Title: An Improved Pair Method to Probe the Dust Extinction Law

Abstract: Dust extinction law is crucial to recover the intrinsic energy distribution of celestial objects and infer the characteristics of interstellar dust. Based on the traditional pair method, an improved pair method is proposed to model the dust extinguished spectral energy distribution (SED) of an individual star. Instead of the mathematically parameterizing extinction curves, the extinction curves in this work are directly from the silicate-graphite dust model, so that the dust extinction law can be obtained and the dust properties can be analyzed simultaneously. The ATLAS9 stellar model atmosphere is adopted for the intrinsic SEDs in this work, while the silicate-graphite dust model with a dust size distribution of $dn/da \sim a^{-\alpha}{\rm exp}(-a/a_c),~0.005 < a < 5~\mu{\rm m}$ for each component is adopted for the model extinction curves. One typical extinction tracer in the dense region (V410 Anon9) and one in the diffuse region (Cyg OB2 \#12) of the MW are chosen to test the reliability and the practicability of the improved pair method in different stellar environments. The results are consistent with their interstellar environments and are in agreement with the previous observations and studies, which prove that the improved pair method is effective and applicable in different stellar environments. In addition to the reliable extinction results, the derived parameters in the dust model can be used to analyze the dust properties, which cannot be achieved by other methods with the mathematical extinction models. With the improved pair method, the stellar parameters can also be inferred and the extinction law beyond the wavelengths of observed data can be predicted based on the dust model as well.