Equipartition of Ions and Electrons

While time dependent ionization has become a commonplace assumption in the fitting of the thermal spectra from SNRs, most results tacitly assume equipartition between the ion and electron temperatures.1 Ions are instantaneously heated to a high kinetic temperature as a result of passage through the shock. Models of initial electron heating cover the full range between no heating (Te/Ti— me/mi) and instantaneous equipartition (Te = Ti). The primary process by which electrons are thought to equilibrate is Coulomb collisions, but plasma processes can cause faster electron heating. In typical SNR shocks the collision timescale is long, and equipartition can require an appreciable fraction of the remnant life if it relies solely on Coulomb collisions. The bremsstrahlung continuum underlying the line emission in a SNR spectrum provides a direct measure of the electron temperature; since the electron temperature is expected to evolve behind the shock and vary with shock speed, an accurate measurement requires isolation of a small region of interest. Direct measurement of the ion temperature entails measurement of the thermal broadening of spectral lines. The ion temperature can also be inferred indirectly from the expansion velocity, provided there is not another channel into which shock energy can flow, such as particle acceleration.

While even the earliest time dependent ionization models of SNR spectra considered the effects of nonequipartition (e.g., [44]), X-ray measurements sensitive to the degree of equipartition came only with the high spectral and spatial resolution capabilities of Chandra and XMM-Newton. The primary reason is that previous observatories lacked the angular resolution to isolate regions near the forward shock, or the spectral resolution to sensitively measure the line ratios that allow inference of the ion temperatures. X-ray measurements are only now catching up to the better established optical or UV techniques. Rakowski summarizes all measurements of degree of equilibration [124]. Despite studies of several remnants, SN 1006 is the only one for which the degree of equilibration between particles has been well established. X-ray measurements have been made of SN 1006, DEM L71, Tycho, SN 1987A, and 1E 0102.2-7219. While each has large uncertainties, the measurements (Fig. 17.6) support a trend consistent with measurements in other bands of an inverse proportionality between shock velocity and degree of equilibration, with the youngest remnants (SN 1987A, Tycho, SN 1006) having a low electron-to-proton temperature ratio and the oldest (Cygnus Loop) having ratios consistent with equilibration [125].

Of special note are observations of two remnants: SN 1006 and DEM L71. In SN 1006, an XMM-Newton RGS spectrum was obtained from an isolated knot along the thermal northwestern limb [169]. The RGS measurement of the broadening of O V, O VI, and O VII lines implies a temperature for the O ions of 530 ± 150 keV. The simultaneous EPIC spectrum of the same region yields an electron temperature of 1.5 keV. An upper limit to Te/Tp < 0.05 is obtained. This value is

1 Fitting of moderate resolution X-ray spectra from the CCD detectors on Chandra and XMM-Newton is insensitive to the degree of equipartition.

"o

0.0_I_I_I_I_I_■ Xl- ■ _I_I_I_I_I_I_I_I_'=1 ' ' ' I '_I_I_' <

0 500 1000 1500 2000 2500 3000

shock velocity (km/s)

Fig. 17.6 Measurements to date indicate an inverse correlation between the degree of electron-proton equilibration and shock velocity [125]

consistent with optical and UV measurements of equilibration along the northwestern shock front in SN 1006. For DEM L71, the Chandra ACIS was used to extract spectra of three narrow strips at five positions along and immediately behind the forward shock. From these strips, the evolution of the electron temperature in different locations around the remnant was measured. A proton temperature measured optically was assumed. Three regions show results consistent with no equilibration. One region, with the slowest shock speed, is consistent with complete equilibration. The fifth region, with a shock speed similar to or slightly smaller than the regions with no equilibration, shows partial equilibration (Te/Tp < 0.5).

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