The MUSE Hubble Ultra Deep Field Survey XI. Constraining the low-mass
  end of the stellar mass - star formation rate relation at $z<1$
  Star-forming galaxies have been found to follow a relatively tight relation
between stellar mass ($M_{*}$) and star formation rate (SFR), dubbed the `star
formation sequence'. A turnover in the sequence has been observed, where
galaxies with $M_{*} < 10^{10} {\rm M}_{\odot}$ follow a steeper relation than
their higher mass counterparts, suggesting that the low-mass slope is (nearly)
linear. In this paper, we characterise the properties of the low-mass end of
the star formation sequence between $7 \leq \log M_{*}[{\rm M}_{\odot}] \leq
10.5$ at redshift $0.11 < z < 0.91$. We use the deepest MUSE observations of
the Hubble Ultra Deep Field and the Hubble Deep Field South to construct a
sample of 179 star-forming galaxies with high signal-to-noise emission lines.
Dust-corrected SFRs are determined from H$\beta$ $\lambda 4861$ and H$\alpha$
$\lambda 6563$. We model the star formation sequence with a Gaussian
distribution around a hyperplane between $\log M_{*}$, $\log {\rm SFR}$, and
$\log (1+z)$, to simultaneously constrain the slope, redshift evolution, and
intrinsic scatter. We find a sub-linear slope for the low-mass regime where
$\log {\rm SFR}[{\rm M}_{\odot}/{\rm yr}] = 0.83^{+0.07}_{-0.06} \log
M_{*}[{\rm M}_{\odot}] + 1.74^{+0.66}_{-0.68} \log (1+z)$, increasing with
redshift. We recover an intrinsic scatter in the relation of $\sigma_{\rm intr}
= 0.44^{+0.05}_{-0.04}$ dex, larger than typically found at higher masses. As
both hydrodynamical simulations and (semi-)analytical models typically favour a
steeper slope in the low-mass regime, our results provide new constraints on
the feedback processes which operate preferentially in low-mass halos.
