BoseEinstein Condensation of Dark Matter Axions

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Bose-Einstein Condensationof Dark Matter Axions

• Pierre Sikivie (U. of Florida)
• Center for Particle Astrophysics
• Fermilab, August 6, 2009

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The Dark Matter is Axions
Ill argue

• based on arXiv 0901.1106
• with Qiaoli Yang

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Outline

• Review of axion properties
• Cold dark matter axions form a
• Bose-Einstein condensate
• Axion BEC differs from ordinary CDM
• Compare CDM and axion BEC density perturbations
  with observations in three arenas
• 1. upon entering the horizon
• 2. in the linear regime within the horizon
• 3. in the non-linear regime

axion BEC
CDM
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The Strong CP Problem

• Because the strong interactions conserve P and
  CP, .

The Standard Model does not provide a reason
for to be so tiny, but a relatively small
modification of the model does provide a
reason
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If a symmetry is assumed,

• relaxes to zero,

and a light neutral pseudoscalar particle is
predicted the axion.
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f
f
a
a
0.97 in KSVZ model 0.36 in DFSZ model
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The remaining axion window

• laboratory
• searches

cosmology
stellar evolution
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There are two axion populations hot and cold.

• When the axion mass turns on, at QCD time,

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Axion production by vacuum realignment
V
V
a
a
initial misalignment angle
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Cold axion properties

• number density
• velocity dispersion
• phase space density

if decoupled
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The cold axions thermalize and therefore form a
BEC
a
a
a
a
but
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At high phase space density
scattering rate

• D. Semikoz
• and I. Tkachev,
• 1995, 1997

thermalization rate
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More generally, axion-like particles (ALPs) form
a BEC

• without relationship between and
• ALP oscillations start at
• ALP number density
• ALP velocity dispersion

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• ALP phase space density
• ALP self-coupling strength
• ALP scattering cross-section
• Hence ALP thermalization rate

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• A critical aspect of axion BEC phenomenology is
  whether the BEC continues to thermalize after it
  has formed.
• Axion BEC means that almost all axions go to one
  state.
• However, only if the BEC continually
  rethermalizes does the axion state track
• the lowest energy state.

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After the thermalization rate due to
self-interactions is

• at time

Self-interactions are insufficient to
rethermalize axion BEC after t1 even if they
cause axion BEC at t1.
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However, the thermalization rate due to
gravitational interactions

• at time

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Gravitational interactions thermalize the axions
and cause them to form a BEC when the photon
temperature

• After that

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axion BEC

• Except for a tiny fraction, all axions are in the
  same state

N is the number of axions
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• in a homogeneous and isotropic space-time.

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In Minkowski space-time

• Let
• then
• Let
• then

for non - relativistic motion
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• hence

stresses related to the Heisenberg
uncertainty principle tend to homogenize the
axion BEC
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• We have
• and
• with

To recover CDM, let m go to infinity
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In the linear regime, within the horizon,

• axion BEC density perturbations obey
• Jeans length

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• In the linear regime within the
• horizon, axion BEC and CDM are
• indistinguishable on all scales
• of observational interest,
• but
• axion BEC differs from CDM
• in the non-linear regime
• upon entering the horizon

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CMBmultipoles are aligned
quadrupole
octupole

• M. Tegmark,
• de Oliveira-Costa
• A. Hamilton, 2003

• C. Copi
• Huterer
• D. Schwarz
• G. Starkman, 2006

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Upon entering the horizon

• CDM density perturbations evolve linearly
• the density perturbations in the axion BEC
• evolve non-linearly because the axionBEC
• rethermalizes
• axion BEC provides a possible mechanism
  for
• the alignment of CMBR multipoles through
  the
• ISW effect.

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DM forms caustics in the non-linear regime
.
.
x
x
DM particles in phase space
x
x
x
x
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Phase space distribution of DM in a homogeneous
universe
.
z
z

for WIMPs
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The dark matter particles lie on a 3-dimensional
sheet in 6-dimensional phase space
.
z
the physical density is the projection of the
phase space sheet onto position space
z
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The cold dark matter particles lie on a
3-dimensional sheet in 6-dimensional phase space
.
z
the physical density is the projection of the
phase space sheet onto position space
z
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Phase space structure of spherically symmetric
halos
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(from Binney and Tremaines book)
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Phase space structure of spherically symmetric
halos
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Galactic halos have inner caustics as
well as outer caustics. If the initial
velocity field is dominated by net overall
rotation, the inner caustic is a tricusp
ring. If the initial velocity field is
irrotational, the inner

caustic has a tent-like structure.
(Arvind Natarajan and PS,
2005).
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simulations by Arvind Natarajan
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The caustic ring cross-section
D
-4
an elliptic umbilic catastrophe
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Galactic halos have inner caustics as
well as outer caustics. If the initial
velocity field is dominated by net overall
rotation, the inner caustic is a tricusp
ring. If the initial velocity field is
irrotational, the inner

caustic has a tent-like structure.
(Arvind Natarajan and PS,
2005).
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On the basis of the self-similar infall
model(Filmore and Goldreich, Bertschinger) with
angular momentum (Tkachev, Wang PS), the
caustic rings were predicted to be

• in the galactic plane
• with radii
• was expected for the
  Milky Way halo from the effect of angular
  momentum on the inner rotation curve.

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Effect of a caustic ring of dark matter upon the
galactic rotation curve
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Composite rotation curve(W. Kinney and PS,
astro-ph/9906049)

• combining data on
• 32 well measured
• extended external
• rotation curves
• scaled to our own galaxy

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Inner Galactic rotation curve
Inner Galactic rotation curve
from Massachusetts-Stony Brook North Galactic
Pane CO Survey (Clemens, 1985)
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Outer Galactic rotation curve
R.P. Olling and M.R. Merrifield, MNRAS 311 (2000)
361
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Monoceros Ring of stars

• H. Newberg et al. 2002 B. Yanny et al., 2003
  R.A. Ibata et al., 2003
• H.J. Rocha-Pinto et al, 2003 J.D. Crane et al.,
  2003 N.F. Martin et al., 2005
• in the Galactic plane
• at galactocentric distance
• appears circular, actually seen for
• scale height of order 1 kpc
• velocity dispersion of order 20 km/s
• may be caused by the n 2 caustic ring of
• dark matter (A. Natarajan and P.S. 07)

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from L. Duffy and PS, Phys. Rev. D78 (2008)
063508
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Tidal torque theory with CDM
neighboring protogalaxy

• The velocity field remains irrotational

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Tidal torque theory with axion BEC

• Net overall rotation is produced because, in the
  lowest energy state, all axions fall with the
  same angular momentum

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Summary

• axion BEC and CDM are indistinguishable in the
  
• linear regime inside the horizon on all scales
  of
• observational interest.
• axion BEC may provide a mechanism for net
• overall rotation in galactic halos.
• axion BEC may provide a mechanism for the
• alignment of CMBR multipoles.

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Implications

• At every point in physical space, the
  distribution of velocities is discrete, each
  velocity corresponding to a particular flow
• at that location .
• 2. At some locations in physical space, where
  the number of flows changes, there is a caustic,
  i.e. the density of dark matter is very high
  there.

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• the number of flows at our location in the Milky
  Way halo
• is of order 100
• small subhalos from hierarchical structure
  formation
• produce an effective velocity dispersion
• but do not destroy the sheet structure in
  phase space
• the known inhomogeneities in the distribution of
  matter are
• insufficient to diffuse the flows by
  gravitational scattering
• present N-body simulations do not have enough
  particles to
• resolve all the flows and caustics
• (see however Melott and Shandarin, Stiff
  and Widrow, Shirokov and Bertschinger,
• and more recently White and Vogelsberger,
  Diemand and Kuhlen.)

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Hierarchical clustering introduces effective
velocity dispersion
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The Big Flow

• density
• velocity
• velocity dispersion

previous estimates of the total local halo
density range from 0.5 to 0.75 10 gr/cm
-24
3
in the direction of galactic rotation
in the direction away from the galactic center
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Experimental implications

• for dark matter axion searches
• - peaks in the energy spectrum of microwave
  photons
• from conversion in the
  cavity detector
• - high resolution analysis of the signal yields
  a more sensitive search (L. Duffy and
  ADMX collab.)
• for dark matter WIMP searches
• - plateaux in the recoil energy spectrum from
  elastic WIMP collisions with target nuclei
• - the total flux is largest around December
• (Vergados Green Gelmini and Gondolo Ling,
  Wick PS)