Looking at star clusters by Gordon Dennis

Hertzsprung-Russell diagrams
In July’s WMA webinar, we looked at Hertzsprung-Russell diagrams.  H-R diagrams are one of the most important tools available in stellar physics, since they indicate a great deal about the characteristic of stars. The H-R diagram below, known as a theoretical H-R diagram, is a scatter plot of stars photosphere temperature vs. luminosity.    
Brian Davidson’s last couple of Blogs have mentioned the Summer Triangle asterism, consisting of Vega, Deneb, and Altair. Taking a sample of ‘nearby stars’ as shown below we have marked the Summer Triangle stars on the H-R diagram, showing how different these three stars are:

The spectral classes of the stars are indicated by the familiar ‘OBAFGKM’ legend.  Before looking at the three stars, look at the track running from Alnitak at the top left to Proxima Centuri at the bottom right.  This track is the Main Sequence, where in the stars interior hydrogen is converted into helium by nuclear fusion.  Stars leave the main sequence once about 11% of the hydrogen-mass has fused to helium and the core of the star becomes unstable.
About 90% of stars are on the main sequence. It may not appear like this from the diagram, but that’s because of our sample, which is ‘nearby stars’. 
Altair is a main sequence star, larger and hotter than the Sun.  It will therefore have a shorter main sequence life than the Sun.  Altair’s luminosity is 10.6 L⊙. Recall that luminosity is a measure of the power radiated by a star; the unit of luminosity is the Watt.
Vega has a photospheric temperature similar to that of Altair.  But Vega’s hydrogen burning phase is now over.  The star has entered the main sequence turnoff, on the way to becoming a red giant, before shedding its outer layers to form a planetary nebula.  At that time, what will remain of Vega is a hot white dwarf star at the bottom left of the H-R diagram.  This sequence of events will also be what happens to the Sun when main sequence turnoff occurs.
Deneb is a super-giant star. Although Deneb’s Photospheric temperature is comparable to both Vega and Altair, its luminosity is very much greater.    Deneb has a luminosity of more than 104 L⊙, a mass of 19M⊙ and is destined to end its life in a Type II supernova event.  This will leave a supernova remnant perhaps like the Crab Nebula, M1 and a neutron star which is way off scale at the bottom of the H-R diagram.
 
Open clusters and globular clusters
For this month’s Blog, we’ll consider a question asked at the July WMA webinar, “Can we make H-R diagrams of star clusters to help determine their characteristics?” The answer is yes.
Astronomers are familiar with both open clusters and globular clusters. Their main characteristics are shown in the table below.

How can we conclude that open clusters consist of young stars and globular clusters consist of old stars?  The amount of hydrogen that a star has available for fusion is directly proportional to the star’s mass. In simple terms, the greater the mass of hydrogen packed in, the faster the reaction rate, and the higher the luminosity. The star’s luminosity determines how quickly the star will fuse the hydrogen into helium, and hence how long the star lives on the main sequence according to the relation:

Since from the mass-luminosity relation we know that:

Substituting

The diagram below summarises how stars of different spectral classes leave the main sequence - the “main sequence turnoff” - as they evolve:

Plugging the numbers into the equations, this means that a star of 10M⊙ will have a lifetime of only about 13 million years.
Bear in mind that we know that about 80% of stars are red dwarfs, smaller than the Sun.  A low mass star of about 0.6M⊙ has a life of ~34 billion years.  That time is much greater than the age of the universe which means that no low mass star has yet completed its main sequence lifetime.

H-R diagram for open cluster M45
So, let’s plot an observational H-R diagram, (also known as a “colour-magnitude diagram”) for open cluster M45, known of course as the Pleiades:

The observational H-R diagram above is a plot of absolute magnitude (VMag) vs. colour index (BMag-VMag). The scale ranges are  (x: colour index 0.2 à 1.45; y: absolute magnitude 8 à -2) .
We can see at the top left of the H-R diagram, only a few of the larger, more luminous (which of course implies more massive) stars in the Pleiades have begun their main sequence turnoff. These are the dots at the top left which are turning upward and to the right. The majority of the (less massive) stars in the plot remain very much on the main sequence.  They are so young that hydrogen burning has a while to progress.
It is generally thought that open clusters disperse after a short time (in cosmological terms) before the stars in them have commenced main sequence turnoff.  It is also thought that then Sun formed in an open cluster which subsequently dispersed and that this accounts for the fact that the Sun is isolated and not part of a multiple star system, although that is far less certain.

H-R diagram for globular cluster M14
Now, let’s look at the H-R diagram for globular cluster M14.  This H-R diagram is markedly different to that of M45.  The plot is a subset of the total data of over 1,000 stars and is plotted with the same scale ranges as the M45 plot.

In the M14 H-R diagram, just about no main sequence stars are evident.  The reason is that most stars in M14 are very old, and have completed hydrogen burning and moved off the main sequence.  Low mass stars are either ascending the red giant branch or have already become red giants. Like Altair, Vega, and the Sun, they will end their lives as white dwarfs.   A few at the top right of the H-R diagram are supergiants and, like Deneb, will finish their lives in Type II supernova events.  
The fact that the majority of stars in this globular cluster are grouped at the red end of the colour index confirms the generally red appearance of the globular cluster.

References
Data sources
Contreras Pena, C et al (2013). The globular cluster NGC6402 (M14). A new BV color-magnitude diagram.  ApJ, September 2013.  DOI: 0.1088/0004-6256/146/3/57 Accessed August 10th 2020
Australia Telescope National Facility