Globular cluster M13

As our object we have chosen the globular cluster M13, the reason for this is that we think it is a fascinating object and because M13 and globular clusters in general are important for studying especially stellar evolution. In this report we will try to estimate the distance to M13 from pictures taken with our school’s CCD camera, moreover we will describe how astronomers use globular clusters such as M13 to get information about stars, for instance their evolution.

Short introduction to globular clusters

A globular cluster is, as the name suggests a cluster of stars, which together form a spherical halo. An ordinary globular cluster contains of approximately 100000 stars [1] . Globular clusters are located mainly in the halo of the galaxies and only seldom near the disk. Below is an illustration that shows where globular clusters are located in a galaxy like ours.

A big black spot marks a globular cluster and a smaller grey spot marks an open cluster

What do we know about globular clusters – and how

 

Globular clusters were born a long time ago (but not only in a galaxy far far away) from giant clouds of gas which collapse under their own gravity. The gas is made of hydrogen and helium created in the first three minutes after Big Bang [2] . If the Standard model is correct then stars formed by this gas will almost not contain any metals [3] . This gives a high probability that stars with a low content of metals are old stars because the gas from which younger stars are born normally would have been enriched with heavier elements from supernovas etc. Old stars such as those found in globular clusters is called population II stars and younger stars such as found in the arms of spiral galaxies are called population I stars. So by measuring the content of heavy metals in stars you can find out whether it is an old star or a young star. The amount of metal in stars can be found by making a spectral analysis.

Spectral analysis

As we know stars radiate light or electromagnetic radiation because of nuclear reactions in its interior, this light consists of different wavelengths. Each wavelength has a certain colour and it is the sum of all these wavelengths that gives the star its colour [4] . But as well as the light from the sun can be split into a spectrum when it passes a prism or an optical grating, so can the light from the stars and if you study these star spectres you will find that they are not completely continuos. You will notice thin black lines called absorption lines. To understand how these absorption lines were created we will take a look at a simplified model of a star. In this model the star consists of a non-transparent globe with a thin transparent atmosphere around it. When a photon, after millions of years, approaches the edge of the non transparent globe the density and temperature gets smaller and smaller until suddenly the photon emits from the surface and into the atmosphere. But since there are atoms [5] in the atmosphere an atom will temporarily absorb the photon and therefore this specific wavelength is not visible in the spectrum. Later the energy from the photon is emitted again but as multiple photons with different wavelengths. Which photons get absorbed and which get emitted, depends on the elements in the star atmosphere. Each element have its own unique way of absorbing and emitting and thereby creating its own unique set of absorption lines in and so by comparing with experiments made on Earth we can determine which elements are in the star atmosphere.

The above is spectres from different stars. It starts with warm stars, where you can only see few absorption lines and ends with the coldest stars, where you see lots of absorption lines.

Spectral analysis of stars in globular clusters not only tells us the stars are old but also that they were formed at the same time. Because of this we can determine the age of the cluster more precisely by making a HR diagram and by doing so we will also have a tool for measuring the distance to other stars.

HR diagrams

HR diagrams were invented in 1912 by Danish astronomer Ejnar Hertzsprung and American astronomer Henry Norris Russell hence the name Hertzsprung-Russell or just HR diagrams. What Ejnar Hertzsprung did [6] was to plot stars, with distances measured by the parallax method, in a coordinate-system with colour (b-v) along the x-axis and absolute magnitude along the y-axis, after this were done the diagram surprisingly showed that all fairly young stars were placed along a nice string – called the main sequence.

Here we have a HR diagram with colour-index along the x-axis and absolute magnitude along the y-axis

  This connection between colour and absolute magnitude allowed astronomers to create theoretical HR-diagrams and thus measure distances to stars that were to far away to show any detectable parallax. HR diagram can also tell us something about the temperature, and masses of stars.

The temperature is actually equivalent to the colour-index, because according to Wien’s law the wavelength were the most light is radiated is proportional with the temperature:

  = 2,898 × 10 -3 m × k

  This means that the colour of the stars gives us information about their temperature.

Absolute magnitude is also just a measurement for luminosity and luminosity is connected to the mass of the star as expressed in the following formula: luminosity = mass 3,5 . So as we can see the HR diagram is an important tool for collecting information about the stars, and partly because to HR diagrams and globular clusters we known a lot more about star evolution than we do about, for instance, evolution of galaxies.

As we found out earlier all stars in globular clusters were formed at the same time from the same material and in approximately the same distance. This means that you can measure the apparent magnitude of stars along with their colour-index and make a HR diagram, then you can study how stars evolve when mass is the only factor that distinguishes the stars from each other. If you also now the absolute magnitude it is possible to calculate how big their masses are. (If you only have the apparent magnitude you can only determine the relative masses of the stars) We also mentioned that it is possible to find the age of a globular cluster with a HR diagram, this can be done because of our knowledge of star evolution. Again the following method for estimating the age of globular clusters only gives you a relatively age for one globular cluster compared to an other, so you need to determine the age of at least one globular cluster by using a different method, to get an exact age.

When you want to estimate the age of a globular cluster with a HR diagram the trick is to look at the so-called “turn off”. This is were the main sequence stars have used most of their hydrogen and starts to fuse helium nucleuses, they will then become red giants and move away from the main sequence. The older the globular cluster is the more stars have turned into red giants and if you know how long it will take for stars in a certain spectral class [7] to become a red giant you have the age of the globular cluster.

Distance to M13  

Now we will try to estimate the distance to M13. For that we will need a HR diagram and pictures of M13 which we have taken with the CCD camera at our school. The first thing that has to be done is measurements of the colour-index from a few random stars, but it is a good idea to at least choose the brightest ones.        

Because M13 is very old most bright stars have left the main sequence and turned into red giants, bright giants or supergiants. So thus we assume that the stars at our pictures belongs to one of the mentioned categories giants, because as we can see on the M13 HR diagram below, the apparent magnitude of main sequence stars are between the 19 th and 21 st magnitude, to dim for our camera to detect.

Because we choose to measure the colour-index of only the brightest stars (apparent magnitudes lower than 11 on the above HR diagram) we will assume that they all are bright giants or supergiants, this means that we can find their absolute magnitude with a theoretical calculated HR diagram.

A supergiant Ib has an absolute magnitude about 4,5 and that the brightest bright giants have an absolute magnitude about 3. we will now try to calculate a maximum and a minimum value for the distance of M13.

    

      m – M = 5 ∙ log  

     10,442 – (-3) =  5 ∙ log  

     dist =   ∙ 10pc

     Minimum distance to M13 = 4880 parsec = 15908 light yea rs   

    m – M = 5 ∙ log

     10,442 – (-4,5) =  5 ∙ log  

     dist =   ∙ 10pc

     Maximum distance to M13 = 9736 parsec = 31740 light yea rs  

As we can see there is a big difference between our minimum and maximum value. But because we cannot exactly determine which type of star we are measuring upon. Even if we could it would still be difficult to determine its exact absolute magnitude in the HR diagram consequently we have to choose the absolute magnitude in a quite big interval and therefore we get a big, but reasonably uncertainty.

     

Globular clusters and open clusters – what is the difference

M13 are very similar to other globular clusters, but there is one other type of cluster which is called an open cluster. An open cluster is in many ways opposite to a globular cluster. Globular clusters consist of very old stars while open clusters mostly consist of young stars. Globular clusters will always be held together by their own gravity while open clusters will not, their stars are only tied loose together and will in time move away from each other due to the expansion of the universe. Because of their loose formation open clusters are often more difficult to spot. Also the open clusters are mainly located in the disk of the galaxy while globular clusters, as mentioned earlier, are mainly located in the halo of the galaxy.

Future of M13

M13 is at the present time a beautiful shiny object, tied together by gravity from the stars it consists of. But no new stars are born and eventually all the stars will have used their fuel and become white dwarfs, neutron stars or maybe some will even turn into black holes. Whether the dying star will end up like the one or the other depends on it mass. Small stars like our sun will once become white dwarfs while heavier stars (11 to 35 solar masses) will become neutron stars and even heavier stars (35 or more solar masses) [8] will end up like black holes. This maybe sound as a sombre future - it does to me, but it is a comfort that it will first happen in many years from now, so fortunately M13 will still be there next time we want to look at it in our telescopes.  

Made by Javik, Rasmus Flytkjaer, Morten Moeller and Mikkel Smedemand