We present H-alpha and [O III] (5007 Angstroms) images of the nebula powered by the jet of the black hole candidate and microquasar Cygnus X-1, observed with the 2.5m Isaac Newton Telescope (INT). The ring-like structure is luminous in [O III] and there exists a thin outer shell with a high [O III] / H-alpha flux ratio. This outer shell probably originates in the collisionally excited atoms close to the front of the bow shock. Its presence indicates that the gas is shock excited as opposed to photoionised, supporting the jet-powered scenario. The shock velocity was previously constrained at 20 < v < 360 km/s; here we show that v >= 100 km/s (1 sigma confidence) based on a comparison of the observed [O III] / H-alpha ratio in the bow shock with a number of radiative shock models. From this we further constrain the time-averaged power of the jet: P_Jet = (4 - 14)*10^36 erg/s. The H-alpha flux behind the shock front is typically 4*10^-15 erg/s/cm^2/arcsec^2, and we estimate an upper limit of ~8*10^-15 erg/s/cm^2/arcsec^2 (3 sigma) to the optical (R-band) continuum flux of the nebula. The inferred age of the structure is similar to the time Cyg X-1 has been close to a bright H II region (due to the proper motion of the binary), indicating a dense local medium is required to form the shock wave. In addition, we search a > 1 square degree field of view to the south of Cyg X-1 in H-alpha (provided by the INT Photometric H-alpha Survey of the Northern Galactic Plane; IPHAS) for evidence of the counter jet interacting with the surrounding medium. Two candidate regions are identified, whose possible association with the jet could be confirmed with follow-up observations in [S II] and deeper observations in [O III] and radio.
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