Development of a Method for the Observation of Lightning in Protoplanetary Disks Using Ion Lines

In this paper, we propose observational methods for detecting lightning in protoplanetary disks. We do so by calculating the critical electric field strength in the lightning matrix gas (LMG), the parts of the disk where the electric field is strong enough to cause lightning. That electric field accelerates multiple positive ion species to characteristic terminal velocities. In this paper, we present three distinct discharge models, with corresponding critical electric fields. We simulate the position-velocity diagrams and the integrated emission maps for the models. We calculate the measure of sensitivity values for detection of the models, and for distinguishing between the models. At the distance of TW-Hya (54pc), LMG that occupies $2\pi$ in azimuth and $25 \mathrm{au}<r<50 \mathrm{au}$ is $1200\sigma$- to $4000\sigma$-detectable. The lower limits of the radii of $5\sigma$-detectable LMG clumps are between 1.6 au and 5.3 au, depending on the models.