Optical properties of astronomical silicates with infrared techniques

Correct interpretation of a vast array of astronomical data relies heavily on understanding the properties of silicate dust as a function of wavelength, temperature, and crystallinity. Dust grains play a crucial role in scattering and absorbing visible light, but longer infrared wavelengths can get through the dust unveiling what is behind. This master’s thesis will therefore address the need for high fidelity optical characterization data in the far and mid infrared (40-400 μm). The electromagnetic theory is discussed as a means to introduce the optical constants and the different mathematical models that characterize their behavior. The core of this work is to show the numerical methods developed to implement such models and the results that they provide. The algorithms will be presented with their mathematical bases, and their advantages and disadvantages will be pointed out in terms of accuracy and robustness. The methods are the following: 1) Trust-region dogleg method, 2) Rootfinding Newton’s method, 3) Unconstrained minimization and global evaluation, 4) Constrained minimization and centered evaluation, 5) Constrained minimization and correlation, 6) Constrained minimization on transmittance and reflectance data/equations, 7) Multi-parameter fit. All of the algorithms were tested with simulated data before being applied to laboratory measurements. Results shown are for astronomical silicate spheres and for lossy and non-lossy bulk crystalline silicon slabs in a vacuum with different thicknesses over the aforementioned wavelength range. The best results were obtained by a nonlinear constrained minimization with correlation, whose enormous advantage is that the level of noise is much lower than that found in the results by the other algorithms. Nonetheless, because the evaluation of the model function is carried out at the central point of each interval into which the entire support is divided, the edges are never recovered for a little number of points. The range analyzed did not allow studying all of the features that such materials possess. However, a brief theoretical discussion of them is considered to be useful in gaining a complete overview of their optical properties.