Balmer-dominated spectra of nonradiative shocks in the Cygnus Loop, RCW 86, and Tycho supernova remnants

We present an observational and theoretical study of the optical emission from nonradiative shocks in three supernova remnants: the Cygnus Loop, RCW 86, and Tycho. The spectra of these shocks are dominated by collisionally excited hydrogen Balmer lines, which have both a broad component caused by proton-neutral charge exchange and a narrow component caused by excitation of cold neutrals entering the shock. In each remnant, we have obtained the broad-to-narrow flux ratios of the H alpha and H beta lines and measured the H alpha broad component width. A new numerical shock code computes the broad and narrow Balmer line emission from nonradiative shocks in partially neutral gas. The Balmer line fluxes are sensitive to Lyman line trapping and the degree of electron-proton temperature equilibration. The code calculates the density, temperature, and size of the postshock ionization layer and uses a Monte Carlo simulation to compute narrow Balmer line enhancement from Lyman line trapping. The initial fraction of the shock energy allocated to the electrons and protons (the equilibration) is a free parameter. Our models show that variations in electron-proton temperature equilibration and Lyman line trapping can reproduce the observed range of broad-to-narrow ratios. The results give 80%-100% equilibration in nonradiative portions of the northeast Cygnus Loop (v(s) similar to 300 km s(-1)), 40%-50% equilibration in nonradiative portions of RCW 86 (v(s) similar to 600 km s(-1)), and less than or similar to 20% equilibration in Tycho (v(s) similar to 2000 km s(-1)). Our results suggest an inverse correlation between magnetosonic Mach number and equilibration in the observed remnants.