Can you catch dark matter with a fish hook?

Title:  Hooks & Bends in the radial acceleration relation: discriminatory tests for dark matter and MOND

Authors: F. Mercado et al.

Authors’ Institution:  Pomona College and Caltech

Status: Published in Monthly Notices of the Royal Astronomical Society, Volume 530, Issue 2, pp.1349-1362 [open access]

One of the most persistent unknowns in modern astronomy is dark matter. This substance, while currently unidentified (though many theories are being tested), simply put is matter that does not interact with light. It is inferred from many different observational tests including gravitational lensing, velocity dispersion of stars within a galaxy, and the clustering of galaxies together, and much more. But the first evidence for dark matter came from observations of galactic rotation curves

A galaxy can be thought of like a merry-go-round (without the circus animals): it is a disk that rotates. Inside the disk are many billions of stars that all circle the center of the galaxy.  If we were to count up all the stars inside the disk of the galaxy and weigh their masses, we would get the total mass of the galaxy. Through this, we could measure the gravitational forces on a specific star to compute its velocity. Doing this for many stars at many different radial distances from the center of the galaxy, we can plot out a galactic rotation curve of velocity vs. radial distance from center. Under Newton’s theory of gravity, in a central mass dominated system, we would expect the more distant stars to be moving the slowest. This is what we see on the smaller scale of our solar system: planets closer to the sun move faster around the sun than the further out planets. 

Figure 1: Theory vs. Observations for a galaxy rotation curve. Image credit: Wikipedia 

But in galaxies, we see something surprising: the rotation curve doesn’t go down at large radial distances from the center. Instead, the curve is flat once we get sufficiently far from the super dense core, see Figure 1. That is to say, stars at very far distances are moving at the same speed as stars at medium distances. This would be like if Earth and Neptune moved around the sun at the same speed. It is counter intuitive! The way these rotation curves have been explained is that there must be more matter evenly spread throughout the galaxy to give the further out stars the boost in speed. Since we can’t see this matter because it doesn’t interact with light, we call it Dark Matter. Finding out exactly what dark matter is made up of is an active area of research.

All this said, there is an alternate theory to describe these rotation curves: Modified Newtonian Dynamics, or MOND. This theory essentially states that the force of gravity changes at very small accelerations, like those that are found out at the edges of these galaxies where the orbital velocity of a star is very small. Given that MOND is an alternative theory to that of Dark Matter, there is no dark matter substance within the MOND theory. Like any good scientific theory, both the MOND theory and the Dark Matter theory make predictions that are testable. In today’s paper summary, we detail a new paper that reports findings consistent with one theory and not the other. Let’s get into it!

Similar to the idea that the velocity of a star should be smaller at the edge of the galaxy, the radial acceleration of that star should also be smaller. This is because radial velocity and orbital velocity are related when the only force is that of gravity. Researchers have recently been calculating a new parameter: the Radial Acceleration Ratio (RAR), in which they compute the radial acceleration of a star in a galaxy using only the gravitational force of the baryons (regular matter) in the galaxy and divide by the radial acceleration of the same star if calculated using the gravitational force of all the matter in the galaxy. This helps calibrate if and how much the motion of the stars in the galaxy are deviating from what Isaac Newton’s Theory of Gravity tells us. Computing this RAR value for many stars at different radial distances in a galaxy, and repeating for many galaxies, the theory of MOND, which does not require dark matter, predicts a specific relationship: see the black line in Figure 2 that slopes from the bottom left to the top right of the plot. So if researchers make many measurements and they all fall on the black line, that would be evidence for MOND. 

To date, many such measurements have been made (see the gray points in Figure 2), and there seems to be tentative evidence for this relationship holding true. However, it is an extremely difficult measurement to make, with many sources of uncertainties, so the evidence is currently weak. Furthermore, it is only really possible to make these measurements for large, luminous galaxies; for smaller, fainter galaxies it is nearly impossible at this time. 

The authors of today’s paper approach this problem in a new dimension. Rather than trying to make these difficult observations for faint galaxies, they used simulated galaxies instead. The field of galaxy simulation has taken off in the last few years as computational power has grown and we now have the ability to create very detailed and high resolution simulations of whole galaxies. The authors used a suite of high-resolution galaxy simulations from the FIRE-2 collaboration (read more about the collaboration here), focusing on 20 simulated galaxies. Through these simulations, the researchers have a complete understanding of all of the stars and their velocities/accelerations allowing them to make precise “measurements”. More importantly, the simulations have the precise amounts of dark matter that the researchers can also “measure”. Then they can measure the RAR value with near certainty, and compare to real observations. 

Figure 2: The RAR plot. The black line shows the expected trend if MOND is correct. The gray dots represent real measurements. The rainbow dots represent measurements from the simulated galaxies in this paper. Large galaxies follow the expected trend but note that the smallest galaxies deviate from the trend and have hooks in their RAR tracks. This is inconsistent with MOND. This is Figure 2 in the paper.

It is particularly important to note that the simulations used follow the dark matter theory of galaxy formation; they do not follow the proposed physics of the MOND theory. So the authors were intrigued to see that in their simulations, many of the galaxies, particularly the most massive ones in their sample) follow the black curve in Figure 2, see rainbow dots at the top. This implies that the same relationship that MOND predicts can be replicated without MOND at all; the theory of dark matter gives the same observational results. 

But even more interesting, for the smallest, faintest galaxies in the simulations, the relationship that MOND predicts breaks down. Note the small “hooks” and “bends” in the rainbow points towards the bottom left of the plot which occur in the smallest, faintest galaxies in their sample. These curves are not predicted by MOND and in fact are evidence against MOND and in favor of dark matter.

So, at high-mass regimes, MOND can explain the RAR relationship and at low mass-regimes, MOND is untested. In this work, the dark-matter (note: not MOND) simulations also explain the RAR relationship at high-masses, but further predict that the relationship breaks down at the low-mass galaxy regime. This provides a perfect opportunity to directly test the two theories. This work motivates the need for observations of real, small and faint galaxies where these measurements have previously been difficult. These measurements may be difficult, but this paper points towards them being the difference between supporting or rejecting MOND and/or supporting or rejecting the theories that predict dark matter. 

The universe is still a place of many unknowns. Theory and observation are constantly working with and against each other as we try to unravel the mysteries of our universe. 

Astrobite edited by Sonja Panjkov

Featured Image Credit: Mercado et al. 2024

About Jack Lubin

Jack received his PhD in astrophysics from UC Irvine and is now a postdoc at UCLA. His research focuses on exoplanet detection and characterization, primarily using the Radial Velocity method. He enjoys communicating science and encourages everyone to be an observer of the world around them.

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