Co-evolution of Extreme Star Formation and Quasar: hints from {\it Herschel} and the Sloan Digital Sky Survey

Using the public data from the Herschel wide field surveys, we study the far-infrared properties of optical-selected quasars from the Sloan Digital Sky Survey. Within the common area of $\sim 172~deg^2$, we have identified the far-infrared counterparts for 354 quasars, among which 134 are highly secure detections in the Herschel $250~\mu m$ band (signal-to-noise ratios $\geq5$). This sample is the largest far-infrared quasar sample of its kind, and spans a wide redshift range of $0.14{\leq}z\leq 4.7$. Their far-infrared spectral energy distributions, which are due to the cold dust components within the host galaxies, are consistent with being heated by active star formation. In most cases ($\gtrsim80$\%), their total infrared luminosities as inferred from only their far-infrared emissions ($L_{IR}^{(cd)}$) already exceed $10^{12}~L_{\odot}$, and thus these objects qualify as ultra-luminous infrared galaxies. There is no correlation between $L_{IR}^{(cd)}$ and the absolute magnitudes, the black hole masses or the X-ray luminosities of the quasars, which further support that their far-infrared emissions are not due to their active galactic nuclei. A large fraction of these objects ($\gtrsim50\text{--}60\%$) have star formation rates $\gtrsim 300~M_{\odot}yr^{-1}$. Such extreme starbursts among optical quasars, however, is only a few per cent. This fraction varies with redshift, and peaks at around $z\approx2$. Among the entire sample, 136 objects have secure estimates of their cold-dust temperatures ($T$), and we find that there is a dramatic increasing trend of $T$ with increasing $L_{IR}^{(cd)}$. We interpret this trend as the envelope of the general distribution of infrared galaxies on the ($T$, $L_{IR}^{(cd)}$) plane.