The black hole uniqueness and the no-hair theorems imply that the quasinormal spectrum of any astrophysical black hole is determined solely by its mass and spin .
The countably infinite number of quasinormal modes of a Kerr black hole are thus related to each other and any deviations from these relations provide a strong hint for physics beyond the general theory of relativity .
To test the no-hair theorem using ringdown signals , it is necessary to detect at least two quasinormal modes .
In particular , one can detect the fundamental mode along with a subdominant overtone or with another angular mode , depending on the mass ratio and the spins of the progenitor binary .
Also in the light of the recent discovery of GW190412 , studying how the mass ratio affects the prospect of black hole spectroscopy using overtones or angular modes is pertinent , and this is the major focus of our study .
First , we provide ready-to-use fits for the amplitudes and phases of both the angular modes and overtones as a function of mass ratio q \in [ 0 , 10 ] .
Using these fits we estimate the minimum signal-to-noise ratio for detectability , resolvability , and measurability of subdominant modes/tones .
We find that performing black-hole spectroscopy with angular modes is preferable when the binary mass ratio is larger than q \approx 1.2 ( provided that the source is not located at a particularly disfavoured inclination angle ) .
For nonspinning , equal-mass binary black holes , the overtones seem to be the only viable option to perform a spectroscopy test of the no-hair theorem .
However this would require a large ringdown signal-to-noise ratio ( \approx 100 for a 5 \% accuracy test with two overtones ) and the inclusion of more than one overtone to reduce modelling errors , making black-hole spectroscopy with overtones impractical in the near future .