I read that contrails can only form if the outside temperature is below -40 degree Celsius.
But why not earlier?
Water is already super-cooled below 0 degree Celsius. If a condensation nuclei touches the water, it will instantly freeze, from what I understood from this website:
Contrails form at -40 degrees Fahrenheit (which is also -40 Celsius), or colder. At that temperature the tiny drops of condensed water will instantly freeze.
Now, an aircraft outputs lots of soot, that can also act as condensation nuclei.
So, why aren't contrails forming at 0 degree Celsius already?
EDIT:
For example, let's just take a look at this weather balloon data:
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PRES HGHT TEMP DWPT RELH
hPa m C C %
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955.0 614 3.4 -0.6 75
932.0 812 2.2 -2.0 74
925.0 873 1.8 -2.4 74
885.0 1227 -0.3 -5.3 69
850.0 1548 -3.3 -6.2 80
842.0 1622 -4.0 -6.6 82
797.0 2051 -7.8 -8.9 92
781.0 2209 -9.2 -9.8 96
769.0 2330 -10.3 -10.4 99
As we can see, the temperature at a pressure altitude of 769, what is 2330 meter on that day, is -10 degree and the relative humidity is 99%.
My question is: Why can't contrails form in this condition? Or can they? Because the air is very humid and the engine's vapor would give it the rest to be over-saturated, what makes the water vapor condense on the soot. And the temperature would freeze them.
Every internet source says, they can only exist at or below -40 degree Celsius. But what about this condition? What stops them to form at this temperature and humidity?
I need to know this, because I'm writing my pre-scientific work about it. I understand contrail formation pretty much so far, but some small puzzle parts are still missing.