FUV flux density, calibrated with stellar synthesis models [@2013seg..book..419C], and WISE mid-IR flux density, calibrated with infrared bright galaxies [@2013AJ....145....6J][^8]. By adding up the obscured (mid-IR) and unobscured (FUV) SFR, we get the attenuation-corrected SFR [Equation \[eqn:sfr\], see Section 3.3.2 of @2017MNRAS.472.3029W for more details]. It provides reliable SFR estimation independent of FIR or radio calibrations. Throughout the paper, we use Kroupa initial mass function [@2001MNRAS.322..231K].

$$\label{eqn:sfr}
(\mathrm{SFR/1\,M_\odot\,yr^{-1}}) = 1.76\times10^{-10} (L_\mathrm{FUV}/\mathrm{L_\odot}) + 7.50\times10^{-10} (L_\mathrm{22{\ensuremath{\,\mathrm{\mu m}}}}/\mathrm{L_\odot}).$$

![image](fig/sfr_fir.pdf){width="8cm"} ![image](fig/sfr_radio.pdf){width="8cm"}

We confirm the strong correlation between the distance-normalized star formation rates and the FIR or radio flux densities for LVHIS galaxies, with large Spearman rank correlation coefficient (see Table \[tab:stats\]). As shown in Figure \[fig:sfr\], again in log-log space we use the power law model to fit the full sample, with (magenta line) and without upper limits (cyan line). The fitting results suggest that the flux densities do not increase linearly with the distance normalized SFR.

For convenience, here we define the luminosity-to-SFR ratio ($\mathrm{eff}_\mathrm{FIR} \equiv L_\mathrm{FIR}/\mathrm{SFR}$; $\mathrm{eff}_\mathrm{1.4\,GHz} \equiv L_\mathrm{1.4\,GHz}/\mathrm{SFR}$) as “radiation efficiency” (FIR efficiency and radio efficiency, respectively). The physical motivation of this will be mentioned in Section \[subsec:radi\_eff\]. The super-linear best fit model implies a lower radiation efficiency in low SFR 