0239 Hubble constant measurement from gravitational waves

# Hubble constant measurement from gravitational waves There are many ways to measure the Hubble constant. An interesting subset of them use gravitational wave signals! You can find a good introduction [here](https://github.com/jkanner/aapt/blob/master/TalkSlides-Romano.pdf). Below are some relevant references.  ## Refs - parent [[0237 Gravitational wave astronomy]] - [[2017#1710.05835]] - a *first* measurement by identifying the exact host galaxy (NGC 4993) for a particular BNS event (GW170817) - [[2019#1908.06060]] - uses 7 events including 1 BNS (same as in [[2017#1710.05835]]) and 6 BBH - 4 with high SNR (> 12): GW150914, GW151226, GW170608, and GW170814 - 2 needed for consistency with assumed population model: GW170104 and GW170809 ## Standard siren method - [[1710.05835]] - $H_{0}=v / D$ - $v$ = recession velocity - EM observations are good - $D$ = distance - GW observations are good ## Statistical approach - useful e.g. when we do not have redshift data - e.g. BBH has no EM counterparts, unlike BNS - see [[DelPozzo2011]][](https://arxiv.org/abs/1108.1317) - one can collect event-specific redshift data and combine to give a 5% accuracy for Hubble constant - with known *distribution* of sources, $H_0$ can be found just from the observed distance distribution of BBH detections [[ChenHolz2014]][](https://arxiv.org/pdf/1409.0522.pdf). - a single source with different possible locations - [[2018#Fishbach et al.]] ## Simple method from Romano - [GitHub slides](https://github.com/jkanner/aapt/blob/master/TalkSlides-Romano.pdf) - [GitHub codes](https://github.com/jkanner/aapt/blob/master/AAPT-WM19-Romano.ipynb): includes steps and derivations - similar discussion in an article on [Physics Today](http://orca.cf.ac.uk/117836/1/pt.3.4090.pdf) - redshift - look for wavelength shift in sodium D line - $z \equiv \frac{\Delta \lambda}{\lambda} \equiv \frac{\lambda^{\prime}-\lambda}{\lambda} \approx \frac{v}{c}$ - distance method 1 - $D=\frac{4 c}{\pi^{2}} \frac{5}{96}\left(\frac{\dot{f}_{\mathrm{gw}}}{f_{\mathrm{gw}}^{3} h}\right)$ - distance method 2 - $D=(\text{inspiral range}) \cdot \mathrm{SNR}_{\text {threshold }} / \mathrm{SNR}_{\text {measured }}$ ## Selection effects - [[1908.06050]] - a study with mock data - deals with both GW and EM selection effects