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# Calculating and Graphing the Bremsstrahlung Emission Over All Frequencies for the Orion Nebula

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Calculating and Graphing the Bremsstrahlung Emission Over All Frequencies for the Orion Nebula   Problem Calculate and graph the bremsstrahlung emission over all frequencies for the Orion Nebula. (The data are from Anderson and Eastwood (2007).)   Hints:   Use cgs units. Begin by calculating the Planck function for frequency. Calculate the free-free emission coefficient. Calculate the optical depth. Calculate the specific intensity. Plot specfic intensity as a function of frequency.
 Data Temperature in Kelvins Electron Density in cm  Line-of-Sight Thickness in Parsecs Cm per PC Speed of Light in cm/s Planck Constant Boltzmann Constant Gaunt Factor: Free-Free Atomic Number for Hydrogen  Useful Equations Planck's Function  Optical Depth Specific Intensity Solution

Calculate the Planck function:   (4.1)

Calculate the optical depth (τ), using ( ), where (ni*ne) is considered to be equal to :  (4.2)

Calculate J, the specific intensity, and plot it as a function of ν:      (4.3)

Then plot J(ν):    The curve begins on the left as a Planck function (τ>>1). At the top, where τ<<1 (optically thin gas), the emission is no longer a function of ν, and the curve levels off. This is the bremsstrahlung portion of the plot. At high frequency, the emission is a function of both frequency and temperature and falls exponentially. The specific intensity (J) is given in units of erg s-1 cm-2 sr-1. To convert to SI units (W m-2 sr-1), multiply the cgs values by 10-3.

 References --------------------------------------------------------------------------   Anderson, M. and Eastwood, M. (2013). Problem Set 5. AY 121 Radiative Processes. http://www.astro.caltech.edu/~mmanders/ay121/solutions/ps5solutions.pdf. (Accessed: 2016-03-09.)        