We use data from the Sydney-AAO Multi-object Integral-field spectroscopy (SAMI) Galaxy Survey to study the dynamical scaling relation between galaxy stellar mass $M_{*}$ and the general kinematic parameter $S_K = \sqrt{K V_{rot}^2 + \sigma^2}$, that combines rotation velocity $V_{rot}$ and velocity dispersion $\sigma$. We show that the $\log M_{*} - \log S_K$ relation:
(1)~is linear above the spectral resolution limit of the SAMI survey;
(2)~has smaller scatter than either the Tully-Fisher ($\log M_{*} - \log V_{rot}$) or the Faber-Jackson ($\log M_{*} - \log\sigma$) relation;
(3)~has scatter that is only weakly sensitive to the value of $K$;
(4)~has minimum scatter for $K$ in the range 0.4 and 0.7;
and (5) applies to both early-type and late-type galaxies.
We compare $S_K$ to the aperture second moment (the `aperture velocity dispersion') measured from the integrated spectrum within a 3-arcsecond radius aperture ($\sigma_{3\prime\prime}$). We find that while $S_{K}$ and $\sigma_{3\prime\prime}$ are in general tightly correlated, the $\log M_{*} - \log S_K$ relation has scatter less than $\log M_{*} - \log \sigma_{3\prime\prime}$ relation.
Publication Date:
December 2018
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