The APR equation of state for simulations of supernovae, neutron stars and binary mergers

André da Silva Schneider, Constantinos Constantinou, Brian Muccioli, and Madappa Prakash

Submitted to Phys. Rev. C. Available on arXiv!


Differences in the equation of state (EOS) of dense matter translate into differences in astrophysical simulations and their multi-messenger signatures. Thus, extending the number of EOSs for astrophysical simulations allows us to probe the effect of different aspects of the EOS in astrophysical phenomena. In this work, we construct the EOS of hot and dense matter based on the Akmal, Pandharipande, and Ravenhall (APR) model and thereby extend the open-source SROEOS code which computes EOSs of hot dense matter for Skyrme-type parametrizations of the nuclear forces. Unlike Skrme-type models, in which parameters of the interaction are fit to reproduce the energy density of nuclear matter and/or properties of heavy nuclei, the EOS of APR is obtained from potentials resulting from fits to nucleon-nucleon scattering and properties of light nuclei. In addition, this EOS features a phase transition to a neutral pion condensate at supra-nuclear densities. We show that differences in the effective masses between EOSs have consequences for the properties of nuclei in the sub-nuclear inhomogeneous phase of matter. We also test the new EOS of APR in spherically symmetric core-collapse of massive stars with 15 and 40 solar mass stars, respectively. We find that the phase transition in the EOS of APR speeds up the collapse of the star. However, this phase transition does not generate a second shock wave or another neutrino burst as reported for the hadron-to-quark phase transition. The reason for this difference is that the onset of the phase transition in the EOS of APR occurs at larger densities than for the quark-to-hadron transition employed earlier which results in a significantly smaller softening of the high density EOS. 


APR EOS Source Code

The APR source code is released as open source under GPLv3. It is available from the following Bitbucket repository:


The master branch of this repository is the stable code that we recommend to the user. Along with the code comes an extensive user guide: https://bitbucket.org/andschn/apreos/src/master/User_Guide/User_Guide.pdf

If you run into problems using the code or have other questions or comments, please feel free to contact us at andre.schneider __at__ astro.su.se. We hope that you will find our code useful! Please feel free to send us bugfixes and any physics improvements that we can incorporate in future version. Also, please make reference to our paper should you use our code and resulting EOS tables in published work.

EOS Driver and Interpolation Routines

The APR EOS tables use the same overall HDF5 format introduced with the tables of O'Connor & Ott that are available at https://stellarcollapse.org/equationofstate. However, as you will be able to gather from the User Guide, the APR tables contain additional quantities. The standard driver and interpolation routines that we provide below are not set up to handle these. So should you need the new additional quantities, minor code changes are necessary. Also note that there is a difference in the definition of the speed of sound between our tables and those of O'Connor & Ott. We address this in Section 7 of the User Guide. 

EOS driver and interpolation routines for Fortran 90+: These routines are very old, not tuned for performance, and we do not recommend their use in a production code. They are available here:


The much better C/C++ routines are available here:


APR EOS Tables

We provide a set of pre-made EOS tables for the impatient user. For each parametrization, we provide pure SNA and SNA+NSE tables. All tables include photons, electrons, and positrons. Note that the tables are bz2 compressed must be decompressed before use. The standard resolution tables are about 550 MB in compressed state.

Tables can be found on Stockholm University BOX or in links to the individual tables below. 


EOS Variant Download link

APR pure SNA
APR with NSE (3335 nuclides)

APRLDP* with NSE (3335 nuclides)
NRAPR with NSE (3335 nuclides)
SkAPR pure SNA
SkAPR with NSE (3335 nuclides)

*APRLDP contains only the low density part of the APR parametrization.



This work was supported by the US National Science Foundation under awards TCAN AST-1333520, CAREER PHY-1151197, and PHY-1404569, and by the U.S. DOE grant. No. DE-FG02-93ER-40756. 

This work benefited from discussions at the 2018 INT-JINA Symposium on First multi-messenger observation of a neutron star merger and its implications for nuclear physics supported by the National Science Foundation under Grant No. PHY-1430152 (JINA Center for the Evolution of the Elements) as also from discussions at the 2018 N3AS collaboration meeting of the Research Hub for Fundamental Symmetries, Neutrinos, and Applications to Nuclear Astrophysics supported by the National Science Foundation, Grant PHY-1630782, and the Heising-Simons Foundation, Grant 2017-228.