Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.Comment: 19 pages, 17 figure

Fast optimized Monte Carlo phase-space generation and dose prediction for low energy x-ray intra-operative radiation therapy

Low energy x-ray intra-operative radiation therapy (IORT) is used mostly for breast cancer treatment with spherical applicators. X-ray IORT treatment delivered during surgery (ex: INTRABEAM , Carl Zeiss) can benefit from accurate and fast dose prediction in a patient 3D volume. However, full Monte Carlo (MC) simulations are time-consuming and no commercial treatment planning system (TPS) was available for this treatment delivery technique. Therefore, the aim of this work is to develop a dose computation tool based on MC phase space information, which computes fast and accurate dose distributions for spherical and needle INTRABEAM applicators. First, a database of monoenergetic phase-space (PHSP) files and depth dose profiles (DDPs) in water for each applicator is generated at factory and stored for on-site use. During commissioning of a given INTRABEAM unit, the proposed fast and optimized phase-space (FOPS) generation process creates a phase-space at the exit of the applicator considered, by fitting the energy spectrum of the source to a combination of the monoenergetic precomputed phase-spaces, by means of a genetic algorithm, with simple experimental data of DDPs in water provided by the user. An in-house hybrid MC (HMC) algorithm which takes into account condensed history simulations of photoelectric, Rayleigh and Compton interactions for x-rays up to 1 MeV computes the dose from the optimized phase-space file. The whole process has been validated against radiochromic films in water as well as reference MC simulations performed with penEasy in heterogeneous phantoms. From the pre-computed monoenergetic PHSP files and DDPs, building the PHSP file optimized to a particular depth-dose curve in water only takes a few minutes in a single core ([email protected] GHz), for all the applicators considered in this work, and this needs to be done only when the x-ray source (XRS) is replaced. Once the phase-space file is ready, the HMC code is able to compute dose distributions within 10 min. For all the applicators, more than 95% of voxels from dose distributions computed with the FOPS+hybrid code agreed within 7%-0.5 mm with both reference MC simulations and measurements. The method proposed has been fully validated and it is now implemented into radiance (GMV SA, Spain), the first commercial IORT TPS