Ultralight Dark Matter

By You-Rong F. Wang

Ultralight Dark Matter (ULDM), also called “Fuzzy” Dark Matter, is a class of hypothetical dark matter candidates in cosmology. It postulates that very-low-mass particles (so-called ultralight axions) from beyond the Standard Model are responsible for some observed large-scale structures of the universe but remain elusive at lab-accessible scales of physics.

Due to the axions’ low mass, ULDM behaves almost entirely according to the laws of quantum mechanics. With a typical de Broglie wavelength at the order of kiloparsecs, i.e. tens of quadrillions of kilometres, ULDM can give rise to a range of galactic-scale phenomena analogous to what you might only associate with a microscopic particle (of course, the effects are mediated here by gravity instead), such as superposition, interference and tunnelling. Therefore, ULDM is poised to leave behind unique signatures in a range of astrophysical systems, from stellar rotational curves in core regions of galaxies to the origin of certain gravitational wave events.

The dynamics of ultralight axions may be described collectively as a single wavefunction evolving according to modified Schrödinger Equations. In the simplest of ULDM models, one takes into consideration the gravitational potential generated by the wavefunction itself. This modification, known as the Schrödinger-Poisson equation, introduces nonlinearity to our system of partial differential equations. In addition, there also exist more exotic models that hypothesise complex self-interaction terms beyond just gravity, requiring even more sophisticated numerical techniques to simulate and understand.

As my first project during my PhD at Auckland Cosmology under Prof. Richard Easther, I am working on such numerical simulations, developing a scheme through which we can study the influence that Ultralight Dark Matter (ULDM) has on N-body particle systems. This effort offers us an opportunity to test the validity of ULDM theories and is relevant for our understanding of, for example, the interaction between supermassive black holes during galaxy mergers.

The figure shows a massive point particle’s motion into a ULDM halo. The colour represents ULDM density in a plane, and the quantum “fuzziness” is evident as the mass reaches the core. This simulation is achieved using Auckland Cosmology’s PyUltraLight2 simulation program, and a paper with detailed discussions of such interaction models is currently in preparation.

Further Reading

[1] John Preskill, Mark B. Wise, and Frank Wilczek. Cosmology of the Invisible Axion. Phys. Lett. B 120:127–132, 1983.

[2] Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, and Edward Witten. Ultralight scalars as cosmological dark matter. Phys. Rev. D, 95(4), 2017.

[3] Faber Edwards, Emily Kendall, Shaun Hotchkiss, and Richard Easther. PyUltraLight: A pseudo-

spectral solver for ultralight dark matter dynamics. J. Cosmol. Astropart. Phys., 2018(10), 2018.

[4] Elisa G. M. Ferreira. Ultra-Light Dark Matter. 2020. https://arxiv.org/abs/2005.03254