Quasi Periodic Oscillations in Low Mass X-Ray Binaries and Constraints on the Equation of State of Neutron Star Matter

Recently discovered quasi periodic oscillations in the X-ray brightness of low mass X-ray binaries are used to derive constraints on the mass of the neutron star component and the equation of state of neutron star matter. The observations are compared with models of rapidly rotating neutron stars which are calculated by means of an exact numerical method in full relativity. For the equations of state we select a broad collection of models representing different assumptions about the many-body structure and the complexity of the composition of super dense matter. The mass constraints differ from their values in the approximate treatment by \sim 10%. Under the assumption that the maximum frequency of the quasi periodic oscillations originates from the innermost stable orbit the mass of the neutron star is in the range: $M\sim 1.92-2.25 M_\odot$. Especially the quasi periodic oscillation in the Atoll-source 4U 1820-30 is only consistent with equations of state which are rather stiff at high densities which is explainable, so far, only with pure nucleonic/leptonic composition. This interpretation contradicts the hypothesis that the protoneutron star formed in SN 1987A collapsed to a black hole, since this would demand a maximum neutron star mass below $1.6 M_\odot$. The recently suggested identification of quasi periodic oscillations with frequencies around 10 Hz with the Lense-Thirring precession of the accretion disk is found to be inconsistent with the models studied in this work, unless it is assumed that the first overtone of the precession is observed.Comment: 12 pages including figures, to be published in MNRA

Tight Bounds for Consensus Systems Convergence

We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set, by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with period smaller than a certain value converge to zero, and bounds exist on that value. We provide a stronger bound holding for both polyhedral norms and polyhedral seminorms. In the latter case, the matrix products do not necessarily converge to 0, but all trajectories of the associated system converge to a common invariant space. We prove our bound to be tight, in the sense that for any polyhedral seminorm, there is a set of matrices such that not all infinite products converge, but every periodic product with period smaller than our bound does converge. Our technique is based on an analysis of the combinatorial structure of the face lattice of the unit ball of the nonincreasing seminorm. The bound we obtain is equal to half the size of the largest antichain in this lattice. Explicitly evaluating this quantity may be challenging in some cases. We therefore link our problem with the Sperner property: the property that, for some graded posets, -- in this case the face lattice of the unit ball -- the size of the largest antichain is equal to the size of the largest rank level. We show that some sets of matrices with invariant polyhedral seminorms lead to posets that do not have that Sperner property. However, this property holds for the polyhedron obtained when treating sets of stochastic matrices, and our bound can then be easily evaluated in that case. In particular, we show that for the dimension of the space $n \geq 8$, our bound is smaller than the previously known bound by a multiplicative factor of $\frac{3}{2 \sqrt{\pi n}}$

Study of hot hardness characteristics of tool steels

Hardness measurements of tool steel materials in electric furnace at elevated temperatures and low oxygen environment are discussed. Development of equation to predict short term hardness as function of intial room temperature hardness of steel is reported. Types of steel involved in the process are identified

Diffusive foam wetting process in microgravity

We report the experimental study of aqueous foam wetting in microgravity. The liquid fraction $\ell$ along the bubble edges is measured and is found to be a relevant dynamical parameter during the capillary process. The penetration of the liquid in the foam, the foam inflation, and the rigidity loss are shown all to obey strict diffusion processes.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

Radio and X-ray Observations of the Type Ic SN 2007gr Reveal an Ordinary, Non-relativistic Explosion

We present extensive radio and X-ray observations of the nearby Type Ic SN 2007gr in NGC 1058 obtained with the Very Large Array and the Chandra X-ray Observatory and spanning 5 to 150 days after explosion. Through our detailed modeling of these data, we estimate the properties of the blastwave and the circumstellar environment. We find evidence for a freely-expanding and non-relativistic explosion with an average blastwave velocity, v~0.2c, and a total internal energy for the radio emitting material of E ~ 2 x 10^46 erg assuming equipartition of energy between electrons and magnetic fields (epsilon_e=epsilon_B=0.1). The temporal and spectral evolution of the radio emission points to a stellar wind-blown environment shaped by a steady progenitor mass loss rate of Mdot ~ 6 x 10^-7 solar masses per year (wind velocity, v_w=10^3 km/s). These parameters are fully consistent with those inferred for other SNe Ibc and are in line with the expectations for an ordinary, homologous SN explosion. Our results are at odds with those of Paragi et al. (2010) who recently reported evidence for a relativistic blastwave in SN 2007gr based on their claim that the radio emission was resolved away in a low signal-to-noise Very Long Baseline Interferometry (VLBI) observation. Here we show that the exotic physical scenarios required to explain the claimed relativistic velocity -- extreme departures from equipartition and/or a highly collimated outflow -- are excluded by our detailed Very Large Array radio observations. Moreover, we present an independent analysis of the VLBI data and propose that a modest loss of phase coherence provides a more natural explanation for the apparent flux density loss which is evident on both short and long baselines. We conclude that SN 2007gr is an ordinary Type Ibc supernova.Comment: 14 pages, 6 figures, submitted to Ap

Short-term hot hardness characteristics of rolling-element steels

Short-term hot hardness studies were performed with five vacuum-melted steels at temperatures from 294 to 887 K (70 to 1140 F). Based upon a minimum Rockwell C hardness of 58, the temperature limitation on all materials studied was dependent on the initial room temperature hardness and the tempering temperature of each material. For the same room temperature hardness, the short-term hot hardness characteristics were identical and independent of material composition. An equation was developed to predict the short-term hardness at temperature as a function of initial room temperature hardness for AISI 52100, as well as the high-speed tool steels

Axisymmetric circumstellar interaction in supernovae

Multiwavelength observations of Type II supernovae have shown evidence for the interaction of supernovae with the dense slow winds from the red supergiant progenitor stars. Observations of planetary nebulae and the nebula around SN 1987A show that the slow winds from extended stars frequently have an axisymme- tric structure with a high density in the equatorial plane. We have carried out numerical calculations of the interaction of a supernova with such an axisymme- tric density distribution. For small values of the angular density gradient at the pole, the asymmetry in the interaction shell is greater than, but close to, that expected from purely radial motion. If the angular density gradient is above a moderate value, the flow qualitatively changes and a protrusion emerges along the axis. For a power-law supernova density profile, the flow approaches a self-similar state in which the protrusion length is $2-4$ times the radius of the main shell. The critical density gradient is larger for steeper density profiles of the ejecta. Most of our calculations are axisymmetric, but we have carried out a 3-dimensional calculation to show that the protrusion is not a numerical artifact along the symmetry axis. For typical supernova parameters, the protrusions take $\gtrsim$ several years to develop. The appearance of the shell with protrusions is similar to that observed in VLBI radio images of the remnant 41.9 +58 in M82 and, possibly, of SN 1986J. We also considered the possibility of asymmetric ejecta and found that it had a relatively small effect on the asymmetry of the interaction region.Comment: 22 page postscript file (gzipped and uuencoded), 10 gzipped postscript figures may be retrieved from ftp://www.astro.su.se/pub/supernova/blc96_asym/ Submitted to Ap