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We propose an "extended Schmidt law" with explicit dependence of the star formation efficiency (SFE = SFR/Mgas) on the stellar mass surface density (Σstar). This relation has a power-law index of 0.48 ± 0.04 and a lσ observed scatter on the SFE of 0.4 dex, which holds over five orders of magnitude in the stellar density for individual global galaxies, including various types and especially the low-surface-brightness (LSB) galaxies that deviate significantly from the Kennicutt-Schmidt (KS) law. When applying it to regions of a sample of 12 spiral galaxies at sub-kiloparsec resolution, the extended Schmidt law not only holds for LSB regions but also shows significantly smaller scatters both within and across galaxies compared with the KS law. We argue that this new relation points to the role of existing stars in regulating the SFE, thus better encoding the star formation physics. Comparison with physical models of star formation recipes shows that the extended Schmidt law can be reproduced by some models including gas free fall in a stellar-gravitational potential and pressure-supported star formation. By implementing this new law into the analytic model of gas accretion in ACDM, we show that it can reproduce the observed main sequence of star-forming galaxies (a relation between the SFR and stellar mass) from z = 0 up to z = 2. [ABSTRACT FROM AUTHOR]

A spectral principal component (SPC) analysis of a sample of 87 Palomar-Green (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 per cent 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 µm silicate feature; the 3rd and 4th eigenspectra represent the silicate features at 18 and 9.7 µm, respectively. With the principal components (PC) from optical principal component analysis, 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 µm and the Eddington ratio. For the ratio of the silicate strength at 9.7 µmto that at 18 µm, 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 SFR and the central accretion rate in PG QSOs. [ABSTRACT FROM AUTHOR]