Effective order strong stability preserving Runge–Kutta methods

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of effective order methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods—like classical order five methods—require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge–Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice

The Molecular Structure of Cyclopropene, C_3C_4

Cyclopropene, C_3H_4, has been investigated by the electron diffraction method. The cyclic structure is confirmed and the following interatomic distances and angles are found: C–C, 1.525±0.02 A; C=C, 1.286±0.04 A; 〈C–H〉, 1.087±0.04 A; ∠H–C–H, 118° (assumed); ∠C=C–H, 152±12°

An Atlas of Computed Equivalent Widths of Quasar Broad Emission Lines

We present graphically the results of several thousand photoionization calculations of broad emission line clouds in quasars, spanning seven orders of magnitude in hydrogen ionizing flux and particle density. The equivalent widths of 42 quasar emission lines are presented as contours in the particle density - ionizing flux plane for a typical incident continuum shape, solar chemical abundances, and cloud column density of $N(H) = 10^{23} cm^{-2}$. Results are similarly given for a small subset of emission lines for two other column densities ($10^{22} cm^{-2}$ and $10^{24} cm^{-2}$), five other incident continuum shapes, and a gas metallicity of 5 \Zsun. These graphs should prove useful in the analysis of quasar emission line data and in the detailed modeling of quasar broad emission line regions. The digital results of these emission line grids and many more are available over the Internet.Comment: 16 pages, LaTeX (AASTeX aaspp4.sty); to appear in the 1997 ApJS: full contents of the 9 photoionization grids presented in this paper may be found at http://www.pa.uky.edu/~korista/grids/grids.htm

The Observability of Metal Lines Associated with the Lyman-alpha Forest

We develop a prescription for characterizing the strengths of metal lines associated with Lyman-alpha forest absorbers (LYFAs) of a given neutral hydrogen column density N_HI and metallicity [Fe/H]. This Line Observability Index (LOX) is line-specific and translates, for weak lines, into a measure of the equivalent width. It can be evaluated quickly for thousands of transitions within the framework of a given model of the Lyman-alpha forest, providing a ranking of the lines in terms of their strengths and enabling model builders to select the lines that should be detectable in observed spectra of a given resolution and signal-to-noise ratio. We compute the LOX for a large number of elements and transitions in two cosmological models of the Lyman-alpha forest at z=3 derived from a hydrodynamic simulation of structure formation, and we discuss how the LOX depends on redshift and on model parameters such as the mean baryonic density and radiation field. We find that the OVI (1032,1038) doublet is the best probe of the metallicity in low column density LYFAs N_{HI} \approx 10^{14.5} cm^{-2}). Metallicities down to [O/H] \sim -3 ([Fe/H] \sim -3.5 with the assumed [O/Fe] ratio) yield OVI absorption features that should be detectable in current high-quality spectra, provided that the expected position of the OVI feature is not contaminated by HI absorption. The strongest transitions in lower ionisation states of oxygen are OV(630), OIV(788), and OIII(833), and are likely to be detected with next generation UV instruments. Of the lines with rest wavelengths \lambda_r > 1216, which can potentially be observed redwards of the \lya forest, the CIV(1548,1551) doublet is expected to dominate in all LYFAs, regardless of the value of N_HI.Comment: Substantially revised version: larger line database, additional cosmological model analyzed. Accepted for Ap

The D/H Ratio in the Interstellar Medium toward the White Dwarf PG0038+199

We determine the D/H ratio in the interstellar medium toward the DO white dwarf PG0038+199 using spectra from the Far Ultraviolet Spectroscopic Explorer (FUSE), with ground-based support from Keck HIRES. We employ curve of growth, apparent optical depth and profile fitting techniques to measure column densities and limits of many other species (H2, NaI, CI, CII, CIII, NI, NII, OI, SiII, PII, SIII, ArI and FeII) which allow us to determine related ratios such as D/O, D/N and the H2 fraction. Our efforts are concentrated on measuring gas-phase D/H, which is key to understanding Galactic chemical evolution and comparing it to predictions from Big Bang nucleosynthesis. We find column densities log N(HI) = 20.41+-0.08, log N(DI)=15.75+-0.08 and log N(H2) = 19.33+-0.04, yielding a molecular hydrogen fraction of 0.14+-0.02 (2 sigma errors), with an excitation temperature of 143+-5K. The high HI column density implies that PG0038+199 lies outside of the Local Bubble; we estimate its distance to be 297 (+164,-104)pc (1 sigma). D/[HI+2H2] toward PG0038+199 is 1.91(+0.52,-0.42) e-5 (2 sigma). There is no evidence of component structure on the scale of Delta v > 8 km/s based on NaI, but there is marginal evidence for structure on smaller scales. The D/H value is high compared to the majority of recent D/H measurements, but consistent with the values for two other measurements at similar distances. D/O is in agreement with other distant measurements. The scatter in D/H values beyond ~100pc remains a challenge for Galactic chemical evolution.Comment: 59 pages, 7 tables, 18 figures (1 standalone), accepted by ApJ v2 minor typos correcte

Strong stability preserving explicit Runge-Kutta methods of maximal effective order

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge-Kutta methods. Relative to classical Runge-Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods - like classical order five methods - require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge-Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.Comment: 17 pages, 3 figures, 8 table

Ultraviolet observations of the X-ray photoionized wind of Cygnus X-1 during X-ray soft/high state

(Shortened) Ultraviolet observations of the black hole X-ray binary Cygnus X-1 were obtained using the STIS on HSTubble. We detect P Cygni line features show strong, broad absorption components when the X-ray source is behind the companion star and noticeably weaker absorption when the X-ray source is between us and the companion star. We fit the P Cygni profiles using the SEI method applied to a spherically symmetric stellar wind subject to X-ray photoionization from the black hole. The Si IV doublet provides the most reliable estimates of the parameters of the wind and X-ray illumination. The velocity $v$ increases with radius $r$ according to $v=v_\infty(1-r_\star/r)^\beta$, with$\beta\approx0.75$ and $v_\infty\approx1420$ km s$^{-1}$.The microturbulent velocity was $\approx160$ km s$^{-1}$. Our fit implies a ratio of X-ray luminosity to wind mass-loss rate of L$_{X,38}/\dot M_{-6} \approx 0.33$, measured at $\dot M_{-6}$ = 4.8. Our models determine parameters that may be used to estimate the accretion rate onto the black hole and independently predict the X-ray luminosity. Our predicted L$_x$ matches that determined by contemporaneous RXTE ASM remarkably well, but is a factor of 3 lower than the rate according to Bondi-Hoyle-Littleton spherical wind accretion. We suggest that some of the energy of accretion may go into powering a jet.Comment: 34 pages, 21 figures, 4 tables, accepted for publication in Ap

The Molecular Structure of Cyclopropene, C_3C_4

Cyclopropene, C_3H_4, has been investigated by the electron diffraction method. The cyclic structure is confirmed and the following interatomic distances and angles are found: C–C, 1.525±0.02 A; C=C, 1.286±0.04 A; 〈C–H〉, 1.087±0.04 A; ∠H–C–H, 118° (assumed); ∠C=C–H, 152±12°

On the Absorption of X-rays in the Interstellar Medium

We present an improved model for the absorption of X-rays in the ISM intended for use with data from future X-ray missions with larger effective areas and increased energy resolution such as Chandra and XMM, in the energy range above 100eV. Compared to previous work, our formalism includes recent updates to the photoionization cross section and revised abundances of the interstellar medium, as well as a treatment of interstellar grains and the H2molecule. We review the theoretical and observational motivations behind these updates and provide a subroutine for the X-ray spectral analysis program XSPEC that incorporates our model.Comment: ApJ, in press, for associated software see http://astro.uni-tuebingen.de/nh

A hydrodynamic study of the circumstellar envelope of alpha Scorpii

Context: Both the absolute mass-loss rates and the mechanisms that drive the mass loss of late-type supergiants are still not well known. Binaries such as alpha Sco provide the most detailed empirical information about the winds of these stars. Aims: The goal was to improve the binary technique for the determination of the mass-loss rate of alpha Sco A by including a realistic density distribution and velocity field from hydrodynamic and plasma simulations. Methods: We performed 3D hydrodynamic simulations of the circumstellar envelope of alpha Sco in combination with plasma simulations accounting for the heating, ionization, and excitation of the wind by the radiation of alpha Sco B. These simulations served as the basis for an examination of circumstellar absorption lines in the spectrum of alpha Sco B as well as of emission lines from the Antares nebula. Results: The present model of the extended envelope of alpha Sco reproduces some of the structures that were observed in the circumstellar absorption lines in the spectrum of alpha Sco B. Our theoretical density and velocity distributions of the outflow deviate considerably from a spherically expanding model, which was used in previous studies. This results in a higher mass-loss rate of (2 +/- 0.5) x 10^-6 M_sun/yr. The hot H II region around the secondary star induces an additional acceleration of the wind at large distances from the primary, which is seen in absorption lines of Ti II and Cr II at -30 km/s.Comment: 12 pages, 14 figures, accepted for publication in A&