Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies

The internal space for a molecule, atom, or other n-body system can be conveniently parameterised by 3n-9 kinematic angles and three kinematic invariants. For a fixed set of kinematic invariants, the kinematic angles parameterise a subspace, called a kinematic orbit, of the n-body internal space. Building on an earlier analysis of the three- and four-body problems, we derive the form of these kinematic orbits (that is, their topology) for the general n-body problem. The case n=5 is studied in detail, along with the previously studied cases n=3,4.Comment: 38 pages, submitted to J. Phys.

A new clue to the transition mechanism between optical high and low states of the supersoft X-ray source RX J0513.9-6951, implied from the recurrent nova CI Aquilae 2000 outburst model

We have found a new clue to the transition mechanism between optical high/X-ray off and optical low/X-ray on states of the LMC supersoft X-ray source RX J0513.9-6951. A sharp ~1 mag drop is common to the CI Aql 2000 outburst. These drops are naturally attributed to cessation of optically thick winds on white dwarfs. A detailed light-curve analysis of CI Aql indicates that the size of a disk drastically shrinks when the wind stops. This causes ~1-2 mag drop in the optical light curve. In RX J0513.9-6951, the same mechanism reproduces sharp ~1 mag drop from optical high to low states. We predict this mechanism also works on the transition from low to high states. Interaction between the wind and the companion star attenuates the mass transfer and drives full cycles of low and high states.Comment: 9 pages including 5 figures, to appear in the Astrophysical Journa

Phase equilibrium modelling of the amphibolite to granulite facies transition in metabasic rocks (Ivrea Zone, NW Italy)

The development of thermodynamic models for tonalitic melt and the updated clinopyroxene and amphibole models now allow the use of phase equilibrium modelling to estimate P–T conditions and melt production for anatectic mafic and intermediate rock types at high‐temperature conditions. The Permian mid‐lower crustal section of the Ivrea Zone preserves a metamorphic field gradient from mid amphibolite facies to granulite facies, and thus records the onset of partial melting in metabasic rocks. Interlayered metabasic and metapelitic rocks allows the direct comparison of P–T estimates and partial melting between both rock types with the same metamorphic evolution. Pseudosections for metabasic compositions calculated in the Na2O–CaO–K2O–FeO–MgO–Al2O3–SiO2–H2O–TiO2–O (NCKFMASHTO) system are presented and compared with those of metapelitic rocks calculated with consistent endmember data and a–x models. The results presented in this study show that P–T conditions obtained by phase equilibria modelling of both metabasic and metapelitic rocks give consistent results within uncertainties, allowing integration of results obtained for both rock types. In combination, the calculations for both metabasic and metapelitic rocks allows an updated and more precisely constrained metamorphic field gradient for Val Strona di Omegna to be defined. The new field gradient has a slightly lower dP/dT which is in better agreement with the onset of crustal thinning of the Adriatic margin during the Permian inferred in recent studies

The ROSAT Galactic Plane Survey: analysis of a low latitude sample area in Cygnus

We present the analysis of the point source content of a low galactic latitude region selected from the ROSAT all-sky survey. The test field is centered at l = 90deg, b = 0deg and has an area of 64.5 deg2. A total of 128 soft X-ray sources are detected above a maximum likelihood of 8. Catalogue searches and optical follow-up observations show that in this direction of the galactic plane, 85% of the sources brighter than 0.03 PSPC cts/s are identified with active coronae. F-K type stars represent 67% (+/-13%) of the stellar identifications and M type stars account for 19% (+/- 6%). These results together with those of similar optical campaigns demonstrate that the soft X-ray population of the Milky Way is largely dominated by active stars. The modelling of this population suggests that most of the stars detected by ROSAT in this direction are younger than 1 Gyr. The small number of unidentified sources at low X-ray flux put rather strong constraints on the hypothetical X-ray emission from old neutron stars accreting from the interstellar medium. Our observations clearly rule out models which assume no dynamical heating for this population and a total number of Nns = 10^9 neutron stars in the Galaxy. If accretion on polar caps is the dominant mode then our upper limit may imply Nns ~ 10^8.Comment: 27 pages, 22 figures, Latex. Full resolution PostScript available at ftp://cdsarc.u-strasbg.fr/pub/xray/rgps_cygnus.ps.gz To be published in Astronomy & Astrophysics, Main Journa

Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility

We have performed a molecular dynamics computer simulation of a supercooled binary Lennard-Jones system in order to compare the dynamical behavior of this system with the predictions of the idealized version of mode-coupling theory (MCT). By scaling the time $t$ by the temperature dependent $\alpha$-relaxation time $\tau(T)$, we find that in the $\alpha$-relaxation regime $F(q,t)$ and $F_s(q,t)$, the coherent and incoherent intermediate scattering functions, for different temperatures each follows a $q$-dependent master curve as a function of scaled time. We show that during the early part of the $\alpha$-relaxation, which is equivalent to the late part of the $\beta$-relaxation, these master curves are well approximated by the master curve predicted by MCT for the $\beta$-relaxation. This part is also fitted well by a power-law, the so-called von Schweidler law. We show that the effective exponent $b'$ of this power-law depends on the wave vector $q$ if $q$ is varied over a large range. The early part of the $\beta$-relaxation regime does not show the critical decay predicted by MCT. The $q$-dependence of the nonergodicity parameter for $F_{s}(q,t)$ and $F(q,t)$ are in qualitative agreement with MCT. On the time scale of the late $\alpha$-relaxation the correlation functions show a Kohlrausch-Williams-Watt behavior (KWW). The KWW exponent $\beta$ is significantly different from the effective von Schweidler exponent $b'$. At low temperatures the $\alpha$-relaxation time $\tau(T)$ shows a power-law behavior with a critical temperature that is the same as the one found previously for the diffusion constant [Phys. Rev. Lett. {\bf 73}, 1376 (1994)]. The critical exponent of this power-law and the von Schweidler exponent $b'$ fulfill the connection proposed by MCT between these two quantities. We also show that theComment: 28 Pages of REVTEX, Figures available from W. Ko

Identification of selected sources from the ROSAT Galactic Plane Survey - I

We report on optical searches in the error circles of 93 ROSAT survey sources located at low galactic latitudes (|b| < 20 deg). These sources were extracted from the ROSAT Galactic Plane Survey using various selection criteria on hardness ratio, X-ray and optical brightness and integrated galactic absorption in the direction of the source. We find optical identifications in 76 cases, among which are 25 new AGN, 6 new CVs and a new Be/X-ray binary. In order to illustrate the relevance of the source selections applied here, we cross-correlated the ROSAT all-sky survey bright source list with SIMBAD. Different classes of X-ray emitters populate distinct regions of a multi dimensional parameter space involving flux ratios, galactic latitude and Nh. This relatively good segregation offers the possibility to build source samples with enhanced probability of identification with a given class. Complete optical identification of such subsamples could eventually be used to compute meaningful probabilities of identification for all sources using as basis a restricted set of multi-wavelength information.Comment: 18 pages, 7 figures, Postscript. Optical spectra and finding charts available at ftp://cdsarc.u-strasbg.fr/pub/xray/rgps_idI.ps.gz Submitted to Astronomy & Astrophysics, Supplement Serie

Disk instability and the spectral evolution of the 1992 outburst of the intermediate polar GK Persei

The disk instability model can explain the previous history of dwarf-nova-like outbursts in the intermediate polar GK Per, which occur about once every three years. Disk models that reproduce the recurrence time and outburst light curves suggest that GK Per has a large effective inner disk radius (approx. 30-40 white dwarf radii) truncated by a strong magnetic field (10(exp 7) G). In this context, the effective radius is that of the portion of the disk that participates in the disk thermal instability. The radius derived is larger than the corotation radius, which must be an upper limit on the true dynamical inner radius of the disk. Disk instability models with this large effective inner radius predict that the ultraviolet continuum should be rather flat. Here we compare the predictions of the disk instability model to IUE observations of the 1981 outburst and to IUE and ROSAT observations of the recent 1992 outburst of GK Per. The model disk continuum spectral evolution is consistent with the observed UV and optical spectra, especially at maximum and in the early decay phase of the outburst. The consistency of the model with the observed UV spectra suggests that the effective inner radius of the disk is almost constant, independent of mass accretion rate, and that whatever structure lies between the effective inner radius and the corotation radius neither participates in the disk instability nor radiates substantially in the UV. The related physics of the inner disk region will be briefly discussed

RX J0513.9-6951: The first example of accretion wind evolution, a key evolutionary process to Type Ia supernovae

A new self-sustained model for long-term light curve variations of RX J0513.9-6951 is proposed based on an optically thick wind model of mass-accreting white dwarfs (WDs). When the mass accretion rate to a WD exceeds the critical rate of \sim 1 x 10^{-6} M_\sun yr^{-1}, optically thick strong winds begin to blow from the WD so that a formation of common envelope is avoided. The WD can accrete and burn hydrogen-rich matter atop the WD at the critical rate. The excess matter transferred to the WD above the critical rate is expelled by winds. This is called the accretion wind evolution. This ejection process, however, occurs intermittently because the mass transfer is attenuated by strong winds: the strong winds collide with the secondary surface and strip off the very surface layer of the secondary. The matter stripped-off is lost from the binary system. Properly formulating this mass stripping effect and the ensuing decay of mass transfer rate, we are able to reproduce, in a self-sustained manner, the transition between the optical high/X-ray off and optical low/X-ray on states of RX J0513.9-6951. Thus RX J0513.9-6951 is the first example of the accretion wind evolution, which is a key evolutionary process in a recently developed evolutionary path to Type Ia supernovae.Comment: 22 pages including 13 figures, to appear in the Astrophysical Journa

Moyal star product approach to the Bohr-Sommerfeld approximation

The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The Hamiltonian need only have a Weyl transform (or symbol) that is a power series in $\hbar$, starting with $\hbar^0$, with a generic fixed point in phase space. The Hamiltonian is not restricted to the kinetic-plus-potential form. The method involves transforming the Hamiltonian to a normal form, in which it becomes a function of the harmonic oscillator Hamiltonian. Diagrammatic and other techniques with potential applications to other normal form problems are presented for manipulating higher order terms in the Moyal series.Comment: 27 pages, no figure

A limit cycle model for long-term optical variations of V Sagittae: The second example of accretion wind evolution

V Sagittae shows quasi-periodic optical high (soft X-ray off) and low (soft X-ray on) states with the total period of ~300 days. A binary model is presented to explain orbital light curves both for the high and low states as well as the transition mechanism between them. The binary model consists of a white dwarf (WD), a disk around the WD, and a lobe-filling main-sequence (MS) companion. In the optical high state, the mass transfer rate to the WD exceeds the critical rate of ~1 x 10^{-6} Msun/yr, and the WD blows an optically thick, massive wind. Surface layers of the disk are blown in the wind and the disk surface extends to the companion or over. As a result, optical luminosity of the disk increases by a magnitude because of its large irradiation effect. The massive wind completely obscures soft X-rays. This corresponds to the optical high/soft X-ray off state. The transition between optical high and low states is driven by an attenuation of the mass transfer from the secondary. As the mass supply stops, the WD wind weakens and eventually stops. The disk shrinks to a Roche lobe size and the optical magnitude drops. This phase corresponds to the optical low/soft X-ray on state. This cycle is repeated like a limit cycle. The WD can grow in mass at the critical rate and eventually reach the Chandrasekhar mass limit. This process is called ``accretion wind evolution,'' which is a key evolutionary process in a recently developed evolutionary scenario of Type Ia supernovae. This evolutionary process was first confirmed in the LMC supersoft X-ray source RX J0513.9$-$6951. Thus, V Sge is the second example of accretion wind evolution.Comment: to appear in ApJ, 33 pages including figure