Dynamical histories of the IC348 and NGC1333 star-forming regions in Perseus

We present analyses of the spatial distributions of stars in the young (1 - 3 Myr) star-forming regions IC348 and NGC1333 in the Perseus Giant Molecular Cloud. We quantify the spatial structure using the $\mathcal{Q}$-parameter and find that both IC348 and NGC1333 are smooth and centrally concentrated with $\mathcal{Q}$-parameters of 0.98 and 0.89 respectively. Neither region exhibits mass segregation ($\Lambda_{\rm MSR} = 1.1^{+0.2}_{-0.3}$ for IC348 and $\Lambda_{\rm MSR} = 1.2^{+0.4}_{-0.3}$ for NGC1333, where $\Lambda_{\rm MSR} \sim 1$ corresponds to no mass segregation), nor do the most massive stars reside in areas of enhanced stellar surface density compared to the average surface density, according to the $\Sigma_{\rm LDR}$ method. We then constrain the dynamical histories and hence initial conditions of both regions by comparing the observed values to $N$-body simulations at appropriate ages. Stars in both regions likely formed with sub-virial velocities which contributed to merging of substructure and the formation of smooth clusters. The initial stellar densities were no higher than $\rho \sim 100 - 500$M$_\odot$pc$^{-3}$ for IC348 and $\rho \sim 500 - 2000$M$_\odot$pc$^{-3}$ for NGC1333. These initial densities, in particular that of NGC1333, are high enough to facilitate dynamical interactions which would likely affect $\sim$10 per cent of protoplanetary discs and binary stars.