Description of the `CompOSE` tables

The CompOSE data consists of several files, each of which are briefly described in this Section.

See Section 4.2 in the CompOSE manual at https://compose.obspm.fr/manual for further information.

Grid parameter files `eos.[t,nb,yq]`

These files give respectively the grid points in temperature $T$, baryon number density $n_{B}$ and charge fraction $Y_{q}$ on which the EoS was calculated. For the case of cold neutron star matter, the EoS will only depend only on $n_{B}$, while $T=0$ MeV and $Y_{q}=0$.

In each of the grid parameter files, the first two lines give, respectively, the start and end indices of the grid, while the remaining lines give the actual grid points.

See Section 4.2.7 in the CompOSE https://compose.obspm.fr/manual for further information about the grid parameter files.

Thermodynamic quantities `eos.thermo`

The first line in the file specifies:

The neutron mass $m_{n}$ (MeV),
The proton mass $m_{p}$ (MeV),
A flag indicating whether lepton are included (1) or not (0).

The remaining file gives the following thermodynamic quantities:

Quantity name	Description	Unit
iT	Temperature grid point index
jnB	Baryon number density grid point index
kYq	Charge number fraction grid point index
Q1	Pressure divided by baryon num. density	MeV
Q2	entropy per baryon
Q3	Scaled and shifted baryon chemical potential $\mu_{B}/m_{n}-1$
Q4	Scaled charge chemical potential $\mu_{q}/m_{n}$
Q5	Scaled effective lepton chemical potential $\mu_{l}/m_{n}$
Q6	Scaled free energy per baryon $(f/m_{n}n_{B})-1$
Q7	Scaled internal energy per baryon $(e/m_{n}n_{B})-1
Nextra	Number of additional thermodynamic quantities
Qextra_1	First additional quantity
…	…	…
Qextra_Nextra	Nextra-th additional quantity

Apart from the mandatory quantities Q1 to Q7, the user can also provide optional, additional quantities Qextra_1, Qextra_2, …, Qextra_Nextra.

We note that, for cold, beta-equilibrated tables:

The entropy per baryon, Q2 should be 0,
The scaled effective lepton chemical potential Q5, should be zero,
The internal energy and free energy are equal and so Q6 and Q7 are equal.

See Section 4.2.2 in the CompOSE https://compose.obspm.fr/manual for further information about the table for thermodynamic quantities.

Compositional information `eos.compo`

If available the user can provide information on the composition of matter, specifically:

The number fraction $Y_{i}$ for a particle species $i$. CompOSE and ComPyTools encodes the particle species via an integer, $I_{i}$, as described in Tables 3.2, 3.3 and 3.4 in Section 3.4 of the CompOSE manual. For every particle species $i$ considered, the table contains the corresponding paired quantity $(I_i, Y_{I_{i}})$. If $N$ particles are considered, there will be $N_{pairs}$ pairs $(I_i, Y_{I_{i}})$ in the table,
For a given index, $I_{i}$ that defines a particular group of nuclei $\mathcal{M}_{I_{i}}$, eos.compo also stores the average mass number $A^{av}_{I_{i}}$ , charge number $Z^{av}_{I_{i}}$ and the combined number fraction $Y_{I_{i}}$. These are defined by Eqs. (4.20), (4.21) and (4.22), respectively in the CompOSE manual. If $N$ groups of nuclei are considered, there will by thus $N_{quads}$ of quadruples $(I_i, A^{av}_{I_{i}}, Z^{av}_{I_{i}}, Y_{I_{i}})$ stored in the table. The average mass and charge numbers correspond to those of a representative heavy nucleus if there is only one group of nuclei except the lightest that are considered explicitly. However, it is also possible to define several subsets of nuclei with corresponding average mass numbers, charge numbers and fractions.

Quantity name	Description	Unit
iT	Temperature grid point index
jnB	Baryon number density grid point index
kYq	Charge number fraction grid point index
Iphase	An integer that codes the type of phase of matter (e.g. homogenous core)
Npairs	Number of $(I_{i}, Y_{I_{i}})$ pairs
$I_{1}$	Index of first particle species
$Y_{I_{i}}$	Number fraction of first particle species with index $I_{1}$
…	…	…
$I_{N_{pairs}}$	Index of $N_{pairs}$-th particle species
$Y_{I_{N_{pairs}}}$	Number fraction of $N_{pairs}$-th particle species with index $I_{N_{pairs}}$
Nquads	Number of $(I_i, A^{av}_{I_{i}}, Z^{av}_{I_{i}}, Y_{I_{i}})$ quadruples
$I_{1}$	Index of first nuclei group
$A^{av}_{I_{i}}$	Average mass number of first nuclei group with index $I_{1}$
$Z^{av}_{I_{i}}$	Average charge number of first nuclei group with index $I_{1}$
$Y_{I_{i}}$	Combined number fraction of first nuclei group with index $I_{1}$
…	…	…
$I_{N_{quads}}$	Index of $N_{quads}$-th nuclei group
$A^{av}_{I_{N_{quads}}}$	Average mass number of $N_{quads}$-th nuclei group with index ${I_{N_{quads}}}$
$Z^{av}_{I_{N_{quads}}}$	Average charge number of $N_{quads}$-th nuclei group with index ${I_{N_{quads}}}$
$Y_{I_{N_{quads}}}$	Combined number fraction of $N_{quads}$-th nuclei group with index ${I_{N_{quads}}}$

See Section 4.2.3 in the CompOSE https://compose.obspm.fr/manual for further information about the table for the composition of matter.

Microscopic quantities (`eos.micro`)

The user may also provide microscopic quantities for an individual particle, $i$:

Quantity	Unit
Landau effective mass divided by the particle mass
Dirac effective mass divided by the particle mass
Non-relativistic single-particle potential	MeV
Relativistic vector self-energy	MeV
Relativistic scalar self-energy	MeV
Pairing gap	MeV

The microscopic quantity for a given species, $i$, is encoded using

\[K_{i} = 1000\times I_{i} + J_{i}\]

where $I_{i}$ is the index identifying the particle and $J_{i}$ is an index that identifies the microscopic quantity, and it in Table 7.5 of the CompOSE manual. Similarly to how the number fractions are stored in eos.compo, eos.micro stores the paired quantities $(I_{i}, K_{I_{i}})$.

The eos.micro file contains the following information:

Quantity name	Description	Unit
iT	Temperature grid point index
jnB	Baryon number density grid point index
kYq	Charge number fraction grid point index
Iphase	An integer that codes the type of phase of matter (e.g. homogenous core)
Npairs	Number of $(I_{i}, Y_{I_{i}})$ pairs
$I_{1}$	Index of first particle species
$K_{I_{i}}$	Microscopic quantity of first particle species with index $I_{1}$
…	…	…
$I_{N_{pairs}}$	Index of $N_{pairs}$-th particle species
$K_{I_{N_{pairs}}}$	Microscopic quantity of $N_{pairs}$-th particle species with index $I_{N_{pairs}}$

See Section 4.2.4 in the CompOSE manual https://compose.obspm.fr/manual for further information about the microphysics table.

Static neutron star properties (`eos.mr`)

ComPyTools allows the user to automatically provide the static properties of cold, spherical neutron stars (for example masses, radii and tidal deformabilities) as calculated from the supplied EoS. The file will contain the following:

Column number	Quantity	Unit
1	Radius	km
2	Gravitational mass	$M_{\odot}$
3	Quadrupole tidal deformability ($\ell=2$)
4	Central baryon number density	fm$^{-3}$
5	Baryonic mass	$M_{\odot}$
6	Octupole tidal deformability
7	Hexadecapole tidal deformability

For tables on CompOSE that have not been created using ComPyTools, not all of the above quantities are provided by default and, at the most, users may only find the following:

Column number	Quantity	Unit
1	Radius	km
2	Gravitational mass	$M_{\odot}$
3	Quadrupole tidal deformability ($\ell=2$)

See Section 4.2.6 in the CompOSE manual https://compose.obspm.fr/manual for further information about the neutron star properties table.

When contributing CompOSE tables, the following are mandatory:

eos.[t,nb,yq]
eos.thermo

while the following are optional:

eos.compo,
eos.micro,
eos.mr.

Although not strictly a table, ComPyTools will automatically create the file eos.init that contains the required information to correctly initialise the CompOSE software.

Quantity name	Description	Unit
iT	Temperature grid point index
jnB	Baryon number density grid point index
kYq	Charge number fraction grid point index
Iphase	An integer that codes the type of phase of matter (e.g. homogenous core)
Npairs	Number of \((I_{i}, Y_{I_{i}})\) pairs
\(I_{1}\)	Index of first particle species
\(Y_{I_{i}}\)	Number fraction of first particle species with index \(I_{1}\)
…	…	…
\(I_{N_{pairs}}\)	Index of \(N_{pairs}\)-th particle species
\(Y_{I_{N_{pairs}}}\)	Number fraction of \(N_{pairs}\)-th particle species with index \(I_{N_{pairs}}\)
Nquads	Number of \((I_i, A^{av}_{I_{i}}, Z^{av}_{I_{i}}, Y_{I_{i}})\) quadruples
\(I_{1}\)	Index of first nuclei group
\(A^{av}_{I_{i}}\)	Average mass number of first nuclei group with index \(I_{1}\)
\(Z^{av}_{I_{i}}\)	Average charge number of first nuclei group with index \(I_{1}\)
\(Y_{I_{i}}\)	Combined number fraction of first nuclei group with index \(I_{1}\)
…	…	…
\(I_{N_{quads}}\)	Index of \(N_{quads}\)-th nuclei group
\(A^{av}_{I_{N_{quads}}}\)	Average mass number of \(N_{quads}\)-th nuclei group with index \({I_{N_{quads}}}\)
\(Z^{av}_{I_{N_{quads}}}\)	Average charge number of \(N_{quads}\)-th nuclei group with index \({I_{N_{quads}}}\)
\(Y_{I_{N_{quads}}}\)	Combined number fraction of \(N_{quads}\)-th nuclei group with index \({I_{N_{quads}}}\)

Description of the CompOSE tables

Grid parameter files eos.[t,nb,yq]

Thermodynamic quantities eos.thermo

Compositional information eos.compo

Microscopic quantities (eos.micro)

Static neutron star properties (eos.mr)

Description of the `CompOSE` tables

Grid parameter files `eos.[t,nb,yq]`

Thermodynamic quantities `eos.thermo`

Compositional information `eos.compo`

Microscopic quantities (`eos.micro`)

Static neutron star properties (`eos.mr`)