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THE IB SAYS
THE IB SAYS
Understandings: Hertzsprung-Russell (HR) diagram; Mass-Luminosity relationship for main sequence stars.
Applications and skills: Sketching and interpreting HR diagrams; Identifying the main regions of the HR diagram and describing the main properties of stars in these regions; Applying the Mass-Luminosity relationship
Guidance: Regions of the HR diagram are restricted to the main sequence, white dwarfs, red giants, super giants and the instability strip (variable stars), as well as lines of constant radius; HR diagrams will be labelled with luminosity on the vertical axis and temperature on the horizontal axis; Only one specific exponent (3.5) will be used in the mass-luminosity relation.
Data booklet reference:
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Hertzsprung-Russell diagrams
Hertzsprung-Russell diagrams
The basics of stellar spectra should be familiar from previous units. Most stars are near-perfect blackbody emitters and therefore obey both the Stefan-Boltzmann law and Wien's displacement law. By examining the underlying continuous spectrum we can therefore determine the surface temperature of a star in kelvin. We have also previously looked at the concepts behind absorption spectra. When the light from the star leaves the photosphere of the star it passes through the stellar atmosphere before reaching our observational instruments. The gases it passes through absorb (and then re-emit, but in all directions) precise wavelengths of light corresponding to electron energy level jumps in the atoms making the stellar atmosphere. By this means we can determine what stars are made from.
We can plot a chart of stars luminosities (on a logarithmic scale) versus their surface temperature (or proxies of these, absolute brightness instead of luminosity; colour or stellar class instead of temperature) then we can see several clearly defined areas as shown in the chart above. This chart, the Hertzsprung-Russell diagram, is exceptionally useful. It is easy to determine a star's surface temperature and then use the absorption lines to help determine what type of star it is (normally a main-sequence star). We can then use this information to estimate the stars luminosity. This can then be used to estimate the distance to the star.
Regions of the HR diagram
Regions of the HR diagram
Main sequence: Stars on the main sequence, the long strip running from top-left to bottom-right in the diagram, are in the main and longest living section of their lives, fusing hydrogen to form helium. How long a star lasts on the main-sequence is a function of its mass (see Mass-Luminosity relation). As more massive stars burn through their supplies of fuel much, much faster than low mass stars (even though they have more fuel) they have much shorter lifetimes.
White dwarfs: When all the accessible nuclear fuel in a star's core is exhausted, and as long as the remaining core is less than about 1.4 solar masses, then the exposed, hot, dense, core will slowly cool down over a huge length of time. Such stars are known as white dwarfs and will be described later in the course. Cores more massive than 1.4 solar masses will suffer a different fate.
Red giants: stars nearing the end of their lives, as they move to 'burning' helium instead of hydrogen they swell to huge size. Since they have such large surface areas their surface temperature tends to be cooler. Most red giants slowly transition to white dwarf stars.
Supergiants: this is a slightly fuzzy category that includes a variety of stars, unified by a mass at least 8 times the size of the sun.
Variable stars (the instability strip): Variable stars have a brightness (as observed on Earth) that varies, often because of intrinsic periodic changes to a stars volume, surface temperature and luminosity. These stars are often in transition in the HR diagram and can be found in a region of the the HR diagram called the instability strip. Cepheid variables are an interesting and useful type of variable star because they are intrinsically very bright (they can be seen from far away, including local galaxies) and because their luminosity is closely matched to the period of their variation - hence it can be easily calculated and, therefore, so can their distance.
All these types of stars will be discussed in more detail in the next sections.
Mass-Luminosity relation
Mass-Luminosity relation
The more massive a star, the greater the pressure and temperature in the core of the star. This leads to greatly increased power generation by nuclear fusion in the core and therefore a much greater luminosity. The exponent of the relationship in the mass-luminosity relation is 3.5, meaning that if the mass increases 2x then the luminosity will increase more than 11x, and if the mass increases by 5x then the luminosity will increase 280x.
Calculating distances using the HR diagram (spectroscopic parallax)
Calculating distances using the HR diagram (spectroscopic parallax)
Determine the surface temperature of a star by examining its spectrum
Try to determine the type of star using other information (e.g. the relative abundances of different elements, or strengths of the different spectral lines). This can be difficult to do and is a big source of inaccuracy.
Use the HR diagram to determine the approximate luminosity of the star.
Measure the brightness on Earth using a telescope and photometer.
Use the equation described in a previous section to determine the distance.
The advantages of spectroscopic parallax (note that despite the name this method does NOT use parallax) are that it can be done relatively easily by measuring the spectrum of a star. The disadvantages are that it can be difficult to determine if you are looking at, say, a main sequence star or a red giant, and even if you do know what type of star you're looking at, those regions of the chart can be large and ill-defined leading to significant inaccuracies.
Questions answered:
Questions answered:
What is the Hertzsprung-Russell (HR) diagram?
Additional videos:
Additional videos:
Resources from textbooks
Resources from textbooks
Oxford Physics: pp 655 - 656
Hamper HL (2014): p 544 - 546, including worked examples and exercises on page 546.
Relevant questions from Dot Point Physics (E. Astrophysics)
Relevant questions from Dot Point Physics (E. Astrophysics)
Page 204 - 211, 216 - 218
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