Spectral principal component analysis of mid-infrared spectra of a sample of PG QSOs

A spectral principal component analysis (SPCA) of a sample of 87 PG QSOs at $z < 0.5$ is presented for their mid-infrared spectra from Spitzer Space Telescope. We have derived the first five eigenspectra, which account for 85.2\% of the mid-infrared spectral variation. It is found that the first eigenspectrum represents the mid-infrared slope, forbidden emission line strength and $9.7~\mu m$ silicate feature, the 3rd and 4th eigenspectra represent the silicate features at $18~ \mu m$ and $9.7~\mu m$, respectively. With the principal components (PC) from optical PCA, we find that there is a medium strong correlation between spectral SPC1 and PC2 (accretion rate). It suggests that more nuclear contribution to the near-IR spectrum leads to the change of mid-IR slope. We find mid-IR forbidden lines are suppressed with higher accretion rate. A medium strong correlation between SPC3 and PC1 (Eddington ratio) suggests a connection between the silicate feature at $18~\mu m$ and the Eddington ratio. For the ratio of the silicate strength at 9.7 $\mu m$ to that at 18 $\mu m$, we find a strong correlation with PC2 (accretion rate or QSO luminosity). We also find that there is a medium strong correlation between the star formation rate (SFR) and PC2. It implies a correlation between star formation rate and the central accretion rate in PG QSOs.