Using the PMAS Integral Field Unit on the Calar Alto 3.5m telescope we observed the southern component (Markarian 59) of the cometary' starburst galaxy NGC 4861. Mrk 59 is centred on a giant nebula and concentration of stars 1 kpc in diameter. Strong $\rm Hα$ emission points to a star-formation rate (SFR) at least 0.47 $\rm M_{\odot}yr^{-1}$. Mrk 59 has a very high [OIII]$\rm\lambda5007/Hβ$ ratio, reaching 7.35 in the central nebula, with a second peak at a star-forming hotspot further north. Fast outflows are not detected but nebular motion and galaxy rotation produce relative velocities up to 40 km $\rm s^{-1}$. Spectral analysis of different regions with Fitting Analysis using Differential evolution Optimisation’ (FADO) finds that the stars in the central and spur' nebulae are very young, $\rm \leq125~Myr$ with a large $\rm <10~Myr$ contribution. Older stars ($\rm \sim 1~Gyr$) make up the northern disk component, while the other regions show mixtures of 1 Gyr age with very young stars. This and the high specific SFR $\rm\sim 3.5~Gyr^{-1}$ imply a bimodal star formation history, with Mrk 59 formed in ongoing starbursts fuelled by a huge gas inflow, turning the galaxy into an asymmetric green pea’ or blue compact dwarf. We map the HeII emission, and identify a broad component from the central nebula, consistent with the emission of Wolf-Rayet stars. About a third of the HeII4686 flux is a narrow line emitted from a more extended area covering the central and spur nebulae, and may have a different origin.

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