Equations of State of Hadronic Matter


The hadronic equations of state (EOSs) treat nucleonic (neutrons and protons) matter at zero or finite temperature. There are models which are easily written in terms of the neutron and proton densities:

and those which are more easily written in terms of the neutron and proton chemical potentials:

All of these EOSs are built on the base class eos_had_base, which includes several methods which apply to all of these models. For example, methods which calculate the saturation properties of nuclear matter. These methods are sometimes overloaded in descendants when exact formulas are available.

There is also a set of classes to modify the quartic term of the symmetry energy: eos_had_sym4_rmf, eos_had_sym4_apr, eos_had_sym4_skyrme, and eos_had_sym4_mdi all based on eos_had_sym4_base which can be used in eos_had_sym4.

Akmal-Pandharipande-Ravenhall EOS example

This example computes the APR EOS with eos_had_apr. It computes nuclear and neutron matter and then matter in beta-equilibrium with both a Maxwell construction (as done in the [Akmal98eo]) and a Gibbs construction to match the low- and high-density phases. Afterwards it computes the properties of neutron stars from the EOS. Most of the data is stored in table_units objects and then written to HDF files in the examples directory.

This example is rather lengthy and the full source code is not duplicated here. The class created in that example is documented at ex_eos_had_apr . The EOS and mass radius curves for APR created by this example and for the Skyrme model SLy4 from the next example is below. The third figure below is the Gibbs phase transition for APR.

_images/ex_eos_had_eos.png _images/ex_eos_had_mvsr.png _images/ex_eos_had_gibbs.png

Typical output:

Set output prefix to 'ex_eos_had_apr_' .

--------- Saturation properties --------------------

n_0: 1.598371e-01 fm^{-3}
E_B: -1.600066e+01 MeV
K: 2.659888e+02 MeV
S: 3.258870e+01 MeV
M^{*}/M: 6.982704e-01

--------- Nuclear matter ---------------------------

Mixed phase begins near nb=3.000000e-01 fm^{-3}.
Mixed phase ends near nb=3.440000e-01 fm^{-3}.
Generated file 'ex_eos_had_apr_nuc.o2'.

--------- Neutron matter ---------------------------

Mixed phase begins near nb=1.820000e-01 fm^{-3}.
Mixed phase ends near nb=2.120000e-01 fm^{-3}.
Generated file 'ex_eos_had_apr_neut.o2'.

--------- Neutron star matter ----------------------

Gibbs construction.
Mixed phase begins at nb=2.040000e-01 fm^{-3}.
Mixed phase ends at nb=2.380000e-01 fm^{-3}.

Estimate of transition density.
Without proton drip: density: 9.629128e-02 fm^{-3},
  pressure: 3.378590e-03 fm^{-4}.
9.241336e-02 3.398655e-08
3.473491e-03 3.432771e-09
9.193193e-02 -8.379045e-09
3.262481e-03 6.997727e-10
With proton drip: density: 9.588685e-02 fm^{-3},
  pressure: 3.341151e-03 fm^{-4}.

Generated file 'ex_eos_had_apr_nstar.o2'.

--------- TOV solver, M vs. R. ---------------------

Maximum mass is 2.191057e+00 solar masses.
Generated file 'ex_eos_had_apr_mvsr.o2'.

--------- TOV solver, 1.4 Msun ---------------------

Aprpoximate radius of a 1.4 solar mass neutron star is 1.151686e+01 km.
Generated file 'ex_eos_had_apr_m14.o2'.

5 tests performed.
All tests passed.

Skyrme EOS example

This example computes the EOS and neutron star properties using eos_had_skyrme from a Skyrme model.

This example is rather lengthy and the full source code is not duplicated here. The class created in that example is documented at ex_eos_had_skyrme .

Typical output:

Model: SLy4

n_0=1.595468e-01 fm^-3
E_B=-1.597407e+01 MeV
K=2.299218e+02 MeV
S=3.200056e+01 MeV
S2=3.268041e+01 MeV
L=4.594240e+01 MeV

Pressure increases and energy of neutrons is positive.

Low density neutron matter: 
6.000000e-02 8.000000e-01 9.785527e-01 4.379924e-02
1.400000e-01 6.700000e-01 9.442976e-01 2.301924e-01
2.600000e-01 5.700000e-01 8.857063e-01 7.461391e-01
5.400000e-01 5.200000e-01 7.297300e-01 2.694011e+00
Quality: 2.444527e-01

Starting calc_eos().
n_B         n_n         n_p         n_e         eps         P
[1/fm^3]    [1/fm^3]    [1/fm^3]    [1/fm^3]    [1/fm^4]    [1/fm^4]
5.00000e-02 4.86790e-02 1.32099e-03 1.32099e-03 2.39973e-01 7.63983e-04
6.00000e-02 5.81993e-02 1.80069e-03 1.80069e-03 2.88145e-01 1.03523e-03
7.00000e-02 6.76798e-02 2.32020e-03 2.32020e-03 3.36369e-01 1.38632e-03
8.00000e-02 7.71288e-02 2.87117e-03 2.87117e-03 3.84649e-01 1.83840e-03
9.00000e-02 8.65531e-02 3.44694e-03 3.44694e-03 4.32993e-01 2.41253e-03
1.00000e-01 9.59578e-02 4.04217e-03 4.04217e-03 4.81408e-01 3.12949e-03
1.10000e-01 1.05347e-01 4.65252e-03 4.65252e-03 5.29903e-01 4.00968e-03
1.20000e-01 1.14721e-01 5.27916e-03 5.27291e-03 5.78486e-01 5.07150e-03
1.30000e-01 1.23997e-01 6.00337e-03 5.87151e-03 6.27165e-01 6.30622e-03
1.40000e-01 1.33218e-01 6.78222e-03 6.45771e-03 6.75946e-01 7.74724e-03
1.50000e-01 1.42407e-01 7.59255e-03 7.03628e-03 7.24838e-01 9.42084e-03
1.60000e-01 1.51576e-01 8.42410e-03 7.60858e-03 7.73850e-01 1.13486e-02
1.70000e-01 1.60729e-01 9.27054e-03 8.17515e-03 8.22991e-01 1.35505e-02
1.80000e-01 1.69873e-01 1.01275e-02 8.73625e-03 8.72270e-01 1.60454e-02
1.90000e-01 1.79008e-01 1.09918e-02 9.29200e-03 9.21695e-01 1.88518e-02
2.00000e-01 1.88139e-01 1.18610e-02 9.84250e-03 9.71278e-01 2.19872e-02
2.10000e-01 1.97267e-01 1.27333e-02 1.03878e-02 1.02103e+00 2.54692e-02
2.20000e-01 2.06393e-01 1.36072e-02 1.09281e-02 1.07095e+00 2.93145e-02
2.30000e-01 2.15518e-01 1.44816e-02 1.14634e-02 1.12105e+00 3.35398e-02
2.40000e-01 2.24644e-01 1.53556e-02 1.19938e-02 1.17135e+00 3.81615e-02
2.50000e-01 2.33771e-01 1.62286e-02 1.25195e-02 1.22185e+00 4.31955e-02
2.60000e-01 2.42900e-01 1.71000e-02 1.30406e-02 1.27256e+00 4.86577e-02
2.70000e-01 2.52031e-01 1.79695e-02 1.35573e-02 1.32348e+00 5.45635e-02
2.80000e-01 2.61163e-01 1.88368e-02 1.40697e-02 1.37464e+00 6.09285e-02
2.90000e-01 2.70298e-01 1.97018e-02 1.45781e-02 1.42602e+00 6.77676e-02
3.00000e-01 2.79436e-01 2.05644e-02 1.50826e-02 1.47766e+00 7.50960e-02
3.10000e-01 2.88575e-01 2.14246e-02 1.55835e-02 1.52954e+00 8.29283e-02
3.20000e-01 2.97717e-01 2.22825e-02 1.60810e-02 1.58169e+00 9.12792e-02
3.30000e-01 3.06862e-01 2.31382e-02 1.65753e-02 1.63411e+00 1.00163e-01
3.40000e-01 3.16008e-01 2.39919e-02 1.70666e-02 1.68680e+00 1.09595e-01
3.50000e-01 3.25156e-01 2.48437e-02 1.75553e-02 1.73978e+00 1.19588e-01
3.60000e-01 3.34306e-01 2.56940e-02 1.80415e-02 1.79305e+00 1.30156e-01
3.70000e-01 3.43457e-01 2.65430e-02 1.85256e-02 1.84663e+00 1.41315e-01
3.80000e-01 3.52609e-01 2.73910e-02 1.90077e-02 1.90051e+00 1.53076e-01
3.90000e-01 3.61762e-01 2.82383e-02 1.94882e-02 1.95472e+00 1.65455e-01
4.00000e-01 3.70915e-01 2.90854e-02 1.99674e-02 2.00924e+00 1.78464e-01
4.10000e-01 3.80067e-01 2.99325e-02 2.04454e-02 2.06410e+00 1.92118e-01
4.20000e-01 3.89220e-01 3.07802e-02 2.09226e-02 2.11930e+00 2.06429e-01
4.30000e-01 3.98371e-01 3.16287e-02 2.13993e-02 2.17485e+00 2.21410e-01
4.40000e-01 4.07521e-01 3.24785e-02 2.18758e-02 2.23076e+00 2.37075e-01
4.50000e-01 4.16670e-01 3.33301e-02 2.23523e-02 2.28703e+00 2.53437e-01
4.60000e-01 4.25816e-01 3.41840e-02 2.28291e-02 2.34367e+00 2.70509e-01
4.70000e-01 4.34960e-01 3.50405e-02 2.33065e-02 2.40069e+00 2.88304e-01
4.80000e-01 4.44100e-01 3.59001e-02 2.37849e-02 2.45810e+00 3.06833e-01
4.90000e-01 4.53237e-01 3.67634e-02 2.42645e-02 2.51590e+00 3.26111e-01
5.00000e-01 4.62369e-01 3.76308e-02 2.47455e-02 2.57410e+00 3.46149e-01
5.10000e-01 4.71497e-01 3.85028e-02 2.52284e-02 2.63272e+00 3.66960e-01
5.20000e-01 4.80620e-01 3.93800e-02 2.57133e-02 2.69174e+00 3.88556e-01
5.30000e-01 4.89737e-01 4.02627e-02 2.62007e-02 2.75119e+00 4.10949e-01
5.40000e-01 4.98848e-01 4.11515e-02 2.66907e-02 2.81107e+00 4.34152e-01
5.50000e-01 5.07953e-01 4.20470e-02 2.71837e-02 2.87139e+00 4.58177e-01
5.60000e-01 5.17050e-01 4.29497e-02 2.76799e-02 2.93215e+00 4.83035e-01
5.70000e-01 5.26140e-01 4.38600e-02 2.81797e-02 2.99336e+00 5.08739e-01
5.80000e-01 5.35221e-01 4.47786e-02 2.86834e-02 3.05503e+00 5.35300e-01
5.90000e-01 5.44294e-01 4.57059e-02 2.91913e-02 3.11717e+00 5.62730e-01
6.00000e-01 5.53358e-01 4.66424e-02 2.97035e-02 3.17977e+00 5.91041e-01
6.10000e-01 5.62411e-01 4.75887e-02 3.02206e-02 3.24286e+00 6.20243e-01
6.20000e-01 5.71455e-01 4.85454e-02 3.07426e-02 3.30644e+00 6.50349e-01
6.30000e-01 5.80487e-01 4.95129e-02 3.12700e-02 3.37050e+00 6.81369e-01
6.40000e-01 5.89508e-01 5.04918e-02 3.18030e-02 3.43507e+00 7.13316e-01
6.50000e-01 5.98517e-01 5.14826e-02 3.23419e-02 3.50014e+00 7.46199e-01
6.60000e-01 6.07514e-01 5.24859e-02 3.28870e-02 3.56573e+00 7.80031e-01
6.70000e-01 6.16498e-01 5.35022e-02 3.34386e-02 3.63183e+00 8.14821e-01
6.80000e-01 6.25468e-01 5.45321e-02 3.39970e-02 3.69847e+00 8.50580e-01
6.90000e-01 6.34424e-01 5.55760e-02 3.45624e-02 3.76563e+00 8.87321e-01
7.00000e-01 6.43365e-01 5.66345e-02 3.51352e-02 3.83334e+00 9.25052e-01
7.10000e-01 6.52292e-01 5.77083e-02 3.57156e-02 3.90159e+00 9.63784e-01
7.20000e-01 6.61202e-01 5.87977e-02 3.63040e-02 3.97039e+00 1.00353e+00
7.30000e-01 6.70097e-01 5.99033e-02 3.69005e-02 4.03975e+00 1.04429e+00
7.40000e-01 6.78974e-01 6.10258e-02 3.75056e-02 4.10968e+00 1.08609e+00
7.50000e-01 6.87834e-01 6.21655e-02 3.81194e-02 4.18018e+00 1.12893e+00
7.60000e-01 6.96677e-01 6.33231e-02 3.87423e-02 4.25126e+00 1.17283e+00
7.70000e-01 7.05501e-01 6.44991e-02 3.93745e-02 4.32292e+00 1.21778e+00
7.80000e-01 7.14306e-01 6.56940e-02 4.00163e-02 4.39518e+00 1.26381e+00
7.90000e-01 7.23092e-01 6.69083e-02 4.06680e-02 4.46803e+00 1.31092e+00
8.00000e-01 7.31857e-01 6.81426e-02 4.13299e-02 4.54148e+00 1.35912e+00
8.10000e-01 7.40603e-01 6.93974e-02 4.20022e-02 4.61555e+00 1.40842e+00
8.20000e-01 7.49327e-01 7.06733e-02 4.26852e-02 4.69022e+00 1.45883e+00
8.30000e-01 7.58029e-01 7.19707e-02 4.33791e-02 4.76552e+00 1.51036e+00
8.40000e-01 7.66710e-01 7.32901e-02 4.40844e-02 4.84145e+00 1.56302e+00
8.50000e-01 7.75368e-01 7.46322e-02 4.48011e-02 4.91801e+00 1.61681e+00
8.60000e-01 7.84003e-01 7.59974e-02 4.55296e-02 4.99522e+00 1.67175e+00
8.70000e-01 7.92614e-01 7.73863e-02 4.62702e-02 5.07306e+00 1.72785e+00
8.80000e-01 8.01201e-01 7.87992e-02 4.70230e-02 5.15156e+00 1.78511e+00
8.90000e-01 8.09763e-01 8.02368e-02 4.77884e-02 5.23072e+00 1.84354e+00
9.00000e-01 8.18300e-01 8.16996e-02 4.85666e-02 5.31053e+00 1.90315e+00
9.10000e-01 8.26812e-01 8.31881e-02 4.93579e-02 5.39102e+00 1.96394e+00
9.20000e-01 8.35297e-01 8.47026e-02 5.01626e-02 5.47218e+00 2.02594e+00
9.30000e-01 8.43756e-01 8.62438e-02 5.09807e-02 5.55403e+00 2.08914e+00
9.40000e-01 8.52188e-01 8.78122e-02 5.18127e-02 5.63655e+00 2.15355e+00
9.50000e-01 8.60592e-01 8.94082e-02 5.26588e-02 5.71977e+00 2.21918e+00
9.60000e-01 8.68968e-01 9.10322e-02 5.35191e-02 5.80369e+00 2.28604e+00
9.70000e-01 8.77315e-01 9.26848e-02 5.43940e-02 5.88831e+00 2.35414e+00
9.80000e-01 8.85634e-01 9.43664e-02 5.52837e-02 5.97364e+00 2.42348e+00
9.90000e-01 8.93922e-01 9.60776e-02 5.61883e-02 6.05968e+00 2.49407e+00
1.00000e+00 9.02181e-01 9.78186e-02 5.71082e-02 6.14645e+00 2.56592e+00
1.01000e+00 9.10410e-01 9.95900e-02 5.80435e-02 6.23393e+00 2.63903e+00
1.02000e+00 9.18608e-01 1.01392e-01 5.89945e-02 6.32215e+00 2.71341e+00
1.03000e+00 9.26774e-01 1.03226e-01 5.99614e-02 6.41110e+00 2.78908e+00
1.04000e+00 9.34909e-01 1.05091e-01 6.09444e-02 6.50080e+00 2.86602e+00
1.05000e+00 9.43012e-01 1.06988e-01 6.19437e-02 6.59124e+00 2.94426e+00
1.06000e+00 9.51082e-01 1.08918e-01 6.29595e-02 6.68243e+00 3.02380e+00
1.07000e+00 9.59119e-01 1.10881e-01 6.39919e-02 6.77437e+00 3.10464e+00
1.08000e+00 9.67123e-01 1.12877e-01 6.50413e-02 6.86708e+00 3.18680e+00
1.09000e+00 9.75093e-01 1.14907e-01 6.61078e-02 6.96056e+00 3.27027e+00
1.10000e+00 9.83030e-01 1.16970e-01 6.71915e-02 7.05481e+00 3.35506e+00
1.11000e+00 9.90931e-01 1.19069e-01 6.82927e-02 7.14983e+00 3.44119e+00
1.12000e+00 9.98799e-01 1.21201e-01 6.94115e-02 7.24564e+00 3.52864e+00
1.13000e+00 1.00663e+00 1.23370e-01 7.05481e-02 7.34223e+00 3.61744e+00
1.14000e+00 1.01443e+00 1.25573e-01 7.17026e-02 7.43961e+00 3.70759e+00
1.15000e+00 1.02219e+00 1.27812e-01 7.28753e-02 7.53780e+00 3.79909e+00
1.16000e+00 1.02991e+00 1.30088e-01 7.40662e-02 7.63678e+00 3.89195e+00
1.17000e+00 1.03760e+00 1.32399e-01 7.52755e-02 7.73657e+00 3.98617e+00
1.18000e+00 1.04525e+00 1.34748e-01 7.65033e-02 7.83717e+00 4.08175e+00
1.19000e+00 1.05287e+00 1.37133e-01 7.77498e-02 7.93859e+00 4.17871e+00
1.20000e+00 1.06044e+00 1.39556e-01 7.90151e-02 8.04082e+00 4.27705e+00
1.21000e+00 1.06798e+00 1.42016e-01 8.02993e-02 8.14389e+00 4.37678e+00
1.22000e+00 1.07549e+00 1.44513e-01 8.16026e-02 8.24778e+00 4.47789e+00
1.23000e+00 1.08295e+00 1.47049e-01 8.29250e-02 8.35251e+00 4.58039e+00
1.24000e+00 1.09038e+00 1.49623e-01 8.42666e-02 8.45807e+00 4.68429e+00
1.25000e+00 1.09777e+00 1.52235e-01 8.56276e-02 8.56448e+00 4.78960e+00
1.26000e+00 1.10512e+00 1.54885e-01 8.70079e-02 8.67174e+00 4.89631e+00
1.27000e+00 1.11243e+00 1.57574e-01 8.84078e-02 8.77985e+00 5.00443e+00
1.28000e+00 1.11970e+00 1.60302e-01 8.98272e-02 8.88881e+00 5.11397e+00
1.29000e+00 1.12693e+00 1.63069e-01 9.12663e-02 8.99864e+00 5.22493e+00
1.30000e+00 1.13412e+00 1.65875e-01 9.27250e-02 9.10934e+00 5.33732e+00
1.31000e+00 1.14128e+00 1.68720e-01 9.42035e-02 9.22090e+00 5.45113e+00
1.32000e+00 1.14840e+00 1.71605e-01 9.57017e-02 9.33334e+00 5.56638e+00
1.33000e+00 1.15547e+00 1.74529e-01 9.72198e-02 9.44665e+00 5.68306e+00
1.34000e+00 1.16251e+00 1.77492e-01 9.87577e-02 9.56085e+00 5.80118e+00
1.35000e+00 1.16951e+00 1.80495e-01 1.00315e-01 9.67594e+00 5.92075e+00
1.36000e+00 1.17646e+00 1.83537e-01 1.01893e-01 9.79192e+00 6.04177e+00
1.37000e+00 1.18338e+00 1.86619e-01 1.03491e-01 9.90879e+00 6.16424e+00
1.38000e+00 1.19026e+00 1.89740e-01 1.05108e-01 1.00266e+01 6.28817e+00
1.39000e+00 1.19710e+00 1.92902e-01 1.06745e-01 1.01452e+01 6.41356e+00
1.40000e+00 1.20390e+00 1.96102e-01 1.08402e-01 1.02648e+01 6.54041e+00
1.41000e+00 1.21066e+00 1.99342e-01 1.10079e-01 1.03853e+01 6.66873e+00
1.42000e+00 1.21738e+00 2.02622e-01 1.11776e-01 1.05067e+01 6.79852e+00
1.43000e+00 1.22406e+00 2.05941e-01 1.13493e-01 1.06290e+01 6.92979e+00
1.44000e+00 1.23070e+00 2.09299e-01 1.15229e-01 1.07523e+01 7.06253e+00
1.45000e+00 1.23730e+00 2.12697e-01 1.16985e-01 1.08765e+01 7.19676e+00
1.46000e+00 1.24387e+00 2.16134e-01 1.18760e-01 1.10016e+01 7.33248e+00
1.47000e+00 1.25039e+00 2.19609e-01 1.20555e-01 1.11276e+01 7.46969e+00
1.48000e+00 1.25688e+00 2.23124e-01 1.22370e-01 1.12546e+01 7.60838e+00
1.49000e+00 1.26332e+00 2.26677e-01 1.24204e-01 1.13825e+01 7.74858e+00
1.50000e+00 1.26973e+00 2.30269e-01 1.26057e-01 1.15114e+01 7.89028e+00
1.51000e+00 1.27610e+00 2.33900e-01 1.27930e-01 1.16412e+01 8.03348e+00
1.52000e+00 1.28243e+00 2.37569e-01 1.29821e-01 1.17720e+01 8.17819e+00
1.53000e+00 1.28872e+00 2.41275e-01 1.31732e-01 1.19037e+01 8.32441e+00
1.54000e+00 1.29498e+00 2.45020e-01 1.33661e-01 1.20364e+01 8.47214e+00
1.55000e+00 1.30120e+00 2.48802e-01 1.35610e-01 1.21701e+01 8.62140e+00
1.56000e+00 1.30738e+00 2.52622e-01 1.37577e-01 1.23047e+01 8.77217e+00
1.57000e+00 1.31352e+00 2.56478e-01 1.39562e-01 1.24403e+01 8.92447e+00
1.58000e+00 1.31963e+00 2.60372e-01 1.41566e-01 1.25769e+01 9.07830e+00
1.59000e+00 1.32570e+00 2.64302e-01 1.43588e-01 1.27144e+01 9.23366e+00
1.60000e+00 1.33173e+00 2.68269e-01 1.45629e-01 1.28529e+01 9.39056e+00
1.61000e+00 1.33773e+00 2.72272e-01 1.47687e-01 1.29925e+01 9.54900e+00
1.62000e+00 1.34369e+00 2.76310e-01 1.49763e-01 1.31330e+01 9.70898e+00
1.63000e+00 1.34962e+00 2.80384e-01 1.51857e-01 1.32745e+01 9.87051e+00
1.64000e+00 1.35551e+00 2.84493e-01 1.53969e-01 1.34170e+01 1.00336e+01
1.65000e+00 1.36136e+00 2.88637e-01 1.56097e-01 1.35604e+01 1.01982e+01
1.66000e+00 1.36718e+00 2.92816e-01 1.58243e-01 1.37049e+01 1.03644e+01
1.67000e+00 1.37297e+00 2.97029e-01 1.60406e-01 1.38504e+01 1.05322e+01
1.68000e+00 1.37872e+00 3.01276e-01 1.62586e-01 1.39969e+01 1.07015e+01
1.69000e+00 1.38444e+00 3.05556e-01 1.64783e-01 1.41445e+01 1.08724e+01
1.70000e+00 1.39013e+00 3.09869e-01 1.66996e-01 1.42930e+01 1.10448e+01
1.71000e+00 1.39578e+00 3.14216e-01 1.69225e-01 1.44426e+01 1.12189e+01
1.72000e+00 1.40141e+00 3.18594e-01 1.71471e-01 1.45931e+01 1.13945e+01
1.73000e+00 1.40699e+00 3.23005e-01 1.73732e-01 1.47447e+01 1.15717e+01
1.74000e+00 1.41255e+00 3.27448e-01 1.76009e-01 1.48974e+01 1.17505e+01
1.75000e+00 1.41808e+00 3.31921e-01 1.78302e-01 1.50510e+01 1.19309e+01
1.76000e+00 1.42357e+00 3.36426e-01 1.80610e-01 1.52057e+01 1.21129e+01
1.77000e+00 1.42904e+00 3.40962e-01 1.82933e-01 1.53615e+01 1.22965e+01
1.78000e+00 1.43447e+00 3.45527e-01 1.85272e-01 1.55183e+01 1.24817e+01
1.79000e+00 1.43988e+00 3.50122e-01 1.87624e-01 1.56761e+01 1.26685e+01
1.80000e+00 1.44525e+00 3.54747e-01 1.89992e-01 1.58350e+01 1.28569e+01
1.81000e+00 1.45060e+00 3.59401e-01 1.92374e-01 1.59949e+01 1.30469e+01
1.82000e+00 1.45592e+00 3.64083e-01 1.94770e-01 1.61559e+01 1.32385e+01
1.83000e+00 1.46121e+00 3.68793e-01 1.97180e-01 1.63179e+01 1.34318e+01
1.84000e+00 1.46647e+00 3.73531e-01 1.99603e-01 1.64810e+01 1.36267e+01
1.85000e+00 1.47170e+00 3.78297e-01 2.02040e-01 1.66452e+01 1.38233e+01
1.86000e+00 1.47691e+00 3.83089e-01 2.04491e-01 1.68104e+01 1.40215e+01
1.87000e+00 1.48209e+00 3.87908e-01 2.06954e-01 1.69767e+01 1.42213e+01
1.88000e+00 1.48725e+00 3.92753e-01 2.09431e-01 1.71441e+01 1.44227e+01
1.89000e+00 1.49238e+00 3.97624e-01 2.11920e-01 1.73125e+01 1.46259e+01
1.90000e+00 1.49748e+00 4.02520e-01 2.14422e-01 1.74820e+01 1.48306e+01
1.91000e+00 1.50256e+00 4.07440e-01 2.16936e-01 1.76526e+01 1.50371e+01
1.92000e+00 1.50761e+00 4.12386e-01 2.19462e-01 1.78243e+01 1.52452e+01
1.93000e+00 1.51264e+00 4.17355e-01 2.22000e-01 1.79971e+01 1.54550e+01
1.94000e+00 1.51765e+00 4.22348e-01 2.24549e-01 1.81710e+01 1.56664e+01
1.95000e+00 1.52264e+00 4.27365e-01 2.27110e-01 1.83460e+01 1.58795e+01
1.96000e+00 1.52760e+00 4.32404e-01 2.29682e-01 1.85220e+01 1.60944e+01
1.97000e+00 1.53253e+00 4.37465e-01 2.32265e-01 1.86992e+01 1.63108e+01
1.98000e+00 1.53745e+00 4.42549e-01 2.34860e-01 1.88775e+01 1.65290e+01
1.99000e+00 1.54235e+00 4.47654e-01 2.37464e-01 1.90568e+01 1.67489e+01
2.00000e+00 1.54722e+00 4.52781e-01 2.40079e-01 1.92373e+01 1.69705e+01
 ix ed           pr           cs2
  0 2.399735e-01 7.639827e-04 5.301871e-03
  1 2.881453e-01 1.035234e-03 6.288984e-03
  2 3.363685e-01 1.386323e-03 8.275365e-03
  3 3.846488e-01 1.838402e-03 1.054078e-02
  4 4.329927e-01 2.412530e-03 1.327846e-02
  5 4.814081e-01 3.129487e-03 1.639626e-02
  6 5.299031e-01 4.009676e-03 2.000956e-02
  7 5.784861e-01 5.071503e-03 2.358014e-02
  8 6.271646e-01 6.306221e-03 2.732870e-02
  9 6.759458e-01 7.747239e-03 3.181610e-02
 10 7.248379e-01 9.420841e-03 3.671438e-02
 11 7.738499e-01 1.134861e-02 4.200946e-02
 12 8.229908e-01 1.355049e-02 4.766085e-02
 13 8.722696e-01 1.604544e-02 5.364938e-02
 14 9.216955e-01 1.885177e-02 5.995609e-02
 15 9.712776e-01 2.198724e-02 6.656517e-02
 16 1.021025e+00 2.546916e-02 7.346192e-02
 17 1.070947e+00 2.931449e-02 8.063267e-02
 18 1.121052e+00 3.353983e-02 8.806445e-02
 19 1.171349e+00 3.816149e-02 9.574489e-02
 20 1.221847e+00 4.319550e-02 1.036621e-01
 21 1.272555e+00 4.865767e-02 1.118045e-01
 22 1.323482e+00 5.456354e-02 1.201610e-01
 23 1.374636e+00 6.092848e-02 1.287208e-01
 24 1.426025e+00 6.776763e-02 1.374733e-01
 25 1.477659e+00 7.509597e-02 1.464083e-01
 26 1.529545e+00 8.292829e-02 1.555158e-01
 27 1.581692e+00 9.127921e-02 1.647860e-01
 28 1.634108e+00 1.001632e-01 1.742094e-01
 29 1.686802e+00 1.095947e-01 1.837767e-01
 30 1.739781e+00 1.195877e-01 1.934789e-01
 31 1.793054e+00 1.301564e-01 2.033070e-01
 32 1.846629e+00 1.413147e-01 2.132525e-01
 33 1.900513e+00 1.530763e-01 2.233070e-01
 34 1.954715e+00 1.654550e-01 2.334621e-01
 35 2.009243e+00 1.784644e-01 2.437100e-01
 36 2.064103e+00 1.921178e-01 2.540427e-01
 37 2.119305e+00 2.064286e-01 2.644528e-01
 38 2.174855e+00 2.214101e-01 2.749326e-01
 39 2.230761e+00 2.370754e-01 2.854752e-01
 40 2.287032e+00 2.534375e-01 2.960734e-01
 41 2.343674e+00 2.705093e-01 3.067204e-01
 42 2.400695e+00 2.883036e-01 3.174096e-01
 43 2.458102e+00 3.068332e-01 3.281345e-01
 44 2.515903e+00 3.261107e-01 3.388890e-01
 45 2.574105e+00 3.461487e-01 3.496669e-01
 46 2.632715e+00 3.669595e-01 3.604624e-01
 47 2.691741e+00 3.885555e-01 3.712698e-01
 48 2.751191e+00 4.109490e-01 3.820836e-01
 49 2.811070e+00 4.341521e-01 3.928984e-01
 50 2.871386e+00 4.581768e-01 4.037092e-01
 51 2.932147e+00 4.830352e-01 4.145109e-01
 52 2.993359e+00 5.087390e-01 4.252988e-01
 53 3.055030e+00 5.353001e-01 4.360682e-01
 54 3.117166e+00 5.627301e-01 4.468146e-01
 55 3.179775e+00 5.910406e-01 4.575338e-01
 56 3.242862e+00 6.202430e-01 4.682217e-01
 57 3.306436e+00 6.503489e-01 4.788742e-01
 58 3.370503e+00 6.813695e-01 4.894876e-01
 59 3.435069e+00 7.133158e-01 5.000582e-01
 60 3.500142e+00 7.461992e-01 5.105825e-01
 61 3.565728e+00 7.800305e-01 5.210571e-01
 62 3.631834e+00 8.148207e-01 5.314789e-01
 63 3.698466e+00 8.505804e-01 5.418447e-01
 64 3.765632e+00 8.873206e-01 5.521516e-01
 65 3.833337e+00 9.250516e-01 5.623968e-01
 66 3.901588e+00 9.637841e-01 5.725777e-01
 67 3.970392e+00 1.003528e+00 5.826917e-01
 68 4.039754e+00 1.044295e+00 5.927364e-01
 69 4.109683e+00 1.086093e+00 6.027096e-01
 70 4.180183e+00 1.128934e+00 6.126090e-01
 71 4.251261e+00 1.172828e+00 6.224326e-01
 72 4.322924e+00 1.217783e+00 6.321785e-01
 73 4.395178e+00 1.263811e+00 6.418448e-01
 74 4.468029e+00 1.310920e+00 6.514299e-01
 75 4.541482e+00 1.359120e+00 6.609321e-01
 76 4.615546e+00 1.408420e+00 6.703499e-01
 77 4.690224e+00 1.458830e+00 6.796819e-01
 78 4.765525e+00 1.510360e+00 6.889268e-01
 79 4.841453e+00 1.563017e+00 6.980833e-01
 80 4.918014e+00 1.616812e+00 7.071504e-01
 81 4.995215e+00 1.671752e+00 7.161270e-01
 82 5.073062e+00 1.727847e+00 7.250122e-01
 83 5.151560e+00 1.785105e+00 7.338050e-01
 84 5.230715e+00 1.843535e+00 7.425047e-01
 85 5.310534e+00 1.903145e+00 7.511106e-01
 86 5.391021e+00 1.963944e+00 7.596220e-01
 87 5.472183e+00 2.025939e+00 7.680384e-01
 88 5.554026e+00 2.089139e+00 7.763593e-01
 89 5.636554e+00 2.153551e+00 7.845842e-01
 90 5.719774e+00 2.219184e+00 7.927128e-01
 91 5.803692e+00 2.286045e+00 8.007449e-01
 92 5.888312e+00 2.354141e+00 8.086801e-01
 93 5.973641e+00 2.423480e+00 8.165183e-01
 94 6.059684e+00 2.494070e+00 8.242594e-01
 95 6.146446e+00 2.565917e+00 8.319034e-01
 96 6.233933e+00 2.639029e+00 8.394503e-01
 97 6.322150e+00 2.713413e+00 8.469001e-01
 98 6.411103e+00 2.789075e+00 8.542529e-01
 99 6.500796e+00 2.866022e+00 8.615090e-01
100 6.591236e+00 2.944262e+00 8.686684e-01
101 6.682427e+00 3.023800e+00 8.757315e-01
102 6.774374e+00 3.104642e+00 8.826987e-01
103 6.867083e+00 3.186796e+00 8.895701e-01
104 6.960558e+00 3.270267e+00 8.963463e-01
105 7.054806e+00 3.355061e+00 9.030276e-01
106 7.149830e+00 3.441185e+00 9.096146e-01
107 7.245637e+00 3.528644e+00 9.161077e-01
108 7.342230e+00 3.617444e+00 9.225075e-01
109 7.439615e+00 3.707591e+00 9.288146e-01
110 7.537797e+00 3.799090e+00 9.350297e-01
111 7.636780e+00 3.891946e+00 9.411533e-01
112 7.736569e+00 3.986166e+00 9.471862e-01
113 7.837170e+00 4.081753e+00 9.531291e-01
114 7.938587e+00 4.178714e+00 9.589828e-01
115 8.040824e+00 4.277054e+00 9.647479e-01
116 8.143886e+00 4.376777e+00 9.704254e-01
117 8.247778e+00 4.477888e+00 9.760161e-01
118 8.352505e+00 4.580393e+00 9.815208e-01
119 8.458071e+00 4.684295e+00 9.869405e-01
120 8.564480e+00 4.789599e+00 9.922759e-01
121 8.671738e+00 4.896311e+00 9.975282e-01
122 8.779848e+00 5.004434e+00 1.002698e+00
The EOS is acausal at nb=1.264761e+00, ed=8.723107e+00, pr=4.947617e+00 .
Going to Urca, pass 1: 
Computing adiabatic index: 
Going to Urca, pass 2: 
Urca allowed at 1.416537e+00 fm^{-3}.
Done with calc_eos().

Neutron stars:
M_{max} = 2.050125e+00 R_{max} = 1.004302e+01 cent. density = 1.187992e+00
R_{1.4} = 1.173887e+01 cent. density = 5.348790e-01

3 tests performed.
All tests passed.