A model of the Lyman-c line profile

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. A7, PAGES 15,795-15,805, JULY 1, 2000 A model of the Lyman-c line profile in the proton aurora Jean-Claude G rard and Benoit Hubert Laboratoire de Physique Atmosph rique et Plan taire, Institut d'astrophysiquet de G ophysique, Universit de Liege, Liege, Belgium. Dimitry V. Bisikalo and Valery I. Shematovich Institute of Astronomy, Russian Academy of Sciences, Moscow Abstract. The Lyman- auroral emission is characterized by a broad line profile whose shape depends on the energy and pitch angle distributions of the initial proton beam, whereas its total brightness reflects the proton energy flux precipitated into the auroral upper atmosphere. Global remote sensing of the proton aurora through its ultraviolet signature makes it is increasingly important to relate the characteristics of the Lyman- emission to the physical properties of the precipitated proton flux. We present a numerical model of proton and hydrogen flux transport and kinetics based on the direct simulation Monte Carlo method. In this approach, all elastic and inelastic processes are stochastically simulated as well as is the production of Lyman- photons with the associated Doppler velocity component. The model also includes collisional, geomagnetic, and geometric spreading of the proton-hydrogen beam. We show that consideration of the stochastic character of the H atom velocity redistribution after collisions produces line profiles different from those obtained in the strictly forward or mean scattering angle approximations previously used in proton transport codes. In particular, the predicted fraction of photons due to backscattered particles is considerably larger when stochastic collision scattering is considered than in the strictly forward or mean scattering angle approximations. In contrast to the median wavelength, the position of the peak in the line profile shows a weak inverse dependence on the proton energy. The efficiency of the Lyman- photon production per unit incident energy flux significantly drops as the mean proton energy increases. The line profile and the amount of blue-shifted (for downward viewing) emission depends in a complex way on the initial energy and pitch angle distribution of the protons. The line profiles expected for the noon cusp and midnight proton aurora are shown to be significantly different. 1. Introduction wavelength ( ) by as much as 4, and the line width was larger than the geocoronal midlatitude con- Proton precipitation in the Earth's high latitude ther- tribution. From these line characteristics they derived mosphere was discovered from its optical signature in incident proton energies ranging from about 10 to 50 the polar auroral spectrum. Vegard [1940] first mea- kev during very magnetically active periods. The insured the Ha and H Balmer lines, and Meinel [1951] ferred proton energy flux was about 0.3 erg cm -2 s -1, interpreted the blue Doppler shift of the line as evidence a value consistent with statistical proton precipitation of precipitation of energetic protons. The morphology fluxes derived from satellite in situ observations. of the proton aurora and its optical emission were ex- Precipitating fluxes from the magnetosphere consist tensively studied from the ground as summarized by mostly of electrons and protons with a small admix- Eather [1967]. Doppler-shifted auroral Lyman-c (Ly- ture of other ions. The parameters of these fluxes in c ) emission was observed by Ishimoto et al. [1989] us- the high-altitude region of the Earth's atmosphere have ing nadir FUV satellite spectral observations. The line been considered theoretically and experimentally in varpeaks were shifted toward longer wavelengths from rest ious studies over the years [Sharp et al., 1974; Hardy et al., 1985, 1989]. The electron and proton auro- Copyright 2000 by the American Geophysical Union. Paper number 1999JA / 00 / 1999 J A ,795 rae show different morphological features [Mende and Eather, 1976], although no global view of the proton aurora has been obtained so far.

2 15,796 GERARD ET AL.: LYMA?4-oz IN PROTON AURORA A statistical study of the global characteristics of precipitated ions (mostly protons) was made by Hardy et al. [1989] based on the energy spectra in the range 30 ev to 30 kev measured by the D MSP detectors. They found that the maximum energy flux precipitation occurs premidnight in C-shaped regions symmetric about servers) was examined by Eather [1966] who compared Balmer line profiles observed by various authors with theoretical profiles. He concluded that the calculated backscattered H atom component is too small unless the proton pitch angle distribution is isotropic up to 60ø-70 ø and peaked at higher pitch angles, in contraa meridian running prenoon to premidnight. It gener- diction with most rocket and satellite observations. In ally increases with higher values of Kp. The maximum number flux shows a somewhat different pattern, with largest values observed in the cusp region and exhibits little dependence on magnetic activity. The characteristic ion energy is substantially less in the noon cusp region than along the nightside oval. The maximum average particle energy is observed on the evening side of the oval near the equatorward boundary of the ion precipitation. Typical average energies range from 1 to 2.5 kev in the noon cusp region and from 8 to 19 kev in the midnight sector. The statistical precipitation model reveals that in the afternoon and evening sectors at the lower auroral latitudes, the ions can carry a significant fraction of the total particle energy flux. Therefore ion precipitation plays an important role in the chemistry and physics of the polar atmosphere. Globally, ion precipitation accounts for of the integral energy precipitated in the aurora. As protons penetrate in the atmosphere, they are protheir study of the altitude variation of the pitch angle, Lorentzen et al. [1998] showed that only a narrow range of pitch angle around 65 ø contributes to the observed red shift in the H, ground-based line profile. Protons with small pitch angles at the top of the atmosphere suffer only small angle scattering, whereas particles with initial angles above 65 ø have their mirror points too high above the emission altitude to contribute significantly to the emission. Galand and Richmond [1999] also addressed the question of the origin of the red shift of the HI Balmer emission observed from the ground. Considering that the backscattered H atom flux is due to both direct proton mirroring and the magnetic mirroring of H atoms, they calculate a fraction of less than 1% for the total red-shifted emission. They concluded that the role played by the magnetic field in generating the red-shifted HI emissions is very modest. Several methods have been used to investigate the behavior of proton and hydrogen auroral fluxes in the gressively slowed down by elastic and inelastic collisions atmosphere and their optical signatures in the Balmer with major neutral constituents. During some of these collisions the proton captures an electron leaving a fast hydrogen atom, possibly excited in the upper state of the Ly-c transition. These fast H atoms bear the signature of the proton characteristics before the electron stripping collision. As the hydrogen atoms move away (toward) the observer, the photon is emitted with a Doppler shift to the red (blue) side of the unshifted line line profiles. So far, linearized Boltzmann equations were used for the description of the gas flow in this region. These approaches can be generally categorized as [Decker et al., 1996] (1) continuouslowing-down approximation [Rees, 1982; Galand et al., 1997]; (2) linear transport theory [Basu et al., 1987]; and (3) Monte Carlo test particle method [Kozelov and Ivanov, 1992; $ynnes et al., 1998, Lorentzen et al., 1998]. These nucenter. The observed line profile is the result of the merical methods allow the evaluation of several effects integration of the contributions of all velocity vectors projected on the line of sight. The Doppler formula induced by proton precipitation (escape fluxes, heating rate of the atmospheric gas, optical emission rates, etc.). yields the simple relationship A/k(/ ) x/, where However, for the specific problem of the calculation of synthetic Ly-c profiles in the proton aurora, a more sophisticated model must be used. It is important to take into account the stochastic nature of collisional scat- the proton local energy E is expressed in kev and the Doppler shift is expressed in Angstroms. Modeling the line shape and brightness of hydrogen lines requires the knowledge of the velocity distribution of fast H atoms in the column observed by the instrument. Many of the models developed to calculate the proton energy degradation and the associated emission rates have also been applied to the calcula- tion of the H emission line profiles [Rees, 1982; Galand et al., 1998]. Lorentzen et al. [1998] used NOAA 12 satellite measurements of the incoming auroral proton fluxes to calculate the resulting H, profile and compare it with ground-based observations in the dayside cusp region. They obtained a good match between the observed and calculated emission profiles. From the magnitude of the blue-shifted portion of the profile, they concluded that upward moving hydrogen atoms contribute about 10% of the dayside H emission. The question of the red-shifted component (for ground ob- tering to properly describe the behavior of high-energy protons (or H atoms) which collide with the target particle and change their direction following a probabilistic distribution of the scattering angle [Smith et al., 1991]. This feature was not completely included in previous models and is the most important feature of the kinetic model discussed here. A second important advantage of this model is the use of updated cross sections and scattering angles based on experimental data. A third characteristic is the sellconsistence of the model, as we simultaneously consider all sources (collisional, ge- ometrical, and magnetic mirroring) of spreading of the incident beam. The kinetic model of proton aurora we developed is based on the direct simulation Monte Carlo method described in detail by Marov et al. [1997]. In this paper we present the stochastic model of pro-

3 ton and hydrogen flux transport and its kinetics in the atmospheric gas. This model is applied to the calculation of the Ly-c line profile emitted under a range of energy and pitch angle distributions. Such calculations are important for the interpretation of Ly-c spectral and morphological data such as those obtained with the spectral imager (SI) instrument [Mende et al., 2000] on board the IMAGE satellite or the global ultraviolet imager (GUVI) on the Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics (TIMED) mission. 2. Model Description 2.1. Physical Processes The interactions of precipitating energetic protons of magnetospheric origin with the main atmospheric constituents of the thermosphere are described by the following processes: GERARD ET AL.: LYMAN-a IN PROTON AURORA 15,797 H, + o; ( ) Hf + O > H, e (lb) r + o + (lo) H + N2 Hf+O H, + N (2a) H -, + N2 + + e (2b) + H I, + N 2 H, + O} H, + O + + e H I, + O + (2c) (3a) (3b) (3c) These include momentum and energy transfer in elastic and inelastic collisions (equations(la), (2a), and (3a)); ionization of target particles (equations(lb), (2b), and (3b)); and charge transfer and electron capture (equations(lc), (2c), and (3c)). The excited states of N, O, and O* in the model are considered based Hf + N2 Hi+O H I, + N (5a) Hf, + N + + e (5b) H, + N + e Hf, + O* Hf, + O + + e Hy, + O + e (5c) (6a) (6b) (6c) The inelastic channels considered for H I - (02, N2, O) collisions include excitation of electron states, ionization, and stripping processes, in agreement with Edgar et al. [1973, 1975]. The secondary fast H I, atoms and H, ions produced by momentum transfer and stripping reactions recycle the reaction set (1)-(6). This means that the interaction of the precipitating protons with the main neutral constituents of the atmosphere must be considered as a cascade process, producing a growing set of translationally and internally excited particles of the ambient atmospheric gas Kinetic Equations To analyze the H + - H beam penetration into the Earth's auroral region, we use kinetic Boltzmann equa- tions [Marov et al., 1997]. These coupled equations take into account both scattering and transport of the highenergy proton-hydrogen flux and may be cast into the form o o o a-- fp + V rrfp q- S vvfp - - Y] Qcnt(fp, fi, fh) i=0,n2,02 + (f,, ) + 4 (, ) (7) i--0,n2,02 i=0,n2,02 o o o O-- fu + V rfh + S vvfh -- Z Qcht (fp, fi, fh) i--0,n2,02 - (f,f, )+ J (f, ) (8) i=0,n2,02 i=0,n2,02 where fp(v), fh(v), and fi(v) are the velocity distribution functions for proton, hydrogen, and components of ambient gas, respectively. In the right-hand part of on Edgar et al. [1973, 1975]. the system of kinetic equations (8) and (9) the terms The energetic H atoms produced by proton impact further interact with the main constituents of the atmo-. Qcnt and ( str describe the sources and sinks of p and sphere, transferring their momentum and kinetic energy by elastic and inelastic collisions, ionization, and stripping processes: H/+O2 Hf, + O (4a) H I, e (4b) H, + O + (4c) H due to charge transfer (electron capture) and stripping (electron loss) processes in the proton-hydrogen flux penetration into the ambient atmosphere, i.e. the coupling between p and H fluxes. The charge transfer (and stripping) terms are written as ( cht(fh, fi, fp) --/ dcrcht(lvp -- v/i) Ivp -- vii X[fH(v )f (v;) -- f (v )f (v )] O V,

4 15,798 GERARD ET AL.' LYMAN-o IN PROTON AURORA and the elastic and inelastic scattering terms are given by Jsc(fp, f ) - / dcr, (lvp - v [) Ivp - v I x [J½(v;)f (v ) - fp(vp)fi(v )] dv. For collision terms the standard notations of the particle velocities before and after collisions and of corre- sponding differential collision cross sections are used. It is assumed that the ambient atmospheric gas is characterized by local Maxwellian velocity distribution functions Numerical Model The stochastic direct simulation Monte Carlo method [Marov et al., 1997] was used to solve the system of kinetic equations (7) and (8) and investigate the energy degradation of the H+-H beam and the fbrmation of energetic hydrogen atoms due to auroral proton precipitation in the aurora. In the numerical simulations that follow, the evolution of the system of modeling particles to prtil port is calculated from the initial state to the steady state. The presence of the magnetic field influences the trajectories of proton and hydrogen particles by two distinct mechanisms' (1) In the model the adiabatic motion of protons in the dipole magnetic field obeys the adiabatic invariance relation: sin2t9(z) : (z + Rs)3sin20(z) - const, where 0 is the proton pitch angle, -Rs is the Earth radius, and z is the altitude. (2) As hydrogen atoms travel aceross the magnetic field lines, their pitch angle is modified since the magnetic field lines are not parallel. Magnetic mirroring is implemented in the code by continuously comparing the proton pitch angle with 90 ø. If the pitch angle 0 jumps from below to above this value during one time step, the time step is divided by 10 to determine the location of the mirror point with an increased accuracy of the order of 1/10 of the cell size (minimum value between the mean free path and the density scale height). The sign of the parallel velocity is inverted, while the azimuthal component is kept unchanged. The second mechanism by which the magnetic field influences the particle transport results from its spatial configuration. Neutral H atoms in the upper boundary was set at 700 km, where the atmospheric gas flow is practically collisionless. The region of the atmosphere under study was divided into 49 radial cells. The altitude-dependent cell size was chosen from the condition that it must be equal to or smaller than the free path length and the ambient gas density scale height near the lower boundary of each cell. The relative importance of processes (1)-(6) is governed by their collision cross sections. The adopted cross sections are described below. The interaction of the proton-hydrogen beam with the atmosphere was calculated using the same method as described by Bisilcalo et al. [1995] to investigate the precipitation of energetic O + ions into the high-latitude Earth's thermosphere. It is also similar to the approach used by Bisilcalo et al. [1996] to describe the energy distribution function of fast H atoms in the Jovian thermosphere Input Parameters The concentrations of 02, N2, and O were calculated using the MSIS-90 model atmosphere [Hedin, 1991] with parameters relevanto December 16, 1993, 'the same period as used by Decker ctal., [1996] in their proton aurora model intercomparison. The MSIS parameters were F10.7 and F10.7 values of 150, daily Ap of 20, geographic latitude of 65øN, longitude of 35øE, and local solar time of 0000 (midnight). A key point of the numerical simulation of the proton aurora is the set of cross sections describing processes (1)-(6). The total cross sections used in this model fbr the various inelastic processes (charge exchange, ionization, stripping, and excitation) involving 02 and O were adopted from a data set by Basu et al. [1987, 1993]. The cross sections for proton and H on N2 were taken from approximations by Kozelov and Iranov, 1992]. Elastic cross sections were adopted fi'om approximations by Porter et al. [1976]. The momentum transfbr collisions are strongly affected by the scattering angle as specified by the differential cross sections. It is usual practice in models to use some average value of the scattering angle [e.g., Kozelov and Iranov 1992]. However, this simplification does not reflect the stochastic nature of the collision, which is essential for the fbrmation of the line profile, as will be illustrated in this study. To take this effect into account, we use the available experimental data on the scattering angle distributions in the high-energy collisions between p/h and the main atmospheric constituents. The following atmosphere may travel very large distances aceross the magnetfc field lines. However, the magnetic field lines are not parallel, so that the pitch angle of the H atom is modified from the original field line to the one where measurements were adopted: H++O from Lindsay et al. [1996]; H++O2 from Gao et al. [1990]; H++N2 from Gao et al. [1990]; H+O2 from Newman et al. [1986], Johnson et al. [1988], and Smith et al., [1991]; the atom is again converted to a proton. We include and H+N2 from Newman et al. [1986], Johnson et al. this effect in the model in the same manner as Kozelov [1993]; that is, we recalculate the pitch angle after the [1988], and Smith et al. [1991]. The energy-dependent scattering angle distribution collisionless movement of each hydrogen atom. for H-O momentum transfer collisions was taken the In order to minimize boundary effects, the lower boundary was set at an altitude of 80 km and the upper same as for H-O2 collisions. To account for the differences between momentum transfer and charge trans-

5 GERARD ET AL.' LYMAN-a IN PROTON AURORA 15,799 fer scattering [Smith et al., 1991], the charge transfer 5OO differential cross sections for p-o2 and p-n2 collisions were based on scaled p-o charge transfer cross sections 400 measured by Lindsay et al. [1996]. Unfortunately, all experiments were performed [br only three values of the proton energy 0.5, 1.5, and 5 kev. We interpolated the 300 data for energies between and kev. For energies greater than 5 kev no experimental data exist, and the data were extrapolated. 200 The calculation of synthetic Ly- line profiles requires us to include the cross sections in all processes where excitation into the H(2p) level takes place, that is, pro- 100 cesses (lc), (2c), and (3c) and (4a), (4b), (5a), (5b), (6a), and (6b). We have adopted the Ly-a excitation cross sections due to H+N2 and H++N2 collisions from Energy deposition rate (ev cm '3 S 4) Kozelov and Iranov [1992]. Cross sections for all other Figure 2. Rate of energy deposition versus altitude for processes were taken from Van Zyl and Neumann [1988]. the same proton precipitation as in Figure 1. To verify the validity of this kinetic model, our results were compared with the study by Decker et al. [1996]. In their work, Decker et al. [1996] compared teristic energy E0-8 kev. The precipitated energy flux three widely used methods to calculate the transport is 0.5 erg cm -2 s -x, and the pitch angle distribution of energetic protons and hydrogen atoms in the atmo- isotropic in the sense defined by Decker et al. [1996] sphere. To facilitate this comparison, we use the same (uniform in cos 0). As expected, the initially pure progeophysical inputs and model parameters. As men- ton beam is progressively converted into a H+/H mixtioned before, our model normally considers the effect ture as a result of the charge transfer collisions with the of magnetic mirroring as well as lateral spreading of the atmospheric gas. Below 350 kin, hydrogen atoms domineutral energetic particles. For this comparison, mag- nate the composition. The total downward flux rapidly netic mirroring and geometrical spreading were turned drops to a very small value below 130 kin, the altitude off, and similarly to other models, we assume strictly of the maximum energy deposition. forward scattering. We also simplified the set of cross sections to reduce it to the one described by Decker et 3. Synthetic Lyman-c Line Profiles al. [1996]. The neutral atmosphere was defined for the The essence of the direct simulation Monte Carlo same MSIS parameters as Decker et al. [1996]. Comparison of values of downward proton and hydrogen method is accounting of all possible collisions in the physical region studied. Therefore statistics for all colatom fluxes (Figure 1) and energy deposition (Figure 2) with those presented by Decker et al. [1996] shows a lisional processes are accumulated during the numerical very good agreement. The initial proton beam is char- realization of the kinetic model of the proton aurora. It acterized by a Maxwellian distribution with a charac- provides a good basis for the evaluation of the Ly-a source functions, as bookkeeping of all excitation processes and their spatial characteristics makes it possible to determine the statistical distribution of the emitted 5OO 400 H+,g lo0... i! i i,,,,,i... ' Flux (cm-2 s - sr - ) Ly- photons. The emerging synthetic Ly-a line profile is calculated by numerical integration of the obtained source functions along the line of sight. We first examine the effect of the extrapolation of the energy dependence of the charge transfer collisions above 5 kev. Figure 3 shows the Ly-a profile calculated for three asymptotic dependences: 1/E a for c = 0.5, 1, and 2. This line profile and those discussed in the following figures refer to a downward viewingeometry along the field line, that is, toward the nadir. In all three cases the peak of the line profile is red-shifted by about From the available measurements between 0.5 and 5 kev we deduce that the half width of the scattering angle distribution decreases approximately as l/energy. Therefore all further examples assume distributions Figure 1. Altitude variation of the total downward proton and hydrogen atom fluxes for an initial isotropic a 1/E dependence of the scattering angle proton beam with a Maxwellian energy distribution (Eo of momentum and charge transfer cros sections at en- = 8 kev). The total energy flux is 0.5 erg cm -2 s -1. ergies higher than 5 kev. An extensive red wing is due

6 15,800 GERARD ET AL.' LYMAN-a IN PROTON AURORA i... i [...i... i... i... i... k... I... I Wavelength component. This component accounts for 012% of the total line intensity for this/ 0 = 8 kev Maxwellian distribution. The influence of the initial pitch angle distribution of the precipitated protons is examined in Figure 4. Proton beam intensities independent of the pitch angle in 5 ø, 45 ø, and 90 ø wide half-cones are compared with the isotropic (cos 0) case shown in Figure 3. In a nearly field aligned (+5 ø ) precipitation, no blue wing is observed, and the upward flux of both H and H + is virtually absent. This is a consequence of the quasi-absence of magnetic mirroring and collisional scattering. Virtually no particle can increase its pitch angle from - 0 ø to over - 90 ø before its complete thermalization. The line peak Figure 3. Lyman-c nadir line profile calculated for the is shifted by 01.2 from the rest wavelength. As the same initial proton beam as Figure 1 for the three differ- pitch angle cone opens, the peak wavelength decreases ent high-energy extrapolations of the angular scattering and the blue-shifted wing builds up. The fraction of the crossections: lie (solid curve), 1/v/- (dotted curve), blue-shifted component is thus a sensitive indicator of 1/E 2 (dashed curve). The solid verticaline indicates the pitch angle distribution of the primary protons for the rest wavelength. a given observing geometry. A key component of this model is the stochastic treatment of the scattering angle in momentum and charge to H(2p) atoms with a downward velocity coxnponent. transfer collisions. As mentioned before, strictly for- The backscattered atoms (blue shift) are produced ward scattering [Basu et al., 1993; Galand and Richby (1) collisions of protons which have reached their mond, 1999] or average scattering angle approximamirror point and travel up the magnetic field line, (2) tions [Kozelov and Ivanov, 1992] were used in modparticles which have suffered successive scattering col- els describing the proton energy deposition and optilisions and whose pitch angle has finally exceeded 90 ø, cal emission rates. Tests performed with our code unand (3) a small component of particles which traveled der these approximations confirm that quantities such across magnetic field lines and progressively increased as the vertical profiles of the energy deposition rate, their pitch angle above 90 ø. The presence of the compo- the H+/H fluxes, or the total Ly-c volume emission nent in the Bulmer line profile due to backscattered H rate are largely insensitive to the treatment of scatteratoms was discussed by Eather [1966] in terms of mag- ing following charge transfer collisions. In contrast, the netic mirroring and field line convergence only. The Ly-c line profile is to a large extent controlled by the Ly-c line profiles observed from satellite by Ishimoto angular properties of the scattering process. Figure 5 et al. [1989] also exhibit a blue-shifted (backscattered) clearly illustrates this sensitivity by comparing the line profile calculated with this stochastic treatment based on the experimental cross sections with the deterrain '):45 ø / ; ø....,.,]... i...!...,,,i,,, Wavelength (]k) Figure 4. Ly-c nadir line profile for an initial Maxwellian proton energy distribution (E0 = 8 kev) for three different pitch angle distributions: independent of the pitch angle 0 for 0 = +5 ø (dash-dotted curve), 0 = ø (dotted curve) and 0 = ø (dashed curve), and independent of cos 0 (solid curve) Stochastic ß... i i i...! / / " : /.. _: / Deterministic.00,.,i... i... i... i Wavelength (]k) Figure 5. Ly-c nadir line profile for the same case as Figure I with a deterministic distribution of scattering angles [Kozelov and Ivanov, 1992] and the stochastic approach used in this model.

7 ,..,. GERARD ET AL.' LYMAN-o IN PROTON AURORA 15, lkev i Monoenergefic kev '! -, ,. L._ Wavelength (/ ) 1230 Figure 6. Ly-c nadir line profile ibr three monoener- Figure 7. Same as Figure 6 for three Maxwellian engetic isotropic initial proton beams. The total energy ergy distributions. flux is 0.5 erg cm -2-1 s residual energy. In contrast, the mean wavelength of the line profile shifts toward longer wavelengths with istic approach used by Kozelov and Ivanov [1992] for increasing average initial energy of the protons. a Maxwellian 8-keV proton beam. In the latter case, The case of a MaxwellJan proton energy distribution, an average scattering angle dependent on energy is assumed, and this angle is used in our code following -- Qo E e -E/Eo, (9) ß (s) 2So s0 each collision. The extent of the blue wing is considerably more important in the more realistic stochastic where E0 is the characteristic energy and Q0 = 0.5 erg approach which allows, in agreement with experimencm -2 s - is the total input flux energy, shows a similar tally measured scattering angle distributions, a small behavior (Figure 7). The long-wavelength edges of the fraction of angular scattering to exceed the average an- line profiles are less steep than in the previous case, especially at 1 kev, reflecting the more progressive drop gle. This is important, as previous models of the line profile of the Balmer line were not able to account for the amount of red-shifted component associated with the flux of backscattering protons. Next, we examine the sensitivity of the line profile to the energy of the incident protons (Figure 6). As may be expected, monoenergetic protons produce line profiles with fairly sharp long-wavelength cutoffs associated with the maximum red shift produced by particles with energies close to their initial values: for 1-keV, for 8-keV protons and for 40-keV protons. The peak wavelengths reflect the most probable value of the H* atom velocity projected on the line of sight. A progressive shift toward rest wavelength is observed with increasing energy. This behavior may be accounted for by the increased level of isotropy in H+/H beam when the particles penetrate deeper in the denser atmosphere. As the total number of collisions increases, successive charge exchange processes tend to enhance the backscattered component, as indicated by the fraction of blue-shifted Ly-c photons, and simultaneously shift the ]. ae peak toward shorter wavelengths. A test was performed using the strictly forward scattering approximation. Results indicate that under this assumption, the peak wavelength is shifted by 1.2., independent of the initial proton energy, in agreement with the simulations by Galand et al. [1998]. This invariance of the peak shift is due to the fact that the emission near the peak is excited by protons with a low.0... i... i... i... i... i... i... Maxwellian 1 kev, \ 1.5 / \. / \ ' ' / E m 0.5 / \ 8 kev \ ,.. '. 40 ;, ke.'.'. :, ;.'.:.'. :,'. ::.'...-.a..:.;: Wavelength (/ ) of the high-energy H atom population. Although MaxwellJan distributions have been widely used in models due to their simplicity, growing evidence suggests that kappa distributions providing an additional high-energy nonthermal component are in better agreement with in-situ measurements. Christon et al. [1991] found that in the central plasma sheet an additional power law tail exists which can be fitted by a kappa distribition. Lyons and Evans [1984] showed i... i... i... i... Maxwellian :...i... i....i... i Wavelength (]k) Figure 8. Ly-c nadir line profiles for initial Maxwellian (E0 = 8 kev) and kappa (E0-8 kev, n - 4) proton energy distributions.

8 15,802 GERARD ET AL.' LYMAN-a IN PROTON AURORA Table 1. Characteristics of the Ly-c Line Profiles for a 1 erg cm -2 s -1 Proton Precipitation Energy, kev Energy Emission Rate, Altitude of Peak Blue Wing Distribution kr Emission, km Red Shift Fraction I monoenergetic a monoenergetic monoenergetic Maxwellian b Maxwellian M axwellian kappa c Maxwellian d Maxwellian e midnight cusp a Monoenergetic protons with an isotropic (cos 8) pitch angle distribution b Isotropic Maxwellian energy distribution. c Isotropic kappa distribution characterized by E0 = 8 kev, n = 4. d Same as Maxwellian distribution at 8 kev except forward scattering approximation. e Same as Maxwellian distribution at 8 kev except pitch angles restricted to 4-5 ø ' that the proton distribution at ionospheric altitudes also have high-energy components. Shatbet et al. [1993] also observed with the UARS satellite ion spectra with high-energy tails similar to those measured by Christon et al. [1991]. Therefore we calculated the energy transport and Ly-c line profile for a kappa distribution, 00 (n-1)(n-2) E 1+ in Nx and by Strickland et al. [1993] for Ly-a with a model proton aurora. The photon yield for E0-8 kev varies only slightly between the forward scattering approximation and the stochastic scattering case. The altitude of the emission peak decreases as the mean initial proton energy increases from 1 to 40 kev. It drops by 38 km in the monoenergetic case and 35 km in the Maxwellian case. Table 1 also shows that in the forward ß (z)- Too scattering approximation, the altitude of the emission (lo) peak is about 7 km lower than when the stochastic scatfor E0 = 8 key and n = 4. The kappa distribution is tering is taken into account. As discussed before, the characterized by an averagenergy 2 he0/(n-2), which wavelength shi t of the line peak is relatively insensiis a larger value than the Maxwellian distribution for the same E0 energy. The Ly-c line profile with a kappa distribution is compared with the MaxwellJan case (Figure tive to the proton energy but is more dependent on the angular distribution at the top of the atmosphere. The fraction of emission in the blue-shifted wing reflects 8). The kappa distribution produces a more extended the magnitude of the backscattered fast H(2p) atoms. red wing corresponding to the additional high-energy As discussed be bre, an important component is due to component. The peak is less pronounced than in the MaxwellJan case, but the edge of the blue-shifted wing is quite similar. As expected, the Ly-c production effistochastic collisional scattering. For 8-keV protons, this fraction varies from 1% in the strictly forward scattering approximation to 12% in our standard (stochastic ciency (Table 1) is less than ibr the MaxwellJan distri- scattering) case. bution with the same E0, but the fraction in the blue wing is quite close. Table 1 summarizes some characteristics of the Ly- In addition to the analytical energy distributions described befbre, the Ly-a line profile was calculated for two cases based on the statistical proton energy disc brightness and line profiles for the various cases tribution given by Hardy et al. [1989] at two different discussed before. The total integrated emission rate corrected geomagnetic local times. The incident prodrops by nearly a factor of 4.6 (monoenergetic) or 8 ton distributions given by Hardy et al. for Kp- 3 in the MLT and MLT sectors were (Maxwellian) as the proton characteristic energy increases from 1 to 40 kev. This is a consequence of the latitudinally averaged and used as initial energy distrihigher fraction of hydrogen atoms in the beam at higher bution at the top of the model (Figure 9). The resulting energies and the relative values of the Ly-c excitation Ly-a line profiles fbr vertical viewing given in Figure 10 crossections by processes (lc), (2c), and (3c) compared show distinct features. The midnight proton aurora is with (4a)-(4b),(5a)-(5b), and (6a)-(6b). A drop of the characterized by a relatively hard ( kev) preefficiency of the Ly- production was also calculated by cipitation for an energy flux of 0.7 erg cm - s -1 The Van Zyl et al. [1984] for the Balmer lines for protons corresponding Ly-a profile exhibits a wide red-shifted

9 GERARD ET AL.' LYMAN-a IN PROTON AURORA 15, !... i... i... i...!... i... time cusp 0.25 nightside aurora looo loo nightside aurora ' lo /! \\\ _ 1 lo 1... i,,,,... i,,i Energy (ev) 1213 dayside cusp "-._...,...,......,'U,." Wavelength ( ) Figure 9. Average proton energy distributions for Figure 11. Ly-c profile for a Maxwellian (E0=l kev) nightside (0000 < MLT < 0030) and daytime cusp au- isotropic initial proton energy distribution for three rorae (11:30 < MLT < 1200), Kp- 3. viewing directions: nadir (0ø), 45 ø from vertical, and horizontal (90 ø). wing extending over 10 from rest wavelength. The polar cusp aurora with its softer proton distribution (E This behavior is illustrated in Figure 11, which shows = 2.2 kev) and lower-energy flux (0.15 erg cm -2 s - ) the Ly-c profile calculated for three different viewing presents a different Ly-c signature. In this case, the angles. The profile for the horizontal viewing assumes total brightness is substantially less than in the night- that the minimum altitude of the line of sight coincides time aurora. The line width (Full width at half max- with the emission peak. The large increase of the total imum (FWHM)) is about 1.5 compared with 3.9 emission rate from 45 ø to 90 ø is due to the long slant for the midnight Ly-c profile. The cusp precipitation path integration when the line of sight is tangent to the produces emission peaking 22 km higher than the night- emission layer, which is assumed horizontally homogeneous. side aurora (Table 1). The emission per unit incident flux drops from 5.8 (cusp) to 2.4 kr erg - cm -2 s - as a consequence of the hardening of the proton pre- 4. Summary and Conclusions cipitation from the dayside cusp to the midnight sector aurora. Simulations of the Ly-c auroral line profile have been The actual line profile observed from a spaceborne made under various assumptions of energy and angular instrument will be strongly dependent on the viewing distribution of the incident protons using a direct simugeometry. As the observation axis moves away from the lation Monte Carlo method. This method provides the magnetic field lines, the line profile becomes more sym- altitude-dependent velocity distribution function of the metrical and the peak moves to the rest wavelength. H+-H beam interacting with the atmosphere. In addition to magnetic mirroring and geometric spreading due to the convergent geomagnetic field line, collisional scattering is considered in a stochastic approach based... i... i... i... i... i... i... on experimental doubly differential collisional cross sec- 2.5 / --?0 ø (x 0.1) tions. The model has been validated by comparison with earlier results based on three different modeling approaches. We show that vertical energy deposition iii \,. ",45 ø and the fluxes of protons and hydrogen atoms we calculate agree with previous models. However, the hy- // drogen line profiles are much more sensitive indicators II,,,,"' o \' I \,,,',...::i... -" Wavelength ( ) Figure 10. Ly-c nadir line profile calculated for the nighttime and daytime cusp proton energy spectra shown in Figure 9. of the angular distribution of H+-H beams than other integrated quantities. As was mentioned above, the momentum and charge transfer collisions are strongly affected by the scattering angle, i.e., by differential cross sections. These cross sections are not well known, as laboratory data exist only for three values of energy: 0.5, 1.5, and 5 kev. This parameter is not crucial for the calculation of the macroscopic characteristics, but it is extremely important, for Ly-c line profile analysis. We show that the fraction of backscattered H atoms

10 15,804 GERARD ET AL.' LYMAN-oz IN PROTON AURORA causing the blue-shifted line wing (for a satellite obser- References vation) is also significantly enhanced by the stochastic Basu, B., J.R. Jasperse, R.M. Robinson, R.R. Vondrak, and treatment of collisional scattering. D.S. Evans, Linear transport theory of auroral proton pre- Our results show that the Ly-a profile reflects both cipitation: A comparison with observations, J. Geophys. the energy and the pitch angle distribution of the pro- Res., 92, 5920, tons interacting with the atmosphere. In the absence Basu, B., J.R. Jasperse, D.J. Strickland, and R.E. of collisional scattering, the peak wavelength remains Daniell, Transport theoretic model for the electronproton-hydrogen atom aurora, 1, Theory, J. Geophys. shifted by 1.2 to the red for a downward observer Res., 98, 21,517, for incident between 1 and 40 kev. Stochastically simu- Bisikalo, D.V., V.I. Shematovich, and J.C. 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The instrumental spectral resolution of the observations (8 ) in the presence of the large geocoro- nal Ly-c background does not permit an unambiguous determination of the characteristics of the precipitated protons. Our simulations also show that the efficiency of the Ly-c photon production per unit incident energy flux depends on the energy distribution of the primary pro- tons. This efficiency drops from 5.4 to 0.7 kr erg -1 cm -2 s -1 as the Maxwellian characteristic energy E0 increases from 1 to 40 kev. The kappa distributions for the same E0 yield a slightly lower efficiency, as the average proton energy is higher than in the Maxwellian case. The statistically average proton fluxes fbr noon and midnight precipitation produce different Ly-c profiles. The calculated cusp profile is narrower and globally less bright than the midnight auroral case. The overall Ly-c photon production is more than twice as large in the noon cusp as in the nighttime aurora. 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