The radio galaxy Fornax A ( NGC 1316 ) is a prominent merger remnant in the outskirts of the Fornax cluster .
Its giant radio lobes suggest the presence of a powerful AGN , and thus a central supermassive black hole ( SMBH ) .
Fornax A now seems to be in a transition state between active black hole growth and quiescence , as indicated by the strongly declined activity of the nucleus .
Studying objects in this evolutionary phase is particularly important in order to understand the link between bulge formation and black hole growth , which is manifested in the M _ { \bullet } - \sigma relation between black hole mass and bulge velocity dispersion .
So far a measurement of the SMBH mass has not been possible in Fornax A , as it is enshrouded in dust which makes optical measurements impossible .
We present high-resolution adaptive optics assisted integral-field data of Fornax A , taken with SINFONI at the Very Large Telescope in the K band , where the influence of dust is negligible .
The achieved spatial resolution is 0.085 arcsec , which is about a fifth of the diameter of the expected sphere of influence of the black hole .
The stellar kinematics was measured using the region around the CO bandheads at 2.3 \mu m. Fornax A does not rotate inside the inner \sim 3 arcsec .
The velocity dispersion increases towards the centre .
The weak AGN emission affects the stellar kinematics in the inner \sim 0.06 arcsec only .
Beyond this radius , the stellar kinematics appears relaxed in the central regions .
We use axisymmetric orbit models to determine the mass of the SMBH in the centre of Fornax A .
The three-dimensional nature of our data provides the possibility to directly test the consistency of the data with axisymmetry by modelling each of the four quadrants separately .
According to our dynamical models , consistent SMBH masses M _ { \bullet } and dynamical Ks band mass-to-light ratios \Upsilon are obtained for all quadrants , with \langle M _ { \bullet } \rangle = 1.3 \times 10 ^ { 8 } M _ { \odot } ( \mathrm { rms } ( M _ { \bullet } ) = 0.4 \times 10 ^ { 8 } M _ { \odot } ) and \langle \Upsilon \rangle = 0.68 ( \mathrm { rms } ( \Upsilon ) = 0.03 ) , confirming the assumption of axisymmetry .
For the folded and averaged data we find M _ { \bullet } = 1.5 _ { -0.8 } ^ { +0.75 } \times 10 ^ { 8 } M _ { \odot } and \Upsilon = 0.65 ^ { +0.075 } _ { -0.05 } ( 3 \sigma errors ) .
Thus the black-hole mass of Fornax A is consistent within the error with the M _ { \bullet } - \sigma relation , but is a factor \sim 4 smaller than expected from its bulge mass and the relation .