Standard solar model

The standard solar model (SSM) is a mathematical model of the Sun as a spherical ball of gas. This gas changes from one state to another, with deep inside the Sun being a hot, ionised plasma made mostly of hydrogen. Scientists use this model to understand how stars, including our Sun, work. It is based on basic physics and uses what we know about the Sun's brightness, size, age, and what it is made of.

The Sun's age is not known exactly, but we can guess it by looking at very old rocks from space called meteorites. We also study how our Solar System has changed over time. Today, the Sun is made mostly of hydrogen (about 75%) and helium (about 24%), with only a small amount of heavier elements, which astronomers call metals.

The standard solar model helps scientists test ideas about how stars change and grow. By adjusting two special numbers in the model—the amount of helium and how heat moves in the Sun's outer layers—scientists can make the model match what we see about the Sun today. This helps us learn more about the Sun and other stars too.

A calibrated solar model

A star is considered very young when it starts to shine mainly because of nuclear reactions and has the same mix of elements everywhere. Scientists create a model of the Sun at this young age and then watch it change over time until it reaches the Sun's current age. They use information from meteorites to guess the early mix of elements and adjust the model until it matches what we see today. By solving important physics equations, they can figure out the temperature, pressure, and density at different parts of the Sun. This helps them understand how the Sun works and makes the model even better.

Numerical modelling of the stellar structure equations

Main article: Stellar structure

Scientists use math to understand how stars like our Sun work. They break the Sun into layers and use special equations to see how each layer behaves. These equations help them figure out things like pressure and temperature inside the Sun.

Evolution of the Sun

Main article: Stellar evolution

The Sun is always changing, but very slowly. Inside the Sun, tiny particles called hydrogen nuclei change into helium through special reactions that give off energy. This makes the Sun shine and gives us heat and light. As the Sun uses up its hydrogen, it slowly gets a little bigger and brighter.

The Sun has been shining like this for about 4.6 billion years, and it will keep doing this for a very long time—about 11 billion years in total—before it changes into a much bigger, cooler kind of star called a red giant. Even though the Sun is always changing a little, for most of its life it stays about the same, which makes it easier for scientists to study.

Purpose of the standard solar model

The standard solar model helps us understand the Sun better. It gives us good guesses for things like how much helium is in the Sun and how heat moves through it. This model makes sure the Sun’s brightness and size match what we see today.

Just like models in particle physics and cosmology, the solar model gets updated when scientists find new facts or better ways to understand the Sun. This helps experts test more detailed models that include things like the Sun’s rotation or magnetic fields.

Energy transport in the Sun

The Sun has a radiative core and a convective outer envelope. In the core, energy from nuclear reactions moves outward mainly by radiation. But in the outer layers, the temperature changes so quickly that radiation can't carry enough energy. Instead, hot material rises to the Sun's surface in columns, cools down, and then sinks back down to get more heat.

Scientists study the Sun's structure by looking at things like density, temperature, pressure, and how much energy is produced in different layers. They use special equations to describe how energy moves by radiation and how it moves by convection, which is the rising and falling of hot and cool material.

Simulations of near-surface convection

Scientists use special computer programs to study the top layer of the Sun’s convection zone. These programs look at how the Sun’s surface moves and shines in great detail. They can show patterns called solar granulation and match what we see in the Sun’s light without needing simple guesses about turbulence.

These computer studies only look at a tiny part of the Sun and take too much time to use for the whole Sun. But, by averaging the results and using a theory called mixing-length, scientists found that their studies match what we learn about the Sun’s layers from helioseismology. They also created new theories that include the push from turbulence and the movement of energy, based on these close-up studies.

This section is adapted from the Christensen-Dalsgaard review of helioseismology, Chapter IV.

Equations of state

To understand how stars like our Sun work, scientists use special math rules. These rules, called equations of state, help us figure out how much pressure, how dark the star is, and how much energy it makes. These rules connect to things like how thick or hot the star is, and what it's made of, as explained in stellar structure.

Helioseismology

Main article: Helioseismology

Helioseismology is the study of waves that move through the Sun. By watching how these waves change, scientists can learn about the Sun’s inner layers. This helps them understand how the Sun’s outer layers look and even figure out the Sun’s age, which is different from how we learn the age of very old rocks from space. This shows one way scientists can make their Sun models even better.

Neutrino production

In the Sun, hydrogen changes into helium through different processes. Most neutrinos are made through something called the pp chain, where four protons become two protons, two neutrons, two positrons, and two electron neutrinos. Another process, the CNO cycle, also makes neutrinos, but it is much less important in our Sun compared to other stars.

Most of the Sun's neutrinos come from the first step of the pp chain. These neutrinos have very low energy.

Neutrino detection

The Sun's core produces tiny particles called neutrinos. Because neutrinos hardly interact with other particles, they can pass through the entire Sun and reach Earth. Scientists can study the Sun's core by catching these neutrinos.

The first successful experiment to detect neutrinos from the Sun was led by Ray Davis. It used a tank of special liquid to watch for changes caused by neutrinos. Later, the Kamiokande-II experiment showed that the neutrinos came from the Sun. The Sudbury Neutrino Observatory (SNO) finally explained why fewer neutrinos were detected than expected. It showed that neutrinos change their type as they travel through the Sun.

Different types of neutrinos from the Sun's energy processes have been detected using various methods. Some very high-energy neutrinos have not yet been seen because there are too few of them. Future experiments hope to detect more types of neutrinos to learn even more about the Sun. Main article: Solar neutrino problem

Core temperature prediction

The number of special particles called boron-8 neutrinos that come from the Sun changes a lot depending on how hot the Sun's center is. Scientists can measure these particles to figure out the temperature of the Sun's core. After looking at early results from a study called SNO, two researchers calculated that the Sun's core temperature is about 15.7 million Kelvin, with a small margin of error. They made this discovery by measuring how many of these particles pass through a square centimeter every second.

Lithium depletion at the solar surface

Stellar models of the Sun's evolution do a good job predicting the chemical makeup of the Sun's surface, but they struggle with lithium (Li). The amount of Li on the Sun's surface is 140 times smaller than what it was when the Sun was born. Scientists aren't sure why this happens because the temperature near the Sun's surface isn't hot enough to break down Li.

We see a wide range of Li levels in stars similar in age, size, and composition to the Sun. Some stars with planets (exoplanets) have very little Li, while others have much more. One idea is that planets might change how these stars spin, which could mix materials more deeply and affect Li levels. More study is needed to understand why the models don't match observations perfectly. With better tools to study the Sun's inside, scientists think they may need to improve how they model the very early Sun.