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Tests of the no-hair theorem using astrophysical black holes involve thedetection of at least two quasi-normal modes (QNMs) in the gravitational waveemitted by a perturbed black hole. A detection of two modes -- the dominant,$(\ell, m, n) = (2,2,0)$, mode and its first overtone, the $(2,2,1)$ mode -- inthe post-merger signal of the binary black hole merger GW150914 was claimed inIsi et al. [arXiv:1905.00869], with further evidence provided in Isi \& Farr[arXiv:2202.02941]. However, Cotesta et al. [arXiv:2201.00822] disputed thisclaim, finding that evidence for the overtone only appeared if the signal wasanalyzed before merger, when a QNM description of the signal is not valid. Dueto technical challenges, both of these analyses fixed the merger time and skylocation of GW150914 when estimating the evidence for the overtone. At leastsome of the contention can be attributed to fixing these parameters. Here, wesurmount this difficulty and fully marginalize over merger time and skylocation uncertainty while doing a QNM analysis of GW150914. We alsosimultaneously and independently fit the pre-merger inspiral signal. We findthat marginalizing over all parameters yields low evidence for the presence ofthe overtone, with a Bayes factor of $2.3\pm 0.1$ in favor of a QNM model withthe overtone versus one without. The arrival time uncertainty of GW150914 istoo large to definitively claim detection of the $(2,2,1)$ mode.

Low evidence for ringdown overtone in GW150914 when marginalizing over time and sky location uncertainty