A model for the Z-track phenomenon in GX 5-1 and observational evidence for the physical origins of the kHz QPO

We present results of a combined investigation of the spectral and kHz QPO evolution around the Z-track in GX 5-1 based on high-quality RXTE data. The Extended ADC emission model provides very good fits to the spectra, the results pointing clearly to a model for the nature of the Z-track, in agreement with previous results for the similar source GX 340+0. In this model, at the soft apex of the Z-track, the mass accretion rate Mdot is minimum and the neutron star has its lowest temperature; but as the source moves along the normal branch, the luminosity of the Comptonized emission increases, indicating that Mdot increases and the neutron star gets hotter. The measured flux f of the neutron star emission increases by a factor of ten becoming super-Eddington, and we propose that this disrupts the inner disk so forming jets. In flaring, the luminosity of the dominant Comptonized emission from the ADC is constant, while the neutron star emission increases, and we propose for the first time that flaring consists of unstable nuclear burning on the neutron star, and the measured mass accretion rate per unit area mdot at the onset of flaring agrees well with the theoretical critical value at which burning becomes unstable. There is a striking correlation between the frequencies of the kHz QPO and the ratio of the flux to the Eddington value: f/f_Edd, suggesting an explanation of the higher frequency QPO and of its variation along the Z-track. It is well known that a Keplerian orbit in the disk at this frequency corresponds to a position some distance from the neutron star; we propose that the oscillation always occurs at the inner disk edge, which moves radially outwards on the upper normal and horizontal branches as the measured increasing radiation pressure increasingly disrupts the inner disk.Comment: Astronomy and Astrophysics, in pres

Spectral Investigations of the nature of the Sco X-1 like sources

We present results of spectral investigations of the Sco X-1 like Z-track sources Sco X-1, GX 349+2 and GX 17+2 based on Rossi-XTE observations using an extended accretion disk corona model. The results are compared with previous results for the Cyg X-2 like group: Cyg X-2, GX 340+0 and GX 5-1 and a general model for the Z-track sources proposed. On the normal branch, the Sco-like and Cyg-like sources are similar, the results indicating an increase of mass accretion rate Mdot between soft and hard apex, not as in the standard view that this increases around the Z. In the Cyg-like sources, increasing Mdot causes the neutron star temperature kT to increase from ~1 to ~2 keV. At the lower kT, the radiation pressure is small, but at the higher kT, the emitted flux of the neutron star is several times super-Eddington and the high radiation pressure disrupts the inner disk launching the relativistic jets observed on the upper normal and horizontal branches. In the Sco-like sources, the main physical difference is the high kT of more than 2 keV on all parts of the Z-track suggesting that jets are always possible, even on the flaring branch. The flaring branch in the Cyg-like sources is associated with release of energy on the neutron star consistent with unstable nuclear burning. The Sco-like sources are very different as flaring appears to be a combination of unstable burning and an increase of Mdot which makes flaring much stronger. Analysis of 15 years or RXTE ASM data on all 6 classic Z-track sources shows the high rate and strength of flaring in the Sco-like sources suggesting that continual release of energy heats the neutron star causing the high kT. A Sco X-1 observation with unusually little flaring supports this. GX 17+2 appears to be transitional between the Cyg and Sco-like types. Our results do not support the suggestion that Cyg or Sco-like nature is determined by luminosity.Comment: Astronomy and Astrophysics in press; 21 pages, 13 figure

On the nature of the Cygnus X-2 like Z-track sources

Based on the results of applying the extended ADC emission model for low mass X-ray binaries to three Z-track sources: GX340+0, GX5-1 and CygX-2, we propose an explanation of the CygnusX-2 like Z-track sources. The Normal Branch is dominated by the increasing radiation pressure of the neutron star caused by a mass accretion rate that increases between the soft apex and the hard apex. The radiation pressure continues to increase on the Horizontal Branch becoming several times super-Eddington. We suggest that this disrupts the inner accretion disk and that part of the accretion flow is diverted vertically forming jets which are detected by their radio emission on this part of the Z-track. We thus propose that high radiation pressure is the necessary condition for the launching of jets. On the Flaring Branch there is a large increase in the neutron star blackbody luminosity at constant mass accretion rate indicating an additional energy source on the neutron star. We find that there is good agreement between the mass accretion rate per unit emitting area of the neutron star mdot at the onset of flaring and the theoretical critical value at which burning becomes unstable. We thus propose that flaring in the CygnusX-2 like sources consists of unstable nuclear burning. Correlation of measurements of kilohertz QPO frequencies in all three sources with spectral fitting results leads to the proposal that the upper kHz QPO is an oscillation always taking place at the inner accretion disk edge, the radius of which increases due to disruption of the disk by the high radiation pressure of the neutron star.Comment: Astronomy and Astrophysics, in pres

BeppoSAX observation of the eclipsing dipping X-ray binary X1658-298

Results of a 2000 August 12-13 BeppoSAX observation of the 7.1 hr eclipsing, dipping, bursting, transient, low-mass X-ray binary (LMXRB) X1658-298 are presented. The spectrum outside of eclipses, dips and bursts can be modeled by the combination of a soft disk-blackbody and a harder Comptonized component with a small amount (1.3 10E21 atom/cm2) of low-energy absorption. In contrast, an RXTE observation 18 months earlier during the same outburst, measured an absorption of 5.0 10E22 atom/cm2. Such a change is consistent with a thinning of the accretion disk as the outburst progresses. Structured residuals from the best-fit spectral model are present which are tentatively identified with Ne-K/Fe-L and Fe-K shell emission. The spectral changes during dips are complex and may be modeled by a strong (~3 10E23 atom/cm2) increase in absorption of the Comptonized component only, together with reductions in normalizations of both spectral components. This behavior is in contrast to the ``complex continuum'' model for X-ray dip sources, where the softer blackbody component rapidly suffers strong absorption. It is however, similar to that found during recent XMM-Newton observations of the eclipsing, dipping, LMXRB EXO0748-676.Comment: 11 pages. Accepted for publication in A&A

Uniform Substitution for Differential Game Logic

This paper presents a uniform substitution calculus for differential game logic (dGL). Church's uniform substitutions substitute a term or formula for a function or predicate symbol everywhere. After generalizing them to differential game logic and allowing for the substitution of hybrid games for game symbols, uniform substitutions make it possible to only use axioms instead of axiom schemata, thereby substantially simplifying implementations. Instead of subtle schema variables and soundness-critical side conditions on the occurrence patterns of logical variables to restrict infinitely many axiom schema instances to sound ones, the resulting axiomatization adopts only a finite number of ordinary dGL formulas as axioms, which uniform substitutions instantiate soundly. This paper proves soundness and completeness of uniform substitutions for the monotone modal logic dGL. The resulting axiomatization admits a straightforward modular implementation of dGL in theorem provers