Welcome to the camp for the greatest of space nerds. This past summer I was accepted to Duke University’s astronomy, physics, and astrobiology field studies (run by their Talent Identification Program, TIP). Here students conducted independent research using resources from the Pisgah Astronomical Research Institute (PARI) Observatory. Briefly, we lived and thrived on campus at the institute. Amidst the steeping mountains and majestic forestry, 27 high school kids from around the country fervently worked out a semi-feasible research project to complete within two weeks’ time.
My team studied dark matter content in our neighbor, the Andromeda Galaxy (M31). To do so, we first needed to calculate the velocity of the galaxy’s rotation. We used PARI’s 12-meter radio telescope, aiming at calculated points along M31’s major axis. There, the telescope took spectrum scans across a certain frequency range. These scans detect light emitted by hydrogen, the most abundant element in the universe and every galaxy, so we can measure the emission peak’s shift as we progress across the galaxy.
Here’s what all that means:
The electromagnetic spectrum: how we characterize light waves
First, you need to know a little about the Doppler Shift. The Doppler Shift describes the alteration of a wave as its source changes position. Say you are standing by the side of a road. The pitch of a car’s engine seems to rapidly decrease as it zooms past you. As the car moves in one direction, it begins to catch up with its emitted sound wave. The wavelength of the sound wave gets crunched, increasing its frequency. Similarly, the wavelength on the trailing side gets stretched and decreases its frequency. Frequency is directly related to pitch, so you hear a higher pitch as the car approaches and a lower pitch as it departs.
In astronomy, we apply this same principle to light waves. If something is moving away from us, the wave of light coming from that object will be stretched, increasing its wavelength. This makes the light appear redder than it should. We call this a “redshift”. The same logic applies for light coming towards us, which we accordingly call a “blueshift”.
Lastly, you need to understand that where there is matter, there is a concentration of hydrogen. Hydrogen is the most basic of elements, and is present in all galaxies.
Each element emits characteristic wavelengths of light. One of the waves emitted by hydrogen has a frequency of ~1420 MHz. This is the HI (spoken “H-one”) emission line. Using the radio telescope, we detect light on and about this wavelength. The peaks of the graphs represent spikes in light emission. The shift in peak as we progress along the galaxy is due to red or blue-shifting.
Observe the leftward shift (redshift) in peak as the measurements progress along the galaxy’s major axis. Units along the y-axis are arbitrary.
On our graphs above, the y-axis describes intensity of emission and the x-axis describes frequency. So we’re viewing the galaxy as a single object. However, taking measurements across the galaxy yields a shift in HI emission peak, because of the Doppler effect I mentioned earlier. Galaxies rotate. As one galactic arm moves away from us, the other moves towards us. Thus, the peaks are redshifted or blueshifted accordingly.
The extent of the red/blueshift at either end of the object can be used to calculate rotational velocity. This can then be inserted into a mass equation involving rotational velocity, orbit radius, and the gravitational constant (G). This tells us how massive the galaxy has to be in order to have this velocity and orbit.
We then take a few given values having to do with luminosity, L(essentially brightness) for another mass equation. This returns a fair estimate of the mass of the galaxy’s observable matter. Subtract the amount of observable mass from the total mass and you have your unobservable mass (i.e. dark matter).
Our calculations estimated the dark matter content to be about 28x the mass of its observable matter, which is within reason of most estimates. This is approximately 1,200 billion times the mass of our sun. Pretty cool stuff.
The above graph describes the velocity of M31’s components as a function of distance from its center. As the galaxy is rotating, measurements indicate one side moving significantly slower than the other. This is due to the counteracting velocity of that side’s movement away from us. The reverse logic applies for the opposite side. Because we did not account for rotation, this downward trend is apparent.
Published in Deerfield Academy's science magazine, Door to STEM.