Properties of the Object HESS J1731-347 as a Twin Compact Star

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the manuscript ''Properties of the Object HESS J1731-347 as a Twin Compact Star" the author analyzes the possibility of modelling compact object HESS J1731-347 as a hybrid star. Several astrophysically relevant quantities associated with such objects are obtained and a comparison with modern astronomical observations and laboratory experiments is performed.

The work is interesting and it is a timely topic. Moreover, it is generally speaking well written. Unfortunately, before I can recommend it for publication as a regular article in Universe, the author must perform some improvements.

Below I list my suggestions (in order of appearance):

+ A modern reference regarding the estimations of parameter $L_0$ (slope at saturation density) has to be added.

+ Has the author checked if the EoS fulfils modern cEFT calculations? (see, for example, Drischler et al., PRC (2021) and references therein).

+ On lines 59 and 64 the name of the object HESS J1731-347 is incomplete.

+ Being the central topic of this work, the list of alternative explanations to the nature of object HESS J1731-347 should be enlarged as several works had done this previously. A quick research showed that:

Veselsky et al., PLB (2025) explain this object using $K^-$ condensation;

Di Clemente et al., ApJ (2024), Ju et al., EPJC (2025) Rather et al., EPJC (2023) and Pikonomou and Moustakidis, PRD (2023) consider the possibility that this compact object is a quark star;

Mariani et al., PRD (2024) model HESS J1731-347 as a slow stable hybrid star;

Gao et al., PRC (2024), Laskos-Patkos et al., PRD (2024a,b) considered the possibility that this compact object is a hybrid star;

El Hanafy, EPJC (2024) analyzed quadratic Rastall gravity in the light of astronomical constraints of compact objects including HESS J1731−347;

Hong and Ren, PRD (2024) considered mixed dark matter models to explain HESS J1731-347;

Li and Sedrakian, PLB (2023), Brodie and Haber, PRC (2023) studied baryonic models for this low-mass compact object.

It would be desirable that the author acknowledges previous works on this topic.

+ What is the need of the absolute value used in Eq. (1)? $v$ is a positive value.

+ Please solve the numerical noise clearly visible in several of the Figures.

+ Please explain the expression $\rangle c_s^2 \langle = p/\epsilon$ presented in line 191 as it is confusing to me.

+ On line 192 should be $c^2$ and not $c$.

+ Please unify the use of $P$ and $p$ (and every associated quantity) for the pressure.

+ Regarding stability of hybrid stars with a sharp hadron-quark phase transition. The author must recall the fact that Pereira et al., ApJ (2018) had shown that if the hadron-quark conversion is slow, condition for stability obtained by Wheeler and collaborators is violated and configurations might remain stable in an extended branch where $\partial M/\partial \epsilon_c$ is negative. See a wide variety of applications of the ideas from Pereira et al., ApJ (2018) in Rau and Sedrakian, PRD (2023) and Lugones et al., JCAP (2024) and references therein. A comment on this subject might be in place.

+ For completeness, the author should show mass and radius estimations of PSR J0030 and PSR J0740 presented in Riley et al., ApJL (2019) and Riley et al., ApJL (2021) respectively.

+ On line 244 I suggest changing derived by estimated.

+ On line 261 $\Lambda$ should read $\lambda$ as $\Lambda$ is the dimensionless tidal deformability (see line 268).

+ Why do the authors introduce on line 274 function $f$ which is clearly related to the speed of sound?

+ Caption of the right panel of figure 6 has to be changed as it does not represent what that figure shows.

+ I believe that there is no need to show that many digits in the change of gravitational mass in table 3.

+ The colors in figure 9 seem inverted in relation to other figures. Please check.

+ On lines 401 and 404 and in the caption of table 4 $n_cc$ should be replaced by $n_{cc}$.

+ Please correct the caption of figure 12.

+ On line 510 I believe twins should be changed to hybrid as no high-mass purely-hadronic configuration exists within the presented model. This might be true for low-mass HESS J1731-347. Please rephrase. 

Author Response

Please see the attachment.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In the article the author reviewed present theoretical properties of hybrid twin compact star, showing that they can be in good agreement with state-of-the-art constraints both from laboratory experiments as well as multi-messenger astronomy observations. In particularly, they are consistent with the Object HESS J1731-347 with small mass and radius. It offers interesting results on possible strong hadron-quark first order phase transition and composition of compact stars deserved to be published. However, it seems that the article is finished in a hurry, the author need to check carefully the English writing and details of the article. Especially there are some errors and questions to be addressed.

1. The correspondence of the colors of the curves in different figures are in a mess. Especially in Figure 1. The author need to check and unify them.
2. The formula for C_s under line 174 is wrong
3. Check the value \eps_c in Table 2.
4. Since the vanishing of the trace anomaly, with C_s^2=1/3, is a necessary condition for the restoration of conformal symmetry, and C_s^2 deviate it much in the adopted model, is there necessity to investigate the conformality inside the compact stars?
5. Explain in detail what determines the curves of the theoretical values in Figure 7.
6. Results of the Kepler frequency are suggested to be also included in the article.
7. What is the reference for Eq(45)？

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Manuscript ”Properties of the Object HESS J1731-347 as a Twin Compact Star” by David E. Alvarez-Castillo investigates properties of hybrid stars using several equations of state, mechanism of their formation and attempts to describe properties of recently reported compact object HESS J1731-347 as such hybrid star. While the presented work appears technically correct, my main dilemma is related to the equations of state used, especially to the choice of transition density. In particular, e.g. the transition density 0.19 fm^-3 in Table 1 is just about 20% higher than nuclear saturation density. Assumption that deconfinement phase transition could set on at such low density is in clear contradiction with nuclear reaction data. Such densities can be achieved in nuclear reactions already at low energies, and no such process was ever observed. Instead, hadron colliders like RHIC and LHC were needed to observe deconfinement phase transition. Even if one can argue that in the neutron stars case mostly neutron-rich matter is expected, exterior of nuclei, which mostly participates in reactions at low energies is usually also neutron-rich, especially for heavy nuclei. Concerning compact object HESS J1731-347, it is de-facto addressed only in Figure 4 and the best efforts are only grazing the area constrained by observation data. Also, as one can see in Figure 11, the assumption of hybrid stars does not lead to really dramatic improvement compared to purely hadronic equation of state (yellow dashed line). Based on above, I am not convinced that the concept of hybrid stars leads to significant progress in understanding the properties of the compact object HESS J1731-347, especially since the necessary assumptions concerning transition density are in contradiction with existing nuclear reaction data. Concerning the manuscript, before recommending publication I consider it necessary for author to provide a discussion dealing with the issues mentioned above and corresponding conclusion concerning the applicability of the concept of hybrid stars to the case of compact object HESS J1731-347.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

In his response to my first report on manuscript ”Properties of the Object HESS J1731-347 as a Twin Compact Star” by David E. Alvarez-Castillo, its author uses examples from the reference Sagert et al. Phys. Rev. Lett. 102, 081101 (2009) as arguments toward feasibility of phase transition at relatively low baryonic densities. That reference is 15 years old and some progress in experimental study of the onset of transition into quark phase was reached in the meantime. Accidentally, the recent e-print 2505.00194 by Bao-An Li et al. deals with this problem, shows how indeed the calculations using the model of hybrid star tend to prefer solutions with low density onset of phase transition over equally feasible transition at higher densities and in this context refers to conclusions drawn from the experimental studies performed as a part of the beam energy scan at RHIC where no signs of the onset of phase transition are observed at c.m. energy 3GeV per nucleon where densities reach up to 3.6 to 4 times the saturation density. There is little doubt that such densities can be reached at that beam energy. It is true that the temperature reached at such beam energy can amount to several tens of MeV but as it can be seen also from the example provided by the author, transition density at zero temperature is usually higher than at finite temperature. So the calculations presented by author of the manuscript (and by many others in already published articles) are in tension with existing experimental results and this fact can not be ignored. I suggest to the author to perform additional calculations which would be consistent with conclusions of the e-print of Bao-An Li et al. and thus also with experimental results. I am sure that author will agree that it makes little sense to publish results of calculations which do not take into account the existing experimental constraints from terrestrial experiments. Again it is true that there is much freedom for the form of M-R diagram at low masses, and some form of transition can not be excluded, but it should be taken into account that besides transition into quark matter there exist other non-nucleonic degrees of freedom which could be manifested especially at corresponding lower densities where transition into quark matter appears disfavored. I appreciate the effort of the author and therefore I suggest to perform such calculations to bring the manuscript into the form in which it could be published.

Author Response

The referee comments have been addressed in the attached file.

Author Response File: Author Response.pdf