Measuring Spin of the Remnant Black Hole from Maximum Amplitude

Gravitational waves emitted during the merger of two black holes carry information about the remnant black hole, namely its mass and spin. This information is typically found from the ringdown radiation as the black hole settles to a final state. We find that the remnant black hole spin is already known at the peak amplitude of the gravitational wave strain. Using this knowledge, we present a new method for measuring the final spin that is template independent, using only the chirp mass, the instantaneous frequency of the strain, and its derivative at maximum amplitude, all template independent.

Figure 1

The figure depicts the amplitude and the frequency during merger. The vertical dotted line denotes the time of maximum amplitude and the horizontal dotted line shows the corresponding instantaneous frequency.

Figure 2

We plot the dimensionless spin of the remnant black hole versus a function of symmetric mass ratio, instantaneous dimensionless frequency, and its time derivative at maximum strain for aligned spin numerical relativity waveforms. The solid line shows the fitting relation described in the “Fitting to final spin” subsection.

Figure 3

We plot the cumulative probability distribution of the final dimensionless spin obtained for a GW150914-like signal injected into noise and recovered using BayesWave with SNR 100. The solid black line shows the median recovered spin and the dotted black lines show the 90% confidence interval. The solid red line shows the true spin.