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

Abstract: We present a method to self-consistently propagate M${*}$ and SFR ($\Psi$) 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 $z\sim5$, we test the method and compare to methods in the literature. Simplifying the $\Psi$ 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 $\Psi$ 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$_{}$ at high redshifts. Delayed exponential SFHs have less constrained priors, but do not account for $\Psi$ 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 $z\sim5$ with the James Webb Space Telescope while allowing for stochasticity of star formation.