Particle acceleration above the pick-up energy at Comet 1P/Halley

Particle acceleration above the pick-up energy at Comet 1P/Halley Susan McKenna-Lawlor Space Technology Ireland, National University of Ireland, Maynooth, Co. Kildare

Outline • Ion pickup at comets (theory) • In situ energetic particle measurements at comets • Particle acceleration above the pickup energy • Analysis of the data • Conclusions

Ion pickup at Comets (Theory) An understanding of how comets interact with the solar wind has been developed through theoretical analysis, backed up by in situ measurements made aboard spacecraft at various comets. According to the scenario thereby developed, as a cometary body approaches the Sun, it begins to loose mass due to the sublimation process so that, under the pertaining low gravity conditions, an expanding atmosphere composed of dust, molecules, radicals and molecular ions is formed which escapes from the collision dominated inner region of the coma (velocity ~ 1 - 8 km/s).

Ion pickup at Comets (Contd.) The radially expanding molecules undergo complicated chemical reactions in the inner reaches of the coma. Further out, at distances of several million km ( ≥ 7.5 x 106 km from 1P/Halley) ions are created through photoionization by solar EUV radiation; charge exchange with solar wind ions; electron impact and other processes.

Ion pickup at Comets (Contd.) It is assumed that the solar wind is a fully ionized, highly conducting plasma with the interplanetary magnetic field frozen into its flow due to the high conductivity that pertains. A freshly ionized cometary particle, which is initially practically at rest with respect to the solar wind flow, is accelerated along the ambient motional electric field, while also gyrating about the magnetic field and undergoing E x B drift so that, overall, it follows a cycloidal trajectory.

In the frame of the comet, the energy of the particle along this trajectory varies between ~ 1 km/s and a maximum value: Emax = 4A sin2α Esw where A is the ion mass in a.m.u., α is the angle between the interplanetary magnetic field and the solar wind and Esw is the kinetic energy of a proton traveling with the solar wind velocity. The peak energy attained thus depends on the magnetic field direction and on the solar wind velocity.

In the solar wind reference frame ions are created with a speed equal to the solar wind speed in the comet’s rest frame and they form a ring in velocity space as they gyrate about the magnetic field lines. Excess free energy in the ring distribution renders it highly unstable and low frequency Alfvén waves are generated via the ion cyclotron instability. These waves were predicted by Wu and Davidson, 1972, Wallis, 1973, Gary et al. 1986 and Sagdeev et al. 1986) to scatter the ions in pitch angle so that they form a shell distribution in velocity space (Galeev and Sagdeev, 1988). More recent studies/observations have indicated that the actual configuration more closely resembles a bispherical distribution than a single shell (Johnstone, 1995, Coates, 1997).

If efficient pitch angle scattering occurs in the flow rest frame the peak energy of the ions is: Emax =4A Esw so that the mean direction of motion depends only on the solar wind flow.

Upstream measurements aboard Giotto Measurements made inbound aboard Giotto by the Johnstone Plasma Instrument Implanted Ion Sensor JPA/IIS) showed that, far from comet 1P/Halley the ion distributions detected were ring-like. They became shell-like upstream of the bow shock and the shell thickened substantially downstream (Coates, 2004). Also, very high levels of magnetohydrodynamic turbulence interpreted to be generated by the implanted cometary ion pickup process was detected (Neubauer et al., 1986).

In situ energetic particle measurements at comets At the time of the encounter, the estimated maximum pickup energy of water group ions under the prevailing solar wind conditions was < 60 keV. The energetic particle (EPONA) instrument aboard Giotto, however, detected water group ions with energies > 0.5 MeV (McKenna-Lawlor et al., 1987). This observation was in accord with measurements made by the Tunde Instrument aboard Vega 1 which encountered 1P/Halley from 4-7 March, 1986 and by the EPAS Instrument aboard the ICE spacecraft which encountered comet 21P/Giacobini-Zinner (10-13 September, 1985) [Somogyi et al. 1990, Hynds et al., 1986, Ipavich et al. 1986]. Also particles with greater than the local pickup energies were recorded by EPONA at comet 26P/Grigg-Skjellerup during the Giotto Extended Mission (McKenna-Lawlor et al. (1993).

Candidate Acceleration Processes Several mechanisms have been proposed to explain the presence at comets of ions with energies that significantly exceed the maximum local pickup energy including: Fermi Type I Process: whereby scattering centers move at different speeds on either side of a boundary in the flow (the bow shock), thereby causing particle acceleration (Amata and Formisano, 1985). Fermi Type II Process: particles interact with up-stream and down-stream counter propagating wave “scattering centers” so that a particular particle may undergo acceleration or deceleration as it either takes energy from, or gives energy to, the waves (Terasawa and Scholer, 1989). This process results in broadening the ion shell distribution to both higher and lower energies.

Theory of particle acceleration above the pickup energy at comets In early studies, Ip and Axford (1986) estimated the relative strengths at comets of diffuse shock acceleration and stochastic acceleration from Alfvén wave scattering and concluded that, under conditions of strong scattering such that the ratio (f) of the scattering mean free path to the ion gyroradius was ~ 1, the stochastic process should be more effective in accelerating particles than the First Order Fermi process. This was predicted to occur because the shock in the vicinity of comets was inferred to be weak (M~2) due to continuous mass loading of the solar wind.

The process of stochastic acceleration is described by a Fokker-Planck equation (1) where Do = 3ZeBVA2 /2f represents the energy diffusion coefficient resulting from Alfvén scattering. For an initial delta-function distribution, the time evolution of the particle distribution function is represented by (2) where I½ (x) = sin h (x) /x½

The effects of adiabatic compression were not taken into account in (1). Later Isenberg (1987) presented a solution of the full Fokker-Planck equation under the condition that the plasma parameters (flow velocity, source terms, plasma density and magnetic field strength) follow a power law dependency on the radial distance from the nucleus. In this model it was assumed that ions are immediately isotropized at pickup and the effects of adiabatic acceleration in the slowing solar wind as well as consideration of the continuous pickup of ions as the comet is approached are taken into account.

In situ measurements To characterize particle fluxes measured close to 1P/Halley aboard Giotto by the EPONA instrument (E > 60 keV) and by the Johnstone Plasma Instrument Implanted Ion Sensor (JPA/IIS) in the energy range 2-86 keV, various energy spectra (phase space densities as a function of particle energy) were calculated (McKenna-Lawlor et al. 1987) and transformed into the solar wind frame using: where dj/dE is the differential flux in a moving frame; K is a constant; W is the solar wind velocity, V is the particle velocity; βis the angle between the solar wind and proton propagation directions and γis the spectral index (Ipavich, 1974).

Comparison between measured and theoretical spectra Composite ion measurements made in the SW frame at different distances (inbound) from the Halley nucleus were then compared with theoretical distributions calculated following Ip and Axford (1986) while including adiabatic compression. These theoretical distributions were estimated for water group ions traveling along a stream line that would intersect with the Giotto spacecraft during time intervals in close accordance with the particle measurement times.

The figure shows a comparison between measurements made upstream of the bow shock (at 1.5 x 106 km from the 1P/Halley nucleus) on the assumption of a value of f ~30.

LHS: Corresponding composite measurements made at 1.1 x 106 km from the Halley nucleus during the inbound bow shock transition compared with a theoretical distribution calculated for f (~5). RHS: Composite measurements made at < 106 km compared with a theoretical distribution again for f (~5).

It can be inferred from these comparisons that a relatively weak scattering limit characterized by f ~ 30 is more appropriate to represent conditions upstream of the comet than the initially predicted value of f ~ 1. Near the shock surface where enhanced levels of turbulence were present, a value of f ~ 5 is sufficient to result in rapid isotropization and thermalization of the ions.

Gombosi et al. (1989) suggested a scenario in which the second order Fermi mechanism efficiently accelerates ions to moderate energies in the cometary upstream region. In the foreshock, where the solar wind is substantially slowed, the super-thermal implanted ions are further energized by a diffusive, compressive shock acceleration process. It was argued that the entire foreshock region can serve as a region of diffusive, compressive ion acceleration so that, in effect, a strong shock (M ~ 13) is available to energize particles rather than the weak (M~2) shock envisioned by Ip and Axford (1986). The diffusion coefficient should be sufficiently large to allow the entire foreshock region to act as a shock but small enough that the acceleration time scales are sufficiently short to be relevant.

The energy spectra calculated by Gombosi et al. (1989a) using their (quasi-linear) model were demonstrated to show a satisfactory fit to a spectrum obtained upstream of the shock by combining the EPONA, IIS and Tunde observations.

It was inferred that, initially velocity diffusion can accelerate pickup ions at comets to moderate energies, thereby creating a seed population for the, more efficient, diffusive compressive shock acceleration. Solar wind convection limits the time available for diffusive compressive acceleration and it was predicted by the model of Gombosi et al. (1989b) that, above 100 keV, power law type energy spectra with spectral indices of 5-6 would be observed.

In order to investigate the ion distributions more fully, composite EPONA+JPA spectra were plotted at 8 positions along the Giotto trajectory (Kirsch et al., 1991). The indices of the power law spectra thereby obtained are presented in Table 1. Overall the energy spectra measured were somewhat harder on the inbound than on the outbound side.

A relatively hard spectrum was observed in the inbound foreshock (γ= 3.3). Inside the bow shock itself the spectrum was somewhat softer (γ= 4.1) due to an increase in fluxes in the low energy channels. Further particle acceleration took place inside the cometosheath (γ= 3.5) Outbound, similar, although somewhat steeper spectra, were observed.

Transit Time Damping Magnetometer observations made aboard Giotto indicated that the interaction region between the solar wind and comet Halley was characterized by large amplitude, low frequency magnetic field fluctuations in the upstream region as well as in the cometosheath both inbound and outbound. These compressional magnetic field fluctuations, which had a 3-4 minute quasi-periodicity, were argued by Glassmeier et al. 1987 and Ip and Axford (1987) to have the possibility to contribute to particle acceleration via the Transit Time Damping Mechanism (Fisk, 1976). In this scenario, ions are scattered and accelerated in randomly moving magnetic gradients (a Fermi process with magnetic scattering centers).

The measured spectra suggest that a combination of the First Order and Second Order Fermi processes and the transit time damping effect were the most likely candidates to stimulate the particle acceleration measured by EPONA+ IIS at the inbound and outbound bow shock. TTD would have the effect of lowering the pitch angles of the energetic particles (Fisk, 1976), thereby potentially causing the escape of particles along the magnetic field vector on the outbound side. This is in line with observations by EPONA of an outbound flux anisotropy.

Comet 26P/Grigg Skjellerup Spectral studies were made by McKenna-Lawlor et al. (1997, 1999) using EPONA data recorded at comet 26P/Grigg-Skjellerup during the Extended Giotto Mission. Because of the pertaining flyby geometry, the inbound /outbound passes at 26P/G-S corresponded to the outbound/inbound passes at 1P/Halley. Regular magnetic fluctuations were observed along the inbound spacecraft trajectory and Neubauer et al. (1993) concluded that the large amplitude, compressional magnetic fluctuations observed indicated the presence of a thick pulsation shock.

Comet 26P/Grigg Skjellerupcontd. The spectrum obtained upstream (1 x 105 km) of the (inbound) bow wave indicated that the mean free path corresponding to random scattering by ambient waves was ~ 30 gyroradii.

Right: The energy spectrum just upstream of the outbound Bow Shock/Foreshock transition had a spectral exponent of γ = 5.09 and is interpreted to indicate the influence of diffusive compressive acceleration supplemented by transit time damping. Left: The energy spectrum obtained immediately downstream of the inbound shock can be attributed to 2nd order Fermi acceleration, adiabatic compression and the TTD effect (McKenna-Lawlor et al. 1999).

Differences and Similarities When the ion distributions recorded at P/Halley, P/Grigg-Skjellerup and P/Giacobini-Zinner are intercompared, certain differences, as well as similarities, between the observational data can be identified. When considering how particles are accelerated close to cometary shocks, individual cases should be considered (taking into account both inbound and outbound shock transitions) since the prevailing interplanetary conditions, as well as the circumstances of whether a particular shock is quasiperpendicular or quasiparallel will influence the outcome, as will the presence or absence of large, local fluctuating wave fields, the production of which, in turn, depends on the gas production rate of the comet concerned (McKenna-Lawlor et al., 1999, 2000).

Conclusions Spacecraft observations by EPONA and IIS aboard Giotto and by Tunde aboard Vega-1 at 1P/Halley; by EPAS aboard ICE at 21P/Giacobini-Zinner and by EPONA at 26P/Grigg-Skjellerup indicate that, in each case, cometary ions were accelerated significantly above their highest available pickup energies. Energy spectra obtained using the same instrument (EPONA) at 1P/Halley and at 26P/Grigg-Skjellerup indicate that the mean free path corresponding to random scattering by Alfvén waves was of the order of 30 ion gyroradii upstream of the bow shock, indicating that, at this location, energy diffusion was weak.

Conclusions Close to the inbound and outbound shock surfaces of 1P/Halley and 26P/Grigg-Skjellerup the most likely candidates for accelerating ions are compressive shock acceleration supplemented by transit time damping. When considering how particles are accelerated close to particular comets, the outgassing rate of the body as well as the pertaining interplanetary conditions should be taken into account.

10th Ann. Internat. Astrophys. Conference Maui, Hawai, 13-18 March 2011 page 33

Particle acceleration above the pick-up energy at Comet 1P/Halley