For the carbon AGB star R Sculptoris, the uncertain distance significantly
affects the interpretation of observations regarding the evolution of the
stellar mass loss during and after the most recent thermal pulse. We aim to
provide a new, independent measurement of the distance to R Sculptoris,
reducing the absolute uncertainty of the distance estimate to this source. R
Scl is a semi-regular pulsating star, surrounded by a thin shell of dust and
gas created during a thermal pulse approximately 2000 years ago. The stellar
light is scattered by the dust particles in the shell at a radius of 19 arcsec.
The variation in the stellar light affects the amount of dust-scattered light
with the same period and amplitude ratio, but with a phase lag that depends on
the absolute size of the shell. We measured this phase lag by observing the
star R Scl and the dust-scattered stellar light from the shell at five epochs
between June - December 2017. By observing in polarised light, we imaged the
shell in the plane of the sky, removing any uncertainty due to geometrical
effects. The phase lag gives the absolute size of the shell, and together with
the angular size of the shell directly gives the absolute distance to R
Sculptoris. We measured a phase lag between the stellar variations and the
variation in the shell of 40.0 +/- 4.0 days. The angular size of the shell is
measured to be 19.1 arcsec +/- 0.7 arcsec. Combined, this gives an absolute
distance to R Sculptoris of 361 +/- 44 pc. We independently determined the
absolute distance to R Scl with an uncertainty of 12%. The estimated distance
is consistent with previous estimates, but is one of the most accurate
distances to the source to date. In the future, using the variations in
polarised, dust-scattered stellar light, may offer an independent possibility
to measure reliable distances to AGB stars.Comment: accepted by A&A, 8 pages, 8 figure