<p>What you seem to be overlooking is that the core of a star is a dynamic place.  If there is an additional release of energy, the effect is to cause the the plasma to expand, which cools it and reduces the density, and causes the rate of fusion to slow.  The core of a main sequence star that is fusing hydrogen by the CNO cycle is stabilised by this mechanism.</p>
<p>Hence injecting a &quot;small&quot; amount of lithium won't cause a supernova-type explosion.</p>
<p>However the situation is different in a star composed of degenerate matter, such as a white dwarf.  In such an object, it can't expand and cool to maintain a stable rate of fusion. If a white dwarf begins to fuse (usually carbon fusion) then the rate of fusion will increase uncontrollably and a supernova (in particular, a type 1a supernova) is the result.</p>
<p>(of course in practical terms, it's not possible with our technology or any reasonably conceivable future tech for ten trillion tonne of lithium to be produced or manipulated in this way, that would be a billion years of production at current rates (and at current rates we will run out of lithium long before a billion years have passed!)</p>

CC BY-SA 4.0
2024-07-30T04:56:31.817Z
The Lawson criterion for inertial fusion determines the minimum size, where the reaction rate conditionally ahead of the expansion rate [ https://en.wikipedia.org/wiki/Lawson_criterion#Inertial_confinement ]. Indeed, too small volume expands and cools, extinguishing the reaction, but not if sufficiently large volume. (may be (only) 0,1 trillion ton?)
Imyaf
CC BY-SA 4.0
2024-07-29T21:12:53.753Z
2024-07-29T21:12:53.753Z
James K
<p>Can a relatively small addition of matter to a small volume of a star turn it into a supernova?</p>
<p>The rate of fusion in the CNO cycle increases very rapidly with increasing temperature, as shown in the figure (<a href="https://www.ucolick.org/%7Ewoosley/ay112-16/lectures/lecture13.4x.pdf" rel="nofollow noreferrer">which is from this source</a>) with a slight extrapolation into the diapason <span class="math-container">$10^{9…10…10,3}$</span> K = 100…1000…2000 keV. Compared to the Sun, the rate can be increased in <span class="math-container">$10^{22}$</span> times at a temperature of 2000 keV. This corresponds to a time of <span class="math-container">$10^{-5}$</span> seconds for 10% of fusion and a proton velocity of 20 000 km/s. Using the <a href="https://en.wikipedia.org/wiki/Lawson_criterion#Inertial_confinement" rel="nofollow noreferrer">Lawson criterion for inertial fusion</a>, it turns out that the size of the region that needs to be heated is only about <strong>one kilometer</strong> to trigger an escalating explosion of the entire star and turn it into a supernova. To quickly heat to 2000 keV, lithium will be needed to achieve a rapid <a href="https://en.wikipedia.org/wiki/Aneutronic_fusion#Candidate_reactions" rel="nofollow noreferrer">reaction p+<span class="math-container">$^7$</span>Li = 2 <span class="math-container">$^4$</span>He + 17,2 MeV</a>, that can be start at temperature of million kelvins near the core of any star, not at the centre. <strong>Lithium mass is approximately 10<span class="math-container">$^{14}$</span> kg</strong>, that is small relatively to star mass. How adequate is such an assessment of the mass? Could something be overlooked?</p>
<p><a href="https://i.sstatic.net/xFJAUvGi.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xFJAUvGi.png" alt="The rate of the proton fusion in the CNO cycle." /></a></p>
<p>The issue of mining that mass and delivery into a star is not considered. Only a quantitative assessment of the mass.</p>

CC BY-SA 4.0
2024-07-29T03:23:13.900Z
What is the fundamental difference between 'What if our solar system had two suns' and 'What if a piece of lithium is placed inside the sun'? Is thehe the fundamental difference between 'What if a piece of lithium is placed inside the sun' and 'Can a relatively small addition of matter to a small volume of a star turn it into a supernova?'?
Imyaf
<star><supernova><stellar-astrophysics><fusion>
Can a relatively small addition of matter to a small volume of a star turn it into a supernova?
Imyaf
# Can a relatively small addition of matter to a small volume of a star turn it into a supernova?

(Asked by: username_0 on 2024-07-28)

Can a relatively small addition of matter to a small volume of a star turn it into a supernova?

The rate of fusion in the CNO cycle increases very rapidly with increasing temperature, as shown in the figure ([which is from this source](https://www.ucolick.org/%7Ewoosley/ay112-16/lectures/lecture13.4x.pdf)) with a slight extrapolation into the diapason $10^{9…10…10,3}$ K = 100…1000…2000 keV. Compared to the Sun, the rate can be increased in $10^{22}$ times at a temperature of 2000 keV. This corresponds to a time of $10^{-5}$ seconds for 10% of fusion and a proton velocity of 20 000 km/s. Using the [Lawson criterion for inertial fusion](https://en.wikipedia.org/wiki/Lawson_criterion#Inertial_confinement), it turns out that the size of the region that needs to be heated is only about **one kilometer** to trigger an escalating explosion of the entire star and turn it into a supernova. To quickly heat to 2000 keV, lithium will be needed to achieve a rapid [reaction p+$^7$Li = 2 $^4$He + 17,2 MeV](https://en.wikipedia.org/wiki/Aneutronic_fusion#Candidate_reactions), that can be start at temperature of million kelvins near the core of any star, not at the centre. **Lithium mass is approximately 10$^{14}$ kg**, that is small relatively to star mass. How adequate is such an assessment of the mass? Could something be overlooked?

[![The rate of the proton fusion in the CNO cycle.](https://i.sstatic.net/xFJAUvGi.png)](https://i.sstatic.net/xFJAUvGi.png)

The issue of mining that mass and delivery into a star is not considered. Only a quantitative assessment of the mass.

**Tags:** star, supernova, stellar-astrophysics, fusion

> **Comments:**
> **username_0**: What is the fundamental difference between 'What if our solar system had two suns' and 'What if a piece of lithium is placed inside the sun'? Is thehe the fundamental difference between 'What if a piece of lithium is placed inside the sun' and 'Can a relatively small addition of matter to a small volume of a star turn it into a supernova?'?  

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## 1 answers

### Answer by username_1 on 2024-07-29. Score: 2

What you seem to be overlooking is that the core of a star is a dynamic place. If there is an additional release of energy, the effect is to cause the the plasma to expand, which cools it and reduces the density, and causes the rate of fusion to slow. The core of a main sequence star that is fusing hydrogen by the CNO cycle is stabilised by this mechanism.

Hence injecting a "small" amount of lithium won't cause a supernova-type explosion.

However the situation is different in a star composed of degenerate matter, such as a white dwarf. In such an object, it can't expand and cool to maintain a stable rate of fusion. If a white dwarf begins to fuse (usually carbon fusion) then the rate of fusion will increase uncontrollably and a supernova (in particular, a type 1a supernova) is the result.

(of course in practical terms, it's not possible with our technology or any reasonably conceivable future tech for ten trillion tonne of lithium to be produced or manipulated in this way, that would be a billion years of production at current rates (and at current rates we will run out of lithium long before a billion years have passed!)

> **Comments:**
> **username_0**: The Lawson criterion for inertial fusion determines the minimum size, where the reaction rate conditionally ahead of the expansion rate [ https://en.wikipedia.org/wiki/Lawson_criterion#Inertial_confinement ]. Indeed, too small volume expands and cools, extinguishing the reaction, but not if sufficiently large volume. (may be (only) 0,1 trillion ton?)  

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