UR: The Atomic Dark Matter Model: A Possible Solution to the Shortcomings of CDM

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John Blakely

This post was written by John Blakely, a first year student at Penn State majoring in physics and astronomy. John’s interests include cosmology, and the particle physics of the early universe and its effect on the formation of structures, like black holes and galaxies. In his spare time, he likes to read, do puzzles, and go hiking.

Astrobite edited by Jenny Calahan

A significant amount of modern cosmological research has been in the pursuit of understanding dark matter. Dark matter (DM) has long been assumed as the solution to the “missing mass” problem, originating from astrophysicist Fritz Zwicky’s 1933 observations of the Coma Cluster. This so-called “dark matter” would not emit any light, or interact with light, but would contain most of the mass of the galaxy cluster. Zwicky discovered that the galaxies in the Coma Cluster were moving too fast to be held together by the gravity of the visible matter in the cluster. Since then, many observations have been made, at a wide range of scales, which all point to the existence of dark matter. Despite this, the physics of the dark matter is still largely not known. A model of dark matter that is able to connect observed data with our understanding of physics is sought after. Though there have been many attempts, none have been able to successfully do this completely. 

The Cold Dark Matter Model: Our Best Guess So Far

The most popular model held is the Cold Dark Matter paradigm (CDM). CDM provides a satisfyingly simple answer to the “missing mass” in our observations, stating that there is a cold, dark matter component of the universe. Cold means that it is not energetic and is nonrelativistic, and dark means that it only interacts with itself, and baryonic matter, via gravity. However, the scenario, which CDM creates, provides predictions which are in tension with our observations, specifically on smaller scales. A solution to this can either be in the form of a new understanding of the interactions between CDM and the Standard Model, or a new dark matter model which maintains the successes of CDM, but succeeds where CDM fails. A model which could fulfill this is the Atomic Dark Matter Model.

The Atomic Dark Matter Model: A Possible Solution to the Shortcomings of CDM

The atomic dark matter model (ADM) consists of a type of matter  quite similar to Standard Model atomic and molecular hydrogen. ADM consists of a dark “electron” and “proton” of masses mL and mH, respectively, which interact via a massless dark “photon” at a strength governed by a dark fine structure constant, ɑD. With the model still in its youth, much of the current research in ADM is purposed to whittling down the possible values of mH, mL, and ɑD by restricting them according to our observations and previous theories. In this article we introduce the beginning of how these parameters could be restricted by gravitational wave data.

In ADM, the dark matter particles are able to form atomic and molecular bound states, analogous to baryonic or ‘regular’ hydrogen, and radiate away some of their initial energy in the form of a dark photon, as well as break these bound states and radiate away energy. This is particularly interesting because the dark halos in ADM, unlike in CDM, can dissipate energy and cool, allowing for some to collapse and form dark compact structures, solving some of CDM’s problems. It’s useful to know which dark halos are able to collapse and form compact structures, like black holes, because it allows us to use gravitational wave data to validate the model and restrict the possible parameter values.

Which Dark Halos Can Collapse?

To determine whether a dark halo can collapse, we have to see whether the halo will radiate away the energy it needs to support itself fast enough. To determine this we need to compare the time it takes to collapse under its own gravity to the time it takes to dissipate all of its energy. The free-fall time only depends on the mass density of the halo, but the cooling time depends on the evolution of the number of free and bound dark particles as well as how quickly it can remove its energy. To get the number of free and bound dark particles, we will use what’s known as the ionization fraction, which is just the ratio of how quickly bound states are broken to how quickly they are formed. Once we have this we can compute the volumetric cooling rate, we can get the time it takes to radiate away all of the halos energy. If the halo cools faster than a free-fall time it will collapse, if not then it will remain in hydrostatic equilibrium. This comparison was calculated by Matthew R. Buckley in 2017, and in Figure 1 the solid colored regions show the dark halo masses that can collapse as a function of dark electron mass, mL

However, determining whether or not a halo will collapse relies on the dark halo remaining in equilibrium between the rate it forms dark bound states and the rate at which they are broken, but for certain assumptions about the ADM particles this doesn’t hold. If the dark halo violates equilibrium, it doesn’t mean that it won’t collapse, just that it can’t be determined with an ionization fraction dependent on equilibrium.  

To determine the dark halo masses which violate equilibrium over the ADM parameter space as a function of the mass of the dark electron, we have to compare the time it takes for the dark halo to fully ionize versus the time it takes to cool completely. This results in a region of uncertainty in the results of Matthew R. Buckley in 2017, shown in Figure 1 as the hatched regions. Dark halos that fall in these regions will require to be reanalyzed using an ionization fraction that does not rely on equilibrium. 

With this region of indeterminacy defined, finding a simple expression for an ionization fraction which can account for out-of-equilibrium cooling will be much easier. Ultimately, this simpler expression will make tracking the evolution of ADM dark matter much less rigorous and would provide a useful insight into the dynamics of structure formation in the atomic dark sector.

Special thanks to the STAR undergraduate research program at Penn State for facilitating this project, as well as to James Gurian for advising and teaching the cosmology, physics, and general skills needed for this research.

Figure 1: The solid regions are the results of Matthew R. Buckley in 2017, showing the masses of dark halos that can collapse in collisional ionization equilibrium as a function of dark electron mass (mL), whereas the hatched regions show the halo masses that violate equilibrium as a function of mL. The red and blue regions correspond to a ɑD value of 10-1 and 10-2 respectively.

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