There was an error in equation (7) of Evans et al. (2016). That equation contains the normalising term NP, which is the total number of pixels in the gravitational wave (GW) localisation probability map. The paper states: “NP is the number of pixels in the map, and Ltot is the total catalogued galaxy luminosity within the GW volume, so LLgtotNP gives the ratio of the actual luminosity in pixel p compared to that expected if the galaxies were homogeniously distributed on the sky, i.e. the relative probability of this pixel hosting a merger event compared to any other pixel.”. While this is true, it results in an incorrect overall normalization of the probability that the GW event is in a known galaxy (= Pgal =p(Pgal,p)) compared to not being in such a galaxy (= Pnogal =p(Pnogal,p); P refers to the total probability, Pp is the probability in pixel p). The correct formulation should result in Pgal = C,¯ Pnogal = 1 − C¯ , where C¯ is the mean completeness of the galaxy catalogue employed at the distance of the GW event. Since Pgal is simply the sum over all pixels, p, of equation (7) in Evans et al. (2016), one should find: (Farmula Presented) (Figure Presented) The impact of this error is modest. The incorrect formulation resulted in the over-emphasis of catalogued galaxies within the GW error region. The only GWevent to date for which this may have had an impact was GW170817 (e.g. Abbott et al. 2017), for which the GWmerger was in a catalogued galaxy, thus this error if anything aided the search. Fig. 1 demonstrates quantitatively the impact of the error. Here we show the cumulative probability in the galaxy-convolved skymap as a function of area enclosed (summing over pixels in decreasing probability order). The original equation (7) shown in black clearly overestimates the enclosed probability as a function of area; the discrepency being worse as the fractional probability enclosed becomes high.
All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science