wim de boer, christian sander, valery zhukov univ...

September 29, 2004 Seminar Santa Cruz, W. de Boer, Univ. Karlsruhe 1

Indirect evidence for Dark Matter Annihilationfrom excess of diffuse galactic gamma rays

Wim de Boer, Christian Sander, Valery ZhukovUniv. Karlsruhe

Alex Gladyshev, Dmitri KazakovDubna

Outline (see astro-ph/0408272)

• EGRET Data on diffuse Gamma Rays shows excess in all sky directions with the SAME energy spectrum

• WIMP mass from spectrum

• Halo parameters from sky map

• Data consistent with Supersymmetry


Physics Problems

• Astrophysicists:What is the origin of excess of diffuse Galactic Gamma Rays?

• Astronomers:Why a change of slope in the galactic rotation curve above R0=8.5 kpc?Why ring of stars at 14 kpc so stable?Why ring of molecular hydrogen at 4 kpc so stable?

• Cosmologists:How is Cold Dark Matter distributed?

• Particle physicists:Where are the Supersymmetric Particles?


•DM made of WIMPS annihilating into quarks, which yield hard gammas from π0 decays

•Annihilation cross section is given by the HUBBLE constant!

•Gamma excess shows substructure: a ring of DM at 14-18 kpc correlated with ring of starsthought to originate from infall of a dwarf galaxyand ring of DM at 4 kpc correlated with molecular H2

•From ENERGY SPECTRUM of excess of gamma rays DM: WIMP mass 50-100 GeV

•From INTENSITY: halo distribution and rotation curve

•WIMP has properties of the lightest supersymmetric particle

Proposed Solution


Indirect detection of DM with gamma rays• First question: how to tell source of a gamma ray?• Answer: one cannot, since gammas observed along line of sight,

and many sources in a given direction.•How to distinguish then between sources?•Point sources from intensity (“hot spots”), if strong enough•Diffuse gamma ray sources (pp->π0+x->γγ+x, eγ->eγ, eN->eγN, Extragalactic Background, DMA)all have quite different ENERGY spectra AND different SKYMAPS •Strategy: fit SHAPES of various contributions to energy spectrum(FREE NORMALIZATIONS) in 180 SKY DIRECTIONS ->

•Intensity distribution of background in sky (consistent with data)•Intensity distribution of Extragalactic Background •Intensity distribution of DM in sky (consistent with halo modelsplus interesting substructure)

Beware: errors in EGRET data dominated by systematic uncertainties->strong correlations -> to be taken into account in fits. (as in D’Agostini, dB, Grindhammer, Phys.Lett.B229:160,1989)

Published data not sufficient. Need direct analysis of public EGRET data.


EGRET on CGRO (Compton Gamma Ray Observ.)

9 yrs of data taken in space!


Diffuse gamma raysGamma Ray Flux from WIMP annihilation:

Similar expressions for:pp->π0+x->γγ+x, (ρ given by gas density, highest in disc) eγ->eγ, eN->eγN, (ρ given by electron/gamma density, highest in disc)Extragalactic Background (isotropic)DM annihilation (ρ∝ 1/r2 for flat rotation curve)All have very different, but known energy spectra.Cross sections known. Densities not well known, so keep absolutenormalization free for each process.

Fit shape of various contributions with free normalization, but normalizationlimited by experimental overall normalization error, which is 15% for EGRETdata. Point-to-point errors 5-10% (yield good χ2).


Hubble const. determines WIMP annihilation x-section

WIMP annihilation is a strong source of antiprotons, positrons and gammas by annihilation into quarks.

Thermal equilibrium abundance

Actual abundance

T=M/25

Com

ovin

g nu

mbe

r den

sity

x=m/T

T>>M: f+f->M+M; M+M->f+fT<M: M+M->f+fT=M/25: M decoupled, stable density(wenn annihilation rate ≅ expansion rate, i.e. Γ=<σv>nχ ≅ H !)

Jung

man

n,K

amio

nkow

ski,

Grie

st, P

R 1

995

Boltzmann equation:H-Term takes care of decrease in densityby expansion. Right-hand side:Annihilation and Production.

Present number density (Ωh2=0.113±0.009)requires <σv>=2.10-26 cm3/s assuming no coannihilation


Neutralino Annihilation Final States

χ

χ

χ

χ

χ

χ

χ

χ

χ

χ

f

f

f

f

f

f

Z

Z

W

Wχ± χ0

f~ A Z

B-fragmentation well studied at LEP!Yield and spectra of positrons,gammas and antiprotons well known!

Dominant diagram for WMAPcross section:χ + χ ⇒ A ⇒ b bbar quark pair


Annihilation cross sectionsHelicity suppression for light states at zero momentum

Up-type quarks suppressed at large tan beta


Annihilation cross sectionsin m0-m1/2 plane (µ > 0, A0=0)

tan=5 tan=50bb t t

ττ WW

bb t t

ττ WW

For WMAP x-section of <σv>≅2.10-26 cm3/s one needs large tanβin bulk region (no coannihilation, no resonances)

10-2410-27

EGRETWMAP


Excess of Diffuse Gamma Rays above 1 GeV(first publications by Hunter et al, Sreekumar et al. (1997)St

rong

, M

oska

lenk

o, R

eimer

, to

be

publishe

d

Prel.

A: inner Galaxy (l=±300, |b|<50)B: Galactic plane avoiding AC: Outer Galaxy

D: low latitude (10-200)

E: intermediate lat. (20-600)F: Galactic poles (60-900)

A B C

D E F

π0

Bremsstrahlung

Inv. Compton


Local electron and proton spectradetermine shape of gamma background

Solar modulation (SM) important below 10 GeVProton and electron spectra above 10 GeV well measured ⇒Gamma spectrum well known, unless one assumes “local bubble”,i.e. spectra in galaxy different from locally measured ones.

No SMNo SM

Electrons

Protons

WIMPS


Excess of Diffuse Gamma Rays has same spectrum in all directions compatible with WIMP mass of 50-100 GeV

Important: if experiment measures gamma rays down to 0.1 GeV, then normalizations of DM annihihilation and background can both be left free, so one is not sensitive to abso-lute background estimates, BUT ONLY TO THE SHAPE, which is much better known.

Egret Excess aboveextrapolated backgroundfrom data below 0.5 GeV

Excess same shape in all regions implying same source everywhere

Statistical errors only


Background scaling factors


Longitude and Latitude for Gammas BELOW 0.5 GeV

In the plane (± 50 in lat.) Out of the plane (± 300 in long..)


Longitude and Latitude for Gammas ABOVE 0.5 GeV

Out of the plane (± 300 in long..)In the plane (± 50 in lat.)


Executive Summary

xy

xz

xy

xz

Expected Profile

FGFR

x y

z

2003, Ibata et al, Yanny et al.

Outer RingInner Ring

DM halo

diskbulge

Rotation Curve

Outer Ring

Inner Ring

bulge

DM halodisk

Rotation CurveIsothermal Profile

v2∝M/r=cons.and

ρ∝M/r3

ρ∝1/r2

for const.rotationcurve

Observed Profile

Halo profile


Do other galaxies have bumps in rotation curves?


Diffuse Gamma Rays for different sky regions

A B C

D E F

3 components: galactic background + extragalactic bg + DM annihilationfitted simultaneously with same boostfactor (≈50) in all directions

Flux∝ B<ρ2>In order tomeasure <ρ2>one has to assume sameB in all directions

Flux obviouslystronger in disc of galaxy(regions A,B,C)


Boostfactor

Clumps in N-body simulations with kpc resolution

Clumps in analyt. calculations with pc resolution

Annihilation∝ DM density squared!

Clustersize: 1014 cm =10x solar systemMmin ≅ 10-8 MסCluster density ≅ 25 pc-3

Halo mass fraction in clumps: 0.002

Clumps with Mmin give the dominantcontribution to DM annihilation

Boost factor ∼ <ρ2>/<ρ>2 ∼ 10-100


Halo profiles

α,β,γ define the slopeρ0 = local density 0.3-0.7 GeV/cm3

a -scale parameter (depends on ρ0)

N-body simulations prefer cuspyNFW profile with α,β,γ,a = 1,3,1,10

However many LSB show coredisothermal profile: α,β,γ,a = 2,2,0,4

Furthermore: halo seldom spherical,but ellipsoidal: x2/a2 +y2/b2 + z2/c2 = cwith a>b>c

Isothermal core

NFW cusp

Expect from N-body simulations of galaxy formation:


Why LIGHT traces DM in discReasons for enhanced DM in disc of galaxy:

1)Adiabatic compression of halo by gravity from disc(Blumenthal, Kalnajs, Wilkinson,…..)

(halo distribution may be modified by resonant interactionsbetween bar and halo, Athanassoula, Katz, Weinberg, ..)

2) Anisotropic infall along filaments of DM(e.g. ring of stars at 14-18 kpc thought to originatefrom infall of dwarf galaxy (Yanny et al., Ibata et al., …)

Parametrize with at least 2 rings:Inner ring for 1) Outer ring for 2)


Anisotropic infall during galaxy formation

Anisotropic infall along DM filaments:

Higher density in the discAlignment of angular momenta of discsDisc tends to have angular momentaaligned along minor axis(Bailin, Steinmetz,astro-ph/0408163)

Galaxy Formation on top of DM by Joerg Colberg and Antonaldo Diaferio

vhalo.mpeg


Uncertainties in the background shape

Pulsars (Lorimer,2004)

Galprop sources

XCO=N(H2)/WCO

R (kpc)R (kpc)

Problem in GALPROP:Source distribution of Cosmic Raysvery flat vs. Galactocentric radius in order to get enough gamma rays at large radii. However, pulsar distribution (= Supernovae Remnants) peaked around 4 kpc.

Solution: take pulsar distr. as source distr. and increase gamma ray flux at large radii by radial increase of XCO as expected from metallicitygradient, dust emission, .. -> moremolecular hydrogen at large radii->more gamma rays at larger radii.

Consequences: more freedom in propagation parameters->harder source spectrum of protons possible->less excess -> less WIMP annihilation -> smaller boost factor? No, less mass in rings!


Diffuse Gamma Rays for different sky regions

Conventional Model (CM) Sources distr. as pulsars (PM)


Fit results of halo parameters2 rings with maximumintensity at 4 and 14 kpcEnhancement over isothermalprofile 3 and 8, respectivelySensitive to radius, becauseSun OFF CENTER!

14 kpc coincides with ringof stars at 14-18 kpc due to infall of dwarf galaxy(Yanny, Ibata, …..)

4 kpc coincides with ring ofneutral hydrogen molecules!

(<σv> from WMAP)DM Gamma Ray Flux:

H2

H

R [kpc]4

Boostfactor ≅ 50-70 Dokuchaev et al: 10<B<100, IDM2004


Halo profiles

Isothermal cored profile NFW cuspy profileWITHOUT rings WITH rings WITHOUT rings WITH rings

10 100

α,β,γ=2,2,0 α,β,γ=1,3,1


Longitude fits for isothermal (cored) profile

WITHOUT rings WITH 2 rings

DISC DISC

50<b<100 50<b<100

100<b<200

200<b<900 200<b<900

100<b<200

Halo parameters from fit to 180 sky directions: 4 long. profiles forlatitudes <50, 50<b<100, 100<b<200, 200<b<900 (=4x45=180 directions)


Longitude fits for isothermal (cored) profile

Conventional GALPROP ModelSources distributed as pulsars(harder background spectrum)

DISC DISC

50<b<100 50<b<100

100<b<200

200<b<900 200<b<900

100<b<200

Halo parameters from fit to 180 sky directions: 4 long. profiles forlatitudes <50, 50<b<100, 100<b<200, 200<b<900 (=4x45=180 directions)


Fit with outer ring only in observable star region0.1 < Eγ < 0.5 GeV Eγ > 0.5 GeV

Stars only observed in galactic anticentreEGRET data requires complete ring of DM, not only in region where stars observed


EGRET data compatible with prolate isothermal halo profile with b/a ≅ 0.9, c/a ≅ 0.8

x

z

y

ab

c

W. de Boer et al., astro-ph/0408272Angular momentumalong short axis cas expected fromN-body simulations(Bailin, Steinmetz,astro-ph/0408163))


Galactic Parameters

NFW

isothermal

Mdi

sc/M

halo

Mdi

sc/M

halo

Mhalo Mhalo

Mhalo Mhalo

Con

cent

ratio

nC

once

ntra

tion

NFW: halo too concentrated compared with EGRET data

Isothermal profile: perfectly compatible with EGRET data

Galactic parametersfrom EGRET data

Further parameters:R200=295 kpcDM: 3.1012 MסBaryonic: 6.1010 MסMass of outer (inner) ring <3 (1)% of total DM.Only so important, whilenearby!!!!!!!!!


Rotation curve of our galaxy


bulge

DM halodisk

Rotation Curve (CM) Rotation Curve (PM)

Outer Ring4.1010 M8.1010ס Mס

Rotation curve shows there is a ring of CDM with a mass of (4-8).1010 Mס


Rotation curve for cuspy NFW profile

Cuspy NFW profile needs to be compensated by thick rings-> too large surface density and too large outer rotation curveToo little DM towards pole for constant boostfactor


bulge

DMhalodisk

Rotation Curve (CM)

1.1 1011 Mס

DISC

Polar region


Local surface density ΣHeight distribution and velocity dispersion σ of local stars determinelocal gravitational potential (just like decrease in atmospheric densityis determined by gravity of earth).

Decrease in rotation curve suggests little Dark Matter.

First measurements: Jan Oort in 1932: assuming constant σ: repulsive gravity.

Later: σ(z ) ⇒ E.g. Σ= ∫ρdz = 71±6 Mס/pc-2 for zmax=1.1 kpcby Kuijken+ Gilmore, 1991. They assumed constant DM density and verylittle of it. So they were stretching visible matter by brown dwarfs etc.

2001: Olling +Merrifield: consensus value of Σ from visible matter: 35±10 2002: Bienayme et al.: Σ = 85±? Error strongly dependent on assumptions

of DM distributions. From EGRET data: DM density steep function of z due to ring structure

2004: Present analysis: ΣDM=44 (PM)-60(CM) Mס/pc-2 and Σvis=29 Mס/pc-2 with


Positron fraction and antiprotonsfrom DM annihilation

SAME Halo and MSSM parameters as for GAMMA RAYSbut fluxes strong function of propagation model!s

Positrons AntiprotonsAntiprotonsPositrons


SUSY Mass spectra in mSUGRA

LSP largely Bino ⇒ DM may be supersymmetric partner of CMB

Charginos, neutralinosand gluinos light


Comparison with direct DM Searches

Predictions from EGRET data


Unification of gauge couplingsUpd

ate

from

Amaldi

, dB

,Fu

erst

enau

, PL

B 26

0 19

91

With SUSY spectrum from EGRET data perfect gauge couplingunification possible for αs=0.123 as determined from Rl=Γhad/ΓleptonThis value is independent of luminosity. Note αs=0.115 from Γhad alone,But this value is probably low because of systematic uncertainty in LEP lumi.If lumi increased by 3σ, as=0.122 and Nv=3.0! (dB, Sander, PL B585 (2004))


SummaryThe excess of EGRET diffuse galactic gamma rays in the range between 1

and 100 GeV shows all the key features from WIMP annihilation:

1) the energy spectrum of the excess is the same in all sky directionsand is consistent with the π0 decays from monoenergetic quarksoriginating from WIMP annihilation for a WIMP mass between 50-100 GeV

2) the intensity distribution is used to determine the halo profile, which -outside the plane of the galaxy - was found to correspond to an isothermal (cored) profile and excludes the cuspy NFW profile

3) in the disc of the galaxy the excess shows substructure: two oval rings at radii of 4 and 14 kpc (correlated with the ring of molecular hydrogen at 4 kpc and ring of stars at 14 kpc)

4) these rings yield a change of slope at R=R0 in the rotationcurve and are consistent with the high local surface density

5) all features and cross sections are consistent with the WIMP being the neutralino from Minimal Supersymmetry

6) Alternative “conventional” models cannot explain stability of ring of stars at 14 kpc and H2 ring of molecular gas at 4 kpc,nor change of slope in rotation curve, nor halo shape of excess

wim de boer, christian sander, valery zhukov univ...

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