Brief Quickstart to Stars

In the past few sections, we have discussed the history of astronomy from the ancient Greeks to modern times, covering key figures and discoveries that have shaped our understanding of the cosmos. Stars are the fundamental building blocks of galaxies and play a crucial role in the evolution of the universe. While we will dedicate much more time to discussing stars in the following sections, some readers may want a quick overview of the essential concepts related to stars before diving into the details.

Table of Contents

• Table of Contents
• Stellar Evolution
  • Classification of Stars on the H-R Diagram
  • Stellar Lifecycles Based on Mass

Stellar Evolution

A star is a massive, luminous sphere of plasma held together by its own gravity. Our Sun (denoted with ) is the star at the center of our solar system with a mass of approximately kg (the solar mass ), a radius of about meters (the solar radius ), and a luminosity of roughly watts (the solar luminosity ). Stars are primarily composed of hydrogen and helium, with trace amounts of heavier elements. They are characterized by their mass, luminosity, temperature, and size, with these properties determining their life cycle and evolution. A visual representation of these properties can be found on the Hertzsprung-Russell (H-R) diagram, which plots stars according to their luminosity and temperature.

Before a star forms, a cloud of gas and dust called a nebula collapses under its own gravity. As the cloud collapses, it heats up and forms a protostar, defined as a period where the core temperature is not yet high enough for nuclear fusion to occur. Some stars are able to reach about 10 million Kelvin in their cores, which allows hydrogen nuclei to undergo the proton-proton chain reaction, fusing hydrogen into helium and releasing a tremendous amount of energy in the process. This process, known as nuclear fusion, requires extremely high temperatures and pressures, as well as quantum tunneling, to overcome the electrostatic repulsion between positively charged nuclei.

Once nuclear fusion begins, the star enters the main sequence phase, where it spends the majority of its life fusing hydrogen into helium in its core. The outward pressure from the energy released by fusion balances the inward pull of gravity, creating a stable hydrostatic equilibrium for the star. The star's position on the main sequence is determined by its mass, with more massive stars being hotter and more luminous. Young stars may also form protoplanetary disks around them, which can eventually lead to the formation of planets. These are disk-shaped as a result of the conservation of angular momentum during the collapse of the nebula, and thus rotate around the star in the same direction. This is why planets in our solar system all orbit the Sun in the same direction. When a star exhausts the hydrogen in its core, it leaves the main sequence, and its future evolution depends on its mass.

Classification of Stars on the H-R Diagram

Stars are classified based on their spectral characteristics, which are determined by their surface temperature and the absorption lines in their spectra. The most common classification system is the Morgan-Keenan (MK) system, which uses the letters O, B, A, F, G, K, and M to denote different spectral types. O-type stars are the hottest and most massive, while M-type stars are the coolest and least massive. Each spectral type is further divided into subclasses using numbers from 0 to 9, with 0 being the hottest and 9 being the coolest within that type. For example, our Sun is classified as a G2V star, indicating it is a G-type star with a surface temperature of approximately 5,778 K and is a main-sequence star (denoted by the Roman numeral V).

To visualize the classification of stars, we can plot a simplified Hertzsprung-Russell diagram. It is a scatter plot of stars showing the relationship between their absolute magnitudes or luminosities versus their stellar classifications or effective temperatures.

Observational Hertzsprung-Russell diagram, showing the relationship between stellar luminosity and surface temperature. The main sequence is the prominent diagonal band running from the top left (hot, luminous stars) to the bottom right (cool, dim stars). Other regions include giants, supergiants, and white dwarfs. By Richard Powell - The Hertzsprung Russell Diagram, CC BY-SA 2.5, Link

This diagram was independently developed by Ejnar Hertzsprung and Henry Norris Russell in the early 20th century. It reveals distinct groups of stars, including the main sequence, giants, supergiants, and white dwarfs.

The -axis has two scales: the top scale shows the spectral types (O, B, A, F, G, K, M) and the temperature in Kelvin, while the bottom scale shows the color index (B-V). The usage of spectral types is historical, dating back to the early 20th century when astronomers classified stars based on their spectral lines. It was only later that we realized that the surface temperature was a better indicator of a star's properties.

Recall from our previous discussions that the temperature is directly related to the color of the star, with hotter stars appearing blue and cooler stars appearing red. A simple explanation would be that the color corresponds to the peak wavelength of the star's blackbody radiation, as described by Wien's displacement law.

The color index is the difference between a star's magnitude in the blue () and visual () bands;

We can use the formula

to plug into the above equation:

As the and terms cancel out, we see that the color index is only a function of the temperature . As the temperature increases, the color index decreases, indicating that hotter stars are bluer.

The -axis also has two scales: the left scale shows the absolute magnitude , while the right scale shows the luminosity in terms of the solar luminosity . The absolute magnitude is related to the luminosity by the formula

where is the absolute magnitude of the Sun in the visual band.

Generally, stars on the main sequence follow a mass-luminosity relation, where more massive stars are more luminous. This is because more massive stars exert greater gravitational pressure on their cores, leading to higher temperatures and more rapid fusion rates. The energy produced by fusion is then radiated away from the star's surface, resulting in higher luminosity.

Stellar Lifecycles Based on Mass

The lifecycle of a star is primarily determined by its initial mass, which influences its temperature, luminosity, and the types of nuclear fusion processes that occur in its core.

Generally, stars can be categorized into three main mass ranges: low-mass stars (less than about 2 solar masses), intermediate-mass stars (between about 2 and 8 solar masses), and high-mass stars (greater than about 8 solar masses).

For low-mass stars, such as red dwarfs, they have relatively long lifespans, often exceeding tens of billions of years. Their temperatures are lower, and thus they burn their hydrogen fuel slowly (recall that the rate of a reaction, whether nuclear or chemical, generally increases with temperature). As they exhaust their hydrogen fuel, the helium begins to accumulate in the core, and the star expands into a red giant. Eventually, the core temperature becomes high enough to ignite helium fusion, producing carbon and oxygen. After the helium is exhausted, the star sheds its outer layers, creating a planetary nebula, and the core remains as a white dwarf, which will eventually cool and fade over time.

Intermediate-mass stars, like our Sun, have shorter lifespans of a few billion years. They also expand into red giants after exhausting their hydrogen fuel, but they can ignite helium fusion more easily due to their higher core temperatures. After the helium is exhausted, they may go through additional fusion stages, producing heavier elements up to carbon and oxygen. These stars also end their lives as white dwarfs after shedding their outer layers.

High-mass stars have the shortest lifespans, often only a few million years, due to their high luminosities and rapid consumption of nuclear fuel. They undergo a series of fusion stages, producing heavier elements such as neon, magnesium, silicon, and iron. Once the core is primarily iron, fusion can no longer produce energy, leading to a catastrophic collapse of the core and a subsequent supernova explosion. The remnant core may become a neutron star or, if massive enough, collapse further into a black hole. Neutron stars are incredibly dense objects composed primarily of neutrons, while black holes have gravitational fields so strong that not even light can escape. We will dedicate an entire section to discussing black holes and the Schwarzschild metric later.