Geophysical Research Letters

Plasma temperature distributions in the heliosheath



[1] Voyager 2 crossed the termination shock (TS) in August 2007 and began observations of the heliosheath. We present the first 400 days of heliosheath plasma data and propose a consistent picture of the energy flow across the TS. Roughly 15% of the plasma flow energy lost at the shock heats the thermal ions and most of the rest of this energy heats the pickup ions. The pickup ions make up roughly 20% of the sheath plasma and have energies of about 6 keV in the heliosheath, consistent with STEREO observations. Relative standard deviations of the proton temperature in the upstream solar wind and in the heliosheath are similar, but this similarity is probably accidental since the temperatures are strongly modified at the termination shock. The temperature fluctuations in the heliosheath may be derived from changes in the TS speed and/or temporal changes in the TS structure.

1. Introduction

[2] Before Voyager 2 (V2) entered the heliosheath in 2007, most expectations were for a hot heliosheath with temperatures of a few million degree K as observed in planetary magnetosheaths. Richardson and Liu [2007] suggested that the heliosheath protons could be composed of a cold (100 eV) and a hot (1 keV) Maxwellian component with roughly equal densities analogous to planetary magnetosheaths. The possibility of very low temperatures was suggested by Zank et al. [1996], who showed that for a quasi-perpendicular shock mediated by the presence of pickup ions the thermal plasma could be relatively unaffected by the shock potential.

[3] Voyager 2 crossed the termination shock (TS) in 2007 [Richardson et al., 2008a; Burlaga et al., 2008; Decker et al., 2008; Stone et al., 2008] and entered the heliosheath, the region of shocked solar wind between the TS and heliopause. The solar wind plasma is slowed, compressed, heated, and diverted at the termination shock and begins to turn down the heliotail. The thermal protons in the heliosheath have an average temperature of 180,000 K, much less than the few million degree prediction. The flow remains subsonic in the heliosheath with respect to the thermal plasma and the heliosheath ion spectra measured by the Plasma Science experiment (PLS) are well-simulated by convected isotropic Maxwellian distributions [Richardson et al., 2008a].

[4] The heliosheath region is highly variable, probably due both to changes in the upstream solar wind and changes in the TS. Two of the three TS crossings were classic supercritical, quasi-perpendicular shocks. The third had gradual changes in speed and density and two magnetic ramps and may have been in the process of reforming [Burlaga et al., 2008]. This paper looks at the first 400 days of thermal proton temperatures in the heliosheath and compares the temperature distributions in the heliosheath to those observed in the upstream solar wind. We discuss briefly a possible scenario for the energy balance across the TS. Then we present the temperature data from the heliosheath, compare it to the solar wind temperatures upstream of the TS, and discuss the implications for heating at the TS.

2. Heating at the Shock: A Possible Scenario

[5] The available data support a picture in which most of the plasma flow energy is transferred to the pickup ions at the TS. Zank et al. [1996] show that pickup ions were more likely to be reflected at the TS and gain energy than the thermal plasma. Gloeckler et al. [2005] present energetic particle spectra for energies greater than 30 keV. Extrapolation of these spectra to lower energies implies that 80% of the plasma flow energy ends up in the pickup ions, consistent with the observation that only 15% of the plasma flow energy ends up heating the thermal plasma [Richardson et al., 2008a]. At the TS shock about 20% of the protons are pickup ions [Richardson et al., 2008b]. If the flow energy were mostly going into the pickup ions, then these ions would have a temperature of order 6 keV. Wang et al. [2008] reported STEREO observations of energetic neutral atoms (ENAs) with peak fluxes at energies of 6–10 keV. These ENAs form from charge exchange of pickup ions in the heliosheath with interstellar neutral H and come from the direction of the nose of the TS; the observed ENA fluxes decrease rapidly away from the nose. The 6–10 keV pickup ions have thermal speeds much faster than the average plasma flow speed of 150 km/s in the heliosheath, thus the flow is subsonic with respect to the pickup ions. These observations seem to form a consistent picture if the energy from the plasma flow were transferred at the TS not to the thermal plasma but to the pickup ions.

3. Instrument and Analysis

[6] The Voyager plasma experiment (PLS) observes ions and electrons with energies from 10–5950 eV in four Faraday cups, three of which look towards the Sun and roughly into the solar wind and heliosheath flow [Bridge et al., 1977]. For the heliosheath, the most useful data are the lower-energy resolution L-mode spectra, which have an energy resolution ΔE/E of 29% and a time resolution of 192 s. The electrons in the heliosheath have energies below the 10 eV threshold of the instrument and are generally not observed.

[7] Although the nominal time-resolution of the PLS instrument is 192 s, the data points we show here are much sparser. When densities are very low (less than about 6 × 10−4 cm3), the currents are below the instrument threshold. When radial velocities are inward (which occurs at V1 [Decker et al., 2005] and may have happened just after the V2 TS crossing), the protons do not enter the detectors. Noise is evident in many spectra which can mask the real signal; this noise may be due to other instruments or to the PLS detector itself. This study includes only spectra in which currents are observed in all three sunward-looking detectors and which can be fit with a convected isotropic proton Maxwellian distribution. These spectra give the most reliable temperatures. Only about 15%, or about 7,000, of the available spectra meet this criterion and are included in this study. We do not think this selection affects the conclusions of this work.

4. Results

[8] Figure 1 shows two examples of spectra observed in the heliosheath in the B-cup. The data in the three sunward-looking detectors (A, B, and C) of each set of spectra were fit with convected isotropic Maxwellian distributions. No evidence for a high-energy tail or a second, hotter Maxwellian, either of which could indicate reflection of the thermal population at the TS, is observed here nor elsewhere in the heliosheath. The temperature of the first spectra is 2.2 × 104K and of the second is 2.3 × 105K. The average temperature in the solar wind in 2007 before the TS crossing was 1 × 104 K, so the first spectra is heated by only a factor of 2 above the average solar wind temperature and the second by a factor of 20.

Figure 1.

Two B-cup spectra observed in the heliosheath. The histograms show the observed currents plotted versus the channel number, which increases roughly logarithmically in energy. The curves show the best fit of a convected isotropic proton Maxwellian distribution to the data. (left) A cold heliosheath distribution with a temperature of ≈2 × 104K and (right) a warmer distribution with a temperature of ≈2 × 105K.

[9] Figure 2 shows the temperatures measured upstream and downstream of the TS. Both upstream and downstream the amount of scatter is large; in the solar wind the average temperature is 11,000 K and the relative standard deviation is 0.75 and in the heliosheath the average temperature is 181,000 K and the relative standard deviation is 0.68. The average increase in proton temperature across the TS is a factor of 13.

Figure 2.

The temperatures observed by V2 in the solar wind and heliosheath. The points show high-time-resolution data and the lines show running 5-day averages.

[10] We ask if the scatter in the heliosheath results from the variations in the upstream solar wind or from heating variations at the TS. Figure 3 shows the distributions of the observed proton temperatures upstream and downstream of the TS. The temperatures were divided into 1000 K bins and histograms of the fraction of spectra in each bin are plotted on a log-log scale. The solar wind temperatures have a broad peak at 8,000 K and another peak at 4,000 K. The heliosheath temperatures have a broad peak between 40,000 K and 200,000 K, a fairly sharp drop off above that temperature, and a much slower decrease toward lower temperature. The lower temperature cutoff and peak at 5,000 K are probably instrumental effects; the large width of the energy channels in the L-modes does not lower temperatures to be resolved.

Figure 3.

Histograms of the temperature distributions in the solar wind and the heliosheath. The black shows the solar wind distribution, the red shows the heliosheath distribution, and the blue shows the distribution of the solar wind temperature multiplied by 13, the ratio between the upstream solar wind and downstream heliosheath temperatures.

[11] Figure 3 also shows a histogram of the solar wind data shifted upward by a factor of 13 (the average temperature increase at the TS). The shifted solar wind temperatures have a narrower and higher-energy peak, at about 1.3 × 106 K, and fewer points at the lower energies than the observed temperatures. The observed shock compression is about a factor of 2 [Burlaga et al., 2008; Richardson et al., 2008a], so even in the absence of shock heating conservation of the first adiabatic invariant would give a factor of 2 increase in temperature in the heliosheath. For some of the very cold spectra in the heliosheath, this compression may be the only heating which occurred at the TS. The amount of heating of solar wind ions at the TS seems to vary significantly from the minimal factor of 2 to well above the average factor of 13. The tail of the observed distribution is about 50% higher in energy than that of the shifted solar wind distribution.

5. Discussion

[12] For high-Mach number shocks, the downstream temperature is a weak function of the upstream temperature. The flow energy is roughly a constant and most of this energy must go into heating the plasma. In the heliosheath, the temperature variation is consistently high, with temperature varying between 10,000 K and 1,000,000 K. Even when higher-temperature thermal ion spectra are observed, most energy must reside in the pickup ions. What causes these rapid fluctuations of temperature in the heliosheath? We note above that the temperature in the solar wind is highly variable and that the relative standard deviations in the solar wind were similar those in the heliosheath. However, for high Mach number shocks, the downstream temperature is a weak function of the upstream temperature. The flow energy is roughly a constant and the energy that must go into heating the plasma is generally much greater than the upstream plasma temperature. This scenario holds for planetary magnetosheaths, where the temperature profiles are strongly correlated with the solar wind speed. Thus the upstream solar wind temperature fluctuations probably are not responsible for the heliosheath temperature variations.

[13] Pickup ions are added into the solar wind predominately by charge exchange and the rate is determined mainly by the proton and neutral densities, so the ratio of pickup to thermal ions should be fairly constant. Thus changes in pickup ion density seem unlikely to contribute to the changes in temperature in the heliosheath (although we can not measure the pickup ions directly).

[14] Changes in the TS direction and motion may drive fluctuations in the heliosheath. The data suggest that either motional or structural changes in the TS occur on time scales comparable to a few times the 192-s resolution of the PLS instrument. The multiple crossings of the TS observed by V2 suggest that fluctuations of the TS position occur on scales of at most hours. Temporal changes in the TS also occur; the structure of the TS was very different at the several V2 crossings. Burlaga et al. [2008] suggest the TS may be reforming at one crossing; this result suggests the possibility that some ions essentially miss the shock as it reforms giving the very cool temperatures sometimes observed.

[15] Planetary bow shocks are in constant motion; Formisano et al. [1973] report that the average speed of Earth's bow shock is 85 km/s and more recent work shows that bow shock speeds range up to about 100 km/s [Šafránková et al., 2003; Maksimovic et al., 2003]. Estimates of the TS speed at the V2 crossings were 94 km/s outwards and 68 km/s inwards [Richardson et al., 2008a], similar to the bow shock speeds. The upstream solar wind speed at the V2 TS crossing was about 320 km/s [Richardson et al., 2008a]. If we set bounds for the TS speeds of ±100 km/s, the relative speeds of the solar wind and TS would vary from 220–440 km/s. The Rankine Hugoniot relations (neglecting pickup ions) show that this large a variation in speed would give a factor of ±equation image change in the heliosheath temperature, with the higher-relative speed flow having higher temperatures.

[16] Figure 4 shows the observed T profile with two traces superposed which show 51-point smoothed values of temperature a factor of equation image above and below the mean. This scenario envisions that the larger-scale changes in the plasma result from changes in the large-scale structure of the upstream solar wind and the small scale fluctuations are due to TS motion. This simple approximation does a reasonable job of explaining the scatter of the points, especially at the high-energy limit. The larger number of lower temperature observations could be due to the TS moving outward faster than it does inward or to plasma which passes the TS relatively unheated as the shock reforms.

Figure 4.

Temperatures observed in the heliosheath and lines showing 51-point running averages of equation imageT and T/equation image.

6. Summary

[17] The thermal proton in the heliosheath averages 180,000 K, so most of the flow energy in the solar wind heats the pickup ions, not the thermal plasma. The temperature distribution in the heliosheath is broader than that in the solar wind but has a significant low-energy tail. Some ions may pass through the TS when it is reforming and gain energy only from adiabatic compression of the flow. The relative standard deviation of the temperatures in the solar wind and heliosheath are similar, but shock heating depends only very weakly on the upstream temperature so this similarity is probably serendipitous. The scatter in the heliosheath temperatures implies changes in the shock motion and/or structure on time scales of tens of minutes.


[18] This work was supported under NASA contract 959203 from the Jet Propulsion Laboratory to the Massachusetts Institute of Technology and NASA grants NAG5-8947 and NNX08AC04G. We used the shock solver provided by UCLA (http://www-ssc.igpp. to determine shock jumps expected at the TS.