Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing

By P. Schneider, Dominique Sluse. 2013

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The light travel time di erences 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 H0 from the Planck satellite for a spatially flat six-parameters CDM 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 masssheet 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 20%. Hence we conclude that the impact of degeneracies between parametrized models have been underestimated in current H0 measurements from lensing, and need to be carefully reconsidered.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/f0e675393752e71b13c3a44bf6a93612bc117a22

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Citations in the corpus

TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles (2020, background): “…known and frequently discussed in the literature (e.g., Gorenstein et al. 1988; Kochanek 2002, 2006, 2020a; Saha & Williams 2006; Read et al. 2007; Schneider & Sluse 2013, 2014; Coles et al. 2014; Xu et al. 2016; Birrer et al. 2016; Unruh et al. 2017; Sonnenfeld 2018; Wertz et al. 2018; Blum et…”
H0LiCOW – I. H0 Lenses in COSMOGRAIL's wellspring: program overview (2016, background): “Schneider & Sluse (2013) pointed out that the mass-sheet degeneracy can manifest as a lens mass profile degeneracy, which Xu et al. (2016) investigated using simulated galaxies.”
A SHARP view of H0LiCOW: H0 from three time-delay gravitational lens systems with adaptive optics imaging (2019, background): “As pointed out by Schneider & Sluse (2013), when assuming a specific mass profile, one artificially breaks the internal MST (Koopmans 2004), a special case of the source-position transformation (SPT;, Schneider & Sluse 2014; Wertz et al. 2018; Wertz & Orthen 2018).”
H0LiCOW - V. New COSMOGRAIL time delays of HE 0435-1223: H0 to 3.8 per cent precision from strong lensing in a flat ΛCDM model (2016, background): “…invariance to the lensed images under addition of a uniform mass sheet to our mass model combined with a rescaling of the source plane coordinates—can affect the inferred time delays, and may limit the effectiveness of time delays in constraining cosmology (e.g. Schneider & Sluse 2013, 2014).”
Time delay cosmography (2016, methodology): “While image positions remain invariant under the “mass sheet transformation” (Falco et al. 1985; Schneider and Sluse 2013) (and its generalization, the source-position transformation Schneider and Sluse 2014), the time delays predicted by the model can change significantly.”
Characterization of subhalo structural properties and implications for dark matter annihilation signals (2016, methodology): “In contrast, subhalo concentrations remain more un- 1 Although due to degeneracies, measuring its density profile by only using this technique is not possible (Schneider & Sluse 2013).”
TDCOSMO. I. An exploration of systematic uncertainties in the inference of $H_0$ from time-delay cosmography (2019, background): “As many authors have pointed out (Falco et al. 1985; Read et al. 2007; Schneider & Sluse 2013; Xu et al. 2016; Sonnenfeld 2018; Kochanek 2020), if the models adopted are insufficiently flexible, the resulting uncertainties 2 www.tdcosmo.org are underestimated and potentially biased.”
H0LiCOW - IV. Lens mass model of HE 0435-1223 and blind measurement of its time-delay distance for cosmology (2016, background): “In order to reduce the effects of the mass sheet degeneracy (e.g., Falco et al. 1985; Gorenstein et al. 1988; Saha 2000; Schneider & Sluse 2013; Xu et al. 2016), a measurement of the lens galaxy’s velocity dispersion (e.g., Koopmans et al. 2003; Koopmans 2004) and an estimate of the external…”