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Appendix A: Simultaneity in the multi-instrument observations

The energy coverage as a function of the time for the daily multi-instrument observations from 2010 March 10 (MJD 55 265) to

Fig. A.1 Temporal and energy coverage during the flaring activity from 2010 March 10 (MJD 55 265) to 2010 March 16 (MJD 55 271). Fermi-LAT data were accumulated during two-day time intervals to ensure significant detections of Mrk 421, and is depicted here with a blue band. For better visibility of the observations at UV, optical, and radio band, where the observation time is usually short and the covered frequency band is narrow, an additional 20 min in time and half a decade in frequency are included when displaying the results. The names of all the optical instruments are listed in Table 1.

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2010 March 22 (MJD 55 277) is depicted in Figs. A.1 and A.2, which show that most of the observations used to determine the SEDs reported in Appendix B occur within less than 2 h.

	Fig. A.2 Temporal and energy coverage during the flaring activity from 2010 March 17 (MJD 55 272) to 2010 March 22 (MJD 55 277). See the caption of Fig. A.1 for further details.
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Appendix B: Broadband SEDs for the 13 consecutive days

The measured SEDs for these 13 consecutive days are shown in Figs. B.1 to B.5 with one-zone SSC model curves (from Figs. B.1 to Fig. B.3) and two-zone SSC model curves (Figs. B.4 and B.5). The SED with a two-zone SSC model curve measured on the first day (MJD 55 265) was shown in Fig. 6 in the main text. For comparison, the average SED from the 2009 MW campaign (Abdo et al. 2011) is shown in all the figures, which is a good representation of the SED of Mrk 421 during its nonflaring (typical) state. The details of the models and the characterization of the SED evolution were discussed in Sects. 4.1 and 4.2 in the main text.

The actual MJD date for each data entry is given in the legend of each figure. For optical bands, the reported SED data points correspond to the averaged values (host-galaxy

subtracted) for the specified observing night. As reported in Sect. 3, the variability at the optical band is small and occurs on timescales of several days. Therefore, if there was no instrument observing at a particular optical energy band, then the nearest observation was used, and the corresponding MJD date is described in the legend of the figure.

Although Mrk 421 is cosmologically nearby, at a redshift of 0.03, the absorption of γ-rays by the extragalactic background light (EBL) is not negligible at TeV energies. The VHE spectra are corrected (de-absorbed) with the EBL model provided by Franceschini et al. (2008), where e^{− τ_γγ} = 0.58 at 4 TeV. At this energy, which is roughly the highest energy bin in the VHE spectra, most models provide 0.5 < e^{− τ_γγ}< 0.6, such as models from Kneiske et al. (2004), Finke et al. (2010), and Domínguez et al. (2011), which means that the results are not sensitive to the particular published EBL model that we selected.

Fig. B.1 Largely simultaneous broadband SED of Mrk 421 on MJD 55 265. The correspondence between markers and instruments is given in the legend. The full names of the instruments can be found in Table 1. Because of space limitations, R-band instruments other than GASP, GRT, and NMS are denoted with the symbol “++”. Whenever a simultaneous observation is not available, the fluxes from the closest date are reported, and their observation time in MJD is reported next to the instrument name in the legend. The red curve depicts the one-zone SSC model matching the data. The gray circles depict the average SED from the 2009 MW campaign reported in Abdo et al. (2011), which is a good representation of the nonflaring (typical) SED of Mrk 421.

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	Fig. B.2 Simultaneous broadband SEDs and their one-zone SSC model fits. See caption of Fig. B.1 for further details.
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	Fig. B.3 Simultaneous broadband SEDs and their one-zone SSC model fits. See caption of Fig. B.1 for further details.
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	Fig. B.4 Simultaneous broadband SEDs and their two-zone SSC model fits. See caption of Fig. 6 for further details.
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	Fig. B.5 Simultaneous broadband SEDs and their two-zone SSC model fits. See caption of Fig. 6 for further details. The emission of the quiescent blob was set to the one describing the SED from MJD 55 274, which is the lowest SED among all the 13 dates considered in this paper. Consequently, there is no flaring blob emission for MJD 55 274.
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Appendix C: Physical parameters derived from one-zone and two-zone SSC scenarios

Physical parameters inferred from spectral modeling are tabulated in Table C.1 for the one-zone SSC model and in Table C.2 for the two-zone SSC model. The definition of these quantities are provided by Eqs. (5) to (10).

© ESO, 2015