The stellar velocity dispersion, σ, is a quantity of crucial importance for spiral galaxies, where it enters fundamental dynamical processes such as gravitational instability and disc heating. Here we analyse a sample of 34 nearby spirals from the Calar Alto Legacy Integral Field Area (CALIFA) spectroscopic survey, deproject the line-of-sight σ to σR, and present reliable radial profiles of σR as well as accurate measurements of 〈σR〉, the radial average of σR over one effective (half-light) radius. We show that there is a trend for σR to increase with decreasing R, that 〈σR〉 correlates with stellar mass (M), and tested correlations with other galaxy properties. The most significant and strongest correlation is the one with M: |$\langle \sigma _{R}\rangle \propto M_{\star }^{0.5}$|⁠. This tight scaling relation is applicable to spiral galaxies of type Sa–Sd and stellar mass M ≈ 109.5–1011.5 M. Simple models that relate σR to the stellar surface density and disc scale length roughly reproduce that scaling, but overestimate 〈σR〉 significantly.

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