KEELE UNIVERSITY SCHOOL OF PHYSICAL AND GEOGRAPHICAL SCIENCES Year 1 ASTROPHYSICS LAB LAB B. The Local Stellar Population R. D. Jeffries version January 2010 D. E. McLaughlin Throughout this experiment pay close attention to the aims and objectives listed. Make sure that you record measurements, calculations, details of spreadsheets etc. in your laboratory notebook. Example pages from spreadsheets, graphs etc. should be permanently attached in your notebook. A number of questions are posed in the script to guide your discussion and consideration of your results. Make sure these questions are answered in your notebook. At the end of each laboratory session ensure that your notebook is handed in to a demonstrator or member of staff. There is a mix of background reading and research, spreadsheet work, and astronomical discussion involved in this lab. Read this entire script through before beginning to work on the lab, so that you have a clear idea of the preparation you will need to do as well as the tasks you must perform. This experiment is expected to take two laboratory sessions to complete. There are therefore two weekly attainment targets and milestones. 1. Introduction It is often said that the Sun is a typical star in an unremarkable part of the Galaxy. Stars have a very large range of masses and luminosities and it is this variety that allows astronomers to test theories of their structure and evolution. In the last few years we have gained a new understanding of our place in the local universe by being able to discover and measure the distances to nearby stars. In this experiment you will investigate the properties of this local stellar population.
2. Aims and Objectives The aim of this experiment is to investigate in some detail the properties of the local stellar population using published photometric and parallax data available in spreadsheet format. At the end of the experiment you should appreciate how the properties of the Sun compare with those of other stars, be familiar with various astronomical quantities such as trignometric parallax and the magnitude system and gain valuable experience in the use of spreadsheets for manipulating and plotting tabular data. Practical Skills Be able to use a spreadsheet to manipulate and plot tabular data. To distinguish between the effects of systematic and statistical errors. To gain an appreciation and awareness of how limited data can influence conclusions through incompleteness and selection bias. Astrophysical Relevance To develop an understanding of the Hertzsprung-Russell diagram, the significance of the main sequence and how the appearance of the H-R diagram depends on the timescales for various phases of stellar evolution. To introduce the magnitude system, colour indices and parallax distance measurements. To appreciate the atypical nature of the Sun compared with a representative sample of nearby stars. 3. Procedure Week 1 Obtain the Excel speadsheet called gliese.xls, which can be found in the p1astro folder. This spreadsheet contains a subset of the data from the 3rd catalogue of nearby stars (Gliese & Jahreiss 1991). The four columns list the name (identifier), apparent V-band magnitude, B-V colour, and trigonometric parallax (in units of milli-arcseconds) for the 1000 closest known stars to the Sun. Familiarize yourself with these terms as necessary, before starting any analysis, by referring to Nick Strobel's online Astronomy Notes, or Zombek (1990), or a similar, appropriate introductory source. You also need to know how the temperatures of stars affects their absolute magnitudes in different filters, and their colours. Thus, for example, see the instructive online applets on Blackbody Curves and the Hertzsprung-Russell Diagram at the Nebraska Astronomy Applet Project (links are on the AstroLab web page).
Before proceeding any further, make a copy of gliese.xls on your disk. Work only in the copy file, and save your work frequently. Stars have an apparent brightness that depends both on their intrinsic luminosity and their distance from us. To remove the effects of distance we define the term absolute magnitude, which is the apparent magnitude a star would have if it were viewed from 10 parsecs (check if you do not know what a parsec is). The magnitude system is defined such that a change in brightness of a factor of 100 is equivalent to a decrease in magnitude of 5 (i.e. smaller magnitudes are brighter). This leads to a simple relationship between apparent magnitude m, absolute magnitude M, and distance d (measured in parsecs): m M = 5 log 10 d 5 Using the fact that distance in parsecs is the reciprocal of the trignometric parallax in arcseconds, use a spreadsheet formula to calculate two new columns: one containing the distance to each star in parsecs, and one containing the absolute magnitude of each star. One of the most important diagrams in astrophysics is the Hertzsprung-Russell diagram. This is essentially a plot of luminosity versus surface temperature for a sample of stars. In this experiment we use absolute magnitude to represent luminosity and B-V colour to represent temperature (because a blue star is hotter than a red star be sure that you have understood this point from the preliminary reading you did before beginning this experiment). Use the chart wizard in Excel (see the Excel help on Working with Charts, if necessary) to plot a scatter graph of absolute magnitude on the y-axis versus (B-V) on the x-axis. Create the plot on a separate sheet of your worksheet, and edit it so that it has no gridlines and a white background. Be sure to label both axes correctly and give it a title. Finally, large luminosities (small magnitudes) go at the top, so you will need to reverse the scaling on the y-axis. The stars are not distributed uniformly on this plot. Find out what the major groups or clumps are. Label the regions occupied by main sequence stars, giants and white dwarfs, and mark where the Sun would lie in the plot. On the x-axis, mark on the spectral types and the surface temperatures that correspond to the B-V values. You will need to research reputable and verifiable sources to learn how these quantities are related. Be sure to acknowledge clearly any references you use, both in your lab book and in any written report. Question: Why are there so few giant stars or stars hotter than spectral type F in the diagram? Answer this in your lab book and discuss it in any written report.
Question: Can you explain why there seem to be very few white dwarfs compared to main sequence stars? Answer this in your lab book and discuss it in any written report. Your next task is to plot the number of stars as a function of absolute magnitude along the main sequence. To do this, you will need to filter out the stars above and below the main sequence using logical expressions in the spreadsheet (such as "IF" use the Excel help!). One way to do this is by finding out whether a given point lies in between two straight lines that encompass the main sequence. Thus, you need first to decide on two straight lines that contain all main sequence stars between them and exclude all giants and white dwarfs. When you have decided on the straight lines, copy the columns of absolute V magnitude and B-V colour from the main sheet of your file to a new sheet. Then filter the data in these copied columns on the new sheet, so that you can make a new chart that plots the Hertzsprung-Russell diagram for the main-sequence stars only. You may do this either by using the IF function in Excel or by defining a Custom Filter. Read about these functions in the Excel help; think about how they can be used to do what you need to do; and ask a demonstrator or a member of staff for help or confirmation after you have decided a potential method. Whatever you do, it will involve defining and applying a method of your own devising, which will need to be explained clearly in your lab book and in any written report. Once you have filtered the data appropriately, make a new chart showing the Hertzsprung-Russell diagram for the main-sequence stars only. Again, create this chart on a new sheet in your Excel file. Give the chart a title, label its axes (and make sure the magnitude axis runs the right way), remove any gridlines, and make the background white. By the end of week 1, you will be familiar with the quantities in the spreadsheet, you will have produced a labelled Herzsprung-Russell diagram, and you will have produced a filtered list of main sequence stars. Print your charts and samples of your spreadsheet data, and include these in your lab book. Make sure also to give brief but clear descriptions of everything you have done, including details of any Excel formulae you have used to obtain new columns of data and the complete details of your main-sequence filtering method. Week 2 Use the FREQUENCY spreadsheet command to obtain a histogram of the numbers of main sequence stars per magnitude, with absolute magnitude on the x-axis. This is known as a luminosity function. Use Excel to put errorbars on each histogram value (read about Poisson errors in your Semester 1 Physics Lab Notes, and write down what you do in your lab book).
Question: At what absolute magnitudes are the mode and median of the luminosity function? Answer this in your lab book and discuss it in any written report. Question: What mass and spectral type do these absolute magnitudes correspond to? Answer this in your lab book and discuss it in any written report. Question: Can you think of any reasons why your measured mode and median might be incorrect because of limitations in the dataset (i.e. selection effects...)? Answer this in your lab book and discuss it in any written report. An interesting point is to try and establish how complete your sample is, or whether it is only complete to some limiting magnitude that is, whether or not all the stars that are within some given distance from the Sun have been seen and catalogued. Investigate this however you wish and in the time you have remaining. One idea might be to split the stars into two distance samples and compare (divide?) their luminosity functions, or to look at the stellar density as a function of distance from the Sun (because this would be constant in a complete sample). Whatever you do, describe and justify your method clearly in your lab book and in any written report. Question: Is the sample complete? Can it be considered complete to some absolute magnitude? Answer this in your lab book and discuss it in any written report. Question: How will any incompleteness affect your conclusions about the luminosity function and the nature of a typical star? Answer this in your lab book and discuss it in any written report. Question: How does the Sun compare with a typical star? Answer this in your lab book and discuss it in any written report. Make sure that you keep a copy of your final Excel file on disk (and, ideally, back it up somewhere as well) for use in lab reports. Include copies of all your plots, samples of your spreadsheet data (including manipulated data columns), and complete details of your analysis procedures (including any Excel formulae or functions you used) in your lab book and any written report. 4. Useful Reference Material Strobel, N., Astronomy Notes, http://www.astronomynotes.com Zombeck, M. V., 1990, Handbook of Space Astronomy and Astrophysics, 2nd ed., (Cambridge:CUP). p.64-75.