### How far away are the events that caused the gravitational waves that have been detected?

• A certain number of gravitational wave events have been detected. Is it possible to know how far away the mergers that caused those gravitational wave events are?

2 years ago

Yes, it is possible to calculate (within an error range) the distance of observed gravitational wave events. It is known that a variety of parameters will affect how the amplitude and frequency of the observed gravitational waves will change over time as recorded in the "chirp" event from the interferometers: the parameters include distance of the event, the mass of each of the colliding objects, the angular momentum of each of the colliding objects, the orientation of the objects' angular momentum vectors with respect to each other and with their orbital plane. With general relativity, you can build a model that calculates the expected "chirp" given a value for all these parameters; when a chirp is observed, it is possible to determine the combination of these parameters that result in a chirp that best matches the observation.

The effect of a larger distance parameter is to decrease the amplitude of the expected waves from colliding objects of a given mass, as well as to "slow down" the entire event due to cosmological red shift.

Gravitational waves from compact binaries carry information about the
properties of the source such as the masses and spins. These can be
extracted via Bayesian inference by using theoretical models of the GW
signal that describe the inspiral, merger, and ringdown of the final
object for BBH [23–30] and the inspiral (and merger) for BNS [31–33].
Such models are built by combining post-Newtonian calculations
[34–38], the effective-one-body formalism [39–44], and numerical
relativity [45–50].

Decreasing amplitude -- is this analogous to sounds getting softer due to distance, or is it some other process?

@Barmar yes, the normal thing — the further away you are, the more area the wavefront has to spread out over.

Thought so, but just making sure there's not some additional GR effect involved.