The Mass of the Milky Way. Introduction: The 21-cm line of neutral hydrogen

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1 Astronomy 3 Lab Manual Radio Observing 1 The Mass of the Milky Way Introduction: The 21-cm line of neutral hydrogen Hydrogen is the most abundant element in the cosmos; it makes up 75% of the universe s mass. Therefore, it is no surprise that one of the most significant spectral lines in radio astronomy is the 21-cm hydrogen line. In interstellar space, gas is extremely cold. Therefore, hydrogen atoms in the interstellar medium are at such low temperatures ( 100 K) that they are in the ground electronic state. This means that the electron is as close to the nucleus as it can get, and it has the lowest allowed energy. Radio spectral lines arise from changes between one energy level to another. A neutral hydrogen atom consists of one proton and one electron, in orbit around the nucleus. Both the proton and the electron spin about their individual axes, but they do not spin in just one direction. They can spin in the same direction (parallel) or in opposite directions (anti-parallel). The energy carried by the atom in the parallel spin is greater than the energy it has in the antiparallel spin. Therefore, when the spin state flips from parallel to anti parallel, energy (in the form of a low energy photon) is emitted at a radio wavelength of 21-cm. This 21-cm radio spectral line corresponds to a frequency of 1420 MHz. The 21-cm hydrogen radiation is not impeded by interstellar dust. Optical observations of the Galaxy are limited due to the interstellar dust, which does not allow the penetration of light waves. However, this problem does not arise when making radio measurements of atomic hydrogen. Radiation from this region can be detected anywhere in our Galaxy. Areas which contain cold hydrogen gas are called HI regions. Observations of the 21-cm line from HI regions in our Galaxy can be used to measure the speed of rotation of objects about the center of the Milky Way. Gravity is holding the Milky Way together and preventing stars and HI regions from flying off into intergalactic space. The strength of the gravitational force depends on the mass of the galaxy more massive galaxies have strong gravitational forces and higher rotation speeds. As discussed in Mathematical Insight 19.1 of your textbook, measurements of rotation velocities of objects can be used to estimate the mass of the Milky Way. In this lab, you will use one of the Student Radio Telescope (SRT) on the roof of Wilder Lab to measure the velocity of HI gas in the disk of the Milky Way. These telescopes have a diameter of 2.1m and have a sensitive radio receiver at the focus of the telescope. The radio receiver is designed to scan a range of wavelengths centered about the 21-cm line of hydrogen. As the gas in the Milky Way is moving, it is Doppler shifted and the receiver can determine the velocity of the gas by comparing the observed wavelength to the standard wavelength (21-cm). The telescope and receiver are controlled remotely, using the computers in the astronomy lab (room 200 Wilder). From your measurements of the velocity of the gas orbiting the Milky Way, you will be able to determine the rotation curve of the Milky Way and finally, estimate the mass of the Milky Way.

2 Astronomy 3 Lab Manual Radio Observing 2 Figure 1: Gas clouds rotate around the center of the Milky Way. Clouds at different distances have different velocities and therefore give rise to emission lines with different Doppler shifts. The observed flux profile (solid line in figure on the right) is the sum of the line profiles of all the individual line profiles (dashed lines). The numbers of the line profiles correspond to the clouds in the picture on the left. Theory To first order, we can assume that the gas in the Galaxy is in a circular orbit about the center of the Milky Way. As discussed Mathematical Insight 19.1 of your textbook, the velocity V of a gas cloud at a radius R from the center of the galaxy is GMR V gas = (1) R where M R is the mass of the Milky Way (enclosed within the radius R) and G is the Gravitational Constant, G = m 3 /kg/s 2. Thus, gas clouds at different distances from the center of the Milky Way, will have different velocities. As illustrated in Figure 1, when we point our radio telescope in the disk of the Milky Way, we receive a signal (flux) from a number of clouds along the line of sight. These clouds are orbiting

3 Astronomy 3 Lab Manual Radio Observing 3 the center of the Milky Way at different distances and have different velocities. This leads to different Doppler shifts for each gas cloud. Recall that the Doppler shift (Section 5.5, in your textbook) only measures one component of the velocity the velocity along the line of sight (often referred to as the radial velocity). The maximum Doppler shift (corresponding to the maximum velocity along our line of sight) occurs for cloud 3 in Figure 1, as for this cloud the circular velocity is lined up with our line of sight. The other clouds in Figure 1 only have a small fraction of their total circular velocity lined up with our line of sight, so that the Doppler shift is much smaller. As illustrated in Figure 1, the maximum velocity (cloud 3) occurs at the tangent point, the point where the direction of observation is at right angles to the the Galactic Center. This right angle triangle allows us to easily determine the distance the maximum velocity, R = R o sinl (2) where R o is the distance between the Sun and the Galactic Center and l is the angle that our telescope is pointing with respect to the line between the Sun and the Galactic Center. This is called the Galactic longitude. From other measurements, astronomers have determined the distance to the Galactic center to be R o = 8kpc = 8000parsecs. The Doppler shift (see Mathematical Insight 5.3 for more details) measures the relative velocity of the gas cloud along the line of sight with respect to the our (the Sun s) motion. Thus, the velocity which is observed by the radio telescope is V max,observed = V gas V sun sinl (3) as illustrated in Figure 1. The velocity of the Sun may be written as V sun = ω o R o (4) where ω o is the angular velocity of the Sun about the Galactic center. Combining equations equations (3) and (4) we see that V gas = V max,observed + ω o R o sinl (5) Combining equations (2) and (5) we get V gas = V max,observed + ω o R (6) From other measurements, astronomers have determined that ω o R o = 220kms 1. Finally, rearranging equation (1) we see that the mass of the Milky Way is given by M R = RV 2 gas G. (7) Thus, measuring the maximum velocity of the gas and combining this with equations (2) and (6) will allow us to determine the mass of the Milky Way.

4 Astronomy 3 Lab Manual Radio Observing 4 Procedure Figure 2: SRT screen shot. Each group of two students will obtain data at three or four different points in the plane of the Galaxy. You will share this data with other members of the lab section, so that you will end up with 10 data points to analyze. To obtain a data point, use following procedure: 1. Set the telescope to scan a range of frequencies in order to obtain the spectrum. To do this, click on the freq button on the top of the SRT control panel (see Figure 2) and type in the lower panel either: (for the analog receiver; the center frequency and number of frequency bins); or (for the digital receiver; the center frequency and observing mode). 2. Move the telescope to the Galactic longitude specified by your TA. For example to move to l = 10, click on GL10 in the Elevation/azimuth plot in the middle of the screen. The Status box (middle of screen) will switch to slewing to indicate the telescope is moving. When the telescope has completed its move, the icon you clicked on will switch colors and the Status box will say tracking 3. Click the clear button on the top left of the SRT control panel to clear the old spectrum and to start acquiring new data. After several seconds, the spectrum will appear red, in the av.

5 Astronomy 3 Lab Manual Radio Observing 5 Figure 3: Sample spectrum obtained at Galactic longitude of 40 degrees. spectrum integ. box in the top middle of the screen (Figure 2). This display will be updated as the telescope continues to acquire data. Obtain data for about 5 minutes. 4. Left click the mouse button on the average spectrum. This will pop up a new screen, showing the spectrum. A sample is shown in Figure 3. You can enlarge the window using the mouse. 5. When you are confident that you have a good signal, print the spectrum. To do so, right click on the camera icon in the system tray (bottom right of the screen), go up the menu to select Window/Menu, and then click on the spectrum window. Do this several times, so that you can give copies to other people in your lab section. 6. Repeat steps 2-5 as needed. 7. For each spectrum, estimate the maximum velocity and error in this measurement. Make a table of your results (similar to Table 1). Analysis Complete your results table by calculating the distance to each cloud, R, ω o R and V gas. Make a graph of V gas as a function of distance from the Galactic center, R. Include the error bars on your

6 Astronomy 3 Lab Manual Radio Observing 6 Table 1: Results Table Measured Calculated Galactic Max. velocity estimate error tangential ω o R V gas longitude (deg) (km/s) (km/s) distance (kpc) (km/s) (km/s)

7 Astronomy 3 Lab Manual Radio Observing 7 plot. For each radius for which you have obtained a good measurement, calculate the enclosed mass of the Galaxy (using equation 7). When you make this calculation, make sure you use an consistent set of units it is best to convert everything into meters, kilograms and seconds when doing the calculation. After you have finished the calculation, convert your calculated mass from kilograms into solar masses. Plot enclosed mass in solar masses (M R ) as a function of R. Q1: The analog receiver observed 50 frequency bins, centered at MHz, with a spacing of 40.0 khz. What was the starting and stopping frequency of your observations? Using Mathematical Insight 5.1 what was the starting and stopping wavelength of your observations? Using Mathematical Insight 5.3, what is the range of velocities you could possibly observe? Note that Mhz MegaHertz is millions of cycles per second (10 6 s 1 ), while khz kilohertz is thousands of cycles per second (10 3 s 1 ). Q2: How does your observed mass of the Milky Way compare to the values in the textbook (near the end of Section 19.1)? Q3: What do you estimate is the error your mass estimate of the Milky Way? A complete answer will include a discussion of how you estimated the error in your determination of the maximum velocity at each Galactic location. Q4: The average matter density ρ is simply the mass divided by the volume. The volume of a sphere is given by V = 4πR 3 /3 and so ρ = 3M R 4πR 3 Combining the above equation with equation (7) we see that ρ = 3V 2 gas 4πGR 2 (8) Calculate the average matter density ρ as function of radius R in units of solar masses per cubic parsec and graph the results. How does the average density vary with radius? Q5: What can you conclude from the observed spectrum of the Galactic Center? Q6: How do you explain the sudden transition from the lack of velocity spread in the H-line at Galactic longitude less than 20 degrees to a double peaked spectrum at longitudes greater than 20 degrees?

8 Astronomy 3 Lab Manual Radio Observing 8 Writing up the Lab When you complete the lab, have the TA sign your data sheets (spectrum printouts), which will form part of the lab report. Lab reports are due 1 week after you complete the lab. Lab reports are to be put into the box (labeled with your TAs name) which are located to the left of the main stairs when you enter Wilder Lab. Make sure you follow all of the general guidelines for A3 lab reports, which are discussed in a separate document posted onto Blackboard. You should use complete sentences throughout your lab report. When answering questions, please do so in an essay style, referencing the question you are answering. When you have equations to solve, show all of your work (not just the answer), and include units if needed. Make sure you show all details of your calculations, and describe how you obtained your results. Pre-Lab Questions 1. How many meters are there in 8 kpc? 2. If I determine the line of sight velocity of a cold neutral hydrogen gas cloud to be 150 km/s, at what wavelength do I observe the hydrogen emission line? 3. If I point the radio telescope at a Galactic Longitude of l = 40, at what distance from the Galactic center will I measure a maximum velocity for the gas? Express your answer in parsecs. 4. The Student Radio telescope has a diameter of 2.1m. What is the angular resolution of this telescope when observing the 21cm line of hydrogen? How does this compare to the angular resolution of the human eye?