Retesting the no-hair theorem with GW150914

Abstract: For a distorted black hole (BH), its ringdown waveform is a superposition of quasi-normal modes (QNMs). In general relativity (GR), the lower order QNM frequencies and damping rates can be well approximated by a polynomial of BH's dimensionless spin and overall scaled by BH's mass. That is to say, we can test the no-hair theorem of BH in GR model-independently by allowing not only an overall fractional deviation (as M. Isi {\it et al.} did) but also a set of fractional deviation for every coefficient. In the paper, we will apply the latter method to retest the no-hair theorem with GW150914 and probe hairs' behaviors if hairs exist. Eventually, we find the data favors GR.