We investigate the X-ray properties of PG 1004+130, a low-redshift radio-loud broad absorption line (BAL) quasar with a hybrid FR I/FR II radio morphology. The 22.2 ks XMM-Newton and 41.6 ks Chandra observations presented here are the first X-ray detections of PG 1004+130 and constitute the highest spectral quality X-ray observations of a radio-loud BAL quasar available to date. The Chandra ACIS-S spectrum shows evidence for complex soft X-ray absorption not detected in the data obtained 1.7 yr previously with XMM-Newton, with a best-fit intrinsic column density of N_H=1.2e22 cm-2 for the preferred partial-covering model. There is no significant difference in the hard-band power-law photon index of ~1.5 between the two observations. The Chandra image also reveals extended X-ray emission ~8 (30 kpc) south-east of the nucleus, aligned with the FR I jet but upstream of the 1.4 GHz radio-brightness peak. The jet is not detected by HST, and the optical upper limit rules out a simple single-component synchrotron interpretation of the radio-to-X-ray emission. The multiwavelength characteristics of the PG 1004+130 jet, including its relatively flat X-ray power law and concave spectral energy distribution, are similar to those of powerful FR II jets. The lack of strong beaming in PG 1004+130 limits the efficiency of inverse Compton upscattering, and we consider the X-ray emission to most likely arise from a second synchrotron component generated by highly energetic electrons.
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