In astrophysics, the chirp mass of a compact binary system determines the leading-order orbital evolution of the system as a result of energy loss from emitting gravitational waves. Because the gravitational wave frequency is determined by orbital frequency, the chirp mass also determines the frequency evolution of the gravitational wave signal emitted during a binary's inspiral phase. In gravitational wave data analysis, it is easier to measure the chirp mass than the two component masses alone.
A two-body system with component masses and has a chirp mass of
The chirp mass may also be expressed in terms of the total mass of the system and other common mass parameters:
In general relativity, the phase evolution of a binary orbit can be computed using a post-Newtonian expansion, a perturbative expansion in powers of the orbital velocity . The first order gravitational wave frequency, , evolution is described by the differential equation
where and are the speed of light and Newton's gravitational constant, respectively.
If one is able to measure both the frequency and frequency derivative of a gravitational wave signal, the chirp mass can be determined. [4] [5] [note 1]
(1) |
To disentangle the individual component masses in the system one must additionally measure higher order terms in the post-Newtonian expansion. [1]
One limitation of the chirp mass is that it is affected by redshift; what is actually derived from the observed gravitational waveform is the product
where is the redshift. [7] [8] This redshifted chirp mass is larger [note 2] than the source chirp mass, and can only be converted to a source chirp mass by finding the redshift .
This is usually resolved by using the observed amplitude to find the chirp mass divided by distance, and solving both equations using Hubble's law to compute the relationship between distance and redshift. [note 3]
Xian Chen has pointed out that this assumes non-cosmological redshifts (peculiar velocity and gravitational redshift) are negligible, and questions this assumption. [9] [10] If a binary pair of stellar-mass black holes merge while closely orbiting a supermassive black hole (an extreme mass ratio inspiral), the observed gravitational wave would experience significant gravitational and doppler redshift, leading to a falsely low redshift estimate, and therefore a falsely high mass. He suggests that there are plausible reasons to suspect that the SMBH's accretion disc and tidal forces would enhance the merger rate of black hole binaries near it, and the consequent falsely high mass estimates would explain the unexpectedly large masses of observed black hole mergers. (The question would be best resolved by a lower-frequency gravitational wave detector such as LISA which could observe the extreme mass ratio inspiral waveform.)
(2) |
(3) |
In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single force. Thus, if the temperature is high enough – approximately 1015 K – then the electromagnetic force and weak force merge into a combined electroweak force. During the quark epoch (shortly after the Big Bang), the electroweak force split into the electromagnetic and weak force. It is thought that the required temperature of 1015 K has not been seen widely throughout the universe since before the quark epoch, and currently the highest human-made temperature in thermal equilibrium is around 5.5×1012 K (from the Large Hadron Collider).
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