Bose-Einstein Condensation of Dark Matter Axions Pierre Sikivie (U. of Florida) Center for Particle Astrophysics Fermilab, August 6, 2009

The Dark Matter is Axions based on arXiv: with Qiaoli Yang I’ll argue:

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 CDM axion BEC

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 …

If a symmetry is assumed, relaxes to zero, and a light neutral pseudoscalar particle is predicted: the axion.

ff a a = 0.97 in KSVZ model 0.36 in DFSZ model

The remaining axion window laboratory searches stellar evolution cosmology

There are two axion populations: hot and cold. When the axion mass turns on, at QCD time,

Axion production by vacuum realignment V a V a initial misalignment angle

Cold axion properties number density velocity dispersion phase space density if decoupled

The cold axions thermalize and therefore form a BEC a aa a but …

At high phase space density D. Semikoz and I. Tkachev, 1995, 1997 scattering rate thermalization rate

More generally, axion-like particles (ALPs) form a BEC without relationship between and ALP oscillations start at ALP number density ALP velocity dispersion

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

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.

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.

However, the thermalization rate due to gravitational interactions at time

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

axion BEC Except for a tiny fraction, all axions are in the same state N is the number of axions

in a homogeneous and isotropic space-time.

In Minkowski space-time Let then Let then for non - relativistic motion

hence stresses related to the Heisenberg uncertainty principle tend to homogenize the axion BEC

We have and with To recover CDM, let m go to infinity

In the linear regime, within the horizon, axion BEC density perturbations obey Jeans’ length

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

CMB multipoles are aligned quadrupole: octupole: M. Tegmark, A.de Oliveira-Costa A. Hamilton, 2003 C. Copi D.Huterer D. Schwarz G. Starkman, 2006

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.

x x. DM particles in phase space DM forms caustics in the non-linear regime x x x. x

Phase space distribution of DM in a homogeneous universe z z. for WIMPs

The dark matter particles lie on a 3-dimensional sheet in 6-dimensional phase space the physical density is the projection of the phase space sheet onto position space z z.

The cold dark matter particles lie on a 3-dimensional sheet in 6-dimensional phase space the physical density is the projection of the phase space sheet onto position space z z.

Phase space structure of spherically symmetric halos

(from Binney and Tremaine’s book)

Phase space structure of spherically symmetric halos

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).

simulations by Arvind Natarajan

The caustic ring cross-section an elliptic umbilic catastrophe D -4

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).

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.

Effect of a caustic ring of dark matter upon the galactic rotation curve

Composite rotation curve (W. Kinney and PS, astro-ph/ ) combining data on 32 well measured extended external rotation curves scaled to our own galaxy

Inner Galactic rotation curve from Massachusetts-Stony Brook North Galactic Pane CO Survey (Clemens, 1985)

Outer Galactic rotation curve R.P. Olling and M.R. Merrifield, MNRAS 311 (2000) 361

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)

from L. Duffy and PS, Phys. Rev. D78 (2008)

Tidal torque theory with CDM The velocity field remains irrotational neighboring protogalaxy

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

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.

Implications: 1.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.

-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.)

Hierarchical clustering introduces effective velocity dispersion

The Big Flow density velocity velocity dispersion previous estimates of the total local halo density range from 0.5 to gr/cm in the direction of galactic rotation in the direction away from the galactic center

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)