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Dark MatterCaustics
Pierre Sikivie(U of Florida)
Miami 2007
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Elucidating the structure ofgalactic halos is important for
- understanding galactic
dynamics
- predicting signals for dark
matter searches
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WIMP detectors
CDMS Xenon
Also: DAMA, Edelweiss, CRESST, ZEPLIN,
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WIMP nucleus elastic scattering
ionization, scintillation, phonons
v
v)(vkm/s)220(
2)(
)(vmin
fdET
rE
r
=
)()(0 rr
ETqFdE
dR
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Axions
solve the Strong CP Problem of the
Standard Model
are a cold dark matter candidate when
mass
require only a gentle modification of
the Standard Model
are detectable by the cavity technique
5
10 eVam
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Axion Dark Matter eXperiment
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2 21
2)ah m c = (1 +
1
aQ
1
LQ
dP
d
2/am hc
0Bur
a
X
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ADMX
has reached sufficient sensitivity to detect galactichalo axions in favorable cases (KSVZ coupling)
is being upgraded with SQUIDs (50 mK
noise temperature vs. 2 K with HEMTs)
when cooled to 50 mK, will have sensitivity
to detect dark matter axions at even a fraction of
the halo density. The remaining challenge will
be to extend the searchable mass range.
if a signal is found, will be able to measure the local
CDM velocity distribution in detail
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Galactic halos live in phase space
ordinary fluid
dark matter (collisionless) fluid
);( trdr
);(v trrr
);v,( trfrr
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Galactic halo models
Isothermal sphere late infalling particles
do not thermalize
N-body simulations present resolution
is inadequate
Caustic ring model
complaintmodel
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x
x.
Dark matter particles are red and,on this page, they are free.
Caustics in cold dark matter
x
xx
dd
.x
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Phase space distribution of CDM
in a homogeneous universe
z
z
.
ztHz )(=& v
-1710v =-12
10v =
for axions
for WIMPs
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The cold dark matter particles lie on
a 3-dimensional sheet in6-dimensional phase space
the physical
density is theprojection ofthe phase
space sheetonto positionspace ( , t) = t) ( , t)r r rv v( +
ur r r ur r
z
z.
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The cold dark matter particles lie on
a 3-dimensional sheet in6-dimensional phase space
the physical
density is theprojection ofthe phase
space sheetonto positionspace ( , t) = t) ( , t)r r rv v( +
ur r r ur r
z
z.
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Phase space structure ofspherically symmetric halos
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Implications:1. At every point in physical space, the
distribution of velocities is discrete, eachvelocity corresponding to a particular flow
at that location .
2. At some locations in physical space, where
the number of flows changes, there is acaustic, i.e. the density of dark matter is veryhigh 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;
Vogelsberger, White, Helmi and Springel)
effv 30 km/s
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Hierarchical clustering introduces effective
velocity dispersion
effv
effv 30 km/s
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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;
Vogelsberger, White, Helmi and Springel)
effv 30 km/s
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(from Binney and Tremaines book)
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Phase space structure ofspherically symmetric halos
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Galactic halos have inner caustics aswell as outer caustics.
If the initial velocity field is dominated by netoverall rotation, the inner caustic is a tricusp ring.
If the initial velocity field is irrotational, the innercaustic has a tent-like structure.
(Arvind Natarajan and PS, astro-ph/0510743).
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simulations by Arvind Natarajan
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The caustic ring cross-section
an elliptic umbilic catastrophe
D-4
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Galactic halos have inner caustics aswell as outer caustics.
If the initial velocity field is dominated by netoverall rotation, the inner caustic is a tricusp ring.
If the initial velocity field is irrotational, the innercaustic has a tent-like structure.
(Arvind Natarajan and PS, astro-ph/0510743).
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Effect of a caustic ring of dark matter upon
the galactic rotation curve
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On the basis of the self-similar infall model
(Filmore and Goldreich, Bertschinger) with angularmomentum (Tkachev, Wang + PS), the causticrings were predicted to be
in the galactic plane
with radii
was expected for the Milky Wayhalo from the effect of angular momentum
on the inner rotation curve.
( )1,2,3...n =
rot max40kpc v j
220km/s 0.26n
na =
26.0jmax
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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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from W.B. Burton and W.W. Shane, 1970
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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 distanceappears circular, actually seen forscale height of order 1 kpc
velocity dispersion of order 20 km/s
Natarajan and P.S. (arXiv: 0705.0001) identify twoprocesses through which the Monoceros Ring of starsmay have formed as a result of the presence of thesecond caustic ring of dark matter in the Galaxy
20 kpcr 0 0100 270l