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Dark Matter: halo-shape and relic density constraints on dark matter theories with Sommerfeld enhancement.

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Dark Matter: halo-shape and relic density constraints on dark matter theories with Sommerfeld enhancement

Recent observations by PAMELA, etc. have been interpreted as evidence of cold dark matter self annihilation. If these observations and their speculative interpretation are correct, then the dark matter self interaction cross section would need enhancement. In this journal club talk I will discuss the weakly interacting massive particle (WIMP) 'miracle' that results in the dark matter relic density that we see today, I will review recent observations, and I will discuss how proposed interaction enhancement mechanisms are inconsistent with data. Finally, I will discuss signals that dark matter may have on observable halo-shapes.

Journal Club. A. B. Fry 4/22/2010


Dark Matter: halo-shape and relic density constraints on dark matter theories with Sommerfeld enhancement

Journal Club. A. B. Fry 4/22/2010


Feng, J., Kaplinghat, M., & Yu, H. (2010)Physical Review Letters, 104 (15) DOI:10.1103/PhysRevLett.104.151301

NimaArkani-Hamed, Douglas P. Finkbeiner, Tracy R. Slatyer, Neal Weiner

Halo-Shape and Relic-Density Exclusions of Sommerfeld-Enhanced Dark Matter Explanations of Cosmic Ray Excesses

  • A Theory of Dark Matter
  • Motivation
  • Relic wimps
  • Observations
  • Constraints
  • The dark sector

○ Sommerfeld enhancement

○ halo shape

  • Conclusions
the question
The Question

If the particles that make up most of the mass of the universe are not baryons what are they?

the question1
The Question

If the particles that make up most of the mass of the universe are not baryons what are they?

  • They are dark (doesn’t play well with radiation)
  • They are electrically neutral
  • They are highly non-relativistic (cold)
  • Dissipationless
the answer
The Answer

If the particles that make up most of the mass of the universe are not baryons what are they?

Can we even understand the information data provides us without tying it to any specific models for DM’s nature?


weakly interacting massive particles
Weakly Interacting Massive Particles
  • Massive particles in the Universe decay to lower energetically favored states, however massive particles may survive to the present if they carry some sort of conserved additive or multiplicative number.
weakly interacting massive particles1
Weakly Interacting Massive Particles


  • Assume DM particle in equilibrium χχ↔ff
  • Universe cools χχ→ ff
  • Freeze out χχ↔ff







weakly interacting massive particles2
Weakly Interacting Massive Particles
  • The WIMP miracle is that parameter space perfectly allows for a CDM WIMP particle that is independently predicted in particle physics and it has the right density to be dark matter.
weakly interacting massive particles3
Weakly Interacting Massive Particles
  • In the rest of this talk I will be assuming some sort of supersymmetric dark matter particle.
neutralinos supersymmetry
Neutralinos & Supersymmetry
  • Supersymmetry is a theoretical scheme that pairs every known particle with a heavier, undiscovered superpartner.
  • The lightest superpartner, expected to be a few hundred times as massive as a proton (~1 Tev), is the neutralino which could be a WIMP
  • According to supersymmetry WIMPs act as their own antimatter particles!
neutralinos supersymmetry1
Neutralinos & Supersymmetry
  • Neutralino WIMPs in a galactic halo will collide and annihilate each other to produce high energy gamma ray photons or other ordinary particles like positrons and electrons (consistent because the supersymmetricquantum number is multiplicative)
  • PAMELA: anomalous abundance of positrons in cosmic rays above 10 GeV.
  • ATIC: Excess in total flux of electrons and positrons in cosmic rays
  • WMAP: excess of microwave emission from galactic center “WMAP haze”
  • The time variation of a signal seen by the DAMA-LIBRA collaboration
  • FERMI: despite initial speculation, the 10 month data release seems to be consistent with a single power law distribution of gama-rays as predicted by the cosmic background of AGN.
  • Pulsars can explain PAMELA…
  • Relic density and ΩDM (Arkani-Hamed 2009 et al.)
  • Late decays would modify nucelosynthesis particularity the 7Li/H ratio (Feng lecture slides 2007).
  • CMB observations constrain dark matter annihilation energy injection rate during recombination (Zavala 2010 et al.).
  • The Pamela and Atic signals require a cross section that is of order 100 times greater than what would be expected from thermal relic WIMPs
  • Require a low cross section to hadrons.
  • Require a high cross section into leptons.
the dark sector1
The Dark Sector
  • From a theoretical viewpoint a new interaction for the dark sector arises naturally in a variety of theories beyond the standard model, and is thus well motivated from a theoretical point of view
sommerfeld enhancements
Sommerfeld Enhancements
  • A plethora of papers propose Sommerfeld enhancement, S, to the DM cross section
  • Sommerfeld enhancement increases the cross section of particles at low velocities similarly to classical gravitational enchantment.
  • The Sommerfeld enhancement is the quantum counterpart to the classical gravitational phenomena.
sommerfeld enhancements1
Sommerfeld Enhancements
  • Consider classical gravitational enhancement: for a test particle at velocity ν approaching a massive particle of radius R and mass M it can be shown that the cross section is increased  to

Where σ0=πR2 and νesc2=2GM/R

sommerfeld enhancements2
Sommerfeld Enhancements
  • If you work through the entire derivation the result is that the enhancement leads to a cross section that scales at low energies as S(σν) ∝ 1/ν.
  • It turns out that the velocity of dark matter particles is a factor of 10- 3 smaller now compared to at.
  • It is a miracle of dark matter that Sommerfeldenhancement therefore provides an elegant mechanism for boosting annihilations now.
halo shapes
Halo Shapes
  • Dark matter has an observable effect halo-shapes.
  • Self-interactions can be strong enough to create first order changes in the energies of dark matter particles which will isotropize the velocity dispersion and creative spherical halos (which are not seen)
halo shapes1
Halo Shapes
  • In Feng et al. 2010 they look at the halo of NGC 720 and consider halo-shape constraints from various DM models
halo shapes2
Halo Shapes
  • Strong self-interacting DM would cause the formation of constant density cores.
  • Strong self-interacting DM would make subhalos (which havecomparable or higher densities than that of the halo and also generally have lower velocity dispersions than the approximately thermal bulk) especially important.
  • Strong self-interacting DM would isotropizethe velocity dispersion and creative spherical halos

M and S regions which explain PAMELA and Fermi data

Sommerfeld enhancement factor

Mass of WIMP


Sommerfeld enhancement factor

Halo shape observations set upper limits on the effective mass of the force carrier which mediates interactions in halo

Mass of WIMP


Sommerfeld enhancement factor

Halo shape observations set upper limits on the effective mass of the force carrier which mediates interactions in halo

Mass of WIMP


Sommerfeld enhancement factor

Upper limit from ΩDM

Mass of WIMP

  • A satisfactory solution to the dark matter problem must not only have dark matter annihilating at the correct rate, but it must also produce the right density and structure on all cosmological scales which is consistent with observations…

We weren’t able to get the cross section high enough to explain ATIC or PAMELA results without invoking Sommerfeld enhancement and even then the enhancement was inconsistent with relic DM density and further it changed the halo shapes.

Crash and burn?

conclusions for theorists
Conclusions (for theorists)
  • WIMPs are motivated from fundamental particle physics!
  • A simple modification of a standard candidate such as a neutralino in the supersymmetricstandard model is insufficient.
  • We need a simple theory with a small number of parameters to more quantitatively confront future data.
conclusions for observers
Conclusions (for observers)
  • Hopes for detection of dwarf galaxies through dark matter annihilation
  • Although the cross section is not Sommerfeld enhanced during freeze-out, it keeps pace with the expansion over the cosmic history. This may have significant implications for a variety of early-universe phenomena as well as the cosmic gamma-ray background.
  • Keep analyzing Fermi data.
  • Look for local astrophysical sources of cosmic rays!
image credits
Image Credits
  • NGC 720: X-ray: NASA/CXC/UCI/D.Buote et al., Optical: DSS U.K.SchmidtImage/STScI
  • The Thinker: Rodin
  • DM observations square: WMAP, SDSS, Chandra, Hubble
  • Dark matter decay interactions: NASA
  • Pulsar: NASA
  • Observation interactions: Colanfanseco 2010
  • Dark hallway:
  • Slide background: galaxy cluster CL0025+1654 by J.-P. Kneib (Observatoire Midi-Pyrenees, Caltech) et al., ESA, NASA
  • Calvin & Hobbes: Bill Watterson
  • Square peg: Feng

Hadrons is a particle made of quarks held together by the strong force. Hadrons are categorized into two families: baryons (made of three quarks), and mesons (made of one quark and one antiquark). Protons and neutrons are hadrons. All hadrons except protons are unstable and undergo particle decay.


Fermions include quarks -which are the constituents of protons and neutrons, i.e. nuclear matter- and leptons -the electron and its neutrino, and two pairs of heavier copies of the former. Bosons are the messengers of the forces experienced by fermions; they include the photon, the W and Z bosons, and the gluons. Photons carry electromagnetic forces, W and Z carry the weak forces, and the 8-strong family of gluons keeps quarks bound together.


The enhancement is proportional to the coupling of dark matter to the force carrier, and if the coupling is large enough to give the needed enhancement, then it is too large to be consistent with the relic density, so the desired reconciliation cannot be achieved. Moreover, for very light force carriers, self-interactions of the dark matter in models of this type lead to spherical galactic halos of dark matter, inconsistent with observations of elliptical halos. Unless a way around these problems can be found, this approach to explaining the positron excess seems ruled out. – Stanley Brown