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Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing
The light travel time differences in strong gravitational lensing systems
allows an independent determination of the Hubble constant. This method has
been successfully applied to several lens systems. The formally most precise
measurements are, however, in tension with the recent determination of
from the Planck satellite for a spatially flat six-parameters
cosmology. We reconsider the uncertainties of the method, concerning the mass
profile of the lens galaxies, and show that the formal precision relies on the
assumption that the mass profile is a perfect power law. Simple analytical
arguments and numerical experiments reveal that mass-sheet like transformations
yield significant freedom in choosing the mass profile, even when exquisite
Einstein rings are observed. Furthermore, the characterization of the
environment of the lens does not break that degeneracy which is not physically
linked to extrinsic convergence. We present an illustrative example where the
multiple imaging properties of a composite (baryons + dark matter) lens can be
extremely well reproduced by a power-law model having the same velocity
dispersion, but with predictions for the Hubble constant that deviate by . Hence we conclude that the impact of degeneracies between parametrized
models have been underestimated in current measurements from lensing, and
need to be carefully reconsidered.Comment: Accepted for publication in Astronomy and Astrophysics. Discussion
expanded (MSD and velocity dispersion, MSD and free form lens models, MSD and
multiple source redshifts
Source-position transformation -- an approximate invariance in strong gravitational lensing
The main obstacle for gravitational lensing to determine accurate masses of
deflectors, or to determine precise estimates for the Hubble constant, is the
degeneracy of lensing observables with respect to the mass-sheet transformation
(MST). The MST is a global modification of the mass distribution which leaves
all image positions, shapes and flux ratios invariant, but which changes the
time delay. Here we show that another global transformation of lensing mass
distributions exists which almost leaves image positions and flux ratios
invariant, and of which the MST is a special case. Whereas for axi-symmetric
lenses this source position transformation exactly reproduces all strong
lensing observables, it does so only approximately for more general lens
situations. We provide crude estimates for the accuracy with which the
transformed mass distribution can reproduce the same image positions as the
original lens model, and present an illustrative example of its performance.
This new invariance transformation most likely is the reason why the same
strong lensing information can be accounted for with rather different mass
models.Comment: Submitted to Astronomy and Astrophysics. Comments welcome. 9 page
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