Modeling spectra of the north and south Jovian X-ray auroras

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2008ja013062, 2008 Modeling spectra of the north and south Jovian X-ray auroras V. Kharchenko, 1,2 Anil Bhardwaj, 3 A. Dalgarno, 1 D. R. Schultz, 4 and P. C. Stancil 5 Received 25 January 2008; revised 28 March 2008; accepted 5 May 2008; published 27 August [1] Spectra of Jovian X-ray auroras observed from the North and South poles with the Chandra X-ray telescope are analyzed and compared with predicted spectra of the charge-exchange mechanism. To determine the theoretical spectra of Jovian X-ray auroras, we model numerically the collisionally induced evolution of energy and charge distributions of O q+ and S q+ ions, precipitating into the Jovian atmosphere. Monte Carlo simulations of the energy and charge relaxation of the precipitating ions are carried out with updated cross-sections of the ion stripping, electron capture, and gas-ionization collisions. X-ray and Extreme Ultraviolet (EUV) spectra of cascading radiation induced by individual energetic sulfur and oxygen ions are calculated, and relative intensities of X-ray emission lines are determined. Synthetic spectra of X-ray and EUV photons are computed at different initial kinetic energies and compositions of ion-precipitating fluxes. Theoretical spectra with adjustable initial energies and relative fraction of sulfur and oxygen ions are shown to be in good agreement with the spectra of X rays detected from the South and North polar regions. The abundances and initial energies of the precipitating ions are inferred by comparing synthetic and observed X-ray spectra. Comparisons are performed independently for the North and South pole emissions. Abundances of the precipitating sulfur ions are found to be four to five times smaller than those of oxygen ions, and averaged ion energies are determined to lie between 1 and 2 MeV/amu. Slightly different ion flux compositions are found to describe the observed spectra of X-ray emission from the North and South poles. Citation: Kharchenko, V., A. Bhardwaj, A. Dalgarno, D. R. Schultz, and P. C. Stancil (2008), Modeling spectra of the north and south Jovian X-ray auroras, J. Geophys. Res., 113,, doi: /2008ja Introduction [2] Investigation of the X-ray emission from the Jovian atmosphere has been a long-term priority of planetary X-ray astronomy since the first detection of Jovian X rays in 1979 [Metzger et al., 1983]. Several theoretical models have been suggested to explain the nature of the Jovian X-ray emission, but the low resolution of the first X-ray telescopes, onboard the Einstein X-ray Observatory satellite and ROSAT, was not sufficient to distinguish between the spectra predicted by different models. Significant improvement of spectral and spatial resolution has been achieved in recent observations with the XMM-Newton and Chandra X-ray telescopes [Gladstone et al., 2002; Branduardi-Raymont et al., 2004, 2007a, 2007b; Bhardwaj 1 Harvard-Smithsonian Center for Astrophysics, ITAMP, Cambridge, Massachusetts, USA. 2 Physics Department, University of Connecticut, Storrs, Connecticut, USA. 3 Space Physics Laboratory, Vikram Sarabhai Space Center, Trivandrum, India. 4 Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA. 5 Department of Physics and Astronomy and the Center for Simulational Physics, University of Georgia, Athens, Georgia, USA. Copyright 2008 by the American Geophysical Union /08/2008JA et al., 2005, 2006, 2007; Elsner et al., 2005a; Bhardwaj and Lisse, 2007]. Detailed analysis of observational data has demonstrated a complex morphology and spectral composition of the X-ray emission. Two independent X-ray sources have been proposed to describe Jovian emission: the disk emission, induced by atmospheric scattering and fluorescence of solar X rays, and the auroral X-ray emission, originating from the North and South poles. Strong correlations between the intensity and spectral composition of the solar X rays and the Jovian disk emission were observed and scattering was shown to be the major mechanism of X-ray emission from the Jovian equatorial regions [Maurellis et al., 2000; Branduardi-Raymont et al., 2004, 2007a, 2007b; Bhardwaj et al., 2005, 2006, 2007; Bhardwaj and Lisse, 2007]. Two different mechanisms for the bright polar X-ray emission have been debated for the past two decades. The first mechanism, auroral electron bremsstrahlung, had been proposed in analogy with the EUV auroral events in the Earth s atmosphere [Bhardwaj et al., 2007]. The second mechanism is the charge-exchange emission induced by energetic magnetospheric heavy ions, precipitating into the Jovian atmosphere [Metzger et al., 1983; Horanyi et al., 1988; Waite et al., 1994; Cravens et al., 1995]. The Chandra X-ray telescope has much better spatial resolution than the ROSAT and XMM-Newton telescopes, and observations of the Jovian polar X-rays with Chandra yielded surprising 1of11

2 results on the spatial distribution of the X ray brightness [Gladstone et al., 2002]. It was shown that polar X rays originate from regions located deep inside the auroral oval [Gladstone et al., 2002; Cravens et al., 2003]. The very high intensities of the polar X-ray sources and their morphology contradict predictions of the electron bremsstrahlung model [Cravens et al., 2003]. [3] The resolving power of the latest observations of the Jovian X-ray spectra with Chandra and XMM-Newton telescopes was sufficient to distinguish the radiation of highly-charged excited ions from bremsstrahlung and yield data on the composition of the precipitating ion flux [Elsner et al., 2005a; Branduardi-Raymont et al., 2004, 2007a, 2007b; Kharchenko et al., 2006]. Although recent observations support strongly the charge-exchange mechanism for Jovian X-ray auroras, the detailed characteristics of polar X-ray spectra have not been determined. Future observations and theoretical analysis should clarify such issues as the relative intensities of the sulfur and oxygen ion emission lines, the possible presence of a carbon component, and the contribution of X-ray electron bremsstrahlung. The first steps in this direction have been taken [Kharchenko et al., 2006; Branduardi-Raymont et al., 2007a, 2007b]. The abundances and energy distribution of sulfur and oxygen ions have been inferred from comparisons between the theoretical synthetic spectra of the Jovian X rays and the empirical line emission spectra, obtained by fitting the Chandra and XMM-Newton observations [Kharchenko et al., 2006]. This analysis yielded the average characteristics of the precipitating ions for the North pole, but ignored details of the individual spectra of the polar X-ray emission. Individual features of X-ray auroral spectra are valuable, because they help to determine any asymmetries of the acceleration mechanism for ions precipitating into the South and North poles. Comparative studies of auroral emissions from the South and North poles are able to provide new information on the energy distribution and composition of precipitating ion fluxes. A comprehensive analysis of the Jovian X-ray auroras observed with the XMM-Newton telescope was carried out for a broad photon energy interval [Branduardi-Raymont et al., 2007a, 2007b]. Radiation below 1 kev was explained as due to emission of precipitating heavy ions and radiation above 1 kev was attributed to the bremsstrahlung emission of energetic auroral electrons. The best fits of the observed auroral X-ray spectra were obtained by the independent adjustment of intensities of five X-ray emission lines and two thermal bremsstrahlung spectra with temperatures of 0.27 and 0.34 kev [Branduardi-Raymont et al., 2007a, 2007b]. The derived intensity of the electron bremsstrahlung is significantly lower than the intensities assigned to ion emission lines, but the two sources of emission can be studied simultaneously: bremsstrahlung and charge exchange radiation dominate at different photon energies. Although the fitting procedure employed by Branduardi-Raymont et al. [2007a, 2007b] provides a reasonably good description of the observed spectra, it has to be modified to incorporate the chargeexchange model. Independent adjustments of X-ray line intensities, which were also carried out in several investigations of cometary and planetary X rays [Krasnopolsky et al., 2004, Lisse et al., 2004; Bhardwaj et al., 2007], neglect the strong correlations between the intensities of different X-ray emission lines induced by individual ions. These correlations are a fundamental feature of the chargeexchange mechanism and they reflect the cascading nature of the charge-exchange emission [Kharchenko and Dalgarno, 2000]. Correlations preclude arbitrary changes in the relative intensities of emission lines induced by individual ions and make the fitting procedure more challenging. [4] In this article we report results of our modeling of Jovian polar X-ray emission observed with the Chandra X-ray telescope. The goal of our analysis is to find the simplest composition and initial energy distribution of precipitating ions that reproduce the spectral features of X-ray emission observed from the North and South poles. Our investigation is focused on spectra of X-ray photons with energies below 1 kev, because these photons are responsible for most of the emitted power of the Jovian polar X rays. [5] The charge-exchange mechanism of X-ray emission in Jovian X-ray auroras works differently than the cometary X-ray mechanism. The parameters of the precipitating ion flux are strongly modified as the ions penetrate deeply into the Jovian atmosphere. During the initial stage of precipitation, collisions with atmospheric atoms and molecules reduce the ion translational energies and dramatically increase the fraction of highly charged ions. The abundances of different charge states for the entire stopping process depend on the ion kinetic energies at the top of the Jovian atmosphere. We compute the dynamical energy and charge distributions of the precipitating ions as they travel from the top of Jovian atmosphere to the end of their trajectories. These distributions are used to calculate X-ray spectra induced by the Jovian chargeexchange mechanism. The spectra of X-ray photons are sensitive to the ion flux composition and initial energy of precipitating ions. Comparison between theoretical and observational spectra of the Jovian polar X-ray emissions enables us to infer the energy and elemental compositions of the ion fluxes precipitating into the South and North polar regions. 2. Updated Charge-Exchange Mechanism of Jovian X-rays [6] The charge-exchange mechanism was initially formulated to explain ROSAT observations of the Jovian X rays [Metzger et al., 1983; Horanyi et al., 1988; Cravens et al., 1995; Waite et al., 1994]. According to the original model, Jovian magnetospheric instabilities are capable of accelerating the low-charge magnetospheric ions, such as O q+ or S q+ (q = 1, 2 and 3), to energies of hundreds of kev - several MeV per nucleon. These energetic ions enter into the planetary atmosphere in the polar regions and are completely stopped in collisions with the atmospheric H, H 2, and He. The stopping process requires a large number of ion-atom collisions because the ions have high energies. In the collisions ions may be stripped to higher charges, such as O 6,7,8+ and S 11,12,13+, which may capture electrons into highly excited states in subsequent collisions. Newly produced excited ions relax to the ground states emitting a cascade of photons. The energy of cascading photons induced in a single charge-exchange collision ranges from the X ray to the UV. Stripping and electron-capture collisions happen repeatedly and each precipitating heavy 2of11

3 ion is capable of radiating several X-ray photons before it is brought to rest. The total number of induced EUV and X-ray photons and their spectra depend strongly on the ion kinetic energy at the top of the atmosphere. At the same time, spectra of induced emission are not sensitive to the initial charge states of the precipitating ions. Ions in the precipitating flux keep no memory of their initial charges, because the abundance of different charge states is regulated by the energy-charge relaxation. [7] In earlier charge-transfer modeling of the Jovian X-ray auroras the source of the heavy sulfur and oxygen ions was associated with Io and the Io torus [Horanyi et al., 1988; Waite et al., 1994; Cravens et al., 1995; Kharchenko et al., 1998; Liu and Schultz, 1999; Bhardwaj and Gladstone, 2000], but recent Chandra and XMM-Newton observations narrowed the area of soft X-ray emissions to the vicinity of the North and South poles at latitudes higher than Io s EUV auroral footprints [Gladstone et al., 2002; Bhardwaj et al., 2007; Branduardi-Raymont et al., 2008]. To satisfy this new morphology of the X-ray emissions, the sources of energetic magnetospheric ions must be located at distances larger than 32 Jovian radii R j from the planet [Cravens et al., 2003]. This is significantly larger than the radius of Io s orbit (5.9 R j ). The other Galilean satellites, Callisto, Ganymede and Europa, orbiting at radial distances of 26 R j, 15 R j, and 9.5 R j, contribute heavy ions into the Jovian magnetosphere, as was found in the analysis of the data on energetic neutral atoms from the Cassini mission [Mauk et al., 2003]. Outward radial diffusion of these ions, mostly oxygen, could provide the heavy particles required for the Jovian X-ray auroras. Another potential source of heavy ions, the solar wind, has been discussed by Cravens et al. [2003]. If the solar wind ions are accelerated in Jovian cusp regions and penetrate into the atmosphere, the ions could produce X-ray emission in charge-exchange collisions with the atmospheric gas. [8] The morphology of the Jovian polar X rays, as discovered in the Chandra observations, requires a high density of the precipitating polar ion flux, which could be achieved by increasing the energies of the precipitating particles [Cravens et al., 2003]. Ion kinetic energies at the top of the Jovian atmosphere would be several times higher than those proposed for the Io-source model [Horanyi et al., 1988; Waite et al., 1994; Cravens et al., 1995; Kharchenko et al., 1998; Liu and Schultz, 1999]. The charge-transfer mechanism of the Jovian auroras has been significantly modified and updated in recent theoretical investigations because of new observational data from the Chandra and XMM-Newton X-ray telescope [Cravens et al., 2003; Kharchenko et al., 2006]. Nevertheless, the key feature of the original model, the X-ray production in sequential stripping and charge-exchange collisions, has not been changed since its original formulation [Metzger et al., 1983]. [9] X-ray spectra of the charge-exchange mechanism have been intensively investigated for modeling of X-ray emissions observed from comets, planetary coronae, and interstellar gas interacting with the solar wind plasma. A comprehensive description of the research is presented in recent review articles [Cravens, 2002; Krasnopolsky et al., 2004; Lisse et al., 2004; Bhardwaj et al., 2007; Bhardwaj and Lisse, 2007]. Cometary X-ray spectra differ from the spectra of Jovian X-ray auroras, although both emissions arise from the charge-exchange mechanism. The fraction of energetic photons in the cometary X-ray emission is much smaller than in the Jovian auroral spectra. This may be explained by two effects: the difference between the abundances of ion-charge states in the solar wind and in the precipitating Jovian fluxes, and variations of the emission spectra of individual ions with collisional velocities. The last factor reflects the velocity dependence of the crosssections for population of specific ion excited states in charge-exchange collisions. In a cometary environment, the heavy solar wind ions are highly charged but have low kinetic energies of the order of a few kev/amu (kev per nucleon). At these energies the probability of stripping of highly-charged ions is small, and heavy ions produce only a few X-ray photons emitted in the subsequent neutralizing collisions. The initial highly-charged states of heavy solar wind ions will not be recovered. This type of chargeexchange production of X-ray photons could be characterized as a passive mechanism. On the other hand, heavy ions in the Jovian polar fluxes may have energies of a few MeV/amu [Cravens et al., 2003]. The charge of the precipitating ions increases and decreases many times in sequential collisions with the atmospheric gas. Energetic Jovian ions emit several X-rays photons per ion, depending on the efficiency of stripping collisions. The Jovian polar X-ray production may be described as an active charge-exchange mechanism, because the abundance of highly charged ions significantly increases in interactions with the neutral gas. Fractions of highly-charged ions and the X-ray emission spectra depend strongly on the ion energies at the top of Jovian atmosphere, whereas in the case of cometary X rays they are determined by the composition of the solar wind. [10] Previous investigations have demonstrated the fundamental role of the ion charge relaxation in the formation of X-ray emission spectra [Cravens et al., 1995, 2003; Kharchenko et al., 1998, 2006; Liu and Schultz, 1999]. Accurate information on the charge distributions is critical for modeling specific features of the X-ray spectra induced from the North and South poles [Cravens et al., 2003; Kharchenko et al., 1998, 2006]. Calculation of the charge and energy relaxation of fast precipitating ions is a challenging problem. It requires knowledge of cross-sections of many collisional channels and the spectra of transferred energy, and involves a computation of the cascading photon spectra induced by individual excited ions. We discuss briefly our calculations of the charge and energy distributions of energetic oxygen and sulfur ions, precipitating in the Jovian atmosphere Modeling the Charge and Energy Distributions of Precipitating Ions [11] A detailed description of the computational method has been presented by Kharchenko et al. [1998, 2006]. Here we focus our discussion on issues important for the spectral analysis of the North and South pole emissions. As the first step, we evaluate the dependence of the ion energy-charge distribution on the initial energy of precipitating ions. Then, these distributions will be used to compute induced photon spectra. To describe the evolution of the energy-charge distribution of precipitating sulfur and oxygen ions we have 3of11

4 Figure 1. Channel probabilities in S 14+ +H 2 collisions as functions of the kinetic energy per unit of nuclear mass. Energies are given in kiloelectron volt per atomic mass unit. Curve 1 is the charge-exchange probability p ; curve 2 is the electron stripping probability p +, and curve 3 is the probability p 0 of collisions, preserving the ion charge. The last channel includes several subchannels, such as target ionization, elastic, dissociation, and excitation collisions. employed a Monte Carlo scheme. The energy and charge distribution function f i (E, q, N) of the ensemble of precipitating ions is normalized to a single precipitating atomic particle: Z Eio de Xq¼Z 0 q¼0 f i ðe; q; NÞ ¼1 where the index i = O, S indicates oxygen or sulfur ions, Z = 8, 16 are O and S nuclear charges, E i0 are the initial energies of the ions at the top of the Jovian atmosphere, and N is the number of ion-atom and ion-molecule collisions since beginning the precipitation. The energy and charge distributions in the ensemble of precipitating particles are transformed by collisions with the atmospheric gas. We compute the complete spectra of the X rays induced in the Jovian polar regions. We ignore the absorption of the X rays in the Jovian atmosphere. Previous analyses of the propagation of O ions [Horanyi et al., 1988; Cravens et al., 1995] into the atmosphere indicate that the effect on the X-ray spectra is negligible so that models of the total emission spectra resulting from the entire deposition process do not require data on the atmospheric gas densities. [12] The probabilistic nature of collisions and the presence of several collisional channels make the Monte Carlo simulations the most efficient method to evaluate energycharge distributions of precipitating ions. The channel ð1þ probabilities of charge-changing collisions p + (E, q, i, k) and p (E, q, i, k) describe collisions between the ith ion and kth atmospheric neutrals with increase q! q + 1 and decrease q! q 1 of the ion charge q. Collisions that ionize atmospheric atoms or molecules without changing the ion-charge states are described by a probability p 0 (E, q, i, k) [Kharchenko et al., 1998, 2006]. Channel probabilities p +, p, and p 0 have been computed as a ratio of the channel cross-sections to the total collisional cross-sections, as we described earlier [Kharchenko et al., 1998, 2006]. In calculating the X-ray production we have assumed that the direct impact excitation of the positive ions in collisions with the neutral atmospheric atoms and molecules does not contribute. Excitation cross-sections are not available. We expect them to be small at low collision energies compared to charge exchange and at high energies compared to stripping, but their omission introduces an uncertainty into our predictions. Channel probabilities for collisions of oxygen and sulfur ions with the atmospheric gas have been updated recently [Liu and Schultz, 1999; D. R. Schultz et al., Atomic data and nuclear data tables, in preparation, 2008]. The yield of X-ray photons in the atmospheric stopping of energetic ions is controlled by the channel probabilities, which depend strongly on the collisional energy. The channel probabilities are computed for all O q+ (q =0 8) and S q+ (q =0 16) ions at collisional energies between 10 kev/amu and 50 MeV/amu [Schultz et al., manuscript in preparation, 2008]. To illustrate their energy dependence we show in Figure 1 the channel probabilities of S 14+ +H 2 collisions as functions of the collisional kinetic energy per nucleon. The stripping probability p + monotonically increases with collisional energy and the charge transfer probabilityp decreases.atenergiesbetween2and3mev/amu, the probabilities of capturing and losing an electron in a single collision are approximately equal. Every chargeexchange collision leads to the emission of X-ray photons. In our example, X-ray photons arise from excited S *13+ ions produced in charge-exchange collisions of S 14+ ions. Captures and losses of electrons by precipitating ions in sequential collisions would continue an infinite number of times, if the ion kinetic energies were fixed. In practice, the electron capture and stripping collisions reduce the ion kinetic energy. The probability of the charge preservation collisions, p 0, is 3 4 orders of magnitude higher than the probabilities of charge-changing collisions. In between two sequential charge changing collisions the charge-preserving collisions may significantly reduce the ion kinetic energy and change the probabilities of electron capture and loss. Domination of the p 0 -channel makes the energy loss processes faster than the charge relaxation. This physical picture restricts the validity of the equilibrium charge (EC) model, which is based on the assumption that the charge relaxation happens much faster than energy losses [Cravens et al., 1995, 2003; Kharchenko et al., 1998, 2006] Monte Carlo Simulations of the Charge and Energy Relaxation of the Ensemble of Monoenergetic Ions [13] Initial energies of precipitating ions at the top of the Jovian atmosphere depend on the ion acceleration mechanism. Previous analysis of the observational data on the Jovian polar X rays assigned the ion initial energies 4of11

5 Figure 2. Evolution of the charge distribution of an ensemble of oxygen ions with initial energy E in = 2 MeV/amu and initial ion charge q in =1.N is the number of collisions in units of 10 5 collisions. The charge distribution function f O (q, N), given in equation (2), is normalized to unity. The sharp maximum at low N reflects the initial low-charge distribution of oxygen ions. to the interval MeV/amu [Cravens et al., 2003; Kharchenko et al., 2006; Branduardi-Raymont et al., 2007a, 2007b]. Spectra of the charge-exchange X rays depend on the kinetic energy and composition of the precipitating ion flux, and modeling of X rays observed from the North and South poles may constrain these parameters. To determine the energy dependence of the charge-exchange X-ray spectra we have carried out calculations of X-ray emissions induced by different ensembles of the monoenergetic ions, precipitating into Jovian atmosphere. Computations of the energy-charge distribution functions of the ensemble have been performed for ions traveling in the upper Jovian atmosphere, where H 2 molecular gas is the major constituent with the largest column density. Initial ion energies E in at the top of the Jovian atmosphere were taken between 0.5 and 2 MeV/amu. Precipitating ions with initial energies lower than 0.5 MeV/amu cannot efficiently produce X-rays photons and may be excluded from consideration [Cravens et al., 1995, 2003; Kharchenko et al., 1998, 2006]. Monte Carlo simulations have been carried out with ensembles of 10 4 monoenergetic ions in initially lowcharge states q in = 1 3. Every collision involves three possible channels and each channel is characterized by a specific energy loss [Kharchenko et al., 1998; Liu and Schultz, 1999]. Millions of collisions are necessary to stop heavy ions with initial energies of a few MeV/amu. Our Monte Carlo simulations have been carried out for sets of collisions, depending on ion initial energies. Simulations were stopped when the particles slowed to energies of a few hundred kev/amu and production of X rays became negligible. Energy-charge distribution functions f O (E, q, N) and f S (E, q, N) have been computed for energetic oxygen and sulfur ions as functions of the number of collisions N. These distribution functions Figure 3. Evolution of the charge distribution f S (q, N) of an ensemble of sulfur ions with the initial energy E in = 1 MeV/amu. The initial ion charge is q in =2. 5of11

6 Figure 4. Dynamic population of the different charge states q =0,1, of the precipitating oxygen ions. The initial ion energy is E in = 2 MeV/amu, and the initial charge is q in =2.Nis the number of collisions since the beginning of precipitation. describe completely the charge and energy relaxation of precipitating ions. In Figures 2 and 3, we show the 3Dplots of the charge distribution function f O (q, N) derived from the results of the Monte Carlo simulation: F 0 ðq; NÞ ¼ Z 1 0 def O ðe; q; N Þ and F S ðq; NÞ ¼ Z 1 0 def S ðe; q; NÞ; where the initial energy of oxygen ions is E in = 2 MeV/ amu and sulfur ions E in = 1 MeV/amu. The initial charge state q in = 2 was chosen for both ions. Fast stripping of oxygen ions to the highest charges 7 and 8 happens in the first stage of the collisional evolution, when the ion kinetic energy is still high. Loss of the kinetic energy in the following collisions diminishes the stripping probability, resulting in the degradation of highly charged states in the precipitating ion flux. Charge degradation restricts the X-ray production in the charge-exchange collisions, because energetic X-ray photons can be emitted only by highly charged ions. Evolution of the charge distribution of sulfur ions, shown in Figure 3, demonstrates features different from the behavior of oxygen ions. There is a significant number of unoccupied S q+ charge states even at the high kinetic energies around 1 MeV/amu. Stripping of highly charged S q+ ions at this energy is a low-probability event, and S q+ charge states with q 12 are not accessible. Helium-like and hydrogen-like S q+ ions may radiate energetic X-ray photons between 2.4 and 3.5 kev, but the chance of producing these ions at 1MeV/amu is very low. As a result, emissions of the sulfur ions in highest charge states are absent in the X-ray spectra of the precipitating ions. ð2þ [14] Evolution of the charge distribution induced by ion collisions with the atmospheric gas shows strong correlations between abundances of different ion charge-states. In Figure 4 the populations of ion charge states in the ensemble of oxygen ions with initial energies of 2MeV/ amu are given as functions of the number of collisions N. The total number of ions in the ensemble is taken as 100%, and each curve shows the N-dependence of populations of individual charge states of oxygen ions as percentages. Initially low-charge oxygen ions are quickly stripped to highest ion charges q = 7 and 8 at the beginning of the energy-charge relaxation. This phase of relaxation requires about 10 4 sequential collisions, which reduce the ion kinetic energy by a few percent. An initial energy of 2MeV/amu is high enough to support 80% of oxygen ions in the bare charge state. Strong emission of excited O *7+ ions is expected at this stage of the stopping process. Diminishing of ion kinetic energies with N makes stripping collisions O 7+ + X! O 8+ + X + e with the atmospheric gas (X =H,H 2, and He) less probable than charge-exchange collisions O 8+ + X! O *7+ + X +. This leads to a reduction of the O 8+ fraction and increases the population of O 7+, which becomes a dominant charge state at 10 5 collisions. High-energy X-ray photons from excited O *7+ and O *6+ ions are mostly produced during O 8+! O 7+ and O 7+! O 6+ changes of the leading fractions of the charge distribution. The number of ion-neutral collisions increases as ions penetrate deeply into the Jovian atmosphere and the gradual loss of the ion kinetic energy leads to an alternation of the most probable charge state. The sequence of dominant charge states: O 8+! O 7+! O 6+! O 5+! O 4+...is clearly seen in Figure 4. Charge-state populations provide information on the total numbers of q! q-1 charge-exchange collisions, which have occurred during the entire stopping process. These numbers also represent the numbers of collisions that produced excited O *(q 1)+ ions. Finally, the number of charge-exchange collisions determines the numbers of X-ray photons. [15] A simplified method of computation of the chargedistribution is based on the equilibrium charge model. The major mathematical approximation of the equilibrium charge model is the assumption that the ion charge distribution relaxes very quickly and may be evaluated at fixed current energies of the precipitating ions. In other words, the equilibrium charge model postulates that ion charge distributions are adiabatically transformed by the slow energy relaxation of ions colliding with the neutral gas. However, conditions required for the validity of the equilibrium charge model are not appropriate for ion-atom or ion-molecular collisions: As illustrated in Figure 1, the energy transfer collisions happen times more often than charge changing collisions. The physical reason for the fast energy relaxation is very simple: at high collisional energies the target ionization cross-sections, which control the energy relaxation, are much larger than stripping and charge-exchange cross-sections. Despite its weakness, the equilibrium charge model provides an order of magnitude estimation of the ion charge-distribution because of the relatively small value of energy loss in a single ion-atom collision. In Figure 5, a comparison between the result of our Monte Carlo simulations and the equilibrium charge model is presented for sulfur ions, 6of11

7 Table 1. Yield of Photons Induced by Single Oxygen Ion in the Stopping Process Photon Energy a,ev Photon Yield YE in = 1 MeV/amu Photon Yield YE in = 2 MeV/amu Charge State O q O O O O O O O O O O O O 7+ a X-ray photons with energies larger than 100 ev are listed. Figure 5. The average charge hqi of precipitating sulfur ions as a function of the average ion energy hei. The initial ion energy is E in = 32 MeV (1 MeV/amu), and the initial charge is q in = 2. The upper curve is the prediction of the equilibrium charge (EC) model, calculated with the updated values of cross-sections for collisions between S q+ ions and molecules of the H 2 gas. The lower curve shows the results of the Monte Carlo simulations. precipitating with initial energy of 32 MeV, or 1 MeV/ amu. The average ion charge hqi; is shown as a function of the averaged energy hei of the precipitating sulfur ions. Mathematically, Figure 5 represents a parametric plot of two average values {hq(n)i, he(n)i}, which are calculated after N sequential collisions. Results of calculations with the equilibrium charge model are shown by the upper curve and Monte Carlo simulations by the lower curve. It is not surprising that the equilibrium model overestimates the average charge of precipitating ions; the equilibrium average charge at given energy is never reached in realistic conditions, because the energy loss happens faster than the charge equilibration. [16] We have computed the photon yield functions Y i,k (hw j, q 1, E in ), defined as the numbers of photons with energy hw j induced by excited O *(q 1)+ and S *(q 1)+ ions through the stopping process. These numbers represent the spectra of the charge-exchange emission of the individual O *(q 1)+ and S *(q 1)+ ions. Yield functions Y i,k, normalized per ion, have been computed for the charge-exchange emission of O and S individual ions, using the calculated energy-charge distributions of the precipitating ions: Y i;k Z Nmax hw j ; q 1; E in ¼ 0 Z Ein 0 dnde p ðe; q; i; kþ c i;k hw j ; E fxðe; q; NÞ; ð3þ where c i,k (hw j,e) are the photon cascading functions calculated in our previous investigations [Kharchenko et al., 1998, 2006], and X-index stands for O or S ions. equation (3) clearly indicates that modeling of the chargeexchange emission spectra of precipitating ions requires an accurate evaluation of the energy-charge distribution functions. 3. Modeling of the Charge-Exchange Spectra and Comparisons With the Chandra Observations of the Jovian Polar X-rays [17] We have calculated the dynamical energy-charge distribution functions f O (E, q, N) and f S (E, q, N) of precipitating oxygen and sulfur ions using the results of our Monte-Carlo simulations for a set of different initial energies E in and charges q in that correspond to expected Jovian magnetospheric conditions. Computed distributions have been used to determine the photon yield functions normalized to a single precipitating particle. Dynamical energy- Table 2. Yield of Photons Induced by Single Sulfur Ion in the Stopping Process Photon Energy a,ev Photon Yield YE in = 1 MeV/amu Photon Yield YE in = 2 MeV/amu Charge State S q S S S S S S S S S S S S S S S S S S S S S S S S S S S 14+ a X-ray photons with energies larger than 200 ev are listed. 7of11

8 Figure 6. Synthetic spectra of the charge-exchange emission induced by the precipitating ion flux composed of oxygen and sulfur ions. Spectra computed for equal abundances of O and S ions in the precipitating flux. The initial energies of 2 MeV/amu at the top of Jovian atmosphere are taken equal for oxygen and sulfur ions. Points indicate the number of photons per precipitating ion for the entire stopping process. charge distributions and photon yield functions of the precipitating O and S ions depend strongly on the initial ion energy and are not sensitive to the initial ion charge. This has been established for oxygen [Cravens et al., 1995, 2003; Kharchenko et al., 1998, 2006; Liu and Schultz, 1999] and sulfur [Kharchenko et al., 2006] ions in previous modeling of the Jovian X rays. In Tables 1 and 2 the spectra of photons induced for the entire stopping process are shown respectively for oxygen and sulfur ions with initial energies of 1 and 2 MeV/amu. Spectra are given by the photon yield functions Y i,k from equation (3) and normalized to a single precipitating ion. Emission spectra of individual ions at different initial energies have been used to construct the synthetic spectra. To illustrate the major features of the computed spectra, the synthetic spectrum induced by a precipitating flux of equally abundant oxygen and sulfur ions is shown in Figure 6. Initial kinetic energies of 2 MeV/ amu are chosen for both species. The precipitating particles induce a broad spectrum of charge-exchange emission lines from the EUV to 2 kev X-ray photons. The majority of induced X-ray photons have energies of a few hundred ev. The presence in the spectra of a small fraction of energetic X-ray photons around 2 kev reflects the low-probability events of stripping sulfur K-shell electrons. The relative intensities of the emission lines of the same element at different charge states q are strongly correlated and depend on the initial energy. [18] The abundances of the O and S ions in the precipitating fluxes and their energies at the top of the Jovian atmosphere may be used as disposable parameters to be varied for fitting observational spectra of the Jovian X-ray emission from the North and South poles Chandra Observations of Jovian North and South Polar Auroras [19] Synthetic spectra of the charge-exchange emission with variable O and S abundances have been used to explain specific features of the X-ray emission observed from the North and South poles. The Chandra ACIS-S instrument obtained spectra of the Jovian polar X-ray emission during the February 2003 observations. A general description of the Chandra observational data has been reported in earlier papers [Elsner et al., 2005a, 2005b; Bhardwaj et al., 2006]. In Figures 7 and 8 we show the X-ray photon spectra obtained with the Chandra X-ray telescope for the North and South polar regions respectively. Dots with vertical and horizontal error bars are Chandra data with each spectral point representing at least 10 photons. These Chandra data are for the first ACIS-S/Chandra exposure carried out on February 2003 for 8.5 hr (for details see Figure 1 of Elsner et al. [2005b] and Table 1 of Bhardwaj et al. [2006]). Details on the division of Jupiter s disk into the highlatitude North and South auroral regions and the lowlatitude disk region are presented by Elsner et al. [2005b] and Bhardwaj et al. [2006]. [20] One of the goals of our modeling is to determine initial energy and composition of precipitating ions. These parameters of the precipitating ion flux are independently inferred for the North and South auroras by fitting the Chandra/ACIS-S observed X-ray spectrum with the spectrum obtained from the model simulations Synthetic Spectra of the North and South Pole Auroras [21] Theoretical spectra of the North and South Jovian X-ray auroras have been computed for different initial Figure 7. Observational (dots with error bars) and theoretical (solid line) spectra of the Chandra X-ray detector counts from the Jovian North pole. Theoretical spectra are normalized per single ion and computed for the ion flux composed of O q+ (79%) and S q+ (21%) ions. Average kinetic energies at the top of the Jovian atmosphere are 1.8 and 1.05 MeV/amu for O and S ions, respectively. In the spectrum, shown by the solid curve, the forbidden emission line 2 3 S! 1 1 S of O *6+ at 561 ev is completely suppressed. Dashed lines show the charge-exchange X-ray spectra computed with collisional quenching efficiencies of 85%, 50%, and 0%. Without quenching collisions, the emission line of O *6+ at 561 ev dominates the theoretical spectrum between 500 and 600 ev and removes the agreement between observational and theoretical data. Quenching reduces the intensity of 561 ev line but does not influence other O *6+ emission lines such as the intercombination (569 ev) and resonance (574 ev) transitions. 8of11

9 and during this time interval the oxygen metastable ions will collide with the atmospheric gas, if the ambient gas density is large enough. The abundance of metastable ions and the intensity of their radiation in the Jovian atmosphere can be significantly reduced. The reduced intensity I Q of the forbidden transitions is given by the formula: I Q ¼ I 0 = 1 þ X k hn k Vs Q;k it r! ð4þ Figure 8. Chandra observations (dots with error bars) of the Jovian southern auroral X rays and theoretical spectrum (solid line) normalized per single ion. The model precipitating ion flux is composed of O q+ (85%) and S q+ (15%) ions. Averaged kinetic energies at the top of the Jovian atmosphere are 1.75 and 1.01 MeV/amu for oxygen and sulfur ions, respectively. The forbidden emission line at 561 ev of O *6+ is suppressed by quenching collisions with the atmospheric gas. compositions and energies of precipitating ions and compared with observations. The charge-exchange emission spectra have been derived from the results of the Monte Carlo simulations of ion stopping. As discussed in the introduction, our synthetic spectra include two types of correlation between the intensities of different emission lines. The first type is the correlation between the intensities of the photons emitted in the radiative cascade of individual ions. These correlations are present in the active and passive charge-exchange mechanisms. The second type of correlation, correlations between intensities of emission lines induced by ions of the same element in different charge states, is specific to the active charge-exchange mechanism. The abundances of different charge states in the precipitating flux and hence the emission spectra are controlled by sequential collisions and depend on the initial ion energies. [22] Correlations place strict limits on the fitting procedure, because the relative intensities of different emission lines are fixed. We vary only two physical parameters: the elemental composition and the initial energy of the precipitating ions. Fitting of observational data provides detailed information on the abundances and energies of the radiating ions. The theoretical X-ray spectrum is compared in Figure 7 with the North pole spectrum observed with the Chandra X-ray telescope. The spectra are determined by the relative intensities of lines arising from charge exchange and depend only on the initial energies of the precipitating S and O ions and their relative abundances, possibly modified by the atmospheric absorption. We found that to achieve agreement with the observations it was necessary to suppress the contribution of the 2 3 S! 1 1 S transitions of O *6+ ions at 561 ev. We suggest that the long-lived metastable 2 3 S state of O *6+ which is otherwise a major source of X-ray emission by the charge-exchange mechanism is quenched by collisions with the atmospheric constituents. The 2 3 S state of the helium-like oxygen ion has a radiative lifetime of 0.96 ms where I 0 is the unperturbed intensity of the forbidden emission; n k are the densities of the different constituents of the ambient gas (k = H, He, and H 2 ), V is the velocity of excited ions, s Q,k are the cross-sections of ion quenching collisions with the H, He and H 2 targets, and t r is the radiative lifetime of the excited state. A simple estimate with the formula given by equation (4) shows that quenching of the metastable O *6+ ions could be efficient, where the density of the planetary gas is larger than cm 3. For the Jovian atmosphere, this gas density occurs below an altitude of 1200 km. If the initial energies of the precipitating ions are around an MeV/amu, ions penetrate deeply and X-ray emissions of metastable O *6+ ions will be suppressed by quenching collisions. The forbidden line of the O *6+ emission has been identified as the brightest feature of cometary and planetary chargeexchange X rays [Kharchenko and Dalgarno, 2000; Kharchenko et al., 2003; Krasnopolsky et al., 2004] but may be removed from the Jovian polar X-ray spectra by quenching collisions. Data obtained with the Chandra X-ray telescope, indicated by the dots with error bars in Figure 7, clearly support this conclusion. XMM spectra of X rays from the Jovian polar regions shows the forbidden line as one of the brightest features [Branduardi-Raymont et al., 2007a, 2007b]. However, the relative intensity of the 561 ev line in the O *6+ X-ray multiplet is suppressed by a factor of two with respect to the prediction of the chargeexchange mechanism and related observations of the cometary and planetary X rays induced by the solar wind [Kharchenko et al., 2006; Dennerl et al., 2006]. [23] The quenching effect is important only for the longlived metastable 2 3 S states. Other excited states radiate quickly and are not disturbed by collisions. For example, in the X-ray emission of O *6+ excited ions the quenching collisions remove the forbidden line from the spectra at 561 ev, but do not influence the emission lines of the intercombination (569 ev) and resonance (574 ev) transitions, which have radiative lifetimes of s and s respectively. [24] Precipitation of accelerated solar wind ions has been proposed as an additional source of the Jovian X rays [Cravens et al., 2003]. In this case, the quenching collisions may suppress emissions of 2 3 S metastable states of the helium-like O *6+,N *5+, and C *4+ ions. Their radiative lifetimes t r are 0.96, 3.9, and 20 ms respectively, and quenching of the metastable helium-like carbon would happen at higher altitudes than quenching of N *5+ and O *6+ ions. [25] The most likely quenching mechanism appears to be electron capture by excited O *6+ (2 3 S) in charge-exchange collisions with atmospheric gas followed by Auger decays of the resulting doubly-excited states of O *5+. The excess 9of11

10 energy would be converted into heat in the atmosphere. Figure 7 shows the modifications to the spectra that would result from the quenching efficiency of 0%, 50%, 85% and 100%. The contributions from the 2 3 P! 1 1 S transitions at 569 ev and 2 1 P! 1 1 S at 574 would not be affected. The comparison in Figure 7 supports the assumption of a complete quenching. [26] The relative abundance S to O ions and the energy at the top of the Jovian atmosphere are two variable parameters in our fitting. They have been inferred from least square fitting of observational data. Modeling with the charge-exchange spectra is different from a standard fitting of observational data by arbitrary variations of intensities of individual emission lines [Elsner et al., 2005a; Branduardi-Raymont et al., 2007a, 2007b]. Individual line fitting includes a larger number of variable parameters (degrees of freedom) and may yield relatively small values of c 2. On the other hand, results of independent line fitting may contradict the charge-exchange model, which requires specific intensity ratios for the emission lines. With two adjustable parameters we have obtained good agreement between the observational and theoretical spectra. The value of c 2 is 2.3, computed for our model spectrum of the North pole X rays (solid line in Figure 7). The inferred fractions of energetic O and S ions, precipitating into the North pole, are respectively 79% and 21%. The relative O to S abundance obtained from fitting is higher than that suggested for the average composition of magnetospheric ions [Gehrels and Stone, 1983; Cravens et al., 1995; Kharchenko et al., 1998, 2006; Mauk et al., 2003]. This difference could be explained by an ion acceleration mechanism, if ions are accelerated from the outer magnetosphere regions with a larger than average population of low-energetic oxygen ions. We have employed the simplest monoenergetic composition of precipitating ions and included a small fraction of ions with different energies. For oxygen ions, the initial energies on the top of the North pole atmosphere have been chosen to be 2 MeV/amu for 85% of the ions and 1 MeV/amu for 15%. 95% of the sulfur ions have energy of 1 MeV/amu and 5% of S ions are highly energetic particles with an energy of 2 MeV/amu. The initial average energy per nucleon of the oxygen ions, 1.85 MeV/amu, is almost twice the average energy, 1.05 MeV/amu, of the sulfur ions. This ratio is in a good agreement with the magnetospheric acceleration model suggested by Cravens et al. [2003]: Low-charge oxygen O q+ (q = 1 3) and sulfur S q+ (q = 1 3) ions are accelerated in the magnetosphere by the same field, but the nuclear mass of S q+ ions is twice the O q+ mass. From the mass ratio we expect that the average energy of O q+ ions is twice the average energy of S q+ ions. [27] X rays observed from the Jovian South pole are less intense than from the North pole, due possibly to different precipitating ion fluxes which may reflect specific features of the acceleration mechanism. In Figure 8 we present the theoretical and measured spectra for the South pole. By suppressing the 2 3 S! 1 1 S emission of O *6+, we achieve satisfactory agreement. We have found that the oxygen ions contribute around 85% of the total South pole ion flux and sulfur ions around 15%. The fraction of sulfur ions in the South precipitating flux is lower by a factor of 1.4 than the fraction of sulfur ions in the North pole, indicating a preference for sulfur precipitation to the North pole. Test of the significance of this difference requires more detailed calculations of the model spectra and better photon statistics. Initial average energies of the oxygen and sulfur ions precipitating in the South polar region are respectively 1.75 MeV/amu and 1.01 MeV/amu. Agreement between observational and theoretical spectra of the South polar X rays is better than for the Northern pole spectra. Thus the value of c 2 = 1.7 corresponding to our model predictions and the observational data is smaller than that for the North pole model. The sharp increase of the observed North pole X-ray intensity at photon energies between 640 and 660 ev in Figure 7 is not described by the charge-exchange mechanism. To fit this feature with an increasing contribution of the O *7+ resonance emission line at 653 ev would require simultaneous changes in the intensities of other emission lines of all oxygen ions and the agreement between theory and observations would be lost. An independent increase of the intensity of the 653 ev emission of O *7+ may be achieved by taking into account alternative sources of X rays, such as solar X-ray scattering. In this case, the absence of the sharp 653 ev feature in the Chandra South pole X-ray spectrum could be explained by less contamination by solar X rays because of specific observational geometry. 4. Conclusion [28] Spectra of the Jovian X-ray auroras observed from the South and North polar regions with the Chandra X-ray telescope have been analyzed and compared with the predictions of the charge-exchange mechanism. We have shown that theoretical spectra describe well the Chandra observational data on the X-ray emission from both the South and North poles. The relative abundances of precipitating oxygen and sulfur ions and their energies at the top of the Jovian atmosphere are inferred from comparisons between our synthetic spectra and observational data. We found that elemental compositions of the precipitating ion fluxes in the South and North polar regions are slightly different: 79% oxygen and 21% sulfur ions in the North and 85% and 15% in the South. Average initial energies of precipitating oxygen and sulfur ions are respectively 1.85 MeV/amu and 1.05 MeV/amu for the North and 1.75 MeV/amu and 1.01 MeV/amu for the South aurora. These numbers support the magnetosphere ion mechanism, proposed by Cravens et al. [2003]. Energies per nucleon of the accelerated ions have to be about two times smaller for sulfur ions, because they are two times heavier than oxygen. Spectra of the charge-exchange emission induced by ions, precipitating into the Jovian atmosphere, are different from the cometary charge-exchange X rays. The populations of different charge-states of precipitating ions depend on their energies at the top of the Jovian atmosphere. Our theoretical model suggests that the X-ray emission of the long-lived metastable states may be significantly reduced by quenching collisions between excited metastable ions and neutral atmospheric gas. At initial ion energies between 1 and 2 MeV/amu precipitating particles penetrate deeply into the Jovian atmosphere, where the population of O *6+ metastable ions and the intensity of the forbidden X-ray transitions at 561 ev are significantly reduced by quenching processes. Chandra s spectra of the Jovian X-ray auroras do 10 of 11