Review Reports

Round 1

Reviewer 1 Report

The authors use a simple approach to the density dependence of
magnetic fields in neutron stars to study the influence of strong
magnetic fields on the mass-radius relation of such objects. The
results for the masses and radii are compared with observational data
from GW170817 and NICER and critically discussed. The studies are
based on 10 state-of-the-art models for the equation of state of
superdense matter. The parameters of these models are sufficiently
well discussed.  This work provides a new and important contribution
to the understanding and correct interpretation of neutron stars and
is a very appropriate contribution to MDPI's special issue on Nuclear
Physics and Multimessenger Astrophysics. I therefore recommend that
the paper be published as part of this special issue. Grammatically,
the work could be improved somewhat. Nevertheless, the present version
is completely acceptable.

Reviewer 2 Report

I recommend the publication of the paper in the present version.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Report on the paper "Equation of state
.......", by Watanabe et al., your
ref. #1376840 .

The paper presents a study of the 
nuclear Equation of State, in relation 
to the physics of magnetars, in particular
to their maximum mass and their radius.
The aim of the paper is to analyse the
effect of the intense magnetic field
on the mass and radius of these compact
objects.
 The paper is an extension of the authors'
previous paper, ref. [7], in the same
field. The relevant novelty is the
study of the importance of the magnetic
field distribution and the introduction
of the possible quark matter in the star
interior.
 The study is quite extended, the material
is well presented and the results appear
interesting. I am in favor of the publcation
of the paper. However I have few remarks that
demand clarifications and comments.

1. The nucleon EOS adopted by the authors,
with maybe the exception of the DDM set, have 
an unrealistically large incompressibility
at saturation. This is relevant, since the
stiffness allows for a quite large maximum 
mass for nucleon EOS. 

2. Despite that, if the 
EOS is softened with the introduction of 
hyperons, the maximum mass turns out 
below two solar masses, which is the 
oservational limit, see Fig. 1. With the 
introduction of quarks the maximum mass is 
still below two solar masses, see Fig. 5.
With the addition of the strong magnetic
field, the maximum mass is shifted to much
higher value, which is one of the 
interesting results of the paper. However
the observational limit is for Neutron 
Stars which are not magnetars.
 The authors should comment on this points
before publication.

   

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors study the impact of strong magnetic fields on the mass-radius relationship of neutron stars. The equations of state, which even account for hidden-strangeness mesons, are state-of-the art. A possible hadron-quark phase transition is considered. It is models using the Gibbs condition for pressure equilibrium. The impact of strong magnetic field on the bulk properties of neutron stars is well presented and discussed. I recommend the paper for publication without hesitation. 

Some improvements could be made, however.

1. LaTex has a parallel symbol (\parallel), which should be used in Eq. (22).
2. To understand the results shown in tables 3, 4, 5, 6 better it would be helpful to show the magnetic field at say nuclear saturation density or another properly chosen density value. The \alpha  or \gamma values alone do not provide much insight, according to my opinion.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf