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The Winter School "Computational Tools for Compact Stars Astrophysics" with a series of lectures
by experts in the field (see "school section"), 8-13 February.
1- STRUCTURE OF ROTATING NEUTRON STARS
Eric Gourgoulhon, LUTH, France.
Content of the lecture: here.
The framework for computing rotating stellar models within general relativity will be introduced. The equations governing the structure of compact stars will be derived from Einstein equations, under the assumptions of stationarity, axisymmetry and perfect fluid interior. The global properties of the stars (maximum mass, maximum angular velocity, last stable orbit, etc.) will be discussed, as well as the extension to the Einstein-Maxwell system for computing magnetized neutron stars. Lecture notes can be obtained from arxiv.org/abs/1003.5015.
Computational session: We propose to compute various models of rotating neutron stars by means of the RotStar code from the Lorene C++ library (http://www.lorene.obspm.fr/). The studies will be performed by changing the input parameters, as well as the equation of state, or the magnetic field configuration, and by producing various graphical outputs. For the students mostly interested by nuclear physics, the objective could be to implement a new equation of state (prepared e.g. during the EOS session of that School). For the students mostly interested by general relativity, the objective could be to compare two formulations for the equilibrium structure of compact stars, differing by the choice of space-time coordinates (e.g. quasi-isotropic coordinates and Dirac gauge).
2- RELATIVISTIC EQUATION OF STATE FOR HADRONIC AND QUARK MATTER
Stefan Typel, GSI, Germany, and Thomas Klähn, Univ. of Wroclaw.
Content of the lecture: here.
The lecture will cover the following topics: a model for hadron EoS (relativistic mean field theory with hyperons), a model for quark matter (NJL), and the description of the phase transition.
Computational session: a computer code solving the RMF equations in dense matter will be provided (in C).
3- COOLING OF NEUTRON STARS
Dany Page, UNAM, Mexico. (web page),
Content of the lecture: here.
The physical processes controlling the thermal evolution of a neutron star will be presented: neutrino emission, thermal conductivity and specific heat, as well as the occurrence of pairing and its effect on these physical processes. The possible internal heat sources from non-equilibrium processes will be presented, such as magnetic field decay, superfluid differential rotation and nuclear reactions induced by accretion.
Computational session: a 1D (spherical symmetry) NS cooling code will be presented. The code can model isolated cooling NSs as well as accreting ones, with continuous or transient accretion. The code solves for the whole temperature profile inside the star, crust and core, and allows observing in detail its evolution. This can include heating in the crust from pycnonuclear reactions induced by accretion and the relaxation of the crust/core when accretion stops.
4- MAGNETIC FIELDS IN COMPACT STARS
Jose Pons, University of Alicante, Spain.
Content of the lecture: here. (lect1, lect2),
In the first lecture it is described how B fields affect different astrophysical scenarios, as a general overview. Some emphasis is put on the different numerical tools needed and problems that appear in each case. The second lecture has a more technical content, focusing on magnetic diffusion and aspects of non-linear evolution in the EMHD case, which is the valid approximation for the crust of a neutron star.
Computational session: We will study a toy model (purely diffusion, without non-linear terms). The purpose of the session is to get familiar and work with a basic code to solve magnetic diffusion in this simplified toy model. We will study different regimes and explore the limitations of the code.
5- SOLUTIONS OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS (PDEs)
Luciano Rezzolla, AEI Golm, Germany. (web page)
Content of the lecture: here.
The lecture will give a brief introduction to the solution of hyperbolic PDEs such as those that are encountered when simulating the dynamics of neutron stars or fluids around compact objects.
Computational session: The computational session will be devoted to the practical implementation of the theory presented during the lecture and will allow the student to solve in 1D (and possibly in 2D) either linear and nonlinear equations such as the wave equation or the Burgers equation.
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