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.
Authors:
Award ID(s):
Publication Date:
NSF-PAR ID:
10280275
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
501
Issue:
4
Page Range or eLocation-ID:
5021 to 5028
ISSN:
0035-8711
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.