Peer review of: Gravitational-wave asteroseismology with fundamental modes from compact binary inspirals (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

This manuscript deals with the constraints on the fundamental modes (f-mode) in GW170817 by 
using a waveform model with explicit dynamical tides and without assuming universal relations and 
provides a way to measure the frequency of f-mode from the GW data. 

As we know, extracting the information of oscillation modes from the GW radiated from the binary 
neutron star inspiral is a very meaningful but not easy task. This work obtained valued measured 
constraints on the f-mode frequencies of the companions of GW170817, which is very interesting 
and also meaningful in understanding the future detection of GW radiated from the binary neutron 
star inspiral. 

I believe that the methods and the results in this work will be very useful in the studying of compact 
stars and dense matter and thus I recommend the publication of the article. 

 

COMMENTS/SUGGESTIONS 

(1) There are some recent works also focused on the f-mode excited in the last stage of the orbiting 
binary neutron stars, such as PRD 100 (2019) 063001, PRD 100 (2019) 064023, arXiv:1905.00012v1. I 
recommend that the authors could include in their discussion with these relevant papers. 

(2) It is not easy for the readers to understand that which URs are adopted and how the URs get 
involved in the posteriors. 

(3) Please check whether the dimensions of relevant quantities are consistent: in the penultimate
paragraph of the right column in page 3, (3,1)is 410, 9404 Hz,(3,2) is 466,9446), while in the last paragraph of the left column in page 5, (prior, 3,1) is dimensionless. 

(4) The symbols of the quantities, such as (2,1) and (2,A), f(2,1) and f(2,A) and (2A), etc. are easily confused, it is better to explain these symbols in a little more detail. 


I believe that the above comments/suggestions should be taken into account and answered in the 
revised version of the article. 


Reviewer #2 (Remarks to the Author): 

The authors perform for the first time (and without assuming the 

so-called universal relations) a Bayesian study on the data of GW170817 to 

estimate frequencies of the f-modes excited during the final part of the 

merger. Separately from GW170817, such f-modes had also been studied in 

previous works, mentioned in the manuscript. 

 

I believe that the results presented in this manuscript are technically 

sound and expressed in a easy-to-read and convincing manner (actually 

there are some repetitions, therefore the text could be shortened 

somewhat, if necessary). For sure these results are of interest to other 

researchers in the field, but I do not believe that they represent an 

advance in understanding likely to influence thinking in the field. In 

fact, this manuscript shows an application of known techniques and theory 

to some actual data. This is why I do not recommend publication in Nature 

Communications. I would definitely recommend publication in other types of 

journals. 

 

Reviewer #3 (Remarks to the Author): 

Dear Editor, dear Authors, 

I read the manuscript "GW Astroseismology with Fundamental Modes from Compact Binary 
Inspirals" and I provide below my comments about it. 

 
The manuscript deals with a detailed Bayesian analysis of the GW strain data measured on the 
GW170817 event, by using a model for the GW signal that explicitly depends on both the tidal 
deformability and the f-mode frequency, assumed as independent variables. Differently from 
previous analysis, no empirical universal relations (URs) are necessarily assumed and a first 
constraint on the f-mode frequency only based on the available data is deduced. Moreover, a simple 
but clear test is done to reveal how this kind of analysis can improve our understanding of f-modes 
in future, better resolved detection. 

The work is original and has a fairly good significance. Despite the fact that the results obtained are 
still compatible with the (possibly more constrained) bounds obtained by additionally imposing URs, 
this analysis has the potential advantage of revealing systematic uncertainties and of testing some of 
the hypothesis underlying the empirical URs. Moreover, future analysis of this kind, applied to a 
larger sample of good resolved GW events, can potentially reveal new phases of matter at very large 
supra-nuclear densities or test alternative theories of gravity. 

The results presented can be of interest for a large (even if not extremely large) community. The 
Authors did an appreciable attempt to put their results in a broader and more understandable 
contest. However, the work has an intrinsic degree of technicality that cannot be avoided. Still, I do 
not think that this is a severe limitation of the work. 

The data and the methodology are state-of-the-art and the authors are recognized experts in the 
field of GW data analysis. The references and the provided details are enough to enable reproducing 
the results. Bayesian analysis strongly depends, among the others, on the priors used in the analysis. 
The authors have investigated in a satisfactory way the possible dependence of their results on the 
priors on the f-mode frequency. The study presented in the second part of the paper is less accurate, but being a proof-of-principle, this is not necessarily a limitation. 

The conclusions reflect the main points of the paper. Some of the outlooks are not fully motivated, 
but it should be possible to amend. 

Below I list a few possible suggestions to improve the manuscript: 


1) I am not convinced by the switch between the method and the results sections. Some of the 
questions I had while reading the manuscript were (partially) answered in the method section. So, I 
am wondering if a more canonical ordering could be better suited. 

 

2) In a few places in the paper, the Authors speak about ultra-high densities. Since the journal reader 
target is very broad, I would avoid this too general statements and I would replace them with more 
precise statement. At which densities do the authors expect their method to reveal matter 
properties (for example, in units of nuclear saturation density)? 

3) The Authors used TaylorF2 waveform models. This is not the only available one, even if it has 
some advantages. Could the Authors comments on possible pro and cons with respect to other 
approximants, and if they expect possible differences using different approximants? 

 

4) When commenting on "the f_l-dependent phase contribution (which is proportional to \Lambda_l 
f_l^{-2})", a reference could be useful. 

 

5) Very minor: sometimes (more often in the second part of the paper) the Authors do not put a 
comma in subscripts (e.g. \Omega_{2A}), while I think it should be done (e.g. \Omega_{2,A}). 

 

6) Very minor: after eq 3, "we adopt a a low- ..." 

 

7) I do not fully understand why the lower bound on \Omega is sometimes 0 and sometimes 0.182 
(the lower limit of the URs). Is it not possible to have a single choice? Is there something that I am 
missing in using two different values? 

 

8) When discussing the potential relevance of this kind of analysis in future detection, the Authors 
generically say that it will be complementary to post-merger analysis. There is however a possible 
fundamental difference: in the post-merger, the hot nuclear EOS will be proved, while in the inspiral 
the cold one. Could the Authors expand a little bit on that? Moreover, how does the SNR necessary 
in the presented analysis relates with the SNR required by post-merger analysis? This could be a 
relevant term of comparison.