star formation surface densities follow a scaling relation $$\left(\frac{\Sigma_{\rm SFR}}{\rm M_{\odot}\,yr^{-1}\,kpc^{-2}}\right)\,=\,A\left(\frac{\Sigma_{\rm gas}}{\rm M_{\odot}\,pc^{-2}}\right)^{\it n}
  \label{eqn:KS98}$$ For local, star-forming galaxies, the exponent, $n\sim1.5$ and the absolute star formation efficiency, $A$=1.5$\pm$0.4$\times$10$^{-4}$ [@Kennicutt98] implying an efficiency for star formation per unit mass of $\sim $0.04 which holds across at least four orders of magnitude in gas surface density.

Combining these relations, the velocity dispersion, $\sigma$, should therefore scale as $$\frac{\sigma}{\rm km\,s^{-1}}\,=\,\frac{\pi\,\times\,10^6\,G\,R}{\sqrt2\,v_{\rm max}}
  \left(\left(\frac{\Sigma_{\rm SFR}}{A}\right)^{1/n}+\left(\frac{2}{1+f_{\sigma^2}}\right)\frac{\Sigma_{\star}}{10^6}\,\right)
 \label{eqn:sS}$$ where $\Sigma_{\rm SFR}$ and $\Sigma_{\star}$ are measured in M$_{\odot}$yr$^{-1}$ and M$_{\odot}$kpc$^{-2}$ respectively, $R$ is in kpc, $v_{\rm max }$ in kms$^{-1}$, and $G$=4.302$\times$10$^{-6}$kpcM$_{\odot}^{-1}$(kms$^{-1}$)$^2$. With a power law index of $n$=1.4, and a marginally stable disk ($Q$=1), for each galaxy we therefore expect a power law relation $\sigma\propto\Sigma_{\rm SFR}^{0.7}$+$constant$ [@Krumholz12].

  ---------------------- ---------- ------------- ------------------- ------------------------- --------------- ---------------------------- ------------------ ------------- --------------------------------------- -----------------------------------------
  ID                         RA          Dec       $z_{\rm H\alpha}$   SFR$_{\rm H\alpha}^{a}$   $r_{1/2}^{b}$   $\sigma_{\rm H\alpha}^{c}$   $v_{\rm asym}^d$    E(B$-$V)     $\log$($\frac{M_{\star}}{M_{\odot}}$)   $\log$($\frac{M_{\rm gas}}{M_{\odot}}$)
                          (J2000)      (J2000)                            (M$_{\odot}$/yr)           (kpc)              (kms$^{-1}$)            (kms$^{-1}$)                                                          
                                                                                                                                                                                                                      
  SHiZELS-1               021826.3   $-$044701.6        0.8425                    2               1.8$\pm$0.3            98$\pm$15               112$\pm$11      0.4$\pm$0.1              10.03$\pm$0.15                             9.4$\pm$0.4
  SHiZELS-4               100155.3   $+$021402.6        0.8317                    1               1.4$\pm$0.5            77$\pm$20                  ...          0.0$\pm$0.2               9.74$\pm$0.12                             8.9$\pm$0.4
  SHiZELS-7               021700.4   $-$050150.8        1.4550                    8               3.7$\pm$0.2            75$\pm$11               145$\pm$10      0.2$\pm$0.2               9.81$\pm$0.28                             9.8$\pm$0.4
  SHiZELS-8               021821.0   $-$051907.8        1.4608                    7               3.1$\pm$0.3            69$\pm$10               160$\pm$12      0.2$\pm$0.2              10.32$\pm$0.28                             9.8$\pm$0.4
  SHiZELS-9               021713.0   