It is difficult to design empirical tests that specifically check propagation at c, independently of the other features of general relativity. The trouble is that although there are other theories of gravity (e.g., Brans-Dicke gravity) that are consistent with all the currently available experimental data, none of them predict that gravitational disturbances propagate at any other speed than c. Without a test theory that predicts a different speed, it becomes essentially impossible to interpret observations so as to extract the speed.
Has this matter been resolved ? is the measurement valid?
Kopeikin was wrong. See:
The speed of gravity has also been calculated from observations of the orbital decay rate of binary pulsars and found to be consistent to the speed of light within 1% ( same link).
This is not really correct. GR predicts that low-amplitude gravitational waves propagate at c. The binary pulsar observations are in excellent agreement with GR's predictions of energy loss to gravitational waves. That makes it unlikely that GR's description of gravitational waves is wrong. However, it's not a direct measurement of the speed of gravitational waves. There is no way to get such a measurement without a viable theory that predicts some other speed.
Along these lines I was wondering whether studying the second star in
a binary system where the first has gone nova would not give a cleaner
and model independent measurement of the speed of transfer of
information gravitationally.
The fact that a star goes nova doesn't produce any abrupt change in its gravitational field. If mass is expelled, there will be a gradual change.
In the matter of gravity vs. gravitational waves, I've always found it easier to think of (static) electric fields vs. EM waves.
Think of a static field "going out" from a charge. It isn't really going out. The field lines don't have "ends" that travel out at the speed of light. That's because they don't have ends at all. They all end at charges, and they stretch as far as needed. Charge is never created, it's always + - dipoles that are created (like electron-positron pair creation) so there's no problems with field lines that go out from an electron and go to the limits of the universe and end on some + charges out there. They've been stretched for that long, since the Big Bang. We don't think of how fast they move. They've been there since the beginning when the universe was small, and now they span it completely. A billion light years is nothing.
Similarly with static gravity. Mass-energy cannot just appear or disappear, so the field lines never have ends that have to move outward. They're always connected to mass and energy far away, and have had since the Big Bang to do so. There's no point in asking how fast static gravity moves. It's just "there" from here to the edge of the universe.
If you start to suddenly move, with respect to an already established static gravity or electric charge field-line, the field DIRECTION moves immediately with you, and so does the direction to the source. That's just Lorentzian relativity. The speed of light is not being violated. A source a billion light years away would suddenly start to look like it is moving, but that's because its field is already out to where you are, and the field where-you-are, tells you. It changes direction when you move. It responds immediately to relative uniform motion, via the mechanism of the field that is already extended to each.
But if the static or gravitational CHARGE moves (accelerates) then there is a "kink" or update that moves out from it at c. You don't see this at all from far away, until time d/c has passed. That's the EM wave or gravity wave. It's not a relative thing between source and viewer, because acceleration is not "relative" in relativity. You can't pretend that the observer accelerates and the source does not.
The Lienard-Weichert potentials for EM have two terms for this reason. One is the static one that depends only on relative velocity and points at the source (so long as relative velocity has been constant for long enough). The other one shows aberration (does not point at source), retardation, and is a disturbance in the field due to source acceleration (not observer acceleration).
The slow dance of Sun and Moon are a mix of both effects, in the near-field. The static effects point right at the sources, and are due to fields that already extend to infinity. They have no "speed." However, the second order effects due to small amounts of source acceleration (from orbital acceleration) are tiny, but they are genuine gravitational waves, and they move outward at speed c. They are retarded and would show aberration.
Best Answer
Yes. In principle, the speed of gravitational waves can be measured using the data of LIGO. In fact, using a Bayesian approach, the first measurement of the speed of gravitational waves using time delay among the GW detectors was suggested/performed by Cornish, Blas and Nardini. By applying the Bayesian method, they found that the speed of gravitational waves is constrained to 90% confidence interval between $0.55c$ and $1.42c$ by use of the data of binary black hole mergers GW150914, GW151226, and GW170104.
After that, a more precise measurement of the speed of gravitational waves was performed by the measurement of the time delay between GW and electromagnetic observations of the same astrophysical source, as @Andrew nicely mentioned, by use of a binary neutron star inspiral GW170817. They found the speed of gravitational wave signal is the same as the speed of the gamma rays to approximately one part in $10^{15}$. Note that this study is primarily based on the difference between the speed of gravity and the speed of light.
Recently, a new method has been introduced using a geographically separated network of detectors. As the authors mentioned, while this method is far less precise, it provides an independent measurement of the speed of gravitational waves by combining ten binary black hole events and the binary neutron star event from the first and second observing runs of Advanced LIGO and Advanced Virgo. By combining the measurements of LIGO and Virgo, and assuming isotropic propagation, the authors have constrained the speed of gravitational waves to ($0.97c$, $1.01c$) which is within 3% of the speed of light in a vacuum.
In my opinion, the best study is the second one (that @Andrew nicely mentioned), in which multiple measurements can be measured to produce a more accurate result, but the later (the third study) has its scientific significance. This is because the later method is an independent method of directly measuring the speed of gravity which is based solely on GW observations and so not reliant on multi-messenger observations, as the authors mentioned.
Besides these achievements, there are other interesting results that one can extract from LIGO's data. For example, observations of LIGO have constrained a lower bound on the graviton Compton wavelength as
$${{\lambda _{{\rm{graviton}}}} > 1.6 \times {{10}^{13}}{\rm{km}}},$$
which is really interesting. In fact, assuming that gravitons are dispersed in vacuum like massive particles, i.e. ${\lambda _{graviton}} = \frac{h}{{{m_{graviton}}\,c}}$, one can find an upper bound for graviton's mass as ${{m_{{\rm{graviton}}}} \le 7.7 \times {{10}^{ - 23}}eV/{c^2} \sim {{10}^{ - 38}}g}$, which is extremely small, beyond the technology of our detectors.