yi | $\begin{array}[]{c}Y_{I}(N_{\textrm{data}},1,1,N_{\textrm{p}})\\\ Y_{I}(N_{n_{b}},N_{T},N_{Y_{q}},N_{\textrm{p}})\end{array}$ | dimensionless | array of particle fractions
pointspairs | $N_{\textrm{p}}$ | dimensionless | number of pairs
|  |  | for compositional data
index_yi | $I_{i}(N_{\textrm{p}})$ | dimensionless | index identifying
|  |  |  the particle $i$,
|  |  |  see tables 2, 3, 4
yav | $Y^{\textrm{av}}(N_{\textrm{data}},1,1,N_{\textrm{q}})$ | dimensionless | array of combined fractions
| $Y^{\textrm{av}}(N_{n_{b}},N_{T},N_{Y_{q}},N_{\textrm{q}})$ |  | of groups of nuclei
aav | $A^{\textrm{av}}(N_{\textrm{data}},1,1,N_{\textrm{q}})$ | dimensionless | average mass number
| $A^{\textrm{av}}(N_{n_{b}},N_{T},N_{Y_{q}},N_{\textrm{q}})$ |  | of groups of nuclei
zav | $Z^{\textrm{av}}(N_{\textrm{data}},1,1,N_{\textrm{q}})$ | dimensionless | average charge number
| $Z^{\textrm{av}}(N_{n_{b}},N_{T},N_{Y_{q}},N_{\textrm{q}})$ |  | of groups of nuclei
nav | $N^{\textrm{av}}(N_{\textrm{data}},1,1,N_{\textrm{q}})$ | dimensionless | average neutron number
| $N^{\textrm{av}}(N_{n_{b}},N_{T},N_{Y_{q}},N_{\textrm{q}})$ |  | of groups of nuclei
pointsav | $N_{\textrm{q}}$ | dimensionless | number of quadruples
|  |  | for compositional data
index_av | $I_{\textrm{av}}(N_{\textrm{q}})$ | dimensionless | index identifying
|  |  |  the group $\%$ of nuclei,
|  |  |  see tables 2, 3, 4.
micro | $\begin{array}[]{c}q_{\textrm{mic}}(N_{\textrm{data}},1,1,N_{\textrm{mic}})\\\ q_{\textrm{mic}}(N_{n_{b}},N_{T},N_{Y_{q}},N_{\textrm{mic}})\end{array}$ | varying | $\begin{array}[]{c}\textrm{array of microscopic}\\\ \textrm{quantities}\end{array}$
pointsmicro | $N_{\textrm{mic}}$ | dimensionless | number of microscopic
|  |  | quantities
index_micro | $K(N_{\textrm{mic}})$ | dimensionless | index identifying the
|  |  | microscopic quantities,
|  |  |  see subsection 4
error | $\begin{array}[]{c}q_{\textrm{err}}(N_{\textrm{data}},1,1,N_{\textrm{err}})\\\ q_{\textrm{err}}(N_{n_{b}},N_{T},N_{Y_{q}},N_{\textrm{err}})\end{array}$ | varying | array of error quantities
pointserr | $N_{\textrm{err}}$ | dimensionless | number of microscopic quantities
index_err | $J_{\textrm{err}}(N_{\textrm{err}})$ | dimensionless | index identifying the error
|  |  |  quantities, see table 6.

####  6 Web tools

The web tools are constructed as an interface to the CompOSE software, i.e.
all features of the code described in the previous section are available. The
obtained parameter files eos.parameters, eos.quantities as well as the output
table eos.table can be downloaded. In addition, it is possible to visualise
the results, chosing the axis from the different computed quantities on a
linear or a logarthmic scale.

##  Part 3 Appendix

###  Chapter 7 Technical details

The basic EoS tables only give a selected set of thermodynamic quantities at
the grid points that are identified with the index triple
($i_{T},i_{n_{b}},i_{Y_{q}}$). From the stored quantities $Q_{i}$,
$i=1,\dots,6$, see section 2, further relevant thermodynamic quantities can be
derived by a smooth interpolation for all possible values of the parameters
$T$, $n_{b}$ and $Y_{q}$ within the tabulated ranges. For these quantities,
thermodynamic consistency should be respected as far as possible. When the
thermodynamic quantities are interpolated separately, however, this condition
is usually not exactly fulfilled. On the other hand, a separate interpolation
often leads to smoother dependencies of the thermodynamic quantitities on the
parameters avoiding unphysical oscillations. In addition, different ways of
determining a single quantity gives the opportunity to estimate the error in
the interpolation. Thus, in the present code compose.f90 the strategy of a
direct interpolation of individual quantities is followed.

###  Appendix 7.A Interpolation

The interpolation scheme for a quantity in the thermodynamic, compositional
and microscopic EoS tables generally proceeds in several steps. In the
following, the procedure will be explained for a three-dimensional general
purpose EoS table. The interpolation scheme follows the method proposed in
Ref. [26] using polynomials of sufficiently high order.

In the sequel, the generic symbol $Q$ will be used for any tabulated quantity.
Its values are given at the grid points that are specified by a triple of
indices $(i_{T},i_{n_{b}},i_{Y_{q}})=(i,j,k)$, see subsection 1, corresponding
to temperature, baryon number density and charge fraction of strongly
interacting particles. Thus all values $Q(T(i),n_{b}(j),Y_{q}(k))$ are known
at the grid points. In order to calculate the quantity $Q$ at given values of
$T$, $n_{b}$, and $Y_{q}$, first the values of the indices $i=i_{T}$,
$j=i_{n_{b}}$ and $k=i_{Y_{q}}$ are determined such that

$\displaystyle T(i)\leq$ $\displaystyle T$ $\displaystyle<T(i+1)\>,$ (1)
$\displaystyle n_{b}(j)\leq$ $\displaystyle n_{b}$
$\displaystyle<n_{b}(j+1)\>,$ (2) $\displaystyle Y_{q}(k)\leq$ $\displaystyle
Y_{q}$ $\displaystyle<Y_{q}(k+1)\>.$ (3)

Then the interpolation parameters

$\displaystyle\xi$ $\displaystyle=$ $\displaystyle\frac{T-T(i)}{T(i+1)-T(i)}$
(4) $\displaystyle\eta$ $\displaystyle=$
$\displaystyle\frac{n_{b}-n_{b}(j)}{n_{b}(j+1)-n_{b}(j)}$ (5)
$\displaystyle\zeta$ $\displaystyle=$
$\displaystyle\frac{Y_{q}-Y_{q}(k)}{Y_{q}(k+1)-Y_{q}(k)}$ (6)

are introduced with

$0\leq\xi<1\qquad 0\leq\eta<1\qquad 0\leq\zeta<1\>.$ (7)

For the interpolation of a quantity $Q$ at given $(T,n_{b},Y_{q})$ we need the
tabulated values at least at the eight corners of the cube with grid points
$(i,j,k)$, $(i+1,j,k)$, $(i,j+1,k)$, $(i,j,k+1)$, $(i+1,j+1,k)$,
$(i+1,j,k+1)$, $(i,j+1,k+1)$, $(i+1,j+1,k+1)$.

The interpolation proceeds in two steps: first, an interpolation in the
variable $Y_{q}$ such that the three-dimensional grid is mapped to a two-
dimensional grid with four corners of each square; second, a two-dimensional
interpolation in the variables $T$ and $n_{b}$.

For the interpolation in $Y_{q}$ in the three-dimensional cube as defined
above, four separate one-dimensional interpolations along the lines that
connect the grid points $(i,j,k)$ and $(i,j,k+1)$, $(i+1,j,k)$ and
$(i+1,j,k+1)$, $(i,j+1,k)$ and $(i,j+1,k+1)$, $(i+1,j+1,k)$ and
$(i+1,j+1,k+1)$ have to be performed. After this first step, the interpolation
proceeds in the parameters $T$ and $n_{b}$ by a two-dimensional scheme as
discussed in subsection 2.

The interpolation in the variables $T$, $n_{b}$ and $Y_{q}$ can be of
different order in general, defined by the value $I$ of the variables ipl_t,
ipl_n and ipl_y, see section 5. In the following, the case of highest order
($I=3$) is considered first.

#####  1 Interpolation in one dimension

The order $I=3$ of the interpolation requires that the function values, its
first and second derivatives are continuous at the two corner points of each
line, i.e. six values have to be reproduced by the interpolation polynomial.
Hence, a polynomial of at least fifth degree has to be used. The six
independent coefficients $q_{n}$ of a single polynomial

$Q(T(i),n_{b}(j),Y_{q})=\sum_{n=0}^{5}q_{n}\zeta^{n}$ (8)

can determined from the function values and derivatives at the corner points
directly. One finds

$q_{0}=Q_{ijk}^{(0)}\qquad q_{1}=Q_{ijk}^{(1)}\qquad
q_{2}=\frac{1}{2}Q_{ijk}^{(2)}$ (9)

with

$Q^{(n)}_{ijk}=\left[Y_{q}(k+1)-Y_{q}(k)\right]^{n}\left.\frac{\partial^{n}Q}{\partial
Y_{q}^{n}}\right|_{T(i),n_{b}(j),Y_{q}(k)}$ (10)

for $n=0,1,2$, and

$Q_{ijk}^{(0)}=\left.\frac{\partial^{0}Q}{\partial
Y_{q}^{0}}\right|_{T(i),n_{b}(j),Y_{q}(k)}=Q(T(i),n_{b}(j),Y_{q}(k))$ (11)

in particular. The remaining three coefficients are given by

$\displaystyle q_{3}$ $\displaystyle=$ $\displaystyle 10A-4B+\frac{1}{2}C$
(12) $\displaystyle q_{4}$ $\displaystyle=$ $\displaystyle-15A+7B-C$ (13)
$\displaystyle q_{5}$ $\displaystyle=$ $\displaystyle 6A-3B+\frac{1}{2}C$ (14)

with

$\displaystyle A$ $\displaystyle=$ $\displaystyle
Q_{ijk+1}^{(0)}-Q_{ijk}^{(0)}-Q_{ijk}^{(1)}-\frac{1}{2}Q_{ijk}^{(2)}$ (15)
$\displaystyle B$ $\displaystyle=$ $\displaystyle
Q_{ijk+1}^{(1)}-Q_{ijk}^{(1)}-Q_{ijk}^{(2)}$ (16) $\displaystyle C$
$\displaystyle=$ $\displaystyle Q_{ijk+1}^{(2)}-Q_{ijk}^{(2)}\>.$ (17)

Alternatively, the approach of Ref. [26] can be followed. The value of the
quantity $Q$ at given $\zeta$ is found with the help of the quintic basis
functions

$\displaystyle\psi_{0}^{(0)}(z)$ $\displaystyle=$ $\displaystyle
1-10z^{3}+15z^{4}-6z^{5}$ (18) $\displaystyle\psi_{1}^{(0)}(z)$
$\displaystyle=$ $\displaystyle z-6z^{3}+8z^{4}-3z^{5}$ (19)
$\displaystyle\psi_{2}^{(0)}(z)$ $\displaystyle=$
$\displaystyle\frac{1}{2}\left(z^{2}-3z^{3}+3z^{4}-z^{5}\right)$ (20)

that have the properties

$\psi_{m}^{(n)}(0)=\delta_{nm}\qquad\psi_{m}^{(n)}(1)=0$ (21)

for

$\psi_{m}^{(n)}(z)=\frac{d^{n}\psi_{m}^{(0)}}{dz^{n}}$ (22)

with $n,m\in\\{0,1,2\\}$. Then one has

$\displaystyle Q(T(i),n_{b}(j),Y_{q})$ $\displaystyle=$
$\displaystyle\sum_{n=0}^{2}\left[Q^{(n)}_{ijk}\psi_{n}^{(0)}(\zeta)+(-1)^{n}Q^{(n)}_{ijk+1}\psi_{n}^{(0)}(1-\zeta)\right]$
(23)

with six interpolation coefficients that are given by directly by the function
values and derivatives at the corner points defined by the indices.
Derivatives are easily found as

$\displaystyle\frac{\partial^{s}}{\partial Y_{q}^{s}}Q(T(i),n_{b}(j),Y_{q})$
$\displaystyle=$
$\displaystyle\frac{1}{\left[Y_{q}(k+1)-Y_{q}(k)\right]^{s}}\sum_{n=0}^{2}\left[Q^{(n)}_{ijk}\psi_{n}^{(s)}(\zeta)+(-1)^{n+s}Q^{(n)}_{ijk+1}\psi_{n}^{(s)}(1-\zeta)\right]\>.$

The numerical determination of the derivatives depends on the order of
interpolation. For $I=3$, centered five-point finite difference formulas are
used to calculate the first and second derivative of a function. Close to the
boundaries of the EoS, centered difference formulas cannot be applied. In this
case, off-center formulas are used. In the case $I=2$, three-point finite
difference formulas are employed. A continuity of the second derivatives at
the corner points is not required. Only the function and the first derivative
are demanded to be continuous, corresponding to four independent quatities.
Hence, a polynomial of third degree is suffiecient and $q_{4}=q_{5}=0$ in Eq.
(8). Then, the coefficients of the second derivatives have to be defined as

$\displaystyle Q_{ijk}^{(2)}$ $\displaystyle=$ $\displaystyle
6\left[Q_{ijk+1}^{(0)}-Q_{ijk}^{(0)}\right]-2Q_{ijk+1}^{(1)}-4Q_{ijk}^{(1)}$
(25) $\displaystyle Q_{ijk+1}^{(2)}$ $\displaystyle=$
$\displaystyle-6\left[Q_{ijk+1}^{(0)}-Q_{ijk}^{(0)}\right]+4Q_{ijk+1}^{(1)}+2Q_{ijk}^{(1)}\>.$
(26)

For $I=1$, the function has to be continuous at the grid points but there is
no condition on the derivatives. In this case, one sets

$Q_{ijk}^{(1)}=Q_{ijk+1}^{(1)}=Q_{ijk+1}^{(0)}-Q_{ijk}^{(0)}\qquad
Q_{ijk}^{(2)}=Q_{ijk+1}^{(2)}=0\ $ (27)

for given function values $Q_{ijk}^{(0)}$ and $Q_{ijk+1}^{(0)}$. Then the
polynomial (8) reduces to a linear function with $q_{2}=q_{3}=q_{4}=q_{5}=0$.

#####  2 Interpolation in two dimensions

The interpolation in two dimensions with conditions on the continuity of the
function and its derivatives is more complicated than in the one-dimensional
case. For an interpolation order $I=3$ in both variables $\xi$ and $\eta$,
there are four function values, eight first derivatives and the twelve second
derivatives, hence 24 values in total, that can be used to determine the
coefficients of a polynomial in $\xi$ and $\eta$. From this consideration, it
would seem to be sufficient to use a polynomial

$Q(T,n_{b},Y_{q})=\sum_{m=0}^{4}\sum_{n=0}^{4}q_{mn}\xi^{m}\eta^{n}$ (28)

that includes powers up to four in both variables, resulting in $5\times 5=25$
coefficients $q_{nm}$ in total, i.e. one more than required. However, such a
form does not guarantee that the function and the derivatives are continuous
not only at the grid points but also along the boundaries of the interpolation
square. In fact, a continuity of the function $Q$, the first derivatives
$\partial Q/\partial T$ and $\partial Q/\partial n_{b}$, the second
derivatives $\partial^{2}Q/\partial T^{2}$, $\partial^{2}Q/\partial T\partial
n_{b}$ and $\partial^{2}Q/\partial n_{b}^{2}$, the third derivatives
$\partial^{3}Q/\partial T^{2}\partial n_{b}$ and $\partial^{3}Q/\partial
T\partial n_{b}^{2}$ and the fourth derivative $\partial^{4}Q/\partial
T^{2}\partial n_{b}^{2}$ at the corners has to be demanded, determining
$4\times 9=36=6\times 6$ coefficients of a polynomial

$Q(T,n_{b},Y_{q})=\sum_{m=0}^{5}\sum_{n=0}^{5}q_{mn}\xi^{m}\eta^{n}$ (29)

with degree six in each variable.

Instead of determining the coefficients directly as in the case of a one
dimensional interpolation, it is more advantageous to use the biquintic
interpolation scheme as in Ref. [26] with

$\displaystyle Q(T,n_{b},Y_{q})$ $\displaystyle=$
$\displaystyle\sum_{m=0}^{2}\sum_{n=0}^{2}\left[Q^{(mn)}_{ij}\psi_{m}^{(0)}(\xi)\psi_{n}^{(0)}(\eta)+(-1)^{m}Q^{(mn)}_{i+1j}\psi_{m}^{(0)}(1-\xi)\psi_{n}^{(0)}(\eta)\right.$
$\displaystyle\left.+(-1)^{n}Q^{(mn)}_{ij+1}\psi_{m}^{(0)}(\xi)\psi_{n}^{(0)}(1-\eta)+(-1)^{m+n}Q^{(mn)}_{i+1j+1}\psi_{m}^{(0)}(1-\xi)\psi_{n}^{(0)}(1-\eta)\right]$

and $4\times 9=36$ coefficients

$\displaystyle Q^{(mn)}_{ij}$ $\displaystyle=$
$\displaystyle\left[T(i+1)-T(i)\right]^{m}\left[n_{b}(j+1)-n_{b}(j)\right]^{n}\left.\frac{\partial^{m+n}Q}{\partial
T^{m}\partial n_{b}^{n}}\right|_{T(i),n_{b}(j),Y_{q}}$ (31) $\displaystyle
Q^{(mn)}_{i+1j}$ $\displaystyle=$
$\displaystyle\left[T(i+1)-T(i)\right]^{m}\left[n_{b}(j+1)-n_{b}(j)\right]^{n}\left.\frac{\partial^{m+n}Q}{\partial
T^{m}\partial n_{b}^{n}}\right|_{T(i+1),n_{b}(j),Y_{q}}$ (32) $\displaystyle
Q^{(mn)}_{ij+1}$ $\displaystyle=$
$\displaystyle\left[T(i+1)-T(i)\right]^{m}\left[n_{b}(j+1)-n_{b}(j)\right]^{n}\left.\frac{\partial^{m+n}Q}{\partial
T^{m}\partial n_{b}^{n}}\right|_{T(i),n_{b}(j+1),Y_{q}}$ (33) $\displaystyle
Q^{(mn)}_{i+1j+1}$ $\displaystyle=$
$\displaystyle\left[T(i+1)-T(i)\right]^{m}\left[n_{b}(j+1)-n_{b}(j)\right]^{n}\left.\frac{\partial^{m+n}Q}{\partial
T^{m}\partial n_{b}^{n}}\right|_{T(i+1),n_{b}(j+1),Y_{q}}$ (34)

where $m,n\in\\{0,1,2\\}$. Of course, it is possible to express the
coefficients $q_{mn}$ of the polynomial (29) through the coefficients
$Q_{ij}^{(mn)}$, as done in the code compose.f90. The derivatives are obtained
in the same way as in the one-dimensional case for the different
interpolations orders $I$. Derivatives of the function $Q$ with respect to $Y$
and $n_{b}$ can be found with the help of the relation

$\displaystyle\frac{\partial^{s+t}}{\partial T^{s}\partial
n_{b}^{t}}Q(T,n_{b},Y_{q})$ $\displaystyle=$
$\displaystyle\frac{1}{\left[T(i+1)-T(i)\right]^{s}}\frac{1}{\left[n_{b}(j+1)-n_{b}(j)\right]^{t}}$
$\displaystyle\times\sum_{m=0}^{2}\sum_{n=0}^{2}\left[Q^{(mn)}_{ij}\psi_{m}^{(s)}(\xi)\psi_{n}^{(t)}(\eta)+(-1)^{m+s}Q^{(mn)}_{i+1j}\psi_{m}^{(s)}(1-\xi)\psi_{n}^{(t)}(\eta)\right.$
$\displaystyle\left.+(-1)^{n+t}Q^{(mn)}_{ij+1}\psi_{m}^{(s)}(\xi)\psi_{n}^{(t)}(1-\eta)+(-1)^{m+n+s+t}Q^{(mn)}_{i+1j+1}\psi_{m}^{(s)}(1-\xi)\psi_{n}^{(t)}(1-\eta)\right]\>.$

Above considerations apply to the interpolation in all three parameters for a
general purpose EoS table. For neutron matter, i.e. $Y_{q}=0$ the
interpolation in the charge fraction of strongly interacting particles is
trivial since $\zeta=0$ and the tabulated values of the quantities can be used
directly in the second interpolation step in $T$ and $n_{b}$. A similar
procedure applies to the case of an EoS for symmetric nuclear matter of
$\beta$-equilibrium. In the case of a zero-temperature table, the second
interpolation step reduces from two to one dimension.

###  Appendix 7.B Matter in beta equilibrium

In the case of matter in $\beta$ equilibrium, there is an additional condition
on the chemical potentials that reduces the number of independent parameters
by one. Requiring that the weak interaction reactions

$p+e^{-}\leftrightarrow n+\nu_{e}\qquad p+\bar{\nu}_{e}\leftrightarrow
n+e^{+}$ (36)

and, if muons are considered in the model,

$p+\mu^{-}\leftrightarrow n+\nu_{\mu}\qquad p+\bar{\nu}_{\mu}\leftrightarrow
n+\mu^{+}$ (37)

are in weak equilibrium, the relations

$\mu_{p}+\mu_{e}=\mu_{n}+\mu_{\nu_{e}}$ (38)

and

$\mu_{p}+\mu_{\mu}=\mu_{n}+\mu_{\nu_{\mu}}\>,$ (39)

respectively, should hold. The chemical potentials of the neutrinos are
considered to be zero, i.e. $\mu_{\nu_{e}}=\mu_{\nu_{\mu}}=0$. Because
$\mu_{p}=\mu_{n}+\mu_{q}$, $\mu_{e}=\mu_{le}-\mu_{q}$ and
$\mu_{\mu}=\mu_{l\mu}-\mu_{q}$, the constraint can be formulated as

$\mu_{l}=0$ (40)

with the effective lepton chemical potential $\mu_{l}=\mu_{le}=\mu_{l\mu}$.
For given temperature $T$ and baryon number density $n_{b}$ there is a unique
charge fraction of strongly interacting particles $Y_{q}$ that is found by
determining the zero of the function

$f(Y_{q})=\mu_{l}(Y_{q})\>.$ (41)

###  Chapter 8 Structure of input files

During the execution of the program compose for tasks 1 and 2, three files (in
ASCII format) are generated that are used for task 3 as input files. The
structure of these files is described below. Experienced users of compose can
modify the files eos.parameters and eos.quantities according to their needs
when producing a new EoS table with modified parameters by running only task
3. The file eos.init has to be left untouched.

###  Appendix 8.A eos.init

There are 11 rows in the file eos.init. The first three numbers in the first
row indicate whether the EoS dependence on the temperature, the baryon
density, and the hadronic charge fraction (index = 1) or not (index = 0). The
following two integers are presently set to zero and will be used only for
future extensions of the compose code. The next three rows give the minimum
and maximum values for the variables $T$, $n_{b}$, and $Y_{q}$. In the fifth
row the number zero appears twice in the present version as dummy floating-
point variable. Row six contained four integers. The first indicates whether
leptons are included in the EoS (1: yes, 0: no). The second number gives the
number of additional quantities in the file eos.thermo and the third number is
the total number of thermodynamic quantities in each row of the file
eos.thermo. The last integer indicates whether a calculation of an EoS table
for the condition of $\beta$ equilibrium is possible (1) or not (0). Row seven
gives the number of pairs and quadruples in the file eos.compo and the
following two lines contain the corresponding indices according to tables 2,
3, 4 and 5 for pairs (first line) and according to the data sheet for
quadruples (second line). In row ten the number of microscopic quantities is
given and their indices are listed in the last row of the file eos.init.

###  Appendix 8.B eos.quantities

This file contains 18 rows. They determine which and how quantities will be
stored in the final EoS table with the name eos.table. Rows with odd number
(one, three, …) are comment lines beginning with the character #. The second
and fourth lines define the thermodynamic quantities that will be stored in
the output file eos.table. The first entry $N_{\textrm{thermo}}$ in row two
specifies the number of thermodynamic quantities that are selected from tables
1 and 2 followed by the number $N_{\textrm{add}}$ of quantities that are
selected from the stored quantities of the EoS file eos.thermo in addition to
the seven standard quantities as described in subsection 2. The last number
$N_{\textrm{deriv}}$ in row two is the number of quantities from table 3 that
contains the free energy per baryon and various derivatives of it. The fourth
line of the file eos.quantities lists the $N_{\textrm{thermo}}$ indices (if
$N_{\textrm{thermo}}>0$) from the second column of tables 1 and 2. that define
the available thermodynamic quantities, the $N_{\textrm{add}}$ indices (if
$N_{\textrm{add}}>0$) of the additionally stored quantities and the
$N_{\textrm{deriv}}$ indices (if $N_{\textrm{deriv}}>0$) from the first column
of table 3. E.g., the first four lines

> # number of regular, additional and derivative quantities
> 3 1 1
> # indices of regular, additional and derivative quantities
> 6 1 2 1 1

of an example file eos.quantities denote that the quantities
$\mathcal{F}/m_{n}-1$, $p$, $\mathcal{S}$, $q_{1}$ and $\mathcal{F}$ will
appear in the outpout file eos.table or eoscompose.h5. Regular thermodynamic
quantities are those that are obtained by a direct interpolation of the
tabulated quantities $\mathcal{Q}_{1}$, …, $\mathcal{Q}_{7}$ stored in the
file eos.thermo or those that are obtained from them by applying the
thermodynamic relations of section 6. The indices of the regular thermodynamic
quantities can have values of $1$, $2$, …, $23$ corresponding to the
definition in tables 1 and 2. Additional thermodynamic quantities are those
that are denoted $q_{1}$, …, $q_{N_{\textrm{add}}}$ in the file eos.thermo.
Their number $N_{\textrm{add}}$ and meaning depends on the specific EoS table.
Their values are found by a direct interpolation. The values for $\mathcal{F}$
and its derivatives are found from a direct interpolation and subsequent
derivatives of the interpolating function. If $N_{\textrm{thermo}}$,
$N_{\textrm{add}}$ and $N_{\textrm{deriv}}$ are zero the fourth line of the
file eos.quantities is empty.

The sixth row of the file eos.quantities contains the numbers $N_{p}$ and
$N_{q}$ of pairs and quadruples that are selected from the compositional
quantities that are stored in the file eos.compo as described in subsection 3.
In the eigth line the $N_{p}$ particle indices $I_{1}$, …, $I_{N_{p}}$ as
defined in tables 2, 3, 4 and 5 are followed by the $N_{q}$ indices that
identify a particular group of nuclei, see subsection 3. E.g., the four lines

> # number of pairs and quadruples for composition data
> 3 1
> # indices of pairs and quadruples for composition data
> 10 11 0 1

denote that the fractions $Y_{n}$, $Y_{p}$, $Y_{e}$ are stored in the file
eos.table followed by $Y^{\textrm{av}}_{1}$, $A^{\textrm{av}}_{1}$,
$Z^{\textrm{av}}_{1}$, and $N^{\textrm{av}}_{1}$ of the first set of nuclei.
If both $N_{p}$ and $N_{q}$ are zero the eighth line of the file
eos.quantities is empty.

The tenth line of the file eos.quantities contains the number
$N_{\textrm{mic}}$ of microscopic quantities in the file eos.micro to be
stored in the output file eos.table. Then line 12 is a list of
$N_{\textrm{mic}}$ composite indices $K_{i}$ as defined in subsection 4. E.g.,
the four lines

> # number of microscopic quantities
> 2
> # indices of microscopic quantities
> 10050 11050

denote that the nonrelativistic single-particle potentials $U_{n}$ and $U_{p}$
are stored in the file eos.table. If $N_{\textrm{mic}}$ is zero the twelfth
line of the file eos.quantities is empty.

In addition to the quantities considered above, error estimates for the
interpolation of the thermodynamic quantities $\mathcal{F}$, $\mathcal{E}$,
$p/n_{b}$ and $\mathcal{S}$ are available. The free energy per baryon
$\mathcal{F}$ can be obtained by direct interpolation or by using the
homogeneity condition (5) with the interpolated values for the pressure and
chemical potentials. An estimate for the absolute error in $\mathcal{F}$ is
then given by

$\Delta\mathcal{F}=\mathcal{F}+\frac{p}{n_{b}}-\left(\mu_{b}+Y_{q}\mu_{q}\right)$
(1)

in case of an EoS without leptons and

$\Delta\mathcal{F}=\mathcal{F}+\frac{p}{n_{b}}-\left(\mu_{b}+Y_{l}\mu_{l}\right)$
(2)

in case of an EoS with leptons and charge neutrality. The relative error is
then given by $\Delta\mathcal{F}/\mathcal{F}-1$. The consideration above also
apply to the internal energy per baryon $\mathcal{E}$. An estimate for the
absolute error in $p/n_{b}$ is obtained by comparing the directly interpolated
pressure $p$ with that derived from the first derivative of the free energy
per baryon, i.e.

$\Delta\frac{p}{n_{b}}=\frac{p}{n_{b}}-n_{b}\left.\frac{\partial\mathcal{F}}{\partial
n_{b}}\right|_{T,Y_{q}}\>.$ (3)

Similarly, an error estimate for the entropy per baryon is calculated from

$\Delta\mathcal{S}=\mathcal{S}-\left.\frac{\partial\mathcal{F}}{\partial
T}\right|_{n_{b},Y_{q}}\>.$ (4)

The sixteenth line of the file eos.quantities defines the number
$N_{\textrm{err}}$ of error quantities to be stored in the output file. Line
18 is a list of the $N_{\textrm{err}}$ indices $J$ as defined in table 6.
E.g., the four lines

> # number of error quantities
> 2
> # indices of error quantities
> 1 2

denote that the estimates $\Delta\mathcal{F}$ and
$\Delta\mathcal{F}/\mathcal{F}$ are stored in the file eos.table. If
$N_{\textrm{err}}$ is zero the eighteenth line of the file eos.quantities is
empty.

The last row of the file eos.quantities defines the format of the output file
by a single integer $I$. There are two methods that are used for storing the
EoS data. The first ($I=1$) is the simple ASCII format using the file name
eos.table that easily allows to read the data without the need for further
codes. The second method ($I\neq 1$) uses the more advanced HDF5 format (see
http://www.hdfgroup.org/HDF5/) that is widely used in the astrophysics
community. In this case, the output file carries the name eoscompose.h5 and
each data set is designated with a particular identifier $\$$ of the stored
quantity $Q$. Tables 7 and 8 give a list of all tabulated quantities and
corresponding identifiers $\$$.

Note that $\varepsilon=\mathcal{E}/m_{n}-1$ in table 1 is _not_ the specific
internal energy, since the total mass density is not given by $m_{n}n_{b}$. We
do not store $\mathcal{E}/m_{n}$ because it is in many regimes largely
dominated by the rest mass contribution, such that it is numerically difficult
to keep trace of small variations in the internal energy in that case. The
same argument applies to the other thermodynamic quantities $\mathcal{F}$,
$\mathcal{G}$ and $\mathcal{H}$. The present choice of storing $\varepsilon$
is also motivated by the fact that the total mass density is not a conserved
quantity throughout the hydrodynamic evolution, but only the baryon number
density, $n_{b}$.

The individual chemical potentials for all the particles (baryons, mesons,
nuclei, quarks, …) can be calculated from the three ones given in the tables.
Note that we use the relativistic definition of the chemical potentials.

Particle fractions $Y_{i}$ are stored in the data sets with identifier $y\\#$
where $\\#$ stands for the particle index $I_{i}$ as defined in tables 2, 3, 4
and 5. E.g., the data identifier y20 and y400 contain the particle fractions
of $\Delta^{-}$ and $K^{-}$ particles, respectively. Similarly, yav1 stands
for the fraction of the first group of nuclei.

Combining the examples above, the file eos.quantities assumes the form

> # number of regular, additional and derivative quantities
> 3 1 1
> # indices of regular, additional and derivative quantities
> 6 1 2 1 1
> # number of pairs and quadruples for composition data
> 3 1
> # indices of pairs and quadruples for composition data
> 10 11 0 1
> # number of microscopic quantities
> 2
> # indices of microscopic quantities
> 10050 11050
> # number of error quantities
> 2
> # indices of error quantities
> 1 2

and, consequently, each line of the output file eos.table will contain the
following entries:

$\displaystyle T\quad n_{b}\quad Y_{q}$ $\displaystyle\mathcal{F}/m_{n}-1\quad
p\quad\mathcal{S}\quad q_{1}\quad\mathcal{F}\quad Y_{n}\quad Y_{p}\quad
Y_{e}\quad$ $\displaystyle Y^{\textrm{av}}_{1}\quad A^{\textrm{av}}_{1}\quad
Z^{\textrm{av}}_{1}\quad N^{\textrm{av}}_{1}\quad U_{n}\quad
U_{p}\quad\Delta\mathcal{F}\quad\Delta\mathcal{F}/\mathcal{F}$

i.e., in total $19$ quantities.

###  Appendix 8.C eos.parameters

There are at least ten lines in the file eos.parameters. Rows one, three, five
and seven of the file are comment lines indicated by the first character #.
The second row of this file contains three integer numbers $I_{T}$,
$I_{n_{b}}$ and $I_{Y_{q}}$ that specify the interpolation scheme for the
temperature, baryon number density and charge fraction of strongly interacting
particles, respectively. Presently, there is the choice between first order
($I_{x}=1$, $x=T,n_{b},Y_{q}$), second order ($I_{x}=2$) and third order
($I_{x}=3$) interpolation available with continuity of all quantities $Q(x)$,
all quantities $Q(x)$ and their first derivative $\partial Q/\partial x$ or
all quantities $Q(x)$, their first and second derivatives $\partial Q/\partial
x$ and $\partial^{2}Q/\partial x^{2}$, respectively. See appendix 7.A for
details on the interpolation scheme.

The fourth row of the file eos.parameters contains two integers $I_{\beta}$
and $I_{\textrm{entr}}$. The first determines whether the EoS in the output
file eos.table will be generated for matter in $\beta$ equilibrium
($I_{\beta}=1$) or not ($I_{\beta}\neq 1$). Of course, this option is only
effective for EoS tables that include electrons (and muons) and depend on the
parameter $Y_{q}$, e.g. three-dimensional general purpose EoS tables and two-
dimensional zero-temperature EoS tables. The second integer determines whether
the EoS in the output file eos.table will be generated for given entropy per
baryon $\mathcal{S}$ ($I_{\textrm{entr}}=1$) or not ($I_{\textrm{entr}}\neq
1$). If yes, the input parameters that usually define the temperature values
will be interpreted as defining the entropy per baryon. This option can only
be used for EoS that depend on the temperature. However it is not guaranteed
that there are solutions, found by interpoalation, for the given parameter
values.

In the sixth row of the file, the tabulation scheme for the parameters is
defined by the integer $I_{\textrm{tab}}$. For $I_{\textrm{tab}}=0$ the the
parameter values of $T$ (or $\mathcal{S}$), $n_{b}$ and $Y_{q}$ are listed
explicitly in the file eos.parameters as follows: The eighth row contains the
number of data points $N_{\textrm{data}}$ to be generated and each line of the
next $N_{\textrm{data}}$ rows contains the three parameter values in the form

$T\>\>n_{b}\>\>Y_{q}$ (5)

or

$\mathcal{S}\>\>n_{b}\>\>Y_{q}$ (6)

that define the grid points. The EoS data that will be stored in the final EoS
table will appear in the same sequence of the parameters as given in the file
eos.parameters. For $I_{\beta}=1$, $Y_{q}$ can be set to any value. For two-
and one-dimensional EoS tables, the parameters that are not used can be set to
arbitrary values, e.q. for a zero-temperature EoS the first entry in each row
can have any finite value. An example file eos.parameters for the tabulatfor a
zero-temperature EoS the first entry in each row can have any finite value. An
example file eos.parameters for the tabulation scheme with
$I_{\textrm{tab}}=0$ is given by

> # interpolation rules for T, n_b and Y_q
> 3 3 3
> # calculation of beta equilibrium (1: yes, else: no) and for given  entropy
> (1: yes, else: no)
> 0 0
> # tabulation scheme of parameter values (see manual)
> 0
> # parameter values depending on tabulation scheme
> 5
> 0.1 0.1 0.5
> 0.1 0.2 0.5
> 0.1 0.3 0.5
> 0.1 0.4 0.5
> 0.1 0.5 0.5
>

for generating a table using third order interpolations in $T$, $n_{b}$ and
$Y_{q}$. Five data points are calculated for constant $T=0.1$ MeV and
$Y_{q}=0.5$ at densities of $n_{b}=0.1$, $0.2$, $0.3$, $0.4$, and $0.5$ fm-3.

For $I_{\textrm{tab}}\neq 0$ the parameter values are generated in a similar
way as suggested in subsection 1. In this case, only four additional rows
follow the comment line below the row with the specification of
$I_{\textrm{tab}}$. Each column of these rows (in the order temperature,
density, charge fraction) contains the four quantities

$\begin{array}[]{c}p_{\textrm{min}}\\\ p_{\textrm{max}}\\\ N_{p}\\\
I_{p}\end{array}$ (7)

where $p$ stands for the parameters $T$, $n_{b}$ or $Y_{q}$, respectively. The
minimum and maximum values of the parameter $p$ in the EoS table are denoted
by $p_{\textrm{min}}$ and $p_{\textrm{max}}$, respectively. $N_{p}>0$ is the
number of data points in the mesh of the parameter $p$ and $I_{p}$ defines the
discretization scheme. If $I_{p}=0$, the individual points are given by a
linear interpolation

$p_{i}=p_{\textrm{min}}+(p_{\textrm{max}}-p_{\textrm{min}})\frac{i-1}{N_{p}-1}$
(8)

for $i=1,\dots,N_{p}$ with $N_{p}>1$ and

$p_{1}=p_{\textrm{min}}$ (9)

for $N_{p}=1$. For $I_{p}\neq 0$, a logarithmic scaling is used with

$p_{i}=p_{\textrm{min}}\left(\frac{p_{\textrm{max}}}{p_{\textrm{min}}}\right)^{\frac{i-1}{N_{p}-1}}$
(10)

for $i=1,\dots,N_{p}$ with $N_{p}>1$ and

$p_{1}=p_{\textrm{min}}$ (11)

for $N_{p}=1$. For this tabulation scheme an example file eos.parameters has
the form

> # interpolation rules for T, n_b and Y_q
> 3 3 3
> # calculation of beta equilibrium (1: yes, else: no) and for given  entropy
> (1: yes, else: no)
> 0 0
> # tabulation scheme of parameter values (see manual)
> 1
> # parameter values depending on tabulation scheme
> 5.0 0.01 0.3
> 5.0 1.00 0.3
>  1 201 1
>  0 1 0

Here, $T=5$ MeV and $Y_{q}=0.3$ are kept constant and the densities $n_{b}$
cover the range from $0.01$ fm-3 to $1.0$ fm-3 in $200$ intervals with a
logarithmic scaling.

In case the option $I_{\beta}=1$ is set in the third row of the file
eos.parameters, the specification of the parameter grid in $Y_{q}$ is
irrelevant.

###  Chapter 9 Structure of the compose.f90 program

(Remark: This appendix is not yet updated from version 2.00 of the manual.)

Instead of using the code compose.f90 as given, the user can employ the
subroutines directly in her/his program. The file compose.f90 contains one
main program, 31 subroutines and one function. The structure of the program
with the dependencies of the subroutines and functions is depicted in tables
1, 2 and 3. The file composemodules.f90 contains two modules.

The user needs to call the following three subroutines

> init_eos_table(iwr)
> define_eos_table(iwr)
> get_eos(t,n,y,b,ipl,i_beta,i_entr)

from the file compose.f90 in order to generate EoS data. The subroutine

> init_terminal(iwr)

is called only from the main program for running the standard terminal
version. It is usually not relevent for users that want to use subroutines
within their own programs. The first two mentioned subroutines depend on a
single integer parameter iwr. For iwr = 1 a progress report during the
execution of the subroutine will be written to the terminal. Otherwise, this
action will be suppressed. The subroutine get_eos has three double precision
parameters (t, n, y) and three integer parameters (ipl, i_beta, i_entr) as
arguments, where the first is a vector of dimension three. Be sure to include
all (sub)routines, functions and the two modules eos_tables and
compose_internal in your code.

The subroutine init_eos_table has to be called only once in order to
initialize all relevant tables and quantities. The files eos.t, eos.nb, eos.yq
and eos.thermo have to exist in order that init_eos_table is executed
properly. The files eos.compo and eos.micro are optional.

The subroutine define_eos_table defines the quantities that are interpolated
and that will be stored in the EoS table. It reads the file eos.quantities.
The subroutine needs to be called only once. Instead of calling
define_eos_table in the user’s program, it is possible that the relevant
parameters are defined directly in the user’s code. Thus it is possible to
change the selection of quantities that are interpolated during the execution
of the user’s program. In the following, the variable names to be specified by
the user are given according to the structure of the input file
eos.quantities:

> # number of regular, additional and derivative quantities
> n_qty n_add n_df
> # indices of regular, additional and derivative quantities
> idx_qty(1) …idx_qty(n_qty) idx_add(1) …idx_add(n_add) idx_df(1)
> …idx_df(n_df)
> # number of pairs and quadruples for composition data
> n_p n_q
> # indices of pairs and quadruples for composition data
> idx_p(1) … idx_p(n_p) idx_q(1) … idx_q(n_q)
> # number of microscopic quantities
> n_m
> # indices of microscopic quantities
> idx_m(1) … idx_m(n_m)
> # number of error quantities
> n_err
> # indices of error quantities
> idx_err(1) … idx_err(n_err)
> # format of output file
> iout

Note that all variables are integers. The appearing vectors with fixed size
are defined in the module compose_internal:

> idx_qty(dim_qtyt) with dim_qtyt = 23
> idx_err(dim_qtye) with dim_qtye = 8 .

where the dimensions are defined in the module eos_tables.

Finally, the subroutine get_eos can be called as often as needed with the
appropriate arguments. The double precision variables t, n and y define the
temperature $T$ [MeV], baryon number density $n_{b}$ [fm-3] and the charge
fraction of strongly interacting particles $Y_{q}$ [dimensionless],
respectively, where the EoS is evaluated. The integer indices ipl_t, ipl_n and
ipl_y define the interpolation rule in $T$, $n_{b}$ and $Y_{q}$, respectively.
For ipl_t = 1 all selected quantities are interpolated linearly such that the
interpolated values agree with the tabulated values at the grid points of the
EoS table. For ipl_t = 2 the interpolated values of a quantity and its first
derivative with respect to temperature agree with those at the grid points.
For ipl_t = 3 a continuity of also the second derivatives at the grid points
are demanded. Similarly, the interpolation rules for $n_{b}$ and $Y_{q}$ are
determined. If the index is outside the range $[1,3]$ it is set to $3$. See
appendix 7.A for details of the interpolation scheme.

The results of the interpolation are stored in seven double precision
vectors/arrays with dimensions defined in the module eos_tables or defined
according to the EoS input files:

> eos_thermo(dim_qtyt) with dim_qtyt = 23
> eos_thermo_add(dim_qty)
> eos_compo_p(dim_qtyp)
> eos_compo_q(dim_qtyq,3)
> eos_micro(dim_qtym)
> eos_err(dim_qtye) with dim_qtye = 8
> eos_df(dim_df) with dim_df = 10 .

The vector index in eos_thermo corresponds to the index $J$ given in tables 1
and 2. The vector index in eos_thermo_add is just the index
$i=1,\dots,N_{\textrm{add}}$ of the additional quantities stored in each row
of the file eos.thermo. The (first) index of the vectors/arrays eos_compo_p,
eos_compo_q and eos_compo_m corresponds to the index of the vectors idx_p,
idx_q and idx_m that are defined in the file eos.quantities or by the user
before the subroutine get_eos is called. The second index of the array
eos_compo_q is correlated with the index $J$ as given in table 4. The vector
index in eos_err corresponds to the index $J$ given in table 6. The vector
index in eos_df corresponds to the index $J$ given in table 3.

Table 1: Modules, (sub)routines and functions in the file compose.f90 with their dependencies (continued on next page). |  uses MODULE |  uses SUBROUTINE |  uses FUNCTION
---|---|---|---
PROGRAM |  |  |
compose |  | run_terminal |
|  | init_eos_table |
|  | define_eos_table |
|  | get_eos_table |
SUBROUTINE |  |  |
init_eos_table |  | read_eos_tables_tnyb |
|  | read_eos_table_thermo |
|  | read_eos_table_compo |
|  | read_eos_table_micro |
|  | get_diff_rules |
|  | init_ipl_rule |
|  | get_eos_report |
define_eos_table | compose_internal | write_errors |
get_eos_table | compose_internal | get_eos |
| m_out_to_json | write_errors |
|  | out_to_json_write |
get_eos | compose_internal | get_eos_beta |
|  | get_eos_sub |
|  | write_errors |
get_eos_beta | compose_internal | get_eos_sub |
get_eos_sub | compose_internal | get_eos_grid_para |
|  | eos_interpol |
get_eos_grid_para | compose_internal |  |
eos_interpol | compose_internal | eos_interpol_d1 |
|  | eos_interpol_d2 |
|  | eos_interpol_d3 |
eos_interpol_d1 | textttcompose_internal | get_interpol_x | get_ipl_rule
|  | write_errors |
eos_interpol_d2 | compose_internal | get_idx_arg2 | get_ipl_rule
|  | get_diff_rules2 |
|  | get_derivatives |
|  | get_coefficients |
|  | get_interpol_xy |
|  | write_errors |
Table 2: Modules, (sub)routines and functions in the file compose.f90 with their dependencies (continued from previous page). |  uses MODULE |  uses SUBROUTINE |  uses FUNCTION
---|---|---|---
SUBROUTINE |  |  |
eos_interpol_d3 | compose_internal | get_interpol_x | get_ipl_rule
|  | get_idx_arg2 |
|  | get_diff_rules2 |
|  | get_derivatives |
|  | get_coefficients |
|  | get_interpol_xy |
|  | write_errors |
get_idx_arg2 | compose_internal |  |
get_diff_rules | compose_internal |  |
get_diff_rules2 | compose_internal |  | get_ipl_rule
get_interpol_x | compose_internal |  |
get_interpol_xy | compose_internal |  |
get_derivatives | compose_internal |  |
get_coefficients | compose_internal |  |
run_terminal | compose_internal | init_eos_table_term |
|  | init_quant |
|  | init_para |
|  | get_eos_table_term |
init_eos_table_term | compose_internal | read_eos_tables_tnyb |
|  | read_eos_table_thermo |
|  | read_eos_table_compo |
|  | read_eos_table_micro |
get_eos_table_term | compose_internal | read_eos_tables_tnyb |
|  | read_eos_table_thermo |
|  | read_eos_table_compo |
|  | read_eos_table_micro |
|  | get_diff_rules |
|  | get_ipl_rule |
|  | get_eos_report |
|  | define_eos_table |
|  | get_eos_table |
init_quant | compose_internal |  |
init_para | compose_internal |  |
init_ipl_rule | compose_internal |  |
Table 3: Modules, (sub)routines and functions in the file compose.f90 with their dependencies (continued from previous page). |  uses MODULE |  uses SUBROUTINE |  uses FUNCTION
---|---|---|---
FUNCTION |  |  |
get_eos_report | compose_internal | get_eos_nmp |
|  | get_eos |
|  | write_errors |
get_eos_nmp | compose_internal | get_eos_sub |
write_errors | compose_internal |  |
read_eos_tables_tnyb | compose_internal | write_errors |
read_eos_table_thermo | compose_internal | write_errors |
read_eos_table_compo | compose_internal | write_errors |
read_eos_table_micro | compose_internal | write_errors |
get_ipl_rule | compose_internal |  |

###  Chapter 10 Organization of the CompOSE team

CompOSE is developed in close collaboration with the communities the service
is meant for. These are mainly physicists who develop equations of state or
simulate astrophysical phenomena numerically on the computer. Direct
interaction with the users is an essential part in the concept of the project.

The following persons are engaged in the preparation of the web site, the
manual and the tools, numerical codes and tables. labelinglabel FirstName
LongFamilyName

IUCAA, Pune (India),

Kent State University (Ohio, USA),

Tokyo Institute of Technology (Japan),

California State University Long Beach (California, USA),

Tours University (France),

LUTH, Observatoire de Paris (France),

LUTH, Observatoire de Paris (France),

Coimbra University (Portugal)

Coimbra University (Portugal),

NIPNE, Bucharest (Romania)

LUTH, Observatoire de Paris (France),

ICE (CSIC-IEEC), Barcelona (Spain),

Technische Universität Darmstadt and GSI Helmholtzzentrum für
Schwerionenforschung, Darmstadt (Germany).

###  Chapter 11 Citing CompOSE

If you make use of the tables provided in CompOSE, you will be guided on the
CompOSE web pages to the scientific publications where the particular EoS
models have been described in detail. Please cite them when using the tables
for scientific purposes together with a reference to the CompOSE website
(https://compose.obspm.fr) and/or the original CompOSE publications:

    @article{Oertel:2016bki,
        author = "Oertel, M. and Hempel, M. and Klaehn, T. and Typel, S.",
        title = "{Equations of state for supernovae and compact stars}",
        eprint = "1610.03361",
        archivePrefix = "arXiv",
        primaryClass = "astro-ph.HE",
        doi = "10.1103/RevModPhys.89.015007",
        journal = "Rev. Mod. Phys.",
        volume = "89",
        number = "1",
        pages = "015007",
        year = "2017"
    }

    @article{Typel:2013rza,
        author = "Typel, S. and Oertel, M. and Klaehn, T.",
        title = "{CompOSE CompStar online supernova equations of state
                  harmonising the concert of nuclear physics and astrophysics
                  compose.obspm.fr}",
        eprint = "1307.5715",
        archivePrefix = "arXiv",
        primaryClass = "astro-ph.SR",
        doi = "10.1134/S1063779615040061",
        journal = "Phys. Part. Nucl.",
        volume = "46",
        number = "4",
        pages = "633--664",
        year = "2015"
    }

###  Chapter 12 Acknowledgments

CompOSE would not be possible without the financial and organisatorial support
from a large number of institutions and individual contributors. We gratefully
acknowledge support by CompStar, NewCompStar, and PHAROS, Research Networking
Programs of the European Science Foundation (ESF) and the birthplace of the
CompOSE project, by a grant from the Polish Ministry for Science and Higher
Education (MNiSW) supporting the “CompStar”-activity, by the Instytut Fizyki
Teoretycznej of the Uniwersytet Wrocławski, the National Science Centre Poland
(Narodowe Centrum Nauki, NCN) within the “Maestro”-programme under contract
No. DEC-2011/02/A/ST2/00306, by the “hadronphysics3” network within the
seventh framework program of the European Union, by the GSI Helmholtzzentrum
für Schwerionenforschung GmbH, by the Helmholtz International Center for FAIR
within the framework of the LOEWE program launched by the state of Hesse via
the Technical University Darmstadt, by the Helmholtz Association (HGF) through
the Nuclear Astrophysics Virtual Institute (VH-VI-417), by the ExtreMe Matter
Institute EMMI in the framework of the Helmholtz Alliance ‘Cosmic Matter in
the Laboratory’, by the DFG cluster of excellence “Origin and Structure of the
Universe”, by the DFG through grant SFB 1245, by the SN2NS project
ANR-10-BLAN-0503 and by the MPNS COST action MP1304 “Exploring fundamental
physics with compact stars (NewCompStar)” within the EU framework programme.
We thank Jean-Yves Giot for creating the first version of the web site.

### References

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### Index

  * ’quick guide for users item 2
  * $\\#$ Appendix 8.B
  * $\overline{d}$ Table 3
  * $\bar{K}^{0}$ Table 4
  * $\overline{n}$ Table 2, Table 3
  * $\overline{p}$ Table 2, Table 3
  * $\overline{s}$ Table 2, Table 3
  * $\overline{u}$ Table 2, Table 2, Table 3
  * $\overline{\Delta}^{-}$ Table 2, Table 3
  * $\overline{\Delta}^{+}$ Table 2, Table 3
  * $\overline{\Delta}^{++}$ Table 2, Table 3
  * $\overline{\Delta}^{0}$ Table 2, Table 3
  * $\overline{\Lambda}$ Table 2, Table 3
  * $\overline{\Xi}^{-}$ Table 2, Table 3
  * $\overline{\Xi}^{0}$ Table 2, Table 3
  * $\overline{\Sigma}^{-}$ Table 2, Table 3
  * $\overline{\Sigma}^{+}$ Table 2, Table 3
  * $\overline{\Sigma}^{0}$ Table 2, Table 3
  * $\frac{\partial^{2}\mathcal{F}}{\partial n_{b}\partial Y_{q}}$ Table 3
  * $\frac{\partial^{2}\mathcal{F}}{\partial n_{b}^{2}}$ Table 3
  * $\frac{\partial^{2}\mathcal{F}}{\partial T\partial n_{b}}$ Table 3
  * $\frac{\partial^{2}\mathcal{F}}{\partial T\partial Y_{q}}$ Table 3
  * $\frac{\partial^{2}\mathcal{F}}{\partial T^{2}}$ Table 3
  * $\frac{\partial^{2}\mathcal{F}}{\partial Y_{q}^{2}}$ Table 3
  * $\frac{\partial\mathcal{F}}{\partial n_{b}}$ Table 3
  * $\frac{\partial\mathcal{F}}{\partial Y_{q}}$ Table 3
  * $\sum_{i}{}^{\prime}$ 8, 9
  * $\$$ Appendix 8.B
  * ${}^{1}S_{0}$ Table 5
  * ${}^{3}S_{1}$ Table 5
  * $A$ Table 2
  * $A^{\textrm{av}}$ item 2, Table 4, Table 8, Appendix 8.B
  * $A^{\textrm{av}}_{I_{i}}$ 20
  * $A_{i}$ §3, §3
  * antiparticle §3
  * approximation
    * quadratic §1
  * asymmetry §1
  * Atomic Mass Evaluation §1
  * atomic mass unit §3
  * $B$ 2
  * baryon Appendix 8.B
    * number §3, Table 2, Table 4, Table 5
  * basis function
    * quintic §1
  * $B_{i}$ §3, Table 2, Table 4, Table 5, Table 5
  * binding energy §1
  * $B_{\textrm{sat}}$ 2nd item, §1
  * $c$ §1, Table 1
  * charge
    * neutrality §2, §3, §3, §2
    * number Table 2, Table 4, Table 5
  * chemical potential Appendix 7.B
    * lepton
      * effective §2
  * CODATA §1
  * coefficient
    * expansion §6
    * tension §6
    * thermodynamic §6
  * collision
    * heavy-ion §2
  * compiler
    * C §1
    * Fortran90 §1
    * GNU §1
  * compose §1, item 1, item 1, item 1, item 1, item 1, item 2, item 2, item 2, §5, §1, §1, §2, Appendix 8.A, Chapter 8, Chapter 8
  * compose.f90 §3, §1, §1, Chapter 7, Chapter 9, Table 1, Table 1, Table 2, Table 2, Table 3, Table 3
  * composemodules.f90 §1, §1, Chapter 9
  * composition §4
  * compressibility
    * adiabatic §6
    * isothermal §6, 3rd item
  * compression modulus 3rd item
  * consistency
    * thermodynamic §2, Chapter 7
  * constant
    * Boltzmann’s Table 1
    * fine structure Table 1
    * gravitational Table 1
    * Planck’s Table 1
  * correlation §4
  * $c_{p}$ 46, Table 1
  * $c_{s}$ 51, Table 1
  * cube Appendix 7.A, Appendix 7.A
  * curvature 3rd item
  * $c_{V}$ 42, Table 1
  * $d$ Table 3
  * data sheet Chapter 3, §2, §3, §3, §2, §4, §4
  * definition
    * relativistic Appendix 8.B
  * density
    * antiparticle §3
    * central §10, 4th item
    * charge §3
    * composite §5
    * energy
      * free §5
    * entropy §5
    * lepton
      * effective §2
    * mass §3
      * total §3, Appendix 8.B
    * meson §3
    * net §3
    * number §3
      * baryon §3, §4, item 2, item 1
      * composite §3
      * lepton §3
      * strangeness §3, §3
    * saturation 1st item, §1, §1, §2
  * density of states §7
  * derivative §1, §1, §1, §2, §2
  * discretization Chapter 3, §1
  * $E$ 27, 32, §1, Table 1, Table 2, Appendix 8.B, Appendix 8.B
  * $e$ §5, Table 2
  * $e^{2}$ Table 1
  * effective mass
    * Dirac §7
    * Landau §7
  * $E_{i}$ 58
  * electron §2, Chapter 5
  * energy §1
    * binding 2nd item
    * free §5, Chapter 3, Table 3
    * Helmholtz free §5
    * internal §5
      * specific Appendix 8.B
      * total §3
    * kinetic §7
    * per nucleon §1
    * single-particle §7
    * symmetry 3rd item, 5th item, §1
      * slope 6th item
  * enthalpy §5
    * free §5
  * entropy §5
  * eos.beta §4
  * eos.compo 2nd item, item 1, item 1, item 2, Appendix 8.B
  * eos.init item 1, item 2, item 2, item 2, Appendix 8.A, Appendix 8.A, Appendix 8.A, Chapter 8
  * eos.micro 3rd item, item 1, item 1, item 2, Appendix 8.B
  * eos.mr 1st item, item 1
  * eos.nb 2nd item, item 1, item 1, item 2
  * eos.nb.ns item 1
  * eos.parameters item 1, item 2, item 2, item 2, Appendix 8.C, Appendix 8.C, Appendix 8.C, Appendix 8.C, Appendix 8.C, Chapter 8
  * eos.quantities item 1, item 2, item 2, item 2, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Chapter 8, Chapter 9
  * eos.report §4
  * eos.t 1st item, item 1, item 1, item 2
  * eos.table item 2c, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B, Appendix 8.B
  * eos.thermo 1st item, item 1, item 1, item 2, Appendix 8.B
  * eos.thermo.ns item 1
  * eos.yq 3rd item, item 1, item 1, item 2
  * eoscompose.h5 §3, Appendix 8.B, Appendix 8.B
  * equation of state §5
    * general purpose 1st item, Appendix 7.A
    * hadronic §2
    * neutron matter 3rd item, 2nd item
    * one-dimensional item 3
    * selection item 1
    * symmetric matter 2nd item, 1st item
    * table §3
    * three-dimensional item 1
    * two-dimensional item 2
    * zero temperature 1st item
    * $\beta$ equilibrium 4th item, 3rd item, §3
  * equilibrium
    * chemical §2
    * thermodynamic §2, §2, §2
    * weak §2
    * $\beta$ §2, Appendix 7.B
  * error
    * absolute Appendix 8.B
    * estimate Appendix 8.B
    * relative Appendix 8.B
  * error message §5, §5
  * $E_{\textrm{sym}}$ 4
  * $F$ 31, §5, Chapter 3, Table 1, Table 1, Table 2, Table 3, Table 3, Appendix 8.B, Appendix 8.B
  * $f$ 21, 5, 8, 9, §2
  * Fermi gas Chapter 5
  * format
    * ASCII Appendix 8.B
    * HDF5 4th item, Appendix 8.B
    * output Appendix 8.B
  * formula
    * finite difference §1
  * fraction
    * charge §3, §4, item 3, item 1
    * electron §3, item 1
    * lepton
      * total §3
    * particle Appendix 8.B
    * particle mass §3
    * particle number §3
  * $f_{T}$ item 1
  * function
    * homogeneous §5
  * $f_{\gamma}$ 72
  * $G$ 28, 34, Table 1, Table 1, Table 2, Appendix 8.B
  * $g$ §5
  * giant resonance
    * isoscalar monopole 3rd item
  * Gogny item 1
  * grid
    * three-dimensional Appendix 7.A
    * two-dimensional Appendix 7.A
  * grid point §1, Appendix 7.A, Chapter 7, Appendix 8.C
  * $H$ 29, 33, Table 2, Appendix 8.B
  * $h$ §5
  * $\hbar$ §1, Table 1
  * hdf5compose.f90 §1
  * hdf5writecompose.c §1
  * heat capacity §6, §6
  * homogeneity §2, Appendix 8.B
  * hyperon §2, §2
  * $i$ Appendix 7.A
  * $I_{\textrm{add}}$ Table 7
  * $I_{\textrm{av}}$ Table 8
  * identifier Appendix 8.B, Appendix 8.B
    * HDF5 §3, Table 7, Table 8
  * $I_{\textrm{entr}}$ Appendix 8.C
  * $I_{i}$ Table 2, Table 3, Table 4, Table 5, §3, §4, Table 4, Table 8
  * $I_{l}$ §2
  * $I_{n_{b}}$ Appendix 8.C
  * $i_{n_{b}}$ 18, 24, 3, Appendix 7.A, Chapter 7
  * incompressibility 3rd item
    * symmetry 7th item
  * index
    * adiabatic §6
    * composite §4, Appendix 8.B
    * correlation §4
    * particle §4
    * quadruple item 2
    * triple Appendix 7.A, Chapter 7
  * indexing
    * particle §4
  * interpolation Chapter 3, §5, Appendix 7.A, Chapter 7, Appendix 8.B, Appendix 8.C
    * biquintic §2
    * coefficient §1
    * one-dimensional Appendix 7.A, §1
    * order Appendix 7.A, §2
    * two-dimensional Appendix 7.A, Appendix 7.A, §2
  * $I_{p}$ 7
  * $I_{\textrm{phase}}$ item 4, §3, Table 4
  * isospin 5th item
  * $I_{T}$ Appendix 8.C
  * $i_{T}$ 1, 18, 24, Appendix 7.A, Chapter 7
  * $I_{\textrm{tab}}$ Appendix 8.C
  * $I_{Y_{q}}$ Appendix 8.C
  * $i_{Y_{q}}$ 18, 24, 4, Appendix 7.A, Chapter 7
  * $I_{\beta}$ Appendix 8.C
  * $J$ 10, §1, Table 7, Appendix 8.B
  * $j$ Appendix 7.A
  * $J_{\textrm{err}}$ Table 8
  * $J_{i}$ §4
  * $K$ 7, 3rd item, §1, Table 8
  * $k$ Appendix 7.A
  * $K^{-}$ Table 4
  * $K^{\prime}$ §1
  * $K^{+}$ Table 4
  * $K^{0}$ Table 4
  * kaon §2, §2
  * $k_{B}$ §1, Table 1
  * $k_{F}$ §1
  * $K_{i}$ §4, Appendix 8.B
  * $K_{\textrm{sym}}$ 12, §1
  * $L$ 11, §1
  * $L^{e}_{i}$ §3, Table 2, Table 4, Table 5
  * length §1
  * lepton §2
    * number §3, Table 2, Table 4
  * LORENE §10, item 1
  * $L^{\mu}_{i}$ §3, Table 2, Table 4, Table 5
  * $M$ §10, 2nd item
  * Makefile §1
  * manual Chapter 10
  * mass
    * compact star §10, 2nd item
    * electron Table 1
    * muon Table 1
    * neutron §3, Table 1
    * neutron star §10
    * proton Table 1
  * mass formula
    * Bethe-Weizsäcker 2nd item
  * matter
    * cold §2
    * hadronic §2, §1
    * neutron §2
    * nuclear §2
    * quark §2
    * stellar §2
    * symmetric §2
    * uniform §1
    * $\beta$ equilibrium Appendix 7.B
  * maximum mass §3
  * $m^{D}_{i}$ 59, item 2
  * $m^{D}_{I_{i}}$ Table 5
  * $m_{e}$ Table 1
  * meson §3, Appendix 8.B
  * $m_{i}$ §5
  * $m^{L}_{i}$ 54, item 1
  * $m^{L}_{I_{i}}$ Table 5
  * $m_{n}$ Table 1, §2, §2
  * $M_{n_{b}}$ item 2
  * module Chapter 9, Chapter 9, Chapter 9, Table 1, Table 2, Table 3
  * momentum
    * Fermi §1
  * $m_{p}$ Table 1, §2
  * $M_{T}$ item 1
  * muon §2, Chapter 5
  * $M_{Y_{q}}$ item 3
  * $m_{\mu}$ Table 1
  * $n$ Table 2, Table 3
  * $N_{\textrm{add}}$ §2, Table 7, Appendix 8.B, Appendix 8.B
  * $N^{\textrm{av}}$ Table 4, Appendix 8.B
  * $N^{\textrm{av}}_{I_{i}}$ §3
  * $N_{b}$ 35
  * $n_{b}$ 2, §3, §5, item 2, item 2, item 1, Table 7
  * $n_{b}^{\textrm{ref}}$ item 2
  * $n_{b}^{\textrm{sat}}$ 1st item, §1, §1
  * $n_{c}$ §10, 4th item
  * $N_{\textrm{data}}$ Table 7, Appendix 8.C
  * $N_{\textrm{deriv}}$ Appendix 8.B, Appendix 8.B
  * $n_{e}$ §3
  * $N_{\textrm{err}}$ Table 8, Appendix 8.B
  * neutrino §2
  * $N_{i}$ §3, §5, Chapter 3
  * $n_{i}$ 1
  * $n_{l}$ 6
  * $n_{le}$ §3, §5
  * $n_{l\mu}$ §3, §5
  * $N_{\textrm{mic}}$ Table 8, Appendix 8.B
  * $N_{n_{b}}$ Table 7
  * $N_{n_{b}}^{\textrm{max}}$ item 2
  * $N_{n_{b}}^{\textrm{min}}$ item 2
  * $N_{\textrm{p}}$ Table 8, Appendix 8.B, Appendix 8.B, 7
  * $N_{\textrm{pair}}$ §3
  * $N_{\textrm{q}}$ Table 8, Appendix 8.B, Appendix 8.B
  * $n_{q}$ 8, §3, §5
  * $N_{\textrm{qty}}$ §4
  * $N_{\textrm{quad}}$ §3
  * $n_{s}$ 4, §3, §5
  * $N_{T}$ Table 7
  * $N_{\textrm{thermo}}$ Table 7, Appendix 8.B, Appendix 8.B
  * $N_{T}^{\textrm{max}}$ item 1, §7
  * $N_{T}^{\textrm{min}}$ item 1, §7
  * Nubase §1
  * nucleus §3, Appendix 8.B
  * $N_{Y_{q}}$ Table 7
  * $N_{Y_{q}}^{\textrm{max}}$ item 3
  * $N_{Y_{q}}^{\textrm{min}}$ item 3
  * $N_{\beta}$ Appendix 8.C
  * $n_{\mu}$ §3
  * out_to_json.f90 §1
  * $p$ 25, Table 2, Table 3, 6, Table 1, Appendix 8.B, Appendix 8.C
  * pair Appendix 8.B
  * pairing §4
    * gap §7
    * neutron §7
  * parameter Chapter 7
    * independent Appendix 7.B
    * interpolation Appendix 7.A
    * nuclear matter Chapter 5
    * range §1, §1, §2
    * recommended §1, 1st item, 1st item, 2nd item, 3rd item, 4th item, 1st item, 2nd item, 3rd item, Table 1, Table 2, Table 3, Table 4
  * particle
    * fraction §3
    * index §4, Table 2, Table 3, Table 4, Table 5
    * number §3, §5, Chapter 3
  * pasta phase item 2
  * phase §3, §3
    * diagram §2
    * hadronic §2
    * transition §1, §2
  * photon §2, §9, Chapter 5
  * $p_{i}$ 8
  * pion §2
  * $p_{\textrm{max}}$ 7
  * $p_{\textrm{min}}$ 7
  * potential
    * chemical §2, §5
      * baryon §5
      * charge §5
      * electron §5
      * individual Appendix 8.B
      * lepton Appendix 7.B
      * muon §5
      * neutrino Appendix 7.B
      * strangeness §2, §5
    * Gibbs §5
    * grand canonical §5
    * single-particle §7
    * thermodynamic §5
  * precision §9
  * pressure §5, 1st item
  * property
    * thermodynamic §5
  * $p_{\gamma}$ 74
  * $Q$ 8, 9, §1, Table 7, Appendix 7.A
  * $q$ Table 7
  * $Q^{(n)}_{ijk}$ 10
  * QCD §2
  * $q_{\textrm{err}}$ Table 8
  * $Q_{i}$ §3, Table 2, Table 4, Table 5, Table 5, §2, Chapter 7
  * $q_{i}$ §2, 9
  * $Q_{ij}^{(mn)}$ §2
  * $q_{\textrm{mic}}$ Table 8
  * $q_{mn}$ §2
  * quadruple Appendix 8.B
  * quantity
    * additional §2
    * compositional Table 4, Appendix 8.B
    * conserved Appendix 8.B
    * microscopic §4, Table 5, Appendix 8.B
    * stored Chapter 7
    * tabulated Appendix 7.A
    * thermodynamic Table 1, Table 2, Chapter 7
  * quark Appendix 8.B
    * baryon number §3
    * strange §2
  * quark-gluon plasma §2
  * quick guide for providers Chapter 3
  * quick guide for users §1
  * $R$ §10, §10, 1st item
  * radius
    * compact star §10, 1st item
    * neutron star §10
  * reaction
    * rate §2
    * weak interaction Appendix 7.B
  * references §3
  * relation
    * Maxwell §5, §2
  * resolution item 1, §1
  * rest mass §5, §5
  * RNS §10
  * $S$ 23, 4, Table 1, Appendix 8.B
  * $s$ 22, Table 2, Table 3
  * saturation §1
  * self-energy
    * scalar §7
    * vector §7
  * $S_{i}$ 61, §3, Table 2, Table 4, Table 5, Table 5, item 5
  * $S_{I_{i}}$ Table 5
  * skewness 4th item
  * skin thickness
    * neutron 6th item
  * Skyrme item 1
  * speed of light Table 1
  * speed of sound §6
  * spin §3
    * ground state §1
    * half-integer §3
    * integer §3
  * star
    * neutron §2
  * strangeness §2
    * number §3, Table 2, Table 4, Table 5
  * subroutine Chapter 9, Chapter 9, Chapter 9, Table 1, Table 2, Table 3
  * superconductivity §7
  * superfluidity §7
  * supernova
    * core-collapse §2
  * $s_{\gamma}$ 73
  * $T$ §3, §5, Chapter 3, item 1, item 1, item 1, Table 7
  * table
    * composition §1, §3
    * EoS Chapter 3, §2, §1
    * format Chapter 3, §1, §9
    * general purpose §2
    * HDF5 §3
    * identification §8
    * input §1
    * mass-radius §6
    * microscopic §1, §4
    * one-dimensional Appendix 8.C
    * order §2
    * parameter §7
    * thermodynamic §1, §2
    * three-dimensional Appendix 7.A, Appendix 8.C
    * transport §5
    * two-dimensional Appendix 8.C, Appendix 8.C
  * tauon §2
  * team
    * organization Chapter 10
  * temperature §1, §4, §5, Chapter 3, item 1, item 1
  * theorem
    * Euler’s §5
  * $T_{i}$ 56
  * tidal deformability §10, §10, 3rd item
  * time scale §2
  * TOV §10
  * transformation
    * Legendre §5
  * $T^{\textrm{ref}}$ item 1
  * $u$ Table 1, Table 2, Table 2, Table 3
  * $U_{i}$ 57, item 3
  * $U_{I_{i}}$ Table 5
  * units §1
  * Urca §10, §3
  * $V$ §3, §5, Chapter 3
  * valley of stability 5th item
  * variable
    * conjugate §5
    * extensive §5, §5
    * intensive §5
    * natural §5, Chapter 3
  * $V_{i}$ 62, item 4
  * $V_{I_{i}}$ Table 5
  * volume §3, §5, Chapter 3
  * web page §3, §1, §4
  * web site Chapter 10, Chapter 3, §3
  * $x$ 3
  * $X^{\textrm{av}}$ Table 4
  * $X_{i}$ 12
  * $x_{i}$ §5
  * $Y^{\textrm{av}}$ Table 8, Appendix 8.B
  * $Y_{e}$ 14, item 1
  * $Y_{I}$ Table 8
  * $Y_{i}$ 10, item 1, §3, §3, Table 4, Appendix 8.B
  * $Y_{I_{i}}$ 22
  * $Y_{l}$ 15
  * $Y_{q}$ 13, item 3, item 3, item 1, Table 7
  * $Y_{\mu}$ 16
  * $Z$ Table 2
  * $Z^{\textrm{av}}$ item 3, Table 4, Table 8, Table 8, Appendix 8.B
  * $Z^{\textrm{av}}_{I_{i}}$ §3
  * $Z_{i}$ §3
  * $\alpha$ Table 1, 1
  * $\alpha_{p}$ 45, Table 1
  * $\beta_{V}$ 43, Table 1
  * $\Gamma$ 47, Table 1
  * $\gamma$ Table 4
  * $\Delta^{-}$ Table 2, Table 3
  * $\delta^{-}$ Table 4
  * $\Delta^{+}$ Table 2, Table 3
  * $\delta^{+}$ Table 4
  * $\Delta^{++}$ Table 2, Table 3
  * $\Delta^{0}$ Table 2, Table 3
  * $\delta^{0}$ Table 4
  * $\Delta\mathcal{E}$ Table 6
  * $\Delta\mathcal{F}$ Table 6, 1
  * $\Delta_{i}$ 63, item 6
  * $\Delta_{I_{i}}$ Table 5
  * $\Delta\mathcal{S}$ Table 6, 4
  * $\varepsilon$ Table 1, Appendix 8.B
  * $\zeta$ Table 2
  * $\eta$ Table 4, Table 2
  * $\eta^{\prime}$ Table 4
  * $\kappa$ Table 2
  * $\kappa_{S}$ 48, Table 1
  * $\kappa_{T}$ 3rd item, Table 1
  * $\Lambda$ 78, §10, Table 2, Table 3, 3rd item
  * $\mu_{b}$ §5, §2, Table 1
  * $\mu_{i}$ 24, 26
  * $\mu_{l}$ 7, §2, Table 1, 40
  * $\mu_{le}$ §5
  * $\mu_{l\mu}$ §5
  * $\mu_{q}$ §5, §2, Table 1
  * $\mu_{s}$ §3, §5
  * $\mu_{\gamma}$ 75
  * $\Xi$ §5
  * $\Xi^{-}$ Table 2, Table 3
  * $\Xi^{0}$ Table 2, Table 3
  * $\xi_{j}$ §5
  * $\pi^{-}$ Table 4
  * $\pi^{+}$ Table 4
  * $\pi^{0}$ Table 4
  * $\varrho$ §3
  * $\rho^{-}$ Table 4
  * $\rho^{+}$ Table 4
  * $\rho^{0}$ Table 4
  * $\sigma$ Table 4, Table 2
  * $\Sigma^{-}$ Table 2, Table 3
  * $\Sigma^{+}$ Table 2, Table 3
  * $\Sigma^{0}$ Table 2, Table 3
  * $\Sigma_{i}$ 61
  * $\sigma_{s}$ Table 4
  * $\Sigma^{\mu}_{i}$ §7
  * $\phi$ Table 4
  * $\psi_{m}^{(n)}$ 22
  * $\Omega$ 30
  * $\omega$ §5, Table 4