# Stellar space weather effects on potentially habitable planets

A. A. Vidotto  Leiden Observatory, Leiden University, PO Box 9513, 2300 RA
Leiden, The Netherlands

(2022)

###### Abstract

Stellar activity can reveal itself in the form of radiation (eg, enhanced
X-ray coronal emission, flares) and particles (eg, winds, coronal mass
ejections). Together, these phenomena shape the space weather around
(exo)planets. As stars evolve, so do their different forms of activity – in
general, younger solar-like stars have stronger winds, enhanced flare
occurrence and likely more frequent coronal mass ejections. Altogether, these
effects can create harsher particle and radiation environments for habitable-
zone planets, in comparison to Earth, in particular at young ages. In this
article, I will review some effects of these harsher environments on
potentially habitable exoplanets.

###### keywords:

MHD, planets and satellites: atmospheres, magnetic fields, planet-star
interactions

††journal: Astronomy in Focus, Volume 1††editors: Piero Benvenuti, ed.

##  1 Introduction

The short review is based on the review talk I gave at the “Focus Meeting 5:
Beyond the Goldilocks Zone: the Effect of Stellar Magnetic Activity on
Exoplanet Habitability” (August 2022). In line with the theme of the meeting,
my review talk focused in particular on the effects of stellar space weather
on planets that could be potentially habitable. Therefore, two important
concepts are necessary here: what do I mean by potentially habitable planet?
and what do I mean by space weather?

In the context of this article, I consider a potentially habitable planet as a
planet that orbits within the habitable zone. The habitable zone is the region
around a star wherein an orbiting planet can sustain temperatures that allow
water to remain liquid at its surface. Because the planetary equilibrium
temperature depends on the irradiation the planet receives from its host star,
and because the incoming radiation flux depends on orbital distance ($a_{\rm
orb}$) and luminosity ($L_{\star}$) as $\sim L_{\star}a_{\rm orb}^{-2}$, this
means that an Earth twin needs to orbit closer to a less luminous (cooler)
main-sequence star to maintain water in liquid form at its surface. In the
main-sequence phase, the luminosity of the star depends on its mass as
$L_{\star}\propto M_{\star}^{\alpha}$, with $\alpha\simeq 4$. Therefore, this
implies that the distance an Earth twin would have to orbit to remain at the
same temperature as Earth would be $a_{\rm
orb}(\textrm{au})\simeq(L_{\star}/L_{\odot})^{-1/2}\simeq(M_{\star}/M_{\odot})^{2}$.111This
is an rough derivation of the habitable zone distance as a function of the
stellar mass. More rigorous derivations can be found in works that more
completely consider atmospheric properties of planets and mass-luminosity
relations from stellar evolution models (e.g. Selsis et al., 2007; Kopparapu
et al., 2014).

Regarding the concept of exo-space weather, here I consider it to be broadly
related to certain stellar phenomena (“activity”) that shape the environment
around planets. Stellar activity can reveal itself in the form of radiation
(e.g., X-ray coronal emission, flares) and particles (e.g., winds, coronal
mass ejections). In cool main-sequence stars, stellar high-energy radiation
(X-ray and EUV fluxes) decreases with age (e.g., Ribas et al., 2005; Tu et
al., 2015). Likewise, stellar particle fluxes (or mass-loss rates) also decay
with age (Wood et al., 2021; Vidotto, 2021). Together, these two factors
indicate that planets orbiting around more active (which are generally
younger) stars would experience stronger space weather effects compared to
planets in the present-day solar system. Interestingly, similarly harsher
environments are also experienced by planets orbiting older stars at close-in
orbits (Vidotto et al., 2015). Therefore, studying the exo-space weather of
close-in planets orbiting less active, older stars could give us important
clues as to the space weather effects experienced by the (much farther out)
planets in the solar system at younger ages.

##  2 Exo-space weather and planetary magnetic fields

One important ingredient for habitability is the presence of a planetary
atmosphere. For unmagnetised planets, stellar wind particles can directly
interact with the atmosphere of the planet – this could strip away the
atmosphere. For magnetised planets, the situation is less clear. On one hand,
the planetary magnetic field shields (at least, part of) the atmosphere from
the direct interaction with stellar wind particles. In the case of the Earth,
for example, the stand-off distance between the interaction zone with the
stellar wind and the planet surface can be found by equating the ram pressure
(or the dynamic pressure) of the local solar wind and Earth’s magnetic
pressure (Chapman & Ferraro, 1930):
$P_{\textrm{ram}}(\textrm{wind})=P_{B}(\textrm{planet})$. With the assumption
that the magnetic field is well described by a dipole, then $P_{B}\simeq
B_{p}^{2}(R_{p}/r)^{6}/(8\pi)$, with $B_{p}$ being the planetary magnetic
field at the equator of the planet, $R_{p}$ the planetary radius and $r$ the
distance to the centre of the planet. Therefore, one can derive the distance
where this interaction takes place to be
$r_{M}/R_{p}=\sqrt{2}B_{p}^{1/3}/(8\pi
P_{\textrm{ram}}(\textrm{wind}))^{1/6}$222A factor of $\sqrt{2}$ is often
included in the Chapman-Ferraro equation to match Earth’s observation.. In the
case of the Earth, the ram pressure of the local solar wind is
$P_{\textrm{ram}}\simeq m_{p}n_{\rm sw}u_{\rm sw}^{2}=m_{p}(5~{}{\rm
particles/cm}^{3})\times(400{\rm~{}km/s})^{2}\simeq 1.3\times 10^{-8}{\rm
dyn/cm}^{2}$, where the number density and velocity of the local solar wind
(i.e., at Earth’s orbit) is given by $n_{\rm sw}$ and $u_{\rm sw}$,
respectively. With an equatorial magnetic field strength of about 0.3 G, we
find a distance of about $\sim 11R_{\oplus}$ (Bagenal, 2013) for the size of
Earth’s magnetosphere, which is much greater than the thickness of Earth’s
atmosphere.

More generally, the pressure balance equation should take into account not
only the local ram pressure of the stellar wind, but also other pressure terms
(e.g., the magnetic and thermal pressures). In practice, for the planets in
the solar system, these other terms are usually much smaller than the ram
pressure and thus are neglected. However, for a planet orbiting a more active
star (with stronger magnetism), the other terms should also be incorporated.
In Vidotto et al. (2013), I demonstrated that planets with a similar
magnetisation as that of the Earth, if orbiting in the habitable zone of
active M dwarfs, could have magnetospheres substantially smaller than that of
the Earth (see Figure 1). In one case, the fictitious (potentially) habitable
planet orbing WX UMa would have its magnetosphere completely crushed (WX UMa
has a very strong magnetic field Morin et al. 2010 and thus a harsh wind
environment as well, as presented in Kavanagh et al., 2022). Vidotto et al.
(2013) concluded that, even when neglecting the pressure of the stellar wind,
Earth-like planets around M dwarfs might not have Earth-like magnetospheres.
In See et al. (2014), it was shown that for Earth-like planets in the
habitable zone of K, G and F stars with different activity levels, the
situation is less extreme. As the star ages, its activity and wind strength
decrease, and thus magnetospheres are allowed to “expand” (O Fionnagain &
Vidotto, 2018; Carolan et al., 2019), which in theory means that they would
better shield (at least, in part) the atmospheres of potentially habitable
planets.

Figure 1: Earth-analog at habitable zones of M dwarfs: Intense stellar
magnetism can reduce the extent of planetary magnetospheres. Figure based on
Vidotto et al. (2013).

Although the planetary magnetic “bubble” can prevent direct interaction
between the stellar wind and the entire atmosphere of the planet, its
protective effect has been questioned recently (Brain et al., 2013). The
magnetosphere (assuming a dipolar field) consists of regions of closed field
lines and regions of open field lines. The open field line regions do not
provide a shield against stellar wind particles – in fact, an inflowing
stellar wind can be channeled towards the polar regions through open magnetic
field lines. This could then lead to increased local heating which would
enhance atmospheric evaporation through polar/auroral flows. This then leads
to the question whether a magnetic field could lead to retention of planetary
atmosphere (the shield scenario) or could enhance atmospheric loss (the polar
flow scenario).

Maybe the answer is not a clear cut distinction between both arguments, but
rather a combination of them. Blackman & Tarduno (2018) suggested that,
throughout the life of the Earth, there has been a competition between two
processes: an increased collection area for solar wind mass capture and
reduced solar wind flux, but that overall the Earth’s magnetic field has
provided a net protective role throughout Earth’s history.

##  3 Effects of high-energy radiation on planetary atmospheres

In cool main-sequence stars, particle fluxes (winds, coronal mass ejections)
and high-energy radiation are ultimately connected to stellar magnetism:
magnetic fields drive stellar winds and also heat stellar chromosphere and
coronae (Cranmer & Winebarger, 2019). Therefore, it is not surprising that
both stellar wind particle fluxes and high-energy radiation are higher in
younger stars and decrease as stars age (Vidotto, 2021). The EUV flux that a
planet receives plays, in particular, a major role in atmospheric escape.
There are three timescales involved in the process.

  1. 1.

From an evolutionary point of view ($\sim$ several Gyr), the decrease in high-
energy radiation from the host star implies that its effect on atmospheric
evaporation would also decrease with time. Tu et al. (2015) demonstrated that
the hydrogen content of the atmosphere of a terrestrial planet orbiting at 1
au of its solar-like stellar host can evolve significantly through the
evolution of the system. They showed that a planet could even lose its entire
primordial atmosphere very rapidly. This happens, for instance, if the host
star started its life with a higher rotation – in this case, the host star
remains more active (i.e., with a higher EUV luminosity) for the first billion
year of its life than a star that started its life with a slower rotation
(fast rotating stars are more active than slowly rotating stars, e.g.,
Pizzolato et al. 2003). Consequently, the survival of planetary atmospheres
depends on the history of the high-energy radiation of the host star (Tu et
al., 2015; Allan & Vidotto, 2019; Pezzotti et al., 2021). Another interesting
point to notice is that, when substantial material is lost through atmospheric
evaporation, the internal structure of the planet readjusts itself (e.g.,
Kubyshkina et al., 2020; Kubyshkina & Vidotto, 2021), implying that the
evolutionary track of a planet also depends on the history of atmospheric
escape (see Figure 2).333This is not too dissimilar to what happens in the
evolution of massive stars, whereby stellar winds can carry away a substantial
fraction of the stellar mass, changing its internal structure, the amount of
energy it produces, and consequently its evolutionary track in the HR diagram.

  2. 2.

The high-energy radiation of solar-type stars also evolves during activity
cycles. For example, in the case of the Sun, both its X-ray and EUV
luminosities evolve every $\sim 11$ years (Peres et al., 2000; Chadney et al.,
2016), with an evolution that follows closely the trend of sunspot number
(Hazra et al., 2020). As a consequence, as atmospheric escape is influenced by
the high-energy input radiation, escape process should also evolve within
activity cycle timescales.

  3. 3.

On a shorter timescale, on the order of an hour or so, escape can also change
with increase in energy input caused by flares (e.g., Hazra et al., 2020).
Additionally, if flares are accompanied by stellar coronal mass ejections, the
associated particle flux of coronal mass ejections can affect the escape
process momentarily (Cherenkov et al., 2017; Odert et al., 2020; Hazra et al.,
2022).

Figure 2: Evolutionary tracks of the radius of a close-in terrestrial planet,
considering different prescriptions for atmospheric evaporation hydrodynamic
model (red line) and energy limited approximation (black line). Note that in
the absence of atmospheric escape (grey line), the radius of the planet
changes solely due to thermal evolution. Figure based on Kubyshkina et al.
(2020). Planetary evolution with atmospheric escape is computed using MESA and
the inlists are publicly available in Kubyshkina (2020).

##  4 Conclusions

During the Focus Meeting 5 (“Beyond the Goldilocks Zone: the Effect of Stellar
Magnetic Activity on Exoplanet Habitability”), we heard about the importance
of thinking beyond the goldilocks zones. In this (very brief!) review, I
discussed that stellar winds, coronal mass ejections, magnetic activity,
stellar high-energy radiation, and planetary magnetic fields are additional
important aspects to consider when thinking about planetary habitability. I
highlighted 3 key points in my talk and in this article: 1) do planetary
magnetic field act as a shield to prevent the loss of planetary atmospheres or
a channel that could lead to enhanced escape? 2) Earth-like planets around M
dwarfs might not have Earth-like magnetospheres. 3) Atmospheric escape and the
evolution of planets depends on the X-ray and EUV history of the host star.

## Acknowledgements

I thank the organisers of Focus Meeting 5 for hosting a very exciting meeting
and a special thanks to the General Assembly local organisation, for their
huge efforts in making the whole event happen during very difficult pandemic
times. AAV has received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (grant
agreement No 817540, ASTROFLOW).

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