Gas Disks and Supermassive Black Holes in Nearby Radio Galaxies

λvac − λair
λair
= 6.4328 × 10 −5 +
2.94981 × 10−2
146 − (104 2.5540 × 10−4
2 +
/λair)
41 − (10 4 /λair) 2.
63
(3.1)
Using one Gaussian to represent each of these five lines we obtain a set of 7 free
parameters to fit: the continuum flux level, velocity (vr), velocity dispersion (σ), and
the fluxes of each line. The flux of [N II]6550 was fixed in a ratio of 1:3 with the
flux of [N II]6585 based on the transition probabilities derived from atomic physics
(Osterbrock, 1989).
We used a χ 2 minimization routine (using Levenberg-Marquardt iterations, see
Press et al., 1992) to fit the Gaussian template to the observed spectra. The applica-
tion of this fitting technique and development of this routine are described by van der
Marel & van den Bosch (1998). Formal errors are drawn from the covariance matrix
of the fit. As we do not expect the noise in each spectrum to be normally-distributed
after the steps of wavelength calibration and two-dimensional rectification, these error
values should be treated strictly as the formal fit errors under the understanding that
the size of the real errors may be somewhat different (see §4.3 below).
From this point on we only consider data points where the formal errors from
the fits meet the following criteria, allowing us to exclude unreliable data points
originating from poorly constrained fits: