---
abstract: 'More than 4000 planet are known that orbit stars other than our Sun. Many harbor a dynamic atmosphere that is cold enough that cloud particles can form in abundance. The diversity of exoplanets leads to differences in cloud coverage depending on global system parameters. Some planets will be fully covered in clouds, some have clouds on the nightside but are largely cloud-free on the dayside. These cloud particles can easily be charged and lightning discharges will occur in cloudy, dynamic exoplanet atmosphere. Lightning supports a Global Electric Circuit (GCE) on Earth and we argue that exoplanet may develop a GCE in particular if parts of the exoplanet atmospheres can remain cloud free.'
address: 'Centre for Exoplanet Science, University of St Andrews, St Andrews, KY16 9SS, UKSUPA, School of Physics & Astronomy, University of St Andrews, St Andrews, KY16 9SS, UKSRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, NL'
author:
- Christiane Helling
bibliography:
- 'bib.bib'
title: Lightning in other planets
---

Introduction
============

Today, about 4070 planets are known that orbit stars other than our Sun. No Earth-twin has been found so far, instead, planets bigger than Earth (super-Earths) or bigger than Jupiter (giant gas planets), smaller than Neptune (mini-Neptune), to name a few, were discovered. Several of the known exoplanets orbit their host star very closely such that a rocky surface turns into magma or Jupiter-like exoplanets expand their atmosphere considerably. Inside the atmospheres of exoplanets, clouds form and the cloud particles (also called [*aerosols*]{}) are made of a mix of minerals, for example silicates and iron oxide [@annurev-earth-053018-060401]. Spectroscopic studies of exoplanets are repeatedly frustrated by clouds blocking the view into the underlying atmosphere to reveal the existence of potential biosignatures. Observations of the planet’s thermal emission show that the atmosphere of giant gas planets may have very dynamic global circulation [@2014Sci...346..838S] due to a strong day/night temperature difference. Although the solar system gas planets have far less dynamic atmospheres globally, lightning events are directly detected for the cloudy atmospheres of Earth, Jupiter, and Saturn, are debated for Venus, and indirectly inferred for Neptune and Uranus in our solar system. Sprites and high-energy particles are observed above thunderclouds on Earth [@2013SGeo...34....1F; @2013ERL.....8c5027F], and are theoretically predicted for Jupiter, Saturn, and Venus. On Earth, lightning measurements can be conducted in situ, but the lightning statistics for all other solar system planets are rather incomplete [@2016MNRAS.461.3927H; @2018PEPS....5...34L]. Other possible analogs for lightning on exoplanets are terrestrial volcanoes that produce lightning during an eruption inside the plume [@2000JGR...10516641J]. Studying lightning on other planets inside and outside our solar system is of interest because it enables us to study the electrostatic character of such alien atmospheres, but also opens new possibilities for tracking the dynamic behavior and the associated chemical changes in such extraterrestrial environments. The presence of an atmosphere that shelters life may enable the formation of electrified clouds and the emergence of lightning, and hence, the occurrence of an extrasolar Global Electric Circuit (eGEC). In fact, lightning discharges are also studied in other astronomical objects, in brown dwarfs and planet-forming disks [@2016PPCF...58g4003H; @2000Icar..143...87D]. The fascination of this research field lays in the universality of the underlying physical processes which would benefit from a multilateral exchange of ideas [@2016SGeo...37..705H] in contrast to siloing approaches.

Lightning in other planets inside and outside our solar system
==============================================================

How much charges are required for lightning in exoplanet clouds
---------------------------------------------------------------

Lightning occurs if an ensemble of cloud particles has acquired enough charges and if a sufficient electrostatic potential is established to overcome the local breakdown field of the atmospheric gas. A number of free electrons is needed to build an unstable ionisation front that eventually develops into the lightning plasma channel. For astrophysical purposes, the critical electric breakdown field is only marginally depending on the chemical composition of the gas (unless the gas is made of compounds of heavy elements only). The values for the minimum electric potential, $V_{\rm t, min}$, for gases (mixes of CO$_2$, N$_2$, O$_2$, H$_2$, He, CH$_4$) that dominate the solar system planets varies between $\approx 400\,\ldots\,620$V (Table 1 in [@2013ApJ...767..136H]). The solar system’s gas planets Saturn, Jupiter, Uranus and Neptune have atmospheres dominated by H$_2$/He/CH$_4$ (in this order) which is a representative starting point for extrasolar planets, too. The more challenging question is how many charges an ensemble of mineral cloud particles carries under certain environmental conditions. This question can be approached experimentally [@2014RScI...85j3903B; @2018ApJ...867..123M] or theoretically. It is tied to the cloud formation processes which determine the composition, sizes and size distribution of the cloud particles. The cloud formation process in exoplanet atmospheres is strongly affected by changing thermodynamic conditions inside the atmosphere. This results in cloud particles changing their sizes and their material composition (e.g. Fig. 3 in [@2018arXiv181203793H]): Small particles ($\approx
10^{-7}\,\ldots\,10^{-5}$cm) made of a mix of silicates and oxides (e.g. MgSiO$_3$\[s\], Mg$_2$SiO$_4$/Fe$_2$SiO$_4$\[s\], SiO\[s\], SiO$_2$\[s\], MgO\[s\], Fe$_2$O$_3$\[s\]; \[s\] stands for ’solid’) compose the upper and middle part of the clouds (T$_{\rm
  gas}<1000\,\ldots\,$1500K, $p_{\rm gas}<10^{-5}$bar ) and can grow to $10^{-4}\,\ldots\,1$cm in deeper regions with $p_{\rm gas}>1$ bar where the gas temperatures reach 1800K . These big cloud particles are made of mixes of high-temperature condensates (Fe\[s\], CaTiO$_3$\[s\], Al$_2$O$_3$\[s\], TiO$_2$\[s\]). The gas phase is collisional dominated in most of these atmosphere regions, but the cloud particles frictionally decouple quickly, hence, they fall into the atmosphere with a velocity different to that of the gas. The energy balance between frictional and latent heat, and collisional and radiative cooling results in a $\Delta T\approx 3$K only . The relative velocity between gas and cloud particles is, however, insufficient to charge the exoplanet mineral cloud particles. Turbulence driven particle-particle collisions that result from larger-scale convective-hydrodynamic motions provide the required kinetic energy to overcome the work function of the materials that the cloud particles are made of . Charges can only effectively separate between two particles by collisions [@2008SSRv..137..335S], hence, liquid droplets do not charge easily.

The critical charge density, $\sigma_{\rm crit}$, or the number of charges per cloud particle (Eq. \[eq:apart\]) or per total cloud surface per volume (Eq. \[eq:atot\]) can be estimated for a given minimal breakdown voltage, $V_{\rm t, min}$, and a geometrical distance of $d$ of two charge-carrying surfaces, $$\begin{aligned}
\sigma_{\rm crit} &=& \frac{\epsilon_0\,d\,V_{\rm t, min}}{r^2} \\
&\Rightarrow & \sigma_{\rm crib} \times A^{\rm tot}_{\rm cloud}  \,\,\,\,\,\,[e^- \mbox{cm}^{-3}]
\label{eq:atot}\\
&\Rightarrow & \sigma_{\rm crib} \times \frac{ A^{\rm tot}_{\rm cloud} }{n_{\rm d}} \,\,\,\,\,\,[e^- \mbox{grain}^{-1}].
\label{eq:apart}\end{aligned}$$ The charge distribution is assumed to be spherical and of radius $r$ (being either the cloud particle size or the cloud extension; $\epsilon_0= 8.85\,10^{12}$ F m$^{-14}$ – vacuum dielectric constant or electric permittivity of free space). $n_{\rm d}$ and $A^{\rm
  tot}_{\rm cloud}$ are the local number density of cloud particles and the total cloud particle surface per unit volume of atmospheric gas, respectively. The critical charge density per particle needed for an electric field breakdown to initiate an ionisation front as precursor for a lightning strike ranges from $10^{10}$ $e^- \mbox{grain}^{-1}$ in low-pressure regions and and $10^{5}$ $e^- \mbox{grain}^{-1}$ at higher pressures in an exoplanet atmosphere. The exact values will vary for different atmospheric conditions in different extrasolar planets. The number do, however, allow us to make some first comparison with laboratory experiments. Laboratory experiments are an essential tool to test our basic assumptions as modelling the individual charge processes of cloud particles that change size and composition remains a challenge. But also experiments come with challenges as they mainly represent Earth-like conditions with respect to thermodynamics and/or particle composition; a short summary is given in [@2013ApJ...767..136H]. Experiments on frictional electrification of KCl\[s\] and ZnS\[s\] particles [@2018ApJ...867..123M] demonstrate that they attain charge densities similar to those found on volcanic ash particles of $10^{5}\,\ldots\,10^{8}$ $e^- \mbox{grain}^{-1}$. Both are consistent with our theoretical estimates for exoplanet clouds.

How lightning leaves chemical tracers
-------------------------------------

Lightning introduces a drastic change of the atmospheric thermodynamic properties locally. Only during the first stage of the discharge process is the gas chemistry driven by kinetic processes [@2013JGRA..118.5190P] as result of the fast electrons impacting the gas phase. The chemical composition is determined by the local temperature at later stages when thermodynamic equilibrium has been reached. In thermodynamic equilibrium, the drastic increase in temperature alone cause the concentration of molecules that are generally abundant in oxygen-rich planetary atmospheres of solar element composition to drop by orders of magnitudes [@2014ApJ...784...43B]. This includes molecules involved in the formation of cloud particles like H$_2$O, SiO, MgOH, FeO, and others like TiO, CO, CH$_4$. The concentration of CH increases and larger carbohydrate molecule show a marginal increase. While lightning will locally affect the gas-phase chemistry, it is reasonable to expect that there will be no substantial feedback on the cloud formation processes other than due to creating a bulk of free electrons that can attach themselves to the surfaces of the cloud particles.

HCN is suggested to be a byproduct of lightning in the solar system giant planets [@1980Sci...210.1351L], or any discharge for that matter, that could exist long enough to potentially be observable also in extrasolar planets. HCN would be present for 2-3 yrs in the detectable, optical thin atmosphere at $\lesssim 0.1$ bar after the lightning event in the atmosphere of the exoplanet HAT-P-11b (R$_{\rm
  P}\approx 5$R$_{\rm Earth}$, M$_{\rm P}\approx 26$M$_{\rm Earth}$) [@2016MNRAS.461.1222H]. For a mJy- radio emission to be detectable at 150 MHz for HAT-P-11b, a flash rate $\sim4\times 10^5$ flashes km $^{-2}$ h$^{-1}$ is required.

The extrasolar Global Electric Circuit (eGEC)
=============================================

The presence of an atmosphere that shelters life, the formation of electrified clouds and large-scale discharges under the affect of an external radiation field lead to the emergence of a Global Electric Circuit (GEC) on Earth which impacts the daily weather and traces the global climate ([@2009AtmRe..91..140W]). A global electric circuit is an electric current between charge-separating (i.e. clouds) and non-charge-separating (i.e. cloud-free, ’fair weather’) regions in an atmospheres. The atmospheric gas in cloud-free regions has a higher conductivity than in cloudy regions, hence, a leaking current establishes, which was first discovered for Earth [@wilson1906]. Can global electric circuits occur on extrasolar planets? A global electric circuit requires an upper and a lower conducting region, charge separating processes and current flows [@2016SGeo...37..705H; @2012SSRv..168..363R; @2008pae..book...11A]. Lightning plays a key role in discharging the cloudy regions and in closing the electric current cycle by driving a return current into the upper atmosphere, the ionosphere on Earth. Without lightning, the atmosphere’s leaking current would equilibrate atmospheric potential differences quickly.

Three aspects need consideration in view of the large diversity of the known exoplanets and regarding the possibility that we may not yet be aware of all the physio-chemical processes involved. We explicitly include brown dwarfs into this discussion because they have atmospheric thermodynamic conditions comparable to giant gas planets and also form clouds in their atmospheres. [*Firstly*]{}, only exoplanets that have an atmosphere will form clouds with atmospheric lightning that creates the required return current. This excludes exoplanets comparable to Mercury in size, proximity to the host star, planetary mass and radius. According to our present knowledge, brown dwarfs always have an atmosphere. While lightning (as discharges in general) will occur in other electrified environments (like volcanoes on Earth, dust devils on Mars), we will confine ourselves to atmosphere environment to be able to benefit from knowledge about the presently known ensemble of exoplanets (and brown dwarfs). [*Secondly*]{}, we discuss the formation of an ionosphere as upper conducting regions and argue for a lower conducting region in exoplanets and brown dwarfs. [*Thirdly*]{}, we need to consider where in the exoplanet atmosphere clouds may form as this has implication for the emergence of an eGEC.

![Extrasolar planets differ largely with respect to their orbital distance, masses and radii (top) which affect the global (’calculated’) temperature (bottom). The combination of orbital distance, planetary mass, radii and global temperature provide a first indication for the presence of clouds, the possibility of lightning, and if a extrasolar global electric circuit can develop. The shaded areas are regimes of [*full cloud coverage*]{} (gray shaded) and [*particle cloud coverage*]{} (blue shaded). Lightning can occur in cloud-forming exoplanets, but a global electric circuit may establish in planets with partial cloud coverage only. Note: M$_{\rm Earth}\approx3\cdot10^{-3}$ M$_{\rm
    Jup}$, R$_{\rm Earth}\approx9\cdot10^{-2}$, R$_{\rm Jup}$ T$^{\rm
    global}_{\rm Earth}\approx250$K, T$^{\rm global}_{\rm
    Jup}\approx150$K. \[plots based on exoplanet.eu\][]{data-label="diversity"}](MassRadiusOrbit.png "fig:"){width="15.5cm"}\
![Extrasolar planets differ largely with respect to their orbital distance, masses and radii (top) which affect the global (’calculated’) temperature (bottom). The combination of orbital distance, planetary mass, radii and global temperature provide a first indication for the presence of clouds, the possibility of lightning, and if a extrasolar global electric circuit can develop. The shaded areas are regimes of [*full cloud coverage*]{} (gray shaded) and [*particle cloud coverage*]{} (blue shaded). Lightning can occur in cloud-forming exoplanets, but a global electric circuit may establish in planets with partial cloud coverage only. Note: M$_{\rm Earth}\approx3\cdot10^{-3}$ M$_{\rm
    Jup}$, R$_{\rm Earth}\approx9\cdot10^{-2}$, R$_{\rm Jup}$ T$^{\rm
    global}_{\rm Earth}\approx250$K, T$^{\rm global}_{\rm
    Jup}\approx150$K. \[plots based on exoplanet.eu\][]{data-label="diversity"}](CloudCover_exoplanetData2.pdf "fig:"){width="15cm"}\

#### Upper conducting regions: Ionisation of the upper atmosphere: 

The presence of an upper conducting region is determined by the irradiation (incl. cosmic rays) that a planet or a brown dwarf receives. This will depend on the host star (hot vs cool, active vs. inactive). For a given host star, the flux impacting the upper atmosphere will depend on the orbital distance, $a$, as $1/a^2$ between planet and star. Brown dwarfs occur as single stars in the interstellar medium and have recently been found in binary systems with white dwarfs. Both, the interstellar medium and the white dwarfs will have a larger flux of high-energy radiation than most of the presently known planet-hosting stars. The major difference for the formation of an ionosphere is therefore the ionisation process of the upper atmospheric layers. For exoplanets orbiting close to their host star, the very uppermost layers of a planetary atmosphere will be ionised by stellar photons predominantly. Their intermediate atmosphere layers will be heated by the thermal effect of photons being absorped by the atmospheric gas which leads to a gas temperature of 3500K on the dayside of super-hot Jupiter like WASP-18b or HAT-P-7b . No clouds will form here. The nightside can be 2500K colder at similar pressures and clouds can therefore form. In brown dwarfs and planets with large semi-major axis (Fig. \[diversity\]), high-energy radiation fluxes may create a shell of almost completely ionised gas in the outer atmosphere . It is therefore reasonable to assume that, similar to Earth, an electron current forms from these layers of ionised gas to the boundary layers of the clouds. The free electrons attach themselves to the surface of cloud particles which, hence, makes the gaseous charges particular immobile compared to cloud-free parts of atmospheres. The conductivity of the remaining gas phase is therefore low before the discharge, and hence, supports the electrostatic potential difference.

#### Lower conducting regions:

Exoplanets come in many sizes and temperatures (Fig.\[diversity\]), they can be rocky or have large gaseous envelope with only a small rocky core. Brown dwarfs are heavier and form as stars, hence, they are gaseous throughout. The lower conducting region is therefore, similar to Earth, the rocky surface of a rocky planet. Depending on its place in its planetary system, this surface maybe lava-like. Giant gas planets have warmer or even hot inner atmosphere temperatures of 2000K$\,\ldots\,$3500K. Warmer brown dwarfs reach temperatures of upto 4000K in their inner atmosphere. We therefore suggest that this thermally ionised inner atmosphere part of giant gas planets and brown dwarfs serves as lower, inner conducting region because thermal ionisation creates a partially ionised gas (e.g., Fig. 2 in [@2015MNRAS.454.3977R]). Ohmic heating may cause the temperature to rise further, hence, our reasoning adopts a conservative position.

#### The distribution of clouds in exoplanet atmospheres:

The global distribution of clouds in exoplanet atmospheres depends on system parameters like orbital distance, rotational period, mass, radius, global temperature (represented in Fig.\[diversity\]) and stellar spectral type as these determine the local temperature distribution inside a planet’s atmosphere. Several of the known exoplanets are tidally locked, hence, the same side of the planet always receives the highest radiation flux from the host star and the other is in permanent darkness (like the Moon). Giant gas planets like HD189733b and HD209458b with an orbital distance of $\sim0.03$AU and $\sim 0.05$AU, respectively, have a cloud cover that extends across the whole globe . Moving a little further towards the host star increases the dayside temperature of planets like WASP-18b (orbital distance of $\sim0.02$AU) such that clouds only form on the nightside and in some terminator regions. The dayside remains largely cloud free [@2019arXiv190108640H]. All known brown dwarfs that do not orbit a white dwarf will have a global cloud coverage comparable to giant gas planets like HD189733b and HD209458b. Such a cloud coverage can, however, be inhomogeneous showing holes, vortexes or banded structures depending on the atmosphere dynamic which is affected by the brown dwarf rotation rather than by an external radiation source [@2014ApJ...788L...6Z]. Recent observations have compared the banded cloud structure of a brown dwarf with that observed on Jupiter and Neptune in the Solar System [@2017Sci...357..683A].

Conclusion: Which extrasolar planetary objects are favorable for developing a extrasolar Global Electric Circuits?
==================================================================================================================

Every extrasolar planetary object, i.e. exoplanets and brown dwarfs, that harbors an atmosphere can establish a Global Electric Circuit (GEC) if lightning is possible. Lightning will occur where dynamic clouds form. This depends on the planet’s and brown dwarf’s system parameters which change as the planet / brown dwarf evolves. Given the diversity of exoplanets, detailed studies are required for individual objects but three general scenarios can be considered in order to decide which objects may be favorable for extrasolar Global Electric Circuits:

-   [*Full cloud coverage:*]{} If the exoplanet is fully covered in clouds, fair-weather regions through which a leaking current equilibrates large-scale electric potential differences will be difficult to establish but lightning may occur easily. A global circuit system might fail to establish. However, smaller circuit systems may develop on local scales. Giant gas planets that are not too close to their host star (e.g. HD189733b and HD209458b) are fully covered in clouds which extent over several vertical pressure scale heights. Repeated observations of the super-Earth GJ1214b [@2014Natur.505...69K] suggest that a geometrically thick cloud coverage is present here, too. Also most brown dwarfs may fail to establish a eGCE because they are fully covered in clouds unless they are part of a highly-irradiating white dwarf binary system.

-   [*Intermittent cloud coverage:*]{} Earth is an example for intermittent cloud coverage where cloudy and fair-weather regions characterise the atmosphere. Observations point to variable cloud properties (like height, particle size) on brown dwarfs [@2017Sci...357..683A], but it is impossible to draw conclusions about implications for the presence of fair-weather regions. No such measurements can be obtained for exoplanets with the present technology.

-   [*Partial cloud coverage:*]{} Ultra-hot giant gas planets (e.g. WASP-18b, HAT-P-7b) form clouds predominantly on their night side but no clouds on the dayside. In addition, the higher local temperature does increase the dayside’s atmospheres local conductivity compared to the nightside. Brown dwarfs that are part of a white-dwarf binary system may fall into this category (e.g. WD0137-349B [@2017MNRAS.471.1728L]), too. Both classes of objects will, hence, develop a fair-weather dayside and a cloudy, lightning producing nightside. Exoplanet objects that develop a partial cloud coverage may therefore develop a global electric circuit over larger scales than known for Earth.

The funding from the European commission is acknowledged under which part of this research was conducted. We highlight financial support of the European Union under the FP7 by an ERC starting grant number 257431.

References {#references .unnumbered}
==========
