Gravitational Waves in Physics and Astrophysics: An artisan’s guide by M Coleman Miller Nicolás Yunes

Author:M Coleman Miller, Nicolás Yunes
Language: eng
Format: epub
ISBN: 9780750330510
Publisher: IOP Publishing
Published: 2021-12-17T00:00:00+00:00

5.2.3.3 Double White Dwarf Binaries

As we have mentioned before, the foreground noise produced by double white dwarf binaries in our Galaxy is expected to limit the effective sensitivity of LISA up to a few millihertz. We can motivate that in the following way. It is estimated that there are a few tens of millions of double white dwarf systems in our Galaxy that will merge in the year age of the universe, which suggests a merger rate of one per few hundred years. It is also estimated that the rate of white dwarf supernovae is one per few hundred years, so if most of these involve two white dwarfs merging rather than a white dwarf accreting matter from a nondegenerate companion, then the two rates are consistent. Let’s take as our fiducial rate 0.003 yr−1. We will also assume that the typical chirp mass is about (if we take two white dwarfs each of mass , which is average, the chirp mass is ). Finally, given that LISA’s lifetime is expected to be a few years, we will assume that the duration of the observation is , or and thus that the frequency resolution is about Hz.

Using Equation (5.5), then we have an expected number of sources in our Galaxy per Hz frequency bin of

(5.7)

This suggests that Hz is the approximate dividing line between unresolved binaries at low frequencies (where there are on average multiple double white dwarf binaries per Hz frequency bin) and resolved binaries at high frequencies. The best current estimates put the dividing line at Hz, so our estimate is fairly close.

It might occur to you that in this estimate we’ve only considered double white dwarf binaries in our own Galaxy. There are hundreds of billions of galaxies in the universe, so shouldn’t we multiply our number by that factor? Wouldn’t that mean that we’d have to go to really high frequencies to resolve all of those white dwarf binaries? Yes, but there’s another consideration that means we don’t have to. That is the consideration of the amplitude of the signal. Although there are an enormous number of extragalactic white dwarf binaries, they are distant enough that their amplitude is lower than the LISA noise and therefore we don’t need to concern ourselves. The amplitude question here, like the question of the expected amplitude from the population of double supermassive black hole binaries, requires models of the number and distribution of the binaries.

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