By Harry Desmond
The acronym ΛCDM (Lambda-cold dark matter) is shorthand for our current best cosmological model describing the early beginnings, evolution until now, and future development of our entire Universe. It posits a cosmos dominated by a cosmological constant (denoted by Λ, the Greek letter capital lambda) our best guess for the phenomenon of dark energy, and a type of slow-moving, non-interactive matter called cold dark matter that outweighs the ordinary matter making up stars and planets—and us—by more than five to one. ΛCDM does well enough explaining the majority of our astrophysical observations that it is the standard paradigm for most people working in the field.
But asking a pithy acronym like ΛCDM to cover all the fine points from the earliest instants of our Universe all the way until now is asking too much. There may be a consensus that concentrations of dark matter, called haloes, guide the growth and development of galaxies, but that’s far from the entire picture. How does the ratio of dark matter to normal matter affect a galaxy’s evolution? What are the density and dynamics of dark matter in a halo? Do they vary, and if so, how? Is there an actual structure to the dark matter itself? And the most basic, and thus most important, of questions: can dark matter—as we conceive of it—fully explain the Universe we see when we look up into the night sky?
These are not easy questions to answer, but with improvements in observational and analytical techniques we are beginning to get a detailed enough look at individual galaxies to begin to address them. Partly since we have not directly detected dark matter, we have to compare our models to increasingly detailed observations, revising the description as necessary.
The detailed view we need is provided by observational studies such as the Spitzer Photometry and Accurate Rotation Curves (SPARC) study. SPARC comprises a total of 175 nearby galaxies, including detailed photometric measurements from NASA’s Spitzer Space Telescope (which track stellar mass) and high-quality rotation curves for HI and Hα regions (which track hydrogen gas). This gives an unprecedented view of both the total amount of normal matter and how that matter is moving as a function of distance from the center of a galaxy—and hence the distribution of the dark matter largely responsible for determining this motion.
This image shows the rotation curve of M33, a typical spiral galaxy, plotting the orbital velocity of stars and gas at a given radius from the center of the galaxy. The white dotted line shows the expected orbital behavior of M33’s stars, based solely on adding up the gravity of the visible mass using Newton’s laws. After reaching a maximum velocity at around 10,000 light years from the galaxy’s center, the velocities of orbiting stars should begin to taper off. As shown by the upper line, which is from the actual data, that’s not what happens. This ubiquitous behavior of spiral galaxies was one of the earliest motivations for positing the existence of dark matter. (Public domain image.)
The data from SPARC allow us to improve upon two well-known relations that have historically been very useful in galaxy studies: the Faber-Jackson relation, which correlates the total luminosity of an elliptical galaxy with the velocity dispersion of its central stars, and the Tully-Fisher relation, which is a similar relation for spiral galaxies.
These canonical relations only include one data point per galaxy. However, the SPARC study, with its improved resolution, contains around 20 data points per galaxy, providing a much clearer picture against which we can compare our dark matter-driven description of galaxy formation.
To make that comparison, I derived a set of statistics from about 150 SPARC galaxies (resulting in a study published in Monthly Notices of the Royal Astronomical Society (MNRAS) in November 2016). These statistics quantified some important features of the mass discrepancy-acceleration relation (MDAR), a surprisingly strong relation between the ratio of total-to-normal matter in a galaxy (the mass discrepancy) and the acceleration of the stars and gas within that galaxy at different radii throughout the disk. This correlation is tight and regular, and persists for a variety of different galaxy types. I focused on three characteristics of the MDAR:
- The mean shape of the relation
- The scatter, or variance, among the data points (how far from the mean they fall)
- The presence of a “characteristic acceleration,” beyond which the mass discrepancy goes to one and hence dark matter is dynamically insignificant.
Next, I simulated dark matter halos and populated them with galaxies using halo abundance matching techniques pioneered by KIPAC professor Risa Wechsler and her colleagues. Stated simply, this technique relates a galaxy’s mass to the mass of the dark matter halo in which it forms (see the references, below, for links to other relevant papers of mine with Risa). After this, I compared the galaxies I had built to the statistics derived from the SPARC data. In essence, I built galaxies based on the rules of ΛCDM and then compared them to the real things.
The results were mixed.
This figure compares the mean MDAR for the SPARC data (black line) to the MDARs of three sets of simulated galaxies (blue, green, and red lines), where the simulation parameters have been varied in physically realistic ways (see 3.1 in the paper for details). The x-axis shows acceleration and the y-axis shows mass discrepancy. The shaded areas outside the colored lines reflect the scatter in the models. Note how all lines are roughly similar, but the mock MDARs deviate from the data at low acceleration. (Credit: Fig. 3(a) from “A statistical investigation of the mass discrepancy-acceleration relation,” H. Desmond.)
The matter in the simulated galaxies approximated the behavior of the MDAR—but we are reaching the level of detail in our data where “approximated” is not good enough. While I could bring the mock galaxies into greater agreement with the SPARC data by fine-tuning the abundance matching methods, puzzling discrepancies remained (and really, fine-tuning, or adjusting parameters without solid evidence for why they must be adjusted, is never really anything we want to do in physics).
For example, even under conservative assumptions, the models could not reproduce the impressive tightness of the MDAR. The simulated galaxies varied more widely than those in the SPARC data. Furthermore, the mass discrepancies were predicted to be too high at low acceleration, and on average the models put dark matter too close to galaxies' centers. The exact cause of these problems is unknown: do they require our theories to be tweaked, or overhauled? Only further investigation will tell. What we can say for sure is that the mass discrepancy-acceleration relation is there, and any model of galaxy formation must explain it—whichever of our ideas that requires us to call into question. Including the provocative possibility that our theory of gravitation itself (Einsteinian General Relativity) needs to be modified or extended on galactic scales.
This figure compares the distributions of the scatter in the MDAR for various model assumptions (shown by the blue, green, and red areas; these are the same simulated data sets as in the figure above) compared to the scatter in the data (black line). The model in red—a standard abundance matching model commonly used in the field—predicts too high a scatter; only by supposing that galaxies form in a narrow subset of possible halos (model in blue) can this scatter be reduced to acceptable levels. (Credit: Fig. 4 from “A statistical investigation of the mass discrepancy-acceleration relation,” H. Desmond.)
As our view of the galaxies with which we share this Universe improves, we can continue to use statistical tests such as the ones I have described to paint a cosmic portrait that is not only breathtaking in its vision, but also in impressively accurate agreement with the details.
A statistical investigation of the mass discrepancy-acceleration relation, H. Desmond (2016)
The Faber-Jackson relation and Fundamental Plane from halo abundance matching, H. Desmond & R. H. Wechsler (2016)
The Tully-Fisher and mass-size relations from halo abundance matching, H. Desmond & R. H. Wechsler (2015)
Related posts from the KIPAC blog
Using Gravitational Lensing to Hunt for Hidden Knots of Dark Matter (October 19, 2016)
Let there be light upon the dark: digging deeper for dark matter with LUX (January 30, 2015)