Table Format ============ The table is an HDF5 file and the datasets are given below. Several quantities are stored in :ref:`o2scl:tensor_grid` objects, which are stored as HDF5 groups with the name of the group given below. The contents of the rank 3 tensor are stored in the dataset named data in each group. Grid ---- - ``n_nB``: number of points in baryon density grid - ``n_Ye``: number of points in electron fraction grid - ``n_T``: number of points in temperature grid - ``nB_grid``: array containing baryon density grid (in :math:`\mathrm{fm}^{-3}`) - ``Ye_grid``: array containing electron fraction grid - ``T_grid``: array containing temperature grid (in :math:`\mathrm{MeV}`) Physical quantities ------------------- These are stored as double-precision numbers. - ``hc``: :math:`\hbar c` (in :math:`\mathrm{MeV~fm}`) - ``alpha_em``: :math:`\alpha_{\mathrm{EM}}`, the fine structure constant - ``m_neut``: the mass of the neutron (in :math:`\mathrm{MeV}`) - ``m_prot``: the mass of the proton in MeV (in :math:`\mathrm{MeV}`) Flags ----- These are stored as integers. - ``baryons_only``: 1 (true) if the thermodynamic quantities with baryons only are provided (always 1) - ``with_leptons``: 1 (true) if the thermodynamic quantities with leptons are provided, and 0 (false) otherwise. - ``derivs_computed``: 1 (true) if the baryon part of the pressure and the nucleon chemical potentials are included. - ``alg_mode``: an integer representing the algorithm used to compute the table - ``include_muons``: 0 (false) if muons are not included Quantities for the solver ------------------------- These are all :ref:`o2scl:tensor_grid` objects. The contents of the tensor are stored in an HDF5 dataset named "data" in row-major order (the first index is the baryon density, the second is the electron fraction, and the third is the temperature). - ``flag``: A flag indicating if each point is complete, empty, or if a guess has been stored (10 means the point is complete). - ``log_xn``: :math:`\log_{10}(x_n)` where :math:`x_n\equiv n_n^{\prime}/n_B`. - ``log_xp``: :math:`\log_{10}(x_p)` where :math:`x_p\equiv n_p^{\prime}/n_B`. - ``A``: The average nuclear mass number - ``Z``: The average nuclear charge number Also, if ``alg_mode`` is either 2, 3, or 4, then the following tensors are included: - ``A_min``: the smallest value of A in the distribution, not including n, p, d, t, :math:`^{3}\mathrm{He}`, :math:`^{4}\mathrm{Li}`, and :math:`\alpha`. - ``A_max``: largest value of A in the distribution, not including n, p, d, t, :math:`^{3}\mathrm{He}`, :math:`^{4}\mathrm{Li}`, and :math:`\alpha`. - ``NmZ_min``: the smallest value of :math:`N-Z` in the distribution, not including n, p, d, t, :math:`^{3}\mathrm{He}`, :math:`^{4}\mathrm{Li}`, and :math:`\alpha`. - ``NmZ_max``: the largest value of :math:`N-Z` in the distribution, not including n, p, d, t, :math:`^{3}\mathrm{He}`, :math:`^{4}\mathrm{Li}`, and :math:`\alpha`. Composition ----------- These are all :ref:`o2scl:tensor_grid` objects and included for all tables. - ``Xn``: the baryon number fraction of neutrons (this includes only the neutrons in the low-density phase, i.e. the neutrons not inside nuclei) - ``Xp``: the baryon number fraction of protons (this includes only the protons in the low-density phase, i.e. the protons not inside nuclei) - ``Xalpha``: the baryon number fraction of alpha particles - ``Xd``: the baryon number fraction of deuterons - ``Xt``: the baryon number fraction of tritons - ``XHe3``: the baryon number fraction of :math:`^{3}\mathrm{He}`, - ``XLi4``: the baryon number fraction of :math:`^{4}\mathrm{Li}` - ``Xnuclei``: the baryon number fraction of nuclei The sum of these eight quantities should be close to 1 for all points in the table. Note that ``Xn`` and ``Xp`` do not store the local density of neutrons in the gas phase, those quantities are given in Du et al. (2022): :math:`n_n^{\prime}\equiv n_n/\xi` and :math:`n_n^{\prime}\equiv n_p/\xi`. These densities are not stored in the tables, but are accessible, for example, in the ``point-nuclei`` command. At high densities or temperatures when nuclei are not present, :math:`\xi=1`. Thermodynamic quantities ------------------------ In this section, all quantities are stored as :ref:`o2scl:tensor_grid` objects. Three quantities are included for all tables: - ``Fint``: the baryon part of the free energy per baryon (in :math:`\mathrm{MeV}`) - ``Sint``: the baryon part of the entropy per baryon - ``Eint``: the baryon part of the internal energy per baryon (in :math:`\mathrm{MeV}`) The relation :math:`F_{\mathrm{int}}=E_{\mathrm{int}}-T S_{\mathrm{int}}` should hold at all points in the table. If ``include_muons`` is 1, then ``Ymu``, the muon fraction, is also included. If either ``include_muons`` or ``with_leptons`` is 1, then ``mue``, the electron chemical potential is included. The electron chemical potential includes the electron rest mass and is in :math:`\mathrm{MeV}`. If ``derivs_computed`` is 1, then the following quantities are also included: - ``Pint``: the baryon part of the pressure (in :math:`\mathrm{MeV}/\mathrm{fm}^3`) - ``mun``: the neutron chemical potential (in :math:`\mathrm{MeV}`) - ``mup``: the proton chemical potential (in :math:`\mathrm{MeV}`) The thermodynamic identity, .. math:: E_{\mathrm{int}} n_B = - P_{\mathrm{int}} + S_{\mathrm{int}} n_B T + \bar{n}_n \mu_{n} + \bar{n}_p \mu_{p} where :math:`\bar{n}_n\equiv n_B(1-Y_e)` and :math:`\bar{n}_p\equiv n_B Y_e` should be satisfied for all of the points in the table. The rest mass energy, :math:`m_n (1-Y_e) + m_p Y_e`, has been subtracted out from ``Fint`` and ``Eint``. (See :ref:`Rest mass contribution` for more detail.) The neutron and proton rest mass have been subtracted out from the neutron and proton chemical potentials (indepedent of whether or not the model implies a relativistic dispersion relation for the nucleons). See also :ref:`Chemical Potentials` for some helpful information on chemical potentials and the associated thermodynamic identity. If ``with_leptons`` is 1, then the electron chemical potential is included (as described above) and the following four quantities are also included: - ``F``: the total free energy per baryon (in :math:`\mathrm{MeV}`) - ``S``: the total entropy per baryon - ``E``: the total internal energy per baryon (in :math:`\mathrm{MeV}`) - ``P``: the total pressure (in :math:`\mathrm{MeV}/\mathrm{fm}^3`) The thermodynamic identity, .. math:: E n_B = - P + S n_B T + \bar{n}_n \mu_{n} + \bar{n}_p (\mu_{p}+\mu_{e}) should be satisfied for all of the points in the table. Note that ``F`` and ``E`` do not include the baryonic part of the rest mass energy but they *do* include the electron rest mass energy, :math:`m_e Y_e`. String arrays ------------- For compatibility with O\ :sub:`2`\ scl, a set of two string arrays is also included. The first, ``oth_names`` contains the list: ``Xd, Xt, XHe3, XLi4, flag, log_xn, and log_xp``. If ``alg_mode`` is 2 or larger, ``oth_names`` also contains ``A_min, A_max, NmZ_min, NmZ_max``. The second, ``oth_units``, contains a set of empty strings because none of the tensors referred to in the ``oth_names`` list have any units. The unsigned integer ``n_oth`` contains the size of the ``oth_names`` array. Electron and photon table ------------------------- The electron and photon table, contains five :ref:`o2scl:tensor_grid` objects which includes electrons, positrons, and photons, - ``F``: the free energy per baryon (in :math:`\mathrm{MeV}`) - ``S``: the entropy per baryon - ``E``: the internal energy per baryon (in :math:`\mathrm{MeV}`) - ``P``: the pressure (in :math:`\mathrm{MeV}/\mathrm{fm}^3`) - ``mue``: the electron chemical potential (in :math:`\mathrm{MeV}`) Nuclear masses table -------------------- The nuclear massses table, contains a :ref:`o2scl:table` object with the columns - ``Z``: the proton number, - ``N``: the neutron number, - ``g``: the spin degeneracy, - ``m``: the total mass (in :math:`\mathrm{MeV}`), - ``be``: the binding energy (in :math:`\mathrm{MeV}`), - ``Sn``: the neutron separation energy (in :math:`\mathrm{MeV}`), - ``Sp``: the proton separation energy (in :math:`\mathrm{MeV}`), - ``mass_type``: 1 for light nucleus, 2 for AME, 3 for FRDM, and 4 for extrapolated FRDM results, and - ``spin_type``: 1 for light nucleus, 2 for Jexp from HFB fit, 3 for Jth from HFB fit, 4 for simple ansatz.