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At the prompting of @cplberry , a thread about LIGO's recent H0 measurement. It will be long (but hopefully informative). Gird yourselves!
First, you can find "the H0" paper here: nature.com/nature/journal… or here: arxiv.org/abs/1710.05835 or here: dcc.ligo.org/LIGO-P1700296/… (w/data!)
The BLUF (en.wikipedia.org/wiki/BLUF_(com…): We find H_0 = 70.0 + 12.0 - 8.0 km/s/Mpc (maximum a posteriori & minimum 1-sigma interval)
What does this mean? The Hubble constant (H0) measures the expansion rate of the universe. 70 km/s/Mpc = 1/(14 Gyr) google.co.uk/search?client=…
That is an estimate of the age of the universe; alternately, c/H0 = 4.3 Gpc is a (slightly-worse) estimate of the size of the universe.
How do we measure H_0? The fundamental operation is *division*. Find an object and measure (a) redshift and (b) distance.
H_0 = c*z/d Done. So why does it take a whole paper? Well, it's a bit more complicated than this.
Start with distance. Gravitational waves are a "standard siren." See, e.g., @bernardfschutz's paper nature.com/nature/journal…
(@bernardfschutz was a co-author on LIGO's paper, by the way.)
I learned yesterday that the term "standard siren" comes from @seanmcarroll and Sterl Phinney: iopscience.iop.org/article/10.108…
(@decohere is another co-author on LIGO's paper.)
"Standard siren" comes from the fact that we can measure the chirp mass of GW sources *really well* (Figure 4 of journals.aps.org/prl/pdf/10.110…) 
(Chirp mass is the "narrow" direction, and we know it to part-per-thousand precision!) The chirp mass fixes "absolute magnitude" of GW170817
The "apparent magnitude" depends on directional emission factors (inclination) and *distance*. (All this assumes that GR is true.)
So, we get distance "directly," without any distance ladder (en.wikipedia.org/wiki/Cosmic_di…). Hooray for systematics-free measurements!
So, that's the denominator of H_0. What about the numerator, the redshift? Well, GW170817 was very close to the galaxy NGC 4993.
So, one can look up the redshift of NGC 4993 simbad.u-strasbg.fr/simbad/sim-id?… , or (we used this) the group hosting NGC 4993 vizier.u-strasbg.fr/cgi-bin/VizieR…
Done? Not quite. Galaxies and groups move around for a lot of reasons, not just because the universe is expanding.
The part of the motion due to expansion is called the "Hubble velocity" and rest (due to local gravity, etc) is called "peculiar velocity."
We used different methods to estimate the peculiar velocity for NGC 4993's group, e.g. ui.adsabs.harvard.edu/#abs/2014MNRAS… or ui.adsabs.harvard.edu/#abs/2015MNRAS…
In the end, it is a 10% correction, with 5% uncertainty: 300 km/s +/- 150 km/s on c*z = 3000 km/s of recession for NGC 4993's group.
*Now* we're ready to apply our super-sophisticated "division" operation to estimate H0. Here we go:
(We actually did it a bit more carefully in the paper, but it comes out to almost the same thing.)
<plaintive voice>Are we done now?</plaintive voice> No!
(Oops: should explain plot. Errorbars are 1-sigma in d and v_H = c z - v_pec; line and bands are median, 1-, 2-sigma linear relation.)
Compare to Hubble's plot (from pnas.org/content/101/1/…)
OK. Still not done... (if anyone is actually still reading at this point, good job!).
The distance errorbar drives the uncertainty. And it is highly correlated with directional emission; so H0 is correlated with inclination:
See the bands in that plot? They are the EM Hubble measurements from Planck (ui.adsabs.harvard.edu/#abs/2016A&A..…) and SHoES (ui.adsabs.harvard.edu/#abs/2016ApJ..…)
After 100+ years of work, the EM constraints are a bit better than ours from LIGO---but we'll catch up. For now, if we take 'em as given...
...then we can slice through the H0-cos(iota) ellipse in the other direction, and constrain the inclination to the source:
Another way to think of this is that we are using the redshift plus precise H0 to measure the distance, whence apparent magnitude gives inc.
You notice we like face-off (180 degrees) inclinations, not surprising given observed gamma rays from merger.
...to be continued---need to talk to students for a bit.
OK. I'm back. I think that's about it for the *paper*. I leave you with the money plot: p(H_0 | GW170817), i.e. "our H0 inference."
But that's not it for the *thread*! (You though it was over, didn't you?) Here are some things people ask about the measurement:
When will LIGO be as precise as the current EM measurements?
Based on the BNS merger rate we have now measured (I sense another thread in the future...), we could eventually get ~few BNSs per month.
(Rate from journals.aps.org/prl/abstract/1… , detector predictions from @cplberry's excellent obs. scenario doc: arxiv.org/abs/1304.0670)
*If* we get counterparts (they may be ~5 magnitudes dimmer, so > 20 mag---which is harder, but not crazy), then precision ~ 1/sqrt(N).
So after a few tens of events, H0 errorbar goes from ~ 10 km/s/Mpc to 1.few km/s/Mpc. That should be within the decade.
*a* decade, I mean (not before 2020!). Not bad, since it took 100+ yrs for EM to get here. Go LIGO!
At 1.few km/s/Mpc, we have to worry about systematics in the *LIGO* measurement. Mostly calibration, but some astro systematics as well.
Can LIGO settle the question of whether the Planck or SHoES value of H0 is "correct?"
Eventually. (See answer above.) Once we get down to ~few km/s/Mpc uncertainty, we *could* say something (see scale of gap in above plots).
But by that time, the EM measurements may well have moved on, too. We'll have to wait and see.
Are there any other systematic uncertainties in LIGO's results?
Yes. The choice of prior on H0 and distance/redshift can affect the result somewhat. Also if we have under-estimated the p.v. uncertainty.
But things don't change *that* much. And we will become less sensitive to these effects as we accumulate more BNS mergers.
OK. I think that's it for now. If you want to know more, read the paper, or ask me and I'll do my best to tell you.
And if you've actually read this far, go get yourself a cookie! You deserve it! Fin.
