The Galactic Kinematics of Cataclysmic Variables

Kinematical properties of CVs were investigated according to population types and orbital periods, using the space velocities computed from recently updated systemic velocities, proper motions and parallaxes. Reliability of collected space velocity data are refined by removing 34 systems with largest space velocity errors. The 216 CVs in the refined sample were shown to have a dispersion of $53.70 \pm 7.41$ km s$^{-1}$ corresponding to a mean kinematical age of $5.29 \pm 1.35$ Gyr. Population types of CVs were identified using their Galactic orbital parameters. According to the population analysis, seven old thin disc, nine thick disc and one halo CV were found in the sample, indicating that 94% of CVs in the Solar Neighbourhood belong to the thin-disc component of the Galaxy. Mean kinematical ages $3.40 \pm 1.03$ and $3.90 \pm 1.28$ Gyr are for the non-magnetic thin-disc CVs below and above the period gap, respectively. There is not a meaningful difference between the velocity dispersions below and above the gap. Velocity dispersions of the non-magnetic thin-disc systems below and above the gap are $24.95 \pm 3.46$ and $26.60 \pm 4.18$ km s$^{-1}$, respectively. This result is not in agreement with the standard formation and evolution theory of CVs. The mean kinematical ages of the CV groups in various orbital period intervals increase towards shorter orbital periods. This is in agreement with the standard theory for the evolution of CVs. Rate of orbital period change was found to be $dP/dt=-1.62(\pm 0.15)\times 10^{-5}$ sec yr$^{-1}$.Comment: 17 pages, 6 figures and 4 tables, accepted for publication in Astrophysics and Space Scienc

The Catalogue of Stellar Parameters from the Detached Double-Lined Eclipsing Binaries in the Milky Way

The most accurate stellar astrophysical parameters were collected from the solutions of the light and the radial velocity curves of 257 detached double-lined eclipsing binaries in the Milky Way. The catalogue contains masses, radii, surface gravities, effective temperatures, luminosities, projected rotational velocities of the component stars and the orbital parameters. The number of stars with accurate parameters increased 67 per cent in comparison to the most recent similar collection by Torres et al. (2010). Distributions of some basic parameters were investigated. The ranges of effective temperatures, masses and radii are $2750<T_{eff}$(K)$<43000$, $0.18<M/M_{\odot}<33$ and $0.2<R/R_{\odot}<21.2$, respectively. Being mostly located in one kpc in the Solar neighborhood, the present sample covers distances up to 4.6 kpc within the two local Galactic arms Carina-Sagittarius and Orion Spur. The number of stars with both mass and radius measurements better than 1 per cent uncertainty is 93, better than 3 per cent uncertainty is 311, and better than 5 per cent uncertainty is 388. It is estimated from the Roche lobe filling factors that 455 stars (88.5 per cent of the sample) are spherical within 1 per cent of uncertainty.Comment: 22 pages, including 14 figures and 5 tables, accepted for publication in PASA. Table 1 in the manuscript will be published electronicall

Main-Sequence Effective Temperatures from a Revised Mass-Luminosity Relation Based on Accurate Properties

The mass-luminosity (M-L), mass-radius (M-R) and mass-effective temperature ($M-T_{eff}$) diagrams for a subset of galactic nearby main-sequence stars with masses and radii accurate to $\leq 3\%$ and luminosities accurate to $\leq 30\%$ (268 stars) has led to a putative discovery. Four distinct mass domains have been identified, which we have tentatively associated with low, intermediate, high, and very high mass main-sequence stars, but which nevertheless are clearly separated by three distinct break points at 1.05, 2.4, and 7$M_{\odot}$ within the mass range studied of $0.38-32M_{\odot}$. Further, a revised mass-luminosity relation (MLR) is found based on linear fits for each of the mass domains identified. The revised, mass-domain based MLRs, which are classical ($L \propto M^{\alpha}$), are shown to be preferable to a single linear, quadratic or cubic equation representing as an alternative MLR. Stellar radius evolution within the main-sequence for stars with $M>1M_{\odot}$ is clearly evident on the M-R diagram, but it is not the clear on the $M-T_{eff}$ diagram based on published temperatures. Effective temperatures can be calculated directly using the well-known Stephan-Boltzmann law by employing the accurately known values of M and R with the newly defined MLRs. With the calculated temperatures, stellar temperature evolution within the main-sequence for stars with $M>1M_{\odot}$ is clearly visible on the $M-T_{eff}$ diagram. Our study asserts that it is now possible to compute the effective temperature of a main-sequence star with an accuracy of $\sim 6\%$, as long as its observed radius error is adequately small (<1%) and its observed mass error is reasonably small (<6%).Comment: 57 pages, including 12 figures and 7 tables, accepted for publication in Astronomical Journa

The Spectroscopic Orbits of Three Double-lined Eclipsing Binaries: I. BG Ind, IM Mon, RS Sgr

We present the spectroscopic orbit solutions of three double-lines eclipsing binaries, BG Ind, IM Mon and RS Sgr. The first precise radial velocities (RVs) of the components were determined using high resolution echelle spectra obtained at Mt. John University Observatory in New Zealand. The RVs of the components of BG Ind and RS Sgr were measured using Gaussian fittings to the selected spectral lines, whereas two-dimensional cross-correlation technique was preferred to determine the RVs of IM Mon since it has relatively short orbital period among the other targets and so blending of the lines is more effective. For all systems, the Keplerian orbital solution was used during the analysis and also circular orbit was adopted because the eccentricities for all targets were found to be negligible. The first precise orbit analysis of these systems gives the mass ratios of the systems as 0.894, 0.606 and 0.325, respectively for BG Ind, IM Mon and RS Sgr. Comparison of the mass ratio values, orbital sizes and minimum masses of the components of the systems indicates that all systems should have different physical, dynamical and probable evolutionary status.Comment: 17 pages, 6 figures and 4 tables, accepted for publication in New Astronom

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude

Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.Comment: 16