Transcript MackMadison

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