The PAU Survey: An improved photo-$z$ sample in the COSMOS field
  We present -- and make publicly available -- accurate and precise photometric
redshifts in the ACS footprint from the COSMOS field for objects with
$i_{\mathrm{AB}}\leq 23$. The redshifts are computed using a combination of
narrow band photometry from PAUS, a survey with 40 narrow bands spaced at
$100\r{A}$ intervals covering the range from $4500\r{A}$ to $8500\r{A}$, and 26
broad, intermediate, and narrow bands covering the UV, visible and near
infrared spectrum from the COSMOS2015 catalogue. We introduce a new method that
models the spectral energy distributions (SEDs) as a linear combination of
continuum and emission line templates and computes its Bayes evidence,
integrating over the linear combinations. The correlation between the UV
luminosity and the OII line is measured using the 66 available bands with the
zCOSMOS spectroscopic sample, and used as a prior which constrains the relative
flux between continuum and emission line templates. The flux ratios between the
OII line and $\mathrm{H}_{\alpha}$, $\mathrm{H}_{\beta}$ and $\mathrm{OIII}$
are similarly measured and used to generate the emission line templates.
Comparing to public spectroscopic surveys via the quantity
$\Delta_z\equiv(z_{\mathrm{photo}}-z_{\mathrm{spec}})/(1+z_{\mathrm{spec}})$,
we find the photometric redshifts to be more precise than previous estimates,
with $\sigma_{68}(\Delta_z) \approx (0.003, 0.009)$ for galaxies at magnitude
$i_{\mathrm{AB}}\sim18$ and $i_{\mathrm{AB}}\sim23$, respectively, which is
$3\times$ and $1.66\times$ tighter than COSMOS2015. Additionally, we find the
redshifts to be very accurate on average, yielding a median of the $\Delta_z$
distribution compatible with $|\mathrm{median}(\Delta_z)|\leq0.001$ at all
redshifts and magnitudes considered. Both the added PAUS data and new
methodology contribute significantly to the improved results.
