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With the success of LIGO and considering the types of imaging we're able to do with distributed arrays of radio telescopes, what level of detail would we be able to achieve were we to build arrays of gravitational wave detectors around the world? How would the data from such an array of wave detectors differ from a dual detectors of LIGO?

I can imagine with precise timing we could build 3D images using multiple detectors. Would having detectors in multiple orientations also help with reconstructing the precise spacetime curvature of distant interacting masses? Would having space based wave detectors be able to increase our effective aperture and get to a level of sensitivity where we could, say, measure the gravitational waves of close binary stars, or even the waves from the orbit of a hot Jupiter?

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We already have a global array of gravitational wave observatories. In 2017, the two LIGO detectors were joined by Virgo in Italy, and very briefly at the end of the last observing run in 2020 they were joined by a fourth observatory, KAGRA in Japan. There are also plans for a third LIGO detector to be built in India.

A network of detectors allows for a better determination of the sky location of gravitational wave sources. However, how well you can localize a source is determined roughly by the ratio of the wavelength of the signal to the size of the array. For an array the size of the earth observing kHz gravitational waves this amounts to an uncertainty of the sky localization of about 10 square degrees, or roughly 50 times the size of the Moon. With five detectors we will get close to this limit. However this is far from enough resolution to do any imaging of astrophysical sources.

In the future, as detectors get more sensitive, we will be able to see longer lived sources, in which case the movement of the earth around the sun can increase the effective baseline. This is particularly relevant for LISA, which will observe events lasting years. LISA however is also sensitive only in the mHz regime, partially counter acting the effect of the longer baseline. Still LISA should be able to achieve sky localization of 1 square degree.

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About $1$ pixel.

Gravitational waves travel at the speed of light. One wave is generated per revolution of the orbiting pair of black holes. As they close in, orbital speeds approach the speed of light. This means the wavelength roughly approaches the diameter of the orbit.

The smallest detail you can see with wave based imaging is the size of the wavelength.

We won't be able to resolve any detail when equal sized holes merge. What about a small black hole merging with a galactic core black hole? It is the same problem. The size of the final orbit is about the Schwarzchild diameter of the galactic core black hole.

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    $\begingroup$ You actually generate several waves per orbital cycle. 2 for the dominant quadrupole mode. More for higher order modes. $\endgroup$
    – TimRias
    Commented Jan 26, 2023 at 18:34
  • $\begingroup$ @TimRias - So maybe up to 10 pixels? $\endgroup$
    – mmesser314
    Commented Jan 26, 2023 at 23:35

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