tokens: sampling rate. 4. Discussion 4.1. Prominences From the H α tomogram, we can estimate the size and location of the satellite emission that we associate with prominences by assuming that they are corotating with the secondary star. The projected distance of these features from the center of mass (CM) of the binary is simply r = v /Ω, where v is the inclination-corrected velocity amplitude of the emission and Ω is the angular velocity of the secondary. The orbital inclination is expected to be ∼75° based on our assumed stellar masses and the mass function measured by Marsh et al. ( 2016 ). Therefore, the correction between the radial velocity and space velocity is less than 10%. For the orbital period from Marsh et al. ( 2016 ), the inverse angular velocity is 2043 s rad −1 . Assuming a mass for the WD of 0.8 M ⊙ , then the mass ratio of the system is q ≈ 0.3 for a secondary with a mass typical for an M5 dwarf. The radius of the secondary’s Roche lobe is (Eggleton 1983 ). Since the secondary is probably close to filling its Roche lobe, we use this as the stellar radius and compare it to the size of the prominences. The brightest emission from the prominences is seen around 500 km s −1 , corresponding to 4.4 Roche radii from the CM. The prominences precede and trail the secondary by ± 0.15 in phase, meaning that the prominences extend 3 stellar radii from the surface of the secondary. The faint emission behind the secondary at 1000 km s −1 corresponds to 8.7 stellar radii from the CM, or about 5 stellar radii from the backside of the red dwarf. In isolated magnetized stars, the corotation radius is where the gravitational pull of the star balances the centrifugal acceleration of plasma trapped in the field. Prominences found at or beyond the corotation radius are called “slingshot” prominences (Steeghs et al. 1996 ). In binary systems the balance between centrifugal and gravitational forces is found at the Lagrangian points. The L 4 and L 5 points are actually rather broad regions that make an equilateral triangle with the primary and secondary stars. For the assumed parameters of the AR Sco binary, the L 4 and L 5 points are 370 km s −1 from the CM. The prominences extend more than 30% farther than L 4 and L 5 points. The trailing prominence differs in phase from the L 5 point by 20°. The L 2 point is expected to be at 4.5 Roche radii from the CM, or a velocity of 500 km s −1 , while the faint prominence behind the secondary is seen at twice that distance. We conclude that the prominence emission extends well beyond the outer Lagrangian points. The stability of slingshot prominences has been modeled by Ferreira ( 2000 ). Such prominences can be stable out to ∼5 stellar radii if the dipole surface magnetic field is larger than ∼100 G, and out to 10 stellar radii for a 500 G field. A quadrupole field would require ∼500 G for prominence stability at 5 stellar radii. The WD field at the secondary is expected to have an average field strength of order
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