  To date, the hot Jupiter WASP-12 b has been the only planet with confirmed
orbital decay. The late F-type host star has been hypothesized to be surrounded
by a large structure of circumstellar material evaporated from the planet. We
obtained two high-resolution spectral transit time series with CARMENES and
extensively searched for absorption signals by the atomic species Na, H, Ca,
and He using transmission spectroscopy, thereby covering the He I triplet with
high resolution for the first time. We apply SYSREM for atomic line
transmission spectroscopy, introduce the technique of signal protection to
improve the results for individual absorption lines, and compare the outcomes
to those of established methods. No transmission signals were detected and the
most stringent upper limits as of yet were derived for the individual
indicators. Nonetheless, we found variation in the stellar Halpha and He I
lines, the origin of which remains uncertain but is unlikely to be activity. To
constrain the enigmatic activity state of WASP-12, we analyzed XMM-Newton X-ray
data and found the star to be moderately active at most. We deduced an upper
limit for the X-ray luminosity and the irradiating X-ray and extreme
ultraviolet (XUV) flux of WASP-12 b. Based on the XUV flux upper limit and the
lack of the He I signal, our hydrodynamic models slightly favor a moderately
irradiated planet with a thermospheric temperature of <= 12,000 K, and a
conservative upper limit of <= 4e12 g/s on the mass-loss rate. Our study does
not provide evidence for an extended planetary atmosphere or absorption by
circumstellar material close to the planetary orbit.
