# Aggregation and charging of mineral cloud particles under high-energy
irradiation

Nanna Bach-Møller Centre for ExoLife Sciences, Niels Bohr Institute, Øster
Voldgade 5, 1350 Copenhagen, Denmark  Space Research Institute, Austrian
Academy of Science, Schmiedelstraße 6, 8042 Graz, Austria  Institute for
Theoretical Physics and Computational Physics, Graz University of Technology,
Petersgasse 16, 8010 Graz, Austria  Christiane Helling Space Research
Institute, Austrian Academy of Science, Schmiedelstraße 6, 8042 Graz, Austria
Institute for Theoretical Physics and Computational Physics, Graz University
of Technology, Petersgasse 16, 8010 Graz, Austria  Uffe G. Jørgensen Centre
for ExoLife Sciences, Niels Bohr Institute, Øster Voldgade 5, 1350 Copenhagen,
Denmark  Martin B. Enghoff DTU Space, Danish Technical University, Elektrovej
327, 2800 Kgs. Lyngby, Denmark

###### Abstract

It is known from Earth that ionizing high-energy radiation can lead to ion-
induced nucleation of cloud condensation nuclei in the atmosphere. Since the
amount of high-energy radiation can vary greatly based on the radiative
environment of a host star, understanding the effect of high-energy radiation
on cloud particles is critical to understand exoplanet atmospheres. This study
aims to explore how high-energy radiation affects the aggregation and charging
of mineral cloud particles. We present experiments conducted in an atmosphere
chamber on mineral SiO2 particles with diameters of 50 nm. The particles were
exposed to gamma radiation in either low-humidity (RH $\approx$ 20%) or high-
humidity (RH $>$ 50%) environments. The aggregation and charging state of the
particles were studied with a Scanning Mobility Particle Sizer. We find that
the single SiO2 particles (N1) cluster to form larger aggregates (N2 - N4),
and that this aggregation is inhibited by gamma radiation. We find that gamma
radiation shifts the charging of the particles to become more negative, by
increasing the charging state of negatively charged particles. Through an
independent T-test we find that this increase is statistically significant
within a 5% significance level for all aggregates in the high-humidity
environment, and for all except the N1 particles in the low-humidity
environment. For the positively charged particles the changes in charging
state are not within the 5% significance level. We suggest that the overall
effect of gamma radiation could favor the formation of a high number of small
particles over a lower number of larger particles.

Exoplanet atmospheres (487) — Planetary atmospheres (1244) — Atmospheric
clouds (2180) — High-energy cosmic radiation (731) — Gamma-rays (637)

##  1 Introduction

One of the greatest advancements in recent years of exoplanet research is our
improved understanding of exoplanet atmospheres. A major step in this regard
has been the recognition of the critical role cloud formation plays in the
energy balance and chemistry of atmospheres. Exoplanets, as well as many Solar
System objects, display a wide variety of cloud particles that differ greatly
from the cloud formation observed on Earth. In addition to the various water,
ammonia, and condensed hydrocarbon clouds, that are among the many cloud types
observed in the atmospheres of Solar System objects (e.g. Baines et al.
(2009); Brooke et al. (1998); Brown et al. (2002); Gao et al. (2021); Ohno et
al. (2021); Rages & Pollack (1992); Romani & Atreya (1988); Sagan et al.
(1992); Sromovsky et al. (2011); Wong et al. (2017)), studies predict a wide
range of mineral clouds in warmer exoplanet atmospheres (e.g. Gao et al.
(2021); Helling (2020, 2022); Marley et al. (1999); Seager & Sasselov (2000)),
which is believed to greatly influence our observations of these planets (Gao
et al., 2021; Helling, 2022).

One of the less understood aspects of cloud formation, is the effects of the
radiation field from the host star and the influx of high-energy particles
into the atmosphere. Exoplanets are exposed to two major sources of high-
energy particles: stellar energetic particles, and galactic cosmic rays
(reviewed in Rodgers-Lee et al. (2021)). Stellar energetic particles (SEPs,
also known as stellar cosmic rays) are high-energy particles irradiated by the
host star either during stellar flares, or as particles accelerated by the
shock front of coronal mass ejections (Wild et al. (1963); Reames (2013);
Rodgers-Lee et al. (2020)). Galactic cosmic rays (GCRs) are high-energy
particles originating from outside the system, that travel trough
interplanetary space before they reach the planet.

Since younger and more active stars generally have strong magnetic fields and
thereby more stellar flares (as reviewed by Getman & Feigelson (2021)), the
radiative environment around e.g. M-dwarfs will be very different from that of
the Solar System both in relation to SEPs and GCRs. Studies have found that
the high magnetic activity of M-dwarfs causes them to release higher fluxes of
SEPs (Rodgers-Lee et al., 2021; Fraschetti et al., 2019) due to the strong
stellar winds. At the same time, the propagation of GCRs through the stellar
wind has long been studied (Parker, 1965; Jokipii, 1971; Rodgers-Lee et al.,
2020), and it has been found that host stars with strong magnetic fields can
shield their planets from GCRs (as reviewed in e.g. Nandy et al. (2021)). An
exoplanet around an M-dwarf host will therefore have a different influx of
high-energy particles, and in order to understand the atmospheres of these
planets, we need to understand the effect of high-energy radiation.

High-energy particles have been shown to have a significant effect on the
atmosphere as a whole. Based on models, it has been predicted that SEPs can
observably alter the chemical composition of exoplanet atmospheres (Barth et
al., 2021; Chadney et al., 2017; Venot et al., 2016), and destroy potential
ozone layers in Earth-like atmospheres (Segura et al., 2010). The effect of
high-energy particles on cloud formation has been studied extensively for
Earth’s atmosphere, and it has been found that there is a significant
correlation between the influx of high-energy particles and the degree of
cloud formation (Dickinson, 1975; Svensmark & Friis-Christensen, 1997; Marsh &
Svensmark, 2000; Svensmark et al., 2021). As high-energy particles reach the
atmosphere, they form so called cosmic ray showers, where the particles
interact with the gas under the release of gamma rays resulting in an
ionization of the gas. The increased presence of ions has been found to
stabilize and promote the growth of molecular clusters in Earth’s atmosphere,
leading to ion-induced nucleation of cloud particles (Lee et al., 2019; Wagner
et al., 2017). A series of studies (Svensmark et al., 2013; Enghoff &
Svensmark, 2017; Svensmark et al., 2020) have looked at ion-induced nucleation
by imitating high-energy particles using gamma radiation. Svensmark et al.
(2013) found that gamma irradiation increases the nucleation of H2SO4 clusters
from the gas-phase, and induces the nucleated clusters to grow to 50 nm sizes.
Using a similar experimental setup, Enghoff & Svensmark (2017) found that
gamma radiation changes the charging state of the particle population and that
particles react differently to gamma radiation depending on their size and
polarization. Enghoff & Svensmark (2017) suggest that different ions
participate in the charging of positively and negatively charged particles,
and that the differences in the size and mobility of these ions will affect
the charging of the particles by the gamma irradiation.

The effect of high-energy radiation is known to also apply to particles very
different from the ones participating in Earth-like cloud formation (e.g.
metallic nanoparticles Abedini et al. (2013)), indicating a relevance to
fields other than cloud formation. One such example could be the study of
interplanetary dust. Interplanetary dust has long played an important role in
solar system space mission (Grün et al., 1992; Jorgensen et al., 2021), and an
improved understanding of the effect of the radiation environment on particles
could be highly beneficial for future solar system missions, such as Comet
Intercepter (Snodgrass & Jones, 2019), and for our understanding of dust in
planetary systems as a whole.

So far, the effect of high-energy particles on cloud formation has mostly been
studied for the initial molecular nucleation from the gas phase of volatile
species characteristic to the atmosphere of Earth. The aim of this study is to
expand on previous studies, by answering the question of how high-energy
radiation affects the aggregation and charging of already formed mineral cloud
particles. The mineral cloud particles investigated in this study, SiO2, are
relevant both as mineral cloud species on gaseous exoplanets, AGB Stars and
Brown Dwarfs, and as cloud condensation nuclei in Earth-like atmospheres Lee
et al. (2016); Helling et al. (2006).

The experimental setup used in this study is similar to the setup used
previously by Enghoff & Svensmark (2017) and Motzkus et al. (2013), and is
described in Sec. 2. In Sec 3 we present the results of: the general size
distribution of the particles (Sec 3.1), the effect of gamma radiation on the
aggregation of the particles (Sec. 3.2), the effect of gamma radiation on the
charging state of the particles (Sec. 3.3), and the effect of humidity on both
charging and aggregation (Sec. 3.4). In Sec. 4 the results are discussed in
relation to their implication on the population of exoplanet atmospheres.

##  2 Methods

Figure 1: Experimental setup. The process begins with aerosol production
(lower left), continues to the atmosphere chamber (right), and ends with
measurements at the SMPS system (upper left). Arrows mark the airflow through
the system.

The main purpose of the experimental setup is to address the question of how
mineral cloud particles are affected by high-energy radiation. This is
addressed by releasing mineral particles from a liquid solution and introduce
them into an atmosphere chamber where they are irradiated with gamma
radiation. The effect of the gamma radiation on the particle size and charging
state is measured based on their mobility in a known electric field. A single
experiment in this study consists of 50 individual size distribution
measurements, each with a scan time of 240 s, taken consecutively,
corresponding to a total of $\sim$3.5 hours of measurements for each
experiment.

###  2.1 Setup

The experimental setup can be separated into three parts: a) The production of
aerosols (bottom left in Fig. 1). b) The chamber (right in Fig. 1). c)
Measurements using a Scanning Mobility Particle Sizer, SMPS (top left in Fig.
1),

Universal settings for all experiment
---
Scan up time | 180 s
Scan down time | 60 s
Sheath flow | 3 L/min
CPC flow | 0.3 L/min
Multiple charge correction | ON
Particle number density in atomizer |  $\sim 7\cdot 10^{9}$ mL-1
Particle number density in chamber |  $\sim 7\cdot 10^{3}$ cm-3
Total N2 flow to chamber | 16 L/min

Specific settings for each experiment
---
Nr.a | Chargeb | Gammac | Bipolar chargerd | RH | Duratione | Repetitionsf
1 | Pos | No | Yes | $\sim 20\%$ | 3.5 | 6
2 | Pos | No | No | $\sim 20\%$ | 3.5 | 6
3 | Pos | Yes | Yes | $\sim 20\%$ | 3.5 | 6
4 | Pos | Yes | No | $\sim 20\%$ | 3.5 | 6
5 | Neg | No | Yes | $\sim 20\%$ | 3.5 | 6
6 | Neg | No | No | $\sim 20\%$ | 3.5 | 6
7 | Neg | Yes | Yes | $\sim 20\%$ | 3.5 | 6
8 | Neg | Yes | No | $\sim 20\%$ | 3.5 | 6
9 | Neg | No | Yes | $\sim 20\%$ | 20 | 1
10 | Neg | Yes/No | Yes | $\sim 20\%$ | 30 | 1
|  |  |  |  |  |
11 | Pos | No | Yes | $\sim 65\%$ | 3.5 | 3
12 | Pos | No | No | $\sim 65\%$ | 3.5 | 3
13 | Pos | Yes | Yes | $\sim 65\%$ | 3.5 | 3
14 | Pos | Yes | No | $\sim 65\%$ | 3.5 | 3
15 | Neg | No | Yes | $\sim 65\%$ | 3.5 | 3
16 | Neg | No | No | $\sim 65\%$ | 3.5 | 3
17 | Neg | Yes | Yes | $\sim 65\%$ | 3.5 | 3
18 | Neg | Yes | No | $\sim 65\%$ | 3.5 | 3
19 | Pos | Yes/No | Yes | $\sim 50\%$ | 22 | 1

  * a

Identifier for type of experiment.

  * b

Electric charge of measured particles.

  * c

Irradiation with gamma radiation.

  * d

Specifies whether measurements were done with the bipolar charger (yes) or the
dummy (no)

  * e

Total duration of each experiment in hours.

  * f

Number of repetitions of experiments with these settings.

Table 1: Settings for experiments. Top part shows universal settings for all
experiments. Bottom part shows experiment-specific settings for low-humidity
(Nr. 1-10) and high-humidity (Nr. 11-19) environments respectively.

####  2.1.1 Aerosol production

The experiment is started by separating and releasing SiO2 particles from a
liquid solution, to form non-interacting aerosols in an airflow with as low
humidity as possible. The sample used is MSP NanoSilica™; an aqueous
suspension of amorphous SiO2 particles with a highly uniform size distribution
around diameters of 50 nm.

The sample is lowered into a sonic bath to ensure separation of the particles
in the suspension, before it is diluted in Milli-Q water (water that has been
purified and deionized using a Millipore Milli-Q lab water system) to a number
density of $\sim 7\cdot 10^{9}$ particles per mL. The particles are released
from the aqueous suspension by exposing the sample to a jet of compressed air
using an atomizer (TSI 3076). This converts the SiO2 water solution into an
aerosol spray where the individual particles are moving, well separated, with
the air flow.

The atomizer is operated in re-circulation mode using a flow of clean dry
nitrogen at a rate of 3 L/min. To decrease the humidity of the air flow, the
flow from the atomizer is diluted with an extra flow of 1 L/min nitrogen and
led through a diffusion dryer (TSI 3062), lowering the relative humidity from
$\sim 100\%$ to $\sim 60\%$.

####  2.1.2 Atmosphere chamber

The aggregation and gamma irradiation of the particles takes place in the
atmosphere chamber, where the aerosol flow is introduced with an additional
airflow of 12 L/min clean nitrogen from a Parker Midigas 6 nitrogen generator
with a O2 content of max. 10 ppm. The lowest relative humidity in the chamber
from the combined air flows from the nitrogen generator and atomizer is $\sim
20\%$. The humidity can be further increased by passing the nitrogen air
through a humidifier. The final gas composition of the chamber is therefore N2
and H2O. The atmosphere chamber has the dimensions $2m\times 2m\times 2m$, and
is primarily made of stainless steel (with the exception of one side made of
teflon to allow for experiments with UV). All experiments in this study are
conducted at approximate room temperature (around 21-23 ∘C) and slightly above
atmospheric pressure (differential pressure of $\sim$0.2 mbar to the
surroundings) to prevent the inflow of contaminating air from outside the
chamber. The chamber has previously been described by Svensmark et al. (2013).
Two gamma sources (27 MBq Cs-137) are located on opposite sides of the
chamber. The level of irradiation can be controlled by varying the shielding
of the radiation sources, resulting in ion production rates ranging from
16-200 cm-3s-1.
Introducing the particles into the chamber at a steady rate, it takes
approximately 10 hours for the particle number density to reach a steady
state. All measurements are therefore taken 15 hours or more after the first
introduction of the particles. Similarly, if there was a change in the
irradiation of the chamber, at 30 minutes or more were allowed to pass before
further measurements were taken, in order for the ionization to be allowed to
take place. Over time particles will leave the gas phase through collision
with the chamber walls which happens with a rate of $<$0.05 per hour, see
appendix A.

####  2.1.3 SMPS Measurements

In order to determine the potential changes in particle size and charge
distribution the electric mobility distribution of the particles is measured.
The measurements are done using a Scanning Mobility Particle Sizer (SMPS)
system consisting of an Electrostatic Classifier and a Condensation Particle
Counter (CPC), as seen in the upper left of Fig. 1.

The principle behind the SMPS system is the correlation between the size and
charge of the particles and their electrical mobility. The electrical mobility
($Z_{p}$) reflects the ability of a particle to move through an electric field
as described by:

$Z_{p}=\frac{neC}{3\pi\mu D_{p}}$ (1)

Where $n$ is the number of elementary charges on the particle, $e$ is the
elementary charge, $C$ the Cunningham slip correction (that is depending on
the gas mean free path which is calculated continuously and $D_{p}$), $\mu$
the gas viscosity, and $D_{p}$ the particle diameter (TSI Incorporated, 2009).
For small particles or aggregated clusters the particle cannot be assumed to
be spherical and $D_{p}$ will instead be defined as the mobility diameter. The
relationship between the electrical mobility and the parameters of the
Classifier has been determined to (Knutson & Whitby, 1975):

$Z^{*}_{p}=\frac{q_{sh}}{2\pi\bar{V}L}ln\left(\frac{r_{2}}{r_{1}}\right)$ (2)

Where Z${}^{*}_{p}$ is a set mobility, qsh is the sheath flow rate, $\bar{V}$
is the average voltage used for the DMA, L is the distance between the exit
slit and the aerosol inlet in the DMA, and r1 and r2 are the inner and out
radius of the annular space in the DMA.

Combining Eq. 1 and Eq. 2, the particle diameter can be related to the number
of charges on the particles, the collector rod voltage, the flow rate of the
classifier, and the geometry of the DMA (TSI Incorporated, 2009):

$\frac{D_{p}}{C}=\frac{2ne\bar{V}L}{3\mu
q_{sh}ln\left(\frac{r_{2}}{r_{1}}\right)}$ (3)

As can be seen from Eq. 3 the mobility diameter of a particle can be found
based on the charge of the particle and the instrumental setup of the
classifier. The electrostatic classifier obtains a known charging distribution
using a Kr-85 Bipolar Charger (also called a neutralizer). The bipolar charger
ionizes the air and thereby expose the particles to high concentrations of
bipolar ions. Through collisions with these ions the particles themselves are
brought into a known steady-state bipolar charge distribution, where a fixed
percentage of the particles will carry none, one, or multiple charges. The
charged particles are passed into a Long Differential Mobility Analyzer (DMA)
(TSI 3081), where an electric field allows only particles in a specific
electric mobility range to pass through. As the electric field is varied the
particles are being sorted based on their mobility and and the number density
of particles within each mobility range is measured by a Condensation Particle
Counter (CPC) (TSI 3775). Accounting for the known charge distribution
implemented by the bipolar charger (Wiedensohler, 1988) this gives us a
mobility diameter distribution of the particle population. The Electrostatic
classifier is operated with a sheath flow of 3 Lmin-1, the CPC was operated on
low-flow mode at 0.3 Lmin-1, and the long DMA was set to a size range of
13-500 $nm$. Scan times were chosen for the SMPS based on the flow rates and
desired particle size range in addition to the CPC response time. The scan up
time, determining the time spent by the classifier to increase the voltage
over the DMA, was set to 180s, whereas the scan down time, determining the
time taken by the classifier to return to the initial voltage, was set to 60s.
This scan time of a total of 240s is in accordance with the settings
previously used by (Motzkus et al., 2013) to measure SiO2 particles using a
similar setup. The final size distributions are found by averaging over 50
consecutive scans as explained in Sec. 2.2.

In order to study the charging of the SiO2 particles the charging state is
calculated. The charging state is a measure of the charge of the particle
population in relation to the steady-state charge distribution implemented by
the Kr-85 bipolar charger (Laakso et al., 2007). This is done by replacing the
neutralizing Kr-85 charger with a non-neutralizing ”dummy”, that is identical
to the charger but with no Kr-85 source (as explained in Enghoff & Svensmark
(2017)). While using the ”dummy” the particles will maintain their original
charges from the chamber, and the measurements will reflect these charges in
addition to the particle sizes. The charging state is calculated by dividing
measurements performed with the dummy with identical measurements performed
with the Kr-85 bipolar charger.

Since the electric field of the DMA will sort for either positively or
negatively charged particles, these will be measured separately in the SMPS
system. The polarity of the particles being measured is decided by changing
the power supply in the classifier, such that a positive power supply will
result in the negatively charged particles being measured, and a negative
power supply will result in the positively charged particles being measured
(Enghoff & Svensmark, 2017).

###  2.2 Evaluation of measurements

All results in this study are based on size distribution measurements done
with the SMPS. Based on these measurements we calculate: average size
distributions of different ”experiments”, number density of different
aggregates, and charging states, all with associated uncertainties.

Size distribution of experiment: A single experiment in this study consists of
50 individual size distribution measurements (scans) taken consecutively by
the SMPS. The number density for each measurement is found from the normalized
concentration measured by the SMPS (nN/dlogDp) by multiplying it with the
difference in the log of the size bin width. The final size distribution of
each experiment is found as the average of the 50 consecutive measurements.
The standard deviation of each experiment was found from the standard error of
the mean for each size bin.

Number density of aggregates: As shown in Fig. 2 and explained in Sec. 3.1,
the size distribution shows distinct peaks, indicating aggregates of different
sizes. The number of aggregates of each size is found as the sum of measured
particles within the full width half maximum (FWHM) of the peak. The
uncertainty is found from through linear error propagation from the the
standard deviation of each size bin in the size distribution of the
experiment.

Charging state: In order to calculate the charging state, two experiments are
performed after each other, one with the K-85 bipolar charger and one with the
dummy (e.g. experiment 1 and 2 in Tab. 1). The number density of each
aggregate size for each of the experiments is calculated, and the charging
state is found as the number of particles from the measurement with the dummy
divided by the measurement with the bipolar charger. A charging state of 1.0
would indicate that the aggregates in the chamber follow the same steady-state
charge distribution as implemented by the bipolar charger. Charging states
different from 1.0 indicate that the particles deviate from the steady-state
distribution, thereby indicating that the aggregates are actively being
charged. Values above 1.0 indicate an overcharge of the particles (a higher
number of charged particles than in the steady-state), and values below 1.0
indicate an undercharge of the particles (a lower number of charged particles
than in the steady-state). The uncertainty of each charging state calculation
is found using the standard formula for error propagation from the
uncertainties of the particle number densities. For each of the four settings
(positively or negatively charged particles, with or without gamma-
irradiation), the charging states for each of the aggregates are averaged
among the repeated experiments. The uncertainties for the averages are found
in two ways: 1) Error propagation of the errors of each charging state. 2) The
standard deviation among the repeated experiments.

The error bars shown in the figures indicate one standard deviation.

##  3 Results

In this section we show the results for the charging state and aggregation of
positively and negatively charged particles respectively. The results have
been obtained through at number of repeated experiments, all listed in Tab. 1.
The results presented in Sec. 3.1 \- 3.3 are all done in low humidity
environments (RH $\approx$ 20%), whereas the experiments in Sec. 3.4 are done
at higher humidity (RH $>$ 50%).

###  3.1 Size distribution

Figure 2: Size distribution of negatively charged particles measured with and
without bipolar charger. Red shading indicates standard deviation among the 50
measurements constituting each experiment. Shows one repetition of experiment
nr. 5 in Tab. 1. Figure 3: Comparison of size distribution of positively and
negatively particles respectively. Both measurements are done with the bipolar
charger. Red shading indicates standard deviation among the 50 measurements
constituting each experiment. Shows one repetition of experiment nr. 5 and 6
in Tab. 1.

An example of the size distributions measured by the SMPS can be seen in Fig.
2. The two size distributions show experiments with and without the bipolar
charger for the negatively charged particles. Measurements with the bipolar
charger illustrate the actual size distribution of the particles, while
measurements without the charger (dummy) also reflect the inherent charging of
the particles.

The size distributions show 3-4 distinct peaks corresponding to the original
particles (with diameters of d $\approx$ 50 nm) and aggregates of two, three
and four particles (i.e. N1, N2, N3, and N4). The mobility diameters of the
aggregates, as shown on the primary axis, do not correspond exactly to
physical diameter, but rather describe the mobility of the aggregates through
the electric field of the DMA, which depends on the physical diameter as
described in Sec. 2.1.3. The plots in Fig. 2 and 3 show only the relevant
mobility diameter range for the SiO2 aggregates and thereby exclude features
at lower mobility diameters caused by e.g. the Milli-Q water. By comparing the
distribution with and without the bipolar charger for these peaks we see that
more particles are being measured with the charger, indicating that there are
fewer negatively charged particles in the population than we would expect from
the steady-state bipolar charge distribution. This will be further discussed
in Sec. 3.3.

The particles get their positive or negative charge from collisions with ions
in the gas phase. Since the positive and negative ions can have different
mobility (Hõrrak et al., 1998), the ions with the highest mobility will
participate in more collisions, which can affect both the number of charged
particles and their mobility through the DMA in the SMPS system. Fig. 3
illustrates the size distribution of the positively and negatively charged
particles respectively. As can be seen the distributions differ slightly, both
in regard to the particle count and the position of the peaks. The
measurements show a higher number of negatively charged particles at around 50
nm. We also see that the distribution for the negatively charged particles is
shifted slightly towards higher diameters, indicating that their mobility in
the DMA is lower than for the positively charged particles. These differences
are not a major concern as charging state calculations are relative.

###  3.2 Aggregation over time

Figure 4: Number densities of single particles, N1, and each of the
aggregates, N2-N4, over time. Shows experiment nr. 9 in Tab. 1 Figure 5:
Effect of gamma radiation on the aggregation of particles in a low-humidity
environment (RH $\approx$ 20%). A) Number density of single particles, N1, and
each of the aggregates, N2-N4, over time . Arrows indicate the presence of
absence of gamma radiation. B) The change in number density found as the slope
of linear fits for each radiation setting shown in (A) in relation to the
initial slope. Each linear fit is started 30 min after the change in radiation
(gamma being turned on or off), in order to allow for ionization to take
effect, and ended just before the next change. Dashed line at 0.0 indicates no
change in particle number. Show experiment nr. 10 in Tab. 1

As shown in Fig. 2, the original d $\approx$ 50 nm particles (N1) introduced
into the chamber aggregate to form larger clusters of two to four particles
(N2-N4). In order to assess the aggregation of the particles, Fig. 4 shows the
number of each aggregate over time, as defined from the full width half
maximum of the peaks in the size distributions. As can be seen from the figure
the number density of the N1 particles increases steadily up to $\sim$10 hours
after the introduction of the particles. In comparison the number of larger
particles keeps increasing even after the curve for N1 particles have reached
a plateau.

In order to study the effect the gamma radiation on the aggregation of the
particles we looked at the change in the production rate of the particles
before and after gamma radiation was introduced. Fig. 5A, shows how the number
of each aggregate changed with the introduction of gamma radiation. To get a
clearer view of especially the larger aggregates linear curves were fitted to
the data points shown in Fig. 5A, after each change in gamma radiation. The
change in the slopes of each linear fit can be seen in Fig. 5B. Linear fits
were made for each change in the gamma radiation, corresponding to the
sections between the arrows in Fig. 5A and the sections before and after the
first and last arrow respectively. Each linear fit was started 30 min after
the change in radiation in order to allow for the ionization of the gas in the
chamber to adapt to the change. The values plotted in Fig. 5B are calculated
as the slopes of these linear fits subtracted from the initial slope before
the first change in radiation. Here we notice a trend for gamma radiation to
cause an increase in the number of single particles (N1) and a decrease in the
number of aggregates (N2-N4). Similarly, turning the gamma radiation off
caused a decrease in the number of single particles (N1) and an increase in
the number of aggregates (N2-N4). This indicates that gamma radiation inhibits
the aggregation of the particles.

###  3.3 Charging state

Figure 6: Charging state of positively (A) and negatively (B) charged
particles. A1 and B1 show charging state of all repeated experiments with
error bars indicating propagated errors. A2 and B2 show average charging
states for each aggregate, with dark error bars indicating propagated errors
(notice that they are so small that they fit within the data points), and
light error bars indicating standard deviation among repeated experiments.
Horizontal dotted line at 1.0 indicates bipolar charge distribution. Show
experiments nr. 1-8 in Tab. 1

As explained in Sec. 2.1.3 the charging state is a measure of the fraction of
charged particles in the population compared to the fraction of charged
particles in a steady-state bipolar distribution. As such the charging state
indicates the charging relative to a standard distribution, and potential
changes in the charging state due to irradiation with gamma radiation can
indicate how high-energy radiation affects the overall charging of the
particle population.

Fig. 6 shows the charging state, individually and averaged, of all experiments
of positively and negatively charged particles respectively, Each plot shows
the charging state for both non-irradiated particles, and particles irradiated
with gamma radiation. The experiments plotted are listed in Tab. 1.
Experiments with and without bipolar charger are done consecutively, and
charging states are calculated for each pair. A total of six individual
charging state measurements are plotted in A1 and A2 and used to find each
average shown in the figures A2 and B2.

For the non-irradiated case, the positively charged particles in Fig. 6A2 have
charging states just above the steady-state distribution, as illustrated by
the horizontal dotted line. This corresponds to a slight overcharging of the
particles, and indicates that there are more positively charged particles than
expected from the steady-state distribution. Gamma radiation decreases the
number of positively charged particles, thereby lowering the charging state,
resulting in the particle population becoming undercharged compared to the
steady-state distribution.

For the non-irradiated case, the negatively charged particles in Fig. 6B2
generally have charging states below the horizontal line, indicating a lack of
negatively charged particles in the population compared to the steady-state
distribution. Gamma radiation increases the number of negatively charged
particles, bringing the charging state close to the steady-state distribution.

Both plots’ averages in Fig. 6 indicate a shift towards more negatively
charged particles in the population as a result of the gamma radiation.

####  3.3.1 Statistical T-test of charging states

In order to test the effect of gamma radiation on the particles we compare the
mean charging state of irradiated and non-irradiated particles. Since the test
needed would be a comparison of the means of two independent samples, an
independent T-test was chosen. The test was performed for positively and
negatively charged particles separately, and the samples tested correspond to
the data plotted in Fig. 6 A1 and B1.

| N1 | N2 | N3 | N4
---|---|---|---|---
Positively charged | 0.31 | 0.33 | 0.16 | 0.16
Negatively charged | 0.07 | 0.04 | 0.02 | 0.03
Table 2: P-values for t-test of two independent samples comparing irradiated
and non-irradiated particles. Low-humidity environment, Fig. 6.

The probability values (p-values) from the T-test are shown in Tab. 2. For the
positively charged particles we find p-values that are all outside the a
significance level of 5% (i.e. all p-values are above 0.05). For the
negatively charged particles, most of the aggregates have p-values within a
significance level of 5%, the only exception from this is the N1 particles
showing a p-value of 7%. These results indicate that the effect of gamma
radiation seen for the average charging states shown in Fig. 6 is
statistically significant for the negatively charged particles (B2), but not
for the positively charged particles (A2).

###  3.4 Relative humidity

Figure 7: Experiments conducted in a high humidity environment (RH $>$ 50%).
A) Number densities of aggregates over time. The change in density caused by
gamma radiation is shown in A2 as slopes from linear fits for the different
radiation settings as marked by arrows in A1. Experiment nr. 19 in Tab. 1. B)
Average of the charging states calculated for each of the repeated experiments
(nr. 11-18 in Tab. 1). B1 shows the positively charged particles, and B2 shows
the negatively charged particles. Dark error bars indicate propagated errors
(notice that they are so small that they often fit within the data points),
and light error bars indicate standard deviation among repeated experiments.

As mentioned in Sec. 2 the lowest relative humidity reached in the chamber was
RH $\approx$ 20%, and all measurements in the previous sections were done at
this RH value. In order to test the effect of relative humidity on the
aggregation and charging of the particles a set of experiments were repeated
at higher relative humidities with RH $>$ 50%. The experimental settings can
be seen in Tab. 1 (nr. 11-19), and the results are shown in Fig. 7. The top
row of the figure, A1 and A2, shows that gamma radiation also inhibits the
aggregation of the particles in a high-humidity environment, similarly to the
low humidity cases in Fig. 5. Fig. 7A, show a trend of an increase in the
number of N1 particles under irradiation with gamma, similarly to what was
seen for the low-humidity case. The changes observed for the N1 particles
shown in Fig. 7A2 are even more pronounced than those seen for the low-
humidity case in Fig. 5B, with average changes in slopes of $\sim$250 $\pm$ 60
cm-3hr-1 in high humidity compared to $\sim$170 $\pm$ 20 cm-3hr-1 in low
humidity. The trend for the aggregates (N2-N4) is less clear in this high-
humidity case compared to the low-humidity. The bottom row of Fig. 7, B1 and
B2, show the average charging states of positively and negatively charged
particles respectively, corresponding to the low-humidity cases, Fig. 6A2 and
Fig. 6B2. The positively charged particles in Fig. 7B1 show a general trend
for the irradiated particles to be more undercharged than the non-irradiated
particles. This indicates that the number of positively charged particles
decreases under gamma radiation. The opposite trend is seen for the negatively
charged particles in Fig. 7B2, where the irradiated particles are
significantly more overcharged compared to the non-irradiated particles
indicating an increase in the number of negatively charged particles under
gamma radiation. Both these trends are similar to what was seen in the low-
humidity environment, where gamma radiation was observed to shift the
particles population towards a more negative charge.

To test the statistical significance of the effect of gamma radiation on the
charging state in a high-humidity environment a T-test was performed, and the
resulting p-values can be seen in Tab. 3. For the positively charged particles
it is found that the effect of gamma radiation is not statistically
significant for most of the aggregates (the exception being the N1 particles).
For the negatively charged particles it is found that the effect of gamma
radiation is statistically significant for all aggregates, with p-values that
are well within the 5% significance level. The fact that the changes caused by
gamma radiation are more statistically significant in the high-humidity
environment, could indicate that the increase in the number of negatively
charged particles is more pronounced at higher humidity.

| N1 | N2 | N3 | N4
---|---|---|---|---
Positively charged | 0.05 | 0.11 | 0.64 | 0.60
Negatively charged | 0.03 | 0.02 | 0.04 | 0.02
Table 3: P-values for t-test of two independent samples comparing irradiated
and non-irradiated particles. High-humidity environment, Fig. 7 B1 and B2.

##  4 Discussion

If we wish to understand exoplanets in different planetary systems it is
important to understand how the radiation field of the host star influences
the exoplanet atmospheres. Here high-energy radiation plays an important role.

The radiation environment caused by the host star and galactic environment has
been found to have an impact on both dynamics, chemistry, and climate of
exoplanets (reviewed by e.g. Airapetian et al. (2020)). High-energetic
particles, such and cosmic rays and SEPs, have been found to affect both the
chemical composition (Barth et al., 2021) and ionization (Rodríguez-Barrera et
al., 2018) of the atmospheres. Due to the importance of ionization and
charging in ion-induced nucleation (Wagner et al., 2017), high-energetic
particles might play a significant role in cloud formation in environments
with low presence of primary aerosols (Jokinen et al., 2018), such as gas
planets.

The majority of all stars in the Milkyway are M-dwarfs, and given our current
observation biases, these make for interesting targets for transit
observations of exoplanets in the habitable zone (Mesquita et al., 2021a). Due
to the low luminosity of M-dwarfs their habitable zone is very closer to the
star (Kasting et al., 1993; Selsis et al., 2007), which allows for smaller
planets to be observable in the habitable zone. M-dwarfs have been found to
remain magnetically active for longer than Sun-like stars (West et al., 2004;
Scalo et al., 2007; Guinan et al., 2016), which creates a very different
radiative environment than in the Solar System. The high activity causes the
stars to have stronger flares (Vida et al., 2017; Tilley et al., 2019), and
release more stellar energetic particles and gamma radiation (Grießmeier et
al., 2005; Obridko et al., 2020; Sadovski et al., 2018; Fraschetti et al.,
2019). Exoplanets in these systems might therefore be exposed to a higher
degree of high-energy radiation from the host star, both due to the higher
activity and due to the potentially closer proximity to the star.

The exact correlation between the activity of the host star and the total
influx of high energy radiation to an exoplanet is, however, nontrivial. While
the particle influx from the star itself increases with stellar activity, the
corresponding increase in magnetic flux and stellar wind has also been found
to shield the system from the influx of GCR from outside the system (Mesquita
et al. (2021a, b); Nandy et al. (2021), and reviewed in e.g. Potgieter
(2013)). The nature of the high-energy particles in a system will therefore
change depending on the activity of the host star during its evolutionary
phases, such that SEPs might be dominating during the younger active phase of
the star, while GCRs will be dominating later in the evolution or for less
active stars (Rodgers-Lee et al., 2021).

In this study we imitate the high-energy radiation of SEPs and GCRs with gamma
radiation, similarly to what has been done previously (Enghoff & Svensmark,
2017). Gamma radiation is one of the products released in the interaction
between SEPs and GCRs and celestial atmospheres, and high-energy particles
will therefore release gamma radiation both from the host star and from the
atmosphere of the planet itself, making the Earth atmosphere a bright source
of gamma radiation (as reviewed by e.g. Mazziotta et al. (2020) and Dean et
al. (1988)). The Cs-137 sources used in this study release gamma radiation
with energies of 0.66 MeV which lies within the energy range of SEPs and low-
energy GCRs (e.g. Barth et al. (2021)) as well as the range of cosmic ray
showers caused by higher energy GCRs. The duration of each experiment has been
determined by the scan times and number of desired consecutive measurements,
and the chamber has therefore been irradiated with gamma radiation for periods
of $\sim$4 hours at a time. This is longer than the average SEP event, but
still lies well within the general time scales from minutes to hours (e.g.
Firoz et al. (2022); Doyle et al. (2018); Reep & Knizhnik (2019)),while the
influx of GCRs is more continuous. It should be noted that studies have found
that in the case of ion-induced nucleation the nature of the ionizing
radiation is not important as long as the ionizing effect is the same (Enghoff
et al., 2011).

The aim of this paper has been to study how the aggregation and charging of
mineral cloud particles are affected by high-energy radiation and humidity.
Using experiments with SiO2 particles in an atmosphere chamber we observed two
trends: 1) gamma radiation inhibits the aggregation of the particles, and 2)
gamma radiation causes a higher number of particles to become negatively
charged. These trends, of less aggregation and more negative charge, are
observed both in environments with lower relative humidity (RH $\approx$ 20%)
and higher relative humidity (RH $>$ 50%).

The coupling between the effects of gamma radiation (i.e. the inhibited
aggregation and the negative charge of the particles) is uncertain, but it
might be related to a change in the mobility of the particles. As can be seen
from Fig. 3, the mobility size of the negatively charged particles is slightly
larger than for the positively charged particles. As the mobility diameter is
linked to the size of the particles, as described in Sec. 2, this indicates a
slight difference in the size of the positively and negatively charged
particles with the negatively charged particles being larger. Since the gamma
radiation leads to an increase in the number of negatively charged particles
it leads to an overall increase in particle size in the chamber. At these
particle sizes the coagulation coefficient between similar sized particles
decreases with increasing particles size (Fujimoto et al., 2021; Fuchs, 1964)
leading to fewer collisions overall in the chamber. Thus the decrease in
aggregation might be linked to a decrease in the number of collisions caused
by a lower mobility of the negatively charged particles. It is uncertain what
causes the difference in mobility diameter between negatively and positively
charged particles in this study.

The effect of gamma radiation on the charging state, as shown in Fig. 6B and
7B, indicates that gamma radiation causes a decrease in the charging state for
positively charged particles and an increase for negatively charged particles
for both the low-humidity and high-humidity case. However, this change is only
found to be statistically significant for the negatively charged particles and
not the positively charged particles. It is yet unknown whether the decrease
in the number of positively charged particles would get more statistically
significant with more repetitions of the experiments, or it is caused by an
actual physical process allowing the particles to maintain their positive
charge under gamma radiation.

The overall negative charging of the particles might be linked to the mobility
of the ions created by the gamma radiation. In Earth’s atmosphere, high-energy
radiation, such as SEPs and GCRs, lead to the formation of ions and ionic
clusters through the separation of electrons from N2 or O2, that will
subsequently be captured by neutral molecules (reviewed in Harrison & Carslaw
(2003)). Depending on the composition of these ions, they will have different
mobility and thereby different rate of uptake by aerosols. In Earth’s
troposphere, the negative ions generally have higher mobilities than the
positive (e.g. Hõrrak et al. (1998); Harrison & Carslaw (2003)), and some of
the dominating negative ions are O${}_{2}^{-}$(H2O)n and NO${}_{3}^{-}$(H2O)n,
while some of the dominating positive ions are H3O+(H2O)n, H+(H2O)n, and
NO+(H2O)n. Most of these ions could also be present in our experiments, since
they can be formed through ionisation of N2 and H2O (the gas composition used
in this study), and the Cs-137 gamma sources we use can ionize both N2 and
H2O. This could indicate that we might also expect a higher mobility of the
negative compared to the positive ions in our setup, similar to what is seen
in Earth’s atmosphere. A noticeable difference between the gas composition in
this study and Earth’s atmospheric composition is the lack of O2 in the
chamber. A previous study by (Wiedensohler et al., 1986), looked at the
charging distribution of positively and negatively charged particles in
different gas composition. They found a larger split in the charging state of
positively and negatively charged particles in N2 gas compared to air, with a
significantly higher number of negatively charged particles. They suggest that
this might be due to the lack of O2 since this results in a lack of electron
receptors, leading to more free electrons and thereby potentially a higher
average mobility of all negative ions. Exactly how the number and mobility of
the small air ions will affect the final charging of particles is non-trivial,
and depends on a series of chemical and ion exchange reactions where ion
clusters build up before they collide with and are absorbed by the larger
particles (Harrison & Carslaw, 2003). But as observed by Wiedensohler et al.
(1986) the initial composition of air ions can affect the final charging.

Different degrees of relative humidity were tested in this study, and as
mentioned, gamma radiation is shown to have a similar effect on the SiO2
particles in low- and high-humidity environments. Previous studies have
suggested that water molecules structure themselves differently on silicates,
depending on the relative humidity of the environment (Asay & Kim, 2005).
Based on the terminology from Asay & Kim (2005), the two humidity ranges we
are observing lead to structures that are ice-like (RH = $\sim$ 20%) and
transitional/liquid (RH $>$ 50%) respectively. The fact that we observe
similar effects of gamma radiation in the two cases, could indicate that the
charging and inhibition of aggregation is not dependent on the structuring of
water molecules on the surface of the particles. However, the adhesion of
water molecules to solid surfaces (reviewed in e.g. Zhou & Huang (2021);
Sacchi & Tamtögl (2023)), and the resulting effect on charging and aggregation
of particles (He et al., 2019, 2020), is complex and depends on both the
physical and chemical properties of the surfaces, and we have not accounted
for it in this study.

Based on the results of this and previous studies we suggest that high-energy
environments might promote the formation of smaller cloud particles. Previous
studies have shown that high-energy radiation induces the nucleation of cloud
particles in Earth-like atmospheres, thereby increasing the number of new
particles (Lee et al., 2019; Wagner et al., 2017; Svensmark et al., 2013). In
this study, we show that high-energy radiation may inhibit aggregation of the
existing particles, thereby favouring a high number of smaller particles
rather than a low number of larger particles. Together this could indicate
that high-energy radiation increases the number of particles overall. Under
the right conditions, these particles might act directly as cloud particles or
potentially as cloud condensation nuclei for other cloud forming species. For
Earth, it has been speculated that the required size of a cloud condensation
nuclei is 50 nm (e.g. Svensmark et al. (2013); Sarangi et al. (2015); Fan et
al. (2018)), and under Earth-like conditions, previous studies (Svensmark et
al., 2013) have found that gamma radiation promotes the growth of nucleated
particles up to $>$ 50 nm. Since this study has found that gamma radiation
inhibits aggregation of d $\approx$ 50 nm particles, this could indicate that
high-energy radiation will increase the number of cloud condensation nuclei
overall by promoting their formation and preventing the loss in number through
aggregation. We note that the studies promoting nucleation and growth of
smaller aerosols were performed on a different set of species than in this
study.

With telescopes such as James Webb Space Telescope (JWST) our understanding of
cloud formation is being put to the test as it becomes essential in our
analysis of transit spectra. Already the early release observations from JWST
(Pontoppidan et al., 2022) presented planets such as WASP-96b with strong H2O
features, that are also predicted to have mineral cloud particles including
silicate species ($\geq$40%) (Samra et al., 2023), indicating the relevance of
understanding the behaviour of mineral cloud particles in humid environments.
The presence of mineral cloud particles is not unusual, and has been observed
for e.g. WASP-107b both with Hubble Space Telescope (Kreidberg et al., 2018)
and later with JWST (preprint Dyrek et al. (2023)). Another potential JWST
target of interest is HD189733b, that is both expected to have silicate cloud
particles (Lee et al., 2016; Barth et al., 2021), and where observations have
shown flares from the host star (Bourrier et al., 2020), indicating that an
increased level of gamma radiation might be present in the upper atmosphere of
the planet. These observations and models all show the importance of
understanding the interplay between mineral cloud particles and high-energy
radiation.

The results of this study have been primarily qualitative and solely focused
on SiO2 as an analogue to mineral cloud particles. In order to get a better
understanding of the behaviour of mineral cloud particles in general, it would
be highly beneficial to conduct further extensive studies with more
repetitions and other predicted cloud formation species, such as silicate and
magnesium species, like enstatite (MgSiO3) and forsterite (Mg2SiO4) (e.g.
Lunine et al. (1986); Helling et al. (2008a); Carone et al. (2023); Gao &
Powell (2021)), or titanium species such as TiO2 (e.g. Kohn et al. (2021);
Helling et al. (2008b)).

##  5 Summary

In this study we have explored the question of how high-energy radiation
affects the aggregation and charging of mineral cloud particles. We here
present the results of a series of experiments with mineral SiO2 particles in
an atmosphere chamber under varying degrees of high-energy radiation and
relative humidity.

Based on the experiments we observe the following:

  1. 1.

The d $\approx$ 50 nm SiO2 particles (N1) aggregate in the chamber to form
clusters of two, three, and potentially four particles (N2 - N4).

  2. 2.

Gamma radiation inhibits the overall aggregation of the SiO2 particles. This
is observed as an increase in the number of single particles (N1) and a
decrease the number of larger aggregates (N2 - N4). It is unknown if the trend
reflects a prevention of the N1 particles to aggregate, or if it reflects a
fragmentation of existing aggregates (N2-N4), but it could be linked to a
lowered mobility of the N1 particles due to a change in their charging state.

  3. 3.

Gamma radiation causes the particle population to become more negatively
charged. This is observed as an increase in the charging state of the
negatively charged particles and a decrease in the charging state of
positively charged particles, when gamma radiation is present. This change in
charging state is only found to be statistically significant for negatively
charged particles.

  4. 4.

The effect of gamma radiation is visible both at lower ($\sim$20%) and higher
($\geq$50%) relative humidity.

We suggest that gamma radiation may favour the formation of many smaller
particles based on: 1) previous studies have found that gamma radiation
increases ion-induced nucleation, and 2) this study has found that gamma
radiation decreases aggregation. Depending on the environment, the many
smaller particles might act directly as cloud particles or as cloud
condensation nuclei for other cloud forming species.

The authors thank Matthew S. Johnson for insightful discussions on the
background for the study and for the loan of instruments. This project is
funded by the European Union’s Horizon 2020 research and innovation programme
under the Marie Sklodowska-Curie grant No 860470. This project received
funding from St Leonard’s Postgraduate College from the University of St
Andrews.

## References

  * Abedini et al. (2013) Abedini, A., Daud, A. R., Abdul Hamid, M. A., Kamil Othman, N., & Saion, E. 2013, Nanoscale Research Letters, 8, 474, doi: 10.1186/1556-276X-8-474
  * Airapetian et al. (2020) Airapetian, V. S., Barnes, R., Cohen, O., et al. 2020, International Journal of Astrobiology, 19, 136, doi: 10.1017/S1473550419000132
  * Asay & Kim (2005) Asay, D. B., & Kim, S. H. 2005, The Journal of Physical Chemistry B, 109, 16760, doi: 10.1021/jp053042o
  * Baines et al. (2009) Baines, K. H., Delitsky, M. L., Momary, T. W., et al. 2009, Planetary and Space Science, 57, 1650, doi: 10.1016/j.pss.2009.06.025
  * Barth et al. (2021) Barth, P., Helling, C., Stüeken, E. E., et al. 2021, Monthly Notices of the Royal Astronomical Society, 502, 6201, doi: 10.1093/mnras/staa3989
  * Belosi et al. (2013) Belosi, F., Ferrari, S., Poluzzi, V., Santachiara, G., & Prodi, F. 2013, Journal of the Air & Waste Management Association, 63, 918, doi: 10.1080/10962247.2013.800169
  * Bourrier et al. (2020) Bourrier, V., Wheatley, P. J., Lecavelier des Etangs, A., et al. 2020, Monthly Notices of the Royal Astronomical Society, 493, 559, doi: 10.1093/mnras/staa256
  * Brooke et al. (1998) Brooke, T., Knacke, R., Encrenaz, T., et al. 1998, Icarus, 136, 1
  * Brown et al. (2002) Brown, M. E., Bouchez, A. H., & Griffith, C. A. 2002, Nature, 420, 795
  * Carone et al. (2023) Carone, L., Lewis, D. A., Samra, D., Schneider, A. D., & Helling, C. 2023, WASP-39b: exo-Saturn with patchy cloud composition, moderate metallicity, and underdepleted S/O, arXiv.  http://arxiv.org/abs/2301.08492
  * Chadney et al. (2017) Chadney, J. M., Koskinen, T. T., Galand, M., Unruh, Y. C., & Sanz-Forcada, J. 2017, Astronomy & Astrophysics, 608, A75, doi: 10.1051/0004-6361/201731129
  * Dean et al. (1988) Dean, A., Fan, L., & Byard. 1988
  * Dickinson (1975) Dickinson, R. E. 1975, Bulletin of the American Meteorological Society, 56, 1240, doi: 10.1175/1520-0477(1975)056<1240:SVATLA>2.0.CO;2
  * Doyle et al. (2018) Doyle, L., Ramsay, G., Doyle, J. G., Wu, K., & Scullion, E. 2018, Monthly Notices of the Royal Astronomical Society, 480, 2153, doi: 10.1093/mnras/sty1963
  * Dyrek et al. (2023) Dyrek, A., Min, M., Decin, L., et al. 2023, SO2, silicate clouds, but no CH4 detected in a warm Neptune with JWST MIRI, doi: 10.21203/rs.3.rs-3101058/v1
  * Enghoff et al. (2011) Enghoff, M. B., Pedersen, J. O. P., Uggerhøj, U. I., Paling, S. M., & Svensmark, H. 2011, Geophysical Research Letters, 38, doi: 10.1029/2011GL047036
  * Enghoff & Svensmark (2017) Enghoff, M. B., & Svensmark, J. 2017, Journal of Aerosol Science, 114, 13, doi: 10.1016/j.jaerosci.2017.08.009
  * Fan et al. (2018) Fan, J., Rosenfeld, D., Zhang, Y., et al. 2018, Science, 359, 411, doi: 10.1126/science.aan8461
  * Firoz et al. (2022) Firoz, K. A., Gan, W. Q., Li, Y. P., Rodríguez-Pacheco, J., & Dorman, L. I. 2022, Solar Physics, 297, 71, doi: 10.1007/s11207-022-01994-7
  * Fraschetti et al. (2019) Fraschetti, F., Drake, J. J., Alvarado-Gómez, J. D., et al. 2019, The Astrophysical Journal, 874, 21, doi: 10.3847/1538-4357/ab05e4
  * Fuchs (1964) Fuchs, N. 1964, New York
  * Fujimoto et al. (2021) Fujimoto, T., Yamanaka, S., & Kuga, Y. 2021, MATEC Web of Conferences, 333, 02012, doi: 10.1051/matecconf/202133302012
  * Gao & Powell (2021) Gao, P., & Powell, D. 2021, The Astrophysical Journal Letters, 918, L7, doi: 10.3847/2041-8213/ac139f
  * Gao et al. (2021) Gao, P., Wakeford, H. R., Moran, S. E., & Parmentier, V. 2021, Journal of Geophysical Research: Planets, 126, e2020JE006655, doi: 10.1029/2020JE006655
  * Getman & Feigelson (2021) Getman, K. V., & Feigelson, E. D. 2021, The Astrophysical Journal, 916, 32, doi: 10.3847/1538-4357/ac00be
  * Grießmeier et al. (2005) Grießmeier, J.-M., Stadelmann, A., Motschmann, U., et al. 2005, Astrobiology, 5, 587, doi: 10.1089/ast.2005.5.587
  * Grün et al. (1992) Grün, E., Fechtig, H., Hanner, M. S., et al. 1992, Space Science Reviews, 60, 317, doi: 10.1007/BF00216860
  * Guinan et al. (2016) Guinan, E. F., Engle, S. G., & Durbin, A. 2016, The Astrophysical Journal, 821, 81, doi: 10.3847/0004-637X/821/2/81
  * Harrison & Carslaw (2003) Harrison, R. G., & Carslaw, K. S. 2003, Reviews of Geophysics, 41, doi: 10.1029/2002RG000114
  * He et al. (2019) He, Y., Gu, Z., Lu, W., et al. 2019, Atmospheric Environment, 197, 141, doi: 10.1016/j.atmosenv.2018.10.035
  * He et al. (2020) —. 2020, Particuology, 52, 1, doi: 10.1016/j.partic.2019.12.007
  * Helling (2020) Helling, C. 2020, arXiv:2011.03302 [astro-ph, physics:physics].  http://arxiv.org/abs/2011.03302
  * Helling (2022) —. 2022, Cloud formation in Exoplanetary Atmospheres, Tech. Rep. arXiv:2205.00454, arXiv.  http://arxiv.org/abs/2205.00454
  * Helling et al. (2006) Helling, C., Thi, W.-F., Woitke, P., & Fridlund, M. 2006, Astronomy & Astrophysics, 451, L9, doi: 10.1051/0004-6361:20064944
  * Helling et al. (2008a) Helling, C., Woitke, P., & Thi, W. F. 2008a, Astronomy and Astrophysics, 485, 547, doi: 10.1051/0004-6361:20078220
  * Helling et al. (2008b) Helling, C., Ackerman, A., Allard, F., et al. 2008b, Monthly Notices of the Royal Astronomical Society, 391, 1854, doi: 10.1111/j.1365-2966.2008.13991.x
  * Hõrrak et al. (1998) Hõrrak, U., Salm, J., & Tammet, H. 1998, Journal of Geophysical Research: Atmospheres, 103, 13909, doi: 10.1029/97JD01570
  * Jokinen et al. (2018) Jokinen, T., Sipilä, M., Kontkanen, J., et al. 2018, Science Advances, 4, eaat9744, doi: 10.1126/sciadv.aat9744
  * Jokipii (1971) Jokipii, J. R. 1971, Reviews of Geophysics, 9, 27, doi: 10.1029/RG009i001p00027
  * Jorgensen et al. (2021) Jorgensen, J. L., Benn, M., Connerney, J. E. P., et al. 2021, Journal of Geophysical Research (Planets), 126, e06509, doi: 10.1029/2020JE006509
  * Kasting et al. (1993) Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, Icarus, 101, 108, doi: 10.1006/icar.1993.1010
  * Knutson & Whitby (1975) Knutson, E. O., & Whitby, K. T. 1975, Journal of Aerosol Science, 6, 443, doi: 10.1016/0021-8502(75)90060-9
  * Kohn et al. (2021) Kohn, C., Helling, C., Bodker Enghoff, M., et al. 2021, ASTRONOMY & ASTROPHYSICS, 654, A120, doi: 10.1051/0004-6361/202140378
  * Kreidberg et al. (2018) Kreidberg, L., Line, M. R., Thorngren, D., Morley, C. V., & Stevenson, K. B. 2018, The Astrophysical Journal Letters, 858, L6, doi: 10.3847/2041-8213/aabfce
  * Laakso et al. (2007) Laakso, L., Gagne, S., Petaja, T., et al. 2007, Atmos. Chem. Phys., 13
  * Lee et al. (2016) Lee, G., Dobbs-Dixon, I., Helling, C., Bognar, K., & Woitke, P. 2016, Astronomy & Astrophysics, 594, A48, doi: 10.1051/0004-6361/201628606
  * Lee et al. (2019) Lee, S.-H., Gordon, H., Yu, H., et al. 2019, Journal of Geophysical Research: Atmospheres, 124, 7098, doi: 10.1029/2018JD029356
  * Lunine et al. (1986) Lunine, J. I., Hubbard, W. B., & Marley, M. S. 1986, The Astrophysical Journal, 310, 238, doi: 10.1086/164678
  * Marcolli et al. (2016) Marcolli, C., Nagare, B., Welti, A., & Lohmann, U. 2016, Atmospheric Chemistry and Physics, 16, 8915, doi: 10.5194/acp-16-8915-2016
  * Marley et al. (1999) Marley, M. S., Gelino, C., Stephens, D., Lunine, J. I., & Freedman, R. 1999, The Astrophysical Journal, 513, 879
  * Marsh & Svensmark (2000) Marsh, N. D., & Svensmark, H. 2000, Physical Review Letters, 85, 5004, doi: 10.1103/PhysRevLett.85.5004
  * Mazziotta et al. (2020) Mazziotta, M., Luque, P. D. L. T., Di Venere, L., et al. 2020, Physical Review D, 101, 083011, doi: 10.1103/PhysRevD.101.083011
  * Mesquita et al. (2021a) Mesquita, A. L., Rodgers-Lee, D., & Vidotto, A. A. 2021a, Monthly Notices of the Royal Astronomical Society, 505, 1817, doi: 10.1093/mnras/stab1483
  * Mesquita et al. (2021b) Mesquita, A. L., Rodgers-Lee, D., Vidotto, A. A., Atri, D., & Wood, B. E. 2021b, Monthly Notices of the Royal Astronomical Society, 509, 2091, doi: 10.1093/mnras/stab3131
  * Motzkus et al. (2013) Motzkus, C., Vaslin-Reimann, S., Mace, T., et al. 2013, Journal of Nanoparticle Research, 15, 1919, doi: 10.1007/s11051-013-1919-4
  * Nandy et al. (2021) Nandy, D., Martens, P. C. H., Obridko, V., Dash, S., & Georgieva, K. 2021, Progress in Earth and Planetary Science, 8, 40, doi: 10.1186/s40645-021-00430-x
  * Obridko et al. (2020) Obridko, V. N., Ragulskaya, M. V., & Khramova, E. G. 2020, Journal of Atmospheric and Solar-Terrestrial Physics, 208, 105395, doi: 10.1016/j.jastp.2020.105395
  * Ohno et al. (2021) Ohno, K., Zhang, X., Tazaki, R., & Okuzumi, S. 2021, The Astrophysical Journal, 912, 37
  * Parker (1965) Parker, E. N. 1965, Planetary and Space Science, 13, 9, doi: 10.1016/0032-0633(65)90131-5
  * Pontoppidan et al. (2022) Pontoppidan, K. M., Barrientes, J., Blome, C., et al. 2022, The Astrophysical Journal Letters, 936, L14, doi: 10.3847/2041-8213/ac8a4e
  * Potgieter (2013) Potgieter, M. S. 2013, Living Reviews in Solar Physics, 10, 3, doi: 10.12942/lrsp-2013-3
  * Rages & Pollack (1992) Rages, K., & Pollack, J. B. 1992, Icarus, 99, 289
  * Reames (2013) Reames, D. V. 2013, Space Science Reviews, 175, 53
  * Reep & Knizhnik (2019) Reep, J. W., & Knizhnik, K. J. 2019, The Astrophysical Journal, 874, 157, doi: 10.3847/1538-4357/ab0ae7
  * Rodgers-Lee et al. (2021) Rodgers-Lee, D., Taylor, A. M., Vidotto, A. A., & Downes, T. P. 2021, Monthly Notices of the Royal Astronomical Society, 504, 1519, doi: 10.1093/mnras/stab935
  * Rodgers-Lee et al. (2020) Rodgers-Lee, D., Vidotto, A. A., Taylor, A. M., Rimmer, P. B., & Downes, T. P. 2020, Monthly Notices of the Royal Astronomical Society, 499, 2124, doi: 10.1093/mnras/staa2737
  * Rodríguez-Barrera et al. (2018) Rodríguez-Barrera, M. I., Helling, C., & Wood, K. 2018, Astronomy & Astrophysics, 618, A107, doi: 10.1051/0004-6361/201832685
  * Romani & Atreya (1988) Romani, P. N., & Atreya, S. K. 1988, Icarus, 74, 424
  * Sacchi & Tamtögl (2023) Sacchi, M., & Tamtögl, A. 2023, Advances in Physics: X, 8, 2134051, doi: 10.1080/23746149.2022.2134051
  * Sadovski et al. (2018) Sadovski, A. M., Struminsky, A. B., & Belov, A. 2018, Astronomy Letters, 44, 324, doi: 10.1134/S1063773718040072
  * Sagan et al. (1992) Sagan, C., Thompson, W. R., & Khare, B. N. 1992, Accounts of Chemical Research, 25, 286
  * Samra et al. (2023) Samra, D., Helling, C., Chubb, K., et al. 2023, Astronomy & Astrophysics, 669, A142, doi: 10.1051/0004-6361/202244939
  * Sarangi et al. (2015) Sarangi, B., Aggarwal, S. G., & Gupta, P. K. 2015, Aerosol and Air Quality Research, 15, 166, doi: 10.4209/aaqr.2013.12.0350
  * Scalo et al. (2007) Scalo, J., Kaltenegger, L., Segura, A. G., et al. 2007, Astrobiology, 7, 85, doi: 10.1089/ast.2006.0125
  * Seager & Sasselov (2000) Seager, S., & Sasselov, D. 2000, The Astrophysical Journal, 537, 916
  * Segura et al. (2010) Segura, A., Walkowicz, L. M., Meadows, V., Kasting, J., & Hawley, S. 2010, Astrobiology, 10, 751, doi: 10.1089/ast.2009.0376
  * Selsis et al. (2007) Selsis, F., Kasting, J. F., Levrard, B., et al. 2007, Astronomy and Astrophysics, 476, 1373, doi: 10.1051/0004-6361:20078091
  * Snodgrass & Jones (2019) Snodgrass, C., & Jones, G. H. 2019, Nature Communications, 10, 5418, doi: 10.1038/s41467-019-13470-1
  * Sromovsky et al. (2011) Sromovsky, L., Fry, P., & Kim, J. H. 2011, Icarus, 215, 292
  * Svensmark et al. (2013) Svensmark, H., Enghoff, M. B., & Pedersen, J. O. P. 2013, Physics Letters A, 377, 2343, doi: 10.1016/j.physleta.2013.07.004
  * Svensmark & Friis-Christensen (1997) Svensmark, H., & Friis-Christensen, E. 1997, Journal of Atmospheric and Solar-Terrestrial Physics, 59, 1225, doi: 10.1016/S1364-6826(97)00001-1
  * Svensmark et al. (2021) Svensmark, H., Svensmark, J., Enghoff, M. B., & Shaviv, N. J. 2021, Scientific Reports, 11, 19668, doi: 10.1038/s41598-021-99033-1
  * Svensmark et al. (2020) Svensmark, J., Shaviv, N. J., Enghoff, M. B., & Svensmark, H. 2020, Earth and Space Science, 7, e2020EA001142, doi: 10.1029/2020EA001142
  * Tilley et al. (2019) Tilley, M. A., Segura, A., Meadows, V., Hawley, S., & Davenport, J. 2019, Astrobiology, 19, 64, doi: 10.1089/ast.2017.1794
  * TSI Incorporated (2009) TSI Incorporated. 2009, Model 3080 Electrostatic Classifiers Operations and service manual, TSI Incorporated Shoreview, MN, USA
  * Venot et al. (2016) Venot, O., Rocchetto, M., Carl, S., Hashim, A. R., & Decin, L. 2016, The Astrophysical Journal, 830, 77, doi: 10.3847/0004-637X/830/2/77
  * Vida et al. (2017) Vida, K., Kővári, Z., Pál, A., Oláh, K., & Kriskovics, L. 2017, Frequent flaring in the TRAPPIST-1 system - unsuited for life?, doi: 10.3847/1538-4357/aa6f05
  * Wagner et al. (2017) Wagner, R., Yan, C., Lehtipalo, K., et al. 2017, Atmospheric Chemistry and Physics, 17, 15181, doi: 10.5194/acp-17-15181-2017
  * West et al. (2004) West, A. A., Hawley, S. L., Walkowicz, L. M., et al. 2004, The Astronomical Journal, 128, 426, doi: 10.1086/421364
  * Wiedensohler (1988) Wiedensohler, A. 1988, Journal of Aerosol Science, 19, 387, doi: 10.1016/0021-8502(88)90278-9
  * Wiedensohler et al. (1986) Wiedensohler, A., Lütkemeier, E., Feldpausch, M., & Helsper, C. 1986, Journal of Aerosol Science, 17, 413, doi: 10.1016/0021-8502(86)90118-7
  * Wild et al. (1963) Wild, J., Smerd, S., & Weiss, A. 1963, Annual Review of Astronomy and Astrophysics, 1, 291
  * Wong et al. (2017) Wong, M. L., Fan, S., Gao, P., et al. 2017, Icarus, 287, 110
  * Zhou & Huang (2021) Zhou, G., & Huang, L. 2021, Molecular Simulation, 47, 925, doi: 10.1080/08927022.2020.1786086

##  Appendix A Loss rate to chamber

Over time, particles will be lost to the chamber walls due to collisions. In
order to investigate how many particles are lost to the walls, we study the
decrease in particle number density after ending the input of additional
particles. The results can be seen in Fig. 8.

Figure 8: Number density of single particles, N1, and each of the aggregates,
N2-N4, over time after cutting off the flow of particles into the chamber.
Left: The chamber is not irradiated. Right: The chamber is irradiated with
gamma radiation. The lines show exponential curves fitted to the data points
for the last 10 hours for each of the aggregates.

The figures show the total decrease in particle number density over a time
period of 25 hours after the atomizer has been turned off, for non-irradiated
and irradiated particles respectively. The number density of each of the
aggregates can decrease due to three processes: 1) Aggregation leads to a
decrease of one aggregate population, and an increase of an other population.
2) Particles are lost with the airflow, e.g. to the measurements. 3) Particles
collide with the chamber walls and stay there.

If the particles were solely lost to the airflow and the chamber walls, we
would expect the decrease to be exponential for each of the aggregates.
Exponential curves have been fitted to each of the aggregates for the last 10
hours (hour 15 to 25). The plots in Fig. 8 both show that the number density
of smaller aggregates (N1 and partly N2) initially decreases faster than
exponential, whereas the density of the larger aggregates initially decreases
slower than exponential, which confirms that aggregation continues to take
place after the input of new particles has stopped. For the last 10 hours,
where the exponential curves have been fitted, the aggregates follow these
fits with R2-values of $\geq$0.9. Based on the fact that the number densities
follow an exponential fit for the last 10 hours, we assume that aggregation is
insignificant for this time span. Following this assumption the exponent for
the exponential fits should reflect the loss of particles solely due to the
airflow and the chamber walls. Notice that the input airflow was different for
the two cases (13 L/min for the case without radiation and 16 L/min for the
case with gamma radiation), leading to the particles being diluted faster for
the irradiated case.

Given that the exponential loss of particles follow the curve:

$N(t)=N_{0}*exp(-a\cdot t)$ (A1)

Where N(t) is the particle number density at time, t, and a is the loss rate
of the particles. The total loss rate of the particles can be expressed as:

$a=a_{airflow}+a_{walls}=flow_{air}\cdot V_{chamber}^{-1}+a_{walls}$ (A2)

The loss rate of particles lost to the airflow (aairflow) is found as the
total flow of air through the chamber (flowair) over the chamber volume
(Vchamber). Values can be seen in Tab. 4.

In order to find the total particle loss rate to the chamber walls, the
particle number densities shown in Fig. 8 have been added up to find the total
number density in the chamber (N1+N2+N3+N4). Exponential curves were fitted to
the last 10 hours similarly to what is shown in Fig. 8, and the loss rates to
the chamber walls was found from the exponent and the loss rate to the
airflow.

| Total loss rate | Loss rate to airflow | Loss rate to chamber walls
---|---|---|---
No radiation | -0.100 | -0.098 | -0.002
Gamma radiation | -0.142 | -0.120 | -0.022
Table 4: Loss rates of total number of aggregates in units of hr-1.

##  Appendix B Full mobility diameter range

Figure 9: Size distribution of negatively charged particles measured with and
without bipolar charger. Red shading indicates standard deviation among the 50
measurements constituting each experiment. Figure shows full diameter range of
Fig. 2 and displays the results of one of experiment nr. 5 in Tab. 1. Features
at lower mobility diameters are believed to be caused by aerosols released by
the the Milli-Q water (e.g. Belosi et al. (2013); Marcolli et al. (2016)).