Measuring the Milky Way

Printed: Mar/01/2013 Milky Way Lab Page MW- 13 NAME Name Group NAME Name Date Measuring the Milky Way References B Carroll and D. Ostlie, An Introduction to Modern Astrophysics (Addison-Wesley, 1996), Chapter 22 Check your astronomy book for Herschel s measurements of the Milky Way! Telescopes: Eyepiece Design: http://en.wikipedia.org/wiki/eyepiece Web Site has manuals for telescopes: http://www.clifford.org/drbill/lpc/ Ritchey-Chretien Telescopes: http://en.wikipedia.org/wiki/ritchey-chretien Meade Telescope Company: http://www.meade.com/ Meade RCX400 (12 inch, F/8) http://www.meade.com/rcx400/ Meade LCX200GPS (14 inch F/10): http://www.meade.com/catalog/lx/12_14_lx200gps.html (this link no longer works, I think they are no longer selling the LX200GPS model) 2013 W. Pezzaglia Astronomy Lab Manual LPC Update: Feb 28, 2013

Page MW- 14 Milky Way Lab Printed: Mar/01/2013 III. LAB PROCEDURE (Outdoor Version) Below is a compendium of possible activities. Exactly which items you will do (and which questions you will answer) will be assigned by your lab instructor at the beginning of lab. Preparation (indoor) choosing target stars and calibration of space penetrating power of telescope Observations: consists of counting stars in various parts of the sky Reduction: data might be shared between all groups for better statistics Analysis: Plots and calculations will measure the thickness of the Milky Way Part A: Preparation and Calculations The manuals for our telescopes are available at the website. We also setup the computer to simulate what you will see outside with telescope Question A-1: Finderscope Parameters Then the magnification power would be 6x Then the aperture would be 30 mm Look for the notation on the side of the telescope. If for example it says: 6x30 The Apparent Field of View is best looked up in the equipment manual (a) What is the field of view of the finderscope? [Consult the telescope manual] (b) What is the notation on the side of your finderscope? (c) What then is the magnification of the finderscope? (d) What is the aperture of the finderscope (in mm)? (e) How many times bigger is the aperture of the finderscope than the eye? [Hint, biggest eye aperture is 6.5 mm] (f) What is the light gathering power of your finderscope (compared to the eye)? [Hint: LGP= square(ratio of aperture), i.e. square your answer to part (e) ] (g) What is the ideal limiting magnitude of the finderscope? [Hint: m=7.3+5log(aperture in cm) or consult table] = = = = = = = Question A-2: Telescope Parameters At LPC we have two 14 inch scopes and one 12 inch. (a) Aperture (inches) 14 inch 12 inch (b) Aperture (cm) (c) How much bigger is the aperture of the telescope than the eye? [Hint, biggest eye aperture is 6.5 mm=0.65 cm] (d) What is the light gathering power of your telescope (compared to the eye)? [Hint: LGP= square(ratio of aperture), i.e. square your answer to part (c) ] (e) What is the ideal limiting magnitude of the telescope? [Hint: m=7.3+5log(aperture in cm) or consult table] 2013 W. Pezzaglia Astronomy Lab Manual Revised: Jan 30, 2013

Printed: Mar/01/2013 Milky Way Lab Page MW- 15 Question A-3: Eyepiece Field of View Complete the table below The true field of an eyepiece we get from the manufacturer (included in table below) The magnification power is the focal length of telescope (mirror) divided by that of eyepiece The apparent field FOV is the true field of the eyepiece divided by the magnification power. It is useful to express apparent field in arcmin rather than degrees (recall 60 =1) (a) Do any of our eyepieces come close to Herschel s field of view (15 )? (b) How many times bigger is the (apparent) field of view of the finder scope than say the 40 mm eyepiece? Question A-4: Exit Pupil Calculation & Eyepiece Selection The exit pupil is the diameter of the beam of light coming out of the eyepiece. It is calculated to be the the (Aperture of the objective)/(magnification power). At low magnification, the exit pupil will be bigger than the eye, which means you will be losing some light, and not able to see fainter stars! For example, if the exit pupil is 10x bigger than the eye, you will only get 1/100 the light into your eye, reducing you limiting magnitude by 5 magnitudes! Higher magnifications will have an exit pupil which is smaller than the eye s 6.5 mm, then all of the light gets into the eye, but your field of view is smaller, and we would see less stars. (a) Calculate the exit pupil for the finderscope. Is it smaller or bigger than the eye? How does this modify your answer to question A-1g? (b) Given your calculations below, which eyepiece(s) have an exit pupil bigger than the eye (and hence should be avoided), and hence which is the best to use for tonight s star counting? Table 1: Eyepiece Parameters: Focal Length of Scope mm Occular Diameter & Design Focal Length (mm) Magnification Power True FOV* (deg) 1.25 Plossl 40 44 1.25" Plossl 26 52 Apparent FOV* (arcmin) Exit Pupil (mm) *FOV= Field of View. Apparent FOV=(True FOV)/Power Exit Pupil=(Aperture Objective)/Power 2013 W. Pezzaglia Astronomy Lab Manual LPC Update: Feb 28, 2013

Page MW- 16 Milky Way Lab Printed: Mar/01/2013 Part B: Calibration using Computer Program Run The Sky program If you do this by clicking on the Lab_MW icon it will automatically load the proper settings from a script file. Settings/Configurations: All of the following should be properly set if you loaded the script file correctly. Hence you can ignore all of this section unless there is a problem. View Menu Settings: The following probably are already set for you: Filters: Uncheck everything, except for check Star, Constellation Figure, Constellation Boundary, Equatorial Grid, Galactic Equator, Milky Way. For the Star setting, start with magnitude range of 6 to +6 (naked eye). Mode: Set Chart Mode (Black stars on white background). Rest unchecked Toolbars: check Standard, View, Orientation, Objects, Show ToolTips, Show Object Tips Status Bar: check Visible, Field Width, Horizon, Time Reference Lines: Check Constellation Figures, Constellation Boundaries, Milky_Way, Galactic Equator, Equatorial Grid, Auto/Wide Spacing, Local Horizon, Transparent Fill. Labels, Setup: Make sure Common Names is checked. Click on Setup, under Common Names Tab, check Stars, Constellations, Sun-Planets-Moons, Bayer Designation, Flamsteed Designation. Stellar Options: Options Tab click High density, Both Catalogs, make sure the note window says that All stellar databases are present (Hipparcos-Tycho and Guide Star Catalog), Under the Brightness and Contrast Tab, click the Virtual Sky, and adjust the Brightness and Contrast if necessary. [I m not sure what we want here]. Preferences: Here there are a lot of settings. This is where we make the Milky Way green, and set other colors of things. In particular, under Field of View Indicator, under symbol, under edit we have set the Select to the the Metafile empty.wmf to eliminate the dashed line target, which will confuse students. Orientation Menu Settings: The following probably are already set for you: Zenith Up: click this one Zoom To: Naked Eye 100 degree (Ctrl+E) Data Menu Settings: The following probably are already set for you: Site Information: Under Location tab choose San Jose, California for Location, and under Date and Time tab check Use computer s clock. Tools Menu Settings: The following probably are already set for you: Time Skip: set to Stop Test Drive: Lets find a star and count the number of stars in a region around it. FIND: Under Edit do a find, and click on Common Star Names, choose Deneb, and click Center and Frame. It will take you to Deneb, but under very high magnification. Back out until you see other stars appear, then the Galactic Equator appear, the Milky Way appear, the circle for the field of the 26 mm eyepiece, and finally the red Finderscope circle appear. COUNT: You should have perhaps 20 stars in the field of the finder. If stars appear ON the boundary of the finderscope, count them as half a star. STELLAR OPTIONS: Under View menu, choose Stellar Options, and play with the Brightness and Contrast. With the field of view around 50 degrees, it probably says Brightness of 3 and Contrast of 0. You can change these settings to make the stars easier to count. CHANGE MAGNITUDE LIMIT: Under View menu, choose Stellar Options. Click on Stellar Appearance tab, click button Stellar Display Properties. Change the Faintest magnitude limit to go down to +9 (the approximate limit of the finderscope). Make sure that the High Density button on the task bar is pressed (near the red glasses, or under the View menu, Stellar Options submenu, under Options tab) otherwise you will not see all the stars. You ll probably see far too many stars to count. Hence we d like to use a smaller field size! CREATE a Field of View Indicator: You will need to create a field of view indicator which matches the field size of the eyepieces we are using. Click add, and insert the proper field size in arcmin. I suggest you change the color to red so you can see it. 2013 W. Pezzaglia Astronomy Lab Manual Revised: Jan 30, 2013

Printed: Mar/01/2013 Milky Way Lab Page MW- 17 Question B-1 Calibration: Stellar Counts as a function of Limiting Magnitude Center on Star assigned by your instructor (it will probably be a start near Zenith tonight) Set the Magnitude Limit to +4. Make sure High Density button is pressed. Count the number of stars in your simulated eyepiece field (To Be Given). Continue increasing by 1/2 magnitude and take data until the program does not show any more stars (i.e. you reach the limit of its star catalog) or you reach the end of the table. Target Star= Field of View= Data Table 2: Stellar Counts as a function of Limiting Magnitude of Scope Magnitude Count Log(count) 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 2013 W. Pezzaglia Astronomy Lab Manual LPC Update: Feb 28, 2013

Page MW- 18 Milky Way Lab Printed: Mar/01/2013 Question B-2 Analysis of Uniformity of Star Densities from Computer Data Plot Log(Counts) vs Limiting Magnitude Compute the slope of the Line Compute the R-squared of the line (a) We expect that the number of stars you see should increase exponentially with magnitude (hence your counts should become quite large very fast). Does this appear to be true? (b) Whenever something is exponential, if you plot the Log of it, the graph should be a straight line. Plot the Log (base 10) of the star counts vs. magnitude. Is the graph a line? (i.e. is your Rsquared nearly 1?) (c) If the density of stars is approximately uniform in the direction of your target star, then the number of stars seen should go up like the cube of the distance (hence the log of the count is proportional to 3 times the log of the distance). If all stars are about the same absolute brightness, then we expect the magnitude of a star will be proportional to 5 times the log of the distance. Put this altogether, we expect that the slope of the line should be around 3/5. Does this appear to be true? (d) If absorption of light by gas and dust is an issue, then at larger distances the magnitude will NOT be proportional to the log of the distance, and we expect the data to deviate from a line. Do you see any evidence of this? 2013 W. Pezzaglia Astronomy Lab Manual Revised: Jan 30, 2013

Printed: Mar/01/2013 Milky Way Lab Page MW- 19 Part C: Observation (outside) First we do calibration to determine limiting magnitude Observation of stars near Milky Way Observation of stars near Galactic Pole If time, observation of stars between. 1. Naked Eye Observation (a) What time are you starting your observations? (b) Is the sky completely dark at this time? (c) What is the faintest magnitude you can see? [Hint, for winter, use Cancer and see if you can see the 4 th and 5 th magnitude stars with averted vision] (d) Can you see the Milky Way visually? m= 2. Telescope Observation: Magnitude Calibration (a) Eyepiece used (26 mm?) (b) Calibration Star Name (might be same as used for B.1) (c) How many stars do you see in the field? (d) Comparing to your calibration set, what do you estimate is the limiting magnitude through the scope? m= 3. Discussion: Approximately what percentage of the stars in the field are faint such that you must use averted vision to see them? 4. Discussion: Do you and your lab partner(s) get nearly the same star counts, or do you find that one observer always gets a lower number than the other? Can you think of a reason why? 2013 W. Pezzaglia Astronomy Lab Manual LPC Update: Feb 28, 2013

Page MW- 20 Milky Way Lab Printed: Mar/01/2013 5. Telescope Observation: Star Gauging NOTE: The instructor will most likely assign you target stars for this part. Make many star count measurements at different places along the Milky Way. Be sure to record the RA and Dec of the star you used as a target. Make several star count measurements near whichever Galactic Pole is available Make several star count measurements at places which are between the galactic equator and the galactic poles if time. For each target star, also fill in its location in the sky (RA & Dec) To calculate the Galactic Latitude & Longitude, use the program described on page MW-8 (OR you can get it directly from the Starry Night program). Data Table 3: Stellar Counts in our Galaxy StarName Constellation RA Dec Galactic Latitude Galactic Longitude Count 6. Discussion: are there less stars seen near the galactic poles than near the galactic equator (i.e. along the Milky Way)? 2013 W. Pezzaglia Astronomy Lab Manual Revised: Jan 30, 2013

Printed: Mar/01/2013 Milky Way Lab Page MW- 21 Part D: Analysis and Reduction (Data Table 4) Put the data into the bins in data table #4 below. Note, take the absolute values for negative latitudes. Each cell will have several values. Compute Averages for each column and row. Using the bottom row (the averages by latitude), make a plot of the average star count as a function of galactic latitude. 2013 W. Pezzaglia Astronomy Lab Manual LPC Update: Feb 28, 2013

Page MW- 22 Milky Way Lab Printed: Mar/01/2013 Question D-1: Summarize the Data (a) Distribution in Longitude: Along the Milky Way (low latitude) are the star counts similar, or do they vary with longitude? [If they vary significantly, does it have anything to do with the thickness of the Milky Way at that longitude, or presence of dust lanes?] (b). Are the star counts near minimum at the galactic poles, and maximum in the Milky Way? Question D-2: Plot Plot the average count vs galactic latitude (a Bar graph is a good here!) (a). Distribution in Latitude: Does your graph show any overall trend (i.e. does it resemble at all figure 8?). (b) In particular, do you see any evidence of the critical angle? Is the graph roughly constant at higher latitudes, or does it drop off smoothly, or drop off abruptly? 2013 W. Pezzaglia Astronomy Lab Manual Revised: Jan 30, 2013

Printed: Mar/01/2013 Milky Way Lab Page MW- 23 Question D-3: Space Penetrating Power (a) Comparing your observations with Table 2, what is your estimate of the actual limiting magnitude of your telescope this night? (b) How much does your actual limiting magnitude differ from the theoretical one (Question A-2e)? (c) Comment: Are your answers consistent with Question C-1c? m= (d) Space Penetration Power: Assuming all the stars are the same absolute magnitude, the furthest distance that you can see a star was called the Space Penetrating Power by Herschel. See Table 5 below: Calculate the depth you can see into the galaxy (or use supplied table/graph which assumes stars have absolute magnitude of M=+2.5). Do two calculations: Assuming No Absorption: [formula is: m2.5 5 D 10 10 ] With Absorption due to dust in galaxy (approximately 1 magnitude/1000 parsecs) Data Table 5: Space Penetration Item Eye Finderscope Aperture (mm): A= 6 Telescope (12 inch) Telescope (14 inch) Limiting Magnitude Space Penetrating power (parsecs) Theoretical m Actual m= No Absorption: D= With Absorption: D= 6.5 (e). Summary: Compare the space penetrating power of the finderscope to the telescope. Approximately how much further does the telescope see? (i.e. what factor increase). How much further are you seeing in the telescope than by naked eye?] (f). Summary: How much change in the space penetrating power is there (for the telescope) when absorption of light due to the dust in the Milky Way is included? 2013 W. Pezzaglia Astronomy Lab Manual LPC Update: Feb 28, 2013

Page MW- 24 Milky Way Lab Printed: Mar/01/2013 Limiting Magnitude vs Space Penetration Power Magnitude 18.0 17.0 16.0 15.0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 absorption 1 mag/kpc no absorption 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 Distance in Parsecs 2013 W. Pezzaglia Astronomy Lab Manual Revised: Jan 30, 2013

Printed: Mar/01/2013 Milky Way Lab Page MW- 25 Space Penetration Power Avg Absolute Distance Limiting Magnitude: m Magnitude of Stars: M D (parsecs) no absorption absorption 1 mag/kpc 2.5 12.6 3.0 3.0 2.5 15.8 3.5 3.5 2.5 20.0 4.0 4.0 2.5 25.1 4.5 4.5 2.5 31.6 5.0 5.0 2.5 39.8 5.5 5.5 2.5 50.1 6.0 6.1 2.5 63.1 6.5 6.6 2.5 79.4 7.0 7.1 2.5 100.0 7.5 7.6 2.5 125.9 8.0 8.1 2.5 158.5 8.5 8.7 2.5 199.5 9.0 9.2 2.5 251.2 9.5 9.8 2.5 316.2 10.0 10.3 2.5 398.1 10.5 10.9 2.5 501.2 11.0 11.5 2.5 631.0 11.5 12.1 2.5 794.3 12.0 12.8 2.5 1000.0 12.5 13.5 2.5 1258.9 13.0 14.3 2.5 1584.9 13.5 15.1 2.5 1995.3 14.0 16.0 2.5 2511.9 14.5 17.0 2.5 3162.3 15.0 18.2 2.5 3981.1 15.5 19.5 2.5 5011.8 16.0 21.0 2.5 6309.5 16.5 22.8 m2.5 5 Formulae: No absorption D 10 10 D D With Absorption: must solve the non-linear equation: m 2.5 5Log 10 1000 Note: your limiting magnitude m should be the value matching your actual sky conditions, i.e. the theoretical value minus the magnitudes lost by the brightness of your local sky. For example: if the faintest thing you can see in the sky is 4 th magnitude, this is 2.5 magnitudes less than the ideal eye s limit of 6.5 magnitudes. Hence if the theoretical limiting magnitude of the telescope was 18.5, the actual for that evening should be around 18.5-2.5=16 The space penetrating power would be 5012 parsecs if there was no absorption, but only 1995 if there was absorption (a factor of 2.5x smaller!). Hence if you didn t know about absorption, your estimation of the thickness of the galaxy might be 2.5 times bigger than the true value. 2013 W. Pezzaglia Astronomy Lab Manual LPC Update: Feb 28, 2013

Page MW- 26 Milky Way Lab Printed: Mar/01/2013 Question D-4. Thickness of Milky Way (a) Average Star Count near Galactic Pole: (b) Average Star Count near Galactic Equator (Milky Way): (c) Ratio (d) Take Cube Root (e) Multiply by twice the space penetrating power (no absorption) of telescope to get galactic thickness (f) Recalculate thickness assuming absorption: N p = N 0 = R= N p /N 0 = R 1/3 = T = 2D[N p /N 0 ] 1/3 = Parsecs = Parsecs (g) Compare your measurement of the thickness of the Milky Way (with and without absorption) with the generally accepted value of around 500 parsecs. Are you close (what factor are you off)? [Note close in Galactic Astronomy is a factor of 3] Question D-5. Star Densities in the Milky Way (a) Eyepiece Used (focal length in mm): (b) Apparent field (degrees) [see table 1]: (c) Space Penetrating Power (D in parsecs): f e = mm = deg D = parsecs (d) Compute Volume in cubic parsecs: V = (/3)D3[tan(/2)]2= parsecs3 (e) Calculate Density of Stars [stars per cubic parsec] [divide line D-4b above by line D-5d] = N 0 /V stars/parsecs3 (f) Calculate distance between stars: d = (1/)1/3= parsecs (g) Summary: we expect approximately 1 to 5 parsecs between stars. Is your measurement close to this? 2013 W. Pezzaglia Astronomy Lab Manual Revised: Jan 30, 2013