LISA Sensitivity to Gravitational Waves from Sound Waves

Round 1

Reviewer 1 Report

Gravitational waves from the early universe offer an exciting new tool to probe new physics. Quite some effort has been devoted to understand the gravitational wave signal from first order phase transitions.  The current article discusses prospects for the detection of such a gravitational wave signal with the LISA interferometer. This manuscript nicely summarizes the results found by the author in refs [2,3], where a new concept to analyze the signal, the so called peak-integrated sensitivity, is introduced. This is a useful concept, and allows for an efficient comparison for the GW signals of different models.   The article starts with a useful introduction how to compute the GW signal from a first-order phase transition. It includes an interesting discussion on the impact of noise, which is often missing in the literature. It also contains a thorough literature list.   Think the manuscript can basically be published in its present form. I only have to two comments/suggestions:   -- in eq (2.1) S does not have a dependence on v_w, which I think is an idealization. There are indications eg that the slop changes as one goes from detonations to deflagrations. So I am not sure if this product structure is really justified.    -- In the discussion on page 10 it is stated that different models suffer quite differently from the impact of noise. Maybe one could add a few lines explaining why.   Otherwise, I am happy with the current state.

Author Response

Dear Editor,

I thank the referee for their report and am glad that they arrive at a favorable evaluation of my paper. Regarding the two points brought up by the referee, I made the following changes in the manuscript:

(1) Referee: "In eq (2.1) S does not have a dependence on v_w, which I think is an idealization. There are indications eg that the slop changes as one goes from detonations to deflagrations. So I am not sure if this product structure is really justified."

Reply: For any concrete phase transition scenario, the parameters p, q, and n, which are used to parametrize the shape function S, will be functions of the underlying phase transition parameters. However, for the purposes of my analysis, it is not necessary to explicitly specify this dependence. (Let alone that it is not precisely known for most models.) Instead it suffices to vary p, q, and n as independent phenomenological parameters within certain ranges covering all values that one typically finds in theoretical models and numerical simulations. To emphasize this point, I added the following statement at the very end of Sec. 2:

"In this way, we are able to cover a large range of possible spectral shapes and hence implicitly account for the dependence of p, q, and n on the underlying properties of the phase transition."

(2) Referee: "In the discussion on page 10 it is stated that different models suffer quite differently from the impact of noise. Maybe one could add a few lines explaining why."

Reply: To clarify this point, the last few sentences of Sec. 4 now read:

"Extremely strong phase transitions, such as those in Randall–Sundrum and composite-Higgs models, will simply be always observable. The detectability of other models, on the other hand, significantly improves in the course of the LISA mission. This is, e.g., the case for the Z2-symmetric real-scalar-singlet model, for which many benchmark points lie only slightly above the LISA PISC at the beginning of the mission. These points notably benefit from the improving sensitivity as the collected amount of data increases."

I hope that, in light of these changes and clarification, the paper can now be published.

Best regards, Kai Schmitz.

Reviewer 2 Report

A pdf document with comments/suggestions is attached

Comments for author File: Comments.pdf

Author Response

Dear Editor,

I thank the referee for their report and their useful comments on the manuscript. I made the following changes to address the seven points brought up by the referee:

(1) Referee: "In my opinion the author should clearly state what are the underlying assumptions to get (3.9) and it would also be useful to mention the corresponding uncertainties."

Reply: I made several changes in the text (all new text is marked in purple) and added the following discussion below Eq. (3.9)

"This fit has been obtained making use of a variant of the BayesLine algorithm [56] that applies Markov chain Monte Carlo techniques to sample the entire parameter space of the compact-binary population model. The expression in Eq. (3.9) therefore marginalizes over the parameters of the noise model, which allows us to directly compare and add it to the sky- and polarization-averaged instrumental noise in Eq. (3.3)."

as well as the following footnote (now footnote 4) in Sec. 4:

"Another important factor is the efficiency of compact-binary subtraction in the course of the LISA mission. On the one hand, one might not be able to individually resolve and subtract as many compact binaries as initially expected. On the other hand, additional characteristics of the GCN signal, such as its anisotropy and time dependence, might in fact help in its subtraction. We leave a more detailed investigation for future work; in this paper, we are going to follow Refs. [37, 44] and work with the noise model described in Sec. 3."

(2) Referee: "The plots in figure 1 and 2 are not completely clear to me."

Reply: The referee already provides all the correct answers in the report themselves. Nonetheless I added the following clarifying comments in Sec. 4:

"Figs. 1 and 2 provide a graphical illustration of how varying the observing time t _data and spectral shape of the signal affects LISA’s sensitivity reach. For each (p, q, n) tuple, Figs. 1 and 2 show four PISCs that indicate LISA’s sensitivity reach after t_data = 0.5, 1.0, 2.0, 4.0 yr (from top to bottom), respectively. The four times six curves for n = 2 are drawn explicitly in both figures; the envelopes of all other curves are indicated by gray-shaded bands. We moreover repeat that, for any given benchmark point, the distance between this point and any of the PISCs along the y direction equals the corresponding optimal SNR. This is also illustrated by the ruler in the top-right legend box in Figs. 1, which is true to scale."

(3) Referee: "Given the main criticisms on the treatment of the GCN, I think this statement is a bit bold."

Reply: In addition to the changes addressing question (1), I also added the following statement in the Conclusions:

"In this work, we did this using the fit function derived in Refs. [37], which marginalizes over the uncertainties of the GCN model. In future work, it would be interesting to refine our analysis based on a more sophisticated treatment of GCN."

(4) Referee: "Is this claiming that a factor \sqrt{3} is missing in [12] i.e. the signal given in [12] is factor \sqrt{3} smaller than what it should be?"

Reply: Again the referee is right and giving the correct answer to their question themselves. More details on this can be found in the erratum of Phys. Rev. D96 (2017) 103520, [arXiv:1704.05871], which I explicitly mention in my discussion of the different factors entering Eq. (2.2). I was also in contact with David Weir, whom I thank in the Acknowledgments, to confirm this discrepancy between his analysis in 1704.05871 and the second review paper by the LISA Cosmology Working Group.

(5) Referee: "However, the expression for R in (3.6) relies on assumptions (mainly equal-arm) which in reality are most likely going to be violated."

Reply: I added a comment and two more references to very recent papers on this issue below Eq. (3.8):

"For a discussion of the signal response in the case of unequal interferometer arm lengths, which will ultimately correspond to the physical situation during the LISA mission, see also [54, 55]."

(6) Referee: "Some care is required since the results are affected by all the caveats / uncertainties discussed above."

Reply: I included another reference to the "GCN seen by LISA" paper 1703.09858 and the "LISA sensitivity curve" paper 1803.01944 in the Conclusions:

"This number is reduced by roughly a factor of 2 down to roughly 160 points (i.e., roughly 4 %) when GCN is taken into account following the treatment in Refs. [37, 44] (see Fig. 3)."

(7) Referee: "I think few more references on the detection and characterization of stochastic background could be added."

Reply: I added a reference to 1608.06889 in the introduction alongside my other references to papers on the the stochastic gravitational-wave background.

I hope that, in light of these changes and clarification, the paper can now be published.

Best regards, Kai Schmitz.