Instability windows of relativistic r-modes

The detectability of the gravitational-wave signal from $r$-modes depends on the interplay between the amplification of the mode by the CFS instability and its damping due to dissipative mechanisms present in the stellar matter. The instability window of $r$-modes describes the region of stellar parameters (angular velocity, $\Omega$, and redshifted stellar temperature, $T^\infty$), for which the mode is unstable. In this study, we reexamine this problem in nonbarotropic neutron stars, taking into account the previously overlooked nonanalytic behavior (in $\Omega$) of relativistic $r$-modes and enhanced energy dissipation resulting from diffusion in superconducting stellar matter. We demonstrate that at slow rotation rates, relativistic $r$-modes exhibit weaker amplification by the CFS instability compared to Newtonian ones. However, their dissipation through viscosity and diffusion is significantly more efficient. In rapidly rotating neutron stars within the framework of general relativity, the amplification of $r$-modes by the CFS mechanism and their damping due to shear viscosity become comparable to those predicted by Newtonian theory. In contrast, the relativistic damping of the mode by diffusion and bulk viscosity remains significantly stronger than in the nonrelativistic case. Consequently, account for diffusion and general relativity leads to a substantial modification of the $r$-mode instability window compared to the Newtonian prediction. This finding is important for the interpretation of observations of rotating neutron stars, as well as for overall understanding of $r$-mode physics.Comment: 21 pages, 8 figures, accepted for publication in Physical Review

Damping of sound waves in superfluid nucleon-hyperon matter of neutron stars

We consider sound waves in superfluid nucleon-hyperon matter of massive neutron-star cores. We calculate and analyze the speeds of sound modes and their damping times due to the shear viscosity and non-equilibrium weak processes of particle transformations. For that, we employ the dissipative relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated recently [M.E. Gusakov and E.M. Kantor, Phys. Rev. D78, 083006 (2008)]. We demonstrate that the damping times of sound modes calculated using this hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other by several orders of magnitude.Comment: 15 pages, 5 figures, Phys. Rev. D accepte

Bulk viscosity of superfluid hyperon stars

We calculated bulk viscosity due to non-equilibrium weak processes in superfluid nucleon-hyperon matter of neutron stars. For that, the dissipative relativistic hydrodynamics, formulated in paper [1] for superfluid mixtures, was extended to the case when both nucleons and hyperons are superfluid. It was demonstrated that in the most general case (when neutrons, protons, Lambda, and Sigma^{-} hyperons are superfluid), non-equilibrium weak processes generate sixteen bulk viscosity coefficients, with only three of them being independent. In addition, we corrected an inaccuracy in a widely used formula for the bulk viscosity of non-superfluid nucleon-hyperon matter.Comment: 22 pages, 2 figure

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data