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Exploring models of lensing galaxies

On bridging the gap between observations, models, and simulations

PhD colloquium on 29/10/2020
by

Philipp Denzel

Website

phdenzel.github.io/2020/10/29/phd-colloquium/

Light

Speed of light

Sun light

Alpha Centauri

Andromeda

Young galaxies

Cosmic epochs

Gravity

History

Einstein.jpg

\[ R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = 8 \pi T_{\mu\nu} \]

  • matched up with Newton's law of gravity
  • explained the orbit of Mercury exactly
  • many predictions, for example…
    • bending of star light passing by the Sun
      a.k.a. gravitational lensing
  • compatible with the expansion of the Universe

History

eddington_experiment.jpg
Illustrated London News, November 22 1919

nytimes_headline.png
Headline NY Times, November 10 1919

Gravitational lensing

"Wine glass" lensing

Mock lensing


phdenzel.github.io/zurich-lens

phdenzel.github.io/streaming-lens

Zurich lensed

Outline


scheme.png

  1. Measuring the expansion rate of the Universe
  2. Lens modelling & degeneracies
  3. The lens-matching technique
    Studying galaxy formation with lensing






Yesterday's discovery is today's calibration… and tomorrow's background!
— R. Feynman

The Hubble constant

Quasar lensing

RAS PR 17/4, Credit: ESA/Hubble, NASA

Inference through gravitational lensing

Credit: ESA/Hubble, NASA

Are we certain about the value of H\(_0\)?

hubble.png

E. Hubble (1929)

hubble_history.png

Credit: J. Huchra (2010)

H0_tension.png

Verde et al. (2019) Credit: V. Bonvin & M. Millon

Time-delay galaxies

B1608+656_composite.jpg

DESJ0408-5354_composite.jpg

HE0435-1223_composite.jpg

PG1115+080_composite.jpg

RXJ0911+0551_composite.jpg

RXJ1131-1231_composite.jpg

SDSSJ1004+4112_composite.jpg

WFIJ2033-4723_composite.jpg

Denzel et al. (2020b, arxiv:2007.14398)

Lens models

B1608+656_kappa.jpg

DESJ0408-5354_kappa.jpg

HE0435-1223_kappa.jpg

PG1115+080_kappa.jpg

RXJ0911+0551_kappa.jpg

RXJ1131-1231_kappa.jpg

SDSSJ1004+4112_kappa.jpg

WFIJ2033-4723_kappa.jpg

Denzel et al. (2020b, arxiv:2007.14398)

Ensemble

DESJ0408-5354
Ensembles of models: 1000

H\(_0\) inference

\begin{align} H_0 &= 71.3^{+3.9}_{-3.6} \,\mathrm{km/s/Mpc} \\ &\quad \\ &\mathrm{or} \\ &\quad \\ H_0 &= 2.3^{+0.1}_{-0.1} \,\mathrm{aHz} \end{align}

H0_pdf.png

Denzel et al. (2020b, arxiv:2007.14398)

\[ H_0^{-1} = 13.8^{+0.7}_{-0.7} \,\mathrm{Gyr} \]

invH0_pdf.png

Denzel et al. (2020b, arxiv:2007.14398)

\begin{align} \rho_{\mathrm{c}} &= \frac{3c^2}{8\pi Ge}H_0^2 \\ &\quad \\ &= 5.4^{+0.6}_{-0.5} \,\mathrm{GeV/m^3} \end{align}

H02dens_pdf.png

Denzel et al. (2020b, arxiv:2007.14398)

Data vs synthetic images

data.png

Denzel et al. (2020b, arxiv:2007.14398)

Data vs synthetic images

synths.png

Denzel et al. (2020b, arxiv:2007.14398)

Synthetic ensemble optimization

\begin{align} H_0 &= 71.3^{+3.9}_{-3.6} \,\mathrm{km/s/Mpc} \\ &\quad \\ \rightarrow \quad H_0 &= 71.8^{+3.9}_{-3.3} \,\mathrm{km/s/Mpc} \end{align}

H0_filtered.png

Denzel et al. (2020b, arxiv:2007.14398)

Lensing degeneracies

One configuration, multiple solutions

degeneracies.png

Denzel et al. (2020)

The lensing Roche potential

\begin{align} \tau(\pmb\theta) &= \frac{1}{2} \theta^2 - 2\nabla^{-2} \kappa(\pmb\theta) - \pmb\theta\cdot\pmb\beta = \mathcal{P}(\pmb\theta) - \pmb\theta\cdot\pmb\beta \\ \mathcal{P}(\pmb\theta) &= 2\nabla^{-2} \left(1-\kappa(\pmb\theta)\right) \end{align}

data.png

kappa.png

arriv.png

Denzel et al. (2020)

Synthetic images

  • Source reconstruction:
    • \(\pmb\beta = \nabla\mathcal{P}(\pmb\theta)\)
      \[ I(\pmb\theta) = \int\int L(\pmb\theta', \pmb\beta) P(\pmb\theta - \pmb\theta') s(\pmb\beta) \mathrm{d}^2\pmb\theta' \mathrm{d}^2\pmb\beta \]
  • New implementation:

composite.png

composite_synth.png

src.png

resids.png

Denzel et al. (2020d, to be submitted)

Lens matching

Concept

\begin{align} & \\ P(F\,|\,D) &= \frac{P(D\,|\,F) \; P(F)}{P(D)} \\ & \\ P(D\,|\,F) &= \sum_g P(D\,|\,g) \; P(g\,|\,F) \\ & \\ P(D\,|\,g) &= \sum_\nu P(D\,|\,g, \nu)\;P(\nu) \end{align}

Galaxy-formation scenario: \(F\), observed data: \(D\), galaxy properties: \(g\) nuisance paramters: \(\nu\)

Denzel et al. (2020c, submitted to MNRAS)

Markov-Chain Monte-Carlo marginalization

Denzel et al. (2020c, submitted to MNRAS)

Lens matching

A catalogue of 1662 SEAGLE models

catalogue.png

J0029_kappa.png

J0753_kappa.png

J0956_kappa.png

Denzel et al. (2020c, submitted to MNRAS)

Test cases

Lens systems: SDSSJ0029-0055, SDSSJ0753+3416, SDSSJ0956+5100 (out of 7)

test_cases.png

Denzel et al. (2020c, submitted to MNRAS)

Constraints on galaxy formation scenarios

Lens Best SEAGLE match Most-plausible \(F\) \(\chi^2_\nu\)
SDSSJ0029−0055 \(\color{#4E70F2}{\mathsf{FBconst}}\).HH44S1A0B90G0 \(\color{#4E70F2}{\mathsf{FBconst}}\) 2.68
SDSSJ0737+3216 \(\color{#4E70F2}{\mathsf{FBconst}}\).HH21S1A90B0G0 \(\color{#4E70F2}{\mathsf{FBconst}}\) 3.47
SDSSJ0753+3416 \(\color{#4E70F2}{\mathsf{AGNdT8}}\).HH1S9A0B0G90 \(\color{#4E70F2}{\mathsf{AGNdT8}}\) 2.78
SDSSJ0956+5100 \(\color{#4E70F2}{\mathsf{AGNdT8}}\).HH17S1A90B0G0 \(\color{#4E70F2}{\mathsf{AGNdT8}}\) 3.50
SDSSJ1051+4439 \(\color{#4E70F2}{\mathsf{FBconst}}\).HH48S3A0B90G0 \(\color{#4E70F2}{\mathsf{FBconst}}\) 2.69
SDSSJ1430+6104 \(\color{#4E70F2}{\mathsf{AGNdT8}}\).HH3S1A90B0G0 \(\color{#4E70F2}{\mathsf{FBconst}}\) 2.49
SDSSJ1627−0053 \(\color{#4E70F2}{\mathsf{AGNdT8}}\).HH205S0A90B0G0 \(\color{#4E70F2}{\mathsf{FBconst}}\) 2.37

Towards statistically significant constraints

  • Source reconstruction: regularizations, lens subtraction
  • Preselection using:
    • Einstein-radius estimates
    • stellar mass estimates from population synthesis models
  • galactic dynamics through stellar dispersion
  • eventually: substructure constraints using time-delay measurements

Denzel et al. (2020c, submitted to MNRAS)

Summary

  • Lensing galaxies: models, simulations, and observations
  • The Hubble constant from time-delay galaxy lenses
  • Limitations of lens models: degeneracies
  • Lens matching: constraints on galaxy formation theory

SW05 - a fossil group candidate?

SpaceWarps discovery

SW05 composite image (using g, r, and i channels) from CFHLS survey

composite.png

Denzel et al. (2020d, to be submitted)

Initially modelled by citizen scientists

using SpaghettiLens (Küng et al. 2015 & Küng et al. 2017)

arriv.png

Denzel et al. (2020d, to be submitted)

Stellar mass estimates

using stellar population synthesis models

basemodels.png



Marginalized over:

  • redshifts
  • 3 different metallicities
  • 4 age ranges
  • constant star formation rate assumed

Denzel et al. (2020d, to be submitted)

Light vs dark

lightvsdark.png



  • Total mass:
    \((1.12 \pm 0.08) \cdot 10^{13} \mathrm{M}_{\odot}\)
  • Stellar mass:
    \((3.04 \pm 0.22) \cdot 10^{11} \mathrm{M}_{\odot}\)

Denzel et al. (2020d, to be submitted)

Stellar mass \(\neq\) baryonic mass

veldisp.png

Possibly missing mass in gas,
radiating at a temperature of: \[ \left(\frac{GM}{c^3}\right) \left(\frac{c}{r}\right) \times 1\,\mathrm{GeV} \\ \sim 5 \mathrm{keV} \]

Denzel et al. (2020d, to be submitted)

Strong evidence for fossil group

nbrhood_composite.png

nbrhood_zrange.png

Denzel et al. (2020d, to be submitted)

Created by phdenzel.