Andrea Chiappo andrea.chiappo@fysik.su.se Co-authors: Jan Conrad, - - PowerPoint PPT Presentation

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Limits on Dark Matter annihilation in dwarf galaxies with prior-free astrophysical factors

Andrea Chiappo andrea.chiappo@fysik.su.se

Co-authors: Jan Conrad, Nils Håkansson, Johann Cohen-Tanugi, Louis E. Strigari

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Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Photon flux from DM annihilation:

• one of main uncertainties in the statistical analysis of the γ-ray data
• previously obtained with Bayesian methods
• γ-ray analyses are performed in a frequentist manner

Φγ(∆Ω) = ⇥σv⇤ 2m2 ⌥ Emax

Emin

dN dEγ dEγ ⌦

• ↵

particle physics factor

1 4π ⌥

∆Ω

⌥

l.o.s

ρ2(r(l))dl dΩ ⌦

• ↵

J factor

Dwarf spheroidal satellite galaxies (dSphs) of the Milky Way: ideal targets for Dark Matter (DM) indirect detection Searching for DM decay or annihilation products (e+, e-, γ…)

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Premises & Motivation

• nearby
• DM dominated
• low γ-ray contamination
• low Galactic foregrounds

(Bergström et al. 1998)

priors influence on DM particle properties inference

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Objectives

• I. BUILD PRIOR-FREE DSPHS J-FACTORS LIKELIHOODS
• JEANS ANALYSIS ASSUMING SPHERICAL SYMMETRY
• MAXIMUM LIKELIHOOD TECHNIQUE TO FIT PARAMETERS
• VALIDATION ON SIMULATIONS BY GAIA CHALLENGE
• APPLIED ON STELLAR KINEMATIC DATA FROM 9 DSPHS
• II. UPDATE UPPER LIMITS
• COMBINE NEW J-LIKELIHOODS WITH PUBLISHED γ-LIKELIHOODS

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σv⇥95%

(from arxiv:1503.02641)

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Jeans Equation

For dSphs as spherically symmetric, collision-less steady state systems

: line-of-sight velocity dispersion : surface brightness : stellar density profile : velocity anisotropy kernel function : DM Halo mass

I(R)

(Mamon & Łokas 2004)

M(s) = ⌥ s ρ(r) r2 dr

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σ2

los(R) = 2G

I(R) ∞

R

K(r, R)ν(r)M(r)dr r

los(R) ⌃(r) K(r, R)

CAVEAT: only valid for DM-dominated systems (like dSphs)

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Jeans Equation

DM profile: Velocity profile:

⇣ ⌘ βiso(r) = 0

Stellar profile: (generalised NFW)

⌃Plummer(r ; r, ) =

• ⇤

1 +

• r

r⇥

⇥2⌅ 5

2

• ⇥

⌃Plummer-like(r ; r, ) =

• r

r⇥

⇥0.1 ⇤ 1 +

• r

r⇥

⇥2⌅ 4.9

2

• ⇥

⇤

• ⇥ ⌅

⌃non-Plummer(r ; r, ) =

• r

r⇥

⇥ ⇤ 1 +

• r

r⇥

⇥2⌅2

(Hernquist 1990) (Zhao 1996)

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ρDM(r ; r0, ρ0, a, b, c) = ρ0

• r

r0

⇥c 1 +

• r

r0

⇥a⇥ bc

a

(construction of J likelihood is unreliable when the stellar anistropy is allowed as free parameter)

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Likelihood

Unbinned Gaussian Likelihood on stars’ velocity where

• : with the measurement uncertainty of
• : the data vectors

i

vi

From and

J ∝ 2

J-sampling

• sample over with MCMC
• retain the likelihood evaluations
• envelope the likelihood in direction

CAVEAT: Gaussian Likelihood is an approximation to the true underlying velocity distribution function

J = log10(J)

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(Walker et al. 2006, Strigari et al. 2008)

L(⌦ g|D) =

NF i=1

e

− (vi−u)2

22 i

⌦ 2⌥ 2

i

L(⌦ g|D) = − ln L = 1 2

NF

⌥

i=1

⇧ ln(2⌥ 2

i ) + (vi − u)2

2

i

⌃

2

i = ⇧2 i + 2 los(Ri ;⌦

g) D = (⌦ v,⌦ ⇧, ⌦ R)

CAVEAT: only valid for velocity-independent annihilation cross-section

J =

L

2

los(R) ∝ M(r) ∝ 0

2

los(R) ∝

√ J

We fit via two possible schemes:

manual-profiling

• vary over likely range
• sample over with MCMC
• retaining the likelihood evaluations
• intepolate between pairs

J =

L

~ g = J , a, b, c, r0

~ g = a, b, c, r0

(J , LJ )

profile likelihood L(J )

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Profile likelihood: example

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log-normal J likelihood profile J likelihood (manual-profiling) profile J likelihood (J-sampling)

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

GAIA CHALLENGE: one-component, spherical models used to validate the method:

DM profile velocity distribution stellar profile Cusped Isotropic Plummer-like Cusped Isotropic non-Plummer Cored Isotropic Plummer-like Cored Isotropic non-Plummer

CAVEAT:

not generated with Gaussian sampling distribution

Validation

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N★ = 100 N★ = 1000

Examples: Isotropic Cored Plummer-like

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Validation: coverage and bias

1-σ COVERAGE BIAS

Partition the full dataset (N★ = 104) into sets of N★ = 10,100,1000

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Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Validation: bias extended

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Explore the statistical properties by considering the cases: we fit a power law to the bias estimates ➝ index ~ 0.5 using the best-fit power law we get an estimate of the minimum N★ to achieve a bias < 10% in J

↓ (on average) N★ ≳ 200 N★

NPE

10 1000 20 500 50 200 100 100 200 50 500 20 1000 10

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Results for real data: examples

θMAX = 0.5° DM profile: generalised NFW surface brightness: Plummer velocity anisotropy: Isotropic

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Data utilised:

• kinematic data from 9 dSphs

(galaxies with N★ ≳ 200)

• consisting of (R, v, ε)

(projected radius, velocity, velocity uncertainty)

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Updated 〈σv〉upper limits

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preliminary

L(⇥⌅v⇤ |mχ) =

Ndwarfs

⌥

d=1

⇧ min

J

⇤Nbins ⌥

b=1

Ld

b

⇥⌅v⇤ J ⇥⌅v⇤0 J0 Φexp

b

(mχ) ⇥ Ld(J ) ⌅⌃

normalisation values of

⇤ v⌅0 , J0 Φexp

b

(mχ)

• ptimise

where:

103 104 105 Energy (MeV) 10−8 10−7 10−6 10−5 10−4 Energy Flux (MeV cm−2 s−1) Draco 1 2 3 4 5 6 7 8 9 −∆ log L

(Ackermann et al. 2014)

example: Draco

Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

Future work

• Determine frequentist J-factor for recently discovered (DES) dSphs
• Derive new upper limits using more γ-ray data from more dSphs
• Perform coverage test on
• Study systematics arising from different model assumptions or Likelihood
• Improvements to the code (public release is planned)
• implement non-Gaussian likelihoods
• explore different optimisation algorithms
• Include probability of interloper Milky Way stars

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Halo Substructure and Dark Matter searches, Andrea Chiappo, IFT June 2018

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Thank you