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

When a star first starts to shine, it does so because of nuclear reactions and has the same mix of elements everywhere. Scientists make a model of the Sun at this young age and watch it change until it matches the Sun today. They use information from meteorites to guess the early mix of elements. By solving important physics equations, they can learn the temperature, pressure, and density at different parts of the Sun. This helps them understand how the Sun works and makes the model better.

Numerical modelling of the stellar structure equations

Main article: Stellar structure

Scientists use math to learn how stars like our Sun work. They think of the Sun as layers and use special rules to see how each layer acts. These rules help them find out about the pressure and temperature inside the Sun.

Evolution of the Sun

Main article: Stellar evolution

The Sun changes very slowly. Inside the Sun, tiny particles called hydrogen nuclei change into helium. This gives off energy, making the Sun shine and giving 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. It will keep doing this for about 11 billion years 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. It gives good guesses about 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.

Just like models in particle physics, the solar model gets updated when scientists learn new things. This helps experts test more detailed models that include the Sun’s rotation or magnetic fields.

Energy transport in the Sun

The Sun has a part that radiates energy and a part that moves energy by convection. In the center, energy from nuclear reactions moves out mostly by radiation. But in the outer layers, the temperature changes very fast, so radiation cannot carry enough energy. Instead, hot material rises to the Sun's surface, 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 made in different layers. They use special equations to describe how energy moves by radiation and by convection.

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.

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 are called equations of state. They help us learn about the pressure, darkness, and energy of a star. These rules connect to things like how thick or hot the star is, and what it is made of, as explained in stellar structure.

Helioseismology

Main article: Helioseismology

Helioseismology is the study of waves that move through the Sun. By watching these waves, scientists can learn about the Sun’s inside. This helps them understand the Sun’s outer layers and even guess the Sun’s age. This shows one way scientists can improve their Sun models.

Neutrino production

In the Sun, hydrogen changes into helium through different processes. Most neutrinos are made through something called the pp chain. In this process, 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.

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 makes tiny particles called neutrinos. Neutrinos can pass through the whole Sun and reach Earth because they hardly interact with other particles. Scientists 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 look for changes caused by neutrinos. Later, the Kamiokande-II experiment showed that the neutrinos came from the Sun. The Sudbury Neutrino Observatory (SNO) 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 more about the Sun. Main article: Solar neutrino problem

Core temperature prediction

The Sun gives off special particles called boron-8 neutrinos. The number of these particles changes based on the temperature of the Sun's center. Scientists measure these particles to find out how hot the Sun's core is. After looking at early results from a study called SNO, two researchers found that the Sun's core temperature is about 15.7 million Kelvin. They discovered this by measuring how many of these particles pass through a tiny area every second.

Lithium depletion at the solar surface

Stellar models of the Sun's evolution predict the chemical makeup of the Sun's surface well, but they have trouble with lithium (Li). The amount of Li on the Sun's surface is much smaller than when the Sun was born. Scientists do not know why this happens because the temperature near the Sun's surface is not hot enough to break down Li.

We see different amounts of Li in stars that are 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 and affect Li levels. More study is needed to understand why the models and observations do not match perfectly. With better tools, scientists think they may need to improve how they model the very early Sun.