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An argument that the dark matter is axions
Pierre Sikivie
Center for Particle Astrophysics
Fermilab, March 17, 2014
Collaborators: Ozgur Erken, Heywood Tam, Qiaoli Yang
Nilanjan Banik
Outline
1. Cold dark matter axions thermalize and form a Bose-Einstein condensate.
2. The axion BEC rethermalizes sufficiently fast that axions about to fall onto a galactic halo almost all go to the lowest energy state for given total angular momentum.
3. As a result the axions produce - caustic rings of dark matter - in the galactic plane - with radii
4. There is observational evidence for the existence of caustic rings of dark matter - in the galactic plane - with radii - with overall size consistent with tidal torque theory
5. The evidence for caustic rings is not explained if the dark matter is entirely in some other form. Ordinary cold dark matter (WIMPs, sterile neutrinos, non-rethermalizing BEC, …) forms tent-like inner caustics.
The remaining axion window
laboratory searches
510 15101010 (GeV)af
(eV)am 1 510 1010
stellar evolution
cosmology
There are two cosmic axion populations: hot and cold.
When the axion mass turns on, at QCD time,
1T
1t
1 1 GeVT 9
11
1) 3 10 eV(ap t
t
71 2 10 sect
Axion production by vacuum realignment
2 2 21 1 1 1
1
1
2
1
2( ) ( ) ( ) ( )a a at t t t
tn m a f
GeVT GeVT
V
a
V
a
1
0
3 7
60 1( ) ( )a aa a
R
Rt tm mn
initialmisalignmentangle
J. Preskill, F. Wilczek + M.Wise; L. Abbott + P.S.; M. Dine + W. Fischler 1983
Cold axion properties
• number density
• velocity dispersion
• phase space density
5 347 31
3 12
( )4 10( )
cm 10 GeV ( )af a t
n ta t
1
1
( )1
( )v( )
a
a t
m t a tt
83 3
6112
34
3
(2 )( ) 10
10 GeV( v)
a
a
fn t
m
N
ifdecoupled
Bose-Einstein Condensation
if identical bosonic particles
are highly condensed in phase space
and their total number is conserved
and they thermalize
then most of them go to the lowest energy
available state
why do they do that?
by yielding their energy to the
non-condensed particles, the
total entropy is increased.
BECpreBEC
the axions thermalize and form a BEC after a time
the axion fluid obeys classical field equations,behaves like CDM
the axion fluid does not obey classical field equations, does not behave like CDM
the axion BEC rethermalizes
the axion fluid obeys classical field equations,behaves like CDM
the axion fluid does not obey classical field equations,does not behave like CDM
from M.R. Andrews, C.G. Townsend, H.-J. Miesner, D.S. Durfee, D.M. Kurn and W. Ketterle, Science 275 (1997) 637.
Axion field dynamics
From self-interactions
From gravitational self-interactions
O. Erken et al., PRD 85 (2012) 063520
50 quanta among 5 states
316 251 system states
Start with
Number of particles
Total energy
Thermal averages
Thermalization occurs due to gravitational interactions
at time 1t
-1with v)l m
1 ( )( ) / ( ) ( )g a tt H t t a t
2
2
Gm
q
q
PS + Q. Yang, PRL 103 (2009) 111301
Gravitational interactions thermalize the axions and cause them to form a BEC when the photon temperature
After that 1v
m t
3 3( ) / ( ) ( )g t H t t a t
Tidal torque theorywith ordinary CDM
neighboringprotogalaxy
the velocity field remains irrotational
v 0 ����������������������������
Axions rethermalize before falling onto galactic halos and go to their lowest energy state consistent with the total angular momentum they acquired from tidal torquing
provided
i.e.
Axion fraction of dark matter is more than of order 3%.
Tidal torque theorywith axion BEC
v 0 ����������������������������
in their lowest energy available state, the axions fall in with net overall rotation
Caustics of light at the bottom of a swimming pool on a sunny breezy day
watersurface
lightintensity position
poolbottom
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.
1,2,3...n
maxj 0.18
rot max40kpc v j
220km/s 0.18n
na
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
Inner Galactic rotation curveInner Galactic rotation curve
from Massachusetts-Stony Brook North Galactic Pane CO Survey (Clemens, 1985)
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 planeat galactocentric distance appears circular, actually seen forscale height of order 1 kpcvelocity dispersion of order 20 km/s
may be caused by the n = 2 caustic ring of dark matter (A. Natarajan and P.S. ’07)
20 kpcr 0 0100 270l
The caustic ring halo model assumes
• net overall rotation
• axial symmetry
• self-similarity
L. Duffy & PSPRD78 (2008)063508
The specific angular momentum distribution on the turnaround sphere
a
2
m xˆ( , ) ˆ ˆˆ( )( )
nR t
n tt
z nj
2 2
3 9( )R t t
0.25 0.35
Is it plausible in the context of tidal torque theory?
Tidal torque theorywith ordinary CDM
neighboringprotogalaxy
the velocity field remains irrotational
v 0 ����������������������������
Tidal torque theorywith axion BEC
v 0 ����������������������������
net overall rotation is obtained because, in the lowest energy state,all axions fall with the same angular momentum
The specific angular momentum distribution on the turnaround sphere
a
2
m xˆ( , ) ˆ ˆˆ( )( )
nR t
n tt
z nj
2 2
3 9( )R t t
0.25 0.35
Is it plausible in the context of tidal torque theory?
Tidal torque theorywith axion BEC
v 0 ����������������������������
net overall rotation is obtained because, in the lowest energy state,all axions fall with the same angular momentum
Magnitude of angular momentum
fits perfectly ( )0.25 0.35
0.05G. Efstathiou et al. 1979, 1987
max 0.18j
from caustic rings
1
2
5
2
max| | 16 8
5 3 10 3
L E
G M
j
The specific angular momentum distribution on the turnaround sphere
a
2
m xˆ( , ) ˆ ˆˆ( )( )
nR t
n tt
z nj
2 2
3 9( )R t t
0.25 0.35
Is it plausible in the context of tidal torque theory?
Self-Similarity
a comoving volume
3
( )
( ) ( , ) ( ( , )V t
t d r r t r r t
( )r a t x ( ) , ) ( )r a t x t x
( )
( , )( , )
t
r tr t
( ) , ) ( ) ( )r a t x t a t x
4 30( ) ( ) ( ) ( ) ( ( ))x
V
t t a t d x x x x
Self-Similarity (yes!)
time-independent axis of rotation
2
3ˆ ˆ( ) ( )t z a t z t
5
3ˆ( )L t z t
1 4 523 9 3( )
ˆ( , )R t
n t t tt
0.33provided
fromF. van den Bosch,A. Burkert and R. Swaters, MNRAS 326(2001) 1205
Angular momentum distribution of baryons in dwarf galaxies
The angular momentum distribution of CDM in simulations differs from that of baryons in dwarf galaxies
1) the shape is different
2) observed
whereas
in simulations
Processes that allow angular momentum exchange aggravate the discrepancy
rather than resolve it
- Frictional forces among the baryons have the general effect of removing angular momentum from baryons that have little and transferring it to baryons that have a lot.
- Dynamical friction of dark matter on clumps of baryonic matter has the general effect of transferring angular momentum from the baryons to the dark matter.
-> GALACTIC ANGULAR MOMENTUM PROBLEM
Navarro and Steinmetz 2000Burkert and D'Onglia 2004
Tidal torque theorywith axion BEC
v 0 ����������������������������
net overall rotation is obtained because, in the lowest energy state,all axions fall with the same angular momentum
The vortices in the axion BEC are attractive and join into
a big vortex
The infall rate
is not isotropic.
N. Banik & PS, 2013
Baryon/WIMP specific angular momentum distribution on the
turnaround sphere
and infall rate
a
2
m xˆ( , ) ˆ ˆˆ( )( )
nR t
n tt
z nj
fromF. van den Bosch,A. Burkert and R. Swaters, MNRAS 326(2001) 1205
Angular momentum distribution of baryons in dwarf galaxies