Biases in Expansion Distances of Novae Arising from the Prolate Geometry of Nova Shells

Abstract

ABSTRACTExpansion distances (or expansion parallaxes) for classical novae are based on comparing a measurement of the shell expansion velocity, multiplied by the time since outburst, with some measure of the angular size of the shell. We review and formalize this method in the case of prolate spheroidal shells. For such shells there is no unique angular size except when the shell is seen pole‐on, and several different measures of angular size have been used in the literature. We present expressions for the maximum line‐of‐sight velocity from a complete, expanding shell and for its projected major and minor axes, in terms of the intrinsic axis ratio and the inclination of the polar axis to the line of sight. For six distinct definitions of “angular size” we tabulate the error in distance that is introduced under the assumption of spherical symmetry (i.e., without correcting for inclination and axis ratio). The errors can be significant and systematic and can affect studies of novae whether considered individually or statistically. Each of the six estimators overpredicts the distance when the polar axis is close to the line of sight, and most underpredict the distance when the polar axis is close to the plane of the sky. Use of the straight mean of the projected semimajor and semiminor axes gives the least distance bias for an ensemble of randomly oriented prolate shells, and we recommend this method when individual inclinations and axis ratios cannot be ascertained. The best individual expansion distances, however, result from a full spatio‐kinematic modeling of the nova shell. We discuss several practical complications that affect expansion distance measurements of real nova shells. We recommend that nova shell expansion distances be based on velocity and angular size measurements made contemporaneously if possible and that the same ions and transitions be used for the imaging and velocity measurements. We emphasize the need for complete and explicit reporting of measurement procedures and results, regardless of the specific method used.