We present a test of the statistical method introduced by Bernard F. Shutz in 1986 using only gravitational waves to infer the Hubble constant ( H _ { 0 } ) from GW190814 , the first first high-probability neutron-star–black-hole ( NS-BH ) merger candidate detected by the Laser Interferometer Gravitational Wave Observatory ( LIGO ) and the Virgo interferometer .
We apply a baseline test of this method to the binary neutron star ( BNS ) merger GW170817 and find H _ { 0 } = 70 ^ { +35.0 } _ { -18.0 } km s ^ { -1 } Mpc ^ { -1 } ( maximum a posteriori and 68.3 % highest density posterior interval ) for a galaxy B -band luminosity threshold of L _ { B } \geq 0.001 L _ { B } ^ { * } with a correction for catalog incompleteness .
Repeating the calculation for GW190814 , we obtain H _ { 0 } = 67 ^ { +41.0 } _ { -26.0 } km s ^ { -1 } Mpc ^ { -1 } and H _ { 0 } = 71 ^ { +34.0 } _ { -30.0 } km s ^ { -1 } Mpc ^ { -1 } for L _ { B } \geq 0.001 L _ { B } ^ { * } and L _ { B } \geq 0.626 L _ { B } ^ { * } , respectively .
Combining the posteriors for both events yields H _ { 0 } = 70 ^ { +29.0 } _ { -18.0 } km s ^ { -1 } Mpc ^ { -1 } , demonstrating the improvement on constraints when using multiple gravitational wave events .
We also confirm the results of other works that adopt this method , showing that increasing the L _ { B } threshold enhances the posterior structure and slightly shifts the distribution ’ s peak to higher H _ { 0 } values .
We repeat the joint inference using the low-spin PhenomPNRT and combined ( SEOBNRv4PHM + IMRPhenomPv3HM ) posterior samples for GW170817 and GW190814 , respectively , achieving a tighter constraint of H _ { 0 } = 69 ^ { +29.0 } _ { -14.0 } km s ^ { -1 } Mpc ^ { -1 } .