The Weak Lensing Radial Acceleration Relation: Constraining Modified
  Gravity and Cold Dark Matter theories with KiDS-1000
  We present measurements of the radial gravitational acceleration around
isolated galaxies, comparing the expected gravitational acceleration given the
baryonic matter with the observed gravitational acceleration, using weak
lensing measurements from the fourth data release of the Kilo-Degree Survey.
These measurements extend the radial acceleration relation (RAR) by 2 decades
into the low-acceleration regime beyond the outskirts of the observable galaxy.
We compare our RAR measurements to the predictions of two modified gravity (MG)
theories: MOND and Verlinde's emergent gravity. We find that the measured RAR
agrees well with the MG predictions. In addition, we find a difference of at
least $6\sigma$ between the RARs of early- and late-type galaxies (split by
S\'{e}rsic index and $u-r$ colour) with the same stellar mass. Current MG
theories involve a gravity modification that is independent of other galaxy
properties, which would be unable to explain this behaviour. The difference
might be explained if only the early-type galaxies have significant ($M_{gas}
\approx M_*$) circumgalactic gaseous haloes. The observed behaviour is also
expected in $\Lambda$CDM models where the galaxy-to-halo mass relation depends
on the galaxy formation history. We find that MICE, a $\Lambda$CDM simulation
with hybrid halo occupation distribution modelling and abundance matching,
reproduces the observed RAR but significantly differs from BAHAMAS, a
hydrodynamical cosmological galaxy formation simulation. Our results are
sensitive to the amount of circumgalactic gas; current observational
constraints indicate that the resulting corrections are likely moderate.
Measurements of the lensing RAR with future cosmological surveys will be able
to further distinguish between MG and $\Lambda$CDM models if systematic
uncertainties in the baryonic mass distribution around galaxies are reduced.
