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tokens: (cf. Equation ( 1 )). Note that the ionization fractions derived in Ghavamian et al. ( 2002 ) are insensitive to the total preshock gas density n 0 . 2.2.2. Magellanic Supernova Remnants Ghavamian et al. ( 2003 ) study the entire remnant of DEM L71 using Fabry–Perot imaging spectroscopy, with preshock densities inferred from Chandra ACIS-S spectra modeled by Rakowski et al. ( 2003 ). The latter find a range of preshock densities along different regions of the rim of the remnant, roughly bounded by the range ≈0.5–1.5 cm −3 . In particular, n 0 ≈ 0.5 cm −3 is consistent with the majority of the eastern rim of the remnant, while in portions of the northwest rim, n 0 ≈ 1.5 cm −3 . Modeling the observed collisionally excited hydrogen-Balmer emission, Ghavamian et al. ( 2003 ) conclude that a wide range in neutral fraction may be plausible, but that would be necessary in order to produce detectable H α emission. Ghavamian et al. ( 2007 ) revisited DEM L71 in the far-UV, as well as the LMC remnants 0509-67.5, 0519-69.0, and 0548-70.4, using spectra obtained from the Far Ultraviolet Spectroscopic Explorer . The ratio of fluxes in Ly β and O VI 1032 Å depends linearly on the preshock neutral fraction; the observed ratio in DEM L71 requires a hydrogen neutral fraction of 20–40%, consistent with previous limits. No UV lines were found for the remnant 0548-70.4. For the remnants 0509-67.5 and 0519-69.0, the same method constrains the neutral hydrogen fraction in the surrounding ISM to >40%. The best-fitting ambient densities can be found by comparing the present size and ionization state of the remnant with hydrodynamical models: recently, Kosenko et al. ( 2014 ) found n 0 = 0.1–0.3 cm −3 for 0509-67.5, and n 0 = 1.0–2.0 cm −3 for 0519-69.0, although Kosenko et al. ( 2010 ) report densities as high as 2.4 cm −3 . As a conservative estimate, we adopt 0.3 cm −3 and 2.4 cm −3 as our fiducial ISM densities for 0509-67.5 and 0519-69.0, respectively. The radius of the forward shock for both remnants is ∼4 pc, for an LMC distance of 50 kpc. 3. Constraints on the Nature of the Progenitors of Nearby SNe Ia 3.1. Flash Ionization We may now investigate the extent to which the presence of neutral hydrogen at the present radii of all remnants considered above constrains the release of ionizing photons in the last τ rec ≈ 100,000 years. Chevalier Raymond ( 1978 ) were the first to consider the simplest case, a “burst” of ionizing photons from the supernova itself. For a present shock radius R and mean ambient density n , the total number of hydrogen-ionizing photons emitted in such a burst must have been fewer than 4 π R 3 n /3 ≈ (0.2–6) × 10 58 for SN 1006, 0509-67.5, 0519-69.0, and DEM L71 (see Table 1 ). Notably, this upper bound applies not only to the shock breakout from the supernova itself, but to any short-lived phase that the progenitor or its companion underwent immediately preceding or following the explosion, such as any briefly hot, luminous surviving WD