Electron temperatures derived from low-frequency radio observations of planetary nebulae

Planetary nebulae are formed around low- and intermediate-mass stars after the asymptotic giant phase and before the extinction of thermonuclear reactions. Chemical abundances and electron temperatures of planetary nebulae show a dichotomy known as an abundance and temperature discrepancy. Collisionally excited lines show higher temperatures and lower abundances compared to recombination lines. This is explained by the presence of two ionised components: a hot ionised gas and clumps of a cold, metal-rich gas of unknown origin. We sought to map radio free-free emission in order to determine electron temperatures across a sample of planetary nebulae. We compared these temperatures with those derived using other methods to investigate whether the radio emission traces the hot or cold component. Our aim was also to verify the lower radio extinction from the radio data compared to extinction determined from the Balmer decrement. We cross-matched the LoTSS-DR3 catalogue with existing catalogues of Galactic planetary nebulae as well as with archival radio and optical surveys. We fitted free-free and power law spectra to the radio spectra. Determining the electron temperatures required observation of low-frequency turnover, which marks the transition from optically thin to optically thick emission. To derive the radio extinction, we combined our radio observations and optical emission lines. We identified 198 planetary nebulae that are detected in the LoTSS-DR3 maps. We determined the emission mechanism for 147 of them based on their radio spectra. We determined the electron temperatures for 62 planetary nebulae from optically thick thermal free-free emission. The temperatures are significantly lower than those derived from collisionally excited lines and are consistent with temperatures derived from helium recombination lines. This result suggests that a cold ionised component contributes to the radio emission from planetary nebulae. Electron temperatures derived from optically thick free-free emission are used to calculate the unreddened mathrm H β fluxes and estimate the interstellar extinction. The extinction derived in this way is consistent with that obtained from Balmer line ratios. Non-thermal emission can be observed in the largest and low surface brightness planetary nebulae.