M8-S3: Hertzsprung-Russell Diagram and Stars' Life Cycle

  • 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

 

  • HR diagrams can have different axes. Determine as many characteristics of the star as possible, and its evolutionary stage by using other evidence available to you, such as:
  • The vertical axis of the H-R 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.

Magnitude

  • Magnitude of stars is usually expressed relative to the Sun which allows for simpler understanding and comparison. 
    • Magnitude is expressed on a logarithmic scale.
    • Stars with more negative magnitude have greater brightness
    • Stars with more positive magnitude have lower brightness 
    • Magnitude of a star is correlated to its mass but they are not the same thing.

Luminosity

  • Luminosity of stars represents its absolute brightness (how bright it is when observed up front, or hypothetically right next to the star.
  • Luminosity provides a reliable indication of extent of energy production the star is performing. The more reactions (nuclear fusion) that happen, the more luminous a star becomes.
  • Luminosity is proportional to stellar mass because more energy-producing reactions are required to exert force against greater gravitational force.
  • Luminosity is either presented absolutely or relatively to that of the Sun.
  • Luminosity is always presented on logarithmic scale.

 

  • 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.

Spectral Class

  • Spectral class is commonly named under the Morgan-Keenan system whereby stars are grouped into specific temperature groups: 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 indicate luminosity.
        • 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

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

Colour

  • Colour is determined by the wavelength of visible light it emits at the greatest intensity. Wien’s displacement law outlines the relationship between a star’s colour and its surface temperature.
    • Colour of stars can be classified using colour index.

 

Groups of Stars

  • Stars fall into distinct groups in the H-R diagram, with common characteristics of luminosity (hence, mass) and temperature (hence, colour), and at a similar evolutionary stage.
    • Main sequence (diagonally from bottom right to top left),
    • Red giants (middle to upper right side; cool, but very luminous, therefore very large),
    • White dwarfs (bottom middle and left; hot, but low luminosity, therefore small) and
    • Super giants (across the top of the H-R diagram; both very hot and very luminous).

 


 

Evolutionary Paths of Stars

  • Stars pass through a common evolutionary sequence, from protostar to main sequence star. Main sequence stars range vastly in mass and therefore also in temperature and colour. The mass of main sequence stars determines its post-main-sequence evolutionary path.
  • For stars substantially smaller than the Sun (~0.1 solar mass), they are found on the extreme right end of the main sequence group. These stars consume fuel very slowly (thus very dim) and stay as main sequence stars for a very long time. They eventually transition to become white dwarves.
  • For stars of about 1 solar mass, they are found generally in the middle of the diagonally shaped main-sequence group. They become red-giants, followed by white-dwarves
  • For stars about 5 solar masses, they are found to the left of our Sun in the main sequence group. These stars become white dwarves right after depleting carbon or oxygen as sources of fuel.
  • For stars greater than 10 solar masses, they are found within the extreme left end of the main sequence group. These stars consume their fuel very quickly (thus very luminous) and transition to become super giants later on. Super giants are similar to red giants but much larger in magnitude.
  • A higher mass star evolves more quickly than a lower mass star.

 

In the diagram, ‘red giant’ includes giants of various sizes e.g. super giants. Large stars (great than 5 solar masses) evolve into super giants and subsequently supernovae. The precise mass criterion for formation of super giants and supernovae is not well known.

 

Death of Stars

  • Star death occurs when the fusion of elements in the core of the star ceases and the outward pressure of radiation is insufficient to prevent the gravitational collapse of the star.
  • The processes that occur, and the nature of the object that remains, depend on the mass of the star.

 

  • After a low mass star, less than about 2-5 solar masses, has moved into the red giant stage and the helium flash has occurred, carbon and oxygen build up in the core.
    • The core begins to contract, and the star undergoes a series of bursts in luminosity, ejecting successive layers of atmosphere to form expanding shells of material around the core.
    • Viewed from a distance, the shells appear as rings, known as planetary nebulae.
    • The temperature of the core is insufficient to cause fusion of carbon and oxygen into heavier elements.
    • The extremely hot, dense core simply contracts and cools very slowly, remaining white hot for a long time because the mass is great and the surface area small.
    • The small surface area also means that it has a low luminosity and is therefore very faint. It is known as a white dwarf.

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

  • In a more massive star, when mass is greater than about 5-8 solar masses, iron forms by fusion of lighter elements, and is deposited in the core.
    • Collapse of the core is halted only by a quantum effect called electron degeneracy, as electrons resist being forced into the nucleus.
    • However, the density and pressure rise until they exceed this outward degeneracy pressure.
    • The core collapses catastrophically and rebounds, producing shockwaves that totally disrupt the star and blast much of its matter into space.
    • During this phase, the star increases dramatically in luminosity, up to several hundred billion times. This event is called a supernova.

 

  • If the mass of the core is between 1.4 and 3 times the mass of the Sun, the degenerate core consists of neutrons and is known as a neutron star.
    • Further collapse is now halted only by neutron degeneracy pressure.
    • Neutron stars often have strong magnetic fields associated with beams of radiation from the poles.
    • If the neutron star is rotating, the radiation will sweep around the neutron star like a lighthouse beam.
    • If the Earth is in the path of the beam as it rotates, we detect the beacon as rapid regular pulses of radio waves. Such a rotating neutron star is known as a pulsar.

 

  • If the core mass exceeds three solar masses, not even the neutrons can sustain the enormous pressure, and the core continues to collapse.
    • A singularity in space time is formed, known as a black hole.
    • The gravitational field of a black hole is so strong that even light cannot escape.

 

Practice Question 1

Using the following Hertzsprung-Russell diagram, what information of each star (A-F) can be obtained?

 

 

  • Star A is low and to the right of the main sequence, therefore it is a protostar, at a very early stage of its life, and heading for the main sequence. It is very cool, but is nearly as luminous as the sun, therefore it is very large.
  • Star B is on the main sequence, so it has begun to produce energy by fusion of hydrogen into helium. Its low surface temperature shows it to be a red star, while its low luminosity, and position at the bottom of the main sequence, show it to be a dwarf. As a low-mass star, it will consume its fuel very slowly and spend a very long time on the main sequence.
  • Star C is on the main sequence and is steadily converting hydrogen to helium by fusion. Its surface temperature is approximately 6000 K (remember that the scales are logarithmic), so it is a yellow star like the sun. It is also approximately as luminous as the sun; therefore it must be of similar mass to the sun.
  • Star D is in the region of red giant stars. It is relatively cool, but about 1000 times as luminous as the sun, therefore it must be very large. It has consumed most of its fuel and is near the end of its life.
  • Star E is very hot and very luminous, about 10 000 times as luminous as the sun, but it is on the main sequence. It must therefore be a very young star, as such a star consumes its fuel quickly and would not stay on the main sequence very long. It is very massive and will likely have a short, violent life, ending in a supernova.
  • Star F is a hot white star, but from its low luminosity, and its position on the H-R diagram, we can see that it is very small. It is a white dwarf and is at the end of its life.

Practice Question 2

Use the following Hertzsprung-Russell diagram to answer questions (a) and (b).

(a) Circle red giants on the diagram. (1 mark)

(b) Compare the groups of stars at A and B in terms of three key criteria. Write your answer in table form.

 

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