On the wikipedia page of the nova is said that the CNO cyle, which converts hydrogen into helium, starts on the surface of the white dwarf when the temperature reaches about 20 million K. My question is: how can hydrogen be heated to such temperatures by the white dwarf, which has a maximum surface temperature of 40.000 K?
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$\begingroup$ AFAIK the CNO cycle starts at quite a bit lower than 20 million K, so I'm not sure where Wikipedia gets that figure from. The actual temperature for fusion to commence isn't the issue, nor is the surface temperature: the OP is understandably confused about how the accreted hydrogen can get so much hotter than the surface it's being heated by. $\endgroup$– Chappo Hasn't ForgottenCommented Jul 18 at 10:12
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I think what you're missing is that the atmosphere/envelope of the white dwarf is not uniformly (for example) 40,000 K. That's the photosphere -- the visible upper layer -- but the temperature rises rapidly as you move inward, until you reach the core, where the temperature is fairly uniform (and typically several million or tens of millions K). As hydrogen-rich material is accreted from the companion star, the base of the envelope compresses and the lower layers heat up. Eventually, they reach temperatures of several million K, and nuclear fusion (via the p-p chain) starts. The energy release heats the base of the envelope even further, and since it's degenerate, it can't expand and lower the temperature. So the temperature keeps rising, which drives up the nuclear reaction rates (and drives a transition to the CNO cycle), and you get a thermonuclear runaway.
Here's a plot of temperature versus radius for "a model white dwarf" (from here):
Note how the temperature plunges steeply near the outer edge of the white dwarf.
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1$\begingroup$ Ten million is a very hot white dwarf (as is one with a surface of 40,000K. The Q I have is why can't the heat be conducted very efficiently to the entire white dwarf core? $\endgroup$– ProfRobCommented Jul 19 at 18:11
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$\begingroup$ If you look at Figure 9a in this review article by Saumon et al. (2022), which shows temperature profiles for a 0.6 $M_{\odot}$ WD model as it cools, it shows the core temperature dropping below $10^{7}$ K around the same time the surface temp drops below $10^{4}$ K. As for your Q -- I don't know. (Possibly it's a matter of timescales -- e.g., as the thermonuc. runaway starts, the temperature at the base of the envelope rises too fast to be conducted away?) $\endgroup$ Commented Jul 19 at 18:59
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$\begingroup$ You say "As hydrogen-rich material is accreted from the companion star, the base of the envelope compresses and the lower layers heat up" and that "since it's degenerate, it can't expand and lower the temperature" – yet the article you get the chart from says the atmospheric envelope is not degenerate (i.e. it can expand and cool). The article also says "The steep temperature gradient near the surface creates convection zones" (my emphasis) – which would increase the rate of thermal energy loss. $\endgroup$ Commented Jul 22 at 8:40
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$\begingroup$ @ProfRob in the interior, the dominant heat transfer mechanism is by highly degenerate electrons, resulting in a very small temperature gradient (hence nearly isothermal). As degeneracy decreases with distance from the centre, radiative energy transport becomes a more important mechanism. $\endgroup$ Commented Jul 22 at 8:52
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$\begingroup$ @ChappoHasn'tForgotten that why I said "conducted". The dominant heat transfer mechanism is thermal conduction. $\endgroup$– ProfRobCommented Jul 22 at 8:58