HII regions, on-the-spot approximations

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Does anybody know what on- the- spot approximations are and why they are accurate?

Also, I cannot figure out why the temperature of an HII region does not depend on its density. any hints??
 
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sarahrose said:
Does anybody know what on- the- spot approximations are and why they are accurate?

An on the spot approximation, to me, is just another phrase for rough approximation. Each approximation's accuracy needs to be considered in its own right.

Also, I cannot figure out why the temperature of an HII region does not depend on its density. any hints??

The heating of HII regions is dominated by radiation, and hence the temperature is defined by the radiation field strength