  The mid-infrared (IR; 5-15~$\mu$m) spectrum of a wide variety of astronomical
objects exhibits a set of broad emission features at 6.2, 7.7, 8.6, 11.3 and
12.7 $\mu$m. About 30 years ago it was proposed that these signatures are due
to emission from a family of UV heated nanometer-sized carbonaceous molecules
known as polycyclic aromatic hydrocarbons (PAHs), causing them to be referred
to as aromatic IR bands (AIBs). Today, the acceptance of the PAH model is far
from settled, as the identification of a single PAH in space has not yet been
successful and physically relevant theoretical models involving ``true'' PAH
cross sections do not reproduce the AIBs in detail. In this paper, we use the
NASA Ames PAH IR Spectroscopic Database, which contains over 500
quantum-computed spectra, in conjunction with a simple emission model, to show
that the spectrum produced by any random mixture of at least 30 PAHs converges
to the same 'kernel'-spectrum. This kernel-spectrum captures the essence of the
PAH emission spectrum and is highly correlated with observations of AIBs,
strongly supporting PAHs as their source. Also, the fact that a large number of
molecules are required implies that spectroscopic signatures of the individual
PAHs contributing to the AIBs spanning the visible, near-infrared, and far
infrared spectral regions are weak, explaining why they have not yet been
detected. An improved effort, joining laboratory, theoretical, and
observational studies of the PAH emission process, will support the use of PAH
features as a probe of physical and chemical conditions in the nearby and
distant Universe.
