Kinematics from spectroscopy with a wide slit: detecting black holes in galaxy centres

We consider long-slit emission-line spectra of galactic nuclei when the slit is wider than the instrumental point spread function, and the target has large velocity gradients. The finite width of the slit generates complex distributions of brightness at a given spatial point in the measured spectrum, which can be misinterpreted as coming from additional physically distinct nuclear components. We illustrate this phenomenon for the case of a thin disc in circular motion around a nuclear black hole (BH). We develop a new method for estimating the mass of the BH that exploits a feature in the spectrum at the outer edge of the BH's sphere of influence, and therefore gives higher sensitivity to BH detection than traditional methods. Moreover, with this method we can determine the BH mass and the inclination of the surrounding disc separately, whereas the traditional approach to BH estimation requires two long-slit spectra to be taken. We show that, with a given spectrograph, the detectability of a BH depends on the sense of rotation of the nuclear disc. We apply our method to estimate the BH mass in M84 from a publicly available spectrum, and recover a value four times lower than that published previously from the same data.