Why was the Sun's output not as intense in the past?

[PainterGuy]

Hi,

I was reading the Wikipedia article on Faint young Sun paradox, https://en.wikipedia.org/wiki/Faint_young_Sun_paradox.

I couldn't understand the reason why the sun's output wasn't as intense in the past as it is now.

The article says:

Early in Earth's history, the Sun's output would have been only 70 percent as intense as it is during the modern epoch, owing to a higher ratio of hydrogen to helium in its core.

Does it mean that in the past the sun was using most of the hydrogen lying in its outer layers as fuel and it didn't make as much of an efficient fuel but as it started using more and more of hydrogen from its core, it resulted in more heat since the core was richer in hydrogen?

Thanks for the help!

 

[Bandersnatch]

There's a simple rule worth remembering when it comes to stars - the denser the core can get, the higher its temperature, and the faster the fusion reactions can occur. Faster reactions mean more energy production. Changing lighter elements into heavier through fusion allows the core to contract more.
So, as the early Sun was burning hydrogen in the core, helium 'ash' started to accumulate, allowing the core to contract, heat up, and increase the rate of reactions. Since helium keeps being produced in the core, this process is continuous, and the Sun keeps getting brighter.

 

[Drakkith]

Imagine the core of the Sun at the moment hydrogen fusion ignited. It's mostly hydrogen, with a bit of helium and a trace of other elements as well. As fusion ignites, it starts burning hydrogen and turning it into helium. Not only is helium not a fuel for fusion (at this stage), fusion also takes 4 hydrogen nuclei, which were bouncing around very energetically and exerting pressure outwards on the rest of the star, and turns them into a single helium nuclei. Since the pressure exerted by the core is dependent on the number of particles, this reduces the pressure and causes the star to contract every so slightly.

This contraction heats up the core a small amount until the pressure increase from the increased temperature balances out the loss of pressure from the reduction of particles. In addition, since stars are held together by gravity, this contraction increases the density of the star, which increases the inward force of gravity (because the same mass is now closer together), which further increases the temperature until an equilibrium is reached.

Well, except that fusion isn't a one-off event, it's a continuous process, so there is no equilibrium. The star just continues to burn hydrogen, accumulating helium in its core as the core shrinks*, increases in density and temperature, until late in the stars life where it either starts to burn helium (if massive enough) or runs out of fuel entirely.

*In reality, the increasing density and temperature at the border of the core gradually moves the 'burning region' outwards, enabling fusion of new material. But I don't know if it moves outwards fast enough to increase the size of the core against the over contraction. Hope that's not too confusing.

Anyways, the net effect is that the core gradually increases in temperature and density. This increased temperature releases more energy (because the core is hotter, and the hotter something is the more radiation it emits) which is eventually emitted at the stars photosphere as light and other EM radiation.

Note the the ratio of hydrogen to helium is, by itself, irrelevant. What matters is that the ratio has been changing over time as hydrogen is turned into helium.

 

[256bits]

There's a simple rule worth remembering when it comes to stars - the denser the core can get, the higher its temperature, and the faster the fusion reactions can occur. Faster reactions mean more energy production. Changing lighter elements into heavier through fusion allows the core to contract more.
So, as the early Sun was burning hydrogen in the core, helium 'ash' started to accumulate, allowing the core to contract, heat up, and increase the rate of reactions. Since helium keeps being produced in the core, this process is continuous, and the Sun keeps getting brighter.

Shouldn't the stars outer layers somewhat expand in the process? and the star have a cooler surface temperature.

 

[Bandersnatch]

Shouldn't the stars outer layers somewhat expand in the process? and the star have a cooler surface temperature.

Yes. During the hydrogen burning stage, stars evolve across the main sequence track on the H-R diagram, their surface growing cooler while they get brighter. The increase in overall luminosity is from the larger emitting surface, even as surface brightness (i.e. per unit area) goes down.

 

[PainterGuy]

Thank you!

Four volumes of atomic hydrogen gas are used to produce one volume of helium gas. One volume of helium is going to occupy less volume therefore the core collapses. It results in increased density and an increase in pressure.

I have two related questions.

Question 1:
Does the helium sink toward the center as it's denser than hydrogen?

Source: http://chemistry.elmhurst.edu/vchembook/123Adensitygas.html

Question 2:
As it was said earlier, as the core contracts, there is an increase in density and pressure but there are also now helium atoms present in the mixture as a result of hydrogen fusion. Wouldn't these atoms of helium come in way of collisions between hydrogen atoms and consequently have a counter effect to decrease the rate of hydrogen fusion?

 

[Vanadium 50]

our volumes of atomic hydrogen gas are used to produce one volume of helium gas.

You're not going to get anywhere thinking of the sun as a ball of gas. The solar core is 20x denser than iron.

I think this thread is going to have difficulties: "I want to understand stellar modeling without having to understand stellar modeling" is a pretty tall order. If you try and make up your own mental model based on experiences at STP, it will be wrong.

A star is a complicated beast. It's in hydrostatic equilibrium, which means the pressure and density vary with radius in just such a way so that the pressure at a given radius is just enough to support the mass of gas above it. Then the energy flow has to work out so that at each radius r, you emit all the energy created in that shell, plus all the shells underneath it, all the way to the surface. So you have a complex set of interrelations between pressure, density, temperature, fusion rate, etc.

The key driver in the sun's brightening is the opacity. The opacity is driven by the electron density. Proton-proton fusion turns electrons into neutrinos. As I remove electrons from the sun, to stay in hydrostatic equilibrium, the temperature has to go up. That increases the fusion rate, and that in turn increases the luminosity.

 

[256bits]

Does the helium sink toward the center as it's denser than hydrogen?

Your molecular density chart isn't applicable.
Helium is more dense than hydrogen but your chart compares H2 to He, molecules with electron shells.

Something like this would be more applicable ( mass number ), where the number of protons and neutrons relates to the density, with nothing to do with atomic density or molecular density.