What observation can be expected on LIGO if any when Betelgeuse goes supernova? What observation can be expected from the LIGO†  gravitational wave observatory if any when Betelgeuse goes supernova? 

Could we know that Betelgeuse has gone supernova before we see it light up our night sky?

†or other current or soon-to-be completed gravitational wave obervatories
Potentially a short (less than a second) burst of gravitational waves (GWs) would be detected. Much depends on asymmetries in the core collapse, since a spherically (or even axially) symmetric collapse would not produce GWs (e.g. Morozova et al. 2019). However, theoretical models suggest that the GWs start at low frequency (tens of Hz) and are associated with the core bounce at the end of core collapse. After about half a second the frequencies rise to kHz and are associated with the oscillations of the proto-neutron star at the centre. Since LIGO is sensitive from about 10Hz to 1kHz, then only the initial phase that lasts a few tenths of a second would be detectable, but snce GWs can travel through the star without much hindrance they will indicate the moment of core collapse quite accurately. 

The theoretical calculations referenced above suggest GW amplitudes of $h_{+}d \sim 10$, where $h_{+}$ is the dimensionless GW strain and $d$ is the distance to the supernova in cm. Betelgeuse is at a distance of $\sim 6 \times 10^{20}$ cm (600 light years), so the strain at the detector would be $h_{+} \sim 2\times 10^{-20}$. LIGO is sensitive to strains of above $10^{-23}$ in this frequency range, so there should be no problem (according to these models) in detecting such an event.

If they were produced with detectable strength, then they should be received at the same time as ananticipated neutrino burst. The difference would be that the neutrino burst should extend over about 10 s. That is because the dense centre of a supernova is opaque even to neutrinos (but not gravitational waves) for that period and so they "leak out" over that period.

The electromagnetic signature of the supernova (i.e. a visible light increase) would be seen a few hours after that, since that is how long it takes for energy to be transferred to the envelope of the star.

NB: For all practical intents and purposes, over the distance to Betelgeuse, neutrinos, along with light and gravitational waves, travel at the same speed. i.e. The delay of the ($\sim  10$ MeV) neutrino burst due to their non-zero ($\
&lt; 1$ eV) mass would be negligible. If the Lorentz factor is $10^7$, then the neutrino speed is the same as the speed of light to 1 part in $2\times 10^{14}$, which means they take an extra 0.1 ms to arrive from Betelgeuse compared to light speed.