Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models

We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of state we find that this system exhibits a type-I critical behaviour, thus confirming the conclusions reached by Liebling et al. [1] for rotating magnetized stars. Exploiting the relative simplicity of our system, we are able carry out a more in-depth study providing solid evidences of the criticality of this phenomenon and also to give a simple interpretation of the putative critical solution as a spherical solution with the unstable mode being the fundamental F-mode. Hence for any choice of the polytropic constant, the critical solution will distinguish the set of subcritical models migrating to the stable branch of the models of equilibrium from the set of subcritical models collapsing to a black hole. Finally, we study how the dynamics changes when the numerically perturbation is replaced by a finite-size, resolution independent velocity perturbation and show that in such cases a nearly-critical solution can be changed into either a sub or supercritical. The work reported here also lays the basis for the analysis carried in a companion paper, where the critical behaviour in the the head-on collision of two neutron stars is instead considered [2].Comment: 15 pages, 9 figure

An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates

A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity simulations at smaller computational costs and at considerably larger spatial resolutions. We here present a new flux-conservative formulation of the relativistic hydrodynamics equations in cylindrical coordinates. By rearranging those terms in the equations which are the sources of the largest numerical errors, the new formulation yields a global truncation error which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. We illustrate this through a series of numerical tests involving the evolution of oscillating spherical and rotating stars, as well as shock-tube tests.Comment: 19 pages, 9 figure

Molecular dissolved organic matter composition in lakes across Sweden as relative intensities of FT-ICR-MS peaks and PARAFAC components and optical indices

Whether intrinsic molecular properties or extrinsic factors such as environmental conditions control the decomposition of natural organic matter across soil, marine and freshwater systems has been subject to debate. Comprehensive evaluations of the controls that molecular structure exerts on organic matter's persistence in the environment have been precluded by organic matter's extreme complexity. Here we examine dissolved organic matter from 109 Swedish lakes using ultrahigh-resolution mass spectrometry and optical spectroscopy to investigate the constraints on its persistence in the environment. We find that degradation processes preferentially remove oxidized, aromatic compounds, whereas reduced, aliphatic and N-containing compounds are either resistant to degradation or tightly cycled and thus persist in aquatic systems. The patterns we observe for individual molecules are consistent with our measurements of emergent bulk characteristics of organic matter at wide geographic and temporal scales, as reflected by optical properties. We conclude that intrinsic molecular properties are an important control of overall organic matter reactivity