# Hertzsprung-Russell Diagram

This is part of the HSC Physics course under the section Origin of the Elements.

### HSC Physics Syllabus

• investigate the Hertzsprung-Russell diagram and how it can be used to determine the following about a star:

– characteristics and evolutionary stage
– surface temperature
– colour
– luminosity

### Hertzsprung-Russell Diagram

This video discusses the use of Hertzsprung-Russell diagram to distinguish stars based on various characteristics. The video will also discuss the main evolutionary stages of stars.

### What is a Hertzsprung-Russell (HR) Diagram?

The Hertzsprung-Russell diagram provides a visual way to distinguish stars. Different evolutionary stages of stars are plotted on the HR diagram and further separated based on characteristics such as surface temperature and luminosity.

Typically,

• The vertical axis of the HR diagram may show the star’s absolute magnitude, relative magnitude, absolute luminosity or its luminosity relative to the sun. Magnitude and luminosity of a star are correlated; greater the magnitude entails greater luminosity.
• The horizontal axis may show the star’s surface temperature, its spectral class or its colour index. Surface temperature, spectral class and colour (or colour index) are correlated.

### Luminosity of Stars

The luminosity of a star is its power, that is the rate at which the star produces energy. A star which produces more energy per second is described to have a greater luminosity.

• Absolute or true luminosity is expressed in either Watts (W) or Joules per second (J/s)
• Relative luminosity is expressed as a factor of the luminosity of the Sun.

Luminosity is proportional to the mass of a star because greater power is required to counteract the greater gravitational force that acts inwards.

### Magnitude of Stars

The magnitude of a star is its luminosity measured at a standard distance of 10 parsecs (33 light years) from the star. Since the magnitude is measured at an equal distance from each star, it is proportional to a star's luminosity.

• Stars with more negative magnitude have greater luminosity.
• Stars with more positive magnitude have lower luminosity.

Relative magnitude is expressed as a factor of the magnitude of the Sun. It is useful to note that the magnitude of a star is not the mass of the star but they are related. A heavier star tends to have greater luminosity and therefore a smaller magnitude (more negative)

### Spectral Class

Spectral class is commonly named under the Morgan-Keenan system whereby stars are grouped into groups based on their surface temperature: O, B, A, F, G, K, M (hot to cool).

Each spectral class is further subdivided into 10 subclasses, labelled by numerically (0-9) with 0 being the hottest and 9 the coolest.

Sometimes, each spectral class or subclass can be presented with Roman numerals which indicates the stage of evolutionary:

• I indicates a supergiant star
• II indicates a bright giant
• III indicates a giant
• IV indicates a subgiant star
• V indicates a main sequence star

 Spectral Class Effective Surface Temperature (Kelvin) Key Spectral Characteristics O Greater than 25000 Ionised He+ absorption lines, strong UV continuum B 10000-25000 He (neutral) absorption lines A 7500-10000 Strong hydrogen lines, ionised metal lines F 6000-7500 weaker hydrogen lines, weak ionised Ca+ lines G 5000-6000 Weaker hydrogen lines, ionised Ca+, ionised and neutral metal lines K 3500-5000 Strongest Ca+, neutral metal lines e.g. iron and weak hydrogen lines M Less than 3500 TiO, neutral metals

Our Sun belongs to the G2V spectral class.

### Surface Temperature of Stars

Surface temperature is presented on a logarithmic scale in Kelvins (K). It is important to note that surface temperature on a HR diagram typically starts high and becomes lower from left to right.

Surface temperature is different to the temperature of a star's core. For example, a supergiant whose core temperature is much higher than that of a white dwarf, would have a much lower surface temperature.

The relationship between a star's surface temperature and core temperature is determined by its radius and surface area. This is because the surface temperature is dependent on the intensity of radiation at a star's surface.

Intensity is given by

$$I=\frac{P}{A}$$

where P = power or luminosity of a star, A = surface area

A star with a large surface area e.g. super giants usually have a large difference between its core and surface temperature. Despite its high luminosity, a supergiant star has a low intensity of radiation at its surface due to its much larger surface area.

### Colour of Stars

The colour of a star is determined by the wavelengths of visible light it emits. The characteristics of radiation emitted by a star can be modelled as a black body.

Since the colour is mostly determined by the wavelength of light with the greatest intensity (peak wavelength), Wien’s displacement law can be used to analyse the relationship between colour and a star's surface temperature.

Wien's displacement law:

$$\lambda_{max}=\frac{b}{T}$$

where b = 2.898 x 10–3 and T = surface temperature

Stars whose peak wavelengths are on the shorter end of the visible light spectrum will appear to be blue whereas stars whose peak wavelengths are on the longer end of the spectrum will appear to be red. Stars with peak wavelengths in between will have a colour that is in between blue and red (e.g. orange).

### Stages of Evolution of Stars

Stars can be classified into groups based on their stage of evolution. These groups can be easily identified on a HR diagram.

Main Sequence Stars

Main-sequence stars are located in a long strip from the top left to the bottom right of a HR diagram. All stars would have been or will be a main-sequence during some stage of their evolution.

Main-sequence stars vary greatly in luminosity (power), mass, size and surface temperature. Stars in the top left part of the HR diagram are heavier, larger, more luminous and have a higher surface temperature. In contrast, stars in the bottom right part of the HR diagram are lighter, smaller, less luminous and have a lower surface temperature.

Our Sun is a main-sequence star.

Red Giants

Red giants are located above main sequence stars, underneath supergiants.

Red giants evolve from smaller main-sequence stars when they deplete their hydrogen source for nuclear fusion. This occurs because the outer layers of gases expand due to a higher temperature. It is useful to know that the mass of a main-sequence stars determines whether it evolves into a red giant or a supergiant.

A red giant has a much larger surface area compared to the preceding main-sequence star.

Supergiants

Supergiants are located at the top of a HR diagram.

Supergiants evolve from larger main-sequence stars when their hydrogen source are depleted. Supergiants have much greater surface area and luminosity compared to main sequence stars and red giants.

However, due to their much larger surface area, the intensity of radiation is relatively low at the surfaces of supergiants. As a result, supergiants have relatively low surface temperatures despite their greater luminosity.

White Dwarfs

White dwarfs are located at the left bottom of a HR diagram.

White dwarfs are the final stage of evolution following red giants. A red giant will evolve into a white dwarf when there are no more nuclei remaining for nuclear fusion. When nuclear fusion cannot longer occur, the star contracts under the influence of gravitational force.

White dwarfs have relatively high surface temperature, mainly due to smaller surface areas compared to other groups of stars.

### Evolutionary Paths of Stars

Diagram depicts the general evolutionary paths of a star with different masses.

Stars pass through a common evolutionary sequence, from a protostar to a main-sequence star. The mass of a main sequence star determines its post-main-sequence evolutionary path.

In the diagram, ‘red giant’ includes giants of various sizes e.g. super giants. Large stars evolve into super giants and subsequently supernovae. The precise mass criterion for formation of super giants and supernovae is not well known.

For main-sequence stars substantially smaller than or around the same mass as the Sun, they consume fuel very slowly and stay as main sequence stars for a very long time. These stars eventually transition to become red giants followed by white dwarves.

For main-sequence stars heavier than the Sun, they are found within the left end of the main sequence group. These stars consume their fuel very quickly (very luminous) and evolve into supergiants. Supergiants will evolve into either a neutron star or a black hole.

It useful to know that a star with greater mass evolves more quickly than a star with smaller mass. This is because heavier stars have greater luminosity (power) and hence burn through their fuel (e.g. hydrogen) more quickly.

The evolutionary paths of stars can be identified and compared on a HR diagram as shown.

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