Lab: Distance to the Globular Cluster M15 Containing RR Lyrae Stars

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1 Astronomy 1100 Name Lab: Distance to the Globular Cluster M15 Containing RR Lyrae Stars Distance to Stars: This distance to stars, star clusters and galaxies is an essential piece of information in astronomy. If we do not know the distance to a star it is impossible to determine its intrinsic luminosity and all other properties related to luminosity. Parallax measurements have a distance limit of about 100 parsecs (326 light years) which is quite miniscule compared even to the diameter of our Milky Way galaxy which is 30,000 parsecs (100,000 light years). Globular Clusters: Globular stars clusters are somewhat spherical in shape with a radius of between 10 and 50 pc, and contain from 10 5 to 10 6 stars. The clusters are old objects in the universe with ages on the order of 10 billion years. One of the ways that we can determine their age is by looking at the distribution of post main sequence stars in the cluster. Studies of Globular clusters give us clues to the differences in star formation early in the history of the universe. Because of their age globular clusters will contain a variety of post main sequence objects including variable stars such a RR Lyrae. RR Lyrae Stars: Among the post main sequence variable stars that occupy the instability strip on the HR diagram are Cepheids and RR Lyrae stars. RR Lyrae stars are yellow giants with about the same mass as the Sun and 40 times its luminosity (1.6 x watts). These stars have the important property that their luminosity is related to their period of variation. The period of RR Lyrae stars is in the range of 0.3 to 1.5 days and they have an average absolute magnitude of Lab Objective: The objective of this lab is to determine the distance to the globular cluster M15 by finding the apparent magnitude of RR Lyrae stars that exist within the cluster and using the their average absolute magnitude of Data: The data for this lab are 8 photographic plates of the globular cluster M15. The first plate shows location of 6 RR Lyrae stars labeled A through F. On the remaining 7 plates the RR Lyrae stars are indicated and also indicated are other non-variable stars that will be used as references to find the magnitude of the RR Lyrae stars. These nonvariable stars are indicated by their magnitudes. For example if the star is at the end of a line from the number 157 this means that the reference star has a magnitude of +15.7

2 Procedure: There are two requirements to evaluate the distance to the variable stars in order to determine the distance to the cluster M15. First it is necessary to find the period of the stars to verify that they are RR Lyrae stars and second if they are RR Lyrae stars then the average apparent magnitude must be found to calculate the distance to M15. Step 1: For each of the plates 1 through 8 find the apparent magnitude of the labeled RR Lyrae stars by comparing them to the reference star that is closest to their brightness, in many cases you can estimate the magnitude between two of the reference star values. List the apparent magnitudes in the table below. Apparent Magnitude of RR Lyrae Stars Plate # Time (d) A B C D E F 1 (465) (468) (470) (472) (475) (477) (479) (481) Step 2: Plot the apparent magnitude of each star on the accompanying graph (one star for each graph). Estimate the period of each star and enter in the table below: Period of RR Lyrae Variable Stars (days) A B C D E F Do these periods fall with in the range of RR Lyrae stars (0.3 to 1.5 days)?

3 Step 3: Calculate the average apparent magnitude for each star and then the composite average. Average Apparent Magnitude of RR Lyrae Stars in M15 A B C D E F Composite Average Results: Once the average apparent magnitude of the RR Lyrae stars in M15 is known it can be used to determine the distance to these stars (which are all at essentially the same distance since they are in the cluster) and hence to the cluster. In the calculations below M is the absolute magnitude of the RR Lyrae stars (+0.5) and m is their apparent magnitude. There are two ways to find the distance to the cluster: a. log(d) = (m+5-m)/5 Calculate the value of log(d) and then look it up in the table provided by your instructor to find the distance to M15, the distance is in parsecs. i. distance to M15 in parsecs ii. distance to M15 in light years b. find the value of (M-m)/2 and then (2.512) (m-m)/2 the distance in parsecs is d=10*(2.512) (m-m)/2 i. distance to M15 in parsecs ii. distance to M15 in light years

4 Discussion: 1. Explain how variable stars such a RR Lyrae and Cepheids (which have a higher luminosity) are important in the study of globular clusters and galaxies. 2. How would the presence of a nebula along the line of sight between you and M15 affect your determination of the distance to M15 by the methods of this lab? Explain.

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