Video and Slides of a
recent colloquium talk "The Curvature of the Universe: From
Gauss-Bonnet to Black Holes and Dark Matter," summarizing some of
Professor Bray's research.
This article
has some pretty pictures showing Professor Bray's simulations of spiral galaxies
based on his wave dark matter theory.
Below, Professor Hubert Bray gives a 90 second summary of his
research on wave dark matter, his idea for a geometric model for dark
matter, after his presentation at the Journal of Differential Geometry
Conference in May 2013.
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 presentationon
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.
Abstract:
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.
Videos:
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.
Abstract:
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: shells.m
Abstract:
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).
Abstract:
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.
Abstract:
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.
Abstract: 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
bray@math.duke.edu
