An argument that the dark matter is axions

Pierre Sikivie

Miami 2013 Conference

Fort Lauderdale, December 16, 2013

Collaborators: Ozgur Erken, Heywood Tam, Qiaoli Yang

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 by other forms of dark matter. Ordinary cold dark matter (WIMPs, sterile neutrinos, non-rethermalizing BEC, …) forms tent-like inner caustics.

The Strong CP Problem

Because the strong interactions conserve P and CP, .

2

QCD 2...

32a ag

L G G

1010

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,

PQU (1)

2

2

1... .

32 2a a

a

a gL G G a a

f

a

a

f

and a light neutral pseudoscalar particle is predicted: the axion.

f f

a

a

610 GeVeV

aa fm

aa

aL g E B

f

����������������������������

= 0.97 in KSVZ model 0.36 in DFSZ model

g

5fa f fa

aL i g f f

f

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

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

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

Axion field dynamics

From self-interactions

From gravitational self-interactions

After , axions thermalize in the “condensed” regime

implies

for

and for self-gravity

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 and Q. Yang, PRL 103 (2009) 111301 O. Erken, PS, H. Tam and Q. Yang, Phys. Rev. D85 (2012) 063520K. Saikawa and M. Yamaguchi, Phys. Rev. D (2013) 085010

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 theory

neighboringprotogalaxy

Stromberg 1934; Hoyle 1947; Peebles 1969, 1971

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

x

x.

DM particles in phase space

DM forms caustics in the non-linear regime

x

xx

.x

Phase space distribution of DM in a homogeneous universe

z

z.

ztHz )(v

-1210v

for WIMPs

-17v 10 -8v 10

for axions (preBEC)

for sterile neutrinos

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

in case of net overall rotation

The caustic ring cross-section

an elliptic umbilic catastrophe

D-4

in case of irrotational flow

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

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

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)

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 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 ����������������������������

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 =

in case of irrotational flow

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

in case of net overall rotation

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

Conclusion:

The dark matter looks like axions

fromF. Van den Bosch,A. Burkert and R. Swaters, MNRAS 326(2001) 1205

explained by axion BEC

N. Banik & PSarXiv: 1307.3547