  Strong gravitational lensing can detect the presence of low-mass haloes and
subhaloes through their effect on the surface brightness of lensed arcs. We
carry out an extended analysis of the density profiles and mass distributions
of two detected subhaloes, intending to determine if their properties are
consistent with the predictions of the cold dark matter (CDM) model. We analyse
two gravitational lensing systems in which the presence of two low-mass
subhaloes has been previously reported: SDSSJ0946+1006 and JVASB1938+66. We
model these detections assuming four different models for their density
profiles and compare our results with predictions from the IllustrisTNG50-1
simulation. We find that the detected subhaloes are well-modelled by steep
inner density slopes, close to or steeper than isothermal. The NFW profile thus
needs extremely high concentrations to reproduce the observed properties, which
are outliers of the CDM predictions. We also find a characteristic radius
within which the best-fitting density profiles predict the same enclosed mass.
We conclude that the lens modelling can constrain this quantity more robustly
than the inner slope. We find that the diversity of subhalo profiles in TNG50,
consistent with tidally stripping and baryonic effects, is able to match the
observed steep inner slopes, somewhat alleviating the tension reported by
previous works even if the detections are not well fit by the typical subhalo.
However, while we find simulated analogues of the detection in B1938+666, the
stellar content required by simulations to explain the central density of the
detection in J0946+1006 is in tension with the upper limit in luminosity
estimated from the observations. New detections will increase our statistical
sample and help us reveal more about the density profiles of these objects and
the dark matter content of the Universe.
