# Hertzsprung-Russell Diagram and the Main Sequence

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The Hertzsprung-Russell diagram shows the relationship between different properties of stars and illustrates trends among stars. The diagram was created in 1910 by Ejnar Hertzsprung and Henry Norris Russell, and represented a huge leap forward in understanding stellar evolution, or the 'lives of stars'.

The Hertzsprung-Russell diagram (usually referred to by the abbreviation H-R diagram or HRD, also known as a colour-magnitude diagram, or CMD) shows the relationship between absolute magnitude, luminosity, classification, and effective temperature of stars.

In this Hertzsprung-Russell Diagram, 22,000 stars are plotted from the Hipparcos catalogue and 1000 from the Gliese catalogue of nearby stars. An examination of the diagram shows that stars tend to fall only into certain regions on the diagram. The most predominant is the diagonal line going from the upper left (hot and bright) to the lower-right (cooler and less bright), called the main sequence.

The main sequence is visible as a prominent diagonal band that runs from the upper left to the lower right.

## Terminology

• Apparent Magnitude (m) of a star is a measure of its brightness as seen from Earth.
• Absolute Magnitude (M) of a star is its apparent magnitude as seen from the standard distance (10 Parsecs)
• Colour Index (B-V) is a measure of the stars colour, or temperature.

## Colour Index (B-V)

Hot stars give off more blue light than red; cool stars give off more red light than blue. Coloured filters are used to measure different wavelengths of light from stars. The magnitude of the star is measured first through a standardised B-band ("blue") filter. Then the magnitude of the star is measured through a V-band ("visible", peaking in green) filter. The value of V is subtracted from B to get the B-V colour index. This leads to the spectral classification of a star.

By measuring the difference between these values, this eliminates the need to correct the magnitudes for distance. Thus the position of a star on the HR diagram can be used to estimate its radius and temperature.

As a star gets cooler and therefore redder, the B-V colour index increases since smaller magnitudes correspond to brighter light. Hot stars have a small B-V and cool stars have a large B-V. Hotter stars, therefore, appear to the left on the HR diagram and cooler stars appear on the right.

## Hertzsprung-Russell Diagram Interpretation

Most of the stars occupy the region in the diagram along the line called the Main Sequence. During that stage, stars are fusing hydrogen in their cores. The next concentration of stars is on the horizontal branch (helium fusion in the core and hydrogen burning in a shell surrounding the core).

The Hertzsprung-Russell diagram can also be used by scientists to roughly measure how far away a star cluster is from Earth. This can be done by comparing the apparent magnitudes of the stars in the cluster to the absolute magnitudes of stars with known distances (or of model stars). The observed group is then shifted in the vertical direction until the two main sequences overlap. The difference in magnitude that was bridged in order to match the two groups is called the distance modulus and is a direct measure of the distance. This technique is known as main-sequence fitting, or, confusingly, as the spectroscopic parallax.

## The Main Sequence

After a star has formed, it generates energy at the hot, dense core region through the nuclear fusion of hydrogen atoms into helium. During this stage of the stars lifetime, it is located along the main sequence at a position determined primarily by its mass, but also based upon its chemical composition and other factors. In general, the more massive the star the shorter its lifespan on the main sequence. After the hydrogen fuel at the core has been consumed, the star evolves away from the main sequence.

The main sequence is visible as a prominent diagonal band that runs from the upper left to the lower right.

The life span of a star is linked to its mass (in other words the amount of Hydrogen fuel). A star such as Betelgeuse is about 20 times more massive than the Sun and about 14,000 times brighter. Because it is bigger and brighter it burns fuel at a rate 14,000 times faster than our the Sun. Our Sun will still be shining as bright as ever when Betelgeuse has used all its fuel. In fact our Sun will live approx 7000 times longer than Betelgeuse.

Main sequence stars have been extensively studied through stellar models, allowing their formation and evolutionary history to be relatively well understood. The position of the star on the main sequence provides information about its physical properties.

The temperature of a star can be approximately determined by treating it as an idealized energy radiator known as a black body. In this case, the luminosity L and radius R are related to the temperature T by the Stefan-Boltzmann Law:

Equation 26 - Stefan-Boltzmann Law

A star remains near its initial position on the main sequence until a significant amount of hydrogen in the core has been consumed, then begins to evolve into a more luminous star. On the HR diagram, the evolving star moves up and to the right of the main sequence. Thus the main sequence represents the primary hydrogen-burning stage of a stars lifetime.

Last updated on: Wednesday 24th January 2018