FBS solver:

Overview:

The code is written in C++, Cython and Python. The C++ part models the FBS star, integrates the differential equations involved and writes the results to files. There is also a cython wrapper included that wraps the C++ code in a more user friendly python experience and does simple plots. Lastly, there is a some python functionality for reading out the solutions generated by the C++ code, generating the stability curves and much prettier plots.

To compile, a call to

make

should suffice. If you want to only compile the c++ code without the Cython components, call

make fbs

In case dependencies are needed

sudo apt install libboost-dev
pip3 install numpy matplotlib cython pandas

The C++ structure

The file structure is as follows:

• vector.hpp: Defines a simple wrapper of a boost::vector for (mathematical) vectors.
• utilities.hpp: Collection of some utility functions that may be used in other files.
• integrator.hpp: Includes a Runge-Kutta-45-Fehlberg integrator that is accurate to 5th order with variable step size. The integrator allows to define events with an event_condition that will be checked for during the integration. Additional helber functions related to integrtion are also included.
• eos.hpp: Defines a model for different Equations of State. Preimplemented are a Polytropic EoS, a Causal EoS and an effective bosonic EoS for a massive self-interacting complex scalar field. Additional tabulated EoS can be read from files.
• nsmodel.hpp: Gives a base class for a star described by differential equations.
• fbs.hpp The FermionBosonStar class gives the logic and differential equations for an FBS in equilibrium.
• fbstln.hpp: The FBSTLN class extends the functionality to pertubations as described in the paper. The general idea is to first create a FermionBosonStar instance and integrate the equilibrium state, and from there create an instance of the TLN class to extend the computation. There are two conventions implemented, check the econvention branch.
• ns_twofluid.hpp: The NS_TWOFLUID class describes a star consisting of two minimally coupled fluids (each with their own EoS) in equilibrium.
• fbs_twofluid.hpp: A class derived from NS_TWOFLUID. Features custom initial conditions to use it together with the effective bosonic EoS.
• mr_curves.hpp: Defines functions to calculate lists of FBS with OMP support and write them to file.
• plotting.hpp: Allows to plot single integrations of stars. Only for debugging purposes, superseeded by the pyfbs implementation.
• matplotlibcpp.hpp: For aforementioned debugging purposes. Generally not used, only if specified in Makefile. Does not work together with pyfbs. See at the end for more info.

See the main.cpp for some examples of how to integrate a single star, or create an MR-curve.

The pyfbs structure

The pyfbs module contains a wrapper for the C++ files described above. This makes quick calculations and plots of single stars and curves much easier. See the pyfbs/TestFBS.ipynb file for some examples. Unfortunately, the cython wrapper (< version 3) misses some functionality, so usage requires modification of the cython library files as described here. There are also functions for loading the files written by the mr_curves.hpp functions, extracting the stability curves and making pretty plots out of them. See plotting.ipynb for some examples and generating the plots in our publication.

Publication

This code has been used in our publication. The data is generated with the pyfbs/generate_tables.py file, and plotted with the plotting.ipynb files.

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the CRC-TR 211 ’Strong-interaction matter under extreme conditions’– project number 31547758.

matplotlib-cpp

The code includes a modified version of the matplotlib-cpp library. See this for copyright and license purposes. The changes made include a wrapper for the plt::xscale, plt::yscale function included in matplotlib.