  Transit photometry of the exoplanet candidate Kepler-1625b has recently been
interpreted to show hints of a moon. We aim to clarify whether the exomoon-like
signal is really caused by a large object in orbit around Kepler-1625b. We
explore several detrending procedures, i.e. polynomials and the Cosine
Filtering with Autocorrelation Minimization (CoFiAM). We then supply a light
curve simulator with the co-planar orbital dynamics of the system and fit the
resulting planet-moon transit light curves to the Kepler data. We employ the
Bayesian Information Criterion (BIC) to assess whether a single planet or a
planet-moon system is a more likely interpretation of the light curve
variations. We carry out a blind hare-and-hounds exercise using many noise
realizations by injecting simulated transits into different out-of-transit
parts of the original Kepler-1625 data: 100 sequences with 3 synthetic transits
of a Kepler-1625b-like planet and 100 sequences with 3 synthetic transits of
this planet with a Neptune-sized moon. The statistical significance and
characteristics of the exomoon-like signal strongly depend on the detrending
method, and the data chosen for detrending, and on the treatment of gaps in the
light curve. Our injection-retrieval experiment shows evidence for moons in
about 10% of those light curves that do not contain an injected moon.
Strikingly, many of these false-positive moons resemble the exomoon candidate.
We recover up to about half of the injected moons, depending on the detrending
method, with radii and orbital distances broadly corresponding to the injected
values. A $\Delta$BIC of -4.9 for the CoFiAM-based detrending indicates an
exomoon around Kepler-1625b. This solution, however, is only one out of many
and we find very different solutions depending on the details of the detrending
method. It is worrying that the detrending is key to the interpretation of the
data.
