1. INTRODUCTION Solar X-Ray Ñux, and It Appears Not to Be Associated with Dust Or Dust Impacts

X-RAY EMISSION FROM COMETS, COMETARY KNOTS, AND SUPERNOVA REMNANTS R. BINGHAM AND B. J. KELLETT Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, England, UK J. M. DAWSON Department of Physics, UCLA, Los Angeles, CA 90024 AND V. D. SHAPIRO AND D. A. MENDIS Department of Physics, University of California, San Diego, La Jolla, CA 92093 Received 1999 January 19; accepted 1999 December 13

ABSTRACT A comparison is made between one of the processes leading to cometary X-ray emission and X-rays from supernova remnants. We demonstrate that the X-ray emission in both comet and supernova is bremsstrahlung and line radiation created by energetic electrons accelerated by plasma turbulence. We further demonstrate that the most likely source of plasma turbulence is produced by counterstreaming ion populations which result from the mass loading e†ect or from an anisotropic distribution produced by reÑecting ions from a collisionless shock. The instability that gives rise to the plasma turbulence is the modiÐed two-stream instability of counterstreaming ions. A similar instability arises in laser-plasma interactions that have self-generating magnetic Ðelds and Ñowing ions. Subject headings: comets: general È instabilities È radiation mechanisms: nonthermal È supernova remnants È turbulence È X-rays: general

1. INTRODUCTION solar X-ray Ñux, and it appears not to be associated with dust or dust impacts. There is little doubt that the emission Counterstreaming plasma Ñows are produced in many results from the solar wind/cometary atmosphere inter- astrophysical objects: in comets, a counterstreaming Ñow is action. Supernova remnants also have a number of things in set up between the solar wind and the cometary atmo- common with solar wind/comet interactions, namely the sphere; in supernova remnants, the reÑected ions from the shock wave produced creates ring-type ion velocity dis- forward and reverse shocks form counterstreaming Ñows. tribution functions, which generate lower hybrid waves Counterstreaming Ñows are well known in plasma physics capable of accelerating electrons. Therefore, it is perfectly to be responsible for a number of instabilities generating reasonable to propose that the X-ray emission mechanism plasma waves. In a magnetized plasma, one of the most from supernova remnants is similar, i.e., due to a high- important is the modiÐed two-stream instability (MTSI; energy electron tail produced by lower hybrid turbulence. McBride et al. 1972), which generates waves between the High-resolution Hubble Space Telescope (HST ) images of electron and ion gyrofrequencies known as lower hybrid the old planetary nebula NGC 7293 (the Helix Nebula) waves. Lower hybrid waves are particularly important since reveals many Ðne-scale Ðlamentary structures. The Ðla- they couple to both the electrons and ions and are capable ments are generally referred to as cometary knots, and HST of producing high-energy electrons. These waves have inter- revealed that they have radii of 50È100 AU and lengths of esting properties: being able to resonate with ions moving order 1000 AU. They also have luminous cusps on the across Ðeld lines and higher velocity electrons moving surface facing the hot central star which are photoionized parallel to the magnetic Ðeld. This allows the wave to trans- and in hydrostatic equilibrium. fer energy from ion Ñows to electrons. For example, in the The similarity between the solar wind/comet interaction MTSI, ions moving across magnetic Ðeld lines drive up the and the conditions surrounding cometary knots suggests waves, which then energize electrons moving along the that cometary knots are also sources of X-rays. This is an magnetic Ðeld, producing high-energy electron tails. The observation that has yet to be made. MTSI is important at collisionless perpendicular shocks In this paper, we describe a mechanism that could and can explain the energetic electrons observed, for operate in all three situations, namely the production of example, at the earthÏs bow shock (Shapiro & Shevchenko X-rays by a combination of bremsstrahlung and line radi- 1988). In this paper, we show that the instability operates in ation from high-Z atoms. The electrons are energized by comets and supernova remnants and is responsible for plasma turbulence generated by anisotropic ion velocity accelerating and heating electrons to keV temperatures. distributions, such as ion ring distributions due to pick-up Since the Ðrst successful detection of X-rays from comet processes in colliding plasmas or shock reÑection of ions. In Hyakutake in 1996 (Lisse et al. 1996), X-rays from more all three cases, we assume that we have a rapidly moving than 10 other comets have been observed. From the various plasma colliding with a neutral or partially ionized gas. observations, several conclusions can be drawn. (1) The Electron acceleration by lower hybrid waves generated energy of the X-rays is relatively soft in the hundreds of eV by an ion streamingÈtype instability such as the MTSI is a energy range. (2) The emission is conÐned to the cometary phenomenon well known in magnetic fusion studies coma between the nucleus and the Sun, varying in extent (Luckhardt et al. 1982) and to a lesser extent in laser fusion from 104 to 106 km. (3) It appears not to be correlated with studies (Haines 1997), and it is also responsible for electron 233 234 BINGHAM ET AL. Vol. 127 energization in many space environments (Bingham et al. stripping (electron ionization or photoionization) of the 1994; McClements et al. 1993, 1997; Shapiro & Shevchenko neutral atoms, a counterstreaming ion-ion instability 1988; Shapiro et al. 1999). In the cometary case, unstable results. The relative motion between the two populations ion distribution functions are produced by photoionization provides the free energy to drive the instability. of the neutral gas outÑow evaporated from the cometary In the presence of a magnetic Ðeld, the newly created nucleus (Bingham et al. 1997; Shapiro et al. 1999). In the photoions move in cycloidal orbits given by supernova remnant case, unstable ion distributions are pro- v \ u (1 [ cos u t) , (1) duced by either shock waves created by the shocked inter- x M ci \ stellar medium (ISM) or the shocked ejecta. Unstable ion vy uM sin uci t ; (2) distributions could also be due to the relatively fast com- \ \ ponent of the pulsar or neutron star wind mixing with the hereuM cE0/B0 is the transverse (toB0) velocity, uci cooled neutral circumstellar wind, forming the pick-up sce- eB0/mi c is the gyrofrequency of the newly created ion, and nario as in comets. E0 is the electric Ðeld seen by an ion at rest with respect to The emission of Lya from SN 1987A has already been the Ñowing magnetized wind. In the wind frame, the newly observed (Sonneborn et al. 1998) with the Space Telescope created ions form an ion ring distribution. A similar type of Imaging Spectrograph (STIS). The emission comes from a ring distribution is formed by a wind interaction with a reverse shock formed where the outer envelope of SN shocked medium. In this case, however, the wind ion is reÑected moving upstream, and for a perpendicular shock it 1987A strikes ionized gas inside the inner circumstellar ring. ¿ ] Michael et al. (1998) argue that it should be possible, using sees the convective electric ÐeldB resulting in a cycloi- future STIS observations, to predict the time of the impact dal orbit. with the inner circumstellar ring. Soft X-ray emission from In the frame of the shock, the reÑected ions form an ion SN 1987A seen by ROSAT (Beuermann, Brandt, & Pietsch ring distribution penetrating along the magnetic Ðeld B 1994; Hasinger 1996) can be explained by a model attrib- with velocityuA. These ions have a distribution function of uted to Chevalier & Dwarkadas (1995) in which the blast the form wave formed by the outer envelope of the supernova inter- f (r, u , u ) \ n d(v [ u )d(v ] u)/2nu , II 2 i M A i M M A M acts with a relatively dense H region (density nH II B 10 cm~3). This H II region separates the shocked stellar wind whereni is the density of the newly created ions anduM is of the supernova progenitor from the inner circumstellar their perpendicular velocity. ring. Chevalier & Dwarkadas (1995) estimate that the blast The interaction of this ion ring distribution with the wave will strike the circumstellar ring around the middle of ambient plasma behind the shock drives the MTSI, which the next decade, producing a bright source of X-rays. results in strong plasma turbulence around the lower hybrid At the moment, the Lya emission from SN 1987A is frequency range. The interaction of the ion ring or some- coming from hydrogen ions with radial velocity D15,000 times beam with the wind plasma drives the MTSI km s~1 interacting with the reverse shock. Such an inter- described by the following dispersion relation (Shapiro et al. action would result in plasma energization producing ener- 1999): getic electrons and ions, the electrons being responsible for u2 u2 k2 bremsstrahlung and line radiation from high-Z atoms such LH ] ce A u2 u2 k2]u2 /c2 as oxygen, carbon, and nitrogen. pe Cometary knots imaged by the HST resemble in many = Lf /Lv u2 ] 8n2i P dv P dv i M \ 1 ] pe , (3) ways the interaction of a real cometary atmosphere with the A M J 2 2[ 2 k2c2 solar wind. Cometary knots are assumed to be the end u@kM kM vM u result of the Rayleigh-Taylor instability in which a high- whereuLH is the lower hybrid frequency, anduce and upe velocity wind interacts with a dense, slower moving com- are the electron cyclotron and plasma frequencies. ponent. This instability results in Ðnger-like components Lower hybrid waves have the following dispersion law: with a head and tail feature similar in appearance to a real b u2 (k2/k2) comet. At the present time, only optical images taken by u2\u2 A1 ] B ] ce A , (4) HST exist. If these structures are the result of a high- LH 2k2o2 (1 ] b/2k2o2)2 velocity wind impacting a gaseous atmosphere, then X-ray whereu is the lower hybrid frequency emission should exist at the head of the cometary knots LH similar in appearance to the X-ray images of real comets u u (Lisse et al. 1996). In this article, we will outline the mecha- u \ S ce ci ; LH 1 ] u2 /u2 nism that can give rise to high-temperature plasmas and ce pe X-ray emission whenever we have interacting plasma u is the electron, ion gyrofrequency,u is the plasma ce,i \ 2 pe volumes. frequency,b 8nn0 Ti/B0 is the ratio of gas kinetic pressure to magnetic pressure, ando \ (T /m )1@2(1/u ) is the elec- 2. MODEL i e ce tron gyroradius using the ion temperatureTi and density. The interaction of neutral gas with a collisionless plasma The integral over the transverse velocityvM of the gyrat- shock gives rise to a number of collective plasma processes. ing ring ions on the left-hand side of equation (3) can be If the system has no magnetic Ðeld, which is considered easily calculated using the ring distribution function or a unlikely, then ion-ion instabilities will thermalize the beamlike distribution function with the growth rate being system. given by (Shapiro et al. 1999) If there are magnetic Ðelds present, then the most likely 2 2 collective process responsible for thermalization processes ^ ni mp u uLH 1 c 3 3 ] 2 2 . (5) between counterstreaming ions is the MTSI. Due to charge 2n0 mi k uM 1 (b/2k o ) No. 2, 2000 X-RAY EMISSION FROM COMETS 235

We have used here the notationmi to depict the wind ion By balancing the growth ratecLH of the lower hybrid mass assumed to be hydrogen andmp as the mass of the waves due to the instability with the Landau damping rate newly created ion or impact medium. For the cometary due to the wave (inverse Cerenkov) interaction with ener- case,mp is mostly oxygen (Lisse et al. 1996), since the com- getic electrons, we obtain the following relation: etary nucleus contains water and carbon dioxide; for the supernovae and cometary knots,m is the mass of the ejecta nTe ^ ni p 2 . (8) thought to be a mixture of di†erent gases such as hydrogen, ve mi u oxygen, carbon, and nitrogen and dust particulates for SN Combining this with equation (7) gives the following esti- 1987A (Michael et al. 1998). In the case of an atomic mations for the typical energyv of the suprathermal elec- m e mixture,p is determined by trons and their number density: 1 1 na 1@5 \ ; , ^ 2@5AmeB 2 m n m ve a mi u , (9) p p a a mi where a is the atomic species. 1@5 ^ 2@5 AmeB For the laser fusion scenario, we have a rapidly expand- nTe a ni . (10) ing plasma moving across a self-generated magnetic Ðeld. mi Such a model also produces waves at the lower hybrid fre- The distribution function of the electrons forms a high- quency (Haines 1997). energy tail along the magnetic Ðeld direction. Using equa- These lower hybrid waves have a component of momen- tions (9) and (10), we can now estimate the luminosity for + + tum k along the magnetic Ðeld, i.e., kA, k is the wavevec- di†erent astrophysical environments. tor of the wave, which has a component principally perpendicular to the magnetic Ðeld. The wavevector k has 3. X-RAY PRODUCTION MECHANISMS two components:kM andkA. Using this fact and the fact that the waves are driven by the perpendicular velocity 3.1. Comets space component of the distribution function such that The cometary ion ÑuxFi at a distance r from the nucleus of the comet can be obtained by equating the photoionized u part of the cometary gas outÑow to the Ñow of the cometary viM B , kM ions picked up by the solar wind and is given by then it is possible for the wave to have a higher phase Q r \ 2 \ [ ~r@vg q \ s velocity component along the Ðeld direction, i.e., v \ Fi 4nr nci u Qs Qs e , (11) phA vg q u/kA andvphA ? vphM D viM. The component of the wave along the magnetic Ðeld has the possibility of resonating whereQs is the initial Ñux of gas molecules at the comet with faster, more mobile electrons and accelerating them surface ( \ 2 ] 1029 molecules s~1), q~1 is the rate of through inverse Cerenkov resonanceuBk v . The photoionization (q \ 106 s at 1 AU),v is the initial gas A electron \ 5 ~1 g waves grow as a result of the perpendicular (with respect to velocity(vg 10 cm s ), andnci is the cometary ion B) motion of the newly ionized nitrogen ions and can inter- density. A more accurate calculation (Wallis & Ong 1975) act simultaneously with the background ions and electrons. based on the analysis of the solar wind dynamics, mass- ^ loaded by the picked up cometary ions, leads to the same The growth rate of the MTSI is typically0.1uLH. A typical distance needed for the waves to grow exponentially, formula for the ion density. Using equation (11), we can while they are convected through the plasma, is estimate the density of the cometary ionsnci to be B10 cm~3 for u \ 3 ] 106 cm s~1, which corresponds to the r ^ 10uc~1 (6) downstream shocked solar wind velocity at a distance \ (the factor 10 is to allow for signiÐcant e-foldings). r 50,000 km, which is close to the position at which X-ray In the shock frame, in steady state, the energy Ñux lost by emission is being generated. These cometary photoions the picked up ions is equal to the energy Ñux carried away which are picked up by the solar wind excite the lower by the energized particles, electrons, and ions associated hybrid waves, which in turn are absorbed by the supra- with the envelope of the blast wave. The electrons gain thermal electrons through Cerenkov resonance with the energy parallel to the magnetic Ðeld, while the ions gain waves. energy perpendicular to the magnetic Ðeld B. Equipartition Using equation (9), we obtain the average energy of the 1 suprathermal electrons to be D100 eV and their density n of energy takes place, with approximately3 going into elec- ~3 Te trons and2 into the ions (2 degrees of freedom for the ions from equation (10) to be D1cm . This is a powerful 3 source of suprathermal electrons with an energy Ñux of 1019 perpendicular to B, 1 degree of freedom for the electrons ~1 parallel to B). ergs s through the region of X-ray emission. The electron The following energy Ñux balance equation between elec- energy Ñux is about 2 orders of magnitude less than the trons and ions can be written in the form total power available from the solar wind, indicating a rea- sonably high efficiency of energy transformation. This v 1@2 region also corresponds closely to the region in which an m u3 ^ n v A e B ; (7) i i Te e m intense lower hybrid waves were observed by the Vega satel- e lite (Klimov et al. 1986) during its encounter with comet ^ a is a transfer coefficient of efficiency 0.1,ni is the ion Halley. The presence of intense lower hybrid waves can density for the supernova case,mi is the ion mass,nTe is the result in Ðeld-aligned electrons accelerated up to energies in electron density,ve is the typical electron energy, andme is the keV range, exceeding signiÐcantly the average energy the electron mass. derived above (Bingham et al. 1997). 236 BINGHAM ET AL. Vol. 127

The maximum electron energyvemax can be obtained trons. The total luminosity due to recombination or impu- using equation (6) of Bingham et al. (1997), rity radiation from the cometary shell, described earlier, is given by Post et al. (1977): e2 2@3 v ^ C lSE2TD , (12) emax 2nm1@2 f ] ~18 Q*r 1 e L I B 5 10 "ne . (17) v Jv (eV) where l is the interaction length, D109 cm. Using for g e the wave energy spectral density values obtained from The numerical factor " for oxygen atoms has been esti- observations at Halley comet by the Vega spacecraft mated in Dawson (1981) as 0.1, which is close to the value 2 2 2 [SEfT D 1.0(mV /m Hz)], it is possible to estimate from obtained by detailed calculations (Post et al. 1977). equation (7) the maximum energy of accelerated electrons Using equations (16) and (17), we estimate the total lumi- as nosity of bremsstrahlung impurity radiation for the param- 15 ~1 v D 5 keV . (13) eters we have used above asL I B 10 ergs s for photon emax energies in the keV energy range; this corresponds to an We now make an estimate of the luminosity of the X-rays X-ray efficiency of 3 ] 10~6, which is comparable with the assuming that they are a combination of bremsstrahlung values obtained in terrestrial aurorae (Chamberlain 1961). emission and inner shell radiation from collisionally excited X-ray luminosities for a number of comets have been calcu- oxygen atoms. For bremsstrahlung emission, the power lated and compared to observations. The results are in very radiated by one electron in 1 cm~3 is given by good agreement (Shapiro et al. 1999) and are within the error bars for each comet observation. We conclude that g \ P +un v dp(u) , (14) our model can describe the main mechanism for X-ray pro- 0 e duction at comets. wheren is the number density of water molecules \ 0 2 3.2. Supernova Remnants ( Qs/2nr vg) at distance r,ve is the electron velocity, and dp(u) is the di†erential cross section for bremsstrahlung The model of radiation emission derived in the previous given by section can easily be extended to the case of supernova remnants, for which plasma energization takes place by 2 2 \ 16 Z e c 2 GbmaxH du wave turbulence produced at shocks, where the ion dis- dp(u) + 2 r0 ln , (15) 3 v bmin u tribution functions are similar to those found at comets, i.e., \ 2 2 ringlike in velocity space. wherer0 is the classical electron radius ( e /me c ), Ze is The di†erence between the cometary case and the super- the nuclear charge of the oxygen ion, u is the radiation \ 2 + 2 + nova remnant case is the velocity of the wind involved. For frequency, andbmax/bmin mv / u. Note that ln Mmv / uN comets, the wind velocity is typically 400 km s~1, and for is of order 1. remnants in particular the impact expected from SN 1987A 3 /vmax gf dv f The power radiated in 1 cm isvmin e e, wheree is the has a wind speed of 15,000 km s~1, considerably in excess of electron distribution function of suprathermal electrons. If the solar wind. the distribution function is constant in velocity up to a The high impact velocity of the wind reduces the e†ec- maximum valuev , thenf \ n /v and the total lumi- ~1max e e max tiveness of the coupling process. However, the shocked nosity (in ergs s ) from a shell of thickness *r surrounding wind speed has a much lower velocity, creating the right the comet nucleus is given by conditions for lower hybrid generation in the downstream region. \ P 2 ^ ] ~25 L 2n gfe dve r *r 3 10 The total luminosity (bremsstrahlung ] line radiation) per unit volume is given by Q ] *rn Z2Jv (eV) . (16) e emax L \ A3 ] 10~25n n Z2Jv eV ] 5 vg tot e 0 emax In addition to bremsstrahlung radiation, there is also "n n radiation from partially ionized oxygen and other heavy ]10~18 e 0 B ergs cm~3 s~1 J cometary ions whose bound electrons are excited by colli- vemax eV sions with the suprathermal electrons. The bound electrons D D ~3 ^ quickly de-excite and radiate any energy they receive from forne n0 100 cm ,vemax 10 keV. The luminosity per unit volume is 7 ] 10~17 ergs cm~3 this source. ~1 Line radiation produced by excitation of bound electrons s . This value is in reasonable agreement with obser- in inelastic collision with keV plasma electrons is found to vations. be more e†ective than bremsstrahlung. Detailed calculations of the intensity of this radiation known in fusion 3.3. Cometary Knots: T he Helix Nebula research as impurity radiation (Post et al. 1977) have shown The Helix Nebula (NGC 7293) is a newly evolved planet- that this radiation is a powerful source of energy loss in a ary nebula. In the recent listing by Harris et al. (1998), it was fusion reactor. The basic physics of this radiation can be listed as the second closest at a distance of 213 pc. When explained using the simple picture proposed in Dawson combined with its large size (12@ diameter), this makes the (1981), where it is assumed that the cross section of the Helix one of the few planetary nebulae in which signiÐcant process is determined by inelastic Coulomb electron- small-scale structure can be readily resolved. The Helix electron collisions with small impact parameter, thereby Nebula shows ionized knots that display comet-like tails, leading to relatively large angle scattering of plasma elec- the so-called cometary knots (CKs). The CKs are radially No. 2, 2000 X-RAY EMISSION FROM COMETS 237 oriented around the interior of the main nebula ring. The cometopause; we assume the maximum value to be 1200 HST has now shown that these cometary knots are clearly cm~3. The wind kinetic energy, assuming a proton plasma, resolved clouds, with neutral cores and photoionized sur- is of the order of 12 keV. The wind will thermalize when it faces facing the hot central star. The tails are formed from hits the CK, which will then raise the temperature at the material streaming backward from these cores (OÏDell & front of the CK. This value could be of the order of several Handron 1996; OÏDell & Burkert 1998). The central star keV. Using these numbers gives a maximum Ñux of 10~14 itself has an estimated temperature of 123,000 K (Bohlin, ergs cm~2 s~1 for an oxygen plasma. This is larger than Harrington, & Stecher 1982) and a luminosity of 120 L _. that emitted from either the comet or the supernova Cerruti-Sola & Perinotto (1985) could Ðnd no evidence for a remnant and may just be observable. The di†erence in emis- stellar wind. However, given the temperature of the star, sion is due to the much higher density of the cometary many of the usual indicators of a wind might not be visible, knots. even for a wind that is dynamically important. OÏDell & CONCLUSIONS Handron (1996) examined 32 CKs that were well separated 4. from other knots. Their sizes ranged from 125 to 390 AU In this paper, we have presented a model of X-ray emis- (scaled by D1.4 for the new distance). They also estimated sion from three astrophysical objects: comets, supernova ] ~5 individual masses of (1È2) 10 M_ and extrapolated to remnants, and cometary knots. In all three cases, we a total mass of the cometary knots of D0.1M_ (or D10 assumed that the interaction between magnetized Ñowing MJupiter). From the surface brightness in Ha, OÏDell & plasma created a hot plasma medium in the keV range of Burkert (1998) estimate an electron density of 1200 cm~3 temperatures, which was then responsible for bremsstrah- for the ionized portion of the knots and a density of lung and line radiation. A third candidate for X-ray emis- D1 ] 106 cm~3 for the neutral cores. The expected width sion is charge exchange. However, we have found of the ionization front is about D1015 cm. previously (Shapiro et al. 1999) that although this process OÏDell & Burkert (1998) were also able to conÐrm that does occur in comets and could occur in these other objects, the brightness distribution dropped exponentially with a it was an order of magnitude less efficient in generating density scale height of (1È2) ] 1015 cm for Ha. This implies X-rays. A full calculation should take into account all three that the CKs are pressure bounded rather than freely mechanisms. The energization of the plasma was by lower expanding. The stellar wind from the hot star could provide hybrid turbulence produced as a result of an instability well the unobserved pressure without violating other obser- known in fusion plasmas, both magnetic and laser. This vational constraints. instability is found to occur in many laboratory and astro- If we assume that the high-velocity wind speed from the physical plasmas. The model presented will need to be fol- central object is of the order of 1500 km s~1 with a rela- lowed up by extensive numerical simulations, which we are tively low density of 1 cm~3 with a comoving magnetic Ðeld doing at present. of the order of several nanoteslas, which are consistent with those of the solar wind, then we can calculate the X-ray This research has been partly supported by NSF grant luminosity as in the previous sections. The main parameter ATM 97-04193, NASA grant NAGW 4264, a UCLA NSF we have to use is the density of the cometary knot at the grant, a UK, PPARC grant, and an EU TMR grant interface with the wind, i.e., the region equivalent to the FMRX-CT98-0168.

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