# Would it be scientifically useful to put a LIGO or VIRGO on the moon?

Or a couple of them on the moon?

It seems to me that it's seismically pretty quiet there, with no trucks bouncing around on a nearby highway messing things up.

Maybe four LIGOs at the vertices of a regular tetrahedron. That should make for a pretty good gravitational wave observatory, don't ya think?

It seems to me that LIGO in space might be hard to deal with, and having known and fixed positions relative to each other is important and would be hard to guarantee in space.

• It would be waste of money, LISA still would be more powerful. – Mithoron Oct 11 '17 at 23:29
• Meet LISA :) en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna I imagine on the moon the problem would be contamination, so you'd have the unfeasible challenge of assembling housing for the beams. – CDCM Oct 11 '17 at 23:30
• As far I know, LIGO can pretty well - and a little bit cheaper - filter the noise from Earth origin. However, maybe a gravitational observatory using lasers between an Earth satellite and a Moon probe, could work as a cheaper LISA. – user259412 Oct 11 '17 at 23:31
• Do you mean, no hundreds of fracking earthquakes in Nebraska right in the middle between two detectors? – safesphere Oct 11 '17 at 23:32
• yes @safesphere, i mean that. (besides the trucks bouncing on the road a couple kilometers away.) – robert bristow-johnson Oct 11 '17 at 23:37

Scientifically at a first analysis it would make only a small difference. The reason is that there are other sources of noise besides the terrestrial and man made noise, that together are about the same amount of noise.

It's easy to see it in the following summary of the LIGO amplitude spectral density sensitivity of about $10^{-23}$ per sqrt(Hz). http://ligo.org/science/Publication-O1Noise/flyer.pdf See Figure 3 specifically, the seismic and Netwon noise is one of the the plotted curves, it seems the dark grey one, but in any case of approximately the same order of magnitude as more than 10 other noise sources that have to do with the measuring apparatus, and not external noise limited. The red curve is the measured noise, the purple one is the expected noise (probably RSS of the others). It is clear that it is not mainly external noise limited.

So if you placed this Ligo on the Moon, and were able to control all the Moon Related problems as well as on Earth, the sensitivity would not change, for the most part.

Now, it is possible that many of the non-seismic noises were designed that way because it was useless to do better on those and have it all be seismic dominated. You'd have to read detailed papers and designs of the apparatus. It took a long time to design it and build it, this second generation took 3-5 years, the first more than 10.

LISA will definitely do much better. It is much longer so a strain would cause a displacement larger by the ratio of the lengths (see below, this is true for longer wavelengths). LISA, the original space based interferometer was to have 5 million km legs (compare with a few Kms for LIGO), and distances and measurements would be done by an advanced design as well. The latest LISA is proposed to be 2 detectors instead of 3, so you loose a little, but still much better than LIGO because of the much longer lengths. You can see the NASA website or Google it. See the NASA site at https://lisa.nasa.gov. Arm lengths may also be a little less.

There is a review, but I can't locate it, that shows the sensitivities and spectral range, as well as what kind of object emit those frequencies. It might be a Living Review of Relativity, but can't confirm it.

EDIT/ADDITION ON LISA SENSITIVITY AND INTERFEROMETER MEASURE IN SPACE

First, changed the name of the interferometer 'legs' to 'arms' to make it consistent with standard usage on the topic.

More importantly added more on LISA.

I am adding this response to a very good question in the comment by @robert bristow-johnson below. He asked how does the interferometer work in space since the arm lengths do not appear to be rigidly fixed. In fact there are a few things that are done to try to measure the path length changes due to ONLY the gravitational forces (or changes in spacetime curvature, equivalently). The first part is that a drag-free satellite is used so that non-gravitational effects (like solar wind and light pressure ) are eliminated (hugely reduced). A drag-free satellite uses the satellite itself as a container, but lets the detector test masses float inside the satellite and follow spacetime geodesics, i.e. freely floating trajectories. Sensors and small jets keep the container, the satellite, centered around the test masses. See the descriptions of such things in https://en.wikipedia.org/wiki/Zero-drag_satellite.

There's more that they have to do, besides as you'd think besides making sure the sensors and jets don't affect the test masses too much. The arms are not rigidly locked, and they have to keep track and try to offset long term effects (such as changes due to planetary movement), which would be in essence pseudo-static and not gravitational waves. They measure the arms lengths it with lasers, actually keeping track of how many millions of wavelengths are changing constinuously, over short and longer time periods. They separate those changes in the frequency domain and offset and filter out the long period changes while using the rest to look for the gravitational waves.

There's more to the whole story of detecting gravitational waves in space. Since the arms are not rigidly locked they can't use Fabry-Perot cavity type interferometers. The end result is their sensitivity is about 3 orders of magnitude less in strain spectral density, so $10^{-20}$ instead of the number above. On the other hand the arm lengths are about a million times larger, way more than offsetting that for wavelengths larger than the arms length (for smaller wavelengths it's worse). See the description of LISA and some of these issues, as well as one of the latest parameters in the Wikipedia article at https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna

• Now that's a surprising answer! There are also some very good summary noise breakdown curves in the Einstein Telescope design documents. If I'm reading those curves right, it would seem that LISA won't improve the detection threshold much for the kinds of events that have already been seen (i.e. $\ge 100{\rm Hz}$) as the noise becomes quantum dominated for these frequencies, but there is about an order and a half of magnitude improvement possible for lower frequency events. However, it's not clear whether the "quantum noise" curve is simply the $\sqrt{N}$ Poisson photon arrival noise ... – WetSavannaAnimal Oct 12 '17 at 1:01
• ... or whether they've already taken possible squeezed light state improvement into account (this is planned for the Einstein telescope - not sure whether LIGO uses it but would be surprised if not). Of course, one of the other benefits of using a space telescope is the possibility of big arrays of detectors and long baseline interferometry to created and improve imaging resolution, especially for the low frequency events. – WetSavannaAnimal Oct 12 '17 at 1:04
• Yes, I think you're right, but I don't know if they've taken the the squeezed light state into account, and I know tHe Einstein telescope will. In the LISA now planned they are pretty squeezed for funding, not sure what else they are not doing. – Bob Bee Oct 12 '17 at 3:25
• so in LISA the components of a single interferometer are not connected rigidly together? they can't be just drifting independently in space. how is station maintenance done? how are the lengths of the arms of the interferometer measured and controlled? – robert bristow-johnson Oct 12 '17 at 22:56
• @robert bristow-johnson. You are right, the arm lengths are not rigidly fixed, and you have to detect a little differently. See my edited addition to my answer. Great question!! – Bob Bee Oct 13 '17 at 0:59

Bob Bee's answer is a good first cut answer addressing signal to noise issues. I also find it surprising. I make some notes on my reading of Bob Bee's answer and the sources he cites in the footnote.

But signal to noise is not the only issue at play here and there may be some merit in putting detectors on the Moon. The triangulation ability of the two current LIGO stations is limited, but an array of telescopes will be able to fully determine the direction whence gravitational wave signals are coming. The bigger the array, the better the angular resolution. For the measurement of sources which we have no corresponding light emissions for (such as neutron star collisions), say where the events do not emit light or where the light is blocked by interstellar dust, we will in the future turn to images built up from gravitational waves to help probe inaccessible-to-light / radio astronomy regions of the universe.

If we put part of our LIGO array on the Moon, the possibility of very long baseline interferometry arises. Of course, the same could be done for a large freefalling array such as LISA, but there could be some engineering / economic advantages for a Moon based member of such an array.

More on Signal to Noise

There are also some very good summary noise breakdown curves in the Einstein Telescope design documents. If I'm reading the SNR curves right (i.e. those such as Fig. 3 in the LIGO Summary cited by Bob Bee, it would seem that LISA won't improve the detection threshold much for the kinds of events that have already been seen (i.e. ≥100Hz) as the noise becomes quantum dominated for these frequencies, but there is about an order and a half of magnitude improvement possible for lower frequency events. However, it's not clear whether the "quantum noise" curve is simply the $\sqrt{N}$ Poisson photon arrival noise or whether they've already taken possible squeezed light state improvement into account. The use of squeezed light to improve phase resolution at the expense of amplitude is planned for the Einstein telescope.

• I think you are right that angular resolution will be better if you have an array in the moon, but you have to deal with uncertainties in correlating emissions from the same source. Still, it might be useful. LBI is very difficult (to resolve the huge ambiguities in such long baselines of very different environments where noises will not coincide), and anyway the LISA baselines are longer than the Earth-Moon distance. – Bob Bee Oct 13 '17 at 6:53
• Concerning quantum noise: If you are looking at any current Advanced LIGO noise budgets it will show the quantum noise without any squeezed states of light yet. Quantum noise for LIGO is a combination of photon shot noise arising from the random distribution of detected photons, and of radiation pressure noise which is caused by the random force the photons impart on the mirrors. Squeezed states of light can be used to improve both. GEO 600 is currently the only GW detector to use squeezing, but work is ongoing to install squeezed-light sources at the LIGO as well as Virgo sites. – Emil Oct 17 '17 at 7:02
• @Emil Thanks muchly for that. DO you have any idea what practical improvement this will achieve? And you're right: I'd completely forgotten about radiation pressure noise: I read about this some years ago and recall now that you mention it. – WetSavannaAnimal Oct 17 '17 at 8:07
• GEO 600 has achieved slightly over 4 dB of quantum-noise suppression at the high-frequency end of the sensitivity band. A long-term goal for all GW detectors is to eventually reach about 10 dB improvement (corresponding to a $\sqrt{10}$ improvement in amplitude sensitivity) over a wide frequency range. This will be challenging to achieve, especially at the lower frequencies that matter most for binary coalescences. But even small improvements help a lot because the number of detectable events scales with the third power of the sensitivity. – Emil Oct 17 '17 at 8:31
• @Emil Thanks again. Some interesting data there. Do you work in astronomy? – WetSavannaAnimal Oct 17 '17 at 8:46