Lab 8 Cosmic Distance Ladder

The Cosmic Distance Ladder Remember to use blue text for your answers Exercises The Cosmic Distance Ladder Module consists of material on seven different distance determination techniques. Four of the techniques have external simulators in addition to the background pages. Work through the material for each technique before moving on to the next technique. Note: The Distance Modulus (DM) is not a distance determination technique in itself. The DM is the equation used to calculate distances in many of the techniques. Radar Ranging Question 1 : Radar ranging can be used to directly determine the distance to a solid object like Venus or Mercury, but not a gaseous object like the Sun. Do some research and summarize how radar ranging can be used to indirectly determine the distance to the sun. This is how the Earth-Sun distance is most accurately measured, and we must know this distance for the stellar parallax method (and all others) to work. (2 points) Parallax In addition to astronomical applications, parallax is used for measuring distances in other disciplines such as surveying. Open and investigate the Parallax Explorer , where techniques very similar to those used by surveyors are applied to the problem of finding the distance to a boat out in the middle of a large lake. The simulator consists of a map providing a scaled overhead view of the lake, and a road along the bottom edge where our surveyor (represented by a red X) is located. The surveyor is equipped with a theodolite, which is the combination of a small telescope and a large protractor that allows the angle of the telescope orientation to be precisely measured. This instrument is mounted on a tripod that can be moved along the road to establish a baseline. Radar ranging can be used indirectly to find out the distance to the sun by timing the light echo. The time it takes the light echo to return gives us an indirect calculation of the distance to the sun.

An Observer’s View panel shows the appearance of the boat relative to trees on the far shore through the theodolite. Configure the simulator to preset A , which allows us to see the location of the boat on the map. Drag the position of the surveyor around and note how the apparent position of the boat relative to background objects changes. Position the surveyor to the far left of the road and click take measurement. This causes the surveyor to sight the boat through the theodolite and measure the angle between the line of sight to the boat and the road. Now position the surveyor to the far right of the road and click take measurement again. The distance between these two positions defines the baseline of our observations and the intersection of the two red lines of sight indicates the position of the boat. We now need to make a measurement on our scaled map and convert it back to a distance in the real world. Check show ruler and use this ruler to measure the distance from the baseline to the boat in arbitrary map units. The ruler takes the place of the trigonometric calculations the surveyor would actually use to determine the distance. Use the r uler to measure the perpendicular distance from the baseline to the boat in map units. Question 2 : Enter your perpendicular distance to the boat in map units. Convert the map units to meters and show your work in the box below. Configure the simulator to preset B . The parallax explorer now assumes that our surveyor can make angular observations with a typical error of 3°. Due to this error we will now describe an area where the boat must be located as the overlap of two cones as opposed to a definite location that was the intersection of two lines. This preset is more realistic in that it does not illustrate the exact position of the boat on the map. Question 3 : Repeat the process of applying triangulation to determine the distance to the boat and then answer the following: What is your best estimate for the perpendicular distance to the boat (in meters)? 6.6x20m=132m What is the greatest distance to the boat that is still consistent with your observations (in meters)? 7.5x20m=150m What is the smallest distance to the boat that is still consistent with your observations (in meters)? 5.9x20m=118 7.5 unitd 7.5x20=150m

Let’s first find the spectral type. We can see in the Absorption Line Intensities panel that for the star to have any helium lines it must be a very hot blue star. By dragging the vertical cursor we can see that for the star to have very strong helium and moderate ionized helium lines it must either be O6 or O7. Since the spectral lines are all very thick, we can assume that it is a main sequence star. Setting the star to luminosity class V in the Star Attributes panel then determines its position on the HR Diagram and identifies its absolute magnitude as -4.1. We can complete the distance modulus calculation by setting the apparent magnitude slider to 4.2 in the Star Attributes panel. The distance modulus is 8.3, corresponding to a distance of 449 pc. You should keep in mind that spectroscopic parallax is not a particularly precise technique even for professional astronomers. In reality, the luminosity classes are much wider than they are shown in this simulation, and distances determined by this technique probably have uncertainties of about 20%. Question 5 : Complete the table below by applying the technique of spectroscopic parallax. Observational Data Analysis m Description of spectral lines Description of line thickness M m-M d (pc) 5.1 strong hydrogen lines moderate helium lines very thin 0.7 4.40 147 11.5 strong molecular lines very thick 16 -4.5 1.26 4.8 strong ionized metal lines moderate hydrogen lines very thick 3.1 1.7 21.5

Main Sequence Fitting Open up the HR Diagram Star Cluster Fitting Explorer . Note that the main sequence data for nearby stars whose distances are known are plotted by absolute magnitude in red on the HR Diagram. In the Cluster Selection Panel, choose the Pleiades cluster. The Pleiades data are then added in apparent magnitude in blue. Note that the two y-axes are aligned, but the two main sequences don’t overlap due to the distance of the Pleiades (since it is not 10 parsecs away). If you move the cursor into the HR diagram, the cursor will change to a handle, and you can shift the apparent magnitude scale by clicking and dragging. Grab the cluster data and drag it until the two main sequences are best overlapped as shown to the right. We can now relate the two y-axes. Check show horizontal bar, which will automate the process of determining the offset between the m and M axes. Note that it doesn’t matter where the horizontal bar is placed vertically. At any point, the difference between m and M will be the same and will therefore yield the same distance modulus. One set of values for the Pleiades gives m – M = 1.6 – (-4.0) = 5.6, which corresponds to a distance of 132 pc. Question 6 : Determine the distance to the Praesepe cluster. Apparent magnitude m Absolute Magnitude M Distance (pc) 13 6.9 166 Question 7 : Determine the distance to the Hyades cluster. Apparent magnitude m Absolute Magnitude M Distance (pc) 12.1 6.5 132

Hubble’s Law In this part of the lab you will make an investigation of Hubble’s Law; an empirical law that relates the recession velocity of galaxies to their distance from us. You will create a Hubble graph and calculate a value for the Hubble constant, and then use that value to estimate the distance to a very distant galaxy. This is the method used to find distances to galaxies that are too far away to detect Cepheid variable stars, or in galaxies where no other distance indicators (such as white dwarf supernovae) have been observed. Realize that it is more accurate to use a distance indicator if one can be found. The universe contains billions of galaxies, including our own, the Milky Way. With only a few nearby exceptions, these galaxies are all receding from us. Their recession velocity can be measured using the Doppler Effect, which is a change in the observed wavelength of light relative to the wavelength we know must have been emitted by the stars in that galaxy. Since the galaxies are moving away from us, the light is shifted towards longer wavelengths, or is red-shifted . By measuring the Doppler shift of the wavelength, the speed of recession can be calculated. The best way to determine the distance to nearby galaxies is to find Cepheid variable stars in that galaxy, measure their pulsation period, then use the established period- luminosity relationship of Cepheids to determine their distance. The galaxy’s position on a Hubble graph can be plotted once the recession velocity and distance to the galaxy have been determined. Using the recession velocity and distance information for the 5 galaxies listed below, plot all the galaxies on the Hubble graph on the following page. To plot a point, use the ‘Shapes’ option under the ‘Insert’ tab in this Word document to find a ‘Basic Shape’ you would like to use. Insert this shape onto the graph, then resize it and drag the shape to the correct positon on the graph. You do not need to label the data points. Next, use the ‘Shapes’ option to draw a straight “best fit” line that goes from the origin through the middle of the data point distribution. Recall that the Hubble constant (H) is simply the slope of this line. You can determine the slope of a straight line that begins at the origin by picking any point on the line, and then divide the y coordinate (velocity) of the point by its x coordinate (distance). If you cannot get the drawing tools to work in Word, you may print the following page, fill it in by hand, then scan and send it to me along with your Word document. Galaxy cluster Recession Velocity (km/s) Distance (Mpc) Virgo 5000 65 Ursa Major 17,000 225 Corona 27,000 384 Bootes 42,000 600 Hydra 63,000 875

Question 10 : What is the value of the Hubble constant, as determined from this data? Round this value to the nearest whole number and show your work. Be sure to include the units for the Hubble constant. Mpc stands for Megaparsecs, or millions of parsecs. (3 points) Go to the following Astronomy Picture of the Day: https://apod.nasa.gov/apod/ap180305.html and move your cursor around the picture to see (and hear) the distances of different galaxies. The distances to galaxies in this Hubble Space Telescope deep field picture were all found by measuring their redshifts to determine their velocities, then applying Hubble’s Law (H = V/D) to find their distances. Question 11: Using the value you obtained for the Hubble constant in the previous question, use Hubble’s Law to determine the distance to a galaxy whose recession velocity is 100,000 km/s. Show your work and express your answers in Mpc. 1700 km/s /225mpc= 76 km/s/mpc 100000km/s =76km/s/mpc X D 1000000/76=1315.79 76/76= cancels out = 1316 mpc