The Size-Luminosity Relationship in Extra-Galactic Astronomy
When I started undergraduate research at the University of Alabama, I met Dr. Nair, an assistant professor in the Department of Physics & Astronomy. New to the University, she was looking to build a team of undergraduates to help streamline the basic chores involved in her research. Dr. Nair is an extra-galactic astronomer; she studies galaxy evolution and the structural differences between galaxies in the local universe and galaxies at high redshifts — that is, the light of objects moving away from us is in effect stretched into the longer, lower frequency wave lengths, and the further away the object the greater the shift. When I approached her about joining the team, she directed me to the white board in her office, brimming with numbers, astrophysics equations, and hand-drawn graphs of galaxy brightness profiles.
“I’m looking for more undergraduates,” she said. “I have more data to analyze than I have time for. Are you interested in studying galaxies?”
“Sure,” I replied. “I live in one after all.”
The local universe extends from the Milky Way to a redshift of z<0.1 — about one billion light years away—where z is the ratio of the galaxy’s relative speed to the speed of light, from which a distance can be calculated. For Dr. Nair’s research, galaxies anywhere from z=0 up to z»3 — zero to five billion light years away — were studied. More distant galaxies have been discovered, but too few to constitute a statistically significant sample. She focuses on elliptical galaxies within this distance range because they are populous and visible enough to be analyzed and compared with their neighbors. She directed me to download a collection of galaxy cluster images within the z=0 up to z»3 range.
Figure 1: Middle-aged elliptical galaxies between z 0 to 3. — This image includes the distant galaxy cluster Abell 370, one of the very first galaxy clusters in which astronomers observed gravitational lensing, in which gravity warps spacetime and distorts the light we receive from galaxies lying beyond the gravity lens. The arcs and streaks are the gravitationally distorted images of more distant galaxies. Source: Image by NASA, ESA, HST Frontier Fields)
In the following months, to prepare for my image and brightness analyses of elliptical galaxies, I read academic papers on extra-galactic astronomy and filled my hard drive with high-resolution images of galaxy clusters — leaving little room for anything else. It turns out that most scientific data, at least in astronomy, is available online. If you have the drive space, you can download Hubble Space Telescope images and process them yourself with free software. There are also top-of-the-line, high-priced astronomical image processing programs, like MIRA and IRIS. However, even free programs like DS9, named after the Star Trek’s Deep Space Nine, are used by both students and professional astronomers for image processing and scientific analysis. I downloaded it and loaded up all the Hubble Space Telescope images I’d been storing on my computer.
Elliptical galaxies look like giant glowing spheres of stars (Figures 2 and 3). Our own Milky Way is a spiral galaxy 100,000 light years in diameter, with long, star-filled arms curving out from the galactic core. The stars of a spiral galaxy orbit about the center in a flat galactic plane. The Milky Way won’t always be a spiral. In about four billion years, when we collide with our closest galactic neighbor, the Andromeda Galaxy, gravitational effects will cause the two galaxies to restructure. They might become a single elliptical galaxy, in which the stars chaotically orbit about the galactic center without a plane or pattern.
Figure 2: The classification of galaxy shapes, based on Edwin Hubble. (Source: Image by NASA & ESA).
“Interactive Hubble Tuning Fork“, released 19/11/2012 10:00 am; © C. North, M. Galametz & the Kingfish Team
Access the really nice Interactive Hubble Tuning Fork version of this image at http://herschel.cf.ac.uk/kingfish
For those of you who might be depressed by such a future for our beloved Milky Way, fear not. When galaxies merge, their stars and planets rarely collide, because there is so much empty space between them.1 The average distance between stars is about 30 trillion miles.
So, humankind is unlikely to be extinguished by a galactic collision, or by the death of our Sun in five billion years. But in two billion years the Sun’s energy output will have increased to the point where temperatures on Earth will be too hot for liquid water.1 Unless of course we’ve developed technology to move our planet to a safer range.
Galactic merging events are exactly what extra-galactic astronomers like Dr. Nair study to understand the evolution of galaxies. Looking at elliptical galaxies is the best way to do this considering they are the products of mergers. Since the observable universe is billions of light years across — its edge always growing larger as the universe continues to expand — the light we receive from the most distant ellipticals is already billions of years old—meaning we’re seeing them as they were billions of years ago. Looking at progressively closer ellipticals, we can study the entire history of their evolution, from the time they were first formed all the way up to the present.
Figure 3: The image compares an average present-day spiral galaxy (left) with its counterpart in the primordial past (right), when galaxies were likely had more hot, bright stars.
Image credit: NASA/JPL-Caltech/STScI
Extra-galactic astronomers studying the evolution of elliptical galaxies have found a curious anomaly, referred to as the size-luminosity relationship in early-type galaxies. ‘Early-type galaxy’ is the name originally used for elliptical galaxies under the galaxy classification scheme, created by Edwin Hubble, the early 20th century astronomer who discovered that the universe contained galaxies besides our own. The size-luminosity relationship is one of the most fascinating topics in the field of extra-galactic astronomy, and relates to the physical concept of density.
Density here refers to the amount of mass within a given volume of space. A cup of water is denser than a cup of air, and a cup of iron is denser than a cup of water. Though mass and weight aren’t the same thing, they’re directly related, and you can see that a given volume of space would be denser if it has more weight in it than one with less weight.
Galaxies have size and mass just like all other matter in the universe. Galaxies are collections of stars and gas clouds bound together by gravity. The ones with more stars are more massive than the ones with fewer, but a small galaxy with a hundred billion stars is denser than a larger galaxy with the same number of stars.
The most distant elliptical galaxies, and therefore the oldest, are extremely compact. In this context, luminosity directly relates to mass because more mass in a galaxy means more stars, and more stars means more brightness3.
When extra-galactic astronomers like Dr. Nair plot the size-luminosity relationship of elliptical galaxies, they observe something quite unexpected: Billions of years ago these galaxies were quite dense, but the degree of density varied greatly. Yet local, present-day ellipticals vary little in density. This means that over time, regardless of how compact an elliptical galaxy was to begin with, it expands — or ‘puffs out’ — to the density range common to all elliptical galaxies today4. Some physical process we don’t understand is driving all elliptical galaxies to evolve towards a certain common density. Is this an attribute of galaxy structures themselves, or a consequence of an undiscovered physical law? The size-luminosity relationship is a mystery – evidence of a major trend that astronomers never would have expected.
How do elliptical galaxies “know” when to stop growing? Is there a physical process that keeps track of and adjusts their density? How do the ultra-compact ones “know” to grow by a lot, and the less compact ones by only a little? What’s causing them to puff out?
Extra-galactic astronomers have some hypotheses about what mechanisms may be contributing to this phenomenon, the most likely one being mergers. Elliptical galaxies don’t stop merging after just one collision. In fact, they’re expected to be even more likely to collide again after a merger because they now have more mass and attract other objects nearby more intensely.
You might ask: if a merger adds both mass and size to the galaxy, why doesn’t the density stay the same? The mass of a galaxy increases, but proportionally its size increases much more5. Galaxies spin, and when mass is added to them it disturbs the angular momentum of the system, causing the orbiting bodies to spread out. So mostly likely small galaxies merge with these ellipticals in events we call minor mergers, and cause the size evolution over time, the ‘puffing out.’ This adds much more size than mass, meaning the density goes down overall. Minor mergers are also more frequent.
There are different forms of merging events: dry mergers and wet mergers. The former refers to merging events between galaxies lacking appreciable interstellar medium — gas clouds in the space between the stars – where not much interaction happens between the different pockets of gas inside the two galaxies. Because of this, dry mergers don’t have much of an effect on the overall behavior of the resulting galaxy, whereas wet mergers — where galaxies with appreciable interstellar medium are involved — induce star formation due to gravitational instabilities in the merging gas clouds. These processes can change the distribution of the angular momentum in a galaxy as the new stars drift into their orbital positions about the galactic center. It is currently thought that the Milky Way-Andromeda Collision will be a dry merging event, as not much gas will be available during the collision with which to trigger star formation.6
Other hypotheses have been proposed for the existence of the size-luminosity relationship. They range from the spreading out and dissipation of the gas clouds in elliptical galaxies — not related to merging events — to the astronomer’s favorite go-to when something about a galaxy’s mass doesn’t add up: dark matter,3 which makes up most of a galaxy’s mass but can only be indirectly detected. It’s possible that the restructuring of a galaxy’s dark matter during merging events could be causing the size evolution — assuming it interacts with itself at all.
Another hypothesis, gas dissipation, notes that not all distant galaxies are compact; a small minority are not very dense at all. Yet, even these anomalous galaxies eventually puff out — otherwise, we’d still see compact galaxies in the local universe today. Over time, they lose gas and this affects the galactic structure, decreasing size and therefore gaining density, to reach the same value of density most compact early galaxies evolve to. So, whether elliptical galaxies begin with high or low density, they evolve over time to reach the same density as every other elliptical.7
But the merger-driven model of early-type galaxy evolution is the hypothesis that’s gained the most traction. It best fits the computer simulation models that theoretical astrophysicists have, even though it possesses numerous inconsistencies, and researchers are continually finding problems with it. Until a better hypothesis comes along, it’s the one most extra-galactic astronomers are sticking with.
Except for Dr. Nair and her colleagues.
She wrote a paper demonstrating that mergers shouldn’t be able to account for just how small the scatter on the size-luminosity plot is.5 The merger model predicts a narrow range of densities that nearby early-type galaxies can fall into, but Dr. Nair and her colleagues showed, using more recently collected data and different methods of analyzing brightness, that the range of densities is much smaller than predicted by merger-driven models (Figure 4).
Figure 4: The top row shows Dr. Nair’s data, where the range of densities is smaller. The bottom row shows data collected and measured by an older method of measuring a galaxy’s brightness. (Source: Nair, et al. 2011)
And there’s much more to the picture. Before the anomalous size-luminosity relationship in early-type galaxies was discovered, astrophysical computer models predicted that environmental factors were a key influence in the evolution of ellipticals. Early-type galaxies in low density environments, locations without many nearby galaxies or bodies, also called isolated environments, were thought to grow less than those in high density environments like galaxy clusters, where many neighboring galaxies and bodies are in closer proximity. High density environments have a higher number of collisions and merging events and early hypotheses suggested that environment would play a huge role in galaxy evolution.8
Yet, contrary to what our current astrophysical models and simulations of galaxy evolution are still predicting, it’s been observed that environment plays no role in early-type evolution5. Regardless of whether an elliptical is in a galaxy cluster or an isolated environment, it undergoes an evolution with the same end-point, becoming about as dense as every other early-type galaxy in the nearby universe. If mergers are the explanation, how is this possible? How is it that galaxies in clusters evolve exactly as do isolated galaxies? The former undergo extensive collisions and merging events, while the latter might only experience a few merging events over their entire history. The environmental independence of galaxy evolution may be the most perplexing characteristic of the size-luminosity relationship. If the mechanism by which these processes occur were to be discovered, it could provide valuable insight into how galaxies evolve, how matter was distributed in the early universe, and what galaxies might look like in the distant future.
Even if minor mergers prove to be the mechanism by which ellipticals evolve, this doesn’t answer the question as to why compact galaxies in the early universe grew at unique rates to the same final density we observe today. Why, when we look around at the nearby universe, have elliptical galaxies stopped growing? We know of no law that states an elliptical galaxy must fall into this specific and narrow range of densities. But the empirical fact remains that ellipticals evolve to have about the same ratio of mass to volume, i.e., the same slope on the size-luminosity graph. Could this lead to the discovery of a new law of physics? Perhaps one that could describe the behavior of dark matter?
And remember those images Dr. Nair had me download? The ones of galaxy clusters in between the local and the distant universe, between z of 0 to 3? They show what you would expect: mid-distanced, middle-aged, elliptical galaxies aren’t as compact as the most distant ones; they’re larger in size, suggesting they’re getting closer to the density exhibited by early-types in the local universe. We can see them in mid-approach (Figure 1). It can be frustrating to look at. What’s causing it? I wished the answer could leap out of the graph at me. But the size luminosity relationship has remained a mystery even to veteran extra-galactic astronomers who’ve been working on it for years.
The James Webb Space Telescope is set to launch in October of 2018. With its new capabilities — for example its infrared imaging camera9 (able to see through obscuring gas and dust, see Figure 5) — astronomers will be able to make extra-galactic observations at even higher redshifts. Astronomers will be able to gather data about elliptical galaxies even further away, further back in time, and perhaps get closer to solving the size-luminosity mystery, gaining insights into how the universe we live in evolves.
Figure 5: Visible light and infrared views of the Monkey Head Nebula. Credit: NASA and ESA . Acknowledgment: the Hubble Heritage Team (STScI/AURA), and J. Hester. Using infrared we can see through more dust and gas than with visible light.
1 Marel, R; Besla, G; Cox, T.G.; Sohn, S; Anderson, J. American Physics Journal. The M31 Velocity Vector. III. Future Milky Way-M31-M33 Orbital Evolution, Merging, and Fate of the Sun, 2012; Vol. 753, 1
2 Fraser, C. Universe Today. You Could Fit All the Planets Between the Earth and the Moon, 2015
3Nipoti, C; Treu, T; Leauthaud, A; Bundy, K; Newman, B; Auger, M. Monthly Notices of the Royal Astronomical Society. Size and velocity-dispersion evolution of early-type galaxies in a Λ cold dark matter universe, 2012; 422, 2, https://doi.org/10.1111/j.1365-2966.2012.20749.x, pg. 1714-1731
4Shankar, F; Marulli, F; Bernardi, M; Boylin-Kolchin, M; Dai, X; Khochfar, S. Monthly Notices of the Royal Astronomical Society. Further constraining galaxy evolution models through the size function of SDSS early-type galaxies, 2010; 405, 2, https://doi.org/10.1111/j.1365-2966.2010.16540.x, pg. 948-960
5Nair, P; Bergh, S; Abraham, R. The Astrophysical Journal Letters. A Fundamental Line for Elliptical Galaxies, 2011; Vol. 734, 2, 10.1088/2041-8205/734/2/L31
6Cox, T.J; Loeb, A. Monthly Notices of the Royal Astronomical Society. The Collision between The Milky Way and Andromeda, 2008; 386, 1, https://doi.org/10.1111/j.1365-2966.2008.13048.x, pg. 461-474
7Mancini, C; Daddi, E; Renzini, A; Salmi, F; McCracken, H.J; Cimatti, A; Onodera, M; Salvato, M; Koekemoer, A.M.; Aussel, H; Floc’h, E. Le; Willot, C; Capak, P. Monthly Notices of the Royal Astronomical Society. High-redshift elliptical galaxies: are they (all) really compact?, 2010; 401, 10.1111/j.1365-2966.2009.15728.x, pg. 933-940
8Shankar, F; Marulli, F; Bernardi, M; Mei, S; Meert, A; Vikram, V. Monthly Notices of the Royal Astronomical Society. Size Evolution of Spheroids in a Hierarchical Universe, 2013; 428, 1, https://doi.org/10.1093/mnras/sts001, pg. 109-128
9Gardner, J. The Space Science Reviews. The James Webb Space Telescope, 2006; Vol. 123, 4, 10.1007/s11214-006-8315-7, pg. 485-606