### Phys 728, Spring 2012            Homework Problem Set #10

10.1  Using IDL, restore the saveset here, or download the text file here. You will have three arrays, fghz (the frequency in GHz), tbr (brightness temperature in R polarization, in K), and tbl (brightness temperature in L polarization). Plot tbr and tbl vs. frequency on a log-log plot, using solid linestyle for R polarization and dashed linestyle for L. Using what we learned in lecture 3 (see also section 6.2 of chapter 5 of Solar and Space Weather Radiophysics, especially fig. 5.9), answer the following questions: What is the coronal temperature at relatively high heights? What is the polarity of the magnetic field (positive, or negative)? What are the frequencies corresponding to the point of steepest slope in the two polarizations? What is the harmonic ratio for these frequencies? What is the value of the magnetic field at the base of the corona? What is the approximate temperature at which your magnetic field applies?

10.2 Read sections 3.2 and 3.3 of Solar and Space Weather Radiophysics Chapter 6. Explicitly show how 6.29 follows from 6.27. Using the same save set above, what is the polarization, in percent, near 10 GHz? What is the local power-law slope of the spectrum (the slope on a log-log plot)? You will find that the slopes are different for the two polarizations, so just use an average value. What is the value of longitudinal magnetic field in the chromosphere (as determined from the above measurements near 10 GHz)? Using your answer to problem 10.1, what is the angle between the line of sight and the magnetic field direction?