Probability of the Detection of BNS and NSBH
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"the sensitive volume scales with the chirp mass" - Citation needed. I think Finn and Chernoff 1993 is the right reference. Also we should say how it scales (afaik V is proportional to Mc^5/2). -
"the ratio C = VT / V'T'" - defined twice in adjacent paragraphs, the second definition is superfluous -
"the BNS range of the LIGO and Virgo detectors (..) those expected in [O4b]" - here 'range' is singular in the first part of the sentence but 'those' should refer back to a plural noun. Change to 'BNS ranges' -
"The method to calculate the sensitive volumes and a detailed derivation of the results presented here are given in" - can this text be shortened or just replaced by a simple citation to the document? -
"duration of T=235 days for O4b" - is this a calendar duration (slightly under 8 months - why?) or a duration of observing time after accounting for duty cycle? This is not clear from the text. -
"ratio of the O4b time volume over that of" -> ratio of the O4b time volume to that of (..) -
"Given the previously detected number N' = 2 of BNS" - Why is the previously detected number of NSBH not mentioned up to this point, if the figure includes them? The text should introduce all the content of the figure before it is showed so that the reader is not left with unanswered questions when looking at it. -
The figure itself : As it is cumulative, the N=0 point has no information and should probably not be displayed, so start the x axis at or just below 1. This would also avoid the N=0 point(s) appearing inconsistently between BNS and NSBH, as now. -
"Assuming N'=4, which corresponds to the number of NSBH candidates with a FAR lower than 1 as discussed in [3]" - This discussion does not make that much sense to me. First, we have an O3b LVK population paper which sets a FAR threshold of 1/4yr obtaining a count of 2 detections up to the end of O4b. I do not see what would be the motivation for changing the threshold according to a short author paper, given that the resulting sample probably includes more noise events. The VT/V'T' calculation only works if the events counted in N' are signals with high probability. It does not work if a significant fraction are noise.
Second, we detected an NSBH during O4a, namely GW230529, and we detected (and issued a public alert for) another NSBH during ER15, namely S230518h.
If the intention is to give observers an idea how many NSBH signals we are likely to issue alerts for, then I'd actually agree that N'=4 is the correct previous detection count, but with 2 in O3 and 2 in O4a.
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The discussion of the O4a 'C' ratio and revising the BNS rate estimate seems out of place here. The section started by saying that the probability of detecting BNS/NSBH in O4b is a pressing question, which is true. I do not see why presenting a back-of-the-envelope revision of the pre-O4 BNS rate estimate is important enough to be done at the same time - which is also effectively scooping the O4a rates paper as well as the O4a catalog. In particular, 'absence of detection of such sources in O4a' is a statement that we cannot make until the O4a catalog is released. All one can say is that we did not issue any significant BNS alerts. Also, I can't tell if the intention here is to make a new rate statement - which would be implied by the instructions to 'divide previous BNS rates by 1.85' - if so, why not actually give a revised number, rather than invite external people to do the calculation themselves and maybe even publish it ?? But I would rather omit the paragraph completely as it is out of scope for the user guide.
Edited by Thomas Dent