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$_{*}$ 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.
