<p>The <a href="http://csep10.phys.utk.edu/astr162/lect/binaries/masslum.html">mass luminosity relation</a> is non-linear (L = M^3.5 for the main sequence) so more massive stars burn at a much faster rate. This is a non-linear relationship because the fusion is caused by pressure in the core from the star trying to gravitationally collapse on itself.</p>

CC BY-SA 3.0
2014-07-02T06:47:01.687Z
2014-07-02T06:47:01.687Z
Aaron
<p>It's easy: the biggest the star is the more matter it has to burn but also:</p>

<ul>
<li>It has <strong>bigger burning zones</strong>, so it burns at higher rates.</li>
<li>As the star is bigger it reaches to <strong>higher pressures and temperatures</strong> at it's core, so the star can start heavier elements (than H) burning earlier than smaller and cooler stars This creates an onion like structure where different elements are fused at each layer ending in a <strong>core of inert Ni and Fe</strong> that can't be fused to create energy.</li>
</ul>

<p><img src="https://i.sstatic.net/gUiOr.png" alt="enter image description here"></p>

<p>We could compare a big star to a small one like a Formula 1 car to a simple car: the F1 is faster, but it runs out of fuel earlier.</p>

CC BY-SA 3.0
2014-06-27T17:16:47.703Z
But doesn't big stars have more fuel?
ʇolɐǝz ǝɥʇ qoq
CC BY-SA 3.0
2014-06-30T03:36:50.813Z
Yes, they do have more fuel, but the additional gravity pushes that fuel into the centre which burns it brighter and faster.
Carl
CC BY-SA 3.0
2014-06-30T06:12:27.540Z
That's why they are bigger :) there are known star up to 265 solar masses http://en.wikipedia.org/wiki/R136a1
Joan.bdm
CC BY-SA 3.0
2014-07-02T22:41:34.563Z
I don't see how a bigger surface means burning faster. Stars consume their matter by fusing Hydrogen and Helium in their core. This phenomena does not occur on their surface. Please correct that.
harogaston
CC BY-SA 3.0
2014-07-03T06:30:31.757Z
I'm sorry if I didn't explain well. By surface I meant the burning zones. These zones are not exactly at the core but at a shell surrounding it. At the exact core there is a sphere of inert elements that can't be fused to get energy (in big start these are Ni and Fe (nickel & iron)). These zones also create an onion like structure where different elements are fused in each layer. http://upload.wikimedia.org/wikipedia/commons/3/37/Evolved_star_fusion_shells.svg So basically you have higher fusion rates than in smaller stars.
Joan.bdm
CC BY-SA 3.0
2014-07-06T23:38:22.670Z
@Joan.bdm Your answer is a little simplistic, but in the larger stars, nickel and iron can fuse to make heavier elements. Unfortunately, the fusion produces less energy then the silicon fusion. Since less energy is produced, gravity eventually collapses the star. With a catastrophic collapse, the core can produce very heavy elements (maybe even as high as 118) with an explosion of energy (a nova or supernova).
LDC3
CC BY-SA 3.0
2014-06-27T06:11:42.503Z
2014-07-03T06:34:16.953Z
2014-07-03T06:34:16.953Z
Joan.bdm
<p>The easiest way to think of it is terms of the cube square law coming into play. </p>

<p>The speed at which a star can radiate heat is mostly dependent on its surface area. but it's ability to generate heat is dependent on its volume. Surface area increases with the square of the increase in radius but volume increases with cube of the radius. As a star grows in a diameter it's inside grows faster than its outside.</p>

<p>Even if all other factors stayed the same, the star would grow hotter because it has less surface area to radiate from. </p>

<p>Since gravity is dependent on volume, the gravitational compression (simplistically) scales with the cube as well. So, a larger star compresses its interior more per unit of mass than does a smaller star. </p>

<p>As Joan.bdm pointed out, stars have an interior volume, the burning zone down towards the core in which the pressures are high enough for fusion to take place. Probably should call it the burning volume</p>

<p>The burning volume is the volume in which fusion can occur. Fusion occurs once a specific threshold of heat and pressure have been reached. Below that threshold, fuel consumption is zero. </p>

<p>The cube square law means that the relative size of the burning volume to total volume increases faster than the diameter. E.g If a small star has ten percent of its mass inside the burning zone, a star with twice the diameter will have 20% of its total volume inside the burning zone. (actual ratios invented for demonstration purposes.) </p>

<p>A higher percentage of the larger star's total mass is inside the burning zone compared to a smaller star so a higher percentage of the star's mass is subject to fusion at any given time, so a higher percentage of the star's total "fuel" is being "burned" at any one time than in a smaller star.</p>

<p>The addition of more fusible isotopes also does not scale linearly. Fusing heavier elements does not release as much energy per unit of mass as lighter ones and they require higher temperatures to start i.e. heavier elements are a poorer fuel. The heavier elements are also produced by fusing lighter ones so the star has to burn fuel to make fuel. Since heavier elements require higher temperatures to fuse, the burning volume for them is smaller than that for lighter elements. Stars usually can't burn more than small percentage of the elements isotopes they produce so the notional increase in fuel supply doesn't compensate for the higher burn rate of lighter elements. </p>

<p>It's like the bard said, "The candle that burns twice as bright, burns half as long." </p>

CC BY-SA 3.0
2014-12-20T14:22:48.687Z
The rate at which a star radiates is mostly dependent on its photospheric *temperature*. "A larger star compresses its interior more..." - incorrect, central density of main sequence stars decreases with increasing mass.
ProfRob
CC BY-SA 3.0
2015-11-20T04:12:25.243Z
Gravity is not dependent on volume. It is dependent on mass, energy, and momentum.
Sir Cumference
CC BY-SA 3.0
2014-07-06T23:24:25.733Z
2014-07-06T23:24:25.733Z
TechZen
<p>Nuclear fusion rates in the core of a star have very non-linear and strong dependences on temperature, pressure and density (for temperature it's like T^40 for some processes - <a href="http://www.astro.soton.ac.uk/~pac/PH112/notes/notes/node117.html">http://www.astro.soton.ac.uk/~pac/PH112/notes/notes/node117.html</a>). So, as the star gets bigger, denser and hotter at the centre, the rates of fusion rise much faster and the star loses energy quicker, hence living a shorter life.</p>

<p>Note that the star tries to balance itself to maintain stability, so the actual dependence is not that high, and ends up being related to the mass luminosity relationship, where the dependence is not that steep.</p>

CC BY-SA 3.0
2014-12-20T14:23:59.670Z
More massive stars have *less* dense cores. The density dependence of the nuclear burning rate, it is all about the central temperature.
ProfRob
CC BY-SA 3.0
2014-07-03T02:13:51.523Z
"tries" is probably a bit too metaphorical here. Can you describe *how* the process is balanced?
naught101
CC BY-SA 3.0
2014-07-03T08:53:01.157Z
It has to maintain hydrostatic equilibrium (HSE) to be stable (or else the net force will drive it towards HSE, and hence stability). If it compresses too much, the core temperature increases, causing the nuclear reaction rates to increase steeply, which creates enough thermal/radiation pressure to push the star outwards and balance the compression. If it expands too much, it cools, lowers the thermal pressure, allowing gravity to pull the star inwards again. That's what I meant by 'tries to balance', as often it can't, for example in the instability strip containing variable/pulsating stars.
Takku
CC BY-SA 3.0
2014-07-01T12:59:15.273Z
2014-07-01T12:59:15.273Z
Takku
<p>In the book "A Really Short History Of Nearly Everything", I read that the larger the star is, the faster it burns itself. Whys that? Wouldn't there be more energy to burn if it's larger, and just be brighter? Our sun can burn for billions of years, but a planet bigger than our sun will only burn for millions of years. Why is that?</p>

CC BY-SA 3.0
2014-07-03T05:01:09.797Z
How is it that my comment has been deleted here? o.O
Py-ser
CC BY-SA 3.0
2014-07-03T05:01:56.527Z
What comment? You never did.
ʇolɐǝz ǝɥʇ qoq
CC BY-SA 3.0
2014-07-03T05:06:09.037Z
Uhm, yes I did, at the very beginning.
Py-ser
CC BY-SA 3.0
2014-07-03T05:33:43.103Z
Maybe it got flagged and removed.
ʇolɐǝz ǝɥʇ qoq
<star><stellar-evolution>
Burning Out Stars
ʇolɐǝz ǝɥʇ qoq
# Burning Out Stars

(Asked by: username_0 on 2014-06-27)

In the book "A Really Short History Of Nearly Everything", I read that the larger the star is, the faster it burns itself. Whys that? Wouldn't there be more energy to burn if it's larger, and just be brighter? Our sun can burn for billions of years, but a planet bigger than our sun will only burn for millions of years. Why is that?

**Tags:** star, stellar-evolution
> **Comments:**
> **username_1**: How is it that my comment has been deleted here? o.O  
> **username_0**: What comment? You never did.  
> **username_1**: Uhm, yes I did, at the very beginning.  
> **username_0**: Maybe it got flagged and removed.  

---

## 4 answers

### Answer by username_10 on 2014-07-01. Score: 8 | Accepted answer

Nuclear fusion rates in the core of a star have very non-linear and strong dependences on temperature, pressure and density (for temperature it's like T^40 for some processes - <http://www.astro.soton.ac.uk/~pac/PH112/notes/notes/node117.html>). So, as the star gets bigger, denser and hotter at the centre, the rates of fusion rise much faster and the star loses energy quicker, hence living a shorter life.

Note that the star tries to balance itself to maintain stability, so the actual dependence is not that high, and ends up being related to the mass luminosity relationship, where the dependence is not that steep.

> **Comments:**
> **username_11**: "tries" is probably a bit too metaphorical here. Can you describe *how* the process is balanced?  
> **username_10**: It has to maintain hydrostatic equilibrium (HSE) to be stable (or else the net force will drive it towards HSE, and hence stability). If it compresses too much, the core temperature increases, causing the nuclear reaction rates to increase steeply, which creates enough thermal/radiation pressure to push the star outwards and balance the compression. If it expands too much, it cools, lowers the thermal pressure, allowing gravity to pull the star inwards again. That's what I meant by 'tries to balance', as often it can't, for example in the instability strip containing variable/pulsating stars.  
> **username_8**: More massive stars have *less* dense cores. The density dependence of the nuclear burning rate, it is all about the central temperature.  

---

### Answer by username_2 on 2014-07-02. Score: 5

The [mass luminosity relation](http://csep10.phys.utk.edu/astr162/lect/binaries/masslum.html) is non-linear (L = M^3.5 for the main sequence) so more massive stars burn at a much faster rate. This is a non-linear relationship because the fusion is caused by pressure in the core from the star trying to gravitationally collapse on itself.


---

### Answer by username_3 on 2014-06-27. Score: 4

It's easy: the biggest the star is the more matter it has to burn but also:

* It has **bigger burning zones**, so it burns at higher rates.
* As the star is bigger it reaches to **higher pressures and temperatures** at it's core, so the star can start heavier elements (than H) burning earlier than smaller and cooler stars This creates an onion like structure where different elements are fused at each layer ending in a **core of inert Ni and Fe** that can't be fused to create energy.

![enter image description here](https://i.sstatic.net/gUiOr.png)

We could compare a big star to a small one like a Formula 1 car to a simple car: the F1 is faster, but it runs out of fuel earlier.

> **Comments:**
> **username_0**: But doesn't big stars have more fuel?  
> **username_4**: Yes, they do have more fuel, but the additional gravity pushes that fuel into the centre which burns it brighter and faster.  
> **username_3**: That's why they are bigger :) there are known star up to 265 solar masses http://en.wikipedia.org/wiki/R136a1  
> **username_5**: I don't see how a bigger surface means burning faster. Stars consume their matter by fusing Hydrogen and Helium in their core. This phenomena does not occur on their surface. Please correct that.  
> **username_3**: I'm sorry if I didn't explain well. By surface I meant the burning zones. These zones are not exactly at the core but at a shell surrounding it. At the exact core there is a sphere of inert elements that can't be fused to get energy (in big start these are Ni and Fe (nickel & iron)). These zones also create an onion like structure where different elements are fused in each layer. http://upload.wikimedia.org/wikipedia/commons/3/37/Evolved_star_fusion_shells.svg So basically you have higher fusion rates than in smaller stars.  
> **username_6**: @Joan.bdm Your answer is a little simplistic, but in the larger stars, nickel and iron can fuse to make heavier elements. Unfortunately, the fusion produces less energy then the silicon fusion. Since less energy is produced, gravity eventually collapses the star. With a catastrophic collapse, the core can produce very heavy elements (maybe even as high as 118) with an explosion of energy (a nova or supernova).  

---

### Answer by username_7 on 2014-07-06. Score: 3

The easiest way to think of it is terms of the cube square law coming into play.

The speed at which a star can radiate heat is mostly dependent on its surface area. but it's ability to generate heat is dependent on its volume. Surface area increases with the square of the increase in radius but volume increases with cube of the radius. As a star grows in a diameter it's inside grows faster than its outside.

Even if all other factors stayed the same, the star would grow hotter because it has less surface area to radiate from.

Since gravity is dependent on volume, the gravitational compression (simplistically) scales with the cube as well. So, a larger star compresses its interior more per unit of mass than does a smaller star.

As Joan.bdm pointed out, stars have an interior volume, the burning zone down towards the core in which the pressures are high enough for fusion to take place. Probably should call it the burning volume

The burning volume is the volume in which fusion can occur. Fusion occurs once a specific threshold of heat and pressure have been reached. Below that threshold, fuel consumption is zero.

The cube square law means that the relative size of the burning volume to total volume increases faster than the diameter. E.g If a small star has ten percent of its mass inside the burning zone, a star with twice the diameter will have 20% of its total volume inside the burning zone. (actual ratios invented for demonstration purposes.)

A higher percentage of the larger star's total mass is inside the burning zone compared to a smaller star so a higher percentage of the star's mass is subject to fusion at any given time, so a higher percentage of the star's total "fuel" is being "burned" at any one time than in a smaller star.

The addition of more fusible isotopes also does not scale linearly. Fusing heavier elements does not release as much energy per unit of mass as lighter ones and they require higher temperatures to start i.e. heavier elements are a poorer fuel. The heavier elements are also produced by fusing lighter ones so the star has to burn fuel to make fuel. Since heavier elements require higher temperatures to fuse, the burning volume for them is smaller than that for lighter elements. Stars usually can't burn more than small percentage of the elements isotopes they produce so the notional increase in fuel supply doesn't compensate for the higher burn rate of lighter elements.

It's like the bard said, "The candle that burns twice as bright, burns half as long."

> **Comments:**
> **username_8**: The rate at which a star radiates is mostly dependent on its photospheric *temperature*. "A larger star compresses its interior more..." - incorrect, central density of main sequence stars decreases with increasing mass.  
> **username_9**: Gravity is not dependent on volume. It is dependent on mass, energy, and momentum.  

---

