Milky Way dark matter density profile and its reconstruction - - PowerPoint PPT Presentation

Milky Way dark matter density profile and its reconstruction

Ekaterina Karukes

10/04/2019

In collaboration with: Maria Benito, Fabio Iocco, Roberto T rotta and Alex Geringer-Sameth

Accelerating the Search for Dark Matter with Machine Learning, Trieste

arXiv:1901.02463

Direct and indirect dark matter searches

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Motivations

10−5 10−4 10−3 10−2 10−1 M/MTot −1 1 ∆fit

Tollet+ (2016) APOSTLE

10−5 10−4 10−3 10−2 10−1 M/MTot −1 1 ∆fit

Tollet+ (2016) Auriga

Bose et al. 2018 (arXiv:1810.03635)

Placing MW in LCDM paradigm

MW MW

Benito et al. 2017 (arXiv:1810.03635)

MW overview

DM halo

V km/s r kpc

2.5 20

gas clouds masers BHB halo stars

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FERRIERE’98 & FERRIERE ET AL.’07 STANEK ET AL.’96

• M. Pato and F. Iocco’17

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Han & Gould’03

huang et al.’16

Compilation of MW RC

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Bayesian evidence to determine the degree of overlap

(If you are interested ask me later)

Han & Gould’03

FERRIERE’98 & FERRIERE ET AL.’07 S T A N E K E T A L . ’ 9 6

• M. Pato and F. Iocco’17

huang et al.’16

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Compilation of MW RC

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Bayesian evidence to determine the degree of overlap

(If you are interested ask me later)

10/04/2019

Methodology

standard approach

see e.g. Sofue & Rubin’01, Catena & Ullio’09…

total gravitational potential: φtotal φbar φdm = + DM potential assuming spherical symmetry: gNFW DM density profile:

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φdm = −GMdm(r) r2

Mdm(r) = 4π Z R ρdm(r)r2dr

R0 - Sun’s position

ρ0 - density at Sun’s location

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MCMC-based reconstruction

Bayes theorem: Likelihood function:

P(d|Θ) =

m

Y

i=1

( 1 p 2πσ¯

ω,i

exp " 1 2

• ωc(ri, Θ) ¯

ωi2 σ2

¯ ω,i

#) ⇥ 1 p 2πσhτi exp " 1 2

• hτi hτiobs

σ2

hτi

# ⇥ 1 p 2πσΣ∗ exp " 1 2

• Σ⇤ Σobs

⇤

• σ2

Σ∗

#

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2.17 ± 0.47

38 ± 4M/pc2

Pato et al.’15

Note that the angular velocity ωc is used instead of the actual circular

Vc ≡ rωc

velocity

POSTERIOR ∝ PRIOR × LIKELIHOOD

we adopt flat priors

In the wake of standard approach

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. 4 . 8 1 . 2 1 . 6 γ 6 1 2 1 8 2 4 3 rs . 3 2 . 4 . 4 8 . 5 6 ρ0 . 4 . 8 1 . 2 1 . 6 γ . 3 2 . 4 . 4 8 . 5 6 ρ0

Precise!

0.43 ± 0.02 GeV/cm3

Results

• bservational data

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~ 5 % statistical uncertainty

Can we trust it, i.e. is it accurate?

MCMC-based reconstruction and mock RCs

The idea is to test the MCMC-based reconstruction by creating mock rotation curves based on “underlying known” DM profiles (+ visible) and with the same statistical properties of the observed RC

We use the following way to create the mock data: with

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ωfid(i)

c

= (ω2

NFW(rs, γ, ρ0, r(i)) + ω2 baryons(Σ∗, hτi , r(i)))1/2

ωmock(i)

c

= ωfid(i)

c

+ δi

• i is the index number of a bin
• rs, γ, ρ0, Σ∗, hτi are the fiducial parameters
• is a random sample from a normal distribution with mean 0

and variance equal to the observational error

δi

g

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MCMC-based reconstruction and mock RCs

ωmock(i)

c

= ωfid(i)

c

+ δi

101 102

R [kpc]

10−3 10−2 10−1 100

ρ0 [GeV/cm3]

rs = 20 kpc, ρ0 = 0.4 GeV/cm3

γ=0.0 γ=0.6 γ=1.5

x

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MCMC-based reconstruction and mock RCs

ωmock(i)

c

= ωfid(i)

c

+ δi

20 40 60 80 100

R [kpc]

100 200 300 400

V [km/s]

rs = 20 kpc, ρ0 = 0.4 GeV/cm3

γ=0.0 γ=0.6 γ=1.5

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Results

100 mock realisations 25 points in the parameter space

. 4 . 8 1 . 2 1 . 6 2 . γ 8 1 6 2 4 3 2 4 rs [kpc] . 2 4 . 3 2 . 4 . 4 8 . 5 6 ρ0 [GeV/cm3] . 4 . 8 1 . 2 1 . 6 2 . γ . 2 4 . 3 2 . 4 . 4 8 . 5 6 ρ0 [GeV/cm3]

true parameters

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Results

100 mock realisations 25 points in the parameter space

Results

• bservational data

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. 4 . 8 1 . 2 1 . 6 γ 6 1 2 1 8 2 4 3 rs . 3 2 . 4 . 4 8 . 5 6 ρ0 . 4 . 8 1 . 2 1 . 6 γ . 3 2 . 4 . 4 8 . 5 6 ρ0

Precise!

0.43 ± 0.02 GeV/cm3

Results

• bservational data

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15 30 45 c 0.4 0.8 1.2 1.6 γ 6.0 7.5 9.0 10.5 12.0 Mvir × 1011 15 30 45 c 6.0 7.5 9.0 10.5 12.0 Mvir × 1011

Preliminary

Mvir = 8.1+0.92

0.86 M

Summary

Bayesian reconstruction of the Milky Way dark matter distribution:

• precise reconstruction of the dark matter density distribution;
• high accuracy on the local dark matter density;
• weak accuracy on the inner dark matter density slope and

scale radius . Preliminary

• accurate and precise estimation of the Milky Way mass .

γ

rs

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Backup slides

Compatibility of data sets via the Bayesian evidence

for details on the methodology see e.g. arXiv: 1101.1521, astro-ph/

0203259, 0807.4512, 0903.2487

is the Bayesian evidence for data given model

p(d|M) M

galkin 12 data sets + 2 data sets of Huang et al.

B = p(d1, d2|M) p(d1|M1)p(d2|M2)

Compilation of MW RC