Proc R Soc A

Astrobiology, Extrasolar planets

R. J. Anslow

# Can comets deliver prebiotic molecules to rocky exoplanets?

R. J. Anslow1 A. Bonsor1 and P. B. Rimmer2 1Institute of Astronomy, University
of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
2Astrophysics Group, Cavendish Laboratory, University of Cambridge, JJ Thomson
Ave, Cambridge, CB3 0HE, UK<EMAIL_ADDRESS>
###### Abstract

In this work we consider the potential of cometary impacts to deliver complex
organic molecules and the prebiotic building blocks required for life to rocky
exoplanets. Numerical experiments have demonstrated that for these molecules
to survive, impacts at very low velocities are required. This work shows that
for comets scattered from beyond the snow-line into the habitable zone, the
minimum impact velocity is always lower for planets orbiting Solar-type stars
than M-dwarfs. Using both an analytical model and numerical N-body
simulations, we show that the lowest velocity impacts occur onto planets in
tightly-packed planetary systems around high-mass (i.e. Solar-mass) stars,
enabling the intact delivery of complex organic molecules. Impacts onto
planets around low-mass stars are found to be very sensitive to the planetary
architecture, with the survival of complex prebiotic molecules potentially
impossible in loosely-packed systems. Rocky planets around M-dwarfs also
suffer significantly more high velocity impacts, potentially posing unique
challenges for life on these planets. In the scenario that cometary delivery
is important for the origins of life, this study predicts the presence of
biosignatures will be correlated with i) decreasing planetary mass (i.e.
escape velocity), ii) increasing stellar-mass, and iii) decreasing planetary
separation (i.e. exoplanets in tightly-packed systems).

###### keywords:

Origins of life, prebiotic chemistry, planetary dynamics, hydrogen cyanide,
habitable planets, impacts

††journal: rspa

##  1 Introduction

The initial emergence of life on Earth will require some initial inventory of
prebiotic molecules, for which there are two leading supply mechanisms,
endogenous synthesis on the early-Earth and exogenous delivery. There are a
number of synthesis pathways, such as via lightning discharge [1, 2],
atmospheric proton irradiation [3], atmospheric photochemical networks [4, 5],
and the shock-synthesis of carbonaceous and nitrogenous molecules during high
velocity impacts [6, 7]. The efficacy of these pathways, however, is dependent
on the atmospheric oxidation state of the early-Earth, decreasing
significantly in more oxidised atmospheres [8].

The exogenous delivery of prebiotic molecules is an attractive, atmosphere-
independent supply mechanism encompassing the delivery of extraterrestrial
objects including asteroids, comets and interplanetary dust particles [9, 10,
11, 12]. Return samples from the Ryugu asteroid have revealed a diverse
inventory of prebiotic molecules [13, 14], with the discovery of intact amino
acids in meteorite samples [15, 16] highlighting that at least some prebiotic
molecules are able to survive atmospheric entry. The survival of prebiotic
molecules in meteorites may not even be necessary, given that carbonaceous
chondrites are able to catalyze a range of prebiotic molecules in aqueous
conditions, and thereby fertilise the early-Earth [17, 18].

Comets have been suggested as potentially important sources of prebiotic
delivery (e.g. [19]) as they are known to contain large amounts of the
prebiotic feedstock molecule hydrogen cyanide (HCN) [20], as well as simple
amino acids [21]. The discovery of a rich diversity of CHN- and CHS-bearing
molecules on the comet 67P [22] has further supported the potential importance
of cometary impacts in delivering part of the early-Earth’s organic inventory.
Despite the relatively small number of cometary impacts on the early-Earth (in
comparison to asteroids and left-over planetesimals) [23, 24], it has been
estimated that comets delivered 2 orders of magnitude more organic material
than meteorites [12]. This is a consequence of the extremely high carbon
content of comets ($\sim 10$% [10, 20]) in comparison to both C-and S-type
asteroids (2% [25] and 0.2% [26] respectively).

There has, however, been longstanding debate surrounding the plausibility and
efficiency of cometary delivery given the pyrolysis, or thermal decomposition,
of constituent organics during impacts (e.g. [19]), and the subsequent
dilution of surviving molecules in the atmosphere and oceans. The ‘warm comet
pond’ [27] has been proposed as a specific origins scenario, able to alleviate
both of these concerns and support the initial emergence of life. The scenario
requires the ‘soft-landing’ of a cometary nucleus, which excavates the impact
point and forms a dirty pond from the cometary components. Climatic variations
are thought to cause the episodic drying of these ponds, promoting the rapid
polymerisation of constituent prebiotic molecules. It is thought this wet-dry
cycling will effectively drive the required biogeochemical reactions crucial
for RNA production on the early-Earth, and therefore play an important role in
the initial emergence of life (e.g. [28, 29]). Relatively high concentrations
of prebiotic molecules are required for there to be sufficient polymerisation,
and so this scenario still requires low-velocity impacts. Specific prebiotic
molecules are more (or less) susceptible to thermal decomposition by virtue of
their molecular structure, and so the inventory of molecules that can be
effectively delivered to a planet is very sensitive to impact velocity.

HCN is an example of a prebiotic molecule that is particularly suited to this
warm comet pond scenario, as its strong carbon-nitrogen triple bond confers
much greater durability to the temperatures experienced during impacts. Given
also the abundance of HCN in comets [20], cometary delivery onto the early-
Earth is thought to have been able to successfully deliver high concentrations
of HCN to local environments, which can survive over 0.1-1 Myr timescales
[30]. This has significant biological implications, since HCN is a key
feedstock molecule in multiple prebiotic syntheses, as a precursor to amino
acids through Strecker synthesis [31], invoked in the Miller-Urey experiments
[32]. Further studies have demonstrated the role of HCN in the synthesis of
lipids, sugars, nucleobases and nucleotides [33, 34, 35], four key building
blocks of life, as summarised in [36]. The strict velocity constraints
required in the comet pond scenario naturally prompt the question of whether
the Earth is somewhat special in this regard.

Exoplanets are observed across a wide range of environments, with M-dwarf
stars the most numerous spectral-class in our galaxy, comprising $\sim$70% of
all stars in the Solar-neighbourhood [37]. Many of these stars host large
outer reservoirs of planetesimals in belts analogous to the Solar System
asteroid and Kuiper belts, which generate infrared excesses through the
collisional production of dust [38, 39]. These belts are inferred to have
masses $\sim 10^{2}M_{\mathrm{Earth}}$, roughly 6 orders of magnitude larger
than the Kuiper belt [40]. The detection of carbon monoxide gas in several of
these systems indicates the presence of volatile-rich cometary bodies,
suggesting a similarity to Solar System comets [41, 42]. There are relatively
few known debris discs around M-dwarfs, but systems such as the nearby M-dwarf
AU Microscopii, with its two warm-Neptunes [43, 44] orbiting interior to a
cold, dusty debris belt [45], provide key examples that architectures similar
to that proposed here do exist.

Thus, in this study we hypothesize that comets host comparable prebiotic
molecular diversity in other planetary systems, and ask the question "Which
planets, and planetary systems are the most susceptible to successful cometary
delivery?". The detection of habitable planets around F- and G-type stars
remains a formidable observational challenge, and there exist unique
challenges facing the habitability of planets around both M-dwarfs and F-type
stars [46, 47]. Nonetheless, by addressing this question, we can begin to test
the hypothesis that cometary delivery plays an important role in origins
scenarios against data from the next generation of great observatories.

The paper starts in Section 2.1 by introducing an idealised planetary
architecture based on observations of tightly-packed multiple planet systems.
We present in Section 2.2 an analytical method to determine how slowly comets
are potentially able to impact onto rocky habitable planets. Section 2.3
describes the numerical simulations that will be used to confirm this result
and investigate how frequently low velocity impacts can occur. In Section 3 we
present the results of these simulations in the context of our analytical
predictions. In Section 4 we discuss the results of our analytical model and
simulations, and present predictions for future correlations between
biosignatures and exoplanet populations. Finally, Section 5 summarises our
conclusions.

##  2 Methods

The cometary delivery of prebiotically interesting molecules requires very low
impact velocities, to minimise the amount of thermal degradation and allow a
substantial quantity to survive the impact. To understand the importance of
cometary delivery in an exoplanetary context, we study the scattering of
volatile-rich bodies from beyond the snow-line into the habitable zone. We
consider an idealised planetary system with equally spaced and equal-mass
planets, as sketched in figure 1, which allows us to make analytical
predictions for the minimum impact velocity onto the inner habitable planet.
We then use N-body simulations to study the overall changes to the velocity
distribution and test our analytical predictions.

###  2.1 Idealised planetary architecture

Figure 1: Schematic diagram of the idealised planetary system considered in
this work with equally spaced planets (brown circles, semi-major axis $a_{i}$)
scattering comets (small dark blue circles) from the snow-line. The blue
region represents the volatile-rich region of the disc where comets occur, and
the green region represents the habitable zone. Low velocity cometary impacts
onto habitable planets will follow the lower arrows, which sketch the
dynamically cold scattering between adjacent planets. The dynamically hot
scattering as shown by the upper arrows, will result in high velocity impacts.

We consider a chain of co-planar planets, each with mass $M_{\mathrm{Earth}}$,
on circular orbits around a central star (mass $M_{\ast}\in$ [0.1, 2]
$M_{\mathrm{Sun}}$). The semi-major axis of the inner planet is fixed in the
centre of the star’s habitable zone, which is calculated using the stellar
mass-luminosity relationship and habitable zone prescription from [48, 49]
respectively. The semi-major axes of the other planets are chosen such that
the planets are equally spaced in units of their mutual Hill radius,

$\displaystyle a_{i+1}$ $\displaystyle=a_{i}+\Delta R_{H_{i,i+1}},$ (1)
$\displaystyle R_{H_{i,i+1}}$
$\displaystyle=\left(\frac{2M_{\mathrm{Earth}}}{3M_{\ast}}\right)^{1/3}\left(\frac{a_{i}+a_{i+1}}{2}\right)\equiv
X\left(a_{i}+a_{i+1}\right).$ (2)

We are interested in the scattering of volatile-rich material onto the inner
planet, and so use the snow-line to delineate the boundary between the
populations of rocky and volatile-rich bodies in the disc. The number of
planets is chosen to span the gap between the habitable zone and snow-line.
The location of the snow-line is calculated under the assumption of an
optically thick, steady-state protoplanetary disc as outlined in [50, 51].

This choice of architecture is inspired by the prevalence of so-called ’peas
in a pod’ systems [52]. This describes the observed phenomenon that individual
exoplanet systems have much smaller dispersion in mass, radius, and orbital
period in comparison to the system-to-system variation of the exoplanet
population as a whole [53, 54, 55]. The observed correlation between the size
of the planets and their orbital period ratios implies that gravitational
interactions between neighboring planets are responsible for this effect, for
which the mutual Hill radius is the natural length scale.

Whilst this chosen architecture is clearly idealised, numerical simulations
have demonstrated that pebble accretion may naturally form these tight multi-
planet systems, in addition to outer giant planets [56, 57]. These giant
planets may be an important source of comets into the inner planetary system,
given their efficiency at scattering comets onto habitable zone-crossing
orbits [58]. In this work, however, we do not specify the outer planetary
architecture in an attempt to keep the model as general as possible.

In the Kepler systems, the interplanetary separations typically range between
10-30 mutual Hill radii ($\Delta$) [53, 59]. Below 10 $\Delta$ the stability
dramatically decreases, due to the high degree of dynamical complexity present
in these tightly-packed systems [60, 61]. For separations below a critical
value $\Delta_{c}$ [62, 63], these systems are stable for less than 102
conjunctions. We therefore consider planetary spacings in the range 10 to 80
mutual Hill radii, which spans both the Kepler systems and terrestrial Solar
System planets. Numerical simulations have demonstrated that tightly-packed
systems with equal and low mass planets are particularly efficient at
scattering comets into the innermost planets [64]. These results ensure
efficient cometary scattering into the habitable zone, and are used to guide
the range of spacings we consider in section 2.3.

###  2.2 Analytical predictions

Simulations have demonstrated that the scattering of particles by multiple
planets can be well-approximated by a series of three-body interactions [65],
between which the orbits of the particles conserve their Tisserand parameter
[66, 67]. We therefore separate the dynamics of particles into two distinct
regions - inside and outside of the scattering planet’s Hill sphere. Inside
the Hill sphere we assume the particle feels only the attraction of the
central planet, so is pulled onto a hyperbolic orbit with the planet at the
focus. With $v_{\infty}$ the relative velocity to the planet "at infinity",
the impact velocity onto the planet is given by
$v_{\mathrm{imp}}^{2}=v_{\mathrm{esc}}^{2}+v_{\infty}^{2}$. The relative
velocity at infinity is determined by the particle’s orbital elements outside
of the Hill sphere, and is given by [68]

$v_{\infty}^{2}=v_{\mathrm{pl}}^{2}\left(3-\frac{a_{\mathrm{pl}}}{a}-2\cos{i}\sqrt{\frac{a(1-e^{2})}{a_{\mathrm{pl}}}}\right)=v_{\mathrm{pl}}^{2}\left(3-\mathcal{T}\right).$
(3)

There are therefore three key factors to consider when determining the minimum
impact velocity; the planet’s escape velocity, the planet’s orbital
(Keplerian) velocity, and the particle’s orbit relative to the planet, as
characterised by the Tisserand parameter, $\mathcal{T}$. The maximum Tisserand
parameter of the particle is constrained by the planetary architecture,
corresponding to an orbit with apocentre $Q=a_{1}$, and pericentre $q=a_{0}$.
We are able to analytically calculate both the maximum Tisserand parameter,
and minimum impact velocity for our idealised planetary architecture,

$\displaystyle\mathcal{T}_{\mathrm{max}}$ $\displaystyle=\left(1-\Delta
X\right)+2\sqrt{1+\Delta X},$ (4) $\displaystyle
v_{\mathrm{imp},\mathrm{min}}^{2}$
$\displaystyle=v_{\mathrm{esc}}^{2}+\left(\frac{GM_{\ast}}{d_{\mathrm{HZ}}}\right)\left(2+\Delta
X-2\sqrt{1+\Delta X}\right),$ (5)

where $d_{\mathrm{HZ}}=d_{\mathrm{HZ}}\left(M_{\ast}\right)$ is the radial
location of the habitable zone.

###  2.3 Numerical simulations

The overall velocity distribution onto a planet will be determined by the
inwards flux of particles (on a range of orbits), and the accretion cross
section of the planet111The accretion cross section of a planet is a function
of the planetary and stellar properties, and the particle’s orbit. It is given
by $\sigma_{\mathrm{acc}}\propto
R_{\mathrm{pl}}^{2}\left(1+v_{\mathrm{esc}}^{2}/v_{\infty}^{2}\right)$, which
we note is a function of the particle’s Tisserand parameter.. The location of
planets in $(a_{\mathrm{pl}},M_{\mathrm{pl}})$ space determines the dynamics
of the scattered particles, with the equality of the escape velocity and
Keplerian velocity roughly constraining the efficiency of particle ejection
from the system [69]. The details of the planetary architecture is therefore
able to dramatically alter the inwards flux and relative velocities of the
scattered particles in the system. Whilst the Tisserand parameter is conserved
during interactions with a single planet, it is not conserved in the scenario
that a particle has multiple interactions and is exchanged between two
scattering planets [70], making it challenging to make analytical predictions
about the overall velocity distribution. We therefore turn to N-body
simulations, which are well-suited to studying the effects of both the
planetary architecture and stellar-mass on the overall velocity distribution.

N-body simulations were carried out using the MERCURIUS hybrid integrator [71]
from the open source code REBOUND [72]. This integrator allows us to speed up
the long-term integrations during distant interactions, without losing
precision during close encounters. The scheme uses the 15th order adaptive
integrator IAS15 [73] during close encounters, and otherwise uses the
symplectic Wisdom-Holman integrator WHFast [74, 75]. All planets are chosen to
have the same mass and radius as the Earth, and we adopt a timestep of
$P_{0}/50$, where $P_{0}$ represents the period of the innermost planet. The
inner planet is fixed in the star’s habitable zone, and the semi-major axes of
the scattering planets are given by

$a_{n}=a_{0}\left(\frac{1+\Delta X}{1-\Delta X}\right)^{n}.$ (6)

The number of planets, $n$, is chosen to fully span the gap between the
habitable zone and snow-line (i.e. $a_{n}>d_{\mathrm{SL}}$). The conservation
of the Tisserand parameter determines the minimum pericentre each test-
particle can be scattered to [70], and so we use the requirement for planet-
crossing orbits to generate the test-particles’ Tisserand parameter
distribution. We inject test-particles into the chaotic zone of the outer
planet [74], and record the impact velocities when the particles collide with
the physical radius of each planet in the simulation.

##  3 Results

In this section we first discuss our analytical predictions for the minimum
impact velocities onto the habitable planet in our idealised planetary system.
We then present the results of the N-body simulations, and discuss how the
overall velocity distribution is affected by the stellar-mass and planetary
architecture. Our analytical predictions are then compared with the N-body
simulations to verify their accuracy.

###  3.1 Analytical results

Figure 2: Left panel. Analytical predictions for the maximum Tisserand
parameter of comets onto an Earth-like planet in the habitable zone of
M-dwarf, K- and G-type stars, as a function of the spacing between scattering
planets (in units of mutual Hill radius). Typical values for the terrestrial
planets in the Solar System, and the tightly-packed TRAPPIST-1 planets are
added for reference. Right panel. The corresponding analytical predictions for
the minimum velocity impacts onto the planet. Rough velocity thresholds, based
off values for HCN survival [30] are added for reference. In both panels, the
grey shaded region is an unstable region ($\Delta<\Delta_{c}$), for which
planets will have close encounters in less than $\sim 10^{2}$ orbits.

In order to analytically predict the minimum impact velocities, we consider
the comet’s Tisserand parameter, conserved during three-body interactions with
the scattering planets. The maximum Tisserand parameter (equation 4),
corresponding to comets scattered between neighbouring planets, is shown in
figure 2(a). We see the maximum Tisserand parameter decreases with the
planetary separation ($\Delta$), and that the effect of the planetary
architecture is more significant around low-mass stars. The corresponding
minimum impact velocity, given by equation 5 is shown in figure 2(b), and
increases strongly with $\Delta$ for low-mass stars. For low-mass stars (0.1
$M_{\mathrm{Sun}}$), the range of spacings considered corresponds to
scattering directly from the snow-line, all the way up to having 6 planets
spaced equally between the snow-line and habitable zone.

The dependence of both the maximum Tisserand parameter and minimum impact
velocity on $\Delta$ is seen to be stronger around low-mass stars. Since the
planet-to-star mass ratio is larger around low-mass stars, the width of the
resonant regions around these planets will also increase. Consequently, fixed
separations in mutual Hill radius correspond to larger distances in physical-
space around low-mass stars, and therefore lower (higher) Tisserand parameters
(impact velocities).

For the case of direct scattering between the snow-line and habitable zone
(i.e planetary separations of $\sim$ 70 $\Delta$) the minimum impact
velocities reach $\sim$ 20 km/s around low-mass stars. This high velocity is
attributed to the larger ratio of the snow-line to the habitable zone around
low-mass stars, and the (roughly) $M_{\ast}^{-1/2}$ scaling of the orbital
velocity of habitable planets. As velocities exceed 20 km/s, HCN survival
decreases exponentially from $\sim$ 1%, severely limiting the efficiency of
cometary delivery. Above 25 km/s impact blowoff from the atmosphere will
prevent any successful cometary delivery [30].

In summary we find the effectiveness of cometary delivery will depend on the
planet’s escape velocity, the planetary architecture and the stellar-mass, as
illustrated in figure 3. Figure 3(a) shows how reducing the planet’s escape
velocity is able to keep the impact velocity substantially below 15 km/s,
effectively erasing all effects of the planetary architecture and stellar-
mass. For an Earth-like planet, the importance of the planetary architecture
in the context of cometary delivery is almost completely dependent on the
stellar-mass, as shown in figure 3(b).

###  3.2 Numerical results

The results of our N-body simulations, as described in section 2.3, are shown
in figure 4 for a range of stellar masses [0.1, 0.4, 1] $M_{\mathrm{Sun}}$.
Each panel corresponds to a different stellar mass, illustrating the effects
of the planetary architecture for three planetary spacings,
$[10,30,50]\,R_{\rm H,m}$. The velocity distribution onto a habitable planet
orbiting a 1 $M_{\mathrm{Sun}}$ star is included in the background for
comparison. As predicted, there is a large change in the minimum impact
velocity as a function of $\Delta$, which our analytical model is able to
accurately reproduce as indicated by the dashed lines.

Figure 3: The minimum impact velocity onto an Earth-like planet in the
habitable zone is calculated across a wide range of $\Delta$-$M_{\ast}$
parameter space. The planet’s escape velocity is changed between the three
panels. The survival of HCN is used as a proxy for the overall efficiency of
cometary delivery. HCN delivery is most effective below 15 km/s, decreasing
sharply above 20 km/s for which there will be very limited survival [30] Above
25 km/s there will be no HCN survival due to impact blowoff from the
atmosphere.

There are a small number of impacts below our analytical predictions, which
are a consequence of our assumption that comets must have planet-crossing
orbits to be scattered by the planets in the system. Instead, there exists
extended regions surrounding planets ($\sim$ $R_{\mathrm{Hill}}$) within which
particles can be scattered, increasing the available parameter space for the
comets. We expect this effect to be more significant in systems with higher-
mass planets and smaller planetary separations, as comets with low
$v_{\infty}$ will have much longer interaction times with the planets,
allowing impacts from much larger impact parameters222The conservation of
angular momentum determines a maximum impact parameter for impacts,
$b_{\mathrm{max}}=R_{\mathrm{pl}}v_{\mathrm{imp}}/v_{\infty}\sim
R_{\mathrm{pl}}v_{\mathrm{esc}}/v_{\infty}$. Some additional complexity arises
as comets can be scattered backwards and forwards between just two planets,
which can substantially alter their Tisserand parameter [70]. These are,
however, minor effects, as seen in the low-velocity tails of figure 4, and are
actually beneficial to the successful delivery of prebiotic molecules, so do
not substantially affect the main conclusions we reach.

We also see clear qualitative differences between the velocity distributions
in figure 4, highlighting the fact that it is not just the minimum impact
velocity that is affected by the planetary architecture and stellar-mass. A
key takeaway is that there are a much larger fraction of very low-velocity
impacts around Solar-mass stars, which suggests that comets would be able to
deliver a significantly larger inventory of prebiotic molecules. The fraction
of low-velocity impacts is only found to depend on the planetary architecture
for planets around low-mass stars, as seen in figure 5, which is supported by
the general results of our analytical model.

An additional, striking feature of the velocity distributions, is that the
spread in impact velocities is much larger for systems around low-mass stars.
This is driven by the extended high-velocity tails, which remain almost
unchanged by the planetary spacing. These are comets scattered onto highly
eccentric orbits by the outer planets, which remain on such orbits before
impacting the inner habitable planet. This has potentially significant
implications for cometary delivery, as the survival rate decreases
exponentially with impact velocity. Furthermore, the increased fraction of
high-velocity impacts around low-mass stars may be prejudicial to the
development, and persistence of life on these planets [76]. We will discuss
these changes to the velocity distributions, and the associated implications
for cometary delivery in section 4.

###  3.3 Summary of results

Figure 4: Impact velocity distributions from N-body test-particle simulations
onto an Earth-like planet in the habitable zone of an 0.1 $M_{\mathrm{Sun}}$
M-dwarf (a) and an 0.4 $M_{\mathrm{Sun}}$ M-dwarf (b). The planetary spacing,
in units of mutual Hill radius, is varied between $10\,R_{\rm H,m}$ and
$50\,R_{\rm H,m}$ in each panel. This translates to between 2 and 8 planets
spaced equally between the snow-line and habitable zone. The vertical dashed
lines are the analytical predictions for the minimum velocity impacts (as seen
in figure 2). For comparison, the velocity distribution for a planet around a
G-type star (1 $M_{\mathrm{Sun}}$, $\Delta a=50R_{H,m}$) is shaded grey in the
background. The overall shapes of these distributions are very sensitive to
the initial distribution of the test-particles, which we describe in section
2.3.

We have demonstrated analytically and numerically that very low velocity
impacts onto Earth-like planets are possible (impossible) around Solar-type
(M-dwarf) stars for comets scattered directly from beyond the snow-line. We
show, however, that the presence of a number of planets between the habitable
zone and snow-line is able to significantly reduce the minimum impact
velocity, independent of stellar-mass. The dependence of the minimum impact
velocity on the planet’s escape velocity, the stellar-mass and the planetary
architecture is shown in figure 3. The results of our N-body simulations,
figures 4 and 5, demonstrate that the overall velocity distributions onto
habitable planets are also very sensitive to the stellar-mass and planetary
architecture. Importantly for the possibility of cometary delivery, there will
be substantially more low-velocity impacts onto planets in tightly-packed
planetary systems and around higher-mass stars.

##  4 Discussion

###  4.1 For which planets might cometary delivery be important?

As summarised in section 3.3, we find the minimum impact velocity of comets
onto habitable planets is reduced for i) planets with lower escape velocities
(lower mass), ii) planets orbiting higher-mass stars, and iii) planets in
tightly-packed systems, for which comets are delivered on low eccentricity
orbits. The survival of prebiotically interesting molecules in comets depends
on both the impactor’s size and velocity and so, whilst remaining agnostic to
the size-frequency distribution, we are able to make robust statements about
the relative efficiency of cometary delivery.

The most promising planets for any cometary delivery at low impact velocities
will be found around F- and G-type stars, largely irrespective of the
planetary architecture (see figure 3). The simulations presented here indicate
that the delivery of the prebiotically relevant molecule HCN, favoured for
impacts below 15 km/s (low impact angle, small radius) [30], is possible, but
not common for Earth mass planets in the habitable zone of Sun-like stars (see
figure 4).

Delivery at low velocities, including sufficiently gentle impacts for there to
be the successful delivery of an appreciable amount of more complex prebiotic
molecules, such as amino acids [19], will always occur more frequently for
lower mass planets due to their lower escape velocities, as seen in figure 3.
A consequence of this conclusion is that comets could have delivered a larger,
and potentially more complex initial prebiotic inventory to Mars than Earth.
The same is also true for planets around massive stars (i.e.
$M_{\ast}>M_{\mathrm{Sun}}$), given the orbital velocity in the habitable zone
decreases roughly as $M_{\ast}^{-1/2}$. The short main sequence lifetimes, and
inhospitable ionising winds from A-, B- and O- type stars [77, 78] suggest
that there are other reasons why life may not be favoured, pointing to F-type
stars as the most promising high-mass stars to support life. A number of
unique challenges for the emergence and evolution of life (post cometary
delivery) remain for planets around F-type stars, including enhanced UV-fluxes
[79], and the migration of the habitable zone throughout the stellar main
sequence [46].

Figure 5: The fraction of low-velocity impacts as a function of the planetary
spacing for a number of velocity thresholds are shown for a planet around both
an M-dwarf (left panel) and G-type star (right panel). Both the minimum
velocity and the full velocity distribution shift to lower velocities when the
planetary spacing is decreased, seen clearly for planets around M-dwarfs. A
similar trend is only seen for the very lowest velocity impacts around G-type
stars, as predicted by our analytical model (see e.g. figure 2). For
reference, using [30, equation 6], HCN survival is enhanced by roughly 100%
for impacts at 12 km/s compared to 17 km/s. These changes in the velocity
distribution at small $\Delta$ therefore correspond to significant increases
in HCN survival.

Successful cometary delivery at low velocities is significantly more
challenging for planets around low-mass stars. For comets scattered directly
from the snow-line, minimum impact velocities can exceed 20 km/s onto Earth-
like planets. For context, impacts at 20 km/s for a 6 km comet result in
approximately 0.2 % HCN survival, which decreases to 0 % above 25 km/s, where
significant atmospheric blowoff is expected [30]. We show, however, that this
minimum impact velocity can be significantly reduced in multiple-planet
systems, suggesting that successful cometary delivery is possible in tightly-
packed systems, often observed around low-mass stars. The fraction of low
velocity impactors increases in more tightly-packed systems (figure 5), which
further enhances the potential efficiency of cometary delivery in these
scenarios.

TRAPPIST-1 is an example of a tightly-packed planetary system around a low-
mass M-dwarf (0.0898 $M_{\rm Sun}$ [80]), with 3 planets in the habitable zone
(e, f, and g) [81]. Proxima Centauri is another low-mass M-dwarf (0.12 $M_{\rm
Sun}$) also with a habitable zone planet, Proxima Centauri b [82]. A crucial
distinction is that Proxima Centauri b has only one known external companion,
the candidate planet Proxima Cenaturi c, which is on a distant orbit beyond
the snow-line [83]. In the case this interior region truly lacks any
additional planets and debris, this resulting architecture would lead to
significantly higher impact velocities when compared to the TRAPPIST-1
planets. This would, in turn, dramatically reduce the efficiency of any
cometary delivery. We note that these results are in agreement with the
general picture of fast litho-panspermia in the TRAPPIST-1 system presented in
[84].

The dynamical timescales around low-mass stars are much shorter than Solar-
type stars, whilst the pre-main sequence cooling phase is significantly longer
around low-mass stars [85], a prolonged period of enhanced stellar activity
and high XUV-fluxes [86, 87]. These effects combine such that the late-
bombardment of habitable planets will end before the star reaches the main
sequence [88, 89]. These planets will have likely exceeded the runaway
greenhouse threshold [90], and so any cometary delivery during this period
would occur during the planet’s magma ocean epoch [89], unconducive to the
initial emergence of life via the comet pond scenario. More promisingly,
recent work indicates that volatile-rich debris is ubiquitously scattered into
exo-asteroid belts during the planet formation process [88]. This would
support our general picture of scattering from a volatile-rich reservoir
beyond the snow-line, and allow for delayed cometary delivery across a wide
range of stellar-masses.

###  4.2 The effects of the overall velocity distribution

Whilst crucial for cometary delivery, low-velocity impactors constitute only a
small fraction of the overall population of impacting bodies (as seen in
figure 4). The fraction of high-velocity impacts increases significantly
around low-mass stars (see figure 5), which remain even in tightly-packed
systems. These impactors have potentially negative implications for the
habitability of planets around low-mass stars, even in the case of successful
cometary delivery, which we will now discuss.

Comet ponds are particularly exposed settings for abiogenesis, sensitive to
both their immediate environment and also global climatic conditions, so are
very sensitive to a planet’s impact history [76]. Increased fluxes of high-
velocity impactors are therefore likely to be prejudicial to the subsequent
emergence of life. High-velocity impacts are capable of shock heating
atmospheres to very high temperatures ($\sim$ 100° C), which can be followed
by prolonged periods of cooling to temperatures below 0° C due to the
shielding effects of impact ejecta [91]. These ejecta blankets can also
seriously disrupt the chemical evolution of comet ponds due to, and not
limited to, acidification, heating and mixing [76].

Moving beyond the sterilising potential of high-velocity impacts, modelling
the overall velocity distribution is crucial for characterising a planet’s
atmospheric evolution. Atmospheric evolution will depend on the relative
efficiency of volatile delivery to loss from atmospheric stripping, which will
be dependent on impactors’ velocity distribution, size distribution and
composition (e.g. [92]). Habitable planets around low-mass stars will
therefore be more susceptible to atmospheric erosion (see also [93, 23]),
which is largely driven by impacts above twice the planet’s escape velocity
[94]. The sensitivity of atmospheric evolution calculations to the impactors’
velocity distribution means that tailored N-body simulations are necessary to
make accurate conclusions about individual planetary systems, as demonstrated
in [95].

High-velocity impactors might, however, support other origins scenarios that
do not require the initial emergence of life from small surface-level ponds.
High-velocity impacts can enrich a planet’s volatile inventory through the
shock synthesis of prebiotic feedstock molecules [12], in which a number of
chemicals (including HCN) can be synthesised in the impactor’s plasma. As with
many other HCN formation pathways, this effect is found to be most effective
in reduced atmospheres [6, 7]. For the early-Earth it is thought that at least
one impactor will have been able to generate prebiotically relevant
concentrations of HCN, even for an oxidised early-atmosphere [7]. The
increased fraction of high-velocity impacts onto habitable planets around low-
mass stars could therefore indicate more effective endogenous HCN production,
a tentative conclusion contingent on the oxidation state of the planet’s
early-atmosphere. A separate study would therefore be required to understand
the efficiency of impact-driven HCN production in different environments, and
allow for a comparison with cometary delivery.

###  4.3 Model limitations

To analytically explore how the stellar-mass and planetary architecture
affects the impact velocity distribution onto habitable planets, we
necessarily make a number of simplifying assumptions. This enables us to draw
some broad conclusions about the importance of cometary delivery in a wide
range of planetary environments. The main assumptions we make, and the
potential implications for our conclusions, are summarised here.

In this work we have considered highly idealised planetary architectures, with
equal mass planets spaced equally in terms of their mutual Hill radius. This
may be reflected in the observational population of peas-in-a-pod systems
[52], but our architectures are significantly more idealised than these
observed systems. Previous work has demonstrated, however, that a variety of
architectures are able to scatter exocomets onto the inner planets [64], with
the scattering efficiency dependent on both the planet masses and spacings.
This suggests a robustness to minor changes in the planetary architecture,
with the details of the impacting flux and velocity distribution onto
habitable planets changing on a system-by-system basis.

As discussed in Section 2.1, we do not specify the planetary architecture
beyond the snow-line, however the presence of an external giant planet could
be crucial in perturbing comets onto habitable zone-crossing orbits [58].
Given the efficiency of pebble accretion beyond the snow-line [57], we argue
this justifies our choice of architectures, as external giant planets would be
able to provide an inwards cometary flux. The presence of a giant planet could
however effectively prevent inwards scattering depending on its location in
$(a_{\mathrm{pl}},M_{\mathrm{pl}})$ space [69]. We note here that the dynamics
of every individual planetary system will be unique, with particular
(in)efficiencies in scattering dependent on the exact orbital locations of
planets, and that both resonant and secular effects could in principle produce
results that differ significantly from the trends we present in this paper.

The results of our N-body simulations are very sensitive to the assumptions we
make regarding the initial distribution of the test-particles. Our choice of a
dynamically cold distribution of test-particles gives us an upper limit on the
fraction of low-velocity impacts, providing an optimistic picture of the
potential efficiency of cometary delivery. If, however, the outer cometary
belt is dynamically excited, low velocity impacts will be unlikely. Our
assumption of a planet at the inner edge of a static snow-line is also highly
idealised, with the location of the snow-line evolving quickly during initial
planet formation before moving slowly outwards at late times [96]. Every
system will have a different architecture, but if instead a giant planet
beyond the snow-line is the dominant source of volatile-rich comets, this
would have the same effect as changing the initial Tisserand parameter
distribution, shifting the velocity distribution towards higher velocities. We
also acknowledge that in practice outer belts are likely to host very diverse
populations of volatile-rich bodies, as seen in the solar system (e.g. [97]).
These do not necessarily need to be scattered from the snow-line, as near-
Earth asteroids have also been found to host a suite of prebiotically relevant
molecules, with amino acids, amines and the RNA nucleobase Uracil found on the
carbonaceous asteroid Ryugu [13, 14].

Finally, the successful cometary delivery of prebiotic molecules is also
contingent on a number of physical parameters, which include most
significantly the comet’s radius, the atmospheric density, and the location of
impact [11, 19]. For example, the atmospheric density is crucial in
determining the efficiency of aerobraking, which in principle is able to
sufficiently decelerate large comets in very dense ($\sim$10 bar) atmospheres
and facilitate increased organic survival [11]. Smaller bodies (i.e <0.5 km)
will violently disrupt at high altitudes due to comets’ low material strengths
[98], and so it is likely that in this size range these ‘airbursts’ will
prevent successful cometary delivery [99]. Similarly, organic survival will
decrease for larger radius comets, and for impacts onto the continental crust,
rather than deep ocean [19]. In light of the recent atmospheric retrievals of
K2-18b, which is potentially a temperate, water-rich sub-Neptune [100], a
study of cometary delivery onto ‘Hycean’ planets may be of interest, given
their deep atmospheres and oceanic surfaces. Cometary delivery may be
particularly important, given that high pressure ices below the oceans would
likely preclude access to volatile elements in the silicate core [101]. In
this work, however, we remain agnostic to these effects in our analytical
model as they will change on a planet-by-planet basis, and require additional
assumptions, such as the comets’ size-frequency distribution. These effects
will, however contribute additional scatter onto our conclusions regarding the
importance of cometary delivery.

###  4.4 Observational outlook

Exoplanets can be seen as a diverse array of laboratories, which we can use to
study different origins-of-life scenarios (e.g. [102]). In the coming decade,
the HabEx-PLATO-LIFE epoch will facilitate the detection and atmospheric
characterisation of a census of potentially habitable Earth-mass planets,
extending even to planets around Sun-like stars. These are prime candidates
for supporting Earth-like conditions, improving the prospects of detecting the
first signs of life outside our home planet. This work suggests that in the
scenario that the cometary delivery of prebiotically relevant molecules at low
velocities is important for the origin of life, there will be a correlation
between the presence of biosignatures and the following populations,

  1. 1.

Exoplanets with low escape velocities. A strict upper bound at around 25 km/s
would indicate a very strong reliance on cometary delivery.

  2. 2.

Exoplanets in tightly-packed systems. This should be a stronger effect for the
population of planets around low-mass stars (see figure 3).

  3. 3.

Exoplanets around high-mass stars ($M_{\ast}\gtrsim 1M_{\mathrm{Sun}}$). This
effect would be seen roughly independent of planetary spacing.

Alternatively, the absence of such a correlation would strongly indicate that
cometary delivery at low velocities is unimportant for the origins of life on
rocky exoplanets.

##  5 Conclusions

This paper studies the potential of cometary impacts to deliver the initial
prebiotic inventory required for the origins of life on rocky exoplanets. We
consider the scattering of comets by an idealised planetary system, and derive
simple analytical expressions for the minimum impact velocity onto habitable
planets. This allows us to draw a number of broad conclusions about the
importance of cometary delivery across a wide range of planetary environments.

We find that minimum impact velocities are reduced for planets with lower
escape velocities, planets in tightly-packed systems, and for planetary
systems around high-mass stars. Furthermore, the results of our N-body
simulations demonstrate that the overall velocity distribution of impactors
onto habitable planets is very sensitive to both the stellar-mass and
planetary architecture, with the fraction of low-velocity impacts increasing
significantly for planets around Solar-mass stars, and in tightly-packed
systems. It will be these populations of exoplanets where successful cometary
delivery of prebiotic molecules is most likely to be successful, with
significant implications for the resulting prebiotic inventories due to the
exponential decrease in survivability with impact velocity.

Our results highlight the importance of understanding a planet’s bulk
properties, the stellar-mass and the surrounding planetary environment, as all
of these factors individually can drastically affect a comet’s minimum impact
velocity. If future space missions, such as HabEx/LIFE, characterise the
atmospheres of rocky planets around stars with a range of stellar masses, this
work predicts that if cometary delivery is important for the origins of life,
the presence of biosignatures will be correlated with increased stellar-mass,
decreased planetary mass, and decreased planetary spacing (i.e. tightly-packed
systems). The absence of such correlations would suggest that alternate
pathways are required to produce the initial inventories of prebiotic
feedstock molecules on rocky exoplanets.

We thank Matthew Clement and an anonymous reviewer for insightful comments
that have greatly improved this manuscript. RJA acknowledges the Science and
Technology Facilities Council (STFC) for a PhD studentship. AB acknowledges
the support of a Royal Society University Research Fellowship, URF\R1\211421.
Simulations in this paper made use of the REBOUND code which can be downloaded
freely at https://github.com/hannorein/rebound.
Software acknowledgements: Rebound [72], Numpy [103], Matplotlib [104],
Astropy [105].

## References

  * [1] Chameides WL, Walker JCG. 1981 Rates of fixation by lightning of carbon and nitrogen in possible primitive atmospheres. Origins of life 11, 291–302. (10.1007/BF00931483)
  * [2] Barth P et al.. 2023 Isotopic constraints on lightning as a source of fixed nitrogen in Earth’s early biosphere. Nature Geoscience. (10.1038/s41561-023-01187-2)
  * [3] Kobayashi K et al.. 2023 Formation of Amino Acids and Carboxylic Acids in Weakly Reducing Planetary Atmospheres by Solar Energetic Particles from the Young Sun. Life 13. (10.3390/life13051103)
  * [4] Zahnle KJ. 1986 Photochemistry of CH4 and HCN in the primitive atmosphere. Origins of life and evolution of the biosphere 16, 188–189. (10.1007/BF02421973)
  * [5] Tian F, Kasting JF, Zahnle K. 2011 Revisiting HCN formation in Earth’s early atmosphere. Earth and Planetary Science Letters 308, 417–423. (10.1016/j.epsl.2011.06.011)
  * [6] Ferus M, Kubelík P, Knížek A, Pastorek A, Sutherland J, Civiš S. 2017 High Energy Radical Chemistry Formation of HCN-rich Atmospheres on early Earth. Scientific Reports 7, 6275. (10.1038/s41598-017-06489-1)
  * [7] Parkos D, Pikus A, Alexeenko A, Melosh HJ. 2018 HCN Production via Impact Ejecta Reentry During the Late Heavy Bombardment. Journal of Geophysical Research: Planets 123, 892–909. (10.1002/2017JE005393)
  * [8] Rimmer PB, Rugheimer S. 2019 Hydrogen cyanide in nitrogen-rich atmospheres of rocky exoplanets. Icarus 329, 124–131. (10.1016/j.icarus.2019.02.020)
  * [9] Oró J. 1961 Comets and the Formation of Biochemical Compounds on the Primitive Earth. Nature 190, 389–390. (10.1038/190389a0)
  * [10] Anders E. 1989 Pre-biotic organic matter from comets and asteroids. Nature 342, 255–257. (10.1038/342255a0)
  * [11] Chyba CF, Thomas PJ, Brookshaw L, Sagan C. 1990 Cometary Delivery of Organic Molecules to the Early Earth. Science 249, 366–373.
  * [12] Chyba C, Sagan C. 1992 Endogenous production, exogenous delivery and impact-shock synthesis of organic molecules: an inventory for the origins of life. Nature 355, 125–132. (10.1038/355125a0)
  * [13] Oba Y et al.. 2023 Uracil in the carbonaceous asteroid (162173) Ryugu. Nature Communications 14, 1292. (10.1038/s41467-023-36904-3)
  * [14] Naraoka H et al.. 2023 Soluble organic molecules in samples of the carbonaceous asteroid (162173) Ryugu. Science 379, eabn9033. (10.1126/science.abn9033)
  * [15] Kvenvolden K et al.. 1970 Evidence for Extraterrestrial Amino-acids and Hydrocarbons in the Murchison Meteorite. Nature 228, 923–926. (10.1038/228923a0)
  * [16] Cronin JR, Moore CB. 1971 Amino Acid Analyses of the Murchison, Murray, and Allende Carbonaceous Chondrites. Science 172, 1327–1329. (10.1126/science.172.3990.1327)
  * [17] Rotelli L et al.. 2016 The key role of meteorites in the formation of relevant prebiotic molecules in a formamide/water environment. Scientific Reports 6, 38888. (10.1038/srep38888)
  * [18] Trigo-Rodríguez JM, Rimola A, Tanbakouei S, Soto VC, Lee M. 2019 Accretion of Water in Carbonaceous Chondrites: Current Evidence and Implications for the Delivery of Water to Early Earth. Space Science Reviews 215, 18. (10.1007/s11214-019-0583-0)
  * [19] Pierazzo E, Chyba CF. 1999 Amino acid survival in large cometary impacts. Meteoritics & Planetary Science 34, 909–918. (https://doi.org/10.1111/j.1945-5100.1999.tb01409.x)
  * [20] Mumma MJ, Charnley SB. 2011 The Chemical Composition of Comets—Emerging Taxonomies and Natal Heritage. Annual Review of Astronomy and Astrophysics 49, 471–524. (10.1146/annurev-astro-081309-130811)
  * [21] Elsila JE, Glavin DP, Dworkin JP. 2009 Cometary glycine detected in samples returned by Stardust. Meteoritics & Planetary Science 44, 1323–1330. (https://doi.org/10.1111/j.1945-5100.2009.tb01224.x)
  * [22] Altwegg K et al.. 2017 Organics in comet 67P-a first comparative analysis of mass spectra from ROSINA-DFMS, COSAC and Ptolemy. Monthly Notices of the Royal Astronomical Society 469, 130–141. (10.1093/mnras/stx1415)
  * [23] Sinclair CA, Wyatt MC, Morbidelli A, Nesvorný D. 2020 Evolution of the Earth’s Atmosphere during Late Veneer Accretion. Monthly Notices of the Royal Astronomical Society 499, 5334–5362. (https://doi.org/10.1093/mnras/staa3210)
  * [24] Nesvorný D et al.. 2023 Impact Rates in the Outer Solar System. The Planetary Science Journal 4, 139. (10.3847/PSJ/ace8ff)
  * [25] Sephton MA. 2002 Organic compounds in carbonaceous meteorites. Nat. Prod. Rep. 19, 292–311. (10.1039/B103775G)
  * [26] Moore CB, Lewis CF. 1967 Total carbon content of ordinary chondrites. Journal of Geophysical Research (1896-1977) 72, 6289–6292. (https://doi.org/10.1029/JZ072i024p06289)
  * [27] Clark BC. 1988 Primeval procreative comet pond. Origins of life and evolution of the biosphere 18, 209–238. (10.1007/BF01804671)
  * [28] Pearce BKD, Pudritz RE, Semenov DA, Henning TK. 2017 Origin of the RNA world: The fate of nucleobases in warm little ponds. Proceedings of the National Academy of Sciences 114, 11327–11332. (10.1073/pnas.1710339114)
  * [29] Campbell TD, Febrian R, McCarthy JT, Kleinschmidt HE, Forsythe JG, Bracher PJ. 2019 Prebiotic condensation through wet–dry cycling regulated by deliquescence. Nature Communications 10, 4508. (10.1038/s41467-019-11834-1)
  * [30] Todd ZR, Öberg KI. 2020 Cometary Delivery of Hydrogen Cyanide to the Early Earth. Astrobiology 20, 1109–1120. (10.1089/ast.2019.2187)
  * [31] Strecker A. 1854 Ueber einen neuen aus Aldehyd - Ammoniak und Blausäure entstehenden Körper. Justus Liebigs Annalen der Chemie 91, 349–351. (https://doi.org/10.1002/jlac.18540910309)
  * [32] Miller SL. 1953 A Production of Amino Acids under Possible Primitive Earth Conditions. Science 117, 528–529. (10.1126/science.117.3046.528)
  * [33] Ferus M et al.. 2015 High-energy chemistry of formamide: A unified mechanism of nucleobase formation. Proceedings of the National Academy of Sciences 112, 657–662. (10.1073/pnas.1412072111)
  * [34] Patel BH, Percivalle C, Ritson DJ, Duffy CD, Sutherland JD. 2015 Common origins of RNA, protein and lipid precursors in a cyanosulfidic protometabolism. Nature Chemistry 7, 301–307. (10.1038/nchem.2202)
  * [35] Xu J, Ritson DJ, Ranjan S, Todd ZR, Sasselov DD, Sutherland JD. 2018 Photochemical reductive homologation of hydrogen cyanide using sulfite and ferrocyanide. Chemical Communications 54, 5566–5569. (10.1039/C8CC01499J)
  * [36] Sutherland JD. 2016 The Origin of Life—Out of the Blue. Angewandte Chemie International Edition 55, 104–121. (https://doi.org/10.1002/anie.201506585)
  * [37] Bochanski JJ et al.. 2010 The luminosity and mass functions of low-mass stars in the galactic disk. II. The Field. The Astronomical Journal 139, 2679. (10.1088/0004-6256/139/6/2679)
  * [38] Wyatt MC. 2008 Evolution of debris disks.. Annual Review of Astronomy and Astrophysics 46, 339–383. (10.1146/annurev.astro.45.051806.110525)
  * [39] Eiroa C et al.. 2013 DUst around NEarby Stars. The survey observational results. Astronomy & Astrophysics 555, A11. (10.1051/0004-6361/201321050)
  * [40] Krivov AV, Wyatt MC. 2020 Solution to the debris disc mass problem: planetesimals are born small?. Monthly Notices of the Royal Astronomical Society 500, 718–735. (10.1093/mnras/staa2385)
  * [41] Zuckerman B, Song I. 2012 A 40 Myr old gaseous circumstellar disk at 49 Ceti: massive co-rich comet clouds at young A-type stars. The Astrophysical Journal 758, 77. (10.1088/0004-637X/758/2/77)
  * [42] Marino S et al.. 2016 Exocometary gas in the HD 181327 debris ring. Monthly Notices of the Royal Astronomical Society 460, 2933–2944. (10.1093/mnras/stw1216)
  * [43] Plavchan P et al.. 2020 A planet within the debris disk around the pre-main-sequence star AU Microscopii. Nature 582, 497–500. (10.1038/s41586-020-2400-z)
  * [44] Martioli, E., Hébrard, G., Correia, A. C. M., Laskar, J., Lecavelier des Etangs, A.. 2021 New constraints on the planetary system around the young active star AU Mic - Two transiting warm Neptunes near mean-motion resonance. Astronomy & Astrophysics 649, A177. (10.1051/0004-6361/202040235)
  * [45] Kalas P, Liu MC, Matthews BC. 2004 Discovery of a Large Dust Disk Around the Nearby Star AU Microscopii. Science 303, 1990–1992. (10.1126/science.1093420)
  * [46] Sato S, Cuntz M, Guerra Olvera CM, Jack D, Schröder KP. 2014 Habitability around F-type stars. International Journal of Astrobiology 13, 244–258. (10.1017/S1473550414000020)
  * [47] Shields AL, Ballard S, Johnson JA. 2016 The habitability of planets orbiting M-dwarf stars. Physics Reports 663, 1. (10.1016/j.physrep.2016.10.003)
  * [48] Scalo J et al.. 2007 M stars as targets for terrestrial exoplanet searches and biosignature detection. Astrobiology 7, 85–166. Copyright: Copyright 2018 Elsevier B.V., All rights reserved. (10.1089/ast.2006.0125)
  * [49] Kopparapu RK et al.. 2013 Habitable Zones around Main-sequence Stars: New Estimates. The Astrophysical Journal 765, 131. (10.1088/0004-637X/765/2/13110.48550/arXiv.1301.6674)
  * [50] Alcalá JM et al.. 2014 X-shooter spectroscopy of young stellar objects. IV. Accretion in low-mass stars and substellar objects in Lupus. Astronomy & Astrophysics 561, A2. (10.1051/0004-6361/201322254)
  * [51] Min M, Dullemond CP, Kama M, Dominik C. 2011 The thermal structure and the location of the snow line in the protosolar nebula: Axisymmetric models with full 3-D radiative transfer. Icarus 212, 416–426. (https://doi.org/10.1016/j.icarus.2010.12.002)
  * [52] Weiss LM et al.. 2022 Architectures of Compact Multi-planet Systems: Diversity and Uniformity. arXiv e-prints p. arXiv:2203.10076. (10.48550/arXiv.2203.10076)
  * [53] Weiss LM et al.. 2018 The California-Kepler Survey. V. Peas in a Pod: Planets in a Kepler Multi-planet System Are Similar in Size and Regularly Spaced. The Astronomical Journal 155, 48. (10.3847/1538-3881/aa9ff6)
  * [54] Millholland S, Wang S, Laughlin G. 2017 Kepler Multi-planet Systems Exhibit Unexpected Intra-system Uniformity in Mass and Radius. The Astrophysical Journal Letters 849, L33. (10.3847/2041-8213/aa9714)
  * [55] Wang S. 2017 RV-detected Kepler-multi Analogs Exhibit Intra-system Mass Uniformity. Research Notes of the AAS 1, 26. (10.3847/2515-5172/aa9be5)
  * [56] Lambrechts, Michiel et al.. 2019 Formation of planetary systems by pebble accretion and migration - How the radial pebble flux determines a terrestrial-planet or super-Earth growth mode. Astronomy & Astrophysics 627, A83. (10.1051/0004-6361/201834229)
  * [57] Bitsch, B et al.. 2019 Formation of planetary systems by pebble accretion and migration: growth of gas giants. Astronomy & Astrophysics 623, A88. (10.1051/0004-6361/201834489)
  * [58] Dencs Z, Regály Z. 2019 Water delivery to the TRAPPIST-1 planets. Monthly Notices of the Royal Astronomical Society 487, 2191–2199. (10.1093/mnras/stz1412)
  * [59] Pu B, Wu Y. 2015 Spacing of Kepler planets: sculpting by dynamical instability. The Astrophysical Journal 819. (10.3847/0004-637X/819/2/170)
  * [60] Chambers J, Wetherill G, Boss A. 1996 The Stability of Multi-Planet Systems. Icarus 119, 261–268. (https://doi.org/10.1006/icar.1996.0019)
  * [61] Obertas A, Van Laerhoven C, Tamayo D. 2017 The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star. Icarus 293, 52–58. (https://doi.org/10.1016/j.icarus.2017.04.010)
  * [62] Gladman B. 1993 Dynamics of Systems of Two Close Planets. Icarus 106, 247–263. (10.1006/ICAR.1993.1169)
  * [63] Deck KM, Payne M, Holman MJ. 2013 First-order resonance overlap and the stability of close two-planet systems. The Astrophysical Journal 774, 129. (10.1088/0004-637X/774/2/129)
  * [64] Marino S, Bonsor A, Wyatt MC, Kral Q. 2018 Scattering of exocomets by a planet chain: exozodi levels and the delivery of cometary material to inner planets. Monthly Notices of the Royal Astronomical Society 479, 1651–1671. (10.1093/mnras/sty1475)
  * [65] Levison HF, Duncan MJ. 1997 From the Kuiper Belt to Jupiter-family comets: The spatial distribution of ecliptic comets. Icarus 127, 13–32. (10.1006/ICAR.1996.5637)
  * [66] Tisserand FF. 1889 Traité de mécanique céleste. Number v. 4 in Traité de mécanique céleste. Gauthier-Villars.
  * [67] Murray CD, Dermott SF. 1999 Solar system dynamics. Cambridge University Press.
  * [68] Öpik EJ. 1951 Collision Probabilities with the Planets and the Distribution of Interplanetary Matter. Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences 54, 165–199.
  * [69] Wyatt MC, Bonsor A, Jackson AP, Marino S, Shannon A. 2017 How to design a planetary system for different scattering outcomes: Giant impact sweet spot, maximizing exocomets, scattered discs. Monthly Notices of the Royal Astronomical Society 464, 3385–3407. (10.1093/mnras/stw2633)
  * [70] Bonsor A, Wyatt MC. 2012 The scattering of small bodies in planetary systems: constraints on the possible orbits of cometary material. Monthly Notices of the Royal Astronomical Society 420, 2990–3002. (10.1111/j.1365-2966.2011.20156.x)
  * [71] Rein H et al.. 2019 Hybrid symplectic integrators for planetary dynamics. Monthly Notices of the Royal Astronomical Society 485, 5490–5497. (10.1093/mnras/stz769)
  * [72] Rein H, Liu SF. 2012 Astrophysics REBOUND: an open-source multi-purpose N-body code for collisional dynamics. Astronomy & Astrophysics 537, 128. (10.1051/0004-6361/201118085)
  * [73] Rein H, Spiegel DS. 2015 IAS15: a fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits. Monthly Notices of the Royal Astronomical Society 446, 1424–1437. (10.1093/mnras/stu2164)
  * [74] Wisdom J, Holman M. 1991 Symplectic maps for the N-body problem. The Astronomical Journal 102, 1528–1538. (10.1086/115978)
  * [75] Rein H, Tamayo D. 2015 WHFAST: a fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long-term gravitational simulations. Monthly Notices of the Royal Astronomical Society 452, 376–388. (10.1093/mnras/stv1257)
  * [76] Maher KA, Stevenson DJ. 1988 Impact frustration of the origin of life. Nature 331, 612–614. (10.1038/331612a0)
  * [77] Maeder A, Meynet G. 1988 Tables of evolutionary star models from 0.85 to 120 solar masses with overshooting and mass loss. Astronomy and Astrophysics Supplement Series 76, 411–425.
  * [78] Kudritzki RP, Puls J. 2000 Winds from Hot Stars. Annual Review of Astronomy and Astrophysics 38, 613–666. (10.1146/annurev.astro.38.1.613)
  * [79] Cockell CS. 1999 Carbon Biochemistry and the Ultraviolet Radiation Environments of F, G, and K Main Sequence Stars. Icarus 141, 399–407. (https://doi.org/10.1006/icar.1999.6167)
  * [80] Agol E et al.. 2021 Refining the Transit-timing and Photometric Analysis of TRAPPIST-1: Masses, Radii, Densities, Dynamics, and Ephemerides. The Planetary Science Journal 2, 1. (10.3847/PSJ/abd022)
  * [81] Gillon M et al.. 2017 Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1. Nature 542, 456–460. (10.1038/nature21360)
  * [82] Anglada-Escudé G et al.. 2016 A terrestrial planet candidate in a temperate orbit around Proxima Centauri. Nature 536, 437–440. (10.1038/nature19106)
  * [83] Damasso M et al.. 2020 A low-mass planet candidate orbiting Proxima Centauri at a distance of 1.5 AU. Science Advances 6, eaax7467. (10.1126/sciadv.aax7467)
  * [84] Krijt S, Bowling TJ, Lyons RJ, Ciesla FJ. 2017 Fast Litho-panspermia in the Habitable Zone of the TRAPPIST-1 System. The Astrophysical Journal Letters 839, L21. (10.3847/2041-8213/aa6b9f)
  * [85] Ramirez RM, Kaltenegger L. 2014 The habitable zones of pre-main-sequence stars. The Astrophysical Journal Letters 797, 25. (10.1088/2041-8205/797/2/L25)
  * [86] Hawley SL et al.. 2014 Kepler Flares. I. Active and Inactive M Dwarfs. The Astrophysical Journal 797, 121. (10.1088/0004-637X/797/2/121)
  * [87] Baraffe I, Homeier D, Allard F, Chabrier G. 2015 Astrophysics New evolutionary models for pre-main sequence and main sequence low-mass stars down to the hydrogen-burning limit. Astronomy & Astrophysics 577, 42. (10.1051/0004-6361/201425481)
  * [88] Clement MS, Quintana EV, Quarles BL. 2022 Habitable Planet Formation around Low-mass Stars: Rapid Accretion, Rapid Debris Removal, and the Essential Contribution of External Giants. The Astrophysical Journal 928, 91. (10.3847/1538-4357/ac549e)
  * [89] Lichtenberg T, Clement MS. 2022 Reduced Late Bombardment on Rocky Exoplanets around M Dwarfs. The Astrophysical Journal Letters 938, L3. (10.3847/2041-8213/ac9521)
  * [90] Bolmont E et al.. 2017 Water loss from terrestrial planets orbiting ultracool dwarfs: implications for the planets of TRAPPIST-1. Monthly Notices of the Royal Astronomical Society 464, 3728–3741. (10.1093/mnras/stw2578)
  * [91] Toon OB, Pollack JB, Ackerman TP, Turco RP, McKay CP, Liu MS. 1982 Evolution of an impact-generated dust cloud and its effects on the atmosphere. In Geological Implications of Impacts of Large Asteroids and Comets on the Earth , . Geological Society of America. (10.1130/SPE190-p187)
  * [92] Schlichting HE, Sari R, Yalinewich A. 2015 Atmospheric mass loss during planet formation: The importance of planetesimal impacts. Icarus 247, 81–94. (https://doi.org/10.1016/j.icarus.2014.09.053)
  * [93] Wyatt MC, Kral Q, Sinclair CA. 2020 Susceptibility of planetary atmospheres to mass-loss and growth by planetesimal impacts: the impact shoreline. Monthly Notices of the Royal Astronomical Society 491, 782–802. (10.1093/mnras/stz3052)
  * [94] Melosh HJ, Vickery AM. 1989 Impact erosion of the primordial atmosphere of Mars. Nature 338, 487–489. (10.1038/338487a0)
  * [95] Kral Q et al.. 2018 Cometary impactors on the TRAPPIST-1 planets can destroy all planetary atmospheres and rebuild secondary atmospheres on planets f, g, and h. Monthly Notices of the Royal Astronomical Society 479, 2649–2672. (10.1093/MNRAS/STY1677)
  * [96] Zhang Y, Jin L. 2015 The evolution of the snow line in a protoplanetary disk. The Astrophysical Journal 802, 58. (10.1088/0004-637X/802/1/58)
  * [97] Nesvorný D, Brož M, Carruba V. 2015 Identification and Dynamical Properties of Asteroid Families. In Asteroids IV , pp. 297–321. University of Arizona Press. (10.2458/azu_uapress_9780816532131-ch016)
  * [98] Chyba CF, Thomas PJ, Zahnle KJ. 1993 The 1908 Tunguska explosion: atmospheric disruption of a stony asteroid. Nature 361, 40–44. (10.1038/361040a0)
  * [99] Boslough M, Crawford D. 2008 Low-altitude airbursts and the impact threat. International Journal of Impact Engineering 35, 1441–1448. Hypervelocity Impact Proceedings of the 2007 Symposium (https://doi.org/10.1016/j.ijimpeng.2008.07.053)
  * [100] Madhusudhan N et al.. 2023 Carbon-bearing Molecules in a Possible Hycean Atmosphere. arXiv e-prints p. arXiv:2309.05566. (10.48550/arXiv.2309.05566)
  * [101] Madhusudhan N, Moses JI, Rigby F, Barrier E. 2023 Chemical conditions on Hycean worlds. Faraday Discuss. 245, 80–111. (10.1039/D3FD00075C)
  * [102] Rimmer PB. 2023 Origins of Life on Exoplanets. In Smoukov S, Seckbach J, Gordon R, editors, Conflicting Models for the Origin of Life , pp. 407–424. John Wiley & Sons. (10.1002/9781119555568.ch16)
  * [103] Harris CR et al.. 2020 Array programming with NumPy. Nature 585, 357–362. (10.1038/s41586-020-2649-2)
  * [104] Hunter JD. 2007 Matplotlib: A 2D Graphics Environment. Computing in Science and Engineering 9, 90–95. (10.1109/MCSE.2007.55)
  * [105] Astropy Collaboration et al.. 2022 The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package. The Astrophysical Journal 935, 167\. (10.3847/1538-4357/ac7c74)