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1、Name _ Section _6/27/184655e24635ba8b61defac7e5b8da469e.pdfae 41Application Exercise: RR Lyrae Stars and the Distance to M4 (This lab may require on-line measurements.)ObjectiveTo determine the distance to the globular cluster, Messier 4 (M4), by using observations of an RR Lyrae star and the mean a
2、bsolute magnitude for RR Lyrae variables; to compare the use of RR Lyrae variable to Cepheid variables to summarize what we learn about the Milky Way from distances to globular clusters. Introduction As stars evolve, their atmospheres become unstable and the star becomes intrinsically variable. Some
3、 stars vary erratically, some semi-regularly, and some regularly. Two special classes of regular variable stars have become the keys to determining distances within our galaxy and distances to neighboring galaxies. The Cepheid variables are evolved, massive stars and lie within the crowded spiral ar
4、ms of a galaxy. Since they are a stage in the life of a massive star, and the stage is very short-lived, there are relatively few of them in a galaxy. Cepheid variables have periods that range from a few days to a few hundred days. The other class of variable stars, the ones we are concerned with he
5、re, are RR Lyrae variables (named after the prototype star RR in the constellation of Lyra). RR Lyrae stars are evolved old, low-mass stars and can be seen in the halos of galaxies, especially in globular clusters, as well as in the disks of galaxies. They are a stage in the evolution of a lower-mas
6、s star, and therefore are generally more numerous than Cepheids. A single globular cluster may have dozens of RR Lyrae stars within its population of stars. Periods of RR Lyrae stars are typically 0.3 to 1 day, making it possible to see one or more periods (cycles) in a single night of observations.
7、 Astronomers have observed thousands of Cepheid and RR Lyrae variables. As might be expected from the types of stars that become Cepheids, these stars are very luminous, with luminosities ranging from 100 to over 10,000 times that of the Sun. Through calibration of hundreds of RR Lyrae stars, astron
8、omers have found that these stars are much les luminouson average only 40-50 times as luminous as our Sunthan the Cepheids. The RR Lyrae stars have a mean absolute magnitude (M) of 0.75. Even though they are not very luminous, RR Lyrae variables serve an important function. If we can determine a mea
9、n apparent magnitude (m) for an individual star in a globular cluster, we can calculate the distance to the star and thus the globular cluster by using the magnitude equation. Look at the chapter on the Milky Way, and think about what we would learn if we knew the distances to the globular clusters
10、as well as their location in our night sky.In this exercise, we will use this calibration and the equation to determine the distance to the globular cluster, M4. At 7000 light years distance (2150 pc), M4 (fourth object in the Messier Catalog of star clusters and nebulae) is the nearest globular clu
11、ster, as seen from its large apparent size. It contains more than 100,000 stars, including many RR Lyrae variables. M4 lies in a direction close to the huge Rho Ophiuchi dust complex (shown at the left) and therefore suffers substantial dust obscuration. From our point of view, this dust dims the st
12、ars in the globular cluster by about 1 magnitude. 42Procedure View on-line a full-field view of M4 and an enlargement of its northeastern part (PSS #863E). One of the stars in M4, No. 42 in a catalog of the variables found there, is identified. You will also find a series of 20 pictures of #42 and i
13、ts neighboring stars. These 20 pictures were taken over the course of 12 hours one (winter?) night. The star #42 is easy to spot as it is obviously changing size (and thus luminosity) between frames, but if you do not see it right away, it is at the center of each photograph. To determine the magnit
14、ude of a star, astronomers choose a number of “standard“ stars within each frame and calibrate the variable star against these standards. We will do a similar process here, using just one image of the series, frame 1, to do so. Within this frame are six standard stars. They are identified in frame N
15、o. 1 shown below. Using the calibration of standard stars, we find a “diameter-vs-apparent-magnitude” correlation by assuming the two are related linearly. Once we have this, we simply measure the diameter of Star #42 and determine the corresponding apparent magnitude. Since the change in the star t
16、akes as time passes, we then graph apparent magnitude versus time to see the change in its brightness.Exercise(Note This part has already been done for you. See the next page.)At the left is a reproduction of image #1 of the star field showing the standard stars and their calibrated magnitudes. Click on this image (on-line!) to get the interactive image, a
