Modelling the M*-SFR relation at high redshift: untangling factors driving biases in the intrinsic scatter measurement

We present a method to self-consistently propagate M${}_{\ast }$ and SFR ($\mathrm{\Psi }$) uncertainties onto intercept, slope and intrinsic scatter estimates for a simple model of the main sequence of star forming galaxies where $\Psi = \alpha

• \beta$M$_{*} + $\mathcal{N}$(0,\sigma)$. From simple idealised models set up with broad-band photometry from NIRCam filters at $z\sim 5$, we test the method and compare to methods in the literature. Simplifying the $\mathrm{\Psi }$ estimate by basing it on dust-corrected MUV can help to reduce the impact of template set degeneracies on slope and intercept estimates, but act to bias the intrinsic scatter estimate. We find that broad-band fluxes alone cannot constrain the contribution from emission lines, implying that strong priors on the emission-line contribution are required if no medium-band constraints are available. Therefore at high redshifts, where emission lines contribute a higher fraction of the broad-band flux, photometric fitting is sensitive to $\mathrm{\Psi }$ variations on short ($\sim$ 10 Myr) timescales. Priors on age imposed with a constant (or rising) star formation history (SFH) do not allow one to investigate a possible dependence of $\sigma$ on M${}_{\ast }$ at high redshifts. Delayed exponential SFHs have less constrained priors, but do not account for $\mathrm{\Psi }$ variations on short timescales, a problem if $\sigma$ increases due to stochasticity of star formation. A simple SFH with current star formation decoupled from the previous history is appropriate. We show that, for simple exposure-time calculations assuming point sources, with low levels of dust, we should be able to obtain unbiased estimates of the main sequence down to log(M/M${}_{\odot }$) $\sim$ 8 at $z\sim 5$ with the James Webb Space Telescope while allowing for stochasticity of star formation.