skip to main content

Title: Overconstrained models of time delay lenses redux: how the angular tail wags the radial dog
Abstract The two properties of the radial mass distribution of a gravitational lens that are well constrained by Einstein rings are the Einstein radius RE and ξ2 = REα″(RE)/(1 − κE), where α″(RE) and κE are the second derivative of the deflection profile and the convergence at RE, respectively. However, if there is a tight mathematical relationship between the radial mass profile and the angular structure, as is true of ellipsoids, an Einstein ring can appear to strongly distinguish radial mass distributions with the same ξ2. This problem is beautifully illustrated by the ellipsoidal models in Millon et al. When using Einstein rings to constrain the radial mass distribution, the angular structure of the models must contain all the degrees of freedom expected in nature (e.g. external shear, different ellipticities for the stars and the dark matter, modest deviations from elliptical structure, modest twists of the axes, modest ellipticity gradients, etc.) that work to decouple the radial and angular structures of the gravity. Models of Einstein rings with too few angular degrees of freedom will lead to strongly biased likelihood distinctions between radial mass distributions and very precise but inaccurate estimates of H0 based on gravitational lens time delays.
Award ID(s):
Publication Date:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Page Range or eLocation-ID:
5021 to 5028
Sponsoring Org:
National Science Foundation
More Like this
  1. ABSTRACT It is well known that measurements of H0 from gravitational lens time delays scale as H0 ∝ 1 − κE, where κE is the mean convergence at the Einstein radius RE but that all available lens data other than the delays provide no direct constraints on κE. The properties of the radial mass distribution constrained by lens data are RE and the dimensionless quantity ξ = REα″(RE)/(1 − κE), where α″(RE) is the second derivative of the deflection profile at RE. Lens models with too few degrees of freedom, like power-law models with densities ρ ∝ r−n, have a one-to-one correspondence between ξ and κE (for a power-law model, ξ = 2(n − 2) and κE = (3 − n)/2 = (2 − ξ)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of κE and hence H0. Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates of H0 from gravitational lens time delays are more accurate than ${\sim} 10{{\ \rm per\ cent}}$, regardless of the reported precision.
  2. Abstract Strong gravitational lensing of gravitational wave sources offers a novel probe of both the lens galaxy and the binary source population. In particular, the strong lensing event rate and the time-delay distribution of multiply imaged gravitational-wave binary coalescence events can be used to constrain the mass distribution of the lenses as well as the intrinsic properties of the source population. We calculate the strong lensing event rate for a range of second- (2G) and third-generation (3G) detectors, including Advanced LIGO/Virgo, A+, Einstein Telescope (ET), and Cosmic Explorer (CE). For 3G detectors, we find that ∼0.1% of observed events are expected to be strongly lensed. We predict detections of ∼1 lensing pair per year with A+, and ∼50 pairs per year with ET/CE. These rates are highly sensitive to the characteristic galaxy velocity dispersion, σ * , implying that observations of the rates will be a sensitive probe of lens properties. We explore using the time-delay distribution between multiply imaged gravitational-wave sources to constrain properties of the lenses. We find that 3G detectors would constrain σ * to ∼21% after 5 yr. Finally, we show that the presence or absence of strong lensing within the detected population provides useful insightsmore »into the source redshift and mass distribution out to redshifts beyond the peak of the star formation rate, which can be used to constrain formation channels and their relation to the star formation rate and delay-time distributions for these systems.« less
  3. ABSTRACT We present an analysis of Hubble Space Telescope observations of globular clusters (GCs) in six ultradiffuse galaxies (UDGs) in the Coma cluster, a sample that represents UDGs with large effective radii (Re), and use the results to evaluate competing formation models. We eliminate two significant sources of systematic uncertainty in the determination of the number of GCs, NGC by using sufficiently deep observations that (i) reach the turnover of the globular cluster luminosity function (GCLF) and (ii) provide a sufficient number of GCs with which to measure the GC number radial distribution. We find that NGC for these galaxies is on average ∼ 20, which implies an average total mass, Mtotal, ∼ 1011 M⊙ when applying the relation between NGC and Mtotal. This value of NGC lies at the upper end of the range observed for dwarf galaxies of the same stellar mass and is roughly a factor of two larger than the mean. The GCLF, radial profile, and average colour are more consistent with those observed for dwarf galaxies than with those observed for the more massive (L*) galaxies, while both the radial and azimuthal GC distributions closely follow those of the stars in the host galaxy. Finally, we discuss whymore »our observations, specifically the GC number and GC distribution around these six UDGs, pose challenges for several of the currently favoured UDG formation models.« less
  4. ABSTRACT The presence of an invisible substructure has previously been detected in the gravitational lens galaxy SDSSJ0946+1006 through its perturbation of the lensed images. Using flexible models for the main halo and the subhalo perturbation, we demonstrate that the subhalo has an extraordinarily high central density and steep density slope. We robustly infer the subhalo’s projected mass within 1 kpc to be ∼2–3.7 × 109 M⊙ at >95 per cent CL for all our lens models, while the average log-slope of the subhalo’s projected density profile over the radial range 0.75–1.25 kpc is constrained to be steeper than isothermal (γ2D ≲ −1). By modeling the subhalo light, we infer a conservative upper bound on its luminosity LV < 1.2 × 108L⊙ at 95 per cent CL that shows that the perturber is dark matter dominated. We analyse lensing galaxy analogues in the Illustris TNG100-1 simulation over many lines of sight, and find hundreds of subhalos that achieve a mass within 1 kpc ≳ 2 × 109M⊙. However, less than 1 per cent of the mock observations yield a log-slope steep enough to be consistent with our lensing models, and they all have stellar masses exceeding that allowed by observations by an order of magnitude or more. We conclude that the presence of such a darkmore »highly concentrated subhalo is unexpected in a Lambda cold dark matter universe. While it remains to be determined whether this tension can be reduced by adding more complexity to the primary lens model, it is not significantly alleviated if the perturber is assumed to be a LOS structure, rather than a subhalo.« less
  5. ABSTRACT With high-quality data from programs like the Hubble Frontier Fields, cluster lensing has reached the point that models are dominated by systematic rather than statistical uncertainties. We introduce a Bayesian framework to quantify systematic effects by determining how different lens modelling choices affect the results. Our framework includes a new two-sample test for quantifying the difference between posterior probability distributions that are sampled by methods like Monte Carlo Markov chains. We use the framework to examine choices related to the selection and treatment of cluster member galaxies in two of the Frontier Field clusters: Abell 2744 and MACS J0416.1–2403. When selecting member galaxies, choices about depth and area affect the models; we find that model results are robust for an I-band magnitude limit of mlim ≥ 22.5 mag and a radial cut of rlim ≥ 90 arcsec (from the centre of the field), although the radial limit likely depends on the spatial extent of lensed images. Mass is typically assigned to galaxies using luminosity/mass scaling relations. We find that the slopes of the scaling relations can have significant effects on lens model parameters but only modest effects on lensing magnifications. Interestingly, scatter in the scaling relations affects the twomore »fields differently. This analysis illustrates how our framework can be used to analyse lens modelling choices and guide future cluster lensing programs.« less