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ASTRO 1050 Rotation, Mass, and Distance Measurements for Galaxies

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ASTRO 1050 Rotation, Mass, and Distance Measurements for Galaxies ASTRO 1050 Rotation, Mass, and Distance Measurements for Galaxies ABSTRACT In this lab we will measure the rotation of spiral galaxies by looking at their spectra. We will then use this rotation to estimate the mass of these galaxies. With this we can also find the mass to light ratios of these galaxies and find that there is dark matter in most galaxies we can see. Measuring the rotation of a Galaxy In this section, we will use the doppler shift of an emission line in a galaxy to measure how it is rotating. To do this, we need to use the doppler shift of light. As objects emitting light get closer to us, the light waves they emit are compressed and shorter and they look bluer. And, as objects move away from us, the light waves they emit are stretched and they look redder. See the image below for a visual representation of this: First, for practice, look at the spectra of the star below. Is it moving towards us, or away from us? How can you tell? 1 Now, we are going to make things more complicated. With an edge-on rotating galaxy, some of the stars are moving towards us and some are moving away from us. This means some of the light is blue shifted, and some is red shifted. If an astronomer measures the spectrum of an entire edge on galaxy, they will see a wider line. We will measure the rotation of galaxy UGC 2936, shown below. Why is this a good candidate for this type of measurement? Now, our helpful observer friend has gone out and taken the spectra of this galaxy, getting light along the blue-green light shown in the following image. The spectra they got is shown below. In this image, instead of looking at wavelength versus intensity, we are measuring wavelength vs. position on this blue line. Our friend has already converted the y-axis to kiloparsecs from the center of the galaxy. They did leave the x axis in angstroms though, which are a unit astronomers use. There are 1010 2 angstroms in one meter (or, 1 angstrom =10−10 meters). Using this spectra, what part of the galaxy is rotating towards us? Which is moving away? In order to find the rotation velocity, we need to measure the difference between the ends of the lines extending off the middle bulge. Using this spectra, what is the shift in wavelength from one end of the galaxy to the other? We also need to know the rest wavelength for this line. For this measurement, we will need to measure the wavelength of this line in the center of the galaxy. What is this measurement? 3 Now, use your two measurements to find the rotational velocity of this galaxy. This can be found using the equation: c∆λ vrot = λrest 8 where vrot is the rotational velocity, c is the speed of light (3 × 10 meters/second), ∆λ is the wavelength shift you measured, and λrest is the rest wavelength you measured. 4 Finding the mass of galaxies from rotational velocity Now, we will look at the measurements from a few edge-on spirals to see how mass is related to rotational velocity. Plot the following measurements in rotational velocity and mass on the graph below. Galaxy Name Mass (solar masses) rotational velocity (km/s) Needle Galaxy 30 × 109 254 NGC 672 8 × 109 143 NGC 925 17 × 109 132 NGC 4559 8 × 109 135 NGC 4631 6 × 109 154 NGC 4656 2 × 109 85 Table 1: Data taken from \Rotation curves, mass distributions and total masses of some spiral galaxies" by N. Krumm and E.E. Salpeter 5 Connect these data points with a line, as best you can. Where would UGC 2936 fall on this graph? Use this to estimate the mass of UGC 2936. 6 Type Ia Supernova We can determine the distance to a galaxy by using the brightness of a type Ia supernova in the galaxy. Below is a list of type Ia supernova and the galaxies they occurred in. Which galaxy is the closest to us? Hint: remember, magnitudes are backwards! Lower magnitude means brighter source Supernova Name Galaxy Supernova Was Observed In Supernova Apparent Magnitude SN 1937C IC 4182 +8.4 SN 1972E NGC 4526 +8.7 SN 1994D NGC 4526 +15.2 SN 2002bi NGC 1821 +14.7 SN 2011fe M101 +10.0 SN 2014J M82 +10.5 Table 2: Data taken from the International Astronomical Union Since we know all Type Ia Supernova have the same absolute magnitude (-19.3) we can find the distance to this nearest galaxy using the formula: m+5=M d = 10 5 where d is the distance to the galaxy, m is the apparent magnitude, and M is the absolute magnitude. 7 Why can we not use Type II supernova (core collapse of a massive star) to find the distance to galaxies? These are some of the ways astronomers can learn about galaxies. Even though they are incredibly distant, we can still find out a lot about them with just a few measurements! 8.
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