An independent distance estimate to CW Leo
CW Leo has been observed six times between October 2009 and June 2012 with the SPIRE instrument on board the Herschel satellite. Variability has been detected in the flux emitted by the central star with a period of 639 \pm 4 days, in good agreement with determinations in the literature. Variability is also detected in the bow shock around CW Leo that had previously been detected in the ultraviolet and Herschel PACS/SPIRE data. Although difficult to prove directly, our working hypothesis is that this variability is directly related to that of the central star. In this case, fitting a sine curve with the period fixed to 639 days results in a time-lag in the variability between bow shock and the central star of 402 \pm 37 days. The orientation of the bow shock relative to the plane of the sky is unknown (but see below). For an inclination angle of zero degrees, the observed time-lag translates into a distance to CW Leo of 130 \pm 13 pc, and for non-zero inclination angles the distance is smaller. Fitting the shape of the bow shock with an analytical model (Wilkin 1996), the effect of the inclination angle on the distance may be estimated. Making the additional assumption that the relative peculiar velocity between the interstellar medium (ISM) and CW Leo is determined entirely by the star space velocity with respect to the local standard of rest (i.e. a stationary ISM), the inclination angle is found to be (-33.3 \pm 0.8) degrees based on the observed proper motion and radial velocity. Using the Wilkin model, our current best estimate of the distance to CW Leo is 123 \pm 14 pc. For a distance of 123 pc, we derive a mean luminosity of 7790 \pm 150 Lsol (internal error).