# Are there any gaps in the range of gravitational wave frequencies we can detect?

We have LIGO and other earth-based interferometers for detecting high-frequency gravitational waves, we're going to have satellites in orbit around the sun for low-frequency waves, and we have a pulsar timing array for very low frequency waves. Are there any wavelengths in between the ranges of these different detectors that we wouldn't be able to detect?

• Wait, we have gravitational wave satellites at L4/L5? Perhaps you should rephrase that? Nov 11 '21 at 1:24
• At least I thought we did. Looks like I was wrong. Will edit. Nov 11 '21 at 3:34
• What observatories are planned at L4/L5? Nov 11 '21 at 9:10
• Actually none. My question was more poorly researched than I thought. Nov 11 '21 at 14:31

Are there any wavelengths in between the ranges of these different detectors that we wouldn't be able to detect?

Yes! There is the millihertz band, which will be detectable by the space-based observatory LISA, and the decihertz band that approximately covers the range from the millihertz band to the range that is observable by ground-based detectors such as aLIGO/Virgo, which will be detectable by observatories such as aTianGO.

This is shown by the sensitivity curves of various detectors in the figure below from this paper which makes the science case for aTianGO, where the curve for LISA is purple, the curve for aLIGO is orange ($$\gtrsim 10$$ Hz), and the curve for aTianGO is red. The nanohertz observatories are off of this figure to the left, and are known as pulsar timing arrays, such as NANOGrav.

Ground-based observatories are not sensitive below the seismic wall at ~10 Hz (though, in the future, this may not be such a problem if they are able to implement real-time feedback seismic detectors in the areas surrounding the g-wave detectors). The decihertz detectors, such as aTianGO and DECIGO, will help to compliment the ground-based detectors in terms of sky localization of sources (crucial for constraining the Hubble parameter), and for the early warning of binary black hole merger events, since the peak sensitivity of these detectors is below the seismic wall, as they are space-based detectors. The Einstein Telescope is a proposed ground-based observatory that would have a triangle geometry like LISA, rather than the L-shaped geometry of LIGO/Virgo, and arms that are a bit more than twice as long as LIGO's.

This paper by Loeb and Moaz (2015) proposes using a network of atomic clocks to detect the effect of gravitational time dilation due to a passing gravitational wave, which would be relevant in the millihertz band as well.

• Somewhat separate question - I assume that all gravity wave detectors based on a concept of measuring differences in orthogonal lengths using light interference. If so, are there any other theoretical methods you could in-theory detect gravitational waves? Phonon variability in huge bose-einstein condensates? ...? ...is this worth asking as a group question? Nov 10 '21 at 18:49
• @Richard There are Weber bars. Nov 10 '21 at 19:32
• @ProfRob Ah yes, good catch Nov 10 '21 at 22:18
• @Richard In principle, gravitational waves can be detected in all sorts of ways, but it usually comes down to whether the engineering is feasible. The essentials of feasibility of interferometric methods were established in the 1970s and 1980s (for instance see Weiss 1972). Joseph Weber attempted to detect g-waves with various instruments, never succeeding ultimately, and so called "weber bars" are named in his honor which is a type of detector called a resonant mass antenna. There is a proposal to build such an antenna on the moon arxiv.org/abs/2010.13726 Nov 10 '21 at 22:22
• @Richard In the theory of general relativity, any time varying mass-quadrupole moment (or higher order currents) produce gravitational radiation, it's just a matter of detecting them. I am not aware of any other type of gravitational wave detector en.wikipedia.org/wiki/… Although there is one exception that I've found: using atomic clocks to observe g-waves by measuring the gravitational time dilation due to the g-wave passing through a network of clocks. See this paper by Loeb and Moaz arxiv.org/abs/1501.00996 Nov 10 '21 at 22:27

Yes, there is a huge range of frequencies between those to which aLIGO is sensitive ($$30$$ -$$3000$$ Hz) and the pulsar timing arrays ($$10^{-10}$$ - $$10^{-7}$$ Hz). The ESA spacecraft LISA, a proposed mission which received approval in 2017 and which may launch in 2037+, is meant to fill this gap.

The plot below represents (roughly speaking) the minimum detectable strain measurable as a function of frequency.

Whether there are gaps between these three instruments depends on what you mean by a gap. There is some sensitivity in the overlaps, but that sensitivity is 2-3 orders of magnitude lower than the peak sensitivity. Thus $$10^{-7}$$ - $$10^{-5}$$ Hz looks poorly covered as does $$0.1$$ - $$10$$ Hz. The latter will to some extent be improved by new ground-based technology such as the Einstein Telescope.

Figure attributable to Christopher Moore, Robert Cole and Christopher Berry and taken from Kohler (2016)

• – uhoh
Nov 10 '21 at 21:24
• – uhoh
Nov 10 '21 at 21:25
• Where did you get the 2037+ number for LISA's launch? Nov 11 '21 at 16:50
• @mmeent sci.esa.int/web/lisa/-/61367-mission-summary Note also, this says LISA "will be proposed for 'adoption' around 2023 before the construction phase begins." Nov 11 '21 at 17:22