Can near-to-mid infrared spectral energy distribution quantitatively trace protoplanetary disk evolution?

Infrared (IR) spectral energy distribution (SED) is the major tracer of protoplanetary disks. It was recently proposed to use the near-to-mid IR (or K-24) SED slope $\alpha$ defined between 2-24$\mu$m as a potential quantitative tracer of disk age. We critically examine the viability of this idea and confront it with additional statistics of IR luminosities and SED shapes. We point out that, because the statistical properties of most of the complicated physical factors involved in disk evolution are still poorly understood in a quantitative sense, the only viable way is to assume them to be random so that an idealized `average disk' can be defined, which allows the $\alpha$ histogram to trace its age. We confirm that the statistics of the zeroth order (luminosity), first order (slope $\alpha$) and second order characteristics (concavity) of the observed K-24 SEDs indeed carry useful information upon the evolutionary processes of the `average disk'. We also stress that intrinsic diversities in K-24 SED shapes and luminosities are always large at the level of individual stars so that the application of the evolutionary path of the `average disk' to individual stars must be done with care. The data of most curves in plots are provided on GitHub.