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Western University
Friday, April 13, 2012
Tales of Dark Matter on Small Scales
Niayesh Afshordi
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
“Friday the 13th is a date considered to be bad luck in Western superstition.”
-Wikipedia.
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Outline
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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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Collaborators
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Roya Mohayaee (IAP, Paris)
Ed Bertschinger (MIT)
Kathryn Zurek (U-Michigan)
Louis Strigari (Stanford)
Shant Baghram (U-Waterloo/PI)
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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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Dark Matter is Collisionless
• Bullet Cluster
Baryons (X-ray)
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Matter (lensing)
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Dark Matter is Cold
Zaldarriaga & Tegmark 2002
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Indirect Detection
• Dark Matter can annihilate to
– photons (Fermi)
– electrons/positrons (PAMELA/Fermi/WMAP…Planck)
– Neutrinos (IceCube)
Springel, et al. 08
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
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
250 km/s
Sciolla et al 2008
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
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 substructure:
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)
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
11
Tales of Dark Matter on Small Scales
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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
12
Tales of Dark Matter on Small Scales
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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
!!??
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Hierarchical Micro-Structure of the
Phase Space
time
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Three types of phase structures
• Bound
(cluster
Hayashisub-haloes
et al. 2003
in real/phase space)
• Tidal debris (cluster in
initial conditions)
• Fundamental discreteness
Kuhlen, Diemand, et al.
NGC 3923
 analogous to galaxy shot noise
(NA, Mohayaee, Bertschinger 2009; Vogelsberger & White
2011)
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Correlation Functions quantify
Hierarchy
Phase Space Correlation Function
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Large Scale Structure
Projected Correlation Function
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SDSS
Masjedi, et al.
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
17
Tales of Dark Matter on Small Scales
Too Big to Fail Problem?
 Subhalos in Λ𝐶𝐷𝑀 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.
Niayesh
Afshordi, Perimeter
Institute/U-Waterloo
Courtesy
of Shant
Baghram: http://pirsa.org/12040110/
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Tricks of the Trade!
*Binning in the Energy and Angular momentum
*Non- smooth phase-space density
𝑓𝑎𝑏
L
E
Number of binning = number of free parameters
 Now we can rewrite the observable density of stars, by plugging the
phase space density function definition as :
 Marginalize over fab’s
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
19
Tales of Dark Matter on Small Scales
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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
20
Tales of Dark Matter on Small Scales
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: subhaloes, sub-sub-haloes, etc. (also much
fewer parameters)
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
sub-haloes and stable clustering
• Stable clustering in phase space can be used
to describe bound subn-halo hierarchy
0.03
Boost » 106 (½crit,0/½)
Kuhlen, Diemand, et al.
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Standard deviation of linear overdensity on
mass scale M
NA, et al. 2010
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
DM annihilation profile:
stable clustering vs. simulations
Annihilation Luminosity (<r)
smooth halo
Msub
Msub
Msub
Msub
>
>
>
>
105M
106M
107M
108M
M(<r)/M200
Bound substructure
+tidal cut-off
Springel, et al. 08
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Massaging the tidal stripping
prescription …
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
sub-haloes in Direct Detection!
• Temporal auto-correlation of DM detection in
several years…
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Hansen et al. 2005, Vogelsberger et al. 2009, Kuhlen et al. 2010
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
Dark Matter subhaloes
may even impact Pulsar Timing
Hertzberg, Siegel, Fry 2007
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
log(Pulsar residual power spectrum)
log(Pulsar residual power spectrum)
Dark Matter subhaloes
may even impact Pulsar Timing
Doppler Effect
Shapiro Delay
Baghram, NA, & Zurek, 2011
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
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Tales of Dark Matter on Small Scales
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
Niayesh Afshordi, Perimeter Institute/U-Waterloo
Western University, Apr. 13, 2012
29
Tales of Dark Matter on Small Scales
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