niayesh afshordi, perimeter institute/u-waterloo western university, apr. 13, 2012 1 tales of dark...

Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012

1

Tales of Dark Matter on Small Scales

Niayesh Afshordi

Western UniversityFriday, April 13, 2012


2 Tales of Dark Matter on Small Scales

“Friday the 13th is a date considered to be bad luck in Western superstition.” -Wikipedia.



Outline

• Introduction: Cold Dark Matter (CDM) • Why phase space of CDM haloes is hierarchical• Too big to Fail? A Tale of Small Scale• Bound Structures & CDM detection• Future Prospects for dark matter astronomy



• Roya Mohayaee (IAP, Paris) • Ed Bertschinger (MIT)• Kathryn Zurek (U-Michigan)• Louis Strigari (Stanford)• Shant Baghram (U-Waterloo/PI)

• NA, Mohayaee, Bertschinger: Phys.Rev.D79:083526,2009 • NA, Mohayaee, Bertschinger: Phys.Rev.D81:101301, 2010• Baghram, NA, Zurek: Phys.Rev.D84:043511,2011• Baghram, NA, Strigari: in preparation

Collaborators



Outline




• Bullet Cluster

Baryons (X-ray) Matter (lensing)

Dark Matter is Collisionless



Dark Matter is Cold

Zaldarriaga & Tegmark 2002



Indirect Detection• Dark Matter can annihilate to– photons (Fermi)– electrons/positrons (PAMELA/Fermi/WMAP…Planck)

– Neutrinos (IceCube)

Springel, et al. 08



Directional DM detection

• Solar system is moving towards the Cygnus constellation in the Milky Way, at 220 km/s

We should see a DM wind coming from Cygnus, which distinguishes it from any other background

Sciolla et al 2008

250 km/s



WIMPs: from gravity to detection

• Gravitational evidence for DM comes from potential: d3x ρ(x)/|x-x’|

• Direct detection: ρ(x) at solar system• Indirect detection (annihilation): d3x ρ(x)2

WIMP detection is much more sensitive to DM sub-structure:Boost = <ρ2>/<ρ>2-1

Boost to annihilation signal (indirect detection) (e.g., Taylor & Silk 2003)

Variance for direct detection(e.g., Stiff, Widrow, & Frieman 2001)



Outline

• Introduction: Cold Dark Matter (CDM)• Why phase space of CDM haloes is hierarchical• Too big to Fail? A Tale of Small Scale• Bound Structures & CDM detection• Future Prospects for dark matter astronomy



Hierarchy in the Phase space

• CDM is really cold– vCDM ~ 10-11c

• Phase space density remains constant in lieu of collisions

(Liouville’s Theorem): – At CDM freeze out:

– Within our Galaxy:

Most of the phase space is empty!Structures on all scales

!!??



Hierarchical Micro-Structure of the Phase Space

time



• Bound sub-haloes (cluster in real/phase space)

• Tidal debris (cluster in initial conditions)

• Fundamental discreteness analogous to galaxy shot noise (NA, Mohayaee, Bertschinger 2009; Vogelsberger & White 2011)

Three types of phase structures

NGC 3923

Kuhlen, Diemand, et al.

Hayashi et al. 2003



Correlation Functions quantify Hierarchy

• Large Scale Structure Projected Correlation Function

• SDSS Masjedi, et al.

unbound structurebound substructure

Phase Space Correlation Function



Outline




Courtesy of Shant Baghram: http://pirsa.org/12040110/

Too Big to Fail Problem?

Subhalos in are dynamically can not host the most luminous dwarf satellites of Milky Way: (Too big to fail?)

(Michael Boylan-Kolchin, James S. Bullock, Manoj Kaplinghat, arXiv :1103.0007)

Aquarius simulation: high resolution simulation of 6 Milky- way type halo

Baghram, NA, & Strigari, in prep.



*Binning in the Energy and Angular momentum

*Non- smooth phase-space density

Now we can rewrite the observable density of stars, by plugging the phase space density function definition as :

Marginalize over fab’s

E

L

𝑓 𝑎𝑏

Number of binning = number of free parameters

Tricks of the Trade!



Outline




Bound Substructures

• Small sub-haloes become resilient to tidal stripping

• Stable clustering hypothesis:# of pairs at small physical separation remains

constant (Davis & Peebles 77)

• We extend this to the phase space

• Unlike the halo model, captures the full hierarchy: sub-haloes, sub-sub-haloes, etc. (also much fewer parameters)



sub-haloes and stable clustering

• Stable clustering in phase space can be used to describe bound subn-halo hierarchy

Kuhlen, Diemand, et al.

Boost » 106 (½crit,0/½)

NA, et al. 2010

0.03

Standard deviation of linear overdensity on mass scale M



DM annihilation profile:stable clustering vs. simulations

smooth halo

M(<r)/M200

Bound substructure+tidal cut-off

Msub > 105M

Msub > 106M

Msub > 107M

Msub > 108M

Springel, et al. 08

Anni

hila

tion

Lum

inos

ity (<

r)



Massaging the tidal stripping prescription …



sub-haloes in Direct Detection!• Temporal auto-correlation of DM detection in

several years…



Dark Matter Astronomy?

• From bound subhaloes:Boost = O(1) = density variance

@ solar radius

• Local DM wind may NOT come from the direction of Cygnus!

• Phase space correlation will be probed by directional DM detection

unbound structure

bound substructure

Hansen et al. 2005, Vogelsberger et al. 2009, Kuhlen et al. 2010



Dark Matter subhaloes may even impact Pulsar Timing

Hertzberg, Siegel, Fry 2007



Dark Matter subhaloes may even impact Pulsar Timing

Doppler Effect Shapiro Delay

Baghram, NA, & Zurek, 2011

log(

Puls

ar re

sidu

al p

ower

spe

ctru

m)

log(

Puls

ar re

sidu

al p

ower

spe

ctru

m)



Lessons

• CDM has lots of structure on small scales:– Boost in DM annihilation – Time dependence in direct detection signal– Rich structure for directional DM detection– Potentially detectable Pulsar Timing residuals

• Correlation Function in Phase Space is a Powerful tool ( stable clustering)

• Measuring Dark Matter masses from stellar kinematics is a tricky business



Two Cautionary Notes…

• What about baryons?– They can enhance CDM structures through

adiabatic contraction, or destroy them via gravitational collisions/heating

– Real haloes are almost certainly more complicated!

• Why not just extrapolate simulations?– Simulations are NOT scale-free tidal limit– Neither is CDM over 10 orders of magnitude!

niayesh afshordi, perimeter institute/u-waterloo western university, apr. 13, 2012 1 tales of dark...

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