Hertzsprung-Russell Diagrams

Astrophysics is a field of study that relies on observation because most of the objects and phenomena it explores cannot be studied in a laboratory. These objects involve things like energy, matter, speed, and distance, which we can't measure directly. For example, even though we have theoretical models for the inner structure of the sun, we haven't been able to measure it directly because of the extreme temperatures of stars.

Ancient astronomers used a strategy of statistical inference to study the sky. They would collect data on the brightness of stars and their positions in the sky. This helped them understand whether the sky or cosmos is the same in every direction.

Modern astronomers have many advanced devices to make more accurate measurements. This has allowed them to create more sophisticated statistical models to study astronomical phenomena. One of the most useful models is the Hertzsprung-Russell diagram. This diagram classifies thousands of stars by their luminosity and surface temperature, giving us a better understanding of how they evolve.

What is the Hertzsprung-Russell diagram?

The Hertzsprung-Russell diagram is a graphical two-dimensional representation of every known star according to its luminosity and surface temperature. The reason for choosing these two variables will be explored below.

Luminosity

uminosity measure of the total electromagnetic power emitted by an object, it's measured in Watts (W). However, measuring luminosity isn't easy due to a few factors. First, electromagnetic radiation spreads over space like waves caused by throwing a stone in a lake. Since we're usually far away from the objects we're measuring, we're only receiving a portion of the energy, which affects the measurement. Second, the transmission of electromagnetic radiation isn't perfect because structures between the emitting body and the measuring device can dissipate the radiation. Finally, we shouldn't limit ourselves to visible light when measuring luminosity because it can vary in other regions of the electromagnetic spectrum.

With modern techniques and technologies, we can estimate the total luminosity by knowing the distance between the measuring device and the star, modeling the dissipation caused by astronomical structures, and measuring in all electromagnetic frequencies. This helps us accurately know the radiating power of stars without being near them.

Luminosity is relevant when characterizing a star because it's a measure of its radiated power, which is related to the star's brightness. A star's luminosity is related to the nuclear power generated inside the star and the star's radius. If two stars have the same reactions happening at the same pace, the bigger one will have higher luminosity. If two stars have same size but different nuclear reactions generating power, the one whose nuclear reactions generate more energy per unit time has higher luminosity. For almost all types of stars, we can assume that the nuclear reactions are similar, and we can take the luminosity as an indirect measurement of the star's radius.

Wien’s law and the chromaticity-temperature relationship

The colour of a star, or its chromaticity, is related to its surface temperature. Stars, like black bodies, have thermodynamic properties that are almost the same, which means that the approximation is true for these astronomical bodies.

Emitting bodies, such as stars or black bodies, emit thermal energy in small amounts. Most of the energy leaves the body as electromagnetic radiation created by thermal processes within the body. We can relate the surface temperature of an emitting body to some characteristics of the emitted electromagnetic radiation. The electromagnetic frequency of the radiation, or the wavelength, is related to the surface temperature.

We classify electromagnetic radiation waves by their frequencies, which correspond to the colours we see in the visible region. Higher frequencies correspond to blue and violet colours, while lower frequencies correspond to red and orange colours.

There is a law for black bodies that determines which frequencies are emitted more intensely for a specific temperature. Since stars are approximated with great accuracy by black bodies, we can apply this law, which is phenomenologically described in the following diagram, also to them.

The relationship between a body's temperature and the electromagnetic radiation it emits is important to understand. At higher temperatures, a body emits radiation with shorter wavelengths (higher frequencies or 'bluer' colours), while at lower temperatures, the intensity of the emission shifts towards longer wavelengths (lower frequencies or 'redder' colours). This is why in the Hertzsprung-Russell diagram, the colours of stars are included, as they are directly related to the surface temperature of the stars. Hot stars are blue, while cold stars are red.

The spectrum of emission can help us determine the thermal properties of the body being studied. By studying the intensity of incoming radiation in all frequencies, we can come to conclusions about both the star's luminosity and its temperature. However, it's important to note that come luminosity is related to the sum of all intensities at all frequencies, while the temperature is related to how these frequencies are distributed.

If two stars have the same shape of the curve of the graphic intensity of emission vs wavelength, they are at the same temperature. But if one has double the height compared to the other, it indicates that the first one has double the luminosity. However, this assumes that they are at the same distance and in the same region, as otherwise, we would have to take into account dissipation and spreading. If two diagrams have the same total sum, but their shapes are completely different, we would have two stars with the same luminosity but different temperatures (given the previous assumptions).

How is the Hertzsprung-Russell diagram used?

Rather than developing a complex model to determine how the surface temperature and luminosity are correlated for all types of stars, we can use the diagram after having collected enough data to make predictions about the nature of these quantities. It turns out that, due to the processes happening inside stars, these two quantities, which are not constant throughout the life of stars, determine their stage of life. The Hertzsprung-Russell diagram can thus be used as a visual way of representing the life of stars.

Main sequence

The main sequence is the stage in which stars spend most of their lives. The initial characteristics of a star, such as its mass, determine where in the main sequence it starts, from where it then slowly evolves down and right-wards, which is to say that stars tend to decrease their temperature and luminosity as they age.

The giants and supergiants branches

Stars do not always remain in the main sequence. Due to internal processes, they can change their luminosity and/or surface temperature drastically and become giants or supergiants (these terms indicate that their radius increases). Stars with the highest masses become supergiants, while those with intermediate or low masses become giants. Our sun, for instance, is close to the point where it will evolve to become a giant in 4-5 billion years.

The white dwarfs branch

The fact that the branch associated with white dwarfs is disconnected from the rest of the diagram indicates that some sudden and drastic event needs to happen for stars in the main sequence to reach this state. At the end of its life, a star either becomes a black hole or explodes in a supernova, which leaves no emitting body behind that whose luminosity and temperature could be studied. However, after certain supernovae corresponding to low-mass stars, astronomical bodies remain that look like a regular star but have a much lower luminosity and surface temperature: white dwarfs.

Hertzsprung-Russell Diagrams - Key takeaways Astrophysics relies on the collection of data and the statistical processing of the information gathered. Relevant quantities of stars, such as their size or temperature, can be estimated through certain models and the measuring of the electromagnetic properties of the spectrum of emission. The Hertzsprung-Russell diagram is a representation of stars according to their luminosity and surface temperature. The pattern formed after the collection of significant amounts of data allows us to study the evolution of stars. The Hertzsprung-Russell diagram has four main regions: the main sequence (where stars spend most of their lives), the giants and supergiants branches, and the white dwarfs branch, which signals the final stage of life of some of the stars of the main sequence.

Hertzsprung-Russell Diagrams

What is the Hertzsprung-Russell diagram?

It is a diagram in which stars are classified according to their luminosity and surface temperature. It allows to track the evolution of stars.

How can stars be classified using the Hertzsprung-Russell diagram?

In the Hertzsprung-Russell diagram, there are four main regions: the main sequence, the giants and supergiants branches, and the white dwarfs branch.

How does the Hertzsprung-Russell diagram relate to the size of stars?

The luminosity gives a very accurate measure of the radius of stars under reasonable assumptions. The higher the luminosity, the larger the radius.

What are the main branches of the Hertzsprung-Russell diagram?

The main sequence, the giants’ branch(es) and the white dwarf branch.

Where do stars spend most of their lives in the Hertzsprung-Russell diagram?

In the main sequence.