X-ray Polarization of the High-Synchrotron-Peaked BL Lac H 1426+428

We report the X-ray polarization properties of the high-synchrotron-peaked BL Lac H 1426+428, based on two-epoch observational data from the Imaging X-ray Polarimetry Explorer (IXPE). For the first observation, only an upper limit of polarization degree (ΠX), ΠX<19.5%, at the $99%$ confidence level (C.L.) is determined. In contrast, for the second observation, we derive ΠX=20.6%±2.9% with a polarization angle (ψX) of ψX=116.1∘±4.1∘ at a C.L. of 7.1 σ. The time-resolved and energy-resolved polarization analysis reveals no significant variation in ψX and no detectable polarization within narrower energy bins for the first observation, while the polarization during the second observation is dominated by low-energy photons. Furthermore, the X-rays during the second observation are found to be in a higher flux state with a harder spectrum compared to that observed during the first observation, consistent with a { harder-when-brighter} behavior. We propose that the enhanced X-ray emission observed during the second observation is produced by shock-accelerated electrons within an ordered magnetic field region via synchrotron radiation. Nonetheless, no significant detection of polarization during the first IXPE observation may be due to the limited number of detected photons.