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Feb 8, 2023 at 20:26 vote accept oliver
Feb 8, 2023 at 18:59 history edited honeste_vivere CC BY-SA 4.0
fixed the exponential rate of change, does change numbers but not interpretation
Feb 8, 2023 at 18:51 comment added honeste_vivere The recombination rate goes as $\sqrt{ \tfrac{ T }{ n^{2} } }$... Oh yes, I see what I missed. Just a second, I will update things accordingly
Feb 8, 2023 at 16:57 comment added oliver How do you arrive at $n_e^2\sim r^{-2}$ in the denominator? If I am not completely mistaken, from $n_e\sim r^{-2}$ follows $n_e^2\sim r^{-4}$. Correct?
Feb 7, 2023 at 20:00 comment added honeste_vivere I think you are missing a step. If you have $\left( \tfrac{ r^{-1.25} }{ r^{-2} } \right)^{1/2}$ = $\left( r^{+0.75} \right)^{1/2}$ = $r^{+0.375}$
Feb 7, 2023 at 15:54 comment added oliver I don't. But the density occurs to the power of two (under the square root) in the recombination time relation you have written. If a power of -2 (the density) is elevated to the power of two, a power of -4 results. Or did I misinterpret something about the formula?
Feb 7, 2023 at 15:52 comment added honeste_vivere Why do you think density changes as $n \sim r^{-4}$ in the solar wind?
Feb 7, 2023 at 15:44 comment added oliver I am not sure if I misunderstand some part of the argument. But shouldn't it be $t_{rec}\approx \sqrt{r^{-1.25}/r^{-4}}=\sqrt{r^{2.75}}=r^{+1.375}$, which would make the dependency much stronger than $r^{+0.375}$?
Feb 7, 2023 at 14:49 history answered honeste_vivere CC BY-SA 4.0