Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics

Conservative numerical schemes for general relativistic magnetohydrodynamics (GRMHD) require a method for transforming between ``conserved'' variables such as momentum and energy density and ``primitive'' variables such as rest-mass density, internal energy, and components of the four-velocity. The forward transformation (primitive to conserved) has a closed-form solution, but the inverse transformation (conserved to primitive) requires the solution of a set of five nonlinear equations. Here we discuss the mathematical properties of the inverse transformation and present six numerical methods for performing the inversion. The first method solves the full set of five nonlinear equations directly using a Newton-Raphson scheme and a guess from the previous timestep. The other methods reduce the five nonlinear equations to either one or two nonlinear equations that are solved numerically. Comparisons between the methods are made using a survey over phase space, a two-dimensional explosion problem, and a general relativistic MHD accretion disk simulation. The run-time of the methods is also examined. Code implementing the schemes is available for download on the web.Comment: Accepted to ApJ, 33 pages, 8 figures (color and greyscale), 1 machine-readable table (tab2.txt), code available at http://rainman.astro.uiuc.edu/codelib, a high-resolution and full-color PDF version is located at http://rainman.astro.uiuc.edu/codelib/codes/pvs_grmhd/ms.pd

Type II critical phenomena of neutron star collapse

We investigate spherically-symmetric, general relativistic systems of collapsing perfect fluid distributions. We consider neutron star models that are driven to collapse by the addition of an initially "in-going" velocity profile to the nominally static star solution. The neutron star models we use are Tolman-Oppenheimer-Volkoff solutions with an initially isentropic, gamma-law equation of state. The initial values of 1) the amplitude of the velocity profile, and 2) the central density of the star, span a parameter space, and we focus only on that region that gives rise to Type II critical behavior, wherein black holes of arbitrarily small mass can be formed. In contrast to previously published work, we find that--for a specific value of the adiabatic index (Gamma = 2)--the observed Type II critical solution has approximately the same scaling exponent as that calculated for an ultrarelativistic fluid of the same index. Further, we find that the critical solution computed using the ideal-gas equations of state asymptotes to the ultrarelativistic critical solution.Comment: 24 pages, 22 figures, RevTeX 4, submitted to Phys. Rev.

Relativistic Hydrodynamics around Black Holes and Horizon Adapted Coordinate Systems

Despite the fact that the Schwarzschild and Kerr solutions for the Einstein equations, when written in standard Schwarzschild and Boyer-Lindquist coordinates, present coordinate singularities, all numerical studies of accretion flows onto collapsed objects have been widely using them over the years. This approach introduces conceptual and practical complications in places where a smooth solution should be guaranteed, i.e., at the gravitational radius. In the present paper, we propose an alternative way of solving the general relativistic hydrodynamic equations in background (fixed) black hole spacetimes. We identify classes of coordinates in which the (possibly rotating) black hole metric is free of coordinate singularities at the horizon, independent of time, and admits a spacelike decomposition. In the spherically symmetric, non-rotating case, we re-derive exact solutions for dust and perfect fluid accretion in Eddington-Finkelstein coordinates, and compare with numerical hydrodynamic integrations. We perform representative axisymmetric computations. These demonstrations suggest that the use of those coordinate systems carries significant improvements over the standard approach, especially for higher dimensional studies.Comment: 10 pages, 4 postscript figures, accepted for publication in Phys. Rev.

Three Dimensional Numerical General Relativistic Hydrodynamics I: Formulations, Methods, and Code Tests

This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and convergence of our general relativistic hydrodynamic treatment and its coupling to the spacetime evolutions described by the full set of Einstein equations with a perfect fluid source. The numerical treatment of the general relativistic hydrodynamic equations is based on high resolution shock capturing schemes. These schemes rely on the characteristic information of the system. A spectral decomposition for general relativistic hydrodynamics suitable for a general spacetime metric is presented. Evolutions based on three different approximate Riemann solvers coupled to four different discretizations of the Einstein equations are studied and compared. The coupling between the hydrodynamics and the spacetime (the right and left hand side of the Einstein equations) is carried out in a treatment which is second order accurate in {\it both} space and time. Convergence tests for all twelve combinations with a variety of test beds are studied, showing consistency with the differential equations and correct convergence properties. The test-beds examined include shocktubes, Friedmann-Robertson-Walker cosmology tests, evolutions of self-gravitating compact (TOV) stars, and evolutions of relativistically boosted TOV stars. Special attention is paid to the numerical evolution of strongly gravitating objects, e.g., neutron stars, in the full theory of general relativity, including a simple, yet effective treatment for the surface region of the star (where the rest mass density is abruptly dropping to zero).Comment: 45 pages RevTeX, 34 figure

Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes

We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and fields are derived in the general case. A complete implementation of the formalism is developed in the case of spherical symmetry. The algorithm is tested in a number of different situations, predisposing for a range of possible applications. We consider the Riemann problem for a polytropic gas, with initial data given on a retarded/advanced time slice of Minkowski spacetime. We compute perfect fluid accretion onto a Schwarzschild black hole spacetime using ingoing null Eddington-Finkelstein coordinates. Tests of fluid evolution on dynamic background include constant density and TOV stars sliced along the radial null cones. Finally, we consider the accretion of self-gravitating matter onto a central black hole and the ensuing increase in the mass of the black hole horizon.Comment: 23 pages, 13 figures, submitted to Phys. Rev.

Hydrodynamics in full general relativity with conservative AMR

There is great interest in numerical relativity simulations involving matter due to the likelihood that binary compact objects involving neutron stars will be detected by gravitational wave observatories in the coming years, as well as to the possibility that binary compact object mergers could explain short-duration gamma-ray bursts. We present a code designed for simulations of hydrodynamics coupled to the Einstein field equations targeted toward such applications. This code has recently been used to study eccentric mergers of black hole-neutron star binaries. We evolve the fluid conservatively using high-resolution shock-capturing methods, while the field equations are solved in the generalized-harmonic formulation with finite differences. In order to resolve the various scales that may arise, we use adaptive mesh refinement (AMR) with grid hierarchies based on truncation error estimates. A noteworthy feature of this code is the implementation of the flux correction algorithm of Berger and Colella to ensure that the conservative nature of fluid advection is respected across AMR boundaries. We present various tests to compare the performance of different limiters and flux calculation methods, as well as to demonstrate the utility of AMR flux corrections.Comment: 22 pages, 14 figures; revised according referee comments, PRD in pres

Dynamical HII Region Evolution in Turbulent Molecular Clouds

We present numerical radiation-hydrodynamic simulations of the evolution of HII regions formed in an inhomogeneous medium resulting from turbulence simulations. We find that the filamentary structure of the underlying density distribution produces a highly irregular shape for the ionized region, in which the ionization front escapes to large distances in some directions within 80,000 years. In other directions, on the other hand, neutral gas in the form of dense globules persists within 1 parsec of the central star for the full duration of our simulation (400,000 years). Divergent photoablation flows from these globules maintain a root-mean-squared velocity in the ionized gas that is close to the ionized sound speed. Simulated images in optical emission lines show morphologies that are in strikingly detailed agreement with those observed in real HII regions.Comment: Minor changes to sync with accepted version. 7 pages, ApJ in press. Accompanying video available at http://ifront.org/wiki/Turbulent_Hii_Regions/Paper

Introducing the INSIGNIA project: environmental monitoring of pesticide use through honey bees

INSIGNIA aims to design and test an innovative, non-invasive, scientifically proven citizen science environmental monitoring protocol for the detection of pesticides by honey bees. It is a 30-month pilot project initiated and financed by the EC (PP-1-1-2018; EC SANTE). The study is being carried out by a consortium of specialists in honey bees, apiculture, statistics, analytics, modelling, extension, social science and citizen science from twelve countries. Honey bee colonies are excellent bio-samplers of biological material such as nectar, pollen and plant pathogens, as well as non-biological material such as pesticides or airborne contamination. Honey bee colonies forage over a circle of 1 km radius, increasing to several km if required, depending on the availability and attractiveness of food. All material collected is accumulated in the hive.The honey bee colony can provide four main matrices for environmental monitoring: bees, honey, pollen and wax. Because of the non-destructive remit of the project, for pesticides, pollen is the focal matrix and used as trapped pollen and beebread in this study. Although beeswax can be used as a passive sampler for pesticides, this matrix is not being used in INSIGNIA because of its polarity dependent absorbance, which limits the required wide range of pesticides to be monitored. Alternatively, two innovative non-biological matrices are being tested: i) the “Beehold tube”, a tube lined with the generic absorbent polyethylene-glycol PEG, through which hive-entering bees are forced to pass, and ii) the “APIStrip” (Absorbing Pesticides In-hive Strips) with a specific pesticide absorbent which is hung between the bee combs.Beebread and pollen collected in pollen traps are being sampled every two weeks to be analysed for pesticide residues and to record foraging conditions. Trapped pollen provides snapshots of the foraging conditions and contaminants on a single day. During the active season, the majority of beebread is consumed within days, so beebread provides recent, random sampling results. The Beehold tube and the APIStrips are present throughout the 2-weeks sampling periods in the beehive, absorbing and accumulating the incoming contaminants. The four matrices i.e. trapped pollen, beebread, Beehold tubes and APIStrips will be analysed for the presence of pesticides. The botanical origin of trapped pollen, beebread and pollen in the Beehold tubes will also be determined with an innovative molecular technique. Data on pollen and pesticide presence will then be combined to obtain information on foraging conditions and pesticide use, together with evaluation of the CORINE database for land use and pesticide legislation to model the exposure risks to honey bees and wild bees. All monitoring steps from sampling through to analysis will be studied and rigorously tested in four countries in Year 1, and the best practices will then be ring-tested in nine countries in Year 2. Information about the course of the project, its results and publications will be available on the INSIGNIA website www.insignia-bee.eu and via social media: on Facebook (https://www.facebook.com/insigniabee.eu/); Instagram insignia_bee); and Twitter (insignia_bee). Although the analyses of pesticide residues and pollen identification will not be completed until December 2019, in my talk I will present preliminary results of the Year 1 sampling.info:eu-repo/semantics/publishedVersio

Introducing the INSIGNIA project: Environmental monitoring of pesticides use through honey bees

INSIGNIA aims to design and test an innovative, non-invasive, scientifically proven citizen science environmental monitoring protocol for the detection of pesticides via honey bees. It is a pilot project initiated and financed by the European Commission (PP-1-1-2018; EC SANTE). The study is being carried out by a consortium of specialists in honey bees, apiculture, chemistry, molecular biology, statistics, analytics, modelling, extension, social science and citizen science from twelve countries. Honey bee colonies are excellent bio-samplers of biological material such as nectar, pollen and plant pathogens, as well as non-biological material such as pesticides or airborne contamination. Honey bee colonies forage over a circle of about 1 km radius, increasing to several km if required depending on the availability and attractiveness of food. All material collected is concentrated in the hive, and the honey bee colony can provide four main matrices for environmental monitoring: bees, honey, pollen and wax. For pesticides, pollen and wax are the focal matrices. Pollen collected in pollen traps will be sampled every two weeks to record foraging conditions. During the season, most of pollen is consumed within days, so beebread can provide recent, random sampling results. On the other hand wax acts as a passive sampler, building up an archive of pesticides that have entered the hive. Alternative in-hive passive samplers will be tested to replicate wax as a “pesticide-sponge”. Samples will be analysed for the presence of pesticides and the botanical origin of the pollen using an ITS2 DNA metabarcoding approach. Data on pollen and pesticides will be then be combined to obtain information on foraging conditions and pesticide use, together with evaluation of the CORINE database for land use and pesticide legislation to model the exposure risks to honey bees and wild bees. All monitoring steps from sampling through to analysis will be studied and tested in four countries in year 1, and the best practices will then be ring-tested in nine countries in year 2. Information about the course of the project and its results and publications will be available in the INSIGNIA website www.insignia-bee.eu.info:eu-repo/semantics/publishedVersio

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls