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Star-forming galaxies have been found to follow a relatively tight relationbetween stellar mass ($M_{*}$) and star formation rate (SFR), dubbed the `starformation sequence'. A turnover in the sequence has been observed, wheregalaxies with $M_{*} < 10^{10} {\rm M}_{\odot}$ follow a steeper relation thantheir higher mass counterparts, suggesting that the low-mass slope is (nearly)linear. In this paper, we characterise the properties of the low-mass end ofthe star formation sequence between $7 \leq \log M_{*}[{\rm M}_{\odot}] \leq10.5$ at redshift $0.11 < z < 0.91$. We use the deepest MUSE observations ofthe Hubble Ultra Deep Field and the Hubble Deep Field South to construct asample 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 Gaussiandistribution around a hyperplane between $\log M_{*}$, $\log {\rm SFR}$, and$\log (1+z)$, to simultaneously constrain the slope, redshift evolution, andintrinsic scatter. We find a sub-linear slope for the low-mass regime where$\log {\rm SFR}[{\rm M}_{\odot}/{\rm yr}] = 0.83^{+0.07}_{-0.06} \logM_{*}[{\rm M}_{\odot}] + 1.74^{+0.66}_{-0.68} \log (1+z)$, increasing withredshift. 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. Asboth hydrodynamical simulations and (semi-)analytical models typically favour asteeper slope in the low-mass regime, our results provide new constraints onthe feedback processes which operate preferentially in low-mass halos.

The MUSE Hubble Ultra Deep Field Survey XI. Constraining the low-mass end of the stellar mass - star formation rate relation at $z<1$