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Apr 11, 2023 261 likes •557 views

Probing dark matter (sub)structure with strong gravitational lensing Simon Birrer, UCLA Collaborators: Tommaso Treu, Daniel Gilman, Anowar Shajib (UCLA) Adam Amara, Alexandre Refregier (ETHZ) Chuck Keeton, Anna Nierenberg IFT, Madrid,

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Simon Birrer, UCLA

Collaborators:

Tommaso Treu, Daniel Gilman, Anowar Shajib (UCLA) Adam Amara, Alexandre Refregier (ETHZ) Chuck Keeton, Anna Nierenberg

IFT, Madrid, 29.6.2018

Probing dark matter (sub)structure with strong gravitational lensing

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Lens unknown Source unknown can be dark! Image data

Metcalf & Madau 2001 Dalal & Kochanek 2002 Bradac+ 2002 Moustakas & Metcalf 2003 Koopmans 2005 Vegetti+ 2010, 2012, 2018 Hezaveh+ 2016 Nierenberg+ 2014, 2017 Birrer+ 2017

Strong gravitational lensing

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Resolved an un-resolved lensing effects: a simplified example

Observable degeneracies:

  • clump mass
  • clump profile
  • clump position
  • source size

resolved un-resolved

credit: Daniel Gilman, UCLA

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Method 1: Quasar flux ratio anomalies

A B C D G A D C B [OIII]

F140W G141

ii)

unresolved strong lensing from quasar narrow line emission region exclusion regions for a certain type of sub-clump small physical source size allows for sensitivity to very low masses

Image credit: Nierenberg+2017 Dalal & Kochanek 2002 Moustakas & Metcalf 2003 Nierenberg+2014, 2017 Hsueh+2017, Gilman, Birrer+2018 Image credit: Nierenberg+2017

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Method 2: gravitational imaging

resolved strong lensing from galaxy surface brightness direct detection through lens modelling of sensitive to individual clumps near the Einstein ring

2 × 108M

Koopmans 2005 , Vegetti+2010, 2012 … Hezaveh+ 2016, Birrer+2017

sensitivity depends on spatial resolution and source structure

Image credit: Vegetti+2012

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Method 2: gravitational imaging example with perfect lens model

software available: $pip install lenstronomy https://github.com/sibirrer/lenstronomy Lensing: Birrer+ 2015, 2016 Shapelets: Refregier 2003 Software: Birrer&Amara 2018

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Method 2: gravitational imaging example with missing substructure

software available: $pip install lenstronomy https://github.com/sibirrer/lenstronomy Lensing: Birrer+ 2015, 2016 Shapelets: Refregier 2003 Software: Birrer&Amara 2018

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Lensing: Birrer+ 2015, 2016 Shapelets: Refregier 2003 Software: Birrer&Amara 2018

High resolution reconstruction

  • f source with Shapelet basis set

Method 2: linear source reconstruction

Requirement: Simultaneous reconstruction of source and lens on all relevant scales computational cost of linear inversion and number of non- linear parameters as limitations

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installation: $pip install lenstronomy https://github.com/sibirrer/lenstronomy

software package publicly available

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sub-structure statistics: cold vs warm (sub-halos only)

CDM

Credit: Daniel Gilman (UCLA) software: lenstronomy

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sub-structure statistics: cold vs warm (sub-halos only)

CDM WDM

Credit: Daniel Gilman (UCLA) software: lenstronomy

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sub-structure statistics: main halo vs LOS (born approximation)

main halo

Credit: Daniel Gilman (UCLA) software: lenstronomy See e.g. Despali+2017

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sub-structure statistics: main halo vs LOS (born approximation)

main halo + LOS main halo

Credit: Daniel Gilman (UCLA) software: lenstronomy See e.g. Despali+2017

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sub-structure statistics: born approximation vs non-linear multi-plane

born approximation

Credit: Daniel Gilman (UCLA) software: lenstronomy

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sub-structure statistics: born approximation vs non-linear multi-plane

born approximation multi-plane (with main deflector)

Credit: Daniel Gilman (UCLA) software: lenstronomy

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sub-structure statistics: warm vs. cold in full LOS

CDM

Credit: Daniel Gilman (UCLA) software: lenstronomy

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sub-structure statistics: warm vs. cold in full LOS

CDM WDM

Credit: Daniel Gilman (UCLA) software: lenstronomy

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substructure quantification

  • Data may show signatures of multiple substructure
  • Inherent degeneracies are present in the observables
  • propagating the complex observables into quantitative

statements about dark matter is difficult

end-to-end forward modelling

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Accept/reject simulations based on summary statistics Approximate Bayesian Computing (ABC) Turn a physical model stochastically into simulated data look for the same features in your simulated data

Forward modelling of gravitational imaging

Birrer+ 2017

no line-of-sight included

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Dark Matter thermal relic mass constraints from lensing substructure

Birrer+ 2017

no line-of-sight included

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Dark Matter thermal relic mass constraints from lensing substructure

excluded ( ) ≥ 2σ

Birrer+ 2017

no line-of-sight included

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Dark Matter thermal relic mass constraints from lensing substructure

Viel et al. 2014 (Lyman-alpha forest) Polisensky & Ricotti 2011 (MW satellites)

excluded ( ) ≥ 2σ

Birrer+ 2017

no line-of-sight included

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Statistical statement of an ensemble of lenses small physical source size allows for sensitivity to low masses

Image credit: Gilman, Birrer+2018

Forecast

Gilman, Birrer+ submitted (ABC application to flux ratios) Gilman, Birrer+ in prep (LOS contribution)

Forward modelling of quasar flux ratios

no line-of-sight included

Simpler observables - lots of degeneracies Forward modelling allows for a hierarchical bayesian analysis with correlated priors

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The way forward 1: combining flux ratios and imaging

discovered: Ostrovski+, Lemon+, Agnello+, Schechter+, … HST follow-up, PI: Treu modelling: Shajib, Birrer+ in prep software: lenstronomy

combining data sets and methods that probe different scales within the same framework… … if possible on the same lens

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The way forward 2: gravitational imaging with extreme AO (in the ELT era) or interferometry

FWHM 0.02” see SHARP for Keck AO

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The challenges

  • forward modelling relies on realistic simulations:

any limitation that may not be identical to the data may impact your statistic

  • luminous (sub) structure: globular clusters, stellar discs, ..
  • precise predictions of (sub- and LOS) halo properties:

dynamical friction, tidal stripping, resolution limit, computational cost, baryonic physics, …

e.g, Hsueh+ 2016, Gilman+ 2017, … e.g. Bullock & Boylan-Kolchin 2017, van den Bosch+2018, …

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Summary

  • Strong lensing is an unique probe to test different dark matter

scenarios in the cosmological context

  • Dark substructure has been directly detected down to 10^8-9

M_sol, statistical signal may be present down to 10^6-7 M_sol in quasar flux ratios (mass definition dependent)

  • Statistical constraints based on one single lens excludes a

thermal relic mass < 2 keV to 2 sigma confidence level

  • Combined flux ratios and imaging applied may provide

constraints on the mass function over a wide range in mass scale

  • lens modelling software package “lenstronomy” is publicly

available

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Thank you!

IFT Madrid, 29.6.2018 Simon Birrer

Collaborators:

Tommaso Treu, Daniel Gilman, Anowar Shajib (UCLA) Adam Amara, Alexandre Refregier (ETHZ) Chuck Keeton, Anna Nierenberg, …