Would LIGO Detect Head-On Collision?

Question

Assume two black holes collide head-on. In other words, they were not orbiting one another before the collision. I know this is unlikely. Further assume that their sizes and distance from Earth are similar to past collisions detected by LIGO.

My understanding is that detectable gravitational waves are caused by massive objects undergoing massive accelerations and that detections so far have been of colliding objects orbiting one another many times within a fraction of a second.

I assume that a head-on collision would create a single gravitational "pulse" instead of a wave. I don't know if "pulse" is the right word for this. Would this pulse be detectable by LIGO?

Answer 1

There are two issues: Would there be gravitational waves to be detected and would LIGO detect them.

On the first issue, gravitational waves are quadrupolar, and a cylindrically symmetric system will not produce any. (Specifically, the second time derivative of the quadrupole moment of an isolated system's stress–energy tensor must be non-zero in order for it to emit gravitational radiation.) So a head-on collision of equally massive black holes would not produce significant gravitational waves. If the BHs were of different masses, or the collision not quite head-on, gravitational waves would be produced.

On the second issue there are at least three ways LIGO might might miss them. First, they might simply be too faint. A merger through rotation is one of the best ways to produce gravitational waves, and a head-on collision is one of the worst (during a BH merger, of course).

A second way it might miss is if the merger is in one of its blind spots. Each LIGO detector has blind spots and there's no rule that says a BH merger can't be in one of them. (In fact, the neutron star merger was located by use of the blind spots. The third gravitational wave (GW) detector, Virgo, in Italy, didn't pick up the neutron star merger. It was bright/loud enough that it should have, which meant that the merger was in one of Virgo's blind spots, which helped to narrow down its location. A GW detected in only one detector would be listed as a possible GW, but not as a detection, because it might simply be terrestrial interference.

But another way it might miss is if LIGO had not been looking for the waveform of that kind of merger. General Relativity allows us to compute in very good detail the GW signal from any type of collision that we think likely. Because the GW signals are so faint, the first step of detection is matching computed GW waveforms to the data and looking for matches. Once a match is found, the signal is analyzed in more detail, but they have to know where to look. If no one expected the waveform and it was not strong enough to pop out of the data and yell "Here I am, dummy!" it might be missed. Since head-on collisions are expected to be very rare, it's possible that they are not in the library of waveforms that LIGO checks.

Answer 2

The waveform of binary inspiral was about 100ms with a peak for every rotation, about 10 waves/rotations were measured, ranging from 30 to 200Hz. The average female voice has a fundamental frequency of about 200hz, to have some idea, and a typical pitchfork is about 440Hz.

The waveform for a head on collision would about 5ms, probably less, kindof like a snap sound.

It would be indistinguishable from background noise. Sounds that consist of a single peak are like snaps on a vynil. you would challenge LIGO to detect a snap on a vynil record every hextillion years.

A direct collision of solar mass bh's is something like 1 in a hextillion years for the entire universe, because the singularities are as big as atoms, distanced by 100ds of kms travelling in the 20kmps kind of range.