This is a follow-on question to Can't pulsars and stars be used for gravitational wave measurement? and the helpful answers there.
The Wikipedia article subsection Pulsar timing array; Active and proposed PTAs mentions:
This is an extremely delicate experiment, although millisecond pulsars are stable enough clocks that the time of arrival of the pulses can be predicted to the required accuracy; the experiments use collections of 20 to 50 pulsars to account for dispersion effects in the atmosphere and in the space between us and the pulsar.
as a way to measure the Gravitational wave background.
Pulsar timing can also be done at X-ray wavelengths and the modest X-ray telescope of the Neutron Star Interior Composition Explorer (NICER) currently mounted on the International Space Station has been used to determine it's orbit to high precision based on a sequence of pulsar timing measurements and a model of the Earth's gravity field as a proof-of-concept demonstration. See Is NICER/SEXTANT the first civilian “spacecraft” to determine it's own position in space without GPS or uplinked data?
Question: Would an X-ray-based pulsar timing array in orbit or on the Moon to study GW background be effective? This coul take some loading off of the large Dishes and possibly offer a lot more time coverage. The X-ray telescopes are fairly small and amenable to deployment in a medium or high Earth orbit. Equipped with radio transponders or corner cube reflectors like LAGEOS their positions would be regularly measurable and highly predictable between measurements. The movement of The Moon's position and orientation is known to essentially centimeter accuracy due to extensive laser ranging of the Apollo-era retroreflectors.
- To what quantum mechanical 'discoveries' have retroreflectors on the Moon contributed?
- How is a result of no time variation in the gravitational constant 𝐺 related to a measurement of no local expansion?
But I don't know if the timing of the pulses in the X-rays would be better or worse for this kind of measurement. As pointed out in International Pulsar Timing Array "The resources of the IPTA are substantial" and dispersion in the ionosphere and atmosphere are a problem for the radio observations and the X-ray measurements above the atmosphere would solve that problem, but there may be others.