Time delay measurements with broken power-law model

ABSTRACT One of the key challenges in strong gravitational lensing cosmography is the accurate measurement of time delays between multiple lensed images, which are essential for constraining the Hubble constant ($H_0$). In this study, we investigate how assumptions about the lens mass profile affect time-delay measurements in strong lensing systems. Specifically, we implement a broken power-law (BPL) mass model within the lenstronomy framework, which introduces additional flexibility in the radial mass distribution and can phenomenologically capture deviations from a single power-law profile. This model is combined with a numerical approach to compute time delays at the image positions. We validate the BPL implementation using simulated lens systems and compare the results with those obtained from the commonly adopted elliptical power-law (EPL) model. We then apply both model families to the quadruply imaged quasar WGD 2038–4008. Both models provide good fits to the imaging and kinematic data overall, with a slight preference for the BPL model. When the internal mass-sheet factor is allowed to vary, the inferred Hubble constant in a flat Lambda cold dark matter cosmology with fixed $\Omega _{ \mathrm{ m}}=0.3$ is $H_0 = 75.2^{+23.0}_{-16.3} \ \mathrm{km \ s^{-1} \ Mpc^{-1}}$ for the BPL model and $H_0 = 61.1^{+19.1}_{-13.1} \ \mathrm{km \ s^{-1} \ Mpc^{-1}}$ for the EPL model. For comparison, in the diagnostic case with the internal mass-sheet factor fixed to unity under the same set-up, we obtain $H_0 = 74.2^{+20.3}_{-13.8} \ \mathrm{km \ s^{-1} \ Mpc^{-1}}$ for the BPL model and $H_0 = 66.1^{+18.8}_{-12.8} \ \mathrm{km \ s^{-1} \ Mpc^{-1}}$ for the EPL model. This highlights how time-delay cosmography remains sensitive to assumptions about the lens mass profile. With current precision, this difference does not favour one cosmological scenario over another, but rather underscores the importance of flexible mass modelling.