astrophysical signals of dark matter...
TRANSCRIPT
Astrophysical Signals of Dark
Matter Annihilation
Positrons and Gamma-Rays
Sheldon Campbell
Texas A&M University PAC Lunch Seminar
September 10, 2008
Outline
1. Why dark matter (in astrophysics, cosmology, and particle physics)?
2. Galactic dark matter annihilation signal: positrons and gamma-rays.positrons and gamma-rays.
3. The importance of halo substructure and some recent results.
4. Extragalactic dark matter annihilation gamma-rays.
5. Conclusions.
Dark Matter in Astronomy
• Spiral galaxy rotation curves
• Velocity dispersions of:
– Matter in elliptical galaxies
– Matter in dwarf galaxies– Matter in dwarf galaxies
– Galaxies in galaxy clusters
Abell 2029
70-90% dark matterM�1014 M�
Dark Matter in Astronomy
• Gravitational Lensing– dark matter maps: subtract visible matter from
observed mass distribution
• Cosmic Microwave Background FluctuationsFluctuations– consistent with ΛCDM cosmology with 23%
cold dark matter energy content
• Large scale structure formation requires cold dark matter
Dark Matter in Astronomy
• Gravitational Lensing– dark matter maps: subtract visible matter from
observed mass distribution
• Cosmic Microwave Background FluctuationsFluctuations– consistent with ΛCDM cosmology with 23%
cold dark matter energy content
• Large scale structure formation requires cold dark matter
Any alternative to dark matter has a lot of work to do.
Dark Matter Properties
Cold dark matter is:
• non-relativistic
• electrically neutral
• massive• massive
• stable
• weakly interacting
• does not form compact objects
– EROS-2 experiment sees very few compact objects in
the galactic halo (Tisserand et al ’07)
Dark Matter in Particle Physics
• Standard Model contains no such matter.
– What about massive neutrinos?
• relativistic (bad for structure formation)
• not abundant enough (small part of DM content)
• Particle candidates found in Extensions to the • Particle candidates found in Extensions to the
Standard Model such as
– supersymmetry with R-parity
– extra dimensions (Kaluza-Klein)
• Models constructed to give correct dark matter
relic density in big bang scenarios.
Particle Physics Prediction
Dark matter particles annihilate.
etc.
ν
γ
e+
p-
etc.
Annihilation products and
their spectra per annihilation
depend on interaction properties.
Astrophysical Signal of Dark Matter
Annihilation
Intensity profile of products depend on:
– particle physics properties of dark matter
• annihilation cross section determines the rate of
annihilation for a given density of dark matterannihilation for a given density of dark matter
• spectrum per annihilation
– dark matter distribution
• intensity traces density squared
– interactions of products with astronomical
background
Signals to look for:
• positrons
– HEAT
– PAMELA
– AMS-02– AMS-02
• gamma-rays
– EGRET
– Fermi Gamma-Ray Space Telescope
Positron Signal
DM+
e- + e+
µ+ + …τ+ + …
e+ + …e+ + …e+ + …
+DM q + …
W + …
e+ + …e+ + …
etc.
Positron Propagation
Tangled magnetic fields randomize the particle motion.
Modeled as a random walk via a diffusion equation. (Lavalle et. al. ’08)equation. (Lavalle et. al. ’08)
)(2
0
0 EQE
n
dt
dE
EE
n
E
EK =
∂
∂
∂
∂+
∂
∂∇
−
δ
diffusion
coefficient
energy
losses
positron
source
3 Main Sources of Energy Loss
• synchrotron emission
B�� µG ⇒ ε���������
� ���������� ����� ������� �������������������� �������������������
��������
� ������ ������� ���������� �����������
3 Main Sources of Energy Loss
• synchrotron emission
B�� µG ⇒ ε���������
� ���������� ����� ������� �������������������� �������������������
��������
� ������ ������� ���������� �����������
EE
E
dt
dE
τ0
2−=
Myrs 3001016 ≈≈Eτ
GeV10 ≡E
Diffusion Equation
Boundary Conditions
Diffusion zone is a pillbox of height 2L.
L ~ distance cosmic ray
travels before escapingtravels before escaping
the galactic disk
2L
0=∂
∂
E
non the boundary
Allowed Diffusion Model
Parameters
Lavalle, et. al. allowable parameter range
– consistent with observed B/C flux ratios in
cosmic rays (Maurin,Trillet,Donato ’02)
δ K0 (kpc2/Myr) L (kpc)
max 0.46 0.0765 15
med 0.70 0.0112 4
min 0.85 0.0016 1
Positron Propagation Length
– emitted at energy ES
– detected at energy E
−
=
−− 11
04δδ
τλ
EEK SE
−
−=
00
0
1
4
δ
τλ
E
E
E
EK SE
D
Positron Propagation Length
– emitted at energy ES
– detected at energy E
−
=
−− 11
04δδ
τλ
EEK SE
−
−=
00
0
1
4
δ
τλ
E
E
E
EK SE
D
Example:−“med” diffusion model
− ES = 200 GeV
E = 190 GeV ⇒ λD = 0.4 kpc
E = 1 GeV ⇒ λD = 5.7 kpc (galactic centre is 7.6 kpc away)
⇒ 2.09.6
3.0
−
≅
−
GeVkpc
EDλ
Barger, Keung, Marfatia, Shaughnessy (2008)
PAMELA Results and
Generic Annihilation Models
Smooth NFW halo profile
γγ
ρρ
−
+
=
3
1
)(
ss
s
r
r
r
r
r
with inner slope γ = 1.Mode Model MDM B · ⟨σ v⟩ · 1025 χ2/dof
(GeV) (cm3/s)
WLWL med 150 6.6 1.2
med 85 2.3 2.8
WTWT med 150 7.3 1.7
med 85 2.1 2.1
e+e- min 150 17.0 5.0
med 150 5.9 0.9
max 150 3.7 1.1
min 85 4.1 5.0
med 85 2.0 1.0
max 85 1.3 1.7
Halo substructures contribute a signal boost B.
PAMELA and mSUGRA
Such a dramatic rise in flux is seen in models in the coannihilation region where mχ ≈ m
ẽ.
The branching ratio for
χ e-
becomes greatly enhanced in this parameter space.
χ
χ
ẽ
e-
γ
e+
GeV
GeV
240
233
~ =
=
em
mχ
PAMELA and mSUGRA
GeV
GeV
240
233
~ =
=
em
mχ
PAMELA and mSUGRA
GeV
GeV
240
233
~ =
=
em
mχ
PAMELA and mSUGRA
Require boost factors of ~104
Substructures boost the
annihilation signal
The cores of NFW haloes become more
dense for smaller mass objects.
0)(
<∂ rρ
0)(
<∂
∂
rM
rρ
profiles halo matter dark smooth to dueIntensity
ressubstructu withondistributi to dueIntensity =B
Boost Factor:
Assumed to be energy independent.
Inside a smooth halo
Siegal-Gaskins (2008)
Subhaloes with Mmin=107 M�
Siegal-Gaskins (2008)
Subhaloes with Mmin=10 M�
Siegal-Gaskins (2008)
Substructure in Simulations
Aquarius Simulations (Virgo Collaboration)
– Springel, et. al. (2008)
– presented by Carlos Frenk at IDM 2008
– 6 galaxy size haloes at various resolutions– 6 galaxy size haloes at various resolutions
Via Lactea Simulations
– Diemand, et. al. (2007)
– Diemand, et. al. (2008)
– presented by Michael Kuhlen at IDM 2008
Resolution of the Simulations
Simulation
Particle
number in
halo
# of resolved
substructures
Mass resolution (M��
Aq-A-5 808,479 299 3.14 x 106
Aq-A-4 6,424,399 1,960 3.92 x 105
Aq-A-3 51,391,468 13,854 4.91 x 104
Aq-A-2 184,243,536 45,024 1.37 x 104
Aq-A-1 1,473,568,512 297,791 1.71 x 103
Via Lactea I 84,700,000 ~10,000 2.18 x 104
Via Lactea II 470,000,000 ~100,000 3.92 x 103
z = 1.5
•N200=3×106
4003
run
Aquarius
z = 1.5
•N200=94×106
12003 run
Aquarius
z = 1.5
N200=750×106
24003 run
Aquarius
z = 1.5
N200=750×106
24003 run
Aquarius~10% halo mass in substructures
Via Lactea II inner 40 kpc
Subhalo abundances:
in agreement
Does spherically averaged
simulated halo profile agree with
NFW profile?
Aquarius shows excellent convergenceat all resolutions.
Profile is approximatelyProfile is approximatelyfit by an NFW profile.
Check the logarithmicslope of the profile.
Logarithmic slope of Aquarius’
spherically averaged density profile
NFW profile
dlo
g r
Shallower than NFWat small radii.
No obviousconvergence to apower law at small
Moore et al
Navarro et al. (2004)
(Einasto profile; α=.19)
dlo
g ρ
/dlo
g r
r [kpc]
power law at smallradius.
Einasto halo profileprovides a better fit.
( )[ ]12 −−=
α
αρρ srr
es
Via Lactea II shows similar results
A sampling of 8 largesubhaloes shows cuspyinteriors, but smaller densitythan main halo.
Red: best fit NFW profilewith γ = 1.24.
Blue: best fit Einasto profilewith α = 0.170.
How scale dependent is the structure?
From Diemand, et. al. (2008):
“Via Lactea II predicts a remarkable self-similar
pattern of clustering properties…. [A] simple pattern of clustering properties…. [A] simple
explanation: subhalo density profiles were
modified by tidal mass loss, which removes
material from the outside in, but does not
change the inner cusp nature.”
How scale dependent is the structure?
“Via Lactea II demonstrates the fractal-like appearance of the dark matter by resolving the second generation of surviving sub-structures from the merging hierarchy. This suggests that at infinite hierarchy. This suggests that at infinite resolution one would find a long nested series of halos within halos etc., reminiscent of a Russian Matryoshka doll, all the way down the first and smallest earth mass haloes that form.”
Carlos Frenk offered a different view at IDM 2008
“The hierarchy is clearly NOT self-similar and is heavily is heavily dependent on the degree of tidal stripping of the subhalo.”
Via Lactea II estimate of boost factors
Assumptions:
– inner profile slope of subhaloes evenly distributed
between 1.0-1.5.
– extrapolate simulation resolution down to earth-size
microstructures.
Positron signal:Positron signal:
– assumed detectable anti-particles produced within
1 kpc.
– average boost B = 1.4.
– 1% of locations (near a large substructure) had B > 10.
Gamma-ray signal:
– estimated B ≈ 4–14.
Aquarius’ prediction for gamma-rays from milky way dark matter annihilation
…and from Via Lactea II
Can you see it? FGST 4-day exposure
Some issues currently being debated in
the substructure community
• Is halo dark matter comprised mostly of small earth sized clumps?
• Do small earth sized clumps dominate the annihilation signal?annihilation signal?
• Are dwarf subhalos the best targets for detecting a signal? (Better than a diffuse signal?)
• Are subhalo emissions boosted by sub-substructure?
Now let us considerextragalactic darkmatter annihilationmatter annihilationsignals.
Extragalactic gamma-rays due to
dark matter annihilation
• Subtraction of the modeled galactic sources reveals isotropic extragalactic gamma-rays.
Ando, Komatsu (2006)Ando, Komatsu (2006)
),(3
2
2
)1(8
),(
1
),]1([)()(
zEe
dE
dNz
m
vzEW
zEzWrdrEI
γτ
γ
γ
γ
ρ
ρ
ρ
γργγ
ρ
π
σ
δ
δ
−+
=
−≡
+= ∫
DM
DM
Spherical halo model provides good
descriptions of dark matter distribution
Cooray, Sheth (2002)
)(
),|(),()(
2
2
z
zMrdV
dM
zMdndMz
Mρ
ρδ ρ
∫∫∞
=
min
Halo mass function well constrained by
simulations at large mass scalesJenkins, et. al. (2001)
Intensity profile contains
unconstrained boost factor
• The signal is again expected to be boosted due to halo substructures.– Can a galactic positron signal provide some
constraint to an extragalactic gamma-ray signal boost factor?signal boost factor?
• Idea: if the boost factor is independent of the gamma-ray energy, then it does not contribute to the angular power spectrum.– angular power spectrum therefore provides a
more robust signal prediction.
Possibility of intensity boosts due to
large velocity effects?
• When the comoving velocity of annihilating particles is relativistic, the annihilation cross section increases with velocity.
( )2)( vbavv +≈σ
• For neutralino dark matter, b/a ≈ mχ / me .
• Velocity effects become important approximately when the maximum circular velocity of a halo satisfies
( )2)(
c
vbavv +≈σ
1
2
≥
c
v
a
b
Conclusions
• The realization that one may learn about particle
interactions through astronomical observation is
remarkable.
• Resolution of a dark matter annihilation signal may
requirerequire
– a stronger understanding of the distribution of dark
matter (particularly small scale structure and
substructures),
– strong propagation models of the annihilation
products,
– an understanding of background processes that
produce high energy particles, and the distribution
and abundance of these processes.
Conclusions
• Current models seem to require very large boost factors
to explain preliminary excesses as dark matter
annihilation.
• These indirect detection experiments, along with direct
detection experiments and collider experiments will detection experiments and collider experiments will
provide independent, complementary constraints that will
provide directions to the correct physics that lies beyond
the standard model.