Is the black hole in NGC 1277 really overmassive?

A recent claim has been made by van den Bosch et al. that the fast-rotator galaxy NGC 1277 hosts an overmassive black hole with a mass (1.7 x 10(10) M-circle dot) larger than half its (central) stellar spheroid mass. We revisit this claim here by examining the predictions from simple dynamical realizations based on new multi-Gaussian expansion (MGE) models of NGC 1277, using the same inclination i = 75 degrees, and constant mass-to-light ratios. We present realizations which fit well the observed photometry taking into account an approximation for the extinction due to the central dust ring. The mass-to-light ratio M/L is fixed following scaling relations which predict a Salpeter-like initial mass function for such a luminous early-type fast rotator, 60 per cent higher than the one of the previously derived best-fitting model. A model without a black hole provides a surprisingly good fit of the observed kinematics outside the unresolved central region, but not, as expected, of the central dispersion and Gauss-Hermite h(4) values. A model with a black hole mass of 5 x 10(9) M-circle dot allows us to fit the central dispersion profile, consistently with models of the same mass and M/L in van den Bosch et al. It departs from the central h(4) values by only about twice the given uncertainty. A slightly varying M/L or the addition of high-velocity stars in the central spatially unresolved region would further lower the need for a very massive black hole in the central region of NGC 1277. These results do not, by themselves, rule out the presence of a presumed overmassive black hole at the centre of NGC 1277. However, they lead us to advocate the use of 3 Sigma (as opposed to 1 Sigma) confidence intervals for derived M-BH as better, more conservative, guidelines for such studies. We also caution for the use of ill-defined spheroidal components as an input for scaling relations, and emphasize the fact that a M-BH in the range 2-5 x 10(9) M-circle dot would represent less than 5 per cent of the spheroid bulge-like mass of our models and less than 2.5 per cent of its total stellar mass. This would make the black hole in NGC 1277 consistent or just twice as large as what a recent version of the M-BH-Sigma predicts, well within the observed scatter. We examine the impact of the presence of an inner bar by running simulations from the same MGE model but with extreme anisotropies. An inner small (600 pc diameter) bar forms, and an end-on view does get closer to fitting the central dispersion profile (and fits the h(3) amplitude) without the need for a central dark mass, while adding a black hole of 2.5 x 10(9) M-circle dot, in line with the prediction from scaling relations, allows us to fit the dispersion peak and h(3) profiles. Both models, however, still fail to fit the central h(4) value (overpredicting the mean velocity). The claimed large mass of the presumed black hole therefore mostly relies on the measured positive high central h(4) (at high dispersion), which can be associated with broad wings in the line-of-sight velocity distribution (high-velocity stars). This emphasizes the need to go beyond medium-resolution long-slit kinematics, with e.g. high-resolution integral-field spectroscopic data. In the specific case of NGC 1277, molecular or ionized gas kinematics (if present) within the central arcsecond (or at large scale) may provide a strong discriminant between these various models. We finally briefly discuss the fact that NGC 1277 resembles a scaled-up version of e.g. NGC 4342, another nearly edge-on fast rotator with a potentially large (but not overmassive) black hole.