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Gas Disks and Supermassive Black Holes in Nearby Radio Galaxies

Gas Disks and Supermassive Black Holes in Nearby Radio Galaxies

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with contributions from thermal <strong>and</strong> non-thermal motion:<br />

156<br />

σ 2 gas = σ2 th + σ2 tur , (4.11)<br />

σ 2 tur(R) = σt0 + σt1e −R/R1 . (4.12)<br />

We label the non-thermal motion as ‘turbulent’ but this is merely a label <strong>and</strong><br />

does not imply a source of the non-thermal motions. This functional form is used<br />

only so that we may provide a fit to the observed dispersion, <strong>and</strong> is not based on<br />

any underly<strong>in</strong>g physical mechanism. The temperature of the gas is not important.<br />

For T ∼ 10 4 K, σth ∼ 10 km s −1 which is always negligible <strong>in</strong> comparison to σtur.<br />

The <strong>in</strong>tr<strong>in</strong>sic l<strong>in</strong>e width is the dom<strong>in</strong>ant source of l<strong>in</strong>e broaden<strong>in</strong>g <strong>in</strong> the data, so<br />

we can fix values for the l<strong>in</strong>e widths from the above parameterization alone; models<br />

with different black hole masses <strong>and</strong> hence different amounts of rotational broaden<strong>in</strong>g<br />

will still have about the same f<strong>in</strong>al l<strong>in</strong>e widths because the <strong>in</strong>tr<strong>in</strong>sic l<strong>in</strong>e width is<br />

significantly larger than the rotational broaden<strong>in</strong>g at most locations, <strong>and</strong> the different<br />

sources of broaden<strong>in</strong>g effectively add <strong>in</strong> quadrature (see Barth et al., 2001).<br />

The predicted velocity profile for any given observation is obta<strong>in</strong>ed through a flux<br />

weighted convolution of the <strong>in</strong>tr<strong>in</strong>sic velocity profile with the PSF of the observation<br />

<strong>and</strong> the size of the aperture (van der Marel & van den Bosch, 1998). Aga<strong>in</strong> the PSF is<br />

represented by a sum of five Gaussians (see above, <strong>and</strong> Table 4.2). The convolutions

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