We analyse a set of collisionless disc galaxy simulations to study the consequences of bar formation and evolution on the M _ { \bullet } - \mbox { $ \sigma _ { e } $ } relation of supermassive black holes .
The redistribution of angular momentum driven by bars leads to a mass increase within the central region , raising the velocity dispersion of the bulge , \sigma _ { e } , on average by \sim 12 \% and as much as \sim 20 \% .
If a disc galaxy with a SMBH satisfying the M _ { \bullet } - \mbox { $ \sigma _ { e } $ } relation forms a bar , and the SMBH does not grow in the process , then the increase in \sigma _ { e } moves the galaxy off the M _ { \bullet } - \mbox { $ \sigma _ { e } $ } relation .
We explore various effects that can affect this result including contamination from the disc and anisotropy .
The displacement from the M _ { \bullet } - \mbox { $ \sigma _ { e } $ } relation for individual model barred galaxies correlates with both { M \mbox { $ \left ( B \right ) $ } / M \mbox { $ \left ( B + D \right ) $ } } and \beta _ { \phi } \mbox { $ \left ( B + D \right ) $ } measured within the effective radius of the bulge .
Overall , this process leads to an M _ { \bullet } - \mbox { $ \sigma _ { e } $ } for barred galaxies offset from that of unbarred galaxies , as well as an increase in its scatter .
We assemble samples of unbarred and barred galaxies with classical bulges and find tentative hints of an offset between the two consistent with the predicted .
Including all barred galaxies , rather than just those with a classical bulge , leads to a significantly larger offset .