Probing CDM on small scales with the convergence

Probing ΛCDM on small scales with the convergence power spectrum in strong lenses Ana Díaz Rivero With Francis-Yan Cyr-Racine and Cora Dvorkin Tensions in the ΛCDM Paradigm MITP May 16, 2018

Outline 1. The ΛCDM Model 2. Strong gravitational lensing as a model-independent probe for dark matter substructure 3. Substructure statistics and the convergence power spectrum: a) Theory b) Simulations c) Observations 4. Conclusion and future directions

ΛCDM on large scales • Extremely successful on cosmological scales. • Cosmic Microwave Background, clustering on large scales, etc.

ΛCDM on small scales • Much harder to gauge its performance on small scales (galactic/subgalactic). • Several interesting features (“tensions”) arise when we compare Nbody CDM simulations with observations of Milky Way dwarf spheroidal galaxies: 1. “Missing Satellites” problem (e. g. Kravtsov 2010) 2. “Core-Cusp” problem (e. g. Walker & Peñarrubia 2011, Amorisco et al. 2013) 3. “Too Big To Fail” (TBTF) problem (Boylan-Kolchin et al. 2011, 2012) Baryonic physics? Ø AGN/supernova feedback, tidal interactions, ram pressure stripping Ø Gas heating during reionization Alternative dark matter scenarios? Ø Alter early times power spectrum cutoff (e. g. WDM) Ø Alter late times density profiles (e. g. SIDM)

Strong Gravitational Lensing In strong gravitational lensing light from a background source gets warped and magnified by a massive foreground object. Induces a mapping between the source and lens planes: Source plane Lens plane It is customary to define the convergence: Surface mass density If > 1 strong lensing Strong gravitational lensing with cluster SDSS J 1038+4849

Strong gravitational lensing as a probe for DM substructure Mao & Schneider (1998): substructure near images of lensed quasars can explain anomalous fluxes. Ø Purely gravitational method Ø Great to look further than the Local Group Several subhalos have been detected using this method. Other newer approaches that are based on the same idea e. g. gravitational imaging and spatially-resolved spectroscopy.

Strong gravitational lensing as a probe for DM substructure Very massive subhalos can locally perturb nearby lensed images! Claim a 12σ detection Example of employing gravitational imaging to detect a subhalo (Vegetti et al. 2012)

Strong gravitational lensing as a probe for DM substructure • These measurements can detect individual mass substructures above ~108 M. • BUT phrasing perturbations to lensed images in terms of individual subhalos is impractical expect a large number of unresolved low-mass substructure. Thus, the much more numerous population of lower mass subhalos may be statistically detected by their collective perturbations on images.

The Convergence Power Spectrum Hezaveh et al. (2016): 3 sigma detection of the convergence power spectrum amplitude is possible using ALMA. Díaz Rivero+ (2018): What can we learn about low-mass subhalos from measuring the substructure convergence power spectrum?

The Convergence Power Spectrum • We develop a complete formalism for the convergence power spectrum where we can include non-trivial correlations between subhalos and non-isotropic subhalo distributions. • We model the convergence as a fluctuation field superimposed on the smooth density profile of the host. Start from first principles to derive the lens plane-averaged convergence correlation function :

The Convergence Power Spectrum 1 -subhalo term: 2 -subhalo term: The total power spectrum is a sum of both contributions:

The Convergence Power Spectrum We apply the formalism to two different subhalo populations: • one in which subhalos are modeled as truncated NFW halos (CDM): • another in which they are modeled as truncated cored halos: • Intrinsic parameters:

Truncated NFW subhalo population: 1 -subhalo term Largest subhalos Inner profile Concentration Subhalo Mass Function

Truncated NFW subhalo population: 1 -subhalo term • The form of the 1 -subhalo term is determined by three key quantities: o low-k amplitude subhalo abundance and specific statistical moments of the subhalo mass function, o turnover ktrunc average truncation radius of the largest subhalos, o kscale smallest scale radii beyond which the slope reflects the subhalo inner density profiles. • Between ktrunc and kscale there is significant variability depending on the statistical properties of subhalos • BUT, the high-k slope is robust to these changes.

Truncated NFW subhalo population: 2 -subhalo term We allow our model to include subhalo correlations. As an illustrative example, we choose a 2 D radial distribution that is cored and decays as 1/r for large r: a = 10 kpc = core size 1/a

Truncated cored subhalo population: 1 -subhalo term High-k slope can distinguish both scenarios

The convergence power spectrum: simulations The ETHOS (Effective Theory of Structure Formation) simulations (Vogelsberger et al. 2016): - Effect on substructure due to a cutoff in the matter power spectrum + dark matter selfinteractions. - From a parent simulation (AREPO, 10243 particles, mass resolution 7. 8 x 107 h-1 M , 100 h-1 Mpc periodic box) resimulate a MW size halo at a higher resolution. Dwarf galaxies vrel ~ 10 km s-1 Clusters vrel > 100 km s-1

Self-Interacting Dark Matter (Spergel & Steinhardt 2000): • Cold, non-dissipative but self-interacting. • Constraints set an upper bound of σT/m ~ 1 cm 2 g-1 at cluster scales: i. Observed ellipticity of galaxy clusters halos (e. g. Miralda Escudé 2002) ii. Clusters mergers, e. g. Bullet Cluster: Clowe et al. (2006)

The convergence power spectrum: simulations The ETHOS (Effective Theory of Structure Formation) simulations (Vogelsberger et al. 2016): - Effect on substructure due to a cutoff in the matter power spectrum + dark matter selfinteractions. - From a parent simulation (AREPO, 10243 particles, mass resolution 7. 8 x 107 h-1 M , 100 h-1 Mpc periodic box) resimulate a MW size halo at a higher resolution. Dwarf galaxies vrel ~ 10 km s-1 Clusters vrel > 100 km s-1

The convergence power spectrum: simulations We consider all subhalos with at least 75 particles and within 300 kpc of the host center Diaz Rivero+ (in prep. )

The convergence power spectrum: simulations We consider all subhalos with at least 75 particles and within 300 kpc of the host center. Suppressed 2 -sh term Diaz Rivero+ (in prep. )

The convergence power spectrum: redshift evolution As z 0 more substructure is accreted and travels toward the center of the host. However, with self-interactions subhalos are stripped. Diaz Rivero+ (in prep. )

The convergence power spectrum: observations Bayer et al. (2018): They relate surface brightness anomalies to the convergence power spectrum. SDSS J 0252+0039: HST U-band in blue, visual in green and infrared in red. Massive elliptical galaxy at zl = 0. 28 acting as a lens for a blue star-forming galaxy at zs = 0. 982. Analysis of a 4. 48 as box, 121 x 121 pixels.

The convergence power spectrum: observations Bayer+ (2018)

The convergence power spectrum: observations We need to improve constraints: - Better data: ALMA! - Understanding model degeneracies between the subhalos, lens and source better. - No distinction between subhalos, other structure in the lens, and structure in the line-of-sight. v Some work has been done to understand the interference by baryonic structures (e. g. He et al. 2017) and by line-of-sight structure (e. g. Li et al. 2017) from a theoretical perspective. v Simulations.

Conclusions and future directions - We have developed an exhaustive formalism for the convergence power spectrum aimed towards observations of strong lensing images. Can input any desired statistical properties of a subhalo population, including an anisotropic distribution. - We show that the high-k (past k ~ 10 kpc-1) slope can distinguish between cuspy and cored subhalos, providing an exciting avenue to test the standard CDM scenario. - The amplitude gives us information about the abundance and mass function of subhalos. - Finally, we are working towards developing a comprehensive understanding of the effect of the assumptions brought about by the subhalo model (all mass bound in – roughly – spherical subhalos) as well as line-of-sight substructure, which are both crucial in order to assess LCDM. - There are still many things to investigate within our framework: a) Higher-order correlation functions (not necessarily small like in LSS). b) Looking past the monopole term: convergence field is not azimuthally symmetric.