Bounds on the Compactness of Neutron Stars from Brightness Oscillations

The discovery of high-amplitude brightness oscillations at the spin frequency or its first overtone in six neutron stars in low-mass X-ray binaries during type~1 X-ray bursts provides a powerful new way to constrain the compactness of these stars, and hence to constrain the equation of state of the dense matter in all neutron stars. Here we present the results of general relativistic calculations of the maximum fractional rms amplitudes that can be observed during bursts. In particular, we determine the dependence of the amplitude on the compactness of the star, the angular dependence of the emission from the surface, the rotational velocity at the stellar surface, and whether there are one or two emitting poles. We show that if two poles are emitting, as is strongly indicated by independent evidence in 4U 1636-536 and KS 1731-26, the resulting limits on the compactness of the star can be extremely restrictive. We also discuss the expected amplitudes of X-ray color oscillations and the observational signatures necessary to derive convincing constraints on neutron star compactness from the amplitudes of burst oscillations.Comment: 8 pages plus one figure, AASTeX v. 4.0, submitted to The Astrophysical Journal Letter

Coronal hole boundaries at small scales: IV. SOT view Magnetic field properties of small-scale transient brightenings in coronal holes

We study the magnetic properties of small-scale transients in coronal hole. We found all brightening events are associated with bipolar regions and caused by magnetic flux emergence followed by cancellation with the pre-existing and newly emerging magnetic flux. In the coronal hole, 19 of 22 events have a single stable polarity which does not change its position in time. In eleven cases this is the dominant polarity. The dominant flux of the coronal hole form the largest concentration of magnetic flux in terms of size while the opposite polarity is distributed in small concentrations. In the coronal hole the number of magnetic elements of the dominant polarity is four times higher than the non-dominant one. The supergranulation configuration appears to preserve its general shape during approximately nine hours of observations although the large concentrations in the network did evolve and were slightly displaced, and their strength either increased or decreased. The emission fluctuations seen in the X-ray bright points are associated with reoccurring magnetic cancellation in the footpoints. Unique observations of an X-ray jet reveal similar magnetic behaviour in the footpoints, i.e. cancellation of the opposite polarity magnetic flux. We found that the magnetic flux cancellation rate during the jet is much higher than in bright points. Not all magnetic cancellations result in an X-ray enhancement, suggesting that there is a threshold of the amount of magnetic flux involved in a cancellation above which brightening would occur at X-ray temperatures. Our study demonstrates that the magnetic flux in coronal holes is continuously recycled through magnetic reconnection which is responsible for the formation of numerous small-scale transient events. The open magnetic flux forming the coronal-hole phenomenon is largely involved in these transient features.Comment: 19 pages, 18 figures, A&A in pres

Darboux transformation and multi-soliton solutions of Two-Boson hierarchy

We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on $SL(2,R)$ within the AKNS framework, this model is based on $SL(2,R)\otimes U(1)$. The connection between the scalar and the matrix descriptions in this case implies that the generic Darboux matrix for the TB hierarchy has a different structure from that in the models based on $SL(2,R)$ studied thus far. The conventional Darboux transformation is shown to be quite restricted in this model. We construct a modified Darboux transformation which has a much richer structure and which also allows for multi-soliton solutions to be written in terms of Wronskians. Using the modified Darboux transformations, we explicitly construct one soliton/kink solutions for the model.Comment:

Coherent vibrations of submicron spherical gold shells in a photonic crystal

Coherent acoustic radial oscillations of thin spherical gold shells of submicron diameter excited by an ultrashort optical pulse are observed in the form of pronounced modulations of the transient reflectivity on a subnanosecond time scale. Strong acousto-optical coupling in a photonic crystal enhances the modulation of the transient reflectivity up to 4%. The frequency of these oscillations is demonstrated to be in good agreement with Lamb theory of free gold shells.Comment: Error in Eqs.2 and 3 corrected; Tabl. I corrected; Fig.1 revised; a model that explains the dependence of the oscillation amplitude of the transient reflectivity with wavelength adde

Instabilities in an Internal Solitary-like Wave on the Oregon Shelf

Observations of internal solitary-like waves (ISWs) on the Oregon Shelf suggest the presence of Kelvin–Helmholtz billows in the pycnocline and larger-scale overturns at the back of the wave above the pycnocline. Numerical simulations designed to explore the mechanisms responsible for these features in one particular wave reveal that shear instabilities occur when (i) the minimum Richardson number Ri in the pycnocline is less than about 0.1; (ii) Lx/λ \u3e 0.8, where Lx is the length of the unstable region with Ri \u3c 0.25 and λ is a half wavelength of the wave; and (iii) a linear spatial stability analysis predicts that ln(af/ai) \u3e≈ 4, where ai and af are the amplitudes of perturbations entering and leaving the unstable region. The maximum energy loss rate in our simulations is 50 W m−1, occurring at a frequency 8% below that with the maximum spatial growth rate. The observations revealed the presence of anomalously light fluid in the center of the wave above the pycnocline. Simulations of a wave encountering a patch of light surface water were used to model this effect. In the presence of a background current with near-surface shear, the simulated ISW has a trapped surface core. As this wave encounters a patch of lighter surface water, the light surface water at first passes beneath the core. Convective instabilities set in and the light fluid is entrained into the core. This results in the formation of overturning features, which exhibit some similarities with the observed overturns

Gamma-Ray Bursts as a Probe of the Very High Redshift Universe

We show that, if many GRBs are indeed produced by the collapse of massive stars, GRBs and their afterglows provide a powerful probe of the very high redshift (z > 5) universe.Comment: To appear in Proc. of the 5th Huntsville Gamma-Ray Burst Symposium, 5 pages, LaTe

Bifurcations of periodic orbits with spatio-temporal symmetries

Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. Our approach is based on centre manifold reduction for maps, and is in the spirit of earlier work by Iooss (1986) on bifurcations of group orbits of spatially symmetric equilibria. Two examples, two-dimensional pulsating waves (PW) and three-dimensional alternating pulsating waves (APW), have discrete spatio-temporal symmetries characterized by the cyclic groups Z_n, n=2 (PW) and n=4 (APW). These symmetries force the Poincare' return map M to be the nth iterate of a map G: M=G^n. The group orbits of PW and APW are generated by translations in the horizontal directions and correspond to a circle and a two-torus, respectively. An instability of pulsating waves can lead to solutions that drift along the group orbit, while bifurcations with Floquet multiplier +1 of alternating pulsating waves do not lead to drifting solutions. The third example we consider, alternating rolls, has the spatio-temporal symmetry of alternating pulsating waves as well as being invariant under reflections in two vertical planes. This leads to the possibility of a doubling of the marginal Floquet multiplier and of bifurcation to two distinct types of drifting solutions. We conclude by proposing a systematic way of analysing steady-state bifurcations of periodic orbits with discrete spatio-temporal symmetries, based on applying the equivariant branching lemma to the irreducible representations of the spatio-temporal symmetry group of the periodic orbit, and on the normal form results of Lamb (1996). This general approach is relevant to other pattern formation problems, and contributes to our understanding of the transition from ordered to disordered behaviour in pattern-forming systems

Boundary Conditions in Stepwise Sine-Gordon Equation and Multi-Soliton Solutions

We study the stepwise sine-Gordon equation, in which the system parameter is different for positive and negative values of the scalar field. By applying appropriate boundary conditions, we derive relations between the soliton velocities before and after collisions. We investigate the possibility of formation of heavy soliton pairs from light ones and vise versa. The concept of soliton gun is introduced for the first time; a light pair is produced moving with high velocity, after the annihilation of a bound, heavy pair. We also apply boundary conditions to static, periodic and quasi-periodic solutions.Comment: 14 pages, 8 figure

Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio