  Ultraslow radiative cooling lifetimes and adiabatic detachment energies for
three astrochemically relevant anions, C$_n^-$ ($n=3-5$), are measured using
the Double ElectroStatic Ion Ring ExpEriment (DESIREE) infrastructure at
Stockholm University. DESIREE maintains a background pressure of
$\approx$10$^{-14}$\,mbar and temperature of $\approx$13\,K, allowing storage
of mass-selected ions for hours and providing conditions coined a "molecular
cloud in a box". Here, we construct two-dimensional (2D) photodetachment
spectra for the target anions by recording photodetachment signal as a function
of irradiation wavelength and ion storage time (seconds to minute timescale).
Ion cooling lifetimes, which are associated with infrared radiative emission,
are extracted from the 2D photodetachment spectrum for each ion by tracking the
disappearance of vibrational hot-band signal with ion storage time, giving
$\frac{1}{e}$ cooling lifetimes of 3.1$\pm$0.1\,s (C$_3^-$), 6.8$\pm$0.5\,s
(C$_4^-$) and 24$\pm$5\,s (C$_5^-$). Fits of the photodetachment spectra for
cold ions, i.e. those stored for at least 30\,s, provides adiabatic detachment
energies in good agreement with values from laser photoelectron spectroscopy.
Ion cooling lifetimes are simulated using a Simple Harmonic Cascade model,
finding good agreement with experiment and providing a mode-by-mode
understanding of the radiative cooling properties. The 2D photodetachment
strategy and radiative cooling modeling developed in this study could be
applied to investigate the ultraslow cooling dynamics of wide range of
molecular anions.
