Operad profiles of Nijenhuis structures

Recently S. Merkulov established a new link between differential geometry and homological algebra by giving descriptions of several differential geometric structures in terms of algebraic operads and props. In particular he described Nijenhuis structures as corresponding to representations of the cobar construction on the Koszul dual of a certain quadratic operad. In this paper we prove, using the PBW-basis method of E. Hoffbeck, that the operad governing Nijenhuis structures is Koszul, thereby showing that Nijenhuis structures correspond to representations of the minimal resolution of this operad. We also construct an operad such that representations of its minimal resolution in a vector space V are in one-to-one correspondence with pairs of compatible Nijenhuis structures on the formal manifold associated to V.Comment: 16 page

Future Probes of the Neutron Star Equation of State Using X-ray Bursts

Observations with NASA's Rossi X-ray Timing Explorer (RXTE) have resulted in the discovery of fast (200 - 600 Hz), coherent X-ray intensity oscillations (hereafter, "burst oscillations") during thermonuclear X-ray bursts from 12 low mass X-ray binaries (LMXBs). It is now beyond doubt that these oscillations result from spin modulation of the thermonuclear burst flux from the neutron star surface. Among the new timing phenomena revealed by RXTE the burst oscillations are perhaps the best understood, in the sense that many of their properties can be explained in the framework of this relatively simple model. Because of this, detailed modelling of burst oscillations can be an extremely powerful probe of neutron star structure, and thus the equation of state (EOS) of supra-nuclear density matter. The new discoveries have spurred much new theoretical work on thermonuclear burning and propagation on neutron stars, so that in the near future it is not unreasonable to think that detailed physical models of the time dependent flux from burning neutron stars will be available for comparison with the observed pulse profiles from a future, large collecting area X-ray timing observatory. In addition, recent high resolution burst spectroscopy with XMM/Newton suggests the presence of redshifted absorption lines from the neutron star surface during bursts. This leads to the possibility of using large area, high spectral resolution measurements of X-ray bursts as a precise probe of neutron star structure. In this work I will explore the precision with which constraints on neutron star structure, and hence the dense matter EOS, can be made with the implementation of such programs.Comment: 8 pages, 7 figures, AIP conference proceedings format. Contribution to "X-ray Timing 2003: Rossi and Beyond." meeting held in Cambridge, MA, November, 200

Precision X-ray Timing of RX J0806.3+1527 with CHANDRA: Evidence for Gravitational Radiation from an Ultracompact Binary

RX J0806.3+1527 is a candidate double degenerate binary with possibly the shortest known orbital period. The source shows an 100% X-ray intensity modulation at the putative orbital frequency of 3.11 mHz (321.5 s). If the system is a detached, ultracompact binary gravitational radiation should drive spin-up with a magnitude of ~10-16 Hz/s. Here we describe the results of the first phase coherent X-ray monitoring campaign on RX J0806.3+1527 with Chandra. We obtained a total of 70 ksec of exposure in 6 epochs logarithmically spaced over 320 days. These data conclusively show that the X-ray frequency is increasing at a rate of 3.77 +- 0.8 x 10-16 Hz/s. Using our new ephemeris we are able to phase up all the earlier Chandra and ROSAT data and show they are consistent with a rate of 3.63 +- 0.06 x 10-16 Hz/s over the past decade. This value appears consistent with that recently derived by Israel et al. largely from monitoring of the optical modulation, and is in rough agreement with the solutions reported initially by Hakala et al., based on ground-based optical observations. The large spin-up is consistent with gravitational radiation losses driving the evolution. An intermediate polar (IP) scenario where the observed X-ray period is the spin period of an accreting white dwarf appears less tenable. If the ultracompact scenario is correct, then the X-ray flux cannot be powered by stable accretion which would drive the components apart, suggesting a new type of energy source (perhaps electromagnetic) may power the X-ray flux.Comment: 23 pages, 9 figures, AASTeX, accepted for publication in the Astrophysical Journa

Millisecond Time Variations of X-Ray Binaries

The Rossi X-Ray Timing Explorer (RXTE) has found that the neutron stars in low-mass X-ray binaries exhibit oscillations in the range 300-1200 Hz. Persistent emission may exhibit one or both of two features. In bursts a nearly coherent pulsation is seen, which may be the rotation period of the neutron star. For some the frequency equals the difference between the two higher frequencies, suggesting a beat frequency model, but in others it is twice the difference. Similar maximum frequencies suggests that it corresponds to the Kepler orbit frequency at the minimum stable orbit or the neutron star surface, either of which would determine the neutron star masses, radii and equation of state. Theories of accretion onto black holes predict a quasi-periodic oscillation (QPO) related to the inner accretion disk. The two microquasar black hole candidates (BHCs) have exhibited candidates for this or related frequencies.Comment: 4 pages, to be published in the proceedings of IAU Symposium 188: The Hot Univers

Discovery of a 115 Day Orbital Period in the Ultraluminous X-ray Source NGC 5408 X-1

We report the detection of a 115 day periodicity in SWIFT/XRT monitoring data from the ultraluminous X-ray source (ULX) NGC 5408 X-1. Our ongoing campaign samples its X-ray flux approximately twice weekly and has now achieved a temporal baseline of ~485 days. Periodogram analysis reveals a significant periodicity with a period of 115.5 +- 4 days. The modulation is detected with a significance of 3.2 e-4. The fractional modulation amplitude decreases with increasing energy, ranging from 0.13 above 1 keV to 0.24 below 1 keV. The shape of the profile evolves as well, becoming less sharply peaked at higher energies. The periodogram analysis is consistent with a periodic process, however, continued monitoring is required to confirm the coherent nature of the modulation. Spectral analysis indicates that NGC 5408 X-1 can reach 0.3 - 10 keV luminosities of ~2 e40 ergs/s. We suggest that, like the 62 day period of the ULX in M82 (X41.4+60), the periodicity detected in NGC 5408 X-1 represents the orbital period of the black hole binary containing the ULX. If this is true then the secondary can only be a giant or supergiant star.Comment: Accepted for Publication in the Astrophysical Journal Letter