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:
eos_had_potential, and
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.
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 1.151767e+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
----------------------------------------------------------------------------
Saturation:
n_0=1.595468e-01 fm^-3
E_B=-1.597407e+01 MeV
K=2.299218e+02 MeV
M^*/M=6.946339e-01
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
EOS:
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.
RMF EOS example¶
This example computes the “FSUGold” EOS and neutron star properties using eos_had_rmf from a Rmf model.
Source code:
/* Example: ex_eos_had_rmf.cpp
-------------------------------------------------------------------
A simple example for an RMF EOS. See "License Information"
section of the documentation for license information.
*/
#include <o2scl/test_mgr.h>
#include <o2scl/eos_had_rmf.h>
#include <o2scl/nstar_cold.h>
#include <o2scl/hdf_eos_io.h>
#include <o2scl/fermion_deriv_rel.h>
using namespace std;
using namespace o2scl;
using namespace o2scl_hdf;
using namespace o2scl_const;
int main(void) {
cout.setf(ios::scientific);
test_mgr t;
t.set_output_level(2);
eos_had_rmf re;
re.def_sat_mroot.def_jac.set_epsrel(1.0e-6);
re.def_sat_mroot.def_jac.set_epsmin(1.0e-15);
re.def_sat_mroot.ntrial*=10;
rmf_load(re,"FSUGold");
cout << re.ms << " " << re.mw << " " << re.mr << endl;
cout << re.cs << " " << re.cw << " " << re.cr << endl;
cout << re.b << " " << re.c << " " << re.mnuc << endl;
cout << re.zeta << " " << re.b1 << endl;
// It turns out that FSUGold needs a better initial
// guess than the default to get saturation right
re.err_nonconv=false;
re.def_sat_mroot.err_nonconv=false;
re.def_sat_mroot.def_jac.err_nonconv=false;
re.def_mroot.err_nonconv=false;
re.def_mroot.def_jac.err_nonconv=false;
int sret=re.saturation();
if (sret!=0 || re.n0<0.08) {
re.set_fields(0.2,0.1,0.01);
re.def_neutron.mu=5.0;
re.def_proton.mu=5.0;
sret=re.saturation();
if (sret!=0) {
O2SCL_ERR("RMF EOS failed.",o2scl::exc_efailed);
}
}
// Return the convergence error flag to the default value
re.err_nonconv=true;
re.def_sat_mroot.err_nonconv=true;
re.def_sat_mroot.def_jac.err_nonconv=true;
re.def_mroot.err_nonconv=true;
re.def_mroot.def_jac.err_nonconv=true;
// Compute the saturation density and the symmetry energy
cout << "FSUGold: " << re.n0 << endl;
cout << "FSUGold: " << re.esym*hc_mev_fm << endl;
t.test_rel(re.n0,0.1481,4.0e-4,"FSUGold saturation density.");
// Commpute the beta-equilibrium EOS and solve the TOV equations
nstar_cold nc;
nc.set_eos(re);
nc.calc_eos();
nc.calc_nstar();
// Output gravitational mass-radius curve
cout << endl;
shared_ptr<table_units<>> tov=nc.get_tov_results();
for(size_t i=0;i<tov->get_nlines();i++) {
cout << tov->get("gm",i) << " " << tov->get("r",i) << endl;
}
t.report();
return 0;
}
Typical output:
2.490790e+00 3.965499e+00 3.866679e+00
4.252639e+00 3.606605e+00 3.043266e+00
7.562836e-04 3.966669e-03 4.758599e+00
6.000000e-02 6.136407e+00
FSUGold: 1.481209e-01
FSUGold: 3.255336e+01
PASS: relative 1.481209e-01 vs. 1.481000e-01 : 1.409922e-04 < 4.000000e-04
FSUGold saturation density.
Mass versus radius mode.
Central P: 7.0000e-07 (Msun/km^3), M: 1.0935e-01 (Msun), R: 5.3736e+01 (km)
Central P: 7.7000e-07 (Msun/km^3), M: 1.1434e-01 (Msun), R: 4.4065e+01 (km)
Central P: 8.4700e-07 (Msun/km^3), M: 1.2005e-01 (Msun), R: 3.7358e+01 (km)
Central P: 9.3170e-07 (Msun/km^3), M: 1.2647e-01 (Msun), R: 3.2494e+01 (km)
Central P: 1.0249e-06 (Msun/km^3), M: 1.3357e-01 (Msun), R: 2.8865e+01 (km)
Central P: 1.1274e-06 (Msun/km^3), M: 1.4141e-01 (Msun), R: 2.6063e+01 (km)
Central P: 1.2401e-06 (Msun/km^3), M: 1.5000e-01 (Msun), R: 2.3861e+01 (km)
Central P: 1.3641e-06 (Msun/km^3), M: 1.5932e-01 (Msun), R: 2.2102e+01 (km)
Central P: 1.5005e-06 (Msun/km^3), M: 1.6949e-01 (Msun), R: 2.0669e+01 (km)
Central P: 1.6506e-06 (Msun/km^3), M: 1.8045e-01 (Msun), R: 1.9495e+01 (km)
Central P: 1.8156e-06 (Msun/km^3), M: 1.9231e-01 (Msun), R: 1.8517e+01 (km)
Central P: 1.9972e-06 (Msun/km^3), M: 2.0509e-01 (Msun), R: 1.7699e+01 (km)
Central P: 2.1969e-06 (Msun/km^3), M: 2.1881e-01 (Msun), R: 1.7009e+01 (km)
Central P: 2.4166e-06 (Msun/km^3), M: 2.3356e-01 (Msun), R: 1.6423e+01 (km)
Central P: 2.6582e-06 (Msun/km^3), M: 2.4933e-01 (Msun), R: 1.5925e+01 (km)
Central P: 2.9241e-06 (Msun/km^3), M: 2.6621e-01 (Msun), R: 1.5499e+01 (km)
Central P: 3.2165e-06 (Msun/km^3), M: 2.8422e-01 (Msun), R: 1.5133e+01 (km)
Central P: 3.5381e-06 (Msun/km^3), M: 3.0341e-01 (Msun), R: 1.4819e+01 (km)
Central P: 3.8919e-06 (Msun/km^3), M: 3.2381e-01 (Msun), R: 1.4549e+01 (km)
Central P: 4.2811e-06 (Msun/km^3), M: 3.4546e-01 (Msun), R: 1.4316e+01 (km)
Central P: 4.7092e-06 (Msun/km^3), M: 3.6842e-01 (Msun), R: 1.4116e+01 (km)
Central P: 5.1802e-06 (Msun/km^3), M: 3.9266e-01 (Msun), R: 1.3943e+01 (km)
Central P: 5.6982e-06 (Msun/km^3), M: 4.1826e-01 (Msun), R: 1.3795e+01 (km)
Central P: 6.2680e-06 (Msun/km^3), M: 4.4521e-01 (Msun), R: 1.3667e+01 (km)
Central P: 6.8948e-06 (Msun/km^3), M: 4.7352e-01 (Msun), R: 1.3556e+01 (km)
Central P: 7.5843e-06 (Msun/km^3), M: 5.0321e-01 (Msun), R: 1.3462e+01 (km)
Central P: 8.3427e-06 (Msun/km^3), M: 5.3426e-01 (Msun), R: 1.3380e+01 (km)
Central P: 9.1770e-06 (Msun/km^3), M: 5.6666e-01 (Msun), R: 1.3309e+01 (km)
Central P: 1.0095e-05 (Msun/km^3), M: 6.0039e-01 (Msun), R: 1.3248e+01 (km)
Central P: 1.1104e-05 (Msun/km^3), M: 6.3540e-01 (Msun), R: 1.3195e+01 (km)
Central P: 1.2215e-05 (Msun/km^3), M: 6.7166e-01 (Msun), R: 1.3148e+01 (km)
Central P: 1.3436e-05 (Msun/km^3), M: 7.0911e-01 (Msun), R: 1.3107e+01 (km)
Central P: 1.4780e-05 (Msun/km^3), M: 7.4767e-01 (Msun), R: 1.3070e+01 (km)
Central P: 1.6258e-05 (Msun/km^3), M: 7.8727e-01 (Msun), R: 1.3036e+01 (km)
Central P: 1.7883e-05 (Msun/km^3), M: 8.2780e-01 (Msun), R: 1.3004e+01 (km)
Central P: 1.9672e-05 (Msun/km^3), M: 8.6916e-01 (Msun), R: 1.2973e+01 (km)
Central P: 2.1639e-05 (Msun/km^3), M: 9.1123e-01 (Msun), R: 1.2943e+01 (km)
Central P: 2.3803e-05 (Msun/km^3), M: 9.5385e-01 (Msun), R: 1.2913e+01 (km)
Central P: 2.6183e-05 (Msun/km^3), M: 9.9691e-01 (Msun), R: 1.2882e+01 (km)
Central P: 2.8801e-05 (Msun/km^3), M: 1.0402e+00 (Msun), R: 1.2850e+01 (km)
Central P: 3.1681e-05 (Msun/km^3), M: 1.0836e+00 (Msun), R: 1.2815e+01 (km)
Central P: 3.4850e-05 (Msun/km^3), M: 1.1270e+00 (Msun), R: 1.2778e+01 (km)
Central P: 3.8335e-05 (Msun/km^3), M: 1.1701e+00 (Msun), R: 1.2738e+01 (km)
Central P: 4.2168e-05 (Msun/km^3), M: 1.2127e+00 (Msun), R: 1.2695e+01 (km)
Central P: 4.6385e-05 (Msun/km^3), M: 1.2547e+00 (Msun), R: 1.2648e+01 (km)
Central P: 5.1023e-05 (Msun/km^3), M: 1.2958e+00 (Msun), R: 1.2598e+01 (km)
Central P: 5.6126e-05 (Msun/km^3), M: 1.3359e+00 (Msun), R: 1.2543e+01 (km)
Central P: 6.1738e-05 (Msun/km^3), M: 1.3748e+00 (Msun), R: 1.2484e+01 (km)
Central P: 6.7912e-05 (Msun/km^3), M: 1.4123e+00 (Msun), R: 1.2421e+01 (km)
Central P: 7.4703e-05 (Msun/km^3), M: 1.4482e+00 (Msun), R: 1.2353e+01 (km)
Central P: 8.2174e-05 (Msun/km^3), M: 1.4824e+00 (Msun), R: 1.2281e+01 (km)
Central P: 9.0391e-05 (Msun/km^3), M: 1.5146e+00 (Msun), R: 1.2204e+01 (km)
Central P: 9.9430e-05 (Msun/km^3), M: 1.5449e+00 (Msun), R: 1.2123e+01 (km)
Central P: 1.0937e-04 (Msun/km^3), M: 1.5729e+00 (Msun), R: 1.2037e+01 (km)
Central P: 1.2031e-04 (Msun/km^3), M: 1.5987e+00 (Msun), R: 1.1947e+01 (km)
Central P: 1.3234e-04 (Msun/km^3), M: 1.6221e+00 (Msun), R: 1.1853e+01 (km)
Central P: 1.4558e-04 (Msun/km^3), M: 1.6430e+00 (Msun), R: 1.1755e+01 (km)
Central P: 1.6013e-04 (Msun/km^3), M: 1.6614e+00 (Msun), R: 1.1653e+01 (km)
Central P: 1.7615e-04 (Msun/km^3), M: 1.6774e+00 (Msun), R: 1.1548e+01 (km)
Central P: 1.9376e-04 (Msun/km^3), M: 1.6907e+00 (Msun), R: 1.1439e+01 (km)
Central P: 2.1314e-04 (Msun/km^3), M: 1.7016e+00 (Msun), R: 1.1328e+01 (km)
Central P: 2.3445e-04 (Msun/km^3), M: 1.7099e+00 (Msun), R: 1.1214e+01 (km)
Central P: 2.5790e-04 (Msun/km^3), M: 1.7158e+00 (Msun), R: 1.1098e+01 (km)
Central P: 2.8369e-04 (Msun/km^3), M: 1.7192e+00 (Msun), R: 1.0981e+01 (km)
Central P: 3.1205e-04 (Msun/km^3), M: 1.7204e+00 (Msun), R: 1.0861e+01 (km)
Central P: 3.4326e-04 (Msun/km^3), M: 1.7193e+00 (Msun), R: 1.0741e+01 (km)
Central P: 3.7759e-04 (Msun/km^3), M: 1.7160e+00 (Msun), R: 1.0619e+01 (km)
Central P: 4.1534e-04 (Msun/km^3), M: 1.7107e+00 (Msun), R: 1.0498e+01 (km)
Central P: 4.5688e-04 (Msun/km^3), M: 1.7035e+00 (Msun), R: 1.0376e+01 (km)
Central P: 5.0257e-04 (Msun/km^3), M: 1.6946e+00 (Msun), R: 1.0255e+01 (km)
Central P: 5.5282e-04 (Msun/km^3), M: 1.6839e+00 (Msun), R: 1.0134e+01 (km)
Central P: 6.0811e-04 (Msun/km^3), M: 1.6718e+00 (Msun), R: 1.0015e+01 (km)
Central P: 6.6892e-04 (Msun/km^3), M: 1.6583e+00 (Msun), R: 9.8969e+00 (km)
Central P: 7.3581e-04 (Msun/km^3), M: 1.6435e+00 (Msun), R: 9.7807e+00 (km)
Central P: 8.0939e-04 (Msun/km^3), M: 1.6277e+00 (Msun), R: 9.6666e+00 (km)
Central P: 8.9033e-04 (Msun/km^3), M: 1.6108e+00 (Msun), R: 9.5549e+00 (km)
Central P: 9.7936e-04 (Msun/km^3), M: 1.5932e+00 (Msun), R: 9.4460e+00 (km)
Central P: 1.0773e-03 (Msun/km^3), M: 1.5748e+00 (Msun), R: 9.3401e+00 (km)
Central P: 1.1850e-03 (Msun/km^3), M: 1.5559e+00 (Msun), R: 9.2374e+00 (km)
Central P: 1.3035e-03 (Msun/km^3), M: 1.5366e+00 (Msun), R: 9.1383e+00 (km)
Central P: 1.4339e-03 (Msun/km^3), M: 1.5168e+00 (Msun), R: 9.0430e+00 (km)
Central P: 1.5773e-03 (Msun/km^3), M: 1.4969e+00 (Msun), R: 8.9516e+00 (km)
Central P: 1.7350e-03 (Msun/km^3), M: 1.4769e+00 (Msun), R: 8.8644e+00 (km)
Central P: 1.9085e-03 (Msun/km^3), M: 1.4568e+00 (Msun), R: 8.7815e+00 (km)
Central P: 2.0993e-03 (Msun/km^3), M: 1.4368e+00 (Msun), R: 8.7031e+00 (km)
Central P: 2.3093e-03 (Msun/km^3), M: 1.4170e+00 (Msun), R: 8.6295e+00 (km)
Central P: 2.5402e-03 (Msun/km^3), M: 1.3974e+00 (Msun), R: 8.5606e+00 (km)
Central P: 2.7942e-03 (Msun/km^3), M: 1.3782e+00 (Msun), R: 8.4966e+00 (km)
Central P: 3.0736e-03 (Msun/km^3), M: 1.3594e+00 (Msun), R: 8.4378e+00 (km)
Central P: 3.3810e-03 (Msun/km^3), M: 1.3410e+00 (Msun), R: 8.3840e+00 (km)
Central P: 3.7191e-03 (Msun/km^3), M: 1.3231e+00 (Msun), R: 8.3354e+00 (km)
Central P: 4.0910e-03 (Msun/km^3), M: 1.3059e+00 (Msun), R: 8.2921e+00 (km)
Central P: 4.5001e-03 (Msun/km^3), M: 1.2893e+00 (Msun), R: 8.2542e+00 (km)
Central P: 4.9501e-03 (Msun/km^3), M: 1.2734e+00 (Msun), R: 8.2215e+00 (km)
Central P: 5.4452e-03 (Msun/km^3), M: 1.2582e+00 (Msun), R: 8.1942e+00 (km)
Central P: 5.9897e-03 (Msun/km^3), M: 1.2438e+00 (Msun), R: 8.1722e+00 (km)
Central P: 6.5886e-03 (Msun/km^3), M: 1.2302e+00 (Msun), R: 8.1555e+00 (km)
Central P: 7.2475e-03 (Msun/km^3), M: 1.2175e+00 (Msun), R: 8.1440e+00 (km)
Central P: 7.9723e-03 (Msun/km^3), M: 1.2057e+00 (Msun), R: 8.1376e+00 (km)
1.093454e-01 5.373553e+01
1.143386e-01 4.406531e+01
1.200453e-01 3.735766e+01
1.264676e-01 3.249407e+01
1.335665e-01 2.886544e+01
1.414105e-01 2.606314e+01
1.499968e-01 2.386083e+01
1.593244e-01 2.210233e+01
1.694862e-01 2.066934e+01
1.804508e-01 1.949471e+01
1.923149e-01 1.851687e+01
2.050856e-01 1.769878e+01
2.188139e-01 1.700876e+01
2.335564e-01 1.642333e+01
2.493318e-01 1.592493e+01
2.662149e-01 1.549851e+01
2.842199e-01 1.513309e+01
3.034084e-01 1.481911e+01
3.238147e-01 1.454891e+01
3.454630e-01 1.431638e+01
3.684158e-01 1.411592e+01
3.926635e-01 1.394334e+01
4.182573e-01 1.379466e+01
4.452130e-01 1.366660e+01
4.735228e-01 1.355640e+01
5.032051e-01 1.346151e+01
5.342598e-01 1.337975e+01
5.666614e-01 1.330919e+01
6.003856e-01 1.324812e+01
6.354010e-01 1.319498e+01
6.716620e-01 1.314839e+01
7.091103e-01 1.310709e+01
7.476746e-01 1.306994e+01
7.872712e-01 1.303590e+01
8.278038e-01 1.300404e+01
8.691627e-01 1.297348e+01
9.112251e-01 1.294344e+01
9.538549e-01 1.291321e+01
9.969074e-01 1.288211e+01
1.040227e+00 1.284958e+01
1.083642e+00 1.281507e+01
1.126979e+00 1.277810e+01
1.170054e+00 1.273824e+01
1.212679e+00 1.269512e+01
1.254661e+00 1.264841e+01
1.295807e+00 1.259784e+01
1.335923e+00 1.254319e+01
1.374820e+00 1.248427e+01
1.412313e+00 1.242095e+01
1.448225e+00 1.235315e+01
1.482389e+00 1.228083e+01
1.514648e+00 1.220398e+01
1.544861e+00 1.212265e+01
1.572903e+00 1.203692e+01
1.598663e+00 1.194692e+01
1.622051e+00 1.185280e+01
1.642994e+00 1.175475e+01
1.661441e+00 1.165300e+01
1.677358e+00 1.154780e+01
1.690734e+00 1.143943e+01
1.701575e+00 1.132819e+01
1.709908e+00 1.121440e+01
1.715774e+00 1.109840e+01
1.719235e+00 1.098053e+01
1.720365e+00 1.086117e+01
1 tests performed.
All tests passed.