Baryon acoustic oscillations with the cross-correlation of spectroscopic
  and photometric samples
  The baryon acoustic oscillation (BAO) experiment requires a sufficiently
dense sampling of large-scale structure tracers with spectroscopic redshift,
which is observationally expensive especially at high redshifts $z\simgt 1$.
Here we present an alternative route of the BAO analysis that uses the
cross-correlation of sparse spectroscopic tracers with a much denser
photometric sample, where the spectroscopic tracers can be quasars or bright,
rare galaxies that are easier to access spectroscopically. We show that
measurements of the cross-correlation as a function of the transverse comoving
separation rather than the angular separation avoid a smearing of the BAO
feature without mixing the different scales at different redshifts in the
projection, even for a wide redshift slice $\Delta z\simeq 1$. The bias,
scatter, and catastrophic redshift errors of the photometric sample affect only
the overall normalization of the cross-correlation which can be marginalized
over when constraining the angular diameter distance. As a specific example, we
forecast an expected accuracy of the BAO geometrical test via the
cross-correlation of the SDSS and BOSS spectroscopic quasar sample with a dense
photometric galaxy sample that is assumed to have a full overlap with the
SDSS/BOSS survey region. We show that this cross-correlation BAO analysis
allows us to measure the angular diameter distances to a fractional accuracy of
about 10% at each redshift bin over $1\simlt z\simlt 3$, if the photometric
redshift errors of the galaxies, $\sigma_z/(1+z)$, are better than 10-20%
level.
