particle acceleration above the pick-up energy at comet 1p/halley

ISSI Meeting Berne, Switzerland, 19-23 November 2012 page 1

Particle acceleration Particle acceleration

above the pick-up energy above the pick-up energy

at Comet 1P/Halleyat Comet 1P/Halley

Susan McKenna-Lawlor

Space Technology Ireland, National University of Ireland,

Maynooth, Co. Kildare


•Ion pickup at comets (theory)

•In situ energetic particle measurements at comets

•Particle acceleration above the pickup energy

•Analysis of the data

•Conclusions

Outline


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 (Theory)


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.

Ion pickup at Comets (Contd.)


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.


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).

Upstream measurements aboard Giotto


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).

In situ energetic particle measurements at comets


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.

Candidate Acceleration Processes


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.

Theory of particle acceleration above the pickup energy at comets


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.


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; β is the angle between the solar wind and proton propagation directions and γ is the spectral index (Ipavich, 1974).

In situ measurements


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.

Comparison between measured and theoretical spectra


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.

Power Law Spectra

Inbound Outbound

1. Foreshock = 3.34 5. Cometosheath = 4.82

2. Minimum = 4.13 6. Bow Shock = 5.87

3. Bow Shock = 4.10 7. Wavefield = 5.34

4. Cometosheath = 3.49 8. End Wavefield = 3.71


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.


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).

Transit Time Damping


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.


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 Skjellerup


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.

Comet 26P/Grigg Skjellerup contd.


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).


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).

Differences and Similarities


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.

Conclusions

ISSI Meeting Berne, Switzerland, 19-23 November 2012 page 3310th Ann. Internat. Astrophys. Conference Maui, Hawai, 13-18 March 2011 page 33

particle acceleration above the pick-up energy at comet 1p/halley

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