Random mixtures of polycyclic aromatic hydrocarbon spectra match interstellar infrared emission

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.