Calculate the Planck function:
![B[nu] = 2*h*nu^3/(c^2*(exp(h*nu/(k*T))-1))](/view.aspx?SI=154307/e5d6ee4a1314761aaa1f4e09094a4cdc.gif)
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![B[nu] = 0.1474508033e-46*nu^3/(exp(0.5997465605e-14*nu)-1)](/view.aspx?SI=154307/1e7e2eedf7578c7f68d389b96b62c114.gif)
| (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):
![loglogplot(J, nu = 10^5 .. 10^17, labels = ["frequency", "specific intensity"], labeldirections = ["horizontal", "vertical"], axis = [gridlines = [50, colour = green, majorlines = 2]])](/view.aspx?SI=154307/ddb20a0755b3956f98b27bfde1122f51.gif)
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.
