TY - JOUR
T1 - Erratum
T2 - Finite-temperature extension for cold neutron star equations of state (Astrophysical Journal (2019) 875 (12) DOI: 10.3847/1538-4357/ab08ea)
AU - Raithel, Carolyn A.
AU - zel, Feryal
AU - Psaltis, Dimitrios
N1 - Publisher Copyright:
© 2021 Institute of Physics Publishing. All rights reserved.
PY - 2021/7/1
Y1 - 2021/7/1
N2 - In the published article, there was a typo in the expression for the effective mass in symmetric nuclear matter. Where the published article stated that Mp Mn 0.5MSM * * * , the correct statement should read that Mp Mn MSM * * *. That is, the average of the neutron and proton effective masses should give the overall effective mass of symmetric nuclear matter. This factor of 2 error in MSM * was carried throughout the framework, including in the calculations of the level-density parameter, a, and the corresponding calculations of Eth and Pth in the degenerate regime. Additionally, the effective mass approximation should be a function of the total baryon density (n), not of the density of each nucleon species (nq = 0.5n). To correct for these errors, every instance of 0.5MSM 0.5n *( )should be replaced with MSM n * ( ). Correcting for this error leads to only minor changes in the agreement we originally reported between the thermal pressure predicted by the M* model and a sample of tabulated equations of state. We provide key updated expressions below and include new figures to summarize the changes. The conclusions of the published article remain unchanged. The correct expressions for the smoothed thermal energy and pressure, given in Boxes I and II in the published article, are now (Equation presented) The emaining derivatives provided in Appendix B are all correct, with the replacement M*(nq) ? MS*M(n). The M* fits reported in Table 2 in the published article are unaffected, as are the M* plots in Figures 4 and 5 in the published article. With the same M* parameters, we now find a slightly improved fit to the tabulated thermal pressures. The revised Figure 6 (which is identical to Figure 6 in the published article but now includes the corrections discussed above) shows the agreement between the M*-approximation of the thermal pressure and that predicted by NL3, which is most visibly improved in the region around and just below nsat. We also find that Pth is more sensitive to the choice of the M* parameters with the corrected model, as shown in the revised Figure 7 (see Figure 7 in the published article). In the published article, the M*-approximation was able to reproduce the thermal pressure of realistic EOS tables to within ?30% at densities above the nuclear saturation density (see Figure 8 in the published article). We show the updated residuals for Pth between the corrected model and a sample of finite-temperature EOSs in Figure 8, where the dotted gray line indicates 30% errors. We find that, in general, the residuals with the corrected M* formalism are comparable to those found in the published article. At (Figure presented) some densities, the errors are actually reduced. For example, the residuals at nsat and T = 10 MeV have been reduced by a factor of 2, from 30% to ?15%, with the corrected framework. We note two additional typos, which do not affect any of the results or other calculations in the published article, but which we correct here for completeness. First, there was a typo in Equation (17) for the kinetic symmetric energy. Equation (17) should be replaced with (Equation presented) Because only the product hEsym n kin ( ) is ever used in the complete framework, these errors cancel and the resulting calculations are not affected. Finally, the ideal-gas entropy in Equation (36) contained a typo. Additionally, the electrons are already accounted for as relativistic species (for kBT >1 MeV), and thus should not enter the expression. The correct ideal-gas entropy for the nucleonic species is given by (Equation presented) All other results of the published article remain unchanged.
AB - In the published article, there was a typo in the expression for the effective mass in symmetric nuclear matter. Where the published article stated that Mp Mn 0.5MSM * * * , the correct statement should read that Mp Mn MSM * * *. That is, the average of the neutron and proton effective masses should give the overall effective mass of symmetric nuclear matter. This factor of 2 error in MSM * was carried throughout the framework, including in the calculations of the level-density parameter, a, and the corresponding calculations of Eth and Pth in the degenerate regime. Additionally, the effective mass approximation should be a function of the total baryon density (n), not of the density of each nucleon species (nq = 0.5n). To correct for these errors, every instance of 0.5MSM 0.5n *( )should be replaced with MSM n * ( ). Correcting for this error leads to only minor changes in the agreement we originally reported between the thermal pressure predicted by the M* model and a sample of tabulated equations of state. We provide key updated expressions below and include new figures to summarize the changes. The conclusions of the published article remain unchanged. The correct expressions for the smoothed thermal energy and pressure, given in Boxes I and II in the published article, are now (Equation presented) The emaining derivatives provided in Appendix B are all correct, with the replacement M*(nq) ? MS*M(n). The M* fits reported in Table 2 in the published article are unaffected, as are the M* plots in Figures 4 and 5 in the published article. With the same M* parameters, we now find a slightly improved fit to the tabulated thermal pressures. The revised Figure 6 (which is identical to Figure 6 in the published article but now includes the corrections discussed above) shows the agreement between the M*-approximation of the thermal pressure and that predicted by NL3, which is most visibly improved in the region around and just below nsat. We also find that Pth is more sensitive to the choice of the M* parameters with the corrected model, as shown in the revised Figure 7 (see Figure 7 in the published article). In the published article, the M*-approximation was able to reproduce the thermal pressure of realistic EOS tables to within ?30% at densities above the nuclear saturation density (see Figure 8 in the published article). We show the updated residuals for Pth between the corrected model and a sample of finite-temperature EOSs in Figure 8, where the dotted gray line indicates 30% errors. We find that, in general, the residuals with the corrected M* formalism are comparable to those found in the published article. At (Figure presented) some densities, the errors are actually reduced. For example, the residuals at nsat and T = 10 MeV have been reduced by a factor of 2, from 30% to ?15%, with the corrected framework. We note two additional typos, which do not affect any of the results or other calculations in the published article, but which we correct here for completeness. First, there was a typo in Equation (17) for the kinetic symmetric energy. Equation (17) should be replaced with (Equation presented) Because only the product hEsym n kin ( ) is ever used in the complete framework, these errors cancel and the resulting calculations are not affected. Finally, the ideal-gas entropy in Equation (36) contained a typo. Additionally, the electrons are already accounted for as relativistic species (for kBT >1 MeV), and thus should not enter the expression. The correct ideal-gas entropy for the nucleonic species is given by (Equation presented) All other results of the published article remain unchanged.
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U2 - 10.3847/1538-4357/ac0630
DO - 10.3847/1538-4357/ac0630
M3 - Comment/debate
AN - SCOPUS:85111565241
SN - 0004-637X
VL - 915
JO - Astrophysical Journal
JF - Astrophysical Journal
IS - 1
M1 - 73
ER -