Planetary and Space Science 77 (2013) 152–157

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Planetary and Space Science

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Dust cloud lightning in extraterrestrial atmospheres

Christiane Helling a,n, Moira Jardine a, Declan Diver b, Soren Witte c

a SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, UKb School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UKc Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany

a r t i c l e i n f o

Article history:

Received 10 December 2011

Received in revised form

13 June 2012

Accepted 3 July 2012Available online 14 July 2012

Keywords:

Extrasolar planets

Discharge processes

Clouds

Dust formation

33/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.pss.2012.07.003

esponding author.

ail address: ch80@st-and.ac.uk (Ch. Helling).

a b s t r a c t

Lightning is present in all solar system planets which form clouds in their atmospheres. Cloud

formation outside our solar system is possible in objects with much higher temperatures than on Earth

or on Jupiter: Brown dwarfs and giant extrasolar gas planets form clouds made of mixed materials and

a large spectrum of grain sizes. These clouds are globally neutral but we argue that mineral clouds in

brown dwarfs and extrasolar planets are susceptible to local discharge events and that the upper cloud

layers are most suitable for powerful lightning-like discharges. We discuss various sources of atmo-

spheric ionisation, including thermal ionisation and a first estimate of ionisation by cosmic rays, and

argue that we should expect thunderstorms also in the atmospheres of brown dwarfs and giant gas

planets which contain mineral clouds.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Until recently, clouds were believed to be unique to Earth-likeplanets and to the gas giant planets that are rather far away fromtheir host star (like Jupiter, Saturn, Uranus in our solar system).Extrasolar planets are now a matter of fact and their diversity hasincreased over the last couple of years due to various groundbased observational efforts like SuperWASP, HAT, TrES andregarding giant gas planets, and by the CoRot and the Keplerspace mission that include Earth-like, low-mass planets. Com-pared to the solar system, however, many giant gas planets areorbiting their host star at very short distance. Observations haverevealed that hazes appear in the upper atmospheres of suchclose-in planets, because the haze absorbing the stellar radiationduring transit makes the planet appear larger than expected. Thetransit spectroscopy of HD 189733b presented in Pont et al.(2008) and in Sing et al. (2011) provides the first proof that smallmineral particles do not only populate the highest layers of theterrestrial atmospheres but are also present in extrasolar Jupiters.Such direct observations of atmospheric dust have not yet beenpossible for brown dwarfs. Brown dwarfs have the same size andeffective temperature as the gas-giants, and they have beensubject to extensive direct spectroscopic observations as theyare much more close by and, hence, it is easier to take directspectroscopic measurements for brown dwarfs than for themajority of the exoplanets. High- and low-resolution spectra,

ll rights reserved.

reaching from the optical into the near-IR, were detected andcompared to synthetic spectra of model atmosphere simulations(e.g., Stephens et al., 2009; Witte et al., 2011; Patience et al.,2012). Researchers are keen to reproduce both observed spectraand also each others model results, leading to dedicated benchmark efforts for example for dust cloud models (e.g., Helling et al.,2008a). More often, we learn something new only if modelsimulations do not fit observations. Jones and Tsuji (1997)compared their static model atmosphere results to late M-dwarfspectra. The synthetic spectra only started to be comparable toobservations when the authors reduced individual element abun-dances artificially, arguing these element would be locked in dustgrains and, hence, be not available to the formation of molecules.Saumond et al. (2006) showed that the Spitzer observation ofammonia (NH3) indicates vertical mixing of hotter material intodetectable layers, hence, a local chemical dis-equilibrium. Theirchemical equilibrium model did not fit the observations unlessthey reduced the NH3 abundances, arguing that the reactiontimescale of N2 to NH3 is much slower than the convective mixingtimescale.

Clearly, clouds play an important role in every atmospherewhere they are forming because they consume elements, and bythis change, the local gas-phase chemistry. Cloud particles havelarge radiation absorption cross sections and they thereforeincrease the greenhouse effects, hence affecting the local tem-perature. Furthermore, these cloud form at a highly convectiveenvironment which drives a vivid turbulence field that caninitiate dust formation (Helling et al., 2001), and which increasesrelative velocities between grains. Clouds have been observed toproduce discharge events like lightning and sprites in planet of

Ch. Helling et al. / Planetary and Space Science 77 (2013) 152–157 153

our solar system that carry clouds. Therefore, we have goodreasons to expect that cloud-forming extrasolar planets andbrown dwarfs show similar electrostatic activities.

We summarise our model of mineral cloud formation (Section2) and discuss in Section 4 if mineral clouds could producelightning-like discharge events. Section 3 describes collisionalionisation and ionisation by cosmic rays as sources of chargeseparation in mineral clouds.

Fig. 1. Dust cloud material composition in volume fractions V s=V tot in a giant gas

planet atmosphere (Helling et al., 2008a) as a result of DRIFT-PHOENIX model

atmosphere simulations that include our kinetic dust formation model (Witte

et al., 2009; Teff—effective temperature of object, log(g)—surface gravity of object).

The composition changes with atmospheric height indicated by the local

temperature.

2. Mineral cloud formation in extrasolar planets and browndwarfs

Brown dwarfs and gas giant planets outside of our solarsystem are likely not to form cloud made only of liquid droplets,but their warmer atmospheres do allow solid dust particles tocondense from the gas phase.

We have modelled the formation of such mineral clouds bydescribing seed formation (by homogeneous nucleation) followedby the growth of 13 silicate and oxide solids by 60 chemicalsurface reactions, evaporation, gravitational settling (rain out),convective element replenishment, and element conservation(Woitke and Helling, 2003, 2004; Helling and Woitke, 2006;Helling et al., 2008c). Our model calculations start from solarelement abundances which are subsequently depleted by seedformation and the growth of the grain mantle. If the grainsbecome thermally unstable and evaporation sets in, the elementabundances will be enriched by those elements previously lockedin grains. Both processes, element depletion and element enrich-ment, are non-uniform and individual for each involved element.Processes between dust particles that lead to a further increase ingrain size, like for example coagulation, are not part of our kineticdust model because coagulation acts at a much longer time scale.Coagulation is about 100� slower than the growth process bysurface reactions, hence, the formation processes (nucleation andgrowth) will be much faster (Helling et al., 2008b).

The onset of dust formation is triggered by a nucleationprocess that strongly depends on the local gas temperature anda high supersaturation of the seed forming gas species whichrequires a temperature well below thermal stability. Typicalsupersaturation ratios of our nucleation species TiO2 are wellabove 104 in the nucleation region of the cloud (Fig. 1 in Hellinget al., 2008c). The onset of growth requires the growing materialto be thermally stable only. The growth rate is determined by theinflow of the growing gas phase constituents, hence, it is propor-tional to the number density of the (grow-) contributingspecies and their velocity distributions. We refer to Helling andRietmeijer (2009) and above mentioned papers for more detailsregarding the model equations. Our solution of the kinetic dustformation predict a cloud structure as function of the local gastemperature and gas density, T and rgas. Our model predicts themean grain size /aSðT,rgasÞ (mm), the number density of dustparticles ndðT ,rgasÞ (cm�3), and the mean material composition ofthe cloud particles Vs=V totðT,rgasÞ (%) (e.g., Fig. 1). We alsocalculate the chemical composition of the gas phase, includingthe degree of ionisation (Section 4). Vs is the dust volumeoccupied by the solid species s, V tot is the total dust volume. Tosome extent, the mean grain size, number of dust particles, thetotal dust volume, and higher dust moments allow us to repro-duce the grain size distribution, f ðV ,T,rgasÞ which provides thenumber of dust grains for each grain volume V.

Clouds in brown dwarfs and extrasolar giant gas planets arecomposed of a mixture of minerals due to the richness of theatmospheric precursor gas in these objects (Fig. 1), henceforthcalled ‘mineral clouds’. The dust formation process (seed forma-tion, growth/evaporation) is influenced by gravitational settling,

hence, particle growth speeds up while the grains fall inward alonga positive density gradient. During this descent, the crystal struc-ture of the cloud particles is evolving (Helling and Rietmeijer,2009). Fig. 1 indicates that such clouds are made of small(10�2 mm) silicate particles at the top which develop into large(10 . . .100 mm) iron/TiO2 particles. For details on grain sizes see e.g.Figure 8 in Helling et al. (2008c).

Would dust–dust collisions change this picture? The mostinteresting changes in the grain size distribution by a dust–dustcollision likely result from the fragmentation of both collisionalpartners and the stick-and-hit events of projectile and target.Fragmentation would increase the number of grains and there-with the number of seeds for further grow. As surface growth israther efficient, the grain fragments can grow rather quickly totheir previous sizes until the gas-phase is undersaturated. Hence,dust–dust collisions tend to increase the number of grains but thegrain size might not change as long as surface growth is efficient.Stick-and-hit events would produce a higher number of largegrains, but the collision energetic need to be just right.

3. Sources of mineral dust cloud ionisation

The reasons for ionisation in clouds are rather diverse, andmore complex processes than thermal ionisation need to be takeninto account because of the rapidly decreasing gas temperaturewith height. They include energetic interstellar or interplanetaryradiation, radioactive decay, differences between surface poten-tials of different materials (e.g., metals vs insulators), frictionalionisation, collisional ionisation of accelerated charges, or frag-mentation of fractal particles (fracturing). Triboelectric chargingis suggested to be of particular interest for dust cloud charging onplanetary surfaces (Sickafoose et al., 2001), a scenario which israther similar to mineral clouds in substellar atmospheres. Seealso Saunders (2008) for an overview of the subject. Also, gas-phase ions can attach themselves to the grain surface, and by this,contribute to the charging of cloud particles. Nicoll and Harrison(2010) have demonstrated this with observation of Earth clouds.

Ch. Helling et al. / Planetary and Space Science 77 (2013) 152–157154

In this paper, we discuss two sources of dust ionisation thatboth result in the ionisation of the cloud particles and eventuallyalso in the ionisation of the gas phase.

3.1. Dust-dust collisions

Helling et al. (2011b) studied dust–dust collision kinematicsusing results of our kinetic dust formation model from the modelatmospheres code DRIFT-PHOENIX (Dehn, 2007; Helling et al., 2008c;Witte et al., 2009). This collisional charge process is know astribo-electric charging and is suggested to work well for dustcharging of Martian dust (Sickafoose et al., 2001). Our results haveshown that dust–gas and dust–dust collisions due to gravitationalsettling (drift, rain out) are not energetic enough to overcome theenergy needed to release an electron from the crystal structure(work function). Only turbulence-enhances dust–dust collisionssuch that tribo-electric charging is possible.

Fig. 2 shows the turbulence-enhanced energy by dust–dustcollisions for three different atmosphere simulations. This ratherlimited number of DRIFT-PHOENIX investigated atmosphere modelssuggests that the pressure range affected by tribo-electric chargesis larger in a compact, low temperature brown dwarf (Teff¼1600 K,log(g)¼5.0) compared to a hot brown dwarf (Teff¼2000 K,log(g)¼5.0) or a giant gas planet (Teff¼1600 K, log(g)¼3.0). Thegeometrical extension of the clouds, however, differs widelybetween brown dwarfs and giant gas planets. Brown dwarfs havemuch less extended clouds than giant gas planets due to theirmuch higher surface gravity, and hence smaller pressure scaleheight. This suggests that a smaller atmospheric volume beingaffected by charged mineral clouds in brown dwarfs compared toJovian plants. However, our comparison of streamer timescale andCoulomb recombination time scale with the time scale on whichdust particles pass through a previously formed electron cloud(streamer), and hence, potentially initiate another electron ava-lanche, suggest a stronger lightning activity in higher densityenvironments such as brown dwarf atmospheres.

Fig. 2. Turbulence enhanced dust–dust collision energies, Ecol, for three different

DRIFT-PHOENIX model atmosphere simulations (pgas). The collision energy is well

above the work function interval (orange bar) for the high-gravity, cool brown

dwarf (Teff¼1600 K, log(g)¼5.0) over a large pressure range in contrast to its

hotter counterpart (Teff¼2000 K, log(g)¼5.0).

3.2. Cosmic ray attenuation

Cosmic rays (CR) appear to be an important source of atmo-spheric ionisation in the solar system planets. Observations of Earthclouds, however, suggest that the actual charge production is notoverly efficient but potentially important for coagulation processes.Nicoll and Harrison (2010) determine a maximum mean dropletcharge of 17e at the cloud edges on Earth which can be directlyrelated to ionisation by cosmic rays. The charging of these watercloud particles is, however, not a direct result of the impact of thehigh energy CRs on the cloud but rather of the ion and electroncurrents that develop from the CR ionisation of the gas above thecloud. These charges attach to the cloud particles. A similar scenariocan be envisioned for close-in exoplanets that form an ionospheredue to the X-ray and the extreme UV radiation of the host star asdemonstrated by Koskinen et al. (2010).

The question is whether galactic cosmic rays could be a globalsource of ionisation for the whole atmosphere of extrasolar low-mass objects which are not exposed to the high-energy radiation ofa nearby host star. Ionisation by CRs includes the effect of secondaryparticles like electrons but also g-rays. Umebayashi and Nakano(1981) show for protoplanetary disks that the CR attenuationincreases exponentially with a characteristic length or columndensity lCR � 96 g cm�2 of a gas where H2 provides the majorityof the mass. This translates into a simple ansatz for the attenuation,

FðzÞ

F0¼ exp �

rcol

lCR

� �, ð1Þ

with F(z) the local CR flux at height z, F0 the incident CR flux, and rcol

the gas column density. Fig. 3 shows FðzÞ=F0, the attenuation ofcosmic rays (solid line, rhs. axis of figure), which is determined by thelocal atmospheric gas-phase column density rcol ¼

R zi

z0rgasðzÞ dz

(g/cm2) (dotted line, lhs. axis of figure) integrated over the

Fig. 3. Cosmic ray attenuation (in %; solid lines, right axis) and gas-phase column

density rcol (in g cm�2; dotted lines, left axis). Top: The cosmic ray attenuation is

shown for two cases in a brown dwarf DRIFT-PHOENIX atmosphere (Teff¼1600 K,

log(g)¼5.0, solar metallicity) with Rn ¼ 109 cm¼ 0:14RJupiter.: lCR ¼ 96 g cm�2 (red

solid line) where H2 provides the majority of the absorbing mass (Umebayashi and

Nakano, 1981) and lCR ¼ 0:01 g cm�2 for which CR attenuation reaches 100% above

the cloud top above which grains do form, too, but at a much lower rate. lCR is the

characteristic CR penetration length. Bottom: Same as above but comparing a brown

dwarf and a gas planet atmosphere. (For interpretation of the references to color in

this figure caption, the reader is referred to the web version of this article.)

Ch. Helling et al. / Planetary and Space Science 77 (2013) 152–157 155

atmosphere extension z0 . . . zi. The attenuation increases inward(downward) with increasing gas-phase column density.

Cosmic rays penetrate the cloud almost unhindered if H2 is theonly absorber (lCR ¼ 96 g cm�2 in Fig. 3). The gas column densityis high enough for complete attenuation only at very high gaspressures in both the brown dwarf and the gas giant. Browndwarfs, on the other hand, have been shown to maintain mag-netic fields (e.g., Reiners and Basri, 2008; Hallinan et al., 2008;Christensen et al., 2009; Berger et al., 2010) and also planets havea magnetosphere (e.g., Zarka et al., 2001; Jardine and Cameron,2008). Dolginov and Stepinski (1993) argue that the magneticfield will diffuse the cosmic rays paths through the atmosphereand, hence, decrease the critical column density (or scale height)lCR for cosmic ray attenuation. Glauser et al. (2009) demonstratethat fast protons and He ions interact with dust grains in disks,hence, the dust will decrease the effective attenuation length inthe atmosphere further. This suggests that a smaller fraction ofthe atmosphere and of the cloud is influenced by cosmic rays.Nontheless, the critical column density needs to be as low aslCR ¼ 0:01 g cm�2 (Fig. 3, black solid line) to achieve 100%attenuation above the cloud in the brown dwarf model atmo-sphere studied here. It is, therefore, not clear if cosmic rays can bea global source for cloud ionisation as brown dwarfs havemagnetic fields which are particularly strong on small scales.The B-field shielding would, however, be less efficient in the polarregions if the magnetic field is predominantly dipolar, an assump-tion which is justified for low-mass objects (see Morin et al.,2010). The consequence would be an increased polar dischargeactivity which is triggered by an increased degree of cloudionisation due to CRs.

4. Should we expect thunderstorms in mineral dust clouds?

Brown dwarf atmospheres are the perfect example for aneutral atmosphere if thermal ionisation is considered only(Mohanty et al., 2002). Fig. 4 shows the degree of thermalionisation of the gas phase in the pressure interval where thecloud forms for three different atmosphere models. The degree ofionisation increases inward towards higher temperature due tothermal ionisation but drops rather quickly in the low pressure

Fig. 4. Degree of thermal gas-ionisation, f e,thermal ¼ pe,thermal=pgas, in the cloud for

the same three example model atmospheres like in Fig. 2. (Teff—effective

temperature of object, log(g)—surface gravity of object).

regime. This figure demonstrates that the degree of thermalionisation, f e,thermal ¼ pe,thermal=pgas, is less than 10�8. It is impor-tant to understand that although thermal ionisation does notprovide enough free charges to produce, for instance, a magneticReynolds number 41, which would indicate the atmospherespotential for coupling to the strong magnetic field of browndwarfs, the number of free electron may be large enough toproduce a streamer between two charged dust grains or a wholefront of charged dust grains (Dowds et al., 2003; Helling et al.2011a,b)

Fig. 5 shows the electric field that needs to be overcome by amineral cloud to initiate a lightning-discharge. The values forEarth (green triangle) and for Jupiter (blue square) are shown forcomparison and pressure unit check. Note that these valuesfollow the classical break-down field parameterisation as givenin Yair et al. (1995) but that field measurements above thunder-clouds suggest an electric break-down field of 1–2 orders ofmagnitude less. Clearly, the break-down is much easier in low-pressure regimes which is apparent from Fig. 5 for the studiedmodel atmospheres. Note, however, that the Paschen curvesshown in Fig. 5 would turn into the Paschen minimum ifcontinued to lower pressures before they become unphysicallyasymptotic at very low pressures.

For a given chemical composition, the break-down field is astrong function of gas pressure, therefore it is of similar orders ofmagnitude for all models which differ in gravity and effectivetemperature. All model simulations are performed for a hydro-gen-dominated gas, with H2 being the main ionised species.Hydrogen remains the most abundant molecule also in the cloudforming part of the atmosphere where far less abundant elements(e.g., Si, Fe, Mg, O) are depleted by dust formation (Fig. 4 inHelling et al., 2008b).

We conclude that mineral clouds should also be able toproduce discharge events as the break-down field is considerably

Fig. 5. The high-pressure end of Paschen curves of the break-down field strengths,

Ecrit , for three different brown dwarf and giant gas planet DRIFT-PHOENIX model

atmosphere of an initial solar element composition: Teff ¼ 1600 K, log(g)¼5.0

(brown dashed line; brown dwarf), Teff ¼ 1600 K, log(g)¼3.0 (red dashed line;

giant gas planet), Teff ¼ 2000 K, log(g)¼5.0 (brown solid line; brown dwarf). The

break-down field is calculated for a H2-rich gas in the model atmosphere

simulations of initial solar element abundances. Values for Earth (green triangle)

and Jupiter (blue square) at 1 bar are shown for comparison. (For interpretation of

the references to color in this figure caption, the reader is referred to the web

version of this article.)

Ch. Helling et al. / Planetary and Space Science 77 (2013) 152–157156

lower than on Earth and Jupiter (� 106 V=m) in the cloud formingregions. We suggest that lightning discharges should be expectedin the upper part of the atmosphere and the mineral cloud, asgravitational settling provides a mechanisms for large-scalecharge separation. Particles of different sizes fall with differentvelocities which leaves the smaller, less negatively charged (e.g.,Merrison et al., 2012) cloud particles suspended for longer in theupper cloud layers. We reached a similar conclusion in a previouspaper (Helling et al., 2011) where we compared streamer time-scales and Coulomb recombination time scales with the timescale on which dust particles pass through a previously formedelectron cloud (streamer) and, hence, potentially initiate furtherelectron avalanches. Our understanding is that a superposition ofavalanche-streamer processes will lead to more and more freeelectrons for a short time period which then may be defined aslightning. Such a superposition is more likely in the upper, low-pressure part of the cloud, too.

How much charges do we need to achieve an electric fieldbreak down? Treating a cloud as a capacitor allows to approx-imate the number of charges per m2, Q cr=A¼ Ecr � E0 (E0 - electricconstant), needed to overcome the break-down field. Fig. 6 showsthe number of charges per surface area needed to overcome the

Fig. 6. Number of charges per m2 (red and brown lines; left axis) needed to

produce the break-down field shown in Fig. 5. The overplotted (green; right axis)

lines is the energy produced during dust–dust collisions as in Fig. 2. The orange

bar indicates the interval of work functions of different materials. This figure

demonstrate where dust-grains can be charged by intra-cloud collisional

processes compared to the distribution of needed break-down charges inside

the cloud. Note that the geometrical extension of the cloud differs between brown

dwarfs and gas giants which is not reflected by the pressure scale shown in this

plot. The comparison is shown for the same three atmosphere models like in Fig. 5.

(For interpretation of the references to color in this figure caption, the reader is

referred to the web version of this article.)

break-down field is strongly height-dependent on the atmo-sphere. The atmosphere’s height is represented by the pressurescale in Fig. 6: high pressures refer to lower atmospheric heightswith high densities, and low pressures refer to the higher atmo-spheric layers with low densities. The number of charges persurface area in Fig. 6 is compared with the pressure regime inwhich dust–dust collisions are most likely producing chargeddust particles. Our results suggest that dust plays an importantrole in producing free charges in most of the cloud of cool browndwarfs, for example by triggering electron avalanches. Only afraction of the cloud can be charged by dust–dust collisions inhotter brown dwarfs and in the less-dense giant gas planetatmospheres. Note, however, that the cloud in a giant gas planetis 100� more extended than the clouds forming in brown dwarfatmospheres with high surface gravity.

5. Conclusions

Assuming that cloud particles are charged in brown dwarf andexoplanetary atmospheres, then electron avalanche processes areinitiated between two charged grains and develop to a streamer’sionisation front (Helling et al., 2011a). We have argued that alarge part of the clouds in brown dwarfs and extrasolar planets issusceptible to local discharge events which are triggered bycharged dust grains. Such discharges occur on time scales shorterthan the time required to neutralise the dust grains, and theirsuperposition might produce enough free charges to suggest apartial and stochastic coupling of the atmosphere to a large-scalemagnetic field. Discharge processes in brown dwarf and exopla-netary atmospheres should not connect to a crust as on terrestrialplanets, hence, they will experience intra-cloud discharges com-parable to volcano plumes and dust devils.

Acknowledgements

ChH acknowledges an ERC starting grant for the LEAP projectof the EU program FP7 Ideas. Most of the literature searches wasdone with the ADS. The computer support at our institutes ishighly acknowledged.

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