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

Milky Way dark matter density profile and its reconstruction Ekaterina Karukes In collaboration with: Maria Benito, Fabio Iocco, Roberto T rotta and Alex Geringer-Sameth arXiv:1901.02463 10/04/2019 Accelerating the Search for Dark Matter with Machine Learning, Trieste

Motivations Placing MW in LCDM paradigm Tollet+ (2016) Tollet+ (2016) APOSTLE Auriga 1 1 ∆ � fit ∆ � fit 0 0 MW MW − 1 − 1 10 − 5 10 − 4 10 − 3 10 − 2 10 − 1 10 − 5 10 − 4 10 − 3 10 − 2 10 − 1 M � /M Tot M � /M Tot Bose et al. 2018 (arXiv:1810.03635) Direct and indirect dark matter searches Benito et al. 2017 (arXiv:1810.03635) 10/04/2019 E. KARUKES 2

MW overview V km/s BHB gas clouds halo stars masers 20 2.5 r kpc DM halo 10/04/2019 E. KARUKES 3

Compilation of MW RC M. Pato and F. Iocco’17 huang et al.’16 Bayesian evidence to determine the degree of overlap (If you are interested ask me later) Han & Gould’03 STANEK ET AL.’96 FERRIERE’98 & FERRIERE ET AL.’07 10/04/2019 E. KARUKES 4

Compilation of MW RC M. Pato and F. Iocco’17 Bayesian evidence to determine the degree of overlap huang et al.’16 (If you are interested ask me later) Han & Gould’03 S T A N E K E T A L . ’ 9 6 FERRIERE’98 & FERRIERE ET AL.’07 10/04/2019 E. KARUKES 4

Methodology standard approach see e.g. Sofue & Rubin’01, Catena & Ullio’09… total gravitational potential: φ total φ bar φ dm + = DM potential assuming spherical symmetry: Z R φ dm = − GM dm ( r ) ρ dm ( r ) r 2 dr M dm ( r ) = 4 π r 2 0 gNFW DM density profile: R 0 - Sun’s position ρ 0 - density at Sun’s location 10/04/2019 E. KARUKES 5

MCMC-based reconstruction Bayes theorem: POSTERIOR ∝ PRIOR × LIKELIHOOD we adopt flat priors Likelihood function: ω i � 2 m ( " #) � ω c ( r i , Θ ) � ¯ 1 � 1 Y p P(d | Θ ) = exp σ 2 2 2 πσ ¯ ω ,i ω ,i ¯ i =1 " # � h τ i � h τ i obs � 1 � 1 2 . 17 ± 0 . 47 ⇥ p exp Pato et al.’15 σ 2 2 2 πσ h τ i h τ i " # � Σ ⇤ � Σ obs � 38 ± 4 M � /pc 2 1 � 1 ⇤ ⇥ p exp σ 2 2 2 πσ Σ ∗ Σ ∗ Note that the angular velocity ω c is used instead of the actual circular velocity V c ≡ r ω c In the wake of standard approach 10/04/2019 E. KARUKES 6

<latexit sha1_base64="w6eQ3jEv/dGQDRLejdXts0sEpEs=">ACBXicbVC7SgNBFJ2Nrxhfq5ZaDAbBQtbdJKBl0ELCOYB2TXMTibJkJnZWZWCEsaG3/FxkIRW/Bzr9xkmyhiQcuHM65l3vCWNGlXbdbyu3tLyupZfL2xsbm3v2Lt7DRUlEpM6jlgkWyFShFB6pqRlqxJIiHjDTD4dXEbz4QqWgk7vQoJgFHfUF7FCNtpI596DqVsh9z6DpuyT9NfcnhNWmcYX5fHnfsopGngIvEy0gRZKh17C+/G+GE6ExQ0q1PTfWQYqkpiRcFPFIkRHqI+aRsqECcqSKdfjOGxUbqwF0lTQsOp+nsiRVypEQ9NJ0d6oOa9ifif10507yJIqYgTQSeLeolDOoITiKBXSoJ1mxkCMKSmlshHiCJsDbBFUwI3vzLi6RcjzX8W4rxeplFkceHIAjcAI8cA6q4AbUQB1g8AiewSt4s56sF+vd+pi15qxsZh/8gfX5A4lulg4=</latexit> <latexit sha1_base64="w6eQ3jEv/dGQDRLejdXts0sEpEs=">ACBXicbVC7SgNBFJ2Nrxhfq5ZaDAbBQtbdJKBl0ELCOYB2TXMTibJkJnZWZWCEsaG3/FxkIRW/Bzr9xkmyhiQcuHM65l3vCWNGlXbdbyu3tLyupZfL2xsbm3v2Lt7DRUlEpM6jlgkWyFShFB6pqRlqxJIiHjDTD4dXEbz4QqWgk7vQoJgFHfUF7FCNtpI596DqVsh9z6DpuyT9NfcnhNWmcYX5fHnfsopGngIvEy0gRZKh17C+/G+GE6ExQ0q1PTfWQYqkpiRcFPFIkRHqI+aRsqECcqSKdfjOGxUbqwF0lTQsOp+nsiRVypEQ9NJ0d6oOa9ifif10507yJIqYgTQSeLeolDOoITiKBXSoJ1mxkCMKSmlshHiCJsDbBFUwI3vzLi6RcjzX8W4rxeplFkceHIAjcAI8cA6q4AbUQB1g8AiewSt4s56sF+vd+pi15qxsZh/8gfX5A4lulg4=</latexit> <latexit sha1_base64="w6eQ3jEv/dGQDRLejdXts0sEpEs=">ACBXicbVC7SgNBFJ2Nrxhfq5ZaDAbBQtbdJKBl0ELCOYB2TXMTibJkJnZWZWCEsaG3/FxkIRW/Bzr9xkmyhiQcuHM65l3vCWNGlXbdbyu3tLyupZfL2xsbm3v2Lt7DRUlEpM6jlgkWyFShFB6pqRlqxJIiHjDTD4dXEbz4QqWgk7vQoJgFHfUF7FCNtpI596DqVsh9z6DpuyT9NfcnhNWmcYX5fHnfsopGngIvEy0gRZKh17C+/G+GE6ExQ0q1PTfWQYqkpiRcFPFIkRHqI+aRsqECcqSKdfjOGxUbqwF0lTQsOp+nsiRVypEQ9NJ0d6oOa9ifif10507yJIqYgTQSeLeolDOoITiKBXSoJ1mxkCMKSmlshHiCJsDbBFUwI3vzLi6RcjzX8W4rxeplFkceHIAjcAI8cA6q4AbUQB1g8AiewSt4s56sF+vd+pi15qxsZh/8gfX5A4lulg4=</latexit> <latexit sha1_base64="w6eQ3jEv/dGQDRLejdXts0sEpEs=">ACBXicbVC7SgNBFJ2Nrxhfq5ZaDAbBQtbdJKBl0ELCOYB2TXMTibJkJnZWZWCEsaG3/FxkIRW/Bzr9xkmyhiQcuHM65l3vCWNGlXbdbyu3tLyupZfL2xsbm3v2Lt7DRUlEpM6jlgkWyFShFB6pqRlqxJIiHjDTD4dXEbz4QqWgk7vQoJgFHfUF7FCNtpI596DqVsh9z6DpuyT9NfcnhNWmcYX5fHnfsopGngIvEy0gRZKh17C+/G+GE6ExQ0q1PTfWQYqkpiRcFPFIkRHqI+aRsqECcqSKdfjOGxUbqwF0lTQsOp+nsiRVypEQ9NJ0d6oOa9ifif10507yJIqYgTQSeLeolDOoITiKBXSoJ1mxkCMKSmlshHiCJsDbBFUwI3vzLi6RcjzX8W4rxeplFkceHIAjcAI8cA6q4AbUQB1g8AiewSt4s56sF+vd+pi15qxsZh/8gfX5A4lulg4=</latexit> Results observational data ~ 5 % statistical uncertainty 6 1 . 2 1 . γ 8 Precise! 0 . 4 0 . 0 . 43 ± 0 . 02 GeV / cm 3 6 5 . 0 8 4 . 0 ρ 0 0 4 . 0 2 3 . 0 6 2 8 4 0 4 8 2 6 2 0 8 6 1 1 2 3 3 4 4 5 . . . . 0 0 1 1 . . . . 0 0 0 0 r s ρ 0 γ Can we trust it, i.e. is it accurate? 10/04/2019 E. KARUKES 7

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: ω mock( i ) = ω fid( i ) + δ i c c with ω fid(i) = ( ω 2 NFW ( r s , γ , ρ 0 , r ( i ) ) + ω 2 baryons ( Σ ∗ , h τ i , r ( i ) )) 1 / 2 c g • i is the index number of a bin • r s , γ , ρ 0 , Σ ∗ , h τ i are the fiducial parameters • is a random sample from a normal distribution with mean 0 δ i and variance equal to the observational error 10/04/2019 E. KARUKES 8

MCMC-based reconstruction and mock RCs ω mock( i ) = ω fid( i ) + δ i c c r s = 20 kpc, ρ 0 = 0 . 4 GeV / cm 3 γ =0.0 10 0 γ =0.6 γ =1.5 ρ 0 [ GeV / cm 3 ] 10 − 1 x 10 − 2 10 − 3 10 1 10 2 R [kpc] 10/04/2019 E. KARUKES 9

MCMC-based reconstruction and mock RCs ω mock( i ) = ω fid( i ) + δ i c c r s = 20 kpc, ρ 0 = 0 . 4 GeV / cm 3 400 γ =0.0 γ =0.6 γ =1.5 300 V [km/s] 200 100 0 20 40 60 80 100 R [kpc] 10/04/2019 E. KARUKES 9

Results 100 mock realisations 25 points in the parameter space true parameters 0 . 2 6 . 1 2 . 1 γ 8 . 0 4 . 0 6 5 . ρ 0 [GeV / cm 3 ] 0 8 4 . 0 0 4 . 0 2 3 . 0 4 2 . 0 8 6 4 2 0 4 8 2 6 0 4 2 0 8 6 1 2 3 4 . . . . . 2 3 4 4 5 0 0 1 1 2 . . . . . 0 0 0 0 0 r s [kpc] ρ 0 [GeV / cm 3 ] γ 10/04/2019 E. KARUKES 10

Results 100 mock realisations 25 points in the parameter space 10/04/2019 E. KARUKES 10

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