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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?

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    $\begingroup$ Wait, we have gravitational wave satellites at L4/L5? Perhaps you should rephrase that? $\endgroup$
    – TonyK
    Nov 11, 2021 at 1:24
  • $\begingroup$ At least I thought we did. Looks like I was wrong. Will edit. $\endgroup$
    – zucculent
    Nov 11, 2021 at 3:34
  • $\begingroup$ What observatories are planned at L4/L5? $\endgroup$
    – TimRias
    Nov 11, 2021 at 9:10
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    $\begingroup$ Actually none. My question was more poorly researched than I thought. $\endgroup$
    – zucculent
    Nov 11, 2021 at 14:31

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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. enter image description here

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.

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  • $\begingroup$ 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? $\endgroup$
    – Richard
    Nov 10, 2021 at 18:49
  • $\begingroup$ @Richard There are Weber bars. $\endgroup$
    – zucculent
    Nov 10, 2021 at 19:32
  • $\begingroup$ @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 $\endgroup$ Nov 10, 2021 at 22:22
  • $\begingroup$ @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 $\endgroup$ Nov 10, 2021 at 22:27
  • $\begingroup$ nanohertz waves?! waves that oscillate every 31.7 years?! Those can be detected?! I suppose it could make sense to find exoplanets... $\endgroup$ Nov 11, 2021 at 10:09
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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.

Frequency response of pulsar timing arrays, eLISA and aLIGO Figure attributable to Christopher Moore, Robert Cole and Christopher Berry and taken from Kohler (2016)

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The questioner and some answerers assume that whether one can receive GW depends solely on the wavelength/antenna length ratio. This is wrong, as examples from radio technology show:

a) For NMR in weak magnetic fields, frequencies below 100 kHz are required. This corresponds to wavelengths longer than 3000 m. The antennas are always smaller than 1 m.

b) The hydrogen line has a wavelength of 0.21m and is generated and absorbed by isolated molecules The 21 cm absorption line are smaller by a factor of $10^{10}$.

c) Ferrite-rod antennas are standard receiving antennas for medium wave ($f\approx 1$ MHz, $\lambda\approx300$ m) in radios and work quite well. Their size is about 2000 times smaller than the wavelength.

These examples show that effective antennas can be significantly smaller than the wavelength. There is no physical reason why GW with $f_{GW}\approx 10~\mu$Hz cannot be received with short antennas.

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    $\begingroup$ EM waves are very different beasts, and a lot easier to detect! I would hesitate to call LIGO etc "antennae", except in a very general sense. In particular LIGO measures strain, not intensity. Every radio detector that I'm aware of measures intensity, and so a signal will be four times weaker at twice the distance. LIGO doesn't, it measures amplitude, and at double the distance the amplitude is only half. I don't know if a radio wave analogy is useful. $\endgroup$
    – James K
    Nov 12, 2023 at 15:47
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    $\begingroup$ Nobody is assuming that. They are showing published sensitivity curves. Strain is a dimensionless factor by which a length is increased. So yes, there is a very good reason why short "antennae" don't work very well. And also a very good physical reason why the antenna can be too long. i.e. There are good physical reasons for a window of frequency sensitivity. $\endgroup$
    – ProfRob
    Nov 12, 2023 at 17:24
  • $\begingroup$ @James: Anything that turns waves into an alternating voltage is an antenna. Without exception, all radio detectors measure amplitudes, not intensities. And $A\propto r^{-1}$ applies to this. $\endgroup$
    – 9herbert9
    Nov 13, 2023 at 17:24
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    $\begingroup$ @9herbert9 You make a good point - anyone who's used an AM radio, or for that matter a VLF receiver aboard a sumarine, or a seismometer or buoy or infrasound receiver (or a gravitational wave detector) has proven that a wave receivers need not be of order $\lambda$ to work well. It's just a question of signal to noise ratio. It doesn't matter if the signal is "low" so much as how low it is relative to real background and instrumental noise. $\endgroup$
    – uhoh
    Nov 15, 2023 at 3:54
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    $\begingroup$ @JamesK waves are waves, SNR is the relevant concept and applies to all kinds of wave detectors. $\endgroup$
    – uhoh
    Nov 15, 2023 at 3:56

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