Analytic modeling of subhalo evolution and annihilation boost - PowerPoint PPT Presentation

Halo Substructure and Dark Matter Searches Madrid, 27 June 2018 Analytic modeling of subhalo evolution and annihilation boost Shin’ichiro Ando U. Amsterdam / U. Tokyo

Annihilation boost L ( M ) = [1 + B sh ( M )] L host ( M ) 1 Z dmdN B sh ( M ) = dmL sh ( m )[1 + B ssh ( m )] L host ( M ) http://wwwmpa.mpa-garching.mpg.de/aquarius/

Motivation for physics • Help increase the rate of dark matter annihilation • Mass of smallest halos is determined by scattering between dark matter and SM particles ( kinetic decoupling + free-streaming) • Boost factor depends on primordial power spectrum at small scales

Impact of the smallest structure Diamanti, Cabrera-Catalan, Ando, Phys. Rev. D 92 , 065029 (2015) Fornasa et al. Phys. Rev. D 94 , 123005 (2016) 10 − 12 − 1 M ⊙ Typical smallest halo mass: • MCMC parameter scan for 10 − 12 − 10 − 4 M ⊙ 9-parameter MSSM

Primordial power spectrum Gosenca et al., Phys. Rev. D 96 , 123519 (2017) 10 17 10 16 Φ astro , tot 10 15 10 14 A b = 0 A b = 10 A b = 10 2 10 13 A b = 10 3 10 2 10 1 z • Some inflation model predicts non-power-law behavior of the primordial spectrum at small scales • This will increase/decrease the number of small halos (e.g., ultracompact mini halos)

Analytic model of subhalo evolution • Complementary to numerical simulations • Light, flexible, and versatile • Can cover large range for halo masses ( micro-halos to clusters ) and redshifts ( z ~ 10 to 0 ) • Physics-based extrapolation • Reliable if it is calibrated with simulations at resolved scales

This talk is based on: • “Boosting the annihilation boost: Tidal e ff ects on dark matter subhalos and consistent luminosity modeling” R. Bartels & S. Ando, Phys. Rev. D 92 , 123508 (2015) Richard Bartels • “Modeling evolution of dark matter substructure and annihilation boost” N. Hiroshima , S. Ando, & T. Ishiyama , Phys. Rev. D 97 , 123002 (2018) Nagisa Hiroshima • “A Gaia DR2 search for dwarf galaxies towards Fermi-LAT sources: implications for annihilating dark matter” I. Ciuc ă , D. Kawata, S. Ando, F . Calore, J. I. Read, & C. Mateu, arXiv:1805.02588 [astro-ph.GA] Tomoaki Ishiyama

Analytic model: Recipe Initial condition: Structures start to form Primordial power spectrum Smaller halos merge and accrete Extended Press-Schechter to form larger ones formalism Modeling for tidal stripping Subhalos experience mass loss and mass-loss rate

Formulation sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc

Formulation Accretion sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc

Formulation Accretion sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc Number of subhalos accreted at z acc with mass m acc

Formulation Accretion Evolution sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc Number of subhalos accreted at z acc with mass m acc

Formulation Accretion Evolution sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc Number of subhalos accreted Luminosity of at z acc with mass m acc the subhalo at z

Halo formation and accretion history • Based on spherical collapse model and extended Press- Schechter formalism (Yang et al. 2011) M ) 3/2 exp [ − ( δ ( z acc ) − δ M ) 2 M ) ] d 2 N sh δ ( z acc ) − δ M 1 ∝ ( σ 2 ( m acc ) − σ 2 2( σ 2 ( m acc ) − σ 2 dm acc dz acc 2 π • Primordial power spectrum + cuto ff scale will change rms over-density σ ( M ) • Halo density profile before accretion: NFW + mass- concentration relation by Correa et al. (2015)

Subhalo accretion rate Yang et al., Astrophys. J. 741 , 13, (2011) d 2 N Infall distribution of subhalos : Extended Press-Schechter formalism d ln m a d ln(1 + z a )

Formulation Accretion Evolution sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc Number of subhalos accreted Luminosity of at z acc with mass m acc the subhalo at z

Formulation Accretion Evolution sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc Number of subhalos accreted Luminosity of at z acc with mass m acc the subhalo at z s ( z | m acc , z acc ) { 1 − [1 + r t ( z | m acc , z acc )/ r s ( z | m acc , z acc )] 3 } 1 L sh ( z | m acc , z acc ) ∝ ρ 2 s ( z | m acc , z acc ) r 3

Formulation Accretion Evolution sh ( M , z ) = ∫ d ln m acc ∫ dz acc d 2 N sh L total L sh ( z | m acc , z acc ) d ln m acc dz acc Number of subhalos accreted Luminosity of at z acc with mass m acc the subhalo at z s ( z | m acc , z acc ) { 1 − [1 + r t ( z | m acc , z acc )/ r s ( z | m acc , z acc )] 3 } 1 L sh ( z | m acc , z acc ) ∝ ρ 2 s ( z | m acc , z acc ) r 3 Parameters subhalo density profile after tidal mass loss

Subhalo mass loss Hiroshima, Ando, Ishiyama, Phys. Rev. D 97 , 123002 (2018) • Monte Carlo approach following Jiang & van den Bosch (2016) • Determine orbital energy and angular momentum • Assume the subhalo loses all the masses outside of its tidal radius instantaneously at its peri-center passage • Mass-loss rate follows power law for wide range of m / M

Subhalo density profile after mass loss Springel et al., Mon. Not. R. Astron. Soc. 391 , 1685, (2008) 10 8 10 8 8 10 8 10 Aq-A-1 Aq-A-2 Aq-A-3 10 6 Aq-A-4 6 10 10 6 10 6 ρ ( r ) / < ρ > Aq-A-5 ρ ( r ) / < > ρ > ρ ( r ) / < ρ ( r ) / < ρ > ρ 10 4 V max = 60.0 km s -1 V max = 48.7 km s -1 V max = 47.3 km s -1 10 4 4 10 10 4 M sub = 1.85E+10 M O M sub = 1.27E+10 M O M sub = 1.06E+10 M O • • • d = 338.0 kpc d = 383.3 kpc d = 371.2 kpc 10 2 α = 0.19 α = 0.15 α = 0.21 10 2 10 2 2 10 10 8 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 10 8 10 8 10 8 10 6 10 6 10 6 6 10 ρ ( r ) / < ρ > > ρ ( r ) / < ρ ρ ( r ) / < ρ > ρ ( r ) / < > ρ 10 4 V max = 42.9 km s -1 V max = 47.9 km s -1 V max = 52.5 km s -1 10 4 10 4 10 4 M sub = 8.37E+09 M O M sub = 6.20E+09 M O M sub = 5.81E+09 M O • • • d = 239.4 kpc d = 147.3 kpc d = 189.4 kpc 10 2 α = 0.17 α = 0.27 α = 0.28 10 2 2 10 2 10 10 8 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 10 8 8 10 10 8 10 6 10 6 6 10 10 6 ρ ( r ) / < ρ > ρ > ( r ) / < ρ > ρ ( r ) / < ρ ρ ( r ) / < ρ > 10 4 V max = 38.1 km s -1 V max = 36.0 km s -1 V max = 19.9 km s -1 10 4 10 4 4 10 M sub = 5.09E+09 M O M sub = 1.90E+09 M O M sub = 3.57E+08 M O • • • d = 192.6 kpc d = 113.1 kpc d = 89.1 kpc 10 2 α = 0.15 α = 0.20 α = 0.16 10 2 10 2 10 2 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 10.0 0.1 1.0 10.0 0.1 1.0 10.0 r [ kpc ] r [ kpc ] r [ kpc ] Truncated NFW

Subhalo density profile after mass loss Springel et al., Mon. Not. R. Astron. Soc. 391 , 1685, (2008) 10 8 10 8 10 8 8 10 Aq-A-1 Aq-A-2 Aq-A-3 10 6 Aq-A-4 10 6 6 10 6 10 ρ ( r ) / < ρ > Aq-A-5 ρ > ( r ) / < ρ > ( r ) / < ρ ρ ρ > ( r ) / < ρ 10 4 V max = 60.0 km s -1 V max = 48.7 km s -1 V max = 47.3 km s -1 10 4 10 4 4 10 M sub = 1.85E+10 M O M sub = 1.27E+10 M O M sub = 1.06E+10 M O • • • d = 338.0 kpc d = 383.3 kpc d = 371.2 kpc 10 2 α = 0.19 α = 0.15 α = 0.21 2 10 2 10 10 2 10 8 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 10 8 10 8 10 8 • Procedure 10 6 10 6 10 6 6 10 ρ ( r ) / < ρ > > ρ ( r ) / < ρ ρ ( r ) / < ρ > ρ ( r ) / < > ρ 10 4 V max = 42.9 km s -1 V max = 47.9 km s -1 V max = 52.5 km s -1 10 4 10 4 10 4 M sub = 8.37E+09 M O M sub = 6.20E+09 M O M sub = 5.81E+09 M O • • • d = 239.4 kpc d = 147.3 kpc d = 189.4 kpc 10 2 α = 0.17 α = 0.27 α = 0.28 10 2 2 10 2 10 10 8 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 10 8 8 10 10 8 10 6 10 6 6 10 10 6 ρ ( r ) / < ρ > ρ > ( r ) / < ρ > ρ ( r ) / < ρ ρ ( r ) / < ρ > 10 4 V max = 38.1 km s -1 V max = 36.0 km s -1 V max = 19.9 km s -1 10 4 10 4 4 10 M sub = 5.09E+09 M O M sub = 1.90E+09 M O M sub = 3.57E+08 M O • • • d = 192.6 kpc d = 113.1 kpc d = 89.1 kpc 10 2 α = 0.15 α = 0.20 α = 0.16 10 2 10 2 10 2 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 r [ kpc ] 10.0 0.1 1.0 10.0 0.1 1.0 10.0 0.1 1.0 10.0 r [ kpc ] r [ kpc ] r [ kpc ] Truncated NFW