ALMA [CI]$^{3}P_{1}-^{3}P_{0}$ observations of NGC6240: a puzzling
  molecular outflow, and the role of outflows in the global $\alpha_{\rm CO}$
  factor of (U)LIRGs
  We present ALMA and ACA [CI]$^{3}P_{1}-^{3}P_{0}$ ([CI](1-0)) observations of
NGC6240, which we combine with ALMA CO(2-1) and IRAM PdBI CO(1-0) data to study
the physical properties of the massive molecular (H$_2$) outflow. We discover
that the receding and approaching sides of the H$_2$ outflow, aligned
east-west, exceed 10 kpc in their total extent. High resolution ($0.24"$)
[CI](1-0) line images surprisingly reveal that the outflow emission peaks
between the two AGNs, rather than on either of the two, and that it dominates
the velocity field in this nuclear region. We combine the [CI](1-0) and CO(1-0)
data to constrain the CO-to-H$_2$ conversion factor ($\alpha_{\rm CO}$) in the
outflow, which is on average $2.1\pm1.2~\rm M_{\odot} (K~km~s^{-1}~pc^2)^{-1}$.
We estimate that $60\pm20$ % of the total H$_2$ gas reservoir of NGC6240 is
entrained in the outflow, for a resulting mass-loss rate of $\dot{M}_{\rm
out}=2500\pm1200~M_{\odot}~yr^{-1}$ $\equiv 50\pm30$ SFR. This energetics rules
out a solely star formation-driven wind, but the puzzling morphology challenges
a classic radiative-mode AGN feedback scenario. For the quiescent gas we
compute $\langle\alpha_{\rm CO}\rangle = 3.2\pm1.8~\rm M_{\odot}
(K~km~s^{-1}~pc^2)^{-1}$, which is at least twice the value commonly employed
for (U)LIRGs. We observe a tentative trend of increasing $r_{21}\equiv
L^{\prime}_{\rm CO(2-1)}/L^{\prime}_{\rm CO(1-0)}$ ratios with velocity
dispersion and measure $r_{21}>1$ in the outflow, whereas $r_{21}\simeq1$ in
the quiescent gas. We propose that molecular outflows are the location of the
warmer, strongly unbound phase that partially reduces the opacity of the CO
lines in (U)LIRGs, hence driving down their global $\alpha_{\rm CO}$ and
increasing their $r_{21}$ values.
