Context. We investigate the optical polarization properties of
high-energy BL Lac objects using data from the RoboPol blazar monitoring
program and the Nordic Optical Telescope.
Aims: We wish to
understand if there are differences between the BL Lac objects that have
been detected with the current-generation TeV instruments and those
objects that have not yet been detected.
Methods: We used a
maximum-likelihood method to investigate the optical polarization
fraction and its variability in these sources. In order to study the
polarization position angle variability, we calculated the time
derivative of the electric vector position angle (EVPA) change. We also
studied the spread in the Stokes Q/I-U/I plane and rotations in the
polarization plane.
Results: The mean polarization fraction of
the TeV-detected BL Lacs is 5%, while the non-TeV sources show a higher
mean polarization fraction of 7%. This difference in polarization
fraction disappears when the dilution by the unpolarized light of the
host galaxy is accounted for. The TeV sources show somewhat lower
fractional polarization variability amplitudes than the non-TeV sources.
Also the fraction of sources with a smaller spread in the Q/I-U/I plane
and a clumped distribution of points away from the origin, possibly
indicating a preferred polarization angle, is larger in the TeV than in
the non-TeV sources. These differences between TeV and non-TeV samples
seem to arise from differences between intermediate and high spectral
peaking sources instead of the TeV detection. When the EVPA variations
are studied, the rate of EVPA change is similar in both samples. We
detect significant EVPA rotations in both TeV and non-TeV sources,
showing that rotations can occur in high spectral peaking BL Lac objects
when the monitoring cadence is dense enough. Our simulations show that
we cannot exclude a random walk origin for these rotations.

Conclusions: These results indicate that there are no intrinsic
differences in the polarization properties of the TeV-detected and
non-TeV-detected high-energy BL Lac objects. This suggests that the
polarization properties are not directly related to the TeV-detection,
but instead the TeV loudness is connected to the general flaring
activity, redshift, and the synchrotron peak location.