Cooking with Strong Lenses and Other Ingredients Adam S. Bolton Department of Physics and Astronomy The University of Utah AASTCS 1: Probes of Dark Matter on Galaxy Scales Monterey, CA, USA 2013-July-17
Introduction Strong lensing provides the most direct measure of total mass in galaxies at cosmological distances Combination of lensing with other ingredients offers further complementary constraints on physical parameters of lens galaxies Complementarities and degeneracies of various combinations of lensing with other data are generally non-intuitive Goal of this talk is to unpack these combinations (and to present several relevant results in prep!)
What other sorts of ingredients? Redshifts Weak lensing Stellar populations Theoretical priors Scaling relations Ensemble analysis Stellar dynamics Nearby-galaxy analysis Non-lenses Single-image lenses Hierarchical statistics
Context I ll be talking about strong galaxy-galaxy lenses Sloan Lens ACS Survey (SLACS): -e.g., Bolton et al. 2006, 2008a -~100 lenses, SDSS-I selection, z 0.1 to 0.4 BOSS Emission-Line Lens Survey -Brownstein et al. 2012 -~25 lenses, SDSS-III/BOSS selection, z 0.4 to 0.7 Spectroscopic redshifts for all lenses and sources Distinguish between: -Zeroth-order dark-matter probe: M (< R) -First-order dark-matter probe: dm / dr
SLACS/BELLS in a nutshell SDSS spectroscopy One spectrum, two redshifts HST follow-up Strong lenses
Importance of spectroscopic redshifts Specify cosmic geometry Convert precise angular observables into precise mass observables
What do galaxy-scale lenses measure? Primarily: mass within Einstein radius Great because this is a unique and direct probe of mass Large numbers now being delivered from large surveys But also: combination of mass, slope, axis ratio,... Constrains cylindrical rather than spherical mass Extracting full info is a challenge for modeling codes (see e.g., Warren & Dye 2003, Wayth et al, 2005, Vegetti et al. 2009-12)
Example: complete Einstein ring Weak constraint on mass slope Parameterized model from Bolton et al. 2008a
Example: complete Einstein ring Strong constraint on Einstein radius
Example: complete Einstein ring Mass axis ratios become unphysical at high gamma Approximate lens-galaxy light axis ratio
Example: asymmetric double More radial coverage gives more mass-slope leverage
Example: asymmetric double Einstein radius still constrained, but less tightly
Example: asymmetric double Stronger variation of axis ratio with power-law index Approximate lens-galaxy light axis ratio
Position angle and flattening Bolton et al. 2008a,b Mass more radially extended than light -or- Mass more flattened than light -or- Large-scale shear aligned with lens-galaxy PA
Combining strong & weak lensing Weak lensing signal must be stacked over many lenses SLACS WL signal consistent with extrapolation of SL Shows approx. isothermal bulge--halo conspiracy Surface mass density 3D mass density Gavazzi et al. 2007
Star/dark-matter decomposition Use photometry to measure light profile Assume parametric model for DM profile Fit for dark-matter fraction, stellar M/L, central DM profile slope, etc. Also can use broadband photometry and/or spectroscopic diagnostics to constrain stellar M/L (e.g., Rusin & Kochanek 2003, Dye & Warren 2005, Jiang & Kochanek 2007, Auger et al. 2009, Grillo et al. 2009, Barnabe et al. 2009-12, Treu et al. 2010, Spiniello et al. 2011, Sonnenfeld et al. 2012)
Fundamental problem for decomposition A well-known degeneracy, worth recalling... When decomposing stars and dark-matter, can slosh back and forth via Subject only to requirement that everywhere leaving all macroscopic lensing and dynamical observables unchanged!
Integrated-light and -mass constraints All macroscopic lensing + dark-matter decompositions invoke theoretical priors on the shape of the DM halo and/or on the stellar M/L or IMF NFW (1996/1997) halo parameters inconvenient for kiloparsec-scale observables. (What robust observables are most relevant to CDM?) Low-mass star diagnostics can break the degeneracy (e.g., van Dokkum & Conroy 2010, Spiniello et al 2013) Quasar microlensing can also break the degeneracy (e.g., Pooley et al. 2012)
Integrated-light and -mass constraints Can still get upper limits on stellar mass robustly Stellar mass fraction Velocity dispersion (km/s) Brewer et al. 2012
Total-mass scaling relations Dynamical mass ~ σ 2 R/G and luminosity supplemented with lensing mass (no dynamical modeling) Lensing Mass Luminosity Luminosity Dynamical Mass Dynamical Mass Lensing Mass Massive galaxies homologous in total mass DM content or stellar M/L increases with galaxy mass Bolton et al. 2008b (cf. Padmanabhan et al. 2004, Cappellari et al. 2006)
Ensemble aperture-mass analysis Scale lensing masses to dynamical mass Scale aperture radii to half-light radii Different lenses probe different (scaled) radii Still no dynamical models Bolton et al. 2008b Scaled aperture mass Scaled aperture radius Mass profile inconsistent with light-traces-mass Similar result for scaling to luminosity (e.g., Rusin et al. 2003, Koopmans et al. 2009)
Adding dynamical models to lensing Basic idea: constrain mass concentration with dynamics Jeans-based or Schwarzschild-based Dynamics + lensing mixes spherical and projection Note mass--anisotropy degeneracy! Self-consistent work is challenge for modeling code
Toy model for lensing & dynamics From Koopmans, astro-ph/0511121 Power-law luminosity & mass-density profiles Aperture mass & velocity-dispersion values Constant velocity-anisotropy parameter Analytic solution for relationship between observables: Lensing velocity dispersion (squared)
Toy model for lensing & dynamics Stellar-to-lensing velocity dispersion ratio is observable proxy for mass slope Inferred (Mass slope)
Lensing mass--anisotropy degeneracy Assumed Measured Inferred (Mass slope)
Jeans-dynamical lensing measurement Isothermal mass profile assuming isotropic velocitydispersion tensor Koopmans et al. 2006 (See also Barnabe et al. 2009-12 for self-consistent modeling approach)
Dynamical mass--concentration degeneracy Measured Inferred Measured (More nuanced in detail: see ATLAS 3D Paper XV, Cappellari et al. 2012, Fig. 3) Assumed (Mass slope)
Virtual combination of strong lenses and local-galaxy dynamics Can break both mass--anisotropy and mass--concentration degeneracies Take mass models from SAURON (Cappellari et al. 2006) Project to typical lens redshifts Predict lensing Einstein radii and aperture vdisps Compare to observed SLACS scaling relations, via the σstar/σlens relation Cherkaev et al., in prep.
Virtual combination of strong lenses and local-galaxy dynamics Stellar velocity dispersion (km/s) SAURON SLACS Cherkaev et al., in prep. Lensing velocity dispersion (km/s) Distributions inconsistent at: ~4.5 sigma for full sample, ~5-sigma for ~150 < vdisp < ~300
Virtual combination of strong lenses and local-galaxy dynamics Possible explanations: Cherkaev et al., in prep. Mass significantly more extended than light even within one effective radius Significant contribution from projected dark-matter at large r in lens systems Lenses non-representative of non-lenses Larger SLACS comparison sample to be published soon (Brownstein et al., in prep.)
Are strong lenses representative? Monte Carlo simulation of spectroscopic gravitational lens selection No significant selection bias in mass profile over physically relevant ranges SLACS-like BELLS-like Mass slope Mass slope Einstein radius (arcsec) Arneson et al. 2012 Einstein radius (arcsec)
Single-image lenses Excluding single-image lenses from analysis at lowmass end can lead to biased population results Can include single-image lenses in self-consistent statistical analysis as upper limits on lens galaxy mass Einstein radius too high predicts non-existent counter-image Shu et al., in prep.
Single-image lenses Write relationship between lensing and stellar velocity dispersions as log σ = a (log σ SIE m)+b Including single-image lenses leads to (weakly) non-homologous result of lower total-mass concentration at higher masses Shu et al., in prep.
Single-image lenses Weak dependence on delta-chi-squared threshold Shu et al., in prep.
Lenses + dynamics + hierarchical stats Combination of SLACS + BELLS lenses gives detection of mass-slope evolution with redshift BOSS vdisps for BELLS galaxies are low-s/n Use full vdisp likelihood function for each lens Parameterize population evolution of mass slope Constrain population parameters hierarchically SLACS BELLS Bolton et al. 2012 (also see Shu et al. 2012)
Conclusions Strong lensing is still the most direct and precise way to measure mass in galaxies across redshift. Combination with other observables increases power for dark & luminous matter decomposition, but requires careful attention to degeneracies and assumptions. Methods for statistical combination of data from multiple lenses and multiple observables are key to future progress. How can we cast CDM parameters & predictions in terms of the robust observables of lensing++? Thank you!