Magnetar QPOs and Neutron Star Crust Elasticity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article reviews mainly the authors' research on the neutron star crustal properties, with the adoption of a phenomenological OI-EOS, by identifying the observed QPO frequencies with the crustal torsional oscillations without magnetic effects. They discuss both polar-type and axial-type oscillations, along with the physical implication in neutron superfluidity, nuclear saturation properties (K0, L) as well as the stellar mass and radius. The paper is well-organized with main conclusions well supported. I think it is suitable for publications on the Special Issue "Compact Objects".

Author Response

Thank you very much for taking the time to review our work. We are very happy to hear the positive comments from you.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper gives us a comprehensive review on the neutron star oscillations excited by the crust elasticity based on the Cowling approximation. The results involved in this manuscript are very interesting and important for the practitioners, especially the newcomers, in the field. The manuscript is well organized and well-rewritten. Therefore, I would like to recommend it for publication in its present form. A minor point, it had better explain the abbreviation "bcc" in the paper.

Author Response

Thank you very much for taking the time to review our work and for giving us a chance to improve the manuscript. As your suggestion, we explain the abbreviation "bcc" in the text. 

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript presented a very comprehensive review of the author's series of works on the interesting topic of neutron star oscillations excited by crust elasticity, particularly torsional oscillations in close connection to observations like QPOs. I would like to recommend publication after some  minor corrections and some clarifications:

1. Missing definitions: In line 125, the definition of ``bcc" is missing.  In Eq. 1 and the text near it, the definition of $S_0$ ( symmetry energy at $n_b$ = $n_0$) is missing.  In line 514, the units of $L$ (which is MeV) is missing. In the right subfigure of Fig. 20, pair of brackets is missing for "1.4 M_\odot, 14 km" at the bottom-left corner. 

2. A question: in line 32, the author commented that GW170817 has constrained the radius of 1.4 M_\odot NS to be less than 13.6 km. Then why the author considered a benchmark radius of 14 km (which is larger than 13.6 km) for 1.4 M_\dot in Fig 20? How sensitive are the results in Fig 20 to radius variations (like a smaller radius 12 km at 1.4 M_\odot)? The author should comment on these aspects for the consideration of consistency.

3. The author adopted Cowling approximations for all the calculations, as clearly stated in the manuscript. However, the author should mention how much differences he would expect compared to Full GR treatment, and whether his main conclusions (especially regarding the identification of the QPOs observed with the overtones of torsional oscillations) would still expect to hold in Full GR, and related reasons. 

Comments on the Quality of English Language

The quality of English is very good. However, I spotted some typos: In line 744, "Namele" should be "Namely". In line 619, "such as" should be "such that".  The author better proofreads the manuscript again to make sure there are no other typos.  

Author Response

Thank you very much for taking the time to review our work and for giving us a chance to improve the manuscript. We revise the manuscript according to the referee's comments one by one. 

1. 
We modified from "bcc" to "body-centered cubic (bcc)"; we added a sentence of "In particular, $w_0$ and $K_0$ ... the symmetry energy at $N_b=n_0$." at the end of the paragraph with Eq. (1); we added "MeV" at the corresponding part; and we added the brackets in the right panel of Fig. 20.

2. 
Here, we do not care about the constraint from the GW170817, because we just try to check whether or not the identification with the 2nd overtone is possible. In fact, the dependence on the stellar model is similar behavior to the right panel of Fig. 17. That is, if the stellar mass is fixed, the suitable value of $\varsigma$ to identify the frequencies increases as the radius decreases. As shown in Fig. 20, the suitable value of $\varsigma$ is out of the constraint using the fiducial value of the saturation parameters even for the stellar model with 1.4M_\odot and 14 km. So, if one considers the star with smaller radius, the situation becomes worse. Anyway, it should be better to mention these points. Thank you very much for pointing. We added the comments at the end of Sec. 5.4. 

3. 
We completely agree with the referee's comments. In general, since the axial-type oscillations do not involve density variations, which leads to quite small perturbations of gravitational potential, one can estimate the frequencies very accurately even with the Cowling approximation. On the other hand, for the polar-type oscillations, one can qualitatively discuss the behavior of the frequencies determined with the Cowling approximation, while it is known that the f-mode frequencies deviate around 20\% from those determined without the Cowling approximation. Unfortunately, it is not studied how well the interface and shear mode frequencies are determined with the Cowling approximation, but we consider that they may be discussed better than the f-mode, because the damping rate for the interface and shear modes are too small (unfortunately no one determined the exact damping rate, because it is too small to calculate). We added the comments about the accuracy for the axial-type oscillations in the 1st paragraph of Sec. 5, while those about the polar-type oscillations at the end of the 2nd paragraph in Sec. 6. 

In addition, thank you very much for carefully checking the text. We revised the typo.