axion bec dark matter pierre sikivie vistas in axion physics seattle, april 22-26, 2012...
TRANSCRIPT
![Page 1: Axion BEC Dark Matter Pierre Sikivie Vistas in Axion Physics Seattle, April 22-26, 2012 Collaborators: Ozgur Erken, Heywood Tam, Qiaoli Yang](https://reader035.vdocument.in/reader035/viewer/2022062515/56649cd75503460f9499ecfb/html5/thumbnails/1.jpg)
Axion BEC Dark Matter
Pierre Sikivie
Vistas in Axion Physics
Seattle, April 22-26, 2012
Collaborators: Ozgur Erken, Heywood Tam, Qiaoli Yang
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An argument why the dark matter is axions
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
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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 by other forms of dark matter. Ordinary cold dark matter (WIMPs, sterile neutrinos, non-rethermalizing BEC, …) forms tent-like inner caustics.
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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
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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
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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
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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
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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
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why do they do that?
by yielding their energy to the
non-condensed particles, the
total entropy is increased.
BECpreBEC
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the axions thermalize and form a BEC after a time
the axion fluid obeys classical field equations
the axion fluid does not obey classical field equations
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the axion BEC rethermalizes
the axion fluid obeys classical field equations
the axion fluid does not obey classical field equations
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Axion field dynamics
From self-interactions
From gravitational self-interactions
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In the “particle kinetic” regime
implies
When
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12
3
4
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D. Semikoz & I. Tkachev, PRD 55 (1997) 489D.
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After , axions thermalize in the “condensed” regime
implies
for
and for self-gravity
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Toy model thermalizing in the condensed regime:
with
i.e.
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50 quanta among 5 states
316 251 system states
Start with
Number of particles
Total energy
Thermal averages
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Integrate
Calculate
Do the approach the on the predicted time scale?
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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
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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
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In the linear regime, within the horizon, the axion BEC remains in the same state
axion BEC density perturbations obey
Jeans’ length
42
0 2 4( , ) 2 ( , ) 4 ( , ) 0
4t tk
k t H k t G k tm a
1 1
1 -5 292 42 144
J10 eV 10 g/cc
16 1.02 10 cmG mm
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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 when it rethermalizes
in the non-linear regime &
upon entering the horizon
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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
in case of net overall rotation
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The caustic ring cross-section
an elliptic umbilic catastrophe
D-4
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in case of irrotational flow
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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.
1,2,3...n
maxj 0.18
rot max40kpc v j
220km/s 0.18n
na
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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 curveInner 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 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
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Rotation curve of Andromeda Galaxyfrom L. Chemin, C. Carignan & T. Foster, arXiv: 0909.3846
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10 arcmin = 2.2 kpc
29.2 kpc15.410.3
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The caustic ring halo model assumes
• net overall rotation
• axial symmetry
• self-similarity
L. Duffy & PSPRD78 (2008)063508
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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?
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Tidal torque theory
neighboringprotogalaxy
Stromberg 1934; Hoyle 1947; Peebles 1969, 1971
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Tidal torque theorywith ordinary CDM
neighboringprotogalaxy
the velocity field remains irrotational
v 0 ����������������������������
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For collisionless particles
If initially,
then for ever after.
v v, ) , ) v( , ) v( , )
, )
dr t r t r t r t
dt t
r t
0v =
0v =
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in case of irrotational flow
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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
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For axion BEC
is minimized for given
when .
2
1 2
Ni
i
LE
I
1
N
ii
L L
1 2 3 ... NL L L L
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in case of net overall rotation
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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?
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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
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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
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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?
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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
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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
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Conclusion:
The dark matter looks like axions
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Baryons and photons may enter into thermal contact with the axions by gravitational interactions as well
a
a
p
p
O. Erken, PS, H.Tam and Q. Yang, PRL 108 (2012) 061304
p may be any species of particle
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Relativistic axion modes and photons reach thermal contact with the cold axions if the cold axion correlation
length reaches horizon size by the time of equality
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If photons, baryons and axions all reach the same temperature before decoupling
photons cool
baryon to photon ratio
effective numberof neutrinos
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Effective number of neutrinos
WMAP 7 year:
J. Hamann et al. (SDSS):
Atacama Cosmology Telescope:
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we will see …