Read me first
This is a short note on the use of the relativistic EOS table. Please read through before
you use it.

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EOS updates

We name different versions of the EOS table as follows. The ranges of the temperature T ,proton fraction Yp , and baryon mass density ρB are listed in Table 1.
• EOS1: 1998-version, with only nucleons.
The detailed description can be found in the file guide EOS1.pdf and the reference
PTP100(1998)1013.

• EOS2: 2010-version, with only nucleons.
The framework and contents in EOS2 are the same as in EOS1, so one can refer tothe same documents and guide EOS2.pdf. Comparing with EOS1, there are mainly six
improvements in EOS2:(1) We have increased T grids as shown in Table 1.
(2) We have used linear mesh for Yp .
(3) We have taken regular logarithmic meshes for T and ρB .
(4) We have consistently used the physical constants given by Table 2 in all codes.
(5) We have deleted column 3 in EOS1 which is log10 (Yp ).
(6) We have corrected wrong µp for the case of Yp = 0 and T = 0 in EOS1.

• EOS3: 2010-version, with nucleons and Λ hyperons.
The framework including Λ hyperons is based on PTP115(2006)325. The ranges andcontents in EOS3 are the same as in EOS2 besides two more columns (columns 17 and18) are added in EOS3.

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Table 1: The ranges of the temperature T , proton fraction Yp , and baryon mass density ρBin these EOSs. In addition, the cases of T = 0 and Yp = 0 are also provided.
VersionParameter

Minimum

Maximum

Mesh

NumberEOS1

log10 (T ) [MeV]

-1.00

2.00

∼0.10

31+1

log10 (Yp )-2.00-0.250.025

71+1log10 (ρB ) [g/cm3 ]

5.10

15.40

∼0.10

104

log10 (T ) [MeV]

-1.00

2.60

0.04

91+1

Yp

0.01

0.65

0.01

65+1

log10 (ρB ) [g/cm3 ]

5.10

16.00

0.10110log10 (T ) [MeV]

-1.00

2.60

0.04

91+1

Yp

0.01

0.65

0.01

65+1

log10 (ρB ) [g/cm3 ]

5.10

16.00

0.10

110

EOS2

EOS3

Table 2: The physical constants used in EOS2 and EOS3 taken from PLB667(2008)103.

1.1

Quantity

SymbolValue

conversion constanth̄c197.327 [MeVfm]

atomic mass unitmu931.494 [MeV]

circumference ratioπ

3.141592653

Contents in EOSs

We briefly list the definitions of the quantities tabulated in EOS2 and EOS3. For moredetailed description of these quantities, one can refer to guide EOS2.pdf, guide EOS3.pdf,and PTP100(1998)1013. The file eos.tab is the main table except the cases of T = 0 (givenby eos.t00) and Yp = 0 (given byeos.yp0). log10 (T ) and T are written at the beginning ofeach block as “Log10(Temp)” and “Temp” in the table, while we use a string of characters“cccccccccccc” to divide blocks with different T . In each block, the quantities in the columns
are• (C1) logarithm of baryon mass density: log10 (ρB ) [g/cm3 ]• (C2) baryon number density: nB [fm−3 ]• (C3) proton fraction: Yp2• (C4) free energy per baryon relative to the free nucleon mass M : F [MeV], F = nfB − M• (C5) internal energy per baryon relative to the atomic mass unit mu : Eint [MeV],
Eint = n²B − mu . Note that we have used mu = 931.494 MeV in EOS2 and EOS3 insteadof mu = 931.49432 MeV in EOS1.
• (C6) entropy per baryon: S [kB ]• (C7) mass number of the heavy nucleus: A• (C8) charge number of the heavy nucleus: Z∗ [MeV]• (C9) effective nucleon mass: MN• (C10) free neutron fraction: Xn• (C11) free proton fraction: Xp• (C12) alpha-particle fraction: Xα• (C13) heavy nucleus fraction: XA• (C14) pressure: p [MeV/fm3 ]• (C15) chemical potential of the neutron relative to the free nucleon mass M : µn [MeV].
In EOS3, neutrons and Λ hyperons have the same chemical potential, µn +M = µΛ +MΛ .
• (C16) chemical potential of the proton relative to the free nucleon mass M : µp [MeV]• (C17) effective Λ mass: MΛ∗ [MeV]• (C18) Λ hyperon fraction: XΛ , which is defined by XΛ = nΛ /nB .

1.2

EOS checking

We have done the following check for these EOSs:(1) the consistency of the fractions,Xp + Xn + XΛ + Xα + XA = 1.
(2) the consistency of the relation between F , Eint , and S,
F = Eint − T S + mu − M.

3(3) the consistency of the thermodynamical quantities,
F = µn (1 − Yp ) + µp Yp −p.
nB

In general, these consistency relations can be satisfied within a few thousandths.

2Documents

The detailed description on EOS1, EOS2, and EOS3 can be found in the files guide EOS1.pdf,guide EOS2.pdf, and guide EOS3.pdf, respectively. Please refer to the following papers when
you publish scientific articles by using these EOSs.
• (1) Relativistic equation of state of nuclear matter for supernova and neutron star,
H. Shen, H. Toki, K. Oyamatsu and K. Sumiyoshi, Nuclear Physics A637 (1998) 435-450.
• (2) Relativistic equation of state of nuclear matter for supernova explosion,
H. Shen, H. Toki, K. Oyamatsu and K. Sumiyoshi, Progress of Theoretical Physics, 100(1998) 1013-1031.
We will write another paper on EOS2 and EOS3 in near future.

3Contact

If you find any error or strange behavior, please contact us. We would appreciate it very much
if you could give us suggestions on these EOSs. Please contact one of the following authors========================================
Hong Shen
School of Physics, Nankai University,Tianjin 300071, China
E-mail: shennankai@gmail.com================================================================================
Kohsuke Sumiyoshi
Physics Group, Numazu College of Technology (NCT),
Ooka 3600, Numazu, Shizuoka 410-8501, Japan
E-mail: sumi@numazu-ct.ac.jp========================================

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