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 f rom nonradiative shocks in three supernova remnants: the Cygnus Loop, RCW 8 6, and Tycho. The spectra of these shocks are dominated by collisionally ex cited hydrogen Balmer lines, which have both a broad component caused by pr oton-neutral charge exchange and a narrow component caused by excitation of cold neutrals entering the shock. In each remnant, we have obtained the br oad-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 emissi on from nonradiative shocks in partially neutral gas. The Balmer line fluxe s are sensitive to Lyman line trapping and the degree of electron-proton te mperature 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 initi al fraction of the shock energy allocated to the electrons and protons (the equilibration) is a free parameter. Our models show that variations in ele ctron-proton temperature equilibration and Lyman line trapping can reproduc e the observed range of broad-to-narrow ratios. The results give 80%-100% e quilibration in nonradiative portions of the northeast Cygnus Loop (v(s) si milar to 300 km s(-1)), 40%-50% equilibration in nonradiative portions of R CW 86 (v(s) similar to 600 km s(-1)), and less than or similar to 20% equil ibration in Tycho (v(s) similar to 2000 km s(-1)). Our results suggest an i nverse correlation between magnetosonic Mach number and equilibration in th e observed remnants.