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OPEN STAR CLUSTERS : 6 of 10



Colour-Magnitude Diagrams : Part 1 of 2


Also see detailed example NGC 4755 : Colour-Magnitude Diagram

I N T R O D U C T I O N

Stellar astronomy and the astrophysical study of stellar evolution is probably one of the truly greatest achievements of Science. These accomplishments though have not been made readily. In just over two hundred years, we have moved from wild speculations about stellar composition and the prodigious source of their heat and light, to understanding nearly all the details of their long stellar evolution - both physically and chemically; and have even quantified their general physical parameters. Today we have also learnt much about the star formation process, and comprehensively understand how they generate such stupendous energies. We also have found how stars are able to create all the basic fundamental chemical elements. Through the whole stellar life cycle, the Hydrogen, and some of the Helium, is fused to make heavier elements like Carbon, Oxygen and Nitrogen, which survives in the stellar cores. At the end of the stellar life cycle, these fused elements are dispersed through stellar winds and are ten again redistributed throughout each plant, star or galaxy in the Universe. If it were not for now ancient stars manufacturing the gamut of chemical elements over the first ten billion years of the Universe existence. Here planets could not have formed, nor would we see life starting or existed on our planet.

Evolution of Stars in Clusters

Observation of many differing coloured stars seen in the majority of the various kinds of star clusters and other stellar aggregates, immediately suggests different evolutionary processes are occurring within their component stars. If we postulate that all these cluster stars were born simultaneously within their primordial and embryonic nebulosity, then as any cluster ages, the individual masses of each star will solely determine the order of each stellar evolutionary process. Hence, the largest stars will evolve first. In turn, these stars are followed in descending order, by the lighter stars.

So if we can understand the various evolutionary states of stars in any well established open or globular cluster, we can therefore work backwards and learn about the cluster’s age and history. Therefore all star ages and the evolution of clusters can be based on real astronomical observations and not mere speculation.

If we plot visual magnitude of the stars in some star cluster against the colour of those stars in terms of the B-V colour index, we obtain the graph often called the Colour-Magnitude Diagram; abbreviated here as CMD. This 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 t he true absolute magnitude or luminosity of the stars may 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 the measured colour is normally placed at the bottom x-axis on the graph. On the upward or y-axis is plotted the 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 distance of the cluster, which is often tainted with the large scatter of less than precise estimates and contamination from field stars not associated with the cluster. For many years the only true method of finding precise distances is by observing the orbits of rare binary stars within open clusters or known variable stars shining as “standard candles”. It was only in latter years that other secondary methods were carefully explored, so that absolute magnitudes could extensively calculated and used.

A slightly more complicated graphical representation that does plot absolute magnitude versus the B-V colour index or temperature produces the better known Hertzsprung Russell Diagram or H-R Diagram. Although this reveals much more 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, with the rest of the open clusters still only being expressed as CMD’s. In most cases the need to produce a more complicated diagram is not often required to determine basic understand of the evolution of stars.

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 using two different standard calibrated filters (B — Blue : 440nm.; V — Visual : 547nm.; and U — ultraviolet : 365nm.) of known wavelengths placed over the optics or by having two different colour sensitive plates.

The B and V filters mimic the visual range of stars. The U filter only covers the portion of visible spectrum whose light is significantly affected by problems like the atmosphere, distance of the star from zenith and the height of the observatory, etc., and must be calibrated against these influences. This system also has other filters in the near infrared and infrared. These are designated as R, I, J, H, K, L and M between 640nm and 4 650nm.

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

Once the B-V has been obtained, with a little manipulation can also find the effective temperature of the star can be expressed. Normally the effective temperature is obtained by inspecting the spectral lines - but this is not always known or even unobservable.

Some astronomers now also express colour using the different photometric filter system called Strömgren photometry abbreviated as uvby or uvbyβ that has begun to replace the older UBV photometric system. The 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 objects known as open star clusters. If we assume that these stars within such groups to form around the same time.

Such star formation 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. The protostar soon reaches its 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 for the youngest open clusters on the CMD, where the brightest and most massive star is at the top-left. Other less massive fainter stars move downward along the curve towards the bottom right corner or lower middle of the curve. This curve only contains dwarf solar-like mass stars typically without giants or supergiant stars.


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Last Update : 25th December 2010

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