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:
Calculate the optical depth (τ), using (), where (ni*ne) is considered to be equal to :
Calculate J, the specific intensity, and plot it as a function of ν:
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
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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.)
