The Memory of GW150914

Most of the RemarXiv contributors and the astronomical community at large have been very busy today watching press conferences (in person in some cases), reading papers, and generally overflowing with excitement over the first direct detection of gravitational waves in an event dubbed GW150914. I personally viewed the press conference remotely at the Green Bank Telescope (see the picture I snapped), which I thought was pretty cool! 

This detection is a triumph for theoretical physics, experimentalists and engineers, computational scientists, and the whole Big Science model. How perfect is it that this detection comes 100 years after general relativity was first let loose on the world? This detection provides unprecedented support for general relativity in the dynamical strong-field regime. As such, I'd like to talk about an aspect of GW150914 that general relativity predicts should be there but that LIGO didn't detect. 

From Favata (2009)

Intense bursts of gravitational waves should be accompanied by something called "memory", a phenomenon that Kip Thorne himself has been writing about since the 1980s (see here). In the case of GW150914, what that means is that through the intense chirp part of the event, a permanent component (called the memory) builds up in the gravitational waveform that causes the wave to never actually relax back to zero amplitude (see the above figure from Favata 2009). As gravitational waves expand and contract the physical distance between free-falling masses, memory permanently changes the separation between two such masses. Now, LIGO won't detect this memory because their test masses aren't technically completely free-falling; they're suspended by these awesome four-stage pendulums that nonetheless provide some small restoring force that will erase the permanent displacement that should be caused by the memory.

Nonetheless, if general relativity is right, the memory should be there. I estimate that the amplitude of the memory component should be about a tenth of the maximum amplitude of the oscillatory part of the wave, or a strain of approximately $10^{-22}$. That means that the permanent displacement from memory of LIGO's mirrors would have been (save for the aforementioned restoring force from the pendulums) about one-ten-thousandths of a proton radius. But let's think big. The Milky Way is about one hundred thousand light years in diameter and is composed of truly free-falling test masses. As GW150914 traverses the Milky Way, the memory it ought to carry with it will permanently change our galaxy's diameter by about one meter.