What actually is cold dark matter?

There are different ways to demonstrate the structure of metallic atoms. The most straightforward way is to study them one by one - for example via measuring the scattering processes of different nuclei, which requires pumping huge amounts of energy into the nuclei. Alternatively, without the access to energy-feeding technologies, metallic atoms can be studied by considering the collection of them in the form of lattice, so that the band structures of metallic materials can be studied. This significantly lowers down the energy required to manifest their properties.

Similarly, the mysterious dark matter can be studied via their collective behaviour. When a large number of dark matter are self-bounded by gravity, achieving a state where a (pseudo)-equilibrium can be defined, the structure of this macroscopic system of dark matter would reflect the per-particle level interaction among dark matter. These macroscopic systems occupied by a huge amount of dark matter are readily available in our universe: dark matter haloes.

An obvious way to study the structures of dark matter haloes is to trace the trajectories of stars residing within the haloes. Of particular importance, the influence of the non-gravity interaction among stars (via various stellar feedback processes) need to be minimised, so as to isolate and highlight the effect of the dark matter haloes. I am now developing software to study dark matter haloes in dynamical equilibrium - that the structure of the dark matter halo is slowly varying in a periodic way.

A crucial task for studying dark matter is to distinguish between the effect of baryons with the gravitational effect of dark matter. Gravitational lensing - tracing only the gravitational field, is considered one of the cleanest probes. Most lensing analysis is based on parametric forward modelling - that a presumed gravitational field is compared against the observed data, making it heavily prior dependent. While this approach is adequate to study the smooth, coarse-grained profile of the dark matter halo, higher order effects that require combinatorially more parameters - such as sub-haloes, are often under-constrained in parametric methods.

I am trying to pioneer non-parametric methods for lensing analysis, with the aim of uncovering the dark matter substructures within dark matter haloes. Non-parametric approaches in general make use of some model-independent, generalizable assumptions to highlight some hidden features in the lens. Being generalizable, such effects are often features of the lens equation itself rather than the lens potential.

Recently, I re-discover a topological property of the lens equation that has been studied by applied mathematicians for decades, but is largely ignored by cosmologists. This is based on the fact that the coarse-grained, flux magnification profile of a gravitational lens is highly related to the number of parity flips in the lens potential. I propose an one-of-the-kind, model-independent algorithm that directly constrains the number of sub-galactic scale parity flips using pairs of strong lensing arcs.

The algorithm is validated by a customised ray-tracing simulation that I developed. With my collaborators, we have applied the algorithm in the first cluster lens field in JWST’s first data release to demonstrate the practical aspect of the algorithm. We are now exploring the systematics involved in the deployment of such method to the foreseen cluster lenses data releases from JWST.

• Paper (Coming Soon)

Within the inflationary paradigm, structures in the universe are grown from primordial fluctuations. The gravitational attraction amplifies the primordial fluctuations, so that fluctuations eventually collapse into dark matter haloes. The growth of these fluctuations are in the (pseudo-) linear regime, in contrast to the fully nonlinear regime of virialization within dark matter haloes. The apparent simplicity of the linear regime makes it one of the most important constraints on the properties of dark matter via the linear evolutionary process.

In one of my work, I have demonstrated that species of dark matter (if more than one) would be scale-segregated during the linear growth process. Intuitively, the free streaming velocity for lower mass dark matter would be higher than the halo escape velocity defined by the heavier dark matter species, and thus refusing to collapse onto the dark matter halo. In the left panel, I showed a species of ultra-light axion (with its relative abundance denoted as “x” in the plot) would require more time to be captured by dark matter haloes, and thus suppress the linear matter power spectrum. This suppression is what is required to reconcile the S8 tension.

• Paper