Exploring the Universe – Project 1

1 Analysis of a Stellar Cluster Report AST201: Exploring the Universe – Project 1 Department of Astronomy, University of Toronto 2 Introduction: In this Project, we are studying Stellar Clusters, in accordance with the Hertzsprung-Russell Diagram. Stellar Clusters (or Star Clusters) are large groups of stars held together and bound by gravity. In this study, we answer the question of how old (the age) the stellar cluster is based on the given data, calculations, and the HR diagram. We also come to conclusions about the stellar evolution of this cluster. Observations: For this study, we were given data on the temperature (in Kelvin), the brightness (in Watts/m²), and parallax (in arcsec). Each part of the data is obtained in a different way. The temperature data (in Kelvin) would be obtained from the star’s spectrum, specifically the rate of energy in its core, its radius, the wavelength of light emitted by the star and its chemical composition. You could also get a general idea of the star’s temperature by looking at a star’s colour (red or blue light). The apparent brightness is defined as the amount of light reaching us per unit area from a luminous object; often measured in units of Watts/m². When looking at brightness you can also look at the size, temperature and distance of a star to get an idea. The equation used to determine the apparent brightness is brightness (Watts/m²) = luminosity/4ㄫ*(distance)². Parallax is defined as the displacement in the apparent direction of an object as seen from two different perspectives and not in a straight line with the object. For example, when thinking that the Sun or Moon follows us everywhere. Parallax (in arcsecs) was calculated using the equation p = 3.26 light-years/distance. With the given information we were able to move on to analysis. 3 Analysis: Figure 1.0: HR Diagram (Luminosity (Lsun) vs. Temperature (K)) Prior to analyzing the data provided there were a few calculations that needed to be done: distance (in light years [ly] and m²) and luminosity (in Watts/m² and Lsun). First, to calculate the distance in units of light years we use the equation d (ly) = 3.26 ly/parallax. After calculating distance in light years, it needed to be converted into metres. The step taken to do this was through the equation d (m²) = d (ly)/1.057E-16. However, another equation that could have been used is: d (m²) = d (ly)*9.461E+15 to get the distance in light years into a unit measure of m². The next calculation that was needed was the luminosity in watts (w). This was done by using the equation: luminosity(watts/m²) = brightness*(4π)*(d²). The final calculation that needed to be made was Lsun. For the final calculation, the equation used was 4 Lsun = L(w)/3.8E+26. After completing my calculations the Hertzsprung-Russell Diagram was created in order to analyze it. Looking at the HR Diagram I located the turn-off star on the main sequence. I then compared my HR diagram to the diagrams discussed in class to find its age. The charts in class gave the temperature and luminosity of stars along with their estimated lifetimes on the graph. Using that I pinpointed my turnoff star with a temperature of nearly 6 000 Kelvin and a luminosity of 1.00E+01. With that information, the turnoff star’s estimated age is between 9 and 10. Since the age of the cluster is equal to the main sequence lifetime of the turnoff star, once I had a general location of the turnoff star I determined that the age of the cluster is 9.5 approximately 10 . Results & Conclusions: 9.5 As previously stated, the general location of the turnoff star is approximately 10 or 3 162 277 660 years. Comparing the age of the Sun which is estimated to be 4 603 000 000 years old to the age of this “new” cluster it is clear that the cluster is fairly new or younger than the cluster that created the Sun. The galaxy on the other hand is 13 610 000 000 years old. Astronomers can infer from this data that the Sun and this Stellar cluster are much younger than the galaxy. Looking with a bit more context at the HR diagram we can infer that most of the stars on this diagram range from M-class stars to F-class stars. This is because the temperature lies between 2 000 to 6 000 Kelvin. Our Sun based on the HR diagrams shown in class is a G-class star. Controversially, the turnoff star on the main sequence on my HR diagram is most likely an F-class star. Looking at the star classes of this cluster of stars, we can hypothesize the future evolution of the cluster. The vast majority of stars in the cluster can be concluded as M-class. M-class stars are typically low mass and therefore have a longer lifetime, which in turn would 5 mean that the cluster is most likely a red-orange colour with a duller brightness than clusters than B and O class stars. In addition to being low-mass stars, these stars as they age will evolve into red giants (or supergiants), where they will leave the main sequence. They will then evolve from red giants to helium-burning stars and then into double-shell-burning red giants. Further on it will develop into a planetary nebula and finally transform into a white dwarf. These are my predictions for the future or evolution of this “new” cluster.