Professor H. L. Bray
                Dark Matter, invisible and mysterious, but accounts for most of the gravity within galaxies

The idea that dark matter may be fundamentally wave-like has been steadily gaining in popularity for decades, most prominently exemplified by the October 2016 paper by Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, and Edward Witten.

Physicists refer to this idea as "fuzzy dark matter," "scalar field dark matter," "Bose-Einstein condensate dark matter," "ultra-light bosonic dark matter," and "wave dark matter." Professor Bray's contributions to this idea include:

1) A geometric motivation for wave dark matter, coming from a geometrically natural tweaking of the axioms of general relativity
2) A demostration that spiral patterns in galaxies can be induced by the gravity of wave dark matter

In other words, one of the most geometrically natural ways to tweak the axioms of general relativity may explain not only dark matter, but also spiral patterns in galaxies.

Here are three more reasons to take wave dark matter seriously:

1) Given the wave-particle duality of matter, does dark matter act like a wave or a particle? If it acts like a wave, this is wave dark matter.

2) Is dark matter a fermion or a boson? If it is a boson, and it is ultra-light, then this is wave dark matter.

3) Currently, there are two reigning theories of physics, the standard model of particle physics as defined by quantum field theory (which is unmatched in its description of the universe on small scales) and general relativity (which is unmatched in its description of the universe on large scales). Until a theory of everything is found, we must also consider the possibility that dark matter is most natural from the geometric point of view implied by general relativity. If dark matter is a geometric phenomenon, then Professor Bray's work explains how this would predict wave dark matter.

The papers below discuss these ideas in detail, as well as further ideas by two of Professor Bray's former students, Alan Parry (on dwarf spheroidal galaxies) and Andrew Geotz (on the Tully-Fisher relation for spiral galaxies with exponent 3.4 - which is consistent with observations - that results by fixing the density of the outer edge of all wave dark matter halos to a universal constant).

May 2016 Presentation:
Professor Bray's latest presentation on how wave dark matter, which has both geometric and particle physics motivations, could explain the phenomenon of dark matter, as well as spiral patterns in galaxies.

Paper #1:
``On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity,'' H. Bray, April 22, 2010.

Beginning with a geometric motivation for dark matter going back to the axioms of general relativity, we show how scalar field dark matter, which naturally forms dark matter density waves due to its wave nature, may cause the observed barred spiral pattern density waves in many disk galaxies and triaxial shapes with plausible brightness profiles in many elliptical galaxies. If correct, this would provide a unified explanation for spirals and bars in spiral galaxies and for the brightness profiles of elliptical galaxies. We compare the results of preliminary computer simulations with photos of actual galaxies.

Click here for the video of a lecture with a description of the above paper plus more recent ideas.  This talk, entitled "On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity" was given at the 41st Barrett Memorial Lectures in Mathematical Relativity at the University of Tennessee, Knoxville on May 12, 2011.  A similar talk was also given at the 26th Annual Geometry Festival at the University of Pennsylvania on April 15, 2011.  The pdf slide show is here.

Click here for the video of a lecture entitled "Dark Matter in Galaxies" that Andriy Badin and I gave at Duke University as part of Dark Matter Awareness Week on December 6, 2010.  The last 25 minutes gives an overview of the above paper.

Spiral Galaxy Simulation using Matlab:

Elliptical Galaxy Simulation using Matlab:


Paper #2:
``On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity,'' H. Bray, December 22, 2012.

This paper is a sequel to the paper listed above.  We give an update on where things stand on this ``wave dark matter'' model of dark matter (aka scalar field dark matter and boson stars), an interesting alternative to the WIMP model of dark matter, and discuss how it has the potential to help explain the long-observed interleaved shell patterns, also known as ripples, in the images of elliptical galaxies.

Shells in Elliptical Galaxies Visualization using Matlab:

Paper #3
``Modeling Wave Dark Matter in Dwarf Spheroidal Galaxies," H. Bray and A. Parry, January 2013.

We compare the mass profiles of spherically symmetric static states of wave dark matter to the Burkert mass profiles that have been shown by Salucci et. al. to predict well the velocity dispersion profiles of the eight classical dwarf spheroidal galaxies.  We show that a reasonable working value for the fundamental constant Upsilon in the wave dark matter model is 50 years^(-1).  We also show that under precise assumptions the value of Upsilon can be bounded above by 1000 years^(-1). 

Matlab code used in this paper, zipped with readme.txt file included:
Modeling WDM in Dsph

Paper #3 is based in part on:

Paper #4
``Spherically Symmetric Static States of Wave Dark Matter,'' A. Parry, December 2012.

Paper #5
``Wave Dark Matter and the Tully-Fisher Relation,'' H. Bray and A. Goetz, September 2014.

We investigate a theory of dark matter called wave dark matter, also known as scalar field dark matter (SFDM) and boson star dark matter or Bose-Einstein condensate (BEC) dark matter, in spherical symmetry and its relation to the Tully-Fisher relation. We show that fixing the oscillation frequency of wave dark matter near the edge of dark galactic halos implies a Tully-Fisher-like relation for those halos. We then describe how this boundary condition, which is roughly equivalent to fixing the half-length of the exponentially decaying tail of each galactic halo mass profile, may yield testable predictions for this theory of dark matter.

Paper #5 pairs naturally with:

Paper #6
``Tully-Fisher Scalings and Boundary Conditions for Wave Dark Matter,'' A. Goetz, February 2015.

We investigate a theory of dark matter called wave dark matter, also known as scalar field dark matter (SFDM) and boson star dark matter or Bose-Einstein condensate (BEC) dark matter (also see axion dark matter), and its relation to the Tully-Fisher relation. We exhibit two boundary conditions that give rise to Tully-Fisher-like relations for spherically symmetric static wave dark matter halos: (BC1) Fixing a length scale at the outer edge of wave dark matter halos gives rise to a Tully-Fisher-like relation of the form M/(v^4) = constant. (BC2) Fixing the density of dark matter at the outer edge of wave dark matter halos gives rise to a Tully-Fisher-like relation of the form M/(v^3.4)=const.

Paper #7
``On wave dark matter in spiral and barred galaxies,'' L. A. Martinez-Medina, Hubert L. Bray, Tonatiuh Matos, December 2015.

We recover spiral and barred spiral patterns in disk galaxy simulations with a Wave Dark Matter (WDM) background (also known as Scalar Field Dark Matter (SFDM), Ultra-Light Axion (ULA) dark matter, and Bose-Einstein Condensate (BEC) dark matter). Here we show how the interaction between a baryonic disk and its Dark Matter Halo triggers the formation of spiral structures when the halo is allowed to have a triaxial shape and angular momentum. This is a more realistic picture within the WDM model since a non-spherical rotating halo seems to be more natural. By performing hydrodynamic simulations, along with earlier test particles simulations, we demonstrate another important way in which wave dark matter is consistent with observations. The common existence of bars in these simulations is particularly noteworthy. This may have consequences when trying to obtain information about the dark matter distribution in a galaxy, the mere presence of spiral arms or a bar usually indicates that baryonic matter dominates the central region and therefore observations, like rotation curves, may not tell us what the DM distribution is at the halo center. But here we show that spiral arms and bars can develop in DM dominated galaxies with a central density core without supposing its origin on mechanisms intrinsic to the baryonic matter.

Right click on the above file links to download the files.  The .m files can be run using Matlab.  As some of these .m files create many image files, we suggest creating a new directory for each run and placing a copy of the .m file in that directory.  Then change to that directory inside Matlab and execute the command line.  If you open the .m files in the Matlab editor, example command lines are usually listed.  There are also example command lines in some of the papers listed above as well.

Have fun!

Hubert L. Bray
Mathematics and Physics Departments
Duke University, Box 90320
Durham, NC  27708  USA

For a complete list of publications, grants, awards, and professional activities, visit Professor Bray's Duke University web page or view this computer generated curriculum vitae.