Why NOx will break the ozone sphere

I've found that a reason for people to oppose supersonic aeroplanes was the $\ce{NO\_{$x$}}$ gases it released would do harm to the ozone layer. So what is the mechanism of this?




According to [Introduction to Atmospheric Chemistry, by Daniel J. Jacob, Princeton University Press, 1999,Chapter 10](http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap10.html),



> 
> An important component of aircraft exhaust is nitric oxide ($\ce{NO}$) formed by oxidation of atmospheric $\ce{N2}$ at the high temperatures of the aircraft engine. In the stratosphere $\ce{NO}$ reacts rapidly with $\ce{O3}$ to produce $\ce{NO2}$, which then photolyzes:
> 
> 
> $$\ce{NO + O3 -> NO2 + O2}$$
> $$\ce{NO2 + $h\nu$ -> NO + O}$$
> 
> 
> 


Note that there is no net consumption of $\ce{NO\_x}$, thus it is able to act as a catalyst such that a single $\ce{NO\_x}$ molecule can destroy many molecules of ozone by these reactions.


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