  Black widows are extreme millisecond pulsar binaries where the pulsar wind
ablates their low-mass companion stars. Their optical light curves vary
periodically due to the high irradiation and tidal distortion of the companion,
which allows us to infer the binary parameters. We present simultaneous
multi-band observations obtained with the HIPERCAM instrument at the 10.4-m GTC
telescope for six of these systems. The combination of this five-band fast
photometer with the world's largest optical telescope enables us to inspect the
light curve range near minima. We present the first light curve for PSR
J1641+8049, as well as attain a significant increase in signal-to-noise and
cadence compared with previous publications for the remaining 5 targets: PSR
J0023+0923, PSR J0251+2606, PSR J0636+5129, PSR J0952-0607 and PSR J1544+4937.
We report on the results of the light curve modelling with the Icarus code for
all six systems, which reveals some of the hottest and densest companion stars
known. We compare the parameters derived with the limited but steadily growing
black widow population for which optical modelling is available. We find some
expected correlations, such as that between the companion star mean density and
the orbital period of the system, but also a puzzling positive correlation
between the orbital inclination and the irradiation temperature of the
companion. We propose such a correlation would arise if pulsars with magnetic
axis orthogonal to their spin axis are capable of irradiating their companions
to a higher degree.
