J1721$+$8842: a gravitationally lensed binary quasar with a proximate
  damped Lyman-$\alpha$ absorber
  High-redshift binary quasars provide key insights into mergers and quasar
activity, and are useful tools for probing the spatial kinematics and chemistry
of galaxies along the line-of-sight. However, only three sub-10-kpc binaries
have been confirmed above $z=1$. Gravitational lensing would provide a way to
easily resolve such binaries, study them in higher resolution, and provide more
sightlines, though the required alignment with a massive foreground galaxy is
rare. Through image deconvolution of StanCam Nordic Optical Telescope (NOT)
monitoring data, we reveal two further point sources in the known, $z \approx
2.38$, quadruply lensed quasar (quad), J1721+8842. An ALFOSC/NOT long-slit
spectrum shows that the brighter of these two sources is a quasar with $z =
2.369 \pm 0.007$ based on the C III] line, while the C III] redshift of the
quad is $z = 2.364 \pm 0.003$. Lens modelling using point source positions
rules out a single source model, favouring an isothermal lens mass profile with
two quasar sources separated by $\sim6.0$ kpc (0.73$^{\prime \prime}$) in
projection. Given the resolving ability from lensing and current lensed quasar
statistics, this discovery suggests a large population of undiscovered,
unlensed sub-10-kpc binaries. We also analyse spectra of two images of the
quad, showing narrow Ly$\alpha$ emission within the trough of a proximate
damped Ly$\alpha$ absorber (PDLA). An apparent mismatch between the continuum
and narrow line flux ratios provides a new potential tool for simultaneously
studying microlensing and the quasar host galaxy. Signs of the PDLA are also
seen in the second source, however a deeper spectrum is still required to
confirm this. Thanks to the multiple lines-of-sight from lensing and two quasar
sources, this system offers simultaneous sub-parsec and kpc-scale probes of a
PDLA.
