  Radio emission is a key indicator of star-formation activity in galaxies, but
the radio luminosity-star formation relation has to date been studied almost
exclusively at frequencies of 1.4 GHz or above. At lower radio frequencies the
effects of thermal radio emission are greatly reduced, and so we would expect
the radio emission observed to be completely dominated by synchrotron radiation
from supernova-generated cosmic rays. As part of the LOFAR Surveys Key Science
project, the Herschel-ATLAS NGP field has been surveyed with LOFAR at an
effective frequency of 150 MHz. We select a sample from the MPA-JHU catalogue
of SDSS galaxies in this area: the combination of Herschel, optical and
mid-infrared data enable us to derive star-formation rates (SFRs) for our
sources using spectral energy distribution fitting, allowing a detailed study
of the low-frequency radio luminosity--star-formation relation in the nearby
Universe. For those objects selected as star-forming galaxies (SFGs) using
optical emission line diagnostics, we find a tight relationship between the 150
MHz radio luminosity ($L_{150}$) and SFR. Interestingly, we find that a single
power-law relationship between $L_{150}$ and SFR is not a good description of
all SFGs: a broken power law model provides a better fit. This may indicate an
additional mechanism for the generation of radio-emitting cosmic rays. Also, at
given SFR, the radio luminosity depends on the stellar mass of the galaxy.
Objects which were not classified as SFGs have higher 150-MHz radio luminosity
than would be expected given their SFR, implying an important role for
low-level active galactic nucleus activity.
