The nuclear starburst in Arp 299-A: from the 5.0 GHz VLBI radio light-curves to its core-collapse supernova rate

Context. The nuclear region of the luminous infrared galaxy (LIRG) Arp 299-A hosts a recent ( {\sime} 10 Myr) intense burst of massive star formation that is expected to lead to numerous core-collapse supernovae (CCSNe). Previous VLBI observations, carried out with the European VLBI Network (EVN) at 5.0 GHz and with the VLBA at 2.3 and 8.4 GHz, resulted in the detection of many compact, bright, non-thermal sources in a region łsim} 150 pc in size. Aims: We aim to establish the nature of all non-thermal compact components in Arp 299-A, as well as to estimate its core-collapse supernova rate. While the majority of the compact components are expected to be young radio supernovae (RSNe) and supernova remnants (SNRs), a definitive classification is still lacking. Yet, this is very relevant for eventually establishing the CCSN rate, as well as the star formation rate, for this galaxy. Methods: We used multi-epoch EVN observations taken at 5.0 GHz to image the compact radio sources in the nuclear region of Arp 299-A with milliarcsecond resolution. We also used one single-epoch 5.0 GHz Multi-Element Radio Linked Interferometer Network (MERLIN) observation to image the extended emission in which these compact radio sources are embedded. Results: We present the first 5.0 GHz radio light-curve (spanning \~{}2.5 yr) of all compact components in the nuclear starburst of Arp 299-A. Twenty-six compact sources are detected, eight of which are new objects. The properties of all detected objects are consistent with them being a mixed population of CCSNe and SNRs. We find clear evidence for at least two new CCSNe, implying a lower limit to the CCSN rate of {$ν$}$_{SN}$ {\gsim} 0.80 SN/yr, indicating that the bulk of the current star formation in Arp 299-A is taking place in the innermost \~{}150 pc.A few more objects show variability consistent with them being recently exploded SNe, but only future observations will clarify this point. Our MERLIN observations trace a region of diffuse extended emission that is cospatial to the region where all compact sources are found. From this diffuse non-thermal radio emission traced by MERLIN we obtain an independent estimate for the CCSN rate, which is in the range {$ν$}$_{SN}$ = 0.40-0.65 SN/yr, in agreement with previous estimates and our direct estimate of the CCSN rate from the compact radio emission. Conclusions: Our \~{}2.5 yr monitoring of Arp 299-A has allowed us to obtain for the first time a direct estimate of the CCSN rate of {$ν$}$_{SN}$ {\gsim} 0.80 SN/yr for the innermost \~{}150 pc of Arp 299-A.