Quasi-Periodic Oscillations in Short Recurring Bursts of the magnetars SGR 1806-20 and SGR 1900+14 Observed With RXTE

Quasi-periodic oscillations (QPOs) observed in the giant flares of magnetars are of particular interest due to their potential to open up a window into the neutron star interior via neutron star asteroseismology. However, only three giant flares have been observed. We therefore make use of the much larger data set of shorter, less energetic recurrent bursts. Here, we report on a search for QPOs in a large data set of bursts from the two most burst-active magnetars, SGR 1806-20 and SGR 1900+14, observed with the Rossi X-ray Timing Explorer (RXTE). We find a single detection in an averaged periodogram comprising 30 bursts from SGR 1806-20, with a frequency of 57 Hz and a width of 5 Hz, remarkably similar to a giant flare QPO observed from SGR 1900+14. This QPO fits naturally within the framework of global magneto-elastic torsional oscillations employed to explain the giant flare QPOs. Additionally, we uncover a limit on the applicability of Fourier analysis for light curves with low background count rates and strong variability on short timescales. In this regime, standard Fourier methodology and more sophisticated Fourier analyses fail in equal parts by yielding an unacceptably large number of false positive detections. This problem is not straightforward to solve in the Fourier domain. Instead, we show how simulations of light curves can offer a viable solution for QPO searches in these light curves.Comment: accepted for publication in ApJ; 12 pages, 7 figures; code + instructions at https://github.com/dhuppenkothen/MagnetarQPOSearchPaper ; associated data products at http://figshare.com/articles/SGR_1900_14_RXTE_Data/1184101 (SGR 1900+14) and http://figshare.com/articles/SGR_1806_20_Bursts_RXTE_data_set/1184427 (SGR 1806-20

The lowest singlet-triplet excitation energy of BN: a converged coupled cluster perspective

The notoriously small $X ^3\Pi-a ^1\Sigma^+$ excitation energy of the BN diatomic has been calculated using high-order coupled cluster methods. Convergence has been established in both the 1-particle basis set and the coupled cluster expansion. Explicit inclusion of connected quadruple excitations $\hat{T}_4$ is required for even semiquantitative agreement with the limit value, while connected quintuple excitations $\hat{T}_5$ still have an effect of about 60 cm$^{-1}$. Still higher excitations only account for about 10 cm$^{-1}$. Inclusion of inner-shell correlation further reduces $T_e$ by about 60 cm$^{-1}$ at the CCSDT, and 85 cm$^{-1}$ at the CCSDTQ level. Our best estimate, $T_e$=183$\pm$40 cm$^{-1}$, is in excellent agreement with earlier calculations and experiment, albeit with a smaller (and conservative) uncertainty. The dissociation energy of BN($X ^3\Pi$) is $D_e$=105.74$\pm$0.16 kcal/mol and $D_0$=103.57$\pm$0.16 kcal/mol.Comment: J. Chem. Phys., in pres

Epidemics and percolation in small-world networks

We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network, and we give exact solutions for the position of this threshold in a variety of cases. We confirm our analytic results by numerical simulation.Comment: 6 pages, including 3 postscript figure

The Number of Incipient Spanning Clusters in Two-Dimensional Percolation

Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison with existing numerical results include

The 2-Dimensional Quantum Euclidean Algebra

The algebra dual to Woronowicz's deformation of the 2-\-di\-men\-sion\-al Euclidean group is constructed. The same algebra is obtained from $SU_{q}(2)$ via contraction on both the group and algebra levels.Comment: 8 pages, LBL-31711 and UCB-PTH-92/0

A crossing probability for critical percolation in two dimensions

Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of pi_h by treating it as a correlation function of boundary operators in the Q goes to 1 limit of the Q state Potts model. We extend his results to find an analogous formula for pi_{hv} which compares very well with the numerical results.Comment: 8 pages, Latex2e, 1 figure, uuencoded compressed tar file, (1 typo changed

Indications for a slow rotator in the Rapid Burster from its thermonuclear bursting behaviour

We perform time-resolved spectroscopy of all the type I bursts from the Rapid Burster (MXB 1730-335) detected with the Rossi X-ray Timing Explorer. Type I bursts are detected at high accretion rates, up to \sim 45% of the Eddington luminosity. We find evidence that bursts lacking the canonical cooling in their time-resolved spectra are, none the less, thermonuclear in nature. The type I bursting rate keeps increasing with the persistent luminosity, well above the threshold at which it is known to abruptly drop in other bursting low-mass X-ray binaries. The only other known source in which the bursting rate keeps increasing over such a large range of mass accretion rates is the 11 Hz pulsar IGR J17480$-$2446. This may indicate a similarly slow spin for the neutron star in the Rapid Burster