# Why does the gravitational wave amplitude at merger of two black hole vary with mass of the blackhole?

I was running a PyCBC simulation of black hole mergers and I found a very peculiar question. When I was simulating two black holes colliding I observed that the peak positive amplitude of the merger varies sometimes. It should intuitively increase with the increase of mass but for some masses, it decreases.

I have plotted a scatter plot of these amplitudes y-Axis - Amplitude x-Axis - Mass M1 Assuming Mass m2 is kept constant at 10 solar masses

Frequency is 60hz

sample rate is 1/4096

spinz is 0.1 The y-axis is in the order of 10-19

Why does this Happen?

• units of y axis. What is the meaning of "the merger", emissions (i.e. units of $10^{-19}$ ?)? – JMLCarter Mar 8 '17 at 13:33
• @JMLCarter as in for example 2.25 * 10^-19 m gravitational wave strain observed – Rahul Aedula Mar 8 '17 at 13:42

If you plot these waveforms that have a reduced amplitude, and compare to nearby masses with a higher one, I suspect you'll see that although the envelope of the waveform increases with mass as you'd expect, that the phase at the time of this peak may cause the actual values to be lower. I suspect that you are using a function such as 'pycbc.waveform.get_td_waveform'. This returns two orthogonal (for non-precessing systems) polarizations. If you instead take the maximum as $$\text{(plus_polarization}^{2.0} + \text{cross_polarization}^{2.0})^{0.5}$$ you'll find the monotonic increase you are expecting.