Paper title: Dwarf galaxies imply dark matter is heavier than \(2.2 \times 10^{-21} \mathrm{eV}\)
Authors: Tim Zimmermann, James Alvey, David J. E. Marsh, Malcolm Fairbairn, and Justin I. Read
First Author’s Institution: Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, Oslo, Norway
Status: Published in Physical Review Letters [closed access]
Scientists have known for over 80 years that the universe has a dark side. There’s a lot of “invisible” matter that doesn’t emit light but still interacts via gravitational forces—pulling on visible matter like stars, galaxies, and even light itself. We call this dark matter. There is an overwhelming amount of evidence to justify the existence of dark matter. In short, astronomers know dark matter is real because:
- Galaxies spin in a way that requires they have more mass than we can see in them through their stars
- The cosmic microwave background shows us the early universe required extra mass to look the way it does now.
- (and many more)
Even though we have tons of indirect evidence, we have yet to understand what dark matter actually is. One idea is that dark matter is made of a new, unfound particle not currently included in the standard model of particle physics. An important attribute of such a particle is its mass: is it heavy, like a black hole? Or lighter than a neutrino?
Today’s paper asks a simple question: if dark matter is made of particles, what’s the smallest possible mass those particles could have? To figure this out, the authors look at small galaxies near the Milky Way called dwarf spheroidal galaxies. These galaxies have a huge mass-to-light ratio, implying that they are almost entirely made from dark matter.
If dark matter is made of fermions (particles like electrons that can’t be in the same place doing the same thing—thanks to the Pauli exclusion principle), you can only pack so many of them into a space. So, if a dwarf galaxy has a specific size and mass, and you try to fit too many light fermions into it, it won’t work—they’d push each other out. Using this idea, scientists figured out that a fermion dark matter particle must be heavier than about 120 electron volts (eV).
But! If dark matter is made of bosons (like photons), this limit doesn’t apply—bosons can share the same space, so you’d have to use different physics to determine their mass limits. Instead of the exclusion principle, we need to use the uncertainty principle. It says that the more precisely you know a particle’s position, the less precisely you can know its momentum (and vice versa).
\(m\sigma_v \sigma_r \geq 3/2 \times \hbar\)
Where:
- m is the mass of the boson,
- \(\sigma_v\) is how fast the particles are moving around (velocity dispersion),
- \(\sigma_m\) is how spread out the particles are in space,
- \(\hbar\) is a fundamental constant in quantum mechanics (reduced Planck constant).
So, if you know how fast the object moves and how much space it is confined to, you can estimate its mass.
They use a small galaxy called Leo II, a dwarf spheroidal galaxy orbiting the Milky Way. It has a virial radius of about 9,000 light-years, and stars (and, therefore, the dark matter) move around at about 15 km/s. Using these numbers in the uncertainty principle formula, they find an incredibly tiny mass — trillions of times lighter than even a neutrino!
However, the authors want to push for a more robust measure.
Step 1: Build galaxy models
They used real data from Leo II — how its stars move and how mass is distributed — to create 5,000 different models of what dark matter could look like in that galaxy. Each model gives a gravitational potential and dark matter density.
Step 2: Reconstruct wave functions
They then treat dark matter like a quantum wave (like in the Schrödinger equation!) and build wave functions that fit each model galaxy.
Then, they test if this wave-like dark matter matches what we see in Leo II. In doing so, they find a much stronger mass limit: m \(> 2.2 \times 10^{-21} \mathrm{eV}\). This means if dark matter is made of wave-like bosons, the particles must be heavier than \(2.2 \times 10^{-21} \mathrm{eV}\), or they wouldn’t be able to form galaxies like Leo II.
Previous limits on the mass of bosonic dark matter have depended on complex astrophysical processes—from gas dynamics to assumptions about the thermal history of the Universe—making them less robust. In contrast, the new limit is derived from first principles, relying only on stellar kinematics and quantum mechanics, making it a cleaner, more universal constraint on bosonic dark matter.
This methodology opens the door to even more sophisticated analyses. In the future, the authors suggest their framework could be extended to mixed dark matter scenarios, where ultra-light bosons make up only a fraction of the total dark matter, with the rest being cold dark matter (CDM). This could lead to competitive constraints on mixed models and potentially probe high-energy physics even deeper.
Astrobite edited by Catherine Slaughter
Featured image credit: Leo II, NASA, ESA, A. del Pino Molina (CEFCA), K. Gilbert and R. van der Marel (STScI), A. Cole (University of Tasmania)
