Lensing Magnification Seen by Gravitational Wave Detectors

Round 1

Reviewer 1 Report

The paper presents an extensive investigation about a probability of magnification of  the gravitational wave signals registered by LIGO - VIRGO instruments, due to gravitational lensing.  The authors describe the sequence of steps, needed for the estimation of lensing probability. 
    There are several points which should be clarified   

1. In the introduction (lines 72-76) the authors claim:

"We present predictions for the probability that an event observed
 by LIGO/Virgo at a given distance has been magnified by a given amount: while the probability for more than one event is very small, it decays very slowly with increasing magnification, i.e. there is a non-negligible probability of having extremely highly
 magnified events."

Here the conclusion about "non-negligible probability" in presence of the situation when "probability for more than one event is very small" is not clearly justified, and needed a more detailed explanation.
    Besides, while the paper contains lot of analytic and numerical computations, it would be good to give the numbers related to words "non-negligible"  and "very small".

2.  In the introduction (lines 38-40) it is written that "we compute the expected magnification as a function of redshift, but also as a function of the observed luminosity distance, which is the only quantity one can access observationally,  in the absence of an electromagnetic counterpart." 
The knowledge of a red shift of GW is used trough all the paper without any explanations. 
     It is accepted, that the redshift of the source is derived from the observations of GW signal. The procedure of this derivation is not trivial, and needed a comparison of the GW signal with the results of complicated theoretical computations of BH merging process. This point should be clarified in the paper. It should be also indicated how to derive the 
red shift of the GW signal which is amplified by a gravitational lensing, and are there features in GW signal which could indicate that the signal is lensed, or there is no way to do it. 

After modification, taking into account these remarks, the paper can be recommended for publication in the Universe. 
  

Author Response

Point 1):

We now have added tentative numbers. They of course depend on the distance of the events considered, so we have taken average distances for the LIGO/Virgo events.

Point 2)
We do not assume the redshift measured from the waveform as for LIGO/Virgo this is not possible. But we assume the redshift obtained by inferring it from the distance D_L assuming a standard Planck cosmology.
We now explain this in the revised version. 
Concerning the possibility of distinguishing a lensed event from an unlensed one, this is not possible in the geometric optics regime (which is a good approximation in the Hz band under exam in the present  work), as the waveform is not distorted by lensing. One possibility is detecting multiple images,  however this is extremely unlikely considered the long delay times (compared with observation time of ground based detectors) and the fact that typically secondary images are faint.

Reviewer 2 Report

The authors provide a semi-analytic approach to compute the probability that an observed event of gravitational wave emission is magnified due to the strong lensing effect.

The manuscript is very well written, the authors explain all the assumptions behind their model and their results. Additionally, the topic is very interesting and timely. Indeed, the estimation of the probability distribution of magnified events will be really important for future gravitational wave detectors that promise to observe events on cosmological scales.

I only have a few questions before recommending to accept it.

1) I believe there is no need to define again the acronyms at lines 107 (SIS is already defined in the Introduction) and 176 (SNR is also already defined).

2) At lines 49/50, the authors state that "magnification induced by cosmological large scale structure is negligible". Why? Is this due to the very low redshift of the events of Virgo/LIGO?

3) Several times, throughout the manuscript, the authors point out that the lens model (in this case the SIS) does not affect their final results. This point is quite obscure to me (since I am not an expert on lensing). Why is irrelevant if the matter distribution is a SIS or a NFW? Would this mean that the lensing effect of GW does not carry any information on Dark Matter?

Author Response

Point 1: We removed the second definitions of SIS and SNR.

Point 2: The referee is correct, at the  distances of LIGO/Virgo events, weak lensing from large scale structure only produces a small correction. We now say this.

Point 3: For the detailed lensing images the lens properties (time delays, relative strength of images etc.) are of course relevant. But here we only care about the magnification of the strongest image. For this details are not very relevant. We now say this more clearly.