## 2 Materials and Methods
The proportionality constant was the beam transmission, which was calculated by compounding losses at the focusing mirror with absorption in air and in the X-ray windows. The absolute energy detector could not be used for all data, since in most of the experimental runs, uncalibrated X-ray attenuators were inserted after the detector. The absolute detector and the relative detectors used the same type of photodiodes and the same type of electronic reading systems [36]. The shot-to-shot measurements of the absolute detector and the relative detectors were proportional, with a linear correlation coefficient r = 0.9998. We therefore expect that (i) the relative accuracy of the pulse energy measurements is close to the one of the absolute detectors, which was estimated [36] at 10\({}^{-3}\), and (ii) the absolute accuracy is also close to the one of the absolute detectors, which was measured at 3.6% at 9.6 keV by comparison with a primary detector standard [37]. To improve the accuracy of measurements of the droplets' surface position, the numerical aperture (NA) of the main imaging system was reduced from the objective specification (NA = 0.55) to NA = 0.3 using irises placed before the condenser lens and in front of the objective lens. The lower NA improved the image contrast and made the edge of the drops perfectly dark (i.e., having a pixel signal of 0 in the camera data), which improved the precision with which the drop surface position was measured. _Data recording and analysis._ The data was recorded at an XFEL pulse rate of 30 Hz, in runs that were approximately 20 min long. During the runs, the time delay of the illumination laser was scanned at a rate of ~10 ps/s, resulting in probing a time delay range of ~12 ns during a run. The relatively slow scan rate of the time delay resulted in finely spaced time delay data, but it also made the measurements sensitive to slow drifts in the droplet diameter and position. The time delay between the XFEL pulse and the illumination of the image could be set statically with 1 ps accuracy. During the time delay scans, we recorded this delay for each XFEL shot using a timer-counter (Keysight 53230A, 20 ps specified accuracy). The timer measured the time delay between the XFEL electronic trigger and the signal from a fast photodiode (Hamamatsu G4176-03) that picked up part of the illumination light. The zero time delay condition between X-rays and illumination was determined before the beamtime using the fast photodiode, and was refined during the beamtime to an accuracy around 2 ps using the onset of the ionization caused by the XFEL beam, at the maximum available intensity. Since the XFEL pulses had a wide distribution of pulse energies, the data was binned by pulse energy in consecutive logarithmic bins with a 0.05 (5%) relative width, i.e., the data in a bin had pulse energies ranging from 0.95 to 1 times of the bin maximum. From one run, nine to 11 binned data sets were extracted, according to the condition that each binned set had sufficient data to sample the time delays with an average time step of \(\sim\)10 ps. The drop images had a magnification of 207 nm/pixel, an optical resolution better than 780 nm, and were recorded with a high-speed camera (Phantom Miro M340, Vison Research). The procedure for determining the droplet diameters is similar to the one described previously [17] with the following differences: (i) We extracted the image data directly from the raw camera data in a compressed 10-bit format and linearized it, instead of converting the data to 8-bit movie format. (ii) Since the raw droplet images already had very good edge contrast, it was not necessary to apply a nonlinear rescaling of the pixel data. Images in which the droplet center was misaligned by more than \(\sim\)0.5 \(\upmu\)m from the XFEL beam were removed from further analysis, because for such drops the shock waves arriving at opposite regions along the drop's equator had sufficiently different arrival times to affect further analysis.