Colour-Magnitude Diagrams : Part 1 of 2

Also see detailed example for NGC 4755 : Colour-Magnitude Diagram


Astrophysical studies of the stars and stellar evolution are most likely among the exceptional achievements of Science. This remarkable accomplishment did not come willingly or quickly, but were reached by gradual smaller increments of key discoveries. In just over two hundred years, we have moved from fantastic speculation to uncovering the exact cause of the stars vast amounts of heat and light. With certainty we grasp how stars evolve and last over millions to billions of years, and can predict their behaviour throughout their lifetime. Astrophysics has also scientifically established the rudimentary basis of star formation processes from their gaseous nebula origins.

Luminous stars also manufacture all the chemical elements throughout the whole stellar life cycle. Under extreme temperatures and pressures, Hydrogen, and some Helium, are fused to invariably produce more complex elements like Carbon, Oxygen and Nitrogen. These survive intact within the stellar cores, throughout their enormous bulk and surface photospheres. At the stellar life cycle end, most of these fused chemical elements are later dispersed by strong stellar winds or superwinds. This material is redistributed or mixed to form the next crop stars or planets. If not for these many generations of ancient stars, the Solar System could not have formed nor could biological life start, exist and evolve on Earth.

Stellar Evolution in Star Clusters

Direct observation of many coloured stars found within star clusters or stellar aggregates suggests stars are at different stages of evolution. If we assume every cluster star simultaneously started to shine, then as the whole cluster ages, the individual stellar masses sets the order and rate of the stellar evolutionary processes. Therefore, more massive stars evolve first followed by lighter stars.

Consequentially, if we can understand the various evolutionary states of stars within any open or globular cluster, we can work backwards and deduce the clusters age and history. From this, astronomical observations are no longer speculation but are based on direct evidence.

If we plot visual stellar magnitudes of some star cluster against expressed star colours in terms of the B−V colour index, we obtain the astronomical important empirical graph or Colour-Magnitude Diagram; sometimes abbreviated as CMD. This very useful graph allows us to determine the general characteristics of its membership and also gives the means to predict the future evolution of each individual star. Stellar membership of open clusters is assumed to lie at similar distances, and if this has been determined, then true stellar absolute magnitude or luminosity can be calculated. Similarly we can also assume that these same cluster have the same chemical composition inherited from the original nebulae. These two quantities alone allow us to predict the evolution of all the stars.

Historically, measured colour is normally placed at the bottom x-axis on the graph. On the upward y-axis plots visual magnitude. We have to use visual magnitudes as we do not know the absolute magnitude. This parameter is quite hard to determine precisely, as we must have some knowledge of the true cluster distance, which is often tainted with large scattering of less precise estimates and unknown contamination from field stars not associated with the cluster. For many years, the only true method of finding precise distances was by observing the orbits of binary stars within open clusters. These are unfortunately rare. Another way is by known variable stars shining as standard candles with known luminosities. I.e. Cepheids or blue RR Lyrae variables. It was only in latter years that other secondary methods were carefully explored, so that definitive absolute magnitudes could extensively calculated and used.

Figure 6-1. Colour-Magnitude Diagrams & Hertzsprung-Russell Diagrams

A slightly more complicated graphical representation, plots absolute magnitude versus the B-V colour index or its derived temperature, producing the better known Hertzsprung Russell Diagram or H-R Diagram. Although this reveals much more useful information about the cluster, obtaining the plotted data also requires additional knowledge of stellar evolution and requires many more assumed steps or calculations – all being prone to significant errors. It is for this reason that only the brightest clusters have useable H-R Diagrams, while the remainder of open clusters still being expressed by their CMDs. In most cases, needing to produce more complicated diagrams are not often required in determining basic understand of the evolutionary state of open or globular star clusters.

Obtaining Star Colours and Magnitudes

Star colours may be described in many different ways. Both star colours and magnitudes in the earlier days were produced using photographic images, but has now has been totally replaced by photoelectric or digital image photometry. Tradition uses the most common expression of the Colour Index (CI) or B−V Colour Index (B−V), (another in the same system is U−B Colour Index) which can be converted, with corrections, to be expressed either as spectral class or surface temperature. This system uses specifically designed coloured filters, under the so-called UBV photometry first recommended by Johnson and Morgan in 1953. Colour determination is obtained mainly using two different standard calibrated filters of known wavelengths which are placed between the optics and detector, such as two different colour sensitive plates or CCD detectors. Important filter used with star clusters include the B or Blue peaking at 440nm., the V or Visual : 547nm.; and the U or Ultraviolet at 365nm.

Both B and V filters mimic the observed visual naked-eye range of stars, while the U filter only covers the portion of visible spectrum into the near ultraviolet, whose light is significantly affected by problems like the atmosphere, distance of the star from zenith and the height of the observatory, etc. U filters must therefore be calibrated against these influences. This system also has other specialised filters in the near infrared and infrared, an are useful towards red or low heat emitting objects like red giants, brown dwarves or even exoplanets. These are now commonly designated in order as; R, I, J, H, K, L and M ranging between 640nm and 4650nm.

This entire photometric system is based on various standard calibration stars, with the prime star being first magnitude Vega in Lyra, which all filters have values of 0.00. Other measured stars that are bluer than 0.00 have negative values that range from 0.0 up to about −0.3. Those redder, only have positive values, mostly ranging between 0.0 to about 3.0. All UBV photometric values work well with blue or solar-like stars, but poorly describe the late-spectral type stars.

Once some B−V value has been obtained, with some mathematical manipulation, we can also find effective stellar temperatures (Teff). Normally obtaining such temperatures are gained by closely inspecting the available spectral lines, however, this is not always known, available, or even observable.

Some astronomers do often express star colours using the different photometric filter system called Strömgren photometry, commonly abbreviated as uvby or uvbyβ, In time, this has begun to be adopted over the older UBV photometric system, only because it have some definite advantages. Using uvbyβ photometry has several advantages over UBV, including the means of direct determination of the amount of interstellar absorption between us and the stars in the cluster.

Origins and Early Evolution of Star Clusters

We already understand that when stars are formed they are manufactured in large numbers in stellar nurseries within nebulae, which in many instances create the open star clusters. From this statement alone, we can reasonably assume that these stars within such groups to form around the same time.

Such assumed same time star formation creation is said to exhibit so-called isochronal behaviour. I.e. All stars being born about the same time forming an isochrone. Once each individual stellar component or protostar collapses within its nebulous cocoon. Protostars soon reach their thermonuclear burning stage temperature by converting hydrogen into helium, and the star starts to shine. These stars are the theoretical termed ZAMS or Zero-Aged Main Sequence stars, which are thought to be slightly larger and cooler than main sequence stars and are undergoing contraction and still heating up. For most purposes, their placement on the CMD is very close to all the main sequence positions, and for general uses have no real significant difference with normal main sequence stars. These ZAMS and main sequence stars form an S-shaped curve in the youngest open clusters on the CMD. Here the brightest and most massive stars are placed at the top-left. Other less massive fainter stars will move downward along the curve and then towards the bottom right corner or lower middle. At the bottom of the curve only contains dwarf solar-like mass stars typically without giants or supergiant stars.

Last Update : 3rd November 2020

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