We present the first high resolution X-ray image of the jet in M 87 using the Chandra X-ray Observatory. There is clear structure in the jet and almost all of the optically bright knots are detected individually. The unresolved core is the brightest X-ray feature but is only 2-3 times brighter than knot A (12.3 from the core) and the inner knot HST-1 (1.0 from the core). The X-ray and optical positions of the knots are consistent at the 0.1 level but the X-ray emission from the brightest knot (A) is marginally upstream of the optical emission peak. Detailed Gaussian fits to the X-ray jet one-dimensional profile show distinct X-ray emission that is not associated with specific optical features. The X-ray/optical flux ratio decreases systematically from the core and X-ray emission is not clearly detected beyond 20 from the core. The X-ray spectra of the core and the two brightest knots, HST-1 and A1, are consistent with a simple power law with alpha = 1.46 +/- 0.05, practically ruling out inverse Compton models as the dominant X-ray emission mechanism. The core flux is significantly larger than expected from an advective accretion flow and the spectrum is much steeper, indicating that the core emission may be due to synchrotron emission from a small scale jet. The spectral energy distributions (SEDs) of the knots are well fit by synchrotron models. The spectral indices in the X-ray band, however are comparable to that expected in the Kardashev-Pacholczyk synchrotron model but are much flatter than expected in the pitch angle isotropization model of Jaffe and Perola. The break frequencies derived from both models drop by factors of 10-100 with distance from the core.
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