Synthetic photometry of OB star clusters with stochastically sampled IMFs: analysis of models and HST observations

We present a pilot library of synthetic NUV, U, B, V, and I photometry of star clusters with stochastically sampled IMFs and ionized gas for initial masses, $M_i=10^3$, $10^4$, and $10^5$ M$_{\odot}$; $t=1$, 3, 4, and 8 Myr; $Z=0.014$ and $Z=0.002$; and log(U$_{\rm S}$) =-2 and -3. We compare the library with predictions from deterministic models and observations of isolated low-mass ($<10^4$ M$_{\odot}$) star clusters with co-spatial compact H\2 regions. The clusters are located in NGC 7793, one of the nearest galaxies observed as part of the \hst LEGUS and H$\alpha$-LEGUS surveys. 1) For model magnitudes that only account for the stars: a) the residual |deterministic mag - median stochastic mag| can be $\ge0.5$ mag, even for $M_i=10^5$ M$_{\odot}$; and b) the largest spread in stochastic magnitudes occurs when Wolf-Rayet stars are present. 2) For $M_i=10^5$ M$_{\odot}$: a) the median stochastic mag with gas can be $>$1.0 mag more luminous than the median stochastic magnitude without gas; and b) nebular emission lines can contribute with $>50\%$ and $>30\%$ to the total emission in the V and I bands, respectively. 3) Age-dating OB-star clusters via deterministic tracks in the U-B vs. V-I plane is highly uncertain at $Z=0.014$ for $M_i\sim10^3$ M$_{\odot}$ and $Z=0.002$ for $M_i\sim10^3-10^5$ M$_{\odot}$. 4) For low-mass clusters, the V-band extinction derived with stochastic models significantly depends on the value of log(U$_{\rm S}$). 5) The youngest clusters tend to have higher extinction. 6) The majority of clusters have multi-peaked age PDFs. 7) Finally, we discuss the importance of characterising the true variance in the number of stars per mass bin in nature.