Following up on a faint detection of a near-infrared (NIR) source at the position of the X-ray thermal isolated neutron star RX J0806.4-4123, we present new Hubble Space Telescope observations in the H-band. The NIR source is unambiguously detected with a Vega magnitude of 23.7 +/- 0.2 (flux density of 0.40 +/- 0.06 microJy at lambda =1.54 microm. The source position is coincident with the neutron star position, and the implied NIR flux is strongly in excess of what one would expect from an extrapolation of the optical-UV spectrum of RX J0806.4-4123. The NIR source is extended with a size of at least 0.8arcsec and shows some asymmetry. The conservative upper limit on the flux contribution of a point source is 50%. Emission from gas and dust in the ambient diffuse interstellar medium can be excluded as cause for the extended emission. The source parameters are consistent with an interpretation as either the first NIR-only detected pulsar wind nebula or the first resolved disk around an isolated neutron star.
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