(a.) if the widths of the broad-emission lines in agn spectra were due to thermal broadening (atoms moving at high speeds because they are at a high temperature), rather than doppler broadening (atoms moving at high orbital speeds deep in a gravitational well), how hot must the gas be? make sure you state (and justify) any assumptions you make. you may use that a typical broad line in an agn has a speed of ~7,500 km/s. hint: check either the book or my noes from chapter 5 for the formula which gives the amount of doppler broadening as a function of temperature (b.) if the temperature of the blr were as high as you calculated in part (a), what would you expect to see any lines at all? why or why not? based on this do you think thermal broadening is the main reason quasars exhibit broad lines? explain your answer.