning stars, which lost almost their entire hydrogen envelope in the red-giant phase. Since a high fraction of those stars are in close binary systems, common envelope ejection is an important formation channel. We identified a total population of 51 close sdB+WD binaries based on time-resolved spectroscopy and multi-band photometry, derive the WD mass distribution and constrain the future evolution of these systems. Most WDs in those binaries have masses significantly below the average mass of single WDs and a high fraction of them might therefore have helium cores. We found 12 systems that will merge in less than a Hubble time and evolve to become either massive C/O WDs, AM\,CVn systems, RCrB stars or even explode as supernovae type Ia.Comment: 5 pages, 2 figures, to appear in the proceedings of the 19th European White Dwarf Workshop, ASP Conf. Se

Hot Subdwarf All Southern Sky Fast Transit Survey with the Evryscope

We have conducted a survey of candidate hot subdwarf (HSD) stars in the southern sky searching for fast transits, eclipses, and sinusoidal-like variability in the Evryscope light curves. The survey aims to detect transit signals from Neptune-size planets to gas giants, and eclipses from M-dwarfs and brown dwarfs. The other variability signals are primarily expected to be from compact binaries and reflection effect binaries. Due to the small size of HSDs (R ≈ 0.2 R o˙), transit and eclipse signals are expected to last only ≈20 minutes, but with large signal depths (up to completely eclipsing if the orientation is edge on). With its 2 minute cadence and continuous observation, the Evryscope is well placed to recover these fast transits and eclipses. The very large field of view (8150 deg2) is critical to obtain enough HSD targets, despite their rarity. We identified ≈11,000 potential HSDs from the 9.3 M Evryscope light curves for sources brighter than m g = 15. With our machine-learning spectral classifier, we flagged high confidence targets and estimate the total HSDs in the survey to be ≈1400. The light-curve search detected three planet transit candidates, shown to have stellar companions from follow-up analysis. We discovered several new compact binaries (including two with unseen degenerate companions), two eclipsing binaries with M-dwarf companions, as well as new reflection effect binaries and others with sinusoidal-like variability. Four of the discoveries are being published in separate follow-up papers, and we discuss the follow-up potential of the other discoveries

Variables in the southern polar region evryscope 2016 data set

The regions around the celestial poles offer the ability to find and characterize long-term variables from groundbased observatories. We used multi-year Evryscope data to search for high-amplitude (5% or greater) variable objects among 160,000 bright stars (mv&lt;14.5) near the South Celestial Pole. We developed a machine-learningbased spectral classifier to identify eclipse and transit candidates with M-dwarf or K-dwarf host stars, and potential low-mass secondary stars or gas-giant planets. The large amplitude transit signals from low-mass companions of smaller dwarf host stars lessens the photometric precision and systematics removal requirements necessary for detection, and increases the discoveries from long-term observations with modest light-curve precision among the faintest stars in the survey. The Evryscope is a robotic telescope array that observes the Southern sky continuously at 2-minute cadence, searching for stellar variability, transients, transits around exotic stars and other observationally challenging astrophysical variables. The multi-year photometric stability is better than 1% for bright stars in uncrowded regions, with a 3σ limiting magnitude of g = 16 in dark time. In this study, covering all stars 9<mv<14.5, in declinations -75° to -90°, and searching for high-amplitude variability, we recover 346 known variables and discover 303 new variables, including 168 eclipsing binaries. We characterize the discoveries and provide the amplitudes, periods, and variability type. A 1.7 RJ planet candidate with a late K-dwarf primary was found and the transit signal was verified with the PROMPT telescope network. Further follow-up revealed this object to be a likely grazing eclipsing binary system with nearly identical primary and secondary K5 stars. Radialvelocity measurements from the Goodman Spectrograph on the 4.1 meter SOAR telescope of the likely lowestmass targets reveal that six of the eclipsing binary discoveries are low-mass (.06-.37Me) secondaries with K-dwarf primaries, strong candidates for precision mass-radius measurements

EVR-CB-001: An Evolving, Progenitor, White Dwarf Compact Binary Discovered with the Evryscope

We present EVR-CB-001, the discovery of a compact binary with an extremely low-mass (0.21 ± 0.05M o) helium core white dwarf progenitor (pre-He WD) and an unseen low-mass (0.32 ± 0.06M o) helium white dwarf (He WD) companion. He WDs are thought to evolve from the remnant helium-rich core of a main-sequence star stripped during the giant phase by a close companion. Low-mass He WDs are exotic objects (only about 0.2% of WDs are thought to be less than 0.3 M o), and are expected to be found in compact binaries. Pre-He WDs are even rarer, and occupy the intermediate phase after the core is stripped, but before the star becomes a fully degenerate WD and with a larger radius (≈0.2R o) than a typical WD. The primary component of EVR-CB-001 (the pre-He WD) was originally thought to be a hot subdwarf (sdB) star from its blue color and under-luminous magnitude, characteristic of sdBs. The mass, temperature (T eff = 18,500 ± 500 K), and surface gravity () solutions from this work are lower than values for typical hot subdwarfs. The primary is likely to be a post-red-giant branch, pre-He WD contracting into a He WD, and at a stage that places it nearest to sdBs on color-magnitude and T eff-log(g) diagrams. EVR-CB-001 is expected to evolve into a fully double degenerate, compact system that should spin down and potentially evolve into a single hot subdwarf star. Single hot subdwarfs are observed, but progenitor systems have been elusive

EVR-CB-004: An Inflated Hot Subdwarf O Star + Unseen WD Companion in a Compact Binary Discovered with the Evryscope

We present the discovery of EVR-CB-004, a close binary with a remnant stellar core and an unseen white dwarf (WD) companion. The analysis in this work reveals that the primary is potentially an inflated hot subdwarf (sdO) and more likely is a rarer post-blue horizontal branch (post-BHB) star. Post-BHBs are the short-lived shell-burning final stage of a blue horizontal star or hot subdwarf before transitioning to a WD. This object was discovered using Evryscope photometric data in a southern all-sky hot subdwarf variability survey. The photometric light curve for EVR-CB-004 shows multicomponent variability from ellipsoidal deformation of the primary and Doppler boosting, as well as gravitational limb darkening. The binary EVR-CB-004 is one of just a handful of known systems and has a long period (6.08426 hr) and large-amplitude ellipsoidal modulation (16.0% change in brightness from maximum to minimum) for these extremely close binary systems, while the properties of the primary make it a truly unique system. It also shows a peculiar low-amplitude (less than 1%) sinusoidal light-curve variation with a period that is a 1/3 resonance of the binary period. We tentatively identify this additional variation source as a tidally induced resonant pulsation, and we suggest follow-up observations that could verify this interpretation. From the evolutionary state of the system, its components, and its mass fraction, EVR-CB-004 is a strong merger candidate to form a single high-mass (1.2 M o˙) WD. It offers a glimpse into a brief phase of remnant core evolution and secondary variation not seen before in a compact binary

Multiwavelength Photometry and Progenitor Analysis of the Nova V906 Car

We present optical and infrared photometry of the classical nova V906 Car, also known as Nova Car 2018 and ASASSN-18fv, which was discovered by the All-Sky Automated Survey for SuperNovae (ASAS-SN) on 2018 March 16.32 UT (MJD 58193.0). The nova reached its maximum on MJD 58222.56 at V max = 5.84 ± 0.09 mag, and had decline times of t2, v = 26.2 days and t3, v = 33.0 days. The data from Evryscope shows that the nova had already brightened to g' ≈ 13 mag five days before discovery, as compared with its quiescent magnitude of g = 20.13 ± 0.03. The extinction toward the nova, as derived from high-resolution spectroscopy, shows an estimate consistent with foreground extinction to the Carina Nebula of Av=1.11+0.54-0.39. The light curve resembles a rare C (cusp) class nova with a steep decline slope of α =-3.94 post-cusp flare. From the light-curve decline rate, we estimate the mass of the white dwarf to be M WD = <0.8M o˙, consistent with MWD = 0.71+0.23-0.19 derived from modeling the accretion disk of the system in quiescence. The donor star is likely a K-M dwarf of 0.23-0.43 Mo˙, which is heated by its companion

Time-integrated luminosity recorded by the BABAR detector at the PEP-II e+e- collider

This article is the Preprint version of the final published artcile which can be accessed at the link below.We describe a measurement of the time-integrated luminosity of the data collected by the BABAR experiment at the PEP-II asymmetric-energy e+e- collider at the ϒ(4S), ϒ(3S), and ϒ(2S) resonances and in a continuum region below each resonance. We measure the time-integrated luminosity by counting e+e-→e+e- and (for the ϒ(4S) only) e+e-→μ+μ- candidate events, allowing additional photons in the final state. We use data-corrected simulation to determine the cross-sections and reconstruction efficiencies for these processes, as well as the major backgrounds. Due to the large cross-sections of e+e-→e+e- and e+e-→μ+μ-, the statistical uncertainties of the measurement are substantially smaller than the systematic uncertainties. The dominant systematic uncertainties are due to observed differences between data and simulation, as well as uncertainties on the cross-sections. For data collected on the ϒ(3S) and ϒ(2S) resonances, an additional uncertainty arises due to ϒ→e+e-X background. For data collected off the ϒ resonances, we estimate an additional uncertainty due to time dependent efficiency variations, which can affect the short off-resonance runs. The relative uncertainties on the luminosities of the on-resonance (off-resonance) samples are 0.43% (0.43%) for the ϒ(4S), 0.58% (0.72%) for the ϒ(3S), and 0.68% (0.88%) for the ϒ(2S).This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat à l’Energie Atomique and Institut National de Physique Nucléaire et de Physiquedes Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e Innovación (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union) and the A.P. Sloan Foundation (USA)

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter