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tokens: SPHERE data We also re-reduced the SPHERE observations of HD 4113 published in Moutou et al. (2017) (Program 096.C-0249, PI: Moutou), taken on 2015-10-08. These observations were taken in IRDIFS-EXT mode following an observing strategy that is similar to our observationsas described above, and are summarized in Table 2 . The IRDIS data were taken in the K1-K2 mode ( λ K 1 = 2.1025 μ m, λ K 2 = 2.2255 μ m), while the IFS data cover a range of wavelengths from 0.97–1.66 μ m with an average spectral resolution of 34.5. These data include a maximum field rotation of 51 deg between coronagraphic frames. Our data reduction procedure was identical to that of the IRDIFS data described in the previous section. 4 Results 4.1 SPHERE 2016 high-contrast imaging data The source HD 4113C was detected at high significance in both IRDIS H2 and IRDIS SDI reductions, but was not recovered in the H3 filter, suggesting the presence of strong methane absorption. The measured relative photometry and astrometry are given in Table 3 , while the IRDIS PSF-subtracted images are shown in Fig. 2 . We adopt a lower limit on the contrast of 14.8 mag for the H3 filter, using the 3 σ contrast curve at the location of the H2 detection. Table 3 Measured astrometry and photometry of HD 4113C from the SPHERE observations. In the IFS data using PCA alone, no significant detection was found in any individual wavelength channel or in the mean taken over wavelength. After we applied SDI to the IFS data, we clearly detected the companion, with 14 of the wavelength channels showing an excess of flux above 1.5 σ significance at the location of the IRDIS detection. A weighted-mean image is shown in Fig. 2 . The data reduction for wavelengths below 1.02 μ m suffer from considerably more residual noise in the SDI+PCA reduction and are not included in the subsequent analysis. The measured contrast ratios from IFS and IRDIS were converted into apparent flux measurements through multiplication by a BT-NextGen spectral model ( Allard et al. 2012 ) with T eff = 5700 K, [Fe/H] = 0.3 dex and log g = 4.5, close to the values determined in Sect. 2 . The model spectrum was flux-scaled using the distance and radius of HD 4113A. The extracted spectrum is shown in Fig. 4 . 4.2 SPHERE archival high-contrast imaging data After processing the 2015 data, we were unable to unambiguously recover the companion HD 4113C in the IRDIS images. Close to the location of the 2016 detection, we find an excess of flux with 2–3 σ significance in the SDI reduction. However, because of the lower S/N, our reduction of the IRDIS data does not provide substantial constraints on the position or flux of the companion, and we have excluded it from the following analysis. In the IFS SDI reduction, we also find an excess of flux in wavelength channels corresponding to the J - and H -band peaks found in the2016 data, again with lower significance. We find six channels at which the companion is visible at S ∕ N > 4, and by