In this paper we examine to what extent the radio continuum can be used as an extinction free probe of star formation in dwarf galaxies .
To that aim we observe 40 nearby dwarf galaxies with the Very Large Array at 6 cm ( 4 – 8 GHz ) in C–configuration .
We obtained images with 3 – 8 ^ { \prime \prime } resolution and noise levels of 3 – 15 { \mu Jy beam ^ { -1 } } .
We detected emission associated with 22 of the 40 dwarf galaxies , 8 of which are new detections .
The general picture is that of an interstellar medium largely devoid of radio continuum emission , interspersed by isolated pockets of emission associated with star formation .
We find an average thermal fraction of \sim 50 – 70 % and an average magnetic field strength of \sim 5 – 8 { \mu G } , only slightly lower than that found in larger , spiral galaxies .
At 100 pc scales , we find surprisingly high values for the average magnetic field strength of up to 50 { \mu G } .
We find that dwarf galaxies follow the theoretical predictions of the radio continuum–star formation rate relation within regions of significant radio continuum emission but that the non-thermal radio continuum is suppressed relative to the star formation rate when considering the entire optical disk .
We examine the far-infrared–star formation rate relation for our sample and find that the far-infrared is suppressed compared to the expected star formation rate .
We discuss explanations for these observed relations and the impact of our findings on the radio continuum–far-infrared relation .
We conclude that radio continuum emission at centimetre wavelengths has the promise of being a largely extinction–free star formation rate indicator .
We find that star formation rates of gas rich , low mass galaxies can be estimated with an uncertainty of \pm 0.2 dex between the values of 2 \times 10 ^ { -4 } and 0.1 { M _ { \odot } yr ^ { -1 } } .