Accurate redshift determination of standard sirens by the luminosity
  distance space-redshift space large scale structure cross correlation
  We point out a new possibility to determine the average redshift distribution
of a large sample of gravitational wave standard sirens, without spectroscopic
follow-ups. It is based on the cross correlation between the
luminosity-distance space large scale structure (LSS) traced by standard
sirens, and the redshift space LSS traced by galaxies in preexisting
electromagnetic wave observations. We construct an unbiased and model
independent estimator $E_z$ to realize this possibility. We demonstrate with
BBO and Euclid that, $0.1\%$ accuracy in redshift determination can be
achieved. This method can significantly alleviate the need of spectroscopic
follow-up of standard sirens, and enhance their cosmological applications.
