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Towards Closing the Window on Strongly Interacting Dark Matter: Far-reaching constraint based on Earth’s heat flow Gregory D. Mack Ohio State Physics (adviser: John Beacom) April 29, 2008 Pheno ’08 --- Madison Dark Matter: More to the Universe than meets the Eye How big can the interaction cross section be? Study it by rates (capture, etc.) Need the number density, which is unknown Every rate therefore has a mass dependence Model-independent The existing constraints on the cross section: (spin-independent) The existing constraints on the cross section: “Strong”: If DM interacted as strongly as baryons, would be observable astrophysically, such as by disrupting the Milky Way disk The existing constraints on the cross section: “Weak”: Can reach underground detectors and transfer a measurable amount of energy The existing constraints on the cross section: There IS an upper limit – enough energy has to be available for transfer to a target nucleus, to have it register in the detector. The existing constraints on the cross section: In between: Balloons and satellites in the atmosphere Tricky region … Original New : April 5, 2007 Erickcek, et. al. arXiv:0704.0794v1 The exclusion region was reanalyzed and changed – in an interesting mass range Our general approach What other effects would dark matter have in this middle region? Our general approach DM scatters off particles in Earth Hit nuclei, lose energy When below Earth’s escape velocity, gravitationally captured Will drift to core, annihilate Products will deposit energy in Earth’s core – Heat flow ! Compare to Earth’s measured heat flow If violated, cannot interact that strongly – can place a limit on the interaction cross section Heat Flow of Earth Heat flow of Earth is measured well 20,200 measurements all over Earth Drill boreholes a number of kilometers into the ground 44.2 ± 1 TeraWatts ~ 40% is from radioactive decay of U and Th in the crust K in the mantle and core is also suspected ~ 20 TW is unclaimed, though attributed to the core Specificities Conservative assumptions: want to maximize the heat coming from the dark matter Capture ~ 90% Set: Minimum path length (L) for capture Density of material through which it passes (n) Target nucleus it encounters (oxygen) Larger L, n, and heavier target = easier capture Details of Capture Each collision, the DM’s velocity drops Compound the loss until capture: Nscat Relate Nscat to Earth ( L/λ = L n σ ) This is the minimum cross section we require for efficient capture Our new exclusion What is captured is annihilated: Heat Flow with these interaction strengths = 3260 TW!!! When DM mass = target, easiest capture Our new exclusion Upper Edge: If DM interacts too strongly, it can’t drift to the core in a decent amount of time (assume equilibrium between capture and annihilation) Right Edge: Quantum mechanical unitarity restriction on the annihilation cross section Extension by Poisson Fluctuations If we reduce the probability for the DM to scatter, can decrease the amount of heat produced, even down to 20 TW More model dependent, so not shaded Now exclude many orders of magnitude Dark matter in this mass range must be weakly interacting, as most often assumed Conclusions Ruled out a large range of spin-independent cross sections for dark matter with nucleons Model-independent constraint, based on Earth’s heat flow Confidently excludes previous regions In an interesting mass range (most preferred DM candidates) In this large mass range we cover, the DM must truly be weakly interacting DM scattering could not have had any significant astrophysical impact Underground detectors should keep looking! Equations