Age of the Universe Lab Session - Example report

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1 Age of the Universe Lab Session - Example report FS 17 Prof. George Lake Assistant: Mischa Knabenhans Office: Y11-F-74, Date: Introduction In physical cosmology, scientists are interested in the origin and evolution of the Universe as a whole. One natural questions arises immediately: How old is the Universe? There are several ways to investigate this question. In this report we will infer the age of the Universe from age estimations of dense, spherically shaped accumulations of stars, called globular clusters (GC) using the obvious fact that the Universe must be at least as old as the oldest GC we can find. The stars belonging to one GC originated from the same gas cloud. Accordingly, they are about the same age and also about equally far away from Earth. Yet, other properties like mass, chemical composition, brightness etc. can vary by a lot from one star to the other. From stellar physics we know that there is a relation between color and magnitude or, equivalently, surface temperature and brightness. We can study the distribution of the stars in a GC following that relation by plotting them into a color-magnitude diagram named after E. Hertzsprung and H. Russel (cf. fig. 1). Further, stars are evolving systems, i.e. they have a finite lifetime. Most of it they spend fusing hydrogen to helium. All stars in this state build up the main sequence. When all hydrogen is burnt to helium, the star dies. A dying star undergoes multiple evolutionary phases until it is actually dead. The first stage is becoming a red (super) giant, meaning that the stars color becomes redder while keeping its magnitude (or equivalently brightness or luminosity) roughly constant. As a result, in the HR diagram, the star shifts away from the main sequence to the right. It is possible to derive from basic physics how long it takes until a star of certain color leaves the main sequence. The brighter a main sequence star (and thus, the bluer it is), the shorter its lifetime. Looking at the HR diagram of a star cluster, we see which stars are in which evolutionary state. Eventually, stars start dying resulting in a turn-off point in the HR diagram (denoted as a green curve in fig. 1) which indicates the transition from the main sequence to the red (super) giant branch. This turn-off point is what we are interested in: The color (the spectral class) of the stars that are currently leaving the main sequence contains all necessary information to estimate the age of these stars and hence of the entire star cluster. Clearly, the star cluster formed after the Big Bang and thus, the age estimate of a star cluster can 1

2 be used as an estimate of the lower bound of the age of the entire Universe. Figure 1: HR Diagram (source: sciencebuddies.org) 2 Methods We investigate the HR diagrams of three different GCs: Name Coordinates [(RA, DEC)] Estimated radius [arcmin] NGC2401 ( , ) 1.2 NGC2420 ( , ) 2 Pal 5 ( , ) 2.25 Table 1: Names, positions (in right ascencion and declination) and estimated radii of the investigated globular clusters From the Sloan Digital Sky Survey (SDSS) image-finding tool we get images of the clusters. By eye we estimated the radii mentioned in the table 1. Using these estimations, we get the values for apparent magnitudes in different wavelength bands from the SDSS radial tool. We focus only the g- and the r-band and derive the color g r for each member of all three clusters. Then we generate an HR diagram for each GC by plotting the g band magnitudes versus the g r color. 2

3 3 3.1 Results NGC2401 Figure 2: left: SDSS picture of NGC2401; right: HR Diagram for NGC2401 The main sequence of the GC NGC2401 is clearly visible but there is no statistically significant turn-off point. This suggests that this particular star cluster is still too young to host a representative number of red (super) giants. As a consequence, this star cluster does not provide any reliable information about the minimal age of the Universe. 3.2 NGC2420 Figure 3: left: SDSS picture of NGC2420; right: HR Diagram for NGC2420 Again, the main sequence of NGC2420 is very clear. At (g r, g)=(0.2, 14.85) we can see that the very brightest stars just start leaving the main sequence. These stars (at the transition 3

4 between A and F stars) have a turn-off age of a few billion years. minimal age of the Universe in this order of magnitude. Hence we can set the 3.3 Pal 5 Figure 4: left: SDSS picture of Pal5; right: HR Diagram for Pal5 The globular cluster Pal5 features both a main sequence and a rather clear red (super) giant branch. The corresponding turn-off point is read off at (g r, g)=(0.325, 20.75). The stars just leaving this main sequence belong to the spectral class G and hence have a lifetime of τ 10 Gyrs. We thus have to update the current estimate of the minimal age of the Universe to roughly 10 billion years. 4 Conclusion In this report we have studied turn-off ages of three different globular clusters in order to estimate a lower bound for the age of the Universe. We have found a value of τ 10 Gyrs in good agreement with the current official value of the age of the Universe being τ 13.8 Gyrs, inferred from measurements of the Hubble parameter H 0 = km/s/mpc [1]. It is also important to mention that we have not looked at proper HR diagrams since the y-axis quantities in our case are apparent magnitudes instead of luminosities or absolute magnitudes. But in order to do the conversion one needs as well the distance between each GC and the Earth which was not provided (and beyond the scope of the present investigations). The results found here are, of course, highly inaccurate. Further improvements could be achieved by cleaner estimation of the radii of the GCs (e.g. by studying their number density profiles) and by proper statistical analysis of the data. This would further allow to quantify the uncertainties, too. 4

5 References [1] Planck Collaboration, Planck 2015 results. XIII. Cosmological parameters, arxiv: v3 (2016) 5

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