Silicate Extinction Profile Based on the Stellar Spectrum by Spitzer/IRS

The 9.7$\mu m$ and 18$\mu m$ interstellar spectral features, arising from the Si--O stretching and O--Si--O bending mode of amorphous silicate dust, are the strongest extinction feature in the infrared. Here we use the "pair method" to determine the silicate extinction profile by comparing the \emph{Spitzer}/IRS spectra of 49 target stars with obvious extinction with that of un-reddened star of the same spectral type. The 9.7$\mu m$ extinction profile is determined from all the 49 stars and the 18$\mu m$ profile is determined from six stars. It is found that the profile has the peak wavelength around $\sim$9.2- 9.8$\mu m$ and $\sim$18-22$\mu m$ respectively. The peak wavelength of the 9.7$\mu m$ feature seems to become shorter from the stars of late spectral type, meanwhile the FWHM seems irrelevant to the spectral type, which may be related to circumstellar silicate emission. The silicate optical depth at 9.7$\mu m$, $\Delta\tau_{9.7}$, mostly increases with the color excess in $J-K_S$ ($E_{\rm JK_S}$). The mean ratio of the visual extinction to the 9.7$\mu m$ silicate absorption optical depth is $A_{\rm V}/\Delta\tau_{9.7}\approx 17.8$, in close agreement with that of the solar neighborhood diffuse ISM. When $E_{\rm JK_S}$ > 4, this proportionality changes. The correlation coefficient between the peak wavelength and FWHM of the 9.7$\mu m$ feature is 0.4, which indicates a positive correlation considering the uncertainties of the parameters. The method is compared with replacing the reference star by an atmospheric model SED and no significant difference is present.