Constraining the star formation rate in the Solar neighbourhood with star clusters

This paper investigates the star formation rate (SFR) in the Solar neighbourhood. First, we build the local age distribution function (ADF) with an updated sample of 442 star clusters located at less than 1\,kpc from the Sun. Next, we define the SFR, compute the individual mass evolution of a population of artificial clusters covering the broad range of parameters observed in actual clusters, and assume 100\,\ms\ as the low-mass limit for effective cluster observation. This leads to a simulated ADF, which is compared to the low-noise Solar neighbourhood ADF. The best match corresponds to a non-constant SFR presenting two conspicuous excesses for ages $\le9$\,Myr and between 220-600\,Myr (the local starburst). The average formation rate is $\bar{SFR}\approx(2500\pm500)\,\mmy$, corresponding to the average surface formation rate $\bar{\ssfr}\approx(790\pm160)\,\mmk$. These values are consistent with the formation rate inferred from embedded clusters (ECs), but much lower ($\la16%$) than that implied by field stars. Both the local starburst and the recent star formation period require $SFR\sim2\times\bar{SFR}$ to be described. The simulations show that $91.2\pm2.7%$ of the clusters created in the Solar neighbourhood do not survive the first 10\,Myr, which is consistent with the rate of EC dissolution.