We aimed to measure the H2O and dust production rates in C/2006 W3 (Christensen) with the Herschel Space Observatory at a heliocentric distance of ~ 5 AU. We have searched for emission in the H2O and NH3 ground-state rotational transitions at 557 GHz and 572 GHz, simultaneously, with HIFI onboard Herschel on UT 1.5 September 2010. Photometric observations of the dust coma in the 70 and 160 {mu}m channels were acquired with the PACS instrument on UT 26.5 August 2010. A tentative 4-{sigma} H2O line emission feature was found in the spectra obtained with the HIFI wide-band and high-resolution spectrometers, from which we derive a water production rate of $2.0(5) times 10^{27}$ molec. s$^{-1}$. A 3-{sigma} upper limit for the ammonia production rate of <$1.5 times 10^{27}$ molec. s$^{-1}$ is obtained taking into account the contribution from all hyperfine components. The blueshift of the water line detected by HIFI suggests preferential emission from the subsolar point. However, it is also possible that water sublimation occurs in small ice-bearing grains that are emitted from an active region on the nucleus surface at a speed of ~ 0.2 km s$^{-1}$. The dust thermal emission was detected in the 70 and 160 {mu}m filters, with a more extended emission in the blue channel. The dust production rates, obtained for a dust size distribution index that explains the fluxes at the photocenters of the PACS images, lie in the range 70-110 kg s$^{-1}$. Scaling the CO production rate measured post-perihelion at 3.20 and 3.32 AU, these values correspond to a dust-to-gas production rate ratio in the range 0.3-0.4. The dust production rates derived in August 2010 are roughly one order of magnitude lower than in September 2009, suggesting that the dust-to-gas production rate ratio remained approximately constant during the period when the activity became increasingly dominated by CO outgassing.
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