pierre sikivie- dark matter caustics

8/3/2019 Pierre Sikivie- Dark Matter Caustics

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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

pierre sikivie- dark matter caustics

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