Hertzsprung-Russell Diagram
Spectral class key
The Hertzsprung-Russell diagram
The Hertzsprung-Russell (H-R) diagram is a standard graph in astrophysics for studying stellar
populations. It plots (
effective) surface temperature (or equivalently spectral class or some
measure of colour such as
B-V) along the bottom axis and luminosity (or magnitude) along the vertical
axis for a large number of stars. Note that when temperature is plotted on the horizontal axis, the axis is
reversed, running from high temperatures on the left to low temperatures on the right (to match the
historic choice of plotting spectral class from O to M). Be careful when magnitude is plotted on the
vertical axis, because the smaller the magnitude, the higher the luminosity, so magnitude will usually also
go in the opposite direction to normal for a graph, from high at the bottom to low at the top! The version
above plots luminosity in units of
solar luminosity (one solar luminosity being equal to the luminosity of
the sun).

Key:

  IS: instability strip, the stars in this region are represented by open circles;
  MS: main sequence; MS - RD: main sequence red dwarfs;
  PN: the position of the central stars of
planetary nebulae;
  RG: red giants;
  sD: sub-dwarfs.
  sG: sub-giants;
  SG: supergiants;
  Sol: the position of the Sun or Sol (yellow circle);
  WD:
white dwarfs.

Often the H-R diagram for a star cluster is plotted, and each star cluster has a unique diagram
depending on the age of the cluster. When stars begin their main life after leaving their embryonic
stages as protostars, they enter the main-sequence (MS). Stars do not move along the MS, but more
massive stars join at the high temperature - high luminosity end and dwarfs at the lower end. As a star
ages, it moves upwards slightly, so the MS becomes a scatter (as shown) rather than a neat curve

Subdwarfs and Metallicity

These are very old stars that have low metallicities (population I stars). Metallicity is the fraction of
elements heavier than helium in a star's atmosphere. After the Big Bang, heavy elements were extremely
rare and the oldest stars are the first-born, made almost entirely of hydrogen and helium, though they
synthesise some heavier elements during their lifetimes. Stars like Sol (the Sun) have higher metallicities
as they are formed from the ashes or star-dust of generations of stars that lived and died before them
(these are population II stars). Stars with lower metallicity are less luminous and so form main sequences
lower down, however, since more massive and hotter stars are shorter lived, these old populations of
stars contain only dwarfs now (unless we are looking back very far in time) and so their MS is apparent
only as a group of so-called subdwarfs below the normal population II MS.

Subgiants, Red Giants and Supergiants

Subgiant stars are giants that are smaller than usual for their spectral class. Many are considered to be
stars in transition from the main sequence (core hydrogen-burning) to the red giant phase (shell
hydrogen-burning).

Red giant stars are stars that have left the main sequence. They have diameters of 10-1000 times that
of the Sun and surface temperatures of 2000-4000 K. These old stars have exhausted the supply of
hydrogen in their cores and instead burn hydrogen in a thin shell around the inert core. This causes the
outer layers to expand massively, cooling as they do so. Though cooler, they have a high luminosity due
to their size.

Supergiants are the largest and most luminous type of star. Red supergiant, or asymptotic giant branch
(ASG) stars, are old and very massive stars in their final centuries or days of life. They typically undergo
periods of instability as they are burning fuel in both a hydrogen shell and a helium shell. The presence
of two burning shells creates instabilities called thermal pulses.

Magnitude

Magnitude is a measure of the brightness of a celestial object. The apparent magnitude is a measure
of how bright the object appears from Earth (adjusted to give the value if the Earth had no atmosphere).
The lower the magnitude, the brighter the object, e.g. the very bright star Sirius has an apparent
magnitude of -1.47 (Sirius is the brightest star, other than the Sun, at visible wavelengths). On the
Pogson scale, a magnitude difference 0f 5 magnitudes corresponds to a hundred-fold difference in
brightness. Tjhis is because the scale is logarithmic to allow for the fact that th eye perceives intensity on
a logarithmic scale - an apparent doubling in brightness, as seen by the human eye, corresponds to a
ten-fold increase in actual brightness. (This property allows the eye to perceive brightnesses over a very
wide range of values). Stars differing by one magnitude differ in brightness by 2.512 fold (the
Pogson
ratio
). Apparent magnitude measured by eye, in this way, is the apparent visual magnitude.

These days magnitude can be measured over a wider range by a variety of instruments and over a
specified range or band of wavelengths, narrow or broad.
Photoelectric magnitudes (measured by a
photometer with a wavelength filter) are typically measured over one of three wavelength bands: U, B or
V (the
UBV system). U is ultraviolet (centred on 365 nm), B is blue light (centred on 440 nm) and V is
visual (centred on 550 nm, yellow-green light to which the eye is most sensitive). Other systems use
different sets of band-pass filters.

Apparent magnitude does not give a measure of an object's actual
luminosity - how much energy the
actual object emits (or reflects), that is its intrinsic brightness (as measured from a set distance).
Bolometric luminosity is the total output over all wavelengths, but luminosity may also be measured or
calculated over a narrower range of wavelengths (so a star might be most luminous in the red or
ultraviolet part of the spectrum, for example). Apparent
bolometric magnitude is a measure of the total
radiation received from the object and differes from the visual magnitude by an amount called the
bolometric correction. Absolute magnitude gives a measure of an object's intrinsic luminosity at a
standard distance of 10 parsecs (and requires a measurement or estimate of the object's actual
distance from the observer).

B-V Color Index

The B-V color index is the blue apparent magnitude minus the visual apparent magnitude. (U-B is also
commonly used). This gives an indication of the star's colour. A0 stars (compensating for Doppler shift,
i.e. unreddened) are given a value of zero. Since smaller magnitudes correspond to brighter objects: a
very hot star will emit more energy at blue wavelengths and so B-V will be negative. For a cooler, redder
star, B-V will be positive. (N.B. This 'counter-intuitive' scale arises because smaller magnitudes are
defined to be brighter!).



Bibliography

Collins Dictionary of Astronomy (2nd ed.), 2000. HarperCollins (pub). [A newer ed. may be available.]

Introductory Astronomy and Astrophysics, Zeilik and Smith (2nd ed.), 1987. CBS College Publishing. [A
newer ed is available].

The Cambridge Atlas of Astronomy, Audouze and Israel (eds.) (3rd ed.), 1994. Cambridge University
Press. [I expect a newer ed. is available!]

The Open University course texts for S381, The Energetic Universe, 2002.