Abstract
Time-delay cosmography measures the Hubble constant from the time delays between multiple images of a lensed source, offering an independent, single-object route to H₀. But the time delays depend on the lensing galaxy's mass distribution, which is not observed, only inferred from a chosen model. Any error there propagates directly into H₀. Using an isolated, shear-free lens from a hydrodynamic simulation, where the true mass distribution is known, I build profile likelihoods in ellipticity to test whether standard modelling recovers the deflector's angular structure across a set of experiments. With point-source constraints alone, the preferred solution sits at the wrong, near-circular ellipticity and yields a catastrophically biased H₀. Adding angular freedom (an m=4 multipole), (i.e.) the standard remedy, does not correct this; a diagnostic on the recovered multipole amplitudes shows why. Adding Einstein-ring surface-brightness information removes the spurious global minimum but still leaves a residual offset. The main message here is that what controls H₀ accuracy is not model flexibility but whether the data constrain the deflector's angular structure, which is a distinction directly relevant to the accuracy budget of time-delay cosmography.
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