RXTE Studies of Long-Term X-ray Spectral Variations in 4U 1820-30

We present the results of detailed spectral studies of the ultra-compact low mass X-ray binary (LMXB) 4U 1820-30 carried out with the Rossi X-ray Timing Explorer (RXTE) during 1996-7. 4U 1820-30 is an ``atoll'' source X-ray burster (XRB) located in the globular cluster NGC 6624. It is known to have an 11 minute binary period and a ~176 day modulation in its 2--12 keV flux. Observations were made with the PCA and HEXTE instruments on RXTE at roughly one-month intervals to sample this long-term period and study flux-related spectral changes. There are clear correlations between our fitted spectral parameters and both the broad-band (2--50 keV) flux and the position in the color-color diagram, as described by the parameter S_a introduced by Mendez et al. (1999). In addition, we find a strong correlation between the position in the color-color diagram and the frequencies of the kilohertz quasi-periodic oscillations (kHz QPOs) reported by Zhang et al. (1998). This lends further support to the notion that evidence for the last stable orbit in the accretion disk of 4U 1820-30 has been observed. For a model consisting of Comptonization of cool photons by hot electrons plus an additional blackbody component, we report an abrupt change in the spectral parameters at the same accretion rate at which the kHz QPOs disappear. For a model consisting of a multicolor disk blackbody plus a cut-off power law, we find that the inner disk radius reaches a minimum at the same accretion rate at which the kHz QPO frequency saturates, as expected if the disk reaches the last stable orbit. Both models face theoretical and observational problems when interpreted physically for this system.Comment: 39 pages, 11 figures, accepted to the Astrophysical Journa

Mass and radius estimation for the neutron star in X-ray burster 4U 1820-30

We present a new method for determining masses and radii of neutron stars residing in thermo-nuclear X-ray burst sources. To illustrate this method we apply it to a burst from the source 4U 1820-30 recorded by the Rossi X-Ray Timing Explorer. Fits of the observed X-ray spectra to grids of Comptonised model atmospheres yield estimates for the mass and radius of the neutron star, M=1.3 \pm 0.6 M_sol and R=11^+3_-2 km, respectively.Comment: MNRAS in prin

Stein structures: existence and flexibility

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure

Six supersoft X-ray binaries: system parameters and twin-jet outflows

A comparison is made between the properties of CAL 83, CAL 87, RX J0513.9-6951, 1E 0035.4-7230 (SMC 13), RX J0019.8+2156, and RX J0925.7-4758, all supersoft X-ray binaries. Spectra with the same resolution and wavelength coverage of these systems are compared and contrasted. Some new photometry is also presented. The equivalent widths of the principal emission lines of H and He II differ by more than an order of magnitude among these sources, although those of the highest ionization lines (e.g. O VI) are very similar. In individual systems, the velocity curves derived from various ions often differ in phasing and amplitude, but those whose phasing is consistent with the light curves (implying the lines are formed near the compact star) give masses of $\sim 1.2M_{\odot}$ and $\sim 0.5M_{\odot}$ for the degenerate and mass-losing stars, respectively. This finding is in conflict with currently prevailing theoretical models for supersoft binaries. The three highest luminosity sources show evidence of "jet" outflows, with velocities of $\sim 1-4 \times10^3 km/s$. In CAL 83 the shape of the He II 4686\AA profile continues to show evidence that these jets may precess with a period of $\sim 69$ days.Comment: 27 pages including 5 tables, plus 6 figures. To appear in Ap

Homotopy types of stabilizers and orbits of Morse functions on surfaces

Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ h^{-1}$, where $h\in Diff(M)$ and $f \in C^{\infty}(M,P)$. Let $f:M \to P$ be a Morse function and $O(f)$ be the orbit of $f$ under this action. We prove that $\pi_k O(f)=\pi_k M$ for $k\geq 3$, and $\pi_2 O(f)=0$ except for few cases. In particular, $O(f)$ is aspherical, provided so is $M$. Moreover, $\pi_1 O(f)$ is an extension of a finitely generated free abelian group with a (finite) subgroup of the group of automorphisms of the Reeb graph of $f$. We also give a complete proof of the fact that the orbit $O(f)$ is tame Frechet submanifold of $C^{\infty}(M,P)$ of finite codimension, and that the projection $Diff(M) \to O(f)$ is a principal locally trivial $S(f)$-fibration.Comment: 49 pages, 8 figures. This version includes the proof of the fact that the orbits of a finite codimension of tame action of tame Lie group on tame Frechet manifold is a tame Frechet manifold itsel

Timing Analysis of the Light Curve of the Dipping-Bursting X-ray Binary X1916-053

We present the timing analysis results for our observations of the x-ray dip source X1916-053 conducted with RXTE between February and October of 1996. Our goal was to finally measure the binary period - as either the x-ray dip period or ~1% longer optical modulation period, thereby establishing if the binary has a precessing disk (SU UMa model) or a third star (triple model). Combined with historical data (1979-96), the x-ray dip period is measured to be 3000.6508 $\pm$ 0.0009 sec with a 2$\sigma$ upper limit $|\dot P| \leq 2.06 \times 10^{-11}$. From our quasi-simultaneous optical observations (May 14-23, 1996) and historical data (1987-96), we measure the optical modulation period to be 3027.5510 $\pm$ 0.0052 sec with a 2$\sigma$ upper limit $|\dot P| \leq 2.28 \times 10^{-10}$. The two periods are therefore each stable (over all recorded data) and require a $3.9087 \pm 0.0008$d beat period. This beat period, and several of its harmonics is also observed as variations in the dip shape. Phase modulation of x-ray dips, observed in a 10 consecutive day observation, is highly correlated with the $\sim$3.9d dip shape modulation. The 1987-1996 optical observations show that the optical phase fluctuations are a factor of 3 larger than those in the x-ray. We discuss SU UMa vs. triple models to describe the X1916-053 light curve behavior and conclude that the x-ray dip period, with smaller phase jitter, is probably the binary period so that the required precession is most likely similar to that observed in SU UMa and x-ray nova systems. However the ``precession'' period stability and especially the fact that the times of x-ray bursts may partially cluster to occur just after x-ray dips, continue to suggest that this system may be a hierarchical triple.Comment: 33 pages, 13 figures, accepted by Ap

Biocompatibility of CaO-Na2O-SiO2/TiO2 Glass Ceramic Scaffolds for Orthopaedic Applications

This work aims to determine the effect of substituting TiO2 for SiO2 in a 0.62SiO2-Na2O-0.24CaO based glass-ceramic scaffold. High temperature X-ray Diffraction (HT-XRD) was used to determine the sintering temperature (700oC). Both optical microscopy and x-ray micotomography was used to determine the average pore size (540-680ìm) of each scaffold. Cytocompatibility of each scaffold was conducted using murine mesenchymal stem cells. © 2013 IEEE

Fabrication of CaO-NaO-SiO2/TiO2 Scaffolds for Surgical Applications

A series of titanium (Ti) based glasses were formulated (0.62 SiO2-0.14 Na2O-0.24 CaO, with 0.05 mol% TiO2 substitutions for SiO2) to develop glass/ceramic scaffolds for bone augmentation. Glasses were initially characterised using X-ray diffraction (XRD) and particle size analysis, where the starting materials were amorphous with 4.5 μm particles. Hot stage microscopy and high temperature XRD were used to determine the sintering temperature (̃700 °C) and any crystalline phases present in this region (Na2Ca3Si6O16, combeite and quartz). Hardness testing revealed that the Ti-free control (ScC- 2.4 GPa) had a significantly lower hardness than the Ti-containing materials (Sc1 and Sc2 ̃6.6 GPa). Optical microscopy determined pore sizes ranging from 544 to 955 lm. X-ray microtomography calculated porosity from 87 to 93 % and surface area measurements ranging from 2.5 to 3.3 SA/mm3. Cytotoxicity testing (using mesenchymal stem cells) revealed that all materials encouraged cell proliferation, particularly the higher Ti-containing scaffolds over 24-72 h. © Springer Science+Business Media, LLC 2012