<p>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 <em>photosphere</em> -- the visible <em>upper</em> 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.</p>
<p>Here's a plot of temperature versus radius for &quot;a model white dwarf&quot; (from <a href="https://people.ast.cam.ac.uk/%7Epettini/Stellar%20Structure%20Evolution/Lecture14.pdf" rel="nofollow noreferrer">here</a>):</p>
<p><a href="https://i.sstatic.net/LRQDhvud.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/LRQDhvud.png" alt="Plot of temperature versus radius for a white dwarf model" /></a></p>
<p>Note how the temperature plunges steeply near the outer edge of the white dwarf.</p>

CC BY-SA 4.0
2024-07-19T18:11:42.447Z
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?
ProfRob
CC BY-SA 4.0
2024-07-19T18:59:18.673Z
If you look at Figure 9a in [this review article by Saumon et al. (2022)](https://arxiv.org/pdf/2209.02846), 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?)
Peter Erwin
CC BY-SA 4.0
2024-07-22T08:40:44.330Z
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.
Chappo Hasn't Forgotten
CC BY-SA 4.0
2024-07-22T08:52:04.750Z
@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.
Chappo Hasn't Forgotten
CC BY-SA 4.0
2024-07-22T08:58:03.153Z
@ChappoHasn'tForgotten that why I said "conducted". The dominant heat transfer mechanism is thermal conduction.
ProfRob
CC BY-SA 4.0
2024-07-22T09:07:03.113Z
@ProfRob Interestingly, I read that early in the WD's evolution (at luminosity >10% of the Sun) the dominant mechanism for energy loss is neutrino emission. Is that related to the initial contraction & the consequent release of gravitational energy?
Chappo Hasn't Forgotten
CC BY-SA 4.0
2024-07-22T09:23:02.557Z
@ChappoHasn'tForgotten it's just because their interiors are very hot and neutrino cooling in a degenerate gas depends on something like $T^{6+}$ (neutrino bremsstrahlung and the like).
ProfRob
CC BY-SA 4.0
2024-07-22T15:33:04.637Z
@ChappoHasn'tForgotten From [this review article about classical novae](https://arxiv.org/abs/1605.04294): "Over long periods of time, the material being accreted from the secondary star forms a layer of nuclear fuel on the WD. The bottom of this layer is gradually compressed by the surface gravity of the WD and ultimately it becomes electron degenerate. The degeneracy of the material acts to prevent the material from expanding even as the temperatures increase from both compression and nuclear fusion." (The article I first linked to is primarily about non-accreting WDs.)
Peter Erwin
CC BY-SA 4.0
2024-07-22T23:56:31.987Z
Thanks Peter: I think that's right. It's frustrating when different sources present contradictory opinions! We know that degeneracy varies with depth in stars and stellar remnants, so the 2 issues are (1) the extent of a WD atmosphere's degeneracy and (2) the constraint that a given level of degeneracy places on thermal expansion (i.e. a mechanism for heat loss). There's also the question of whether the WD is already in a steady burning state (which seems to depend on accretion rate), or whether compression in a degenerate heat trap eventually triggers ignition. Your linked article helps!
Chappo Hasn't Forgotten
CC BY-SA 4.0
2024-07-19T11:25:43.787Z
2024-07-19T11:25:43.787Z
Peter Erwin
<p>On the <a href="https://en.wikipedia.org/wiki/Nova" rel="noreferrer">wikipedia page of the nova</a> 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?</p>

CC BY-SA 4.0
2024-07-18T10:12:36.070Z
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.
Chappo Hasn't Forgotten
<star><white-dwarf><fusion><nova>
Required temperature for a nova
jack_O'Dim
# Required temperature for a nova

(Asked by: username_0 on 2024-07-18)

On the [wikipedia page of the nova](https://en.wikipedia.org/wiki/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?

**Tags:** star, white-dwarf, fusion, nova
> **Comments:**
> **username_1**: 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.  

---

## 1 answers

### Answer by username_2 on 2024-07-19. Score: 4 | Accepted answer

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](https://people.ast.cam.ac.uk/%7Epettini/Stellar%20Structure%20Evolution/Lecture14.pdf)):

[![Plot of temperature versus radius for a white dwarf model](https://i.sstatic.net/LRQDhvud.png)](https://i.sstatic.net/LRQDhvud.png)

Note how the temperature plunges steeply near the outer edge of the white dwarf.

> **Comments:**
> **username_3**: 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?  
> **username_2**: If you look at Figure 9a in [this review article by Saumon et al. (2022)](https://arxiv.org/pdf/2209.02846), 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?)  
> **username_1**: 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.  
> **username_1**: @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.  
> **username_3**: @ChappoHasn'tForgotten that why I said "conducted". The dominant heat transfer mechanism is thermal conduction.  
> **username_1**: @ProfRob Interestingly, I read that early in the WD's evolution (at luminosity >10% of the Sun) the dominant mechanism for energy loss is neutrino emission. Is that related to the initial contraction & the consequent release of gravitational energy?  
> **username_3**: @ChappoHasn'tForgotten it's just because their interiors are very hot and neutrino cooling in a degenerate gas depends on something like $T^{6+}$ (neutrino bremsstrahlung and the like).  
> **username_2**: @ChappoHasn'tForgotten From [this review article about classical novae](https://arxiv.org/abs/1605.04294): "Over long periods of time, the material being accreted from the secondary star forms a layer of nuclear fuel on the WD. The bottom of this layer is gradually compressed by the surface gravity of the WD and ultimately it becomes electron degenerate. The degeneracy of the material acts to prevent the material from expanding even as the temperatures increase from both compression and nuclear fusion." (The article I first linked to is primarily about non-accreting WDs.)  
> **username_1**: Thanks Peter: I think that's right. It's frustrating when different sources present contradictory opinions! We know that degeneracy varies with depth in stars and stellar remnants, so the 2 issues are (1) the extent of a WD atmosphere's degeneracy and (2) the constraint that a given level of degeneracy places on thermal expansion (i.e. a mechanism for heat loss). There's also the question of whether the WD is already in a steady burning state (which seems to depend on accretion rate), or whether compression in a degenerate heat trap eventually triggers ignition. Your linked article helps!  

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