# Panspermia in a Milky Way-like Galaxy

Raphael Gobat Instituto de Física, Pontificia Universidad Católica de
Valparaíso, Casilla 4059, Valparaíso, Chile  Sungwook E. Hong (홍성욱) Korea
Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon
34055, Republic of Korea  Natural Science Research Institute, University of
Seoul, 163 Seoulsiripdaero, Dongdaemun-gu, Seoul, 02504, Republic of Korea
Owain Snaith  GEPI, Observatoire de Paris, PSL Research University, CNRS,
Place Jules Janssen, 92190, Meudon, France  Sungryong Hong (홍성용) Korea
Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon
34055, Republic of Korea Sungwook E. Hong<EMAIL_ADDRESS>
###### Abstract

We study the process of panspermia in Milky Way-like galaxies by modeling the
probability of successful travel of organic compounds between stars harboring
potentially habitable planets. To this end, we apply the modified habitability
recipe of Gobat & Hong (2016) to a model galaxy from the MUGS suite of zoom-in
cosmological simulations. We find that, unlike habitability, which only
occupies narrow dynamic range over the entire galaxy, the panspermia
probability can vary be orders of magnitude between the inner
($R,b=1-4\mathinner{{\rm kpc}}$) and outer disk. However, only a small
fraction of star particles have very large values of panspermia probability
and, consequently, the fraction of star particles where the panspermia process
is more effective than prebiotic evolution is much lower than from naïve
expectations based on the ratio between panspermia probability and natural
habitability.

astrobiology — dust, extinction — Galaxy: stellar content — methods: numerical
— planetary system

††software: IDL, Matplotlib (Hunter, 2007), NumPy/SciPy (Virtanen et al.,
2020), Pandas (McKinney, 2010)

##  1 Introduction

The notion that living organisms could travel between celestial bodies is
almost as old as the concept of habitable worlds (e.g., Lucian’s _Vera
Historia_ , Kepler’s _Somnium_ , or Voltaire’s _Micromégas_). Already present
in embryonic form in some ancient mythologies, it was first formally named
_panspermia_ 25 centuries ago by the philosopher Anaxagoras. The development
of microbiology in the 19${}^{\text{th}}$ century opened up the possibility
that such passage, rather than being directed, could take the form of the
accidental propagation of simple _seeds_ of life (e.g., Arrhenius & Borns,
1908). This idea eventually spread through popular culture and became a minor
staple of early 20${}^{\text{th}}$ century speculative fiction, often playing
on fears of invasion and contamination.

In the modern era of astrophysics, the concept of panspermia was famously
embraced and developed by F. Hoyle and C. Wickramasinghe after the discovery
of organic compounds in the interstellar medium (e.g., Hoyle & Wickramasinghe,
1977, 1978; Hoyle et al., 1983, 1986). Although never gaining widespread
acceptance, likely due to a combination of practical and ideological factors
(i.e., long odds and a perceived non-necessity in explaining our world),
panspermia has been the subject of a steady number of studies since then. It
has experienced a resurgence lately with the discovery of multiple, possibly
habitable exoplanetary systems (Gillon et al., 2016; Zechmeister et al., 2019)
and the recent crossing through the solar system of hyperbolic trajectory
comets of probable interstellar origin (Meech et al., 2017; Higuchi & Kokubo,
2019), starkly illustrating the possibility of matter exchanges between
unbound star systems.

Modern studies involving panspermia broadly fall into three categories. The
first concerns practical evaluations of the survivability of micro-organisms
to the various potentially lethal events that panspermia involves. Namely,
their ejection from and re-entry onto planetary surfaces (e.g., Melosh, 1988;
Burchell et al., 2001; Mastrapa et al., 2001; Stöffler et al., 2007; Burchell,
2007; Price et al., 2013; Pasini & Price, 2015) and transit through the harsh
radiation environment of interplanetary and interstellar space (e.g., Weber &
Greenberg, 1985; Horneck et al., 1994; Secker et al., 1996; Horneck et al.,
2001; Wickramasinghe & Wickramasinghe, 2003; Yamagishi et al., 2018). These
show that bacterial spores can survive hypervelocity impacts, as well as
prolonged exposure to a combination of hard vacuum, low temperatures, and
ionizing radiation. Although experiments were understandably not carried out
over the timescales expected for interstellar panspermia, they nevertheless
suggest that a small but non-insignificant fraction of spores could survive
the kilo- or mega-years of transit, especially when embedded in even a thin
mantle of carbonaceous material.

The second type of study tries to estimate the timescale and types of mass
transfer between planets orbiting a common host star, typically by the
exchange of meteoroids (also called _litho-panspermia_ ; Wells et al., 2003;
Gladman et al., 2005; Krijt et al., 2017; Lingam & Loeb, 2017), or between
stellar systems (e.g., Melosh, 2003; Lingam & Loeb, 2018), with the radiation
pressure on small grains (also called _radio-panspermia_ ; Wallis &
Wickramasinghe, 2004; Napier, 2004; Wesson, 2010; Lingam & Loeb, 2021). To
these, we can also include speculations on the intentional seeding of other
stellar systems via technological means (or _directed panspermia_ ; e.g.,
Crick & Orgel, 1973).

The last category concerns statistical investigations of panspermic
propagation through stellar systems or galaxies using analytical or simple
numerical models (Adams & Spergel, 2005; Lin & Loeb, 2015; Lingam, 2016;
Ginsburg et al., 2018; Đošović et al., 2019; Carroll-Nellenback et al., 2019),
or of the effect of a spatially variable probability of habitable planets
(_habitability_ ; e.g., Gonzalez et al., 2001; Lineweaver et al., 2004;
Gowanlock et al., 2011) on the viability of panspermia.

Here we couple the products of a hydrodynamical simulation of a Milky Way-like
galaxy (Stinson et al., 2010; Nickerson et al., 2013) with a modified galactic
habitability model (Gobat & Hong, 2016, hereafter GH16) to investigate how the
probability and efficiency of panspermia vary with galactic environment. This
paper is structured as follows: Sect. 2 and 3 describe, respectively, the
numerical simulation and habitability model that constitute the base of this
study, while Sect. 4 presents the mathematical formalism we use for computing
the probability of panspermia. We describe and discuss our results in Sect. 5
and summarize our conclusions in Sect. 6.

##  2 Simulation Data

The _McMaster Unbiased Galaxy Simulations_ (MUGS) is a set of 16 simulated
galaxies carried out by Stinson et al. (2010) and Nickerson et al. (2013).
These simulations made use of the cosmological zoom method, which seeks to
focus computational effort into a region of interest, while maintaining enough
of the surrounding large-scale structure to produce a realistic assembly
history. To accomplish this, the simulation was first carried out at low
resolution using N-body physics only. Dark matter halos were then identified,
and a sample of interesting objects selected. The particles making up, and
surrounding, these halos were then traced back to their origin, and the
simulation carried out again with the region of interest simulated at higher
resolution. The sample of galaxies was selected to have a minimal selection
bias on the merging history or spin parameter. To be eligible for re-
simulation halos had to have a mass between $5\times 10^{11}$ and $2\times
10^{12}\,{\rm M}_{\odot}$, and be isolated for any object with a mass greater
than $5\times 10^{11}$ by 2.7 Mpc. MUGS is therefore able to reproduce
realistic infall and merging histories. Furthermore, they are able to
reproduce the metallicity gradients seen in observed galaxies (e.g.,
Pilkington et al., 2012; Snaith et al., 2016), as well as features such as
discs, halos and bulges.

The MUGS galaxies were simulated in the context of a $\Lambda$CDM cosmology in
concordance with the _Wilkinson Microwave Anisotropy Probe_ (WMAP) 3-year
result (Spergel et al., 2007), with
$(h,\Omega_{m},\Omega_{\Lambda},\Omega_{b},\sigma_{8})=(0.73,0.24,0.76,0.04,0.79)$.
The simulations were carried out down to $z=0$ using the GASOLINE (Wadsley et
al., 2004) smoothed-particle hydrodynamics code (SPH).

In the high-resolution region a gravitational softening length of 310 pc was
used, with a hydrodynamical smoothing length of 0.01 times the softening
length. The masses of the dark matter, gas and stellar particles were
$1.1\times 10^{6}$, $1.1\times 10^{6}$, and $6.3\times 10^{6}\mathinner{{\rm
M}_{\odot}}$ respectively. In order to reproduce the baryonic properties of
observed galaxies the simulations made use of ultraviolet (UV) background
radiation, and metal-based cooling at low temperatures (Shen et al., 2010).
These are based on results from CLOUDY (Ferland et al., 1998). To govern star
formation, the simulations used a Schmidt-Kennicutt relation to relate the gas
density to the star formation rate (SFR; Kennicutt, 1998). This is further
influenced by feedback processes from supernovae, which release energy and
metals into the interstellar medium (ISM; see Stinson et al. 2006 for
details). A Kroupa Initial Mass Function (IMF; Kroupa et al., 1993, hereafter
KTG93) was used to calculate the stellar yields produced by each star
particle111It is important to remember that each star particle is an ensemble
of stars with a range of masses but the same metallicity. This is a
consequence of the resolution limits of simulations, which cannot follow
individual stars through time.. The slope of the IMF controls the ratio of
high mass to low mass stars in a given simple stellar population (SSP), and
each star particle is essentially an SSP. The effect of the fraction of high
mass stars is that it directly effects the ratio of Oxygen to Iron, because
Oxygen is produced by core-collapse supernovae, while Iron is predominantly
produced by SNIa. Thus, the IMF affects the stellar yields from star
particles222Pilkington et al. (2012) found that the metallicity, $Z$, is
calculated as ${\rm O+Fe}$, meaning that it is 1.8 times lower then expected.
This may have a small impact on the cooling rate of gas, etc.. Metals are
allowed to diffuse between gas particles, using the method outlined in Wadsley
et al. (2008), in order to improve mixing.

Figure 1: Mock $UVJ$ color images of the simulated galaxy g15784 (Stinson et
al., 2010; Nickerson et al., 2013), for both edge-on (_left_) and face-on
(_right_) orientations, using star and gas particles, and assuming Bruzual &
Charlot (2003) stellar population models and a simple dust attenuation model
(Li & Draine, 2001) with a gas-to-dust ratio of 0.01 at solar metallicity.
Additionally, we include line emission from star particles with ages $\leq
50\mathinner{{\rm Myr}}$, following _case B_ recombination (Osterbrock &
Ferland, 2006) and metallicity-dependent line ratios (Anders & Fritze-v.
Alvensleben, 2003). All panels are $50\mathinner{{\rm kpc}}$ across and have a
resolution of $100\mathinner{{\rm pc}}$. Two spheroidal satellites can be seen
above and below the galactic plane, respectively.

We select one galaxy from MUGS for this study, g15784, which is characterized
by a quiescent merger history. The galaxy has a total and stellar mass of
$1.5\times 10^{12}$ and $1.14\times 10^{11}\mathinner{{\rm M}_{\odot}}$,
respectively, and is therefore slightly larger than the Milky Way (Licquia &
Newman, 2015). g15784 has not experienced a merger with an object more massive
than a 1:3 ratio since $z_{\rm lmm}\simeq 3.42$, similar to our own Galaxy
(e.g., Stewart et al., 2008; Kruijssen et al., 2019; Naidu et al., 2021).
Several spheroidal galaxies can be seen to orbit g15784 within
$25\mathinner{{\rm kpc}}$ of the galactic center (see Fig. 1)333For more
details see https://mugs.mcmaster.ca/g15784.html. For an overview of the
detailed chemical properties of this galaxy, see Gibson et al. (2013) and
Snaith et al. (2016), among other works.

Figure 2: Face-on radial profiles of the surface density (_top_), stellar age
(_middle_), and the metallicity (_bottom_) of g15784 at $z=0$. Shaded regions
show the standard deviation within a given radial bin.

Fig. 2 shows the face-on radial profiles of the surface density, stellar age,
and the metallicity of g15784. By taking the mean value of [Fe/H] in a series
of radial bins between $3\mathinner{{\rm kpc}}$ and $20\mathinner{{\rm kpc}}$
we find this galaxy has a metallicity gradient of $-0.012\,{\rm dex/kpc}$.
Outside of around $10\mathinner{{\rm kpc}}$ the stars have a mean formation
time of $6.5-7\mathinner{{\rm Gyr}}$, rising from a formation time of
$3.6\mathinner{{\rm Gyr}}$ at a $1.5\mathinner{{\rm kpc}}$. The SFR at $z=0$
is approximately $2.5\mathinner{{\rm M}_{\odot}}\,{\rm yr}^{-1}$. One
important caveat is that the bulge-to-disc light ratio ($\log({\rm B/D})$) for
this galaxy is larger than expected for the Milky Way, reaching a value of
$-1.6$ for g15784 (Brook et al., 2012), compared to $+0.14$ for the Milky Way
(McMillan, 2011). This is a known difference between the Milky Way and MUGS
galaxies (Stinson et al., 2010; Allen et al., 2006). This is the effect of
insufficient feedback and resolution to capture all the physical processes
required to produce a realistic simulated galaxy.

From now on, we only consider the star particles located between
$1-25\mathinner{{\rm kpc}}$ from the mass-weighted center of the g15784. We
ignore the inner 1$\mathinner{{\rm kpc}}$ since it is not well resolved. We
find a massive knot of particles in the inner few softening lengths, and the
high stellar and gas density of this region might thus be an artifact of the
simulation (Stinson et al., 2010). The volume we consider contains 977,304
star particles, which we separate into three distinct regions: (1) the
CentralDisk, located in galactocentric radius $R=1-4\mathinner{{\rm kpc}}$
with a thickness of 1 kpc along the galactic plane; (2) the DiskHalo, which
corresponds to both the inner disk ($R=1-4\mathinner{{\rm kpc}}$ with larger
thickness than CentralDisk), outer disk ($R=4-20\mathinner{{\rm kpc}}$), and
galactic halo outside the disk; and (3) the Spheroids that include two
orbiting spheroids.

##  3 Levels of Habitability

For each star $6.3\times 10^{6}\mathinner{{\rm M}_{\odot}}$ particle, we
compute a measure of _habitability_ , that is, the fraction of main-sequence
low-mass stars with terrestrial planets within their habitable zones (HZs). We
mostly follow the model described in GH16 and refer to that paper for more
details on its various components. A quick summary of its formalism is as
follows. The habitability fraction $f_{\rm hab}$ of a given star particle at
the time $t=t_{z}$ is defined as

$f_{\rm hab}=\frac{1}{n_{\star}}\int_{0}^{t_{z}-t_{\rm min}}\mathinner{{\rm
d}\\!}t\,(1-V_{\rm irr})\Psi\\\ \times\int_{m_{\rm min}}^{1.5\mathinner{{\rm
M}_{\odot}}}\mathinner{{\rm d}\\!}m\,m\phi\,\mathcal{H}(t_{\rm MS}-t)w_{\rm
h}$ (1)

with

$n_{\star}(t_{z})=\int_{0}^{t_{z}}\mathinner{{\rm d}\\!}t\,\Psi\int_{m_{\rm
min}}^{m_{\rm max}}\mathinner{{\rm d}\\!}m\,m\phi\,\mathcal{H}(t_{\rm MS}-t)$
(2) $w_{\rm h}(m,Z,t)=f_{\rm T}\,\mathcal{H}(1.5\mathinner{{\rm
M}_{\odot}}-m)\\\ \times\left(\int_{r_{\rm h,i}}^{r_{\rm h,o}}\mathinner{{\rm
d}\\!}r\,P^{\beta_{\rm P}}\frac{\mathinner{{\rm d}\\!}P}{\mathinner{{\rm
d}\\!}r}\right)\big{/}\left(\int\mathinner{{\rm
d}\\!}r\,N\frac{\mathinner{{\rm d}\\!}P}{\mathinner{{\rm d}\\!}r}\right)$ (3)

$f_{\rm T}(Z)=\mathcal{H}(Z-Z_{\rm min})\left[f_{\rm T,0}-f_{\rm
HJ}\left(\frac{Z}{Z_{\odot}}\right)^{\alpha_{\rm P}}\right]\,,$ (4)

where $\mathcal{H}(x)$ is the Heaviside step function, and $(m_{\rm
min},m_{\rm max})=(0.1\mathinner{{\rm M}_{\odot}},100\mathinner{{\rm
M}_{\odot}})$ are the minimum and maximum mass of a star, respectively.
$\Psi(t)$ is the star particle’s star formation history (SFH)444Since star
particles are created just once due to the construction of the numerical
simulation, this simply corresponds to a delta burst, to which we assign a
duration of $100\mathinner{{\rm Myr}}$., $\phi(m)$ is its IMF, and $V_{\rm
irr}(t)$ is its (time-dependent) volume fraction irradiated by SN. $t_{\rm
MS}(m,Z)$ is the main-sequence lifetime of a star with mass $m$ and
metallicity $Z$, and $r_{\rm h,i}(m,Z,t)$ and $r_{\rm h,o}(m,Z,t)$ are the
inner and outer radii of its HZ, respectively. $P(r,m)$ are the orbital
periods of planets orbiting that star, whose distribution follows a simple
power-law $\mathinner{{\rm d}\\!}N\propto P(r,m)^{\beta_{\rm
p}}\mathinner{{\rm d}\\!}P$ (e.g., Cumming et al., 2008; Petigura et al.,
2013; Burke et al., 2015). $f_{\rm T}(Z)$ is the fraction of stars with
terrestrial planets (_Case 2_ of the metallicity dependence in GH16, ), and
$f_{\rm HJ}$ is the fraction of solar-metallicity stars with short-period gas
giants (or, _hot Jupiters_), with $Z_{\rm min}=0.1Z_{\odot}$ being a
metallicity threshold below which we assume that terrestrial planets cannot
form. We do not consider the contribution of the active nucleus in the
galactic core, since the distance at which its additional radiative input
significantly alters HZs is somewhat smaller (GH16) than the radius of the
simulation volume we ignore. The number of (potentially) habitable stellar
systems in each star particle is therefore given as $n_{\rm hab}=f_{\rm
hab}n_{\star}$.

The values of each parameter we used in this paper are the same as in GH16:
$(f_{\rm HJ},\alpha_{\rm P},\beta_{\rm P})=(0.012,2,-0.7)$, with the following
exceptions. First, $t_{\rm min}$, the time after which a planet is considered
able to host life, is decreased from $1\mathinner{{\rm Gyr}}$ to
$500\mathinner{{\rm Myr}}$ in the _natural_ case (see below). Also, we set
$f_{\rm T,0}=1$ (similar to Zackrisson et al., 2016) to reconcile the
predictions of the model with _Kepler_ constraints (He et al., 2019), which
previously differed by a factor of $\sim 2$ (GH16). Finally, we modify the
inner radius of the HZ (Eq. (3) in Kopparapu et al., 2013), to account for
increased flare activity in low-mass stars. In essence, we increase the
luminosity $L$ of every star by the energy-integrated cumulative distribution
of flare frequency (which we approximate as a power-law with an index of
$-0.8$), limited by its mass-dependent maximum flare energy, from Davenport
(2016). Since we are only concerned with average quantities, we simply weigh
this additional luminosity by the fraction of flaring stars to derive the
fractional increase per stellar mass. This has the effect of slightly reducing
the habitability weight $w_{\rm h}(m,Z,t)$ of sub-solar mass stars. However,
the effect is mild enough that it does not modify our results. 555In a similar
way, atmospheric erosion by intense stellar winds might also push the inner
edge of the HZ outwards without impacting its outer radius (e.g., see Dong et
al., 2018), effectively narrowing it further around M-dwarfs as they age.

Figure 3: Rates of Type Ia (red) and Type II (blue) supernovae for selected
star particles in g15784. Particle IDs are shown in the upper right corner of
each panel.

We compute supernova rates (SNR) for each star particle based on its SFH and
neighboring particles at each time step, using simulation snapshots from
$z=10.8$ to $z=0$, spaced by $\sim$200 Myr. We consider Type Ia and II
supernovae, with

$\displaystyle{\rm SNR}_{\rm Ia}(t)$ $\displaystyle=\eta_{\rm WD}\int_{m_{\rm
min}}^{8\mathinner{{\rm M}_{\odot}}}\mathinner{{\rm d}\\!}m\,m$
$\displaystyle\,\times\int_{\tau_{\rm Ia}+t_{\rm MS}(8\mathinner{{\rm
M}_{\odot}})}^{t}\\!\\!\\!\\!\\!\\!\mathinner{{\rm
d}\\!}t^{\prime}\,\Psi(\tau)\phi(m,\tau)$ (5) $\displaystyle{\rm SNR}_{\rm
II}(t)$ $\displaystyle=\Psi(t)\int_{8\mathinner{{\rm M}_{\odot}}}^{m_{\rm
max}}\mathinner{{\rm d}\\!}m\,m\,\phi(m,t)\,,$ (6)

where $\eta_{\rm WD}=0.01$ is the white dwarf (WD) conversion rate (Pritchet
et al., 2008), $\tau=t^{\prime}-t_{\text{MS}}(m)-\tau_{\text{Ia}}$, and
$\tau_{\text{Ia}}=500\mathinner{{\rm Myr}}$ is the average delay time between
stellar death and the detonation of the WD (Raskin et al., 2009). An example
of SNRs for selected star particles in g15784 is given in Fig. 3. The volume
irradiated by supernovae within star particle $i$ is then

$V_{{\rm irr},i}(t)=\frac{\mathcal{H}(t_{\rm rec}-t)}{r_{p}^{3}}\\\
\times\sum_{j}v_{ij}\left({\rm SNR}_{{\rm Ia},j}r_{\rm Ia}^{3}+{\rm SNR}_{{\rm
II},j}r_{\rm II}^{3}\right)\,,$ (7)

where $(r_{\rm Ia},r_{\rm II})=(0.3\mathinner{{\rm pc}},0.5\mathinner{{\rm
pc}})$ are the lethal radii of Type Ia and II supernovae, respectively (GH16).
$v_{ij}$ is the fractional volume where the two $6.3\times
10^{6}\mathinner{{\rm M}_{\odot}}$ particles overlap (with $v_{ii}=1$),
computed assuming that each corresponds to a spherical volume of radius
$r_{p}$, set by the gravitational softening length, homogeneously filled with
stars. As in GH16, the recovery time $t_{\rm rec}$ is set to an arbitrarily
large value so that $V_{\rm irr}$ is always positive.

Figure 4:  Similar to Fig. 1, except showing the median value of the _natural_
habitability ($f_{\rm hab}$; _top_), the fraction of possible _cradles_
($f_{\rm cradle}$; _middle_), and the fraction of possible colonization
_targets_ ($f_{\rm target}$; _bottom_) within each projected column at $z=0$
and in a $1\mathinner{{\rm kpc}}$-wide slice passing through the center of
g15784. The magenta star corresponds to the approximate position of the Sun,
if it were the actual Milky Way. Figure 5: The fraction of _natural_ habitable
planets ($f_{\rm hab}$; _top_), _cradles_ of potential civilizations ($f_{\rm
cradle}$; _middle_), and possible colonization _targets_ ($f_{\rm target}$;
_bottom_), as a function of galactocentric radius in g15784 at $z=0$, drawn in
a logarithmic scale.

In a majority of cases, most of the SNR felt by individual star particles is
contributed by neighboring particles, whose volumes overlap each other. This,
together with their higher metallicity (to which $f_{\rm T}(Z)$ is anti-
correlated), reduces the habitability of star particles within the crowded
galactic bulge, as shown in Fig. 4. On the other hand, the higher density and
SNRs found in spiral arms have little effect, although a smattering of low-
habitability particles exists in these regions. The average $f_{\rm hab}$ of
the disk reaches a (weak) maximum at $\sim 4-5\mathinner{{\rm kpc}}$ from the
center (Fig. 5), decreasing smoothly further out due to an increased fraction
of very low metallicity $f_{\rm hab}=0$ star particles. This behavior is
somewhat similar to the model of Lineweaver et al. (2004) but in contrast with
the radially monotonous trend from Gowanlock et al. (2011). The galactic halo
similarly contains a mix of lower and higher-habitability star particles, with
a significant fraction of $<0.1Z_{\odot}$ non-habitable star particles and a
slightly lower average $f_{\rm hab}$ than the disk.

Overall, we find that the range of positive $f_{\rm hab}$ is somewhat narrow
at $z=0$, with most particles having values within $\sim 5\%$ of each other,
which is similar to Prantzos (2008). This is not entirely surprising since the
probability of terrestrial planets $f_{\rm T}$ is, in this model, only weakly
correlated with metallicity and the effect of supernovae on habitability is
not strong (GH16). However, the variation increases by order of magnitude at
$z>0.5$, due to a significantly higher number of star particles below the
$0.1Z_{\odot}$ threshold (especially at large galactocentric radii) and a much
higher SNR (especially in the core).

Finally, we consider two other levels of habitability in addition to the
_natural_ criterion described above, where a planet is deemed habitable
quickly and SN effects are small. These are intended to describe better the
fraction of planets where life could arise or take hold (see Sect. 4.1), as
opposed to the larger population with just benign surface conditions. The
first habitability level is meant to mirror the present state of the Earth,
where we set $t_{\rm min}=4.5\mathinner{{\rm Gyr}}$ and require that no SNs
happened within $r_{\rm Ia}=r_{\rm II}=8\mathinner{{\rm pc}}$ of planets in
the last $t_{\rm rec}=50\mathinner{{\rm Myr}}$. We regard this habitability
level, $f_{\rm cradle}$, as describing the _cradles_ of potential
civilizations, that is, the origin point of directed panspermia. Also, we
consider a less restrictive case, with $t_{\rm min}=1\mathinner{{\rm Gyr}}$
and $t_{\rm rec}=1\mathinner{{\rm Myr}}$, to describe the potential _targets_
of such directed panspermia ($f_{\rm target}$). The requirement for a small
but non-zero $t_{\rm rec}$ also allows us to sidestep the issue of transit of
organisms through the radiation environment of supernova remnants. Contrarily
to the natural case, here the low-habitability star particles are concentrated
within the CentralDisk , up to $\sim 4\mathinner{{\rm kpc}}$ as shown in Figs.
4 and 5 , due to the higher SN efficiency at suppressing habitability. The
outer galactic disk also has lower averages of $f_{\rm cradle}$ and $f_{\rm
target}$, due to the higher prevalence of recently-formed star particles, and
the distributions of cradles and targets are similar.

##  4 Modelling The Probability Of Panspermia

The probability that seeds of life departed from star particle $i$ at position
$\mathinner{{\mathbf{x}}}_{i}$ at time $t_{i}$ (hereafter,
$(\mathinner{{\mathbf{x}}}_{i},t_{i})$) to be successfully transplanted to
star particle $j$ at $(\mathinner{{\mathbf{x}}}_{j},t_{j})$ can be written as

$\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},t_{i};\mathinner{{\mathbf{x}}}_{j},t_{j})\\\
=f_{\rm oc}(\mathinner{{\mathbf{x}}}_{i},t_{i})f_{\rm
target}(\mathinner{{\mathbf{x}}}_{j},t_{j})f_{\rm
esc}(\mathinner{{\mathbf{x}}}_{i})f_{\rm cap}(\mathinner{{\mathbf{x}}}_{j})\\\
\times\int_{\mathbb{V}_{i}}\\!\\!\mathinner{{\rm
d}\\!}\mathinner{{\mathbf{x}}}^{\prime}_{i}\int_{\mathbb{V}_{j}}\\!\\!\mathinner{{\rm
d}\\!}\mathinner{{\mathbf{x}}}^{\prime}_{j}w_{\rm
damage}(\mathinner{{\mathbf{x}}}^{\prime}_{j},t_{j}|\mathinner{{\mathbf{x}}}^{\prime}_{i},t_{i})\,.$
(8)

where the definitions of $f_{\rm oc}$, $f_{\rm target}$, $f_{\rm esc}$,
$f_{\rm cap}$, and $w_{\rm damage}$ are given progressively in the following
sections. We note that, while we here apply Eq. (8) to what are effectively
groupings of millions of stars, it can also be used to describe panspermia
between two individual stars. Then the total amount transplanted to star
particle at $(\mathinner{{\mathbf{x}}}_{j},t_{j})$ is proportional to

$f_{\rm
pp}(\mathinner{{\mathbf{x}}}_{j},t_{j})=\sum_{\mathinner{{\mathbf{x}}}_{i}}\int_{0}^{t_{j}}\\!\\!\mathinner{{\rm
d}\\!}t_{i}\,\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},t_{i};\mathinner{{\mathbf{x}}}_{j},t_{j})\,,$
(9)

We hereafter call $\mathcal{F}$ and $f_{\rm pp}$ the _panspermia contribution_
and _panspermia probability_ , respectively.666The actual probability that the
panspermia process is successful may not be simply additive as assumed in Eq.
(9), but this is beyond the scope of this paper. While $t_{j}$ should always
be greater than $t_{i}$, $\mathinner{{\mathbf{x}}}_{i}$ and
$\mathinner{{\mathbf{x}}}_{j}$ can be the same since a single star particle in
our analysis contains millions of stars.

###  4.1 Probability of Hosting Life

First, $f_{\rm oc}(\mathinner{{\mathbf{x}}}_{i},t_{i})$ is the probability
that the star particle $i$ has planets bearing living organisms, or their
complex organic precursors, at $t_{i}$. For a star particle having these
seeds, it should be habitable for a period sufficient for successful prebiotic
evolution. This can be written as

$f_{\rm oc}(\mathinner{{\mathbf{x}}},t)=\int_{t-t_{\rm
chem}}^{t}\\!\\!\\!\\!\mathinner{{\rm d}\\!}t^{\prime}f_{\rm
hab}(\mathinner{{\mathbf{x}}},t^{\prime})W_{\rm chem}(t-t^{\prime})\,,$ (10)

where $t_{\rm chem}\sim\mathcal{O}(10^{-1}\mathinner{{\rm Gyr}})$ is the
typical timescale for prebiotic evolution (Mojzsis et al., 1996; van Zuilen et
al., 2002; Dodd et al., 2017), and $W_{\rm chem}$ is a certain time-domain
kernel between $f_{\rm hab}$ and $f_{\rm oc}$, respectively. In practice, as
$W_{\rm chem}$ is unknown and $t_{\rm chem}$ is much smaller than timescales
used in this paper (e.g., timescales for star formation, local SN rates, and
delay time for $f_{\rm hab}$). Therefore, for simplicity, we assume that the
probability of hosting life is similar to the fraction of possible _cradles_
of life, that is, $f_{\rm oc}(\mathinner{{\mathbf{x}}},t)\propto f_{\rm
cradle}(\mathinner{{\mathbf{x}}},t)$.

###  4.2 Escape Fraction

$f_{\rm esc}(\mathinner{{\mathbf{x}}}_{i})$ is a weight proportional to the
escape fraction of life spores, from habitable planets in the star particle
$i$ to the ISM by natural processes. In order to estimate $f_{\rm esc}$ in the
case of natural panspermia, we assume that material carrying spores can be
ejected from the surface of habitable terrestrial planets by surface impacts.
The velocity of ejecta is (Housen & Holsapple, 2011)

$v_{\rm ej}=u\cdot
C_{1}\left[\frac{x}{a_{e}}\left(\frac{\rho}{\delta}\right)^{\nu}\right]^{-\frac{1}{\mu}}\left(1-\frac{x}{n_{2}R}\right)^{p_{e}}$
(11)

at a distance $x$ from the impact center, with $n_{1}a\leq x\leq n_{2}R$,
where $R$ is the radius of the impact crater, and $u$ the impactor’s velocity,
which we assume to be equal to the average orbital velocity
$v_{\text{orb,HZ}}(m_{\star})$ within the star’s habitable zone.777The typical
velocity of impactors may actually be closer to half of the planet’s orbital
velocity (e.g., see Collins et al., 2005), which would naturally decrease the
number of fragments reaching escape velocity. However, this would not change
the “normalized” value of the escape weight $f_{\rm esc}$ which we use here.
For Eq. (11), we use parameter values for low-porosity rock given in Housen &
Holsapple (2011), namely, $\mu=0.55$, $\nu=0.4$, $C_{1}=1.5$, $n_{1}=1.2$,
$n_{2}=1$, $p_{e}=0.5$, $\rho/\delta\sim 1$, and $a_{e}=0.0016$. The radius
$R$ of the crater is related to the impactor’s energy through

$\frac{R}{{\rm km}}\sim\frac{1}{2}\left(\frac{E_{\rm kin}}{9.1\times
10^{24}~{}{\rm ergs}}\right)^{1/2.59}$ (12)

(Hughes, 2003), where $E_{\text{kin}}=\frac{1}{2}m_{\text{i}}v_{\rm
o,HZ}^{2}$, with $m_{\text{i}}$ being the mass of the impactor. Assuming that
the latter follows a distribution of the type $\propto m^{-1.6}$ (Simon et
al., 2017), we can then compute a velocity distribution of ejecta (see Fig.
14).

Only a small fraction of the ejected material will have enough velocity to
escape the planet and thus only an infinitesimal quantity of this material can
ever reach stellar escape velocity in the simulation. On the other hand, we
can expect that a fraction $w_{\rm esc}$ of material ejected into
circumstellar orbit can be accelerated above stellar escape velocity by either
gravitational interactions (in the case of macroscopic fragments, which
corresponds to lithopanspermia; Melosh, 1988) or radiation pressure (in the
case of microscopic fragments; Arrhenius & Borns, 1908). Under the assumption
that the host star mass does not determine the magnitude and frequency of
these boosts, $w_{\rm esc}$ is only a function of orbital and stellar escape
velocities within the HZ:

$w_{\rm esc}(m)=C\int_{r_{\rm h,i}(m)}^{r_{\rm h,o}(m)}\int_{v_{\rm
esc}(r)}\phi_{\rm ej}(v)\mathinner{{\rm d}\\!}v\mathinner{{\rm d}\\!}r\,,$
(13)

where $\phi_{\rm ej}$ is the quantity of ejected material as a function of
velocity (see Fig. 14)and $C$ is a normalizing constant. Following this
scheme, $w_{\rm esc}$ would be higher for higher-mass stars (Fig. 14), as the
radius of the HZ increases with $L^{1/2}$ (that is, with $\sim M^{1.75}$). The
same applies to lower-metallicity stars, which are brighter for the same mass.
Since the magnitude and frequency of the boosts are unknown, a quantitative
estimate for $w_{\rm esc}$ is however not possible. Instead, we compute
relative quantities, rescaled to an arbitrary range of $\left[0,1\right]$ for
our star particles at $z=0$. Integrating this over the age-truncated KTG93 IMF
then yields a weight

$f_{\rm esc}(t)=\int\mathinner{{\rm d}\\!}\,\log m\,\phi(m,t)w_{\rm
esc}(m)N_{\rm impact}(t)$ (14)

for each star particle. Here we assume for simplicity that $w_{\rm esc}$ does
not vary with the age of the stellar particle. However, we note that the
frequency of impacts on Earth has decreased exponentially since the formation
of the Solar System, which would result in a time-varying $f_{\rm esc}$. Since
$w_{\rm esc}$ depends on the position of the HZ, the spatial distribution of
$f_{\rm esc}$ within g15784 is similar to $f_{\rm hab}$ (Figs. 4 & 5), being
low within the CentralDisk, reaching a maximum at $\sim 5\mathinner{{\rm
kpc}}$, and monotonously decreasing at larger galactocentric radii. For a more
detailed description, see Appendix A.

###  4.3 The Capture Fraction

$f_{\rm cap}(\mathinner{{\mathbf{x}}}_{j})$ is the capture fraction of
interstellar spores by target planets in the star particle $j$ by gravity.
Here, we assume that stars are evenly distributed in each star particle, and
that each star is separated from the others by a distance much greater than
the size of its planetary system.

The probability of interstellar objects captured by solar systems can be
sensitive to the structure of planetary systems (e.g., Ginsburg et al., 2018).
However, this fine structure lays considerably beyond the resolution of the
simulation used here. Consequently, and for convenience, we assume $f_{\rm
cap}(\mathinner{{\mathbf{x}}}_{j})$ to be simply constant on average.

###  4.4 Traveling Seeds

The last term of Eq. (8) corresponds to the probability that spores
originating from a habitable planet within the star particle $i$
($\mathbb{V}_{i}$) at $t_{i}$ reach a target planet within the star particle
$j$ ($\mathbb{V}_{j}$) at $t_{j}$. Mathematically, it is calculated as the
double volume integral of $w_{\rm
damage}(\mathinner{{\mathbf{x}}}^{\prime}_{j},t_{j}|\mathinner{{\mathbf{x}}}^{\prime}_{i},t_{i})$,
the survival probability of spores in an interstellar object that starts at
$(\mathinner{{\mathbf{x}}}^{\prime}_{i},t_{i})$ and arrives
$(\mathinner{{\mathbf{x}}}^{\prime}_{j},t_{j})$ (hereafter, the _damage
weight_), where $\mathinner{{\mathbf{x}}}^{\prime}_{i,j}\in\mathbb{V}_{i,j}$.
To compute this numerically, one needs to understand the spatial distribution
of stars in each star particle, as well as consider the traveling distance
($\ell_{\rm surv}$), which is a function of the survival timescale of spores
in the ISM ($t_{\rm surv}$), and how $w_{\rm damage}$ depends on $\ell_{\rm
surv}$.

As mentioned in Sect. 2, each star particle in g15784 is an ensemble of
millions of stars whose total mass is about $6.3\times 10^{6}\mathinner{{\rm
M}_{\odot}}$. While the volume of such an ensemble can be approximated by the
cell from the Voronoi tessellation888Voronoi tessellation partitions a volume
into multiple regions, based on a set of positions
$\left\\{\mathinner{{\mathbf{x}}}_{i}\right\\}$. The Voronoi volume of a
particle $\mathinner{{\mathbf{x}}}_{i}$ is then defined as an ensemble of
points whose closest particle is $\mathinner{{\mathbf{x}}}_{i}$, that is,
$\mathbb{V}_{i}\equiv\left\\{\mathinner{{\mathbf{x}}}||\mathinner{{\mathbf{x}}},\mathinner{{\mathbf{x}}}_{i}|<|\mathinner{{\mathbf{x}}}-\mathinner{{\mathbf{x}}}_{j}|\textrm{
for all }j\neq i\right\\}$. of star particles, the actual distribution of
stars within the volume is unknown. Here we assume that the stars in a star
particle are uniformly distributed in its Voronoi volume by adopting such
numerical limitation. Furthermore, for a fast calculation of the panspermia
probability, we simplify the geometry of the star particle $i$ to a sphere
with center at $\mathinner{{\mathbf{x}}}_{i}$ and radius
$R_{i}\equiv\left(3V_{i}/4\pi\right)^{1/3}$, where $V_{i}$ is its Voronoi
volume. Such assumptions will work well for small-volume star particles at a
relatively dense region of g15784 because the stellar density gradient within
the volume will be low, and the shape of the Voronoi cell will be close to the
sphere due to numerous nearby cells. On the other hand, our assumptions may
poorly work for star particles at the outskirts of g15784. However, these
typically do not contribute much to our main results because of their low
habitability and panspermia probability.

The survival time of microorganism spores under the pressures, temperatures,
and radiation flux expected for panspermia is uncertain. All in-situ
experiments so far have been done in Earth orbit (e.g., Horneck et al., 2001;
Onofri et al., 2012; Kawaguchi et al., 2013) and their conclusions are
typically extrapolated to the requirements for in-system panspermia (e.g.,
between the Earth and Mars). On the other hand, they do not reflect the likely
conditions of interstellar panspermia; in particular, the survival of spores
under hard radiation has been found to increase at low temperatures (Weber &
Greenberg, 1985; Sarantopoulou et al., 2011). Only a few biological studies
concerning an interstellar transit have been carried out (Weber & Greenberg,
1985; Koike et al., 1992; Secker et al., 1994), which suggest that shielding
by a rock or carbonaceous material would be required to ensure the survival of
a sufficient number of spores. With no clear constraints on the survival
timescale, we assume a conservative choice of $t_{\rm
surv}\sim\mathcal{O}(1\,{\rm Myr})$. For simplicity, we also assume that
$t_{\rm surv}$ is negligible compared to the evolution timescale of the Milky
Way so that we can use the characteristics of star particles from the snapshot
data at $z=0$ for both $t_{i}$ and $t_{j}$.

The survival timescale $t_{\rm surv}$ can be rewritten in terms of the travel
distance scale $\ell_{\rm surv}\equiv\bar{v}_{\rm oc}t_{\rm surv}$, where
$\bar{v}_{\rm oc}$ is the mean velocity of the spores. As already discussed in
Sect. 4.3, the distance between different solar systems is much larger than
the typical size of a solar system. Therefore, we assume that, although not
exactly zero, the probability that interstellar objects would significantly
change their trajectories or speed due to the gravity from a single solar
system when they are in the middle of the ISM is low. Here we adopt the
velocity of comet ‘Oumuamua ($26.32\pm 0.01$ km/s; Mamajek, 2017) as typical
of $\bar{v}_{\rm oc}$ for rocky objects crossing the ISM. While the speed of
interstellar objects may depend on their distance from the galactic center, we
do not consider it here for simplicity. Combining $t_{\rm surv}$ and
$\bar{v}_{\rm oc}$ yields a typical scale $\ell_{\rm surv}$ of a few parsecs,
which matches well with the estimation of $\ell_{\rm
surv}=15-30\mathinner{{\rm pc}}$ in Grimaldi et al. (2021). In the following
section, we use a range of $\ell_{\rm surv}=1-10^{4}\mathinner{{\rm pc}}$ to
explore the parameter space and account for simple cases of _directed_
panspermia (e.g., in case of $\ell_{\rm surv}\gtrsim 1\mathinner{{\rm kpc}}$;
see also Stapleton, 1930; Haldane, 1954; Crick & Orgel, 1973), while keeping
in mind that $\ell_{\rm surv}\leq 30\mathinner{{\rm pc}}$ is likely more
appropriate to the _natural_ case.

As the dependency of the damage weight $w_{\rm damage}$ to the travel distance
$\ell\equiv|\mathinner{{\mathbf{x}}}^{\prime}_{i}-\mathinner{{\mathbf{x}}}^{\prime}_{j}|$
($\mathinner{{\mathbf{x}}}^{\prime}_{i,j}\in\mathbb{V}_{i,j}$) is not
precisely known, we consider three different models for $w_{\rm damage}$: (1)
a _sudden_ damage model (sudden hereafter), where spores stay alive at
$\ell<\ell_{\rm surv}$ and suddenly die afterward; (2) a _linear_ damage model
(lin hereafter), in which the population linearly decreases over time until it
becomes zero at $\ell=\ell_{\rm surv}$; and (3) an _exponential_ damage model
(exp hereafter), where the population of viable spores exponentially decreases
over time, assuming that the survival rate over a fixed time period is
constant:

$w_{\rm damage}\left(\frac{\ell}{\ell_{\rm
surv}}\right)=\left\\{\begin{array}[]{ll}\mathcal{H}\left(1-{\ell}/{\ell_{\rm
surv}}\right)&({\tt sudden})\\\ \max\left\\{1-{\ell}/{\ell_{\rm
surv}},0\right\\}&({\tt lin})\\\ \exp\left(-{\ell}/{\ell_{\rm
surv}}\right)&({\tt exp})\\\ \end{array}\right.$ (15)

Finally, we also consider a fourth damage model, noEsc, which is identical to
sudden where $f_{\rm esc}=1$ for all star particles, in order to understand
the dependency of the panspermia probability on $f_{\rm esc}$. We also note
that, unlike sudden and lin, 37% of the spores are still alive at
$\ell=\ell_{\rm surv}$ in exp. Therefore, one should be careful when comparing
the dependency of the panspermia probability on $\ell_{\rm surv}$ between exp
and others.

###  4.5 Numerical Formalism

Summarizing the above subsections, one can rewrite Eqs. (8-9) as follows:

$f_{\rm
pp}(\mathinner{{\mathbf{x}}}_{j})=\sum_{i}\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},\mathinner{{\mathbf{x}}}_{j})\,,$
(16)

where

$\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},\mathinner{{\mathbf{x}}}_{j})\propto
f_{\rm cradle}(\mathinner{{\mathbf{x}}}_{i})f_{\rm
esc}(\mathinner{{\mathbf{x}}}_{i})f_{\rm
target}(\mathinner{{\mathbf{x}}}_{j})\\\ \times\int_{\ell_{\rm
min}}^{\ell_{\rm max}}\\!\\!\mathinner{{\rm
d}\\!}\ell\,F(\ell|R_{i},R_{j},D_{ij})w_{\rm
damage}\left(\frac{\ell}{\ell_{\rm surv}}\right)\,.$ (17)

Since all timescales in Eqs. (8-9) are smaller than the dynamic timescale of
the Galaxy, we neglect time-dependent terms in the original equations. Here,
$D_{ij}\equiv|\mathinner{{\mathbf{x}}}_{i}-\mathinner{{\mathbf{x}}}_{j}|$ is
the distance between the centers of two star particles, considered as volumes
homogeneously filled with stars. Also, $\ell_{\rm
min}\equiv\max\left\\{0,D_{ij}-R_{i}-R_{j}\right\\}$ and $\ell_{\rm
max}\equiv\min\left\\{\alpha_{\rm trunc}\ell_{\rm
surv},D_{ij}+R_{i}+R_{j}\right\\}$ are the minimum and maximum values of
$\ell$ during the integration, respectively. A truncation rate $\alpha_{\rm
trunc}$ is defined as the minimum value that satisfies $w_{\rm
damage}(\alpha_{\rm trunc})=0$, whose value is 1 for sudden and lin. For exp,
we manually set $\alpha_{\rm trunc}^{\tt exp}\gg 1$ for a fast calculation.

$F(\ell|R_{i},R_{j},D_{ij})$ is the probability of having
$|\mathinner{{\mathbf{x}}}^{\prime}_{i}-\mathinner{{\mathbf{x}}}^{\prime}_{j}|=\ell$
given $R_{i}$, $R_{j}$, and $D_{ij}$, and assuming that the timescale for
panspermia is much less than the evolution timescale of the galaxy:

$F(\ell|R_{i},R_{j},D_{ij})\\\ =\frac{3}{R_{i}^{3}}\int\mathinner{{\rm
d}\\!}D\,D^{2}f_{\rm sp}(D|D_{ij},R_{i})f_{\rm sp}(\ell|D,R_{j})\,,$ (18)

where

$\displaystyle f_{\rm sp}(d|D,R)$
$\displaystyle=\left\\{\begin{array}[]{ll}0&{\rm at\,}d>D+R\\\
\mathcal{H}(R-D)&{\rm at\,}d<|D-R|\\\
\displaystyle\frac{R^{2}-(d-D)^{2}}{4Dd}&{\rm otherwise}\end{array}\right.$
(22)

is the fraction of a spherical surface with radius $d$ that belongs to the
volume of another sphere of radius $R$ at distance $D$.

From Eq. (16), one can also estimate a probability that seeds spreading from a
given star particle are successfully transplanted in another (hereafter, the
_successful transplantation probability_):

$f_{\rm
stp}(\mathinner{{\mathbf{x}}}_{i})=\sum_{j}\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},\mathinner{{\mathbf{x}}}_{j})\,.$
(23)

Since several factors in Eqs. (8) & (9) remain unknown, Eqs. (16) & (23) thus
only yield relative, rather than absolute, values of the panspermia
probability. However, since our main focus is a relative comparison between
habitability and panspermia probability, we hereafter normalize $f_{\rm pp}$
and $f_{\rm stp}$ so that their sum over g15784 is same to the sum of the
habitability, that is,

$\sum_{\mathinner{{\mathbf{x}}}}f_{\rm
pp}(\mathinner{{\mathbf{x}}})=\sum_{\mathinner{{\mathbf{x}}}}f_{\rm
stp}(\mathinner{{\mathbf{x}}})=\sum_{\mathinner{{\mathbf{x}}}}f_{\rm
hab}(\mathinner{{\mathbf{x}}})\,.$ (24)

##  5 Results

###  5.1 Panspermia Probability & Successful Transplantation Probability

Figure 6: Panspermia probability ($f_{\rm pp}$; _top_) and successful
transplantation probability ($f_{\rm stp}$; _bottom_) at $z=0$ in g15784,
assuming the exponential damage model (exp) with $\ell_{\rm
surv}=100\mathinner{{\rm pc}}$. The field of view, slice width, and the
magenta star are set to be the same as Fig. 4. Figure 7: Panspermia
probability ($f_{\rm pp}$; _top_) and successful transplantation probability
($f_{\rm stp}$; _bottom_) at $z=0$ in g15784 as a function of galactocentric
radius. The joint distribution is drawn in logarithmic scale and grayscale,
assuming exp and $\ell_{\rm surv}=100\mathinner{{\rm pc}}$. On the other hand,
the median probability for different values of $\ell_{\rm surv}$, for the same
damage model, are shown by colored lines.

Figure 8: Probability distributions of the panspermia ($f_{\rm pp}$; _top_)
and successful transplantation probabilities ($f_{\rm stp}$; _bottom_) in
g15784 at $z=0$. Both $f_{\rm pp}$ and $f_{\rm stp}$ are calculated by
assuming exponential damage model (exp) and various travel distance scales
(_colors_).

Figs. 6–8 show the spatial and probability distributions of the panspermia
probability and successful transplantation probability in g15784 at $z=0$,
normalized following Eq. (24). Similarly to the three habitability levels,
star particles in the CentralDisk have very low $f_{\rm pp}$ and $f_{\rm
stp}$. In the DiskHalo region, both $f_{\rm pp}$ and $f_{\rm stp}$ tend to
have higher values at lower galactocentric radius ($R$) and tangential
distance from the galactic plane ($b$). However, while $f_{\rm pp}$ covers a
wide range of 7 orders of magnitude and shows a somewhat mixed distribution at
$R>5\mathinner{{\rm kpc}}$, the successful transplantation probability $f_{\rm
stp}$ shows a narrower range (3 orders of magnitude) and stronger dependency
on both $R$ and $b$, in the $\ell_{\rm surv}=100\mathinner{{\rm pc}}$ case.
For larger values of $\ell_{\rm surv}$, however, $f_{\rm pp}$ tends to show a
stronger negative slope on a $R$-direction (upper panel of Fig. 7). Such a
negative slope at high-$\ell_{\rm surv}$ might happen because of the
difference, between low-$R$ (high-$\Sigma_{\star}$) and at high-$R$
(low-$\Sigma_{\star}$), in the number of sources that a given star particle
can receive.

The probability distribution of $p(f_{\rm pp})$ peaks around $10^{-4}$ times
the typical value of the habitabilities. As the travel distance increases, the
peak of $p(f_{\rm pp})$ shifts towards lower values, decreases, and widens.
This is because a large $\ell_{\rm surv}$ allows seeds to reach distant star
particles, which naturally increases the total amount of successfully
transplanted seeds in a given galaxy. However, since we normalize $f_{\rm pp}$
so that its sum over the galaxy is constant, the importance of each
successfully transplanted seed decreases. On the other hand, the peak position
of the probability distribution of normalized successful transplantation
probability ($p(f_{\rm stp})$) remains similar regardless of the value of
$\ell_{\rm surv}$. Instead, the probability distribution spreads toward lower
$f_{\rm stp}$ as the travel distance scale increases, especially when
$\ell_{\rm surv}\gtrsim 100\mathinner{{\rm pc}}$.

Figure 9: The panspermia ($f_{\rm pp}$; _top_) and successful transplantation
($f_{\rm stp}$; _bottom_) probabilities as a function of three different types
of habitabilities ($f_{\rm hab}$, $f_{\rm cradle}$, and $f_{\rm target}$) in
g15784 at $z=0$. _Left_ : Sudden damage model with $f_{\rm esc}=1$ for all
star particles (noEsc) and $\ell_{\rm surv}=100\mathinner{{\rm pc}}$. _Right_
: Exponential damage model (exp) with the same travel distance scale. Both the
sudden and lin models give similar results to exp.

Fig. 9 shows $f_{\rm pp}$ and $f_{\rm stp}$ in g15784 at $z=0$ as a function
of the three habitability levels, for various damage models and $\ell_{\rm
surv}=100\mathinner{{\rm pc}}$. From Eqs. (16-17), the panspermia probability
is

$f_{\rm pp}(\mathinner{{\mathbf{x}}}_{j})\propto f_{\rm
target}(\mathinner{{\mathbf{x}}}_{j})\\\ \times\sum_{i}f_{\rm
cradle}(\mathinner{{\mathbf{x}}}_{i})f_{\rm
esc}(\mathinner{{\mathbf{x}}}_{i})\mathbb{F}(R_{i},R_{j},D_{ij}|\ell_{\rm
surv})\,,$ (25)

where

$\mathbb{F}(R_{i},R_{j},D_{ij}|\ell_{\rm surv})\\\ \equiv\int_{\ell_{\rm
min}}^{\ell_{\rm max}}\mathinner{{\rm
d}\\!}\ell\,F(\ell|R_{i},R_{j},D_{ij})w_{\rm
damage}\left(\frac{\ell}{\ell_{\rm surv}}\right)\,,$ (26)

with $\mathbb{F}(\cdots)$ depending only on the geometry (volumes and relative
position) of the source-target star particle pair. Consequently, while
$\mathbb{F}$ may vary from particle to particle, $\sum_{i}\mathbb{F}$ is
mostly determined by the local stellar density around the target star
particle. Accordingly, while $\sum_{i}f_{\rm
cradle}(\mathinner{{\mathbf{x}}}_{i})f_{\rm
esc}(\mathinner{{\mathbf{x}}}_{i})\mathbb{F}(\cdots)$ is sensitive to both
geometry and the baryonic properties of the target star particle, it can be
approximated by a function of only $R_{j}$ in cases where $f_{\rm
cradle}f_{\rm esc}$ does not vary much across all relevant source star
particles. In other words, if the range of $f_{\rm target}$ in g15784 is
significantly larger than that of $f_{\rm cradle}f_{\rm esc}$, then $f_{\rm
pp}\propto f_{\rm target}$. On the other hand, if the range of $f_{\rm
target}$ is similar or narrower than that of $f_{\rm cradle}f_{\rm esc}$, the
above approximation cannot be used. As shown in Figs. 5 & 17, $0.06<f_{\rm
target}<0.1$ while $0<f_{\rm cradle}f_{\rm esc}<0.1$, even in the noEsc with
$f_{\rm esc}=1$. Consequently, $f_{\rm pp}$ does not correlate clearly with
habitability (upper panels of Fig. 9). On the other hand, the successful
transplantation probability can be written as

$f_{\rm stp}(\mathinner{{\mathbf{x}}}_{i})\propto f_{\rm
cradle}(\mathinner{{\mathbf{x}}}_{i})f_{\rm
esc}(\mathinner{{\mathbf{x}}}_{i})\\\ \times\sum_{j}f_{\rm
target}(\mathinner{{\mathbf{x}}}_{j})\mathbb{F}(R_{i},R_{j},D_{ij}|\ell_{\rm
surv})$ (27)

and, in a similar way, we can assume that $\\{\mathbb{F}\\}$ is mostly
determined by $R_{i}$. Since the range of $f_{\rm cradle}f_{\rm esc}$ is
significantly larger than that of $f_{\rm target}$, we can expect $f_{\rm
stp}\propto f_{\rm cradle}f_{\rm esc}$. Indeed, Fig. 9 (bottom panels) shows
strong correlations between $f_{\rm stp}$ and $f_{\rm cradle}f_{\rm esc}$, for
different values $f_{\rm stp}/f_{\rm cradle}f_{\rm esc}$. Most of the DiskHalo
population has high values of both $f_{\rm cradle}$ and $f_{\rm stp}$
($(f_{\rm cradle},f_{\rm stp})\sim(0.09,10^{-1})$), while values for
CentralDisk, on the other hand, are more widely spread, with a $f_{\rm
stp}/f_{\rm esc}f_{\rm cradle}\simeq 2$ linear correlation (upper diagonal
strip at the bottom panels of Fig. 9). Finally, the lower diagonal strips in
the bottom panel of Fig. 9 correspond to the Spheroids. Interestingly, there
appears to be two distinct populations in the $f_{\rm cradle}$-$f_{\rm stp}$
plane, with $f_{\rm stp}/f_{\rm esc}f_{\rm cradle}\simeq 0.5$ and $0.2$,
respectively. They disappear when $\ell_{\rm surv}\geq 10\mathinner{{\rm
kpc}}$, suggesting that they originate from successful panspermia between
Spheroids and the main galaxy at low $\ell_{\rm surv}$. The strength of
correlation between $f_{\rm stp}$ and other two types of habitabilities
depends on the correlation between those habitabilities and $f_{\rm
cradle}$—as $f_{\rm target}$($f_{\rm hab}$) shows a mild(no apparent)
correlation with $f_{\rm cradle}$, so does it with $f_{\rm stp}$ (see Fig. 5,
for example).

At a fixed value of $\ell$, we find that neither the probability and joint
distributions of $f_{\rm pp}$ and $f_{\rm stp}$ strongly depend on the damage
model (sudden, lin, or exp). While the three damage models have different
$w_{\rm damage}(\ell/\ell_{\rm surv})$, and therefore, different
$\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},\mathinner{{\mathbf{x}}}_{j})$, the
normalization of $f_{\rm pp/stp}$ described above weakens the difference
between them. That numerous star particles can affect both $f_{\rm pp}$ and
$f_{\rm stp}$ further lessens it. On the other hand, there is significant
difference between those three damage models and noEsc, mostly due to
differences in escape weight $f_{\rm esc}$.

###  5.2 Panspermia Contributions

By definition, both the $f_{\rm pp}$ and $f_{\rm stp}$ of a given star
particle are affected by numerous source and target particles. This means that
star particles with the same values of $f_{\rm pp}$ or $f_{\rm stp}$ may
however have a completely different panspermia _history_. For example, some
star particles might have received similar amounts of seeds from numerous
particles, while others might have received most of _their seeds from only
one_ or a few dominant sources. As an attempt to quantify the panspermia
history of individual particles, we define the _greatest panspermia
contribution_ as the highest single $f_{\rm pp}$ or $f_{\rm stp}$ contribution
to the sum:999Ideally, all
$\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},\mathinner{{\mathbf{x}}}_{j})$ for
the entire $N_{\star}^{2}$-pairs of possible routes should be considered.
However, the large number of $N_{\star}=746,659$ makes it impractical at the
moment. We consider the full list of panspermia contributions and their
network in a future work.

$\displaystyle\mathcal{F}_{\rm best,pp}(\mathinner{{\mathbf{x}}})$
$\displaystyle\equiv\max_{\mathinner{{\mathbf{x}}}^{\prime}}\mathcal{F}(\mathinner{{\mathbf{x}}}^{\prime},\mathinner{{\mathbf{x}}})$
(28) $\displaystyle\mathcal{F}_{\rm best,stp}(\mathinner{{\mathbf{x}}})$
$\displaystyle\equiv\max_{\mathinner{{\mathbf{x}}}^{\prime}}\mathcal{F}(\mathinner{{\mathbf{x}}},\mathinner{{\mathbf{x}}}^{\prime})$
(29)

Figure 10: Greatest contribution relative to the panspermia probability,
$\mathcal{F}_{\rm best}/f_{\rm pp/stp}$), as a function of galactocentric
radius. The colored lines show the median value, as in Fig. 7.

Both $\mathcal{F}_{\rm best}$ occupy a narrow range of values and are nearly
constant with galactocentric distance. On the other hand, as shown in Fig. 10,
their ratios to $f_{\rm pp}$ and $f_{\rm stp}$ show a clear radial trend:
$\mathcal{F}_{\rm best}/f_{\rm pp}$ tends to be high in the DiskHalo,
increasing with radius up to values of $\sim$1, and low in both the
CentralDisk and Spheroids. This implies that, while in the outer galactic disk
and the halo the panspermia probability of a star particle is on average
dominated by a single other particle (i.e., a one-to-one transmission), closer
to the bulge and in the satellites the $f_{\rm pp}$ of star particles is a sum
of contributions from multiple sources. In this case, the high local density
more than offsets the lower habitability of particles in these regions.
Likewise, $\mathcal{F}_{\rm best}/f_{\rm pp}$ decreases monotonically with
increasing $\ell_{\rm surv}$, as the larger travel distance allows more source
particles to contribute. On the other hand, $\mathcal{F}_{\rm best}/f_{\rm
stp}$ is somewhat insensitive to the travel distance until $\ell_{\rm
surv}\gtrsim 1\mathinner{{\rm kpc}}$, when other routes to target particles in
the DiskHalo and Spheroids become possible.

###  5.3 Self Panspermia in g15784

So far we considered all star particles in our calculation of $f_{\rm pp}$ and
$f_{\rm stp}$, including cases where source and target particles are the same.
This possibility of “self panspermia” accounts for the limited spatial and
mass resolutions of MUGS, where each star particle ($6.3\times
10^{6}\mathinner{{\rm M}_{\odot}}$) contains millions of stars. In this
Section, we investigate the contribution of self panspermia to the panspermia
probability.

Figure 11: The probability of _self panspermia_ ($P_{\rm self}$), where
$\mathcal{F}(\mathinner{{\mathbf{x}}},\mathinner{{\mathbf{x}}})>f_{\rm
pp/stp}(\mathinner{{\mathbf{x}}})/2$, as a function of $R$ and $f_{\rm pp}$

We consider that a given star particle undergoes self panspermia if the
panspermia contribution from/to the same star particle is greater than the sum
of the contributions from/to the all other star particles, i.e., star particle
$i$ undergoes self panspermia when
$\mathcal{F}(\mathinner{{\mathbf{x}}}_{i},\mathinner{{\mathbf{x}}}_{i})>f_{\rm
pp/stp}(\mathinner{{\mathbf{x}}}_{i})/2$. Fig. 11 shows the distribution of
self panspermia in g15784 at $z=0$ as a function of galactocentric radius and
$f_{\rm pp}$, assuming exp with $\ell_{\rm surv}=100\mathinner{{\rm pc}}$.
Self panspermia starts to dominate at $R>2\mathinner{{\rm kpc}}$, where most
of the DiskHalo population exists, and for particles with panspermia
probabilities at or below the median value (here $f_{\rm pp}\sim 10^{-5}$).
This threshold decreases by two orders of magnitude when $\ell_{\rm surv}$
increases from $1\mathinner{{\rm pc}}$ to $10\mathinner{{\rm kpc}}$.
Conversely, no self panspermia occurs in star particles with values of $f_{\rm
pp}$ $\gtrsim 10^{2}$ times greater than the median. On the other hand, star
particles at lower galactocentric radii, both in CentralDisk and DiskHalo,
tend to undergo less self panspermia because the high stellar densities near
the galactic center may prevent the panspermia process from being governed by
a single route. Finally, we find almost no cases of self panspermia for the
successful transplantation probability ($f_{\rm stp}$), except in except in
the outer, underdense region of the DiskHalo.

Having estimated self panspermia, we subtract it from $\mathcal{F}_{\rm
best}$:

$\displaystyle\mathcal{F}_{\rm best,pp}^{\rm nodup}(\mathinner{{\mathbf{x}}})$
$\displaystyle\equiv\max_{\mathinner{{\mathbf{x}}}^{\prime}\neq\mathinner{{\mathbf{x}}}}\mathcal{F}(\mathinner{{\mathbf{x}}}^{\prime},\mathinner{{\mathbf{x}}})$
(30) $\displaystyle\mathcal{F}_{\rm best,stp}^{\rm
nodup}(\mathinner{{\mathbf{x}}})$
$\displaystyle\equiv\max_{\mathinner{{\mathbf{x}}}^{\prime}\neq\mathinner{{\mathbf{x}}}}\mathcal{F}(\mathinner{{\mathbf{x}}},\mathinner{{\mathbf{x}}}^{\prime})\,,$
(31)

with Fig. 12 showing the behavior of $\mathcal{F}_{\rm best}^{\rm
nodup}/f_{\rm pp/stp}$. Contrary to the full case (Fig. 10), $\mathcal{F}_{\rm
best}^{\rm nodup}/f_{\rm pp}$ is strongly suppressed at $R>2\mathinner{{\rm
kpc}}$, in agreement with Fig. 11. This implies that, in the DiskHalo, most of
$f_{\rm pp}$ is self panspermia, but also that the number of sources
contributing to non-self panspermia increases with galactocentric radius. On
the other hand, the latter (i.e.,panspermia from other source particles)
dominates the CentralDisk and Spheroids. We also note that, while the fraction
of star particles dominated by self panspermia is large, these tend to have
lower values of $f_{\rm pp}$, as discussed above and therefore contribute less
to galactic panspermia.

Figure 12: Same as Fig. 10 (_top_), but for $\mathcal{F}_{\rm best}^{\rm
nodup}/f_{\rm pp}$, i.e., without the contribution of self panspermia.

###  5.4 Panspermia vs. Prebiotic Evolution

In this work we have eschewed a key question that implicitly motivates it,
namely: _which could be the dominant source of life on habitable planets in
the galaxy, in-situ evolution or panspermia ?_ Within the methodology used in
this paper, assuming that $f_{\rm oc}$ does not depend on, e.g., metallicity
and that the timescales of prebiotic evolution and transmission are short
compared to the age difference between particles, this could be parameterized
proportionally to the ratio between the sums of panspermia probability and of
natural habitability. Under these conditions, then, panspermia would take
precedence when the habitability of a given particle is lower than the sum of
habitabilities of neighboring particles weighted by escape fraction and
distance.

In practice, however, since $f_{\rm pp/stp}$ have to be arbitrarily scaled due
to the presence of undetermined parameters, this question cannot be answered
quantitatively. The actual, _unnormalized_ panspermia probability can be
defined as $\hat{f}_{\rm pp,stp}=\mathcal{R}\times f_{\rm pp,stp}$, with the
true value of $\mathcal{R}$ being unknown. Varying $\mathcal{R}$ for the
probability of $\hat{f}_{\rm pp}>f_{\rm hab}$ and $\hat{f}_{\rm stp}>f_{\rm
hab}$, we find that matching the naïve expectation that
$P(\mathcal{R})\simeq\mathcal{R}/(\mathcal{R}+1)$ would require
$\mathcal{R}\gtrsim 10^{3.5}$ and $\mathcal{R}\gtrsim 1$, respectively (for
more detail, see Appendix B). Fig. 13 shows the radial distribution of star
particles with $\hat{f}_{\rm pp/stp}>f_{\rm hab}$ for various values of
$\mathcal{R}$ which, for $\mathcal{R}>10^{-2}$, follows a similar slope to
$R$-$\Sigma_{\star}$ in Fig. 2. This confirms that dense regions, such as the
CentralDisk and inner part of the DiskHalo, have a higher chance of being
seeded through panspermia.

Figure 13: Radial distribution of star particles with unnormalized panspermia
probabilities greater than the natural habitability ($p(R|\hat{f}_{\rm
pp/stp}>f_{\rm hab})$) in g15784 at $z=0$, for different values of
$\mathcal{R}$. $p(R|\hat{f}_{\rm pp/stp}>f_{\rm hab})$ is normalized such that
its integral over $R$ is one.

##  6 Conclusions

In this paper, we have modeled the probability of panspermia (i.e., of
successful material transfer between star systems) and its distribution in
Milky Way-like galaxies, using a simulated object from the _McMaster Unbiased
Galaxy Simulations_ (MUGS). To compute panspermia probabilities, we have
expanded on the formalism presented in GH16, adding models for the ejection of
spores from planets, their escape, transit, and in-transit damage. Our
conclusions are summarized as follows:

  1. 1.

While the median habitability of increases with galactocentric radius, the
probability for panspermia behaves inversely, being likelier in the central
regions of the bulge ($R=1-4\mathinner{{\rm kpc}}$), as in the compact dwarf
spheroids orbiting the simulated main galaxy. This is mostly due to higher
stellar densities, which counterbalances their lower habitability. On the
other hand, the panspermia probability is low in the central _disk_ , owing to
a lower escape fraction due to metallicity and higher supernova rates. In
dense regions, many source particles can contribute to panspermia, whereas in
the outer disk and halo the panspermia probability is typically dominated by
one or, at most, a few source star particles. Unlike natural habitability,
whose value varies by only $\sim 5\%$ throughout the galaxy, the panspermia
probability has a wide dynamic range of several orders of magnitudes.

  2. 2.

There is no clear correlation between the panspermia probability and the
habitability of the receiving particle, mainly because the former, especially
at high values, is affected by numerous source star particles. On the other
hand, it is strongly correlated with the habitability of the source particle,
with several distinct stellar populations standing out, corresponding to those
in the central disk, outside of the central disk, and in the satellites.

  3. 3.

Finally, although this cannot be precisely quantified at the moment, we expect
the process of panspermia to be significantly less efficient at seeding
planets than in-situ prebiotic evolution. For example, even in a saturated
case where the total panspermia probability is of the order of the total
habitability in the galaxy, it would only dominate in 3% of all star
particles.

Several caveats remain in our model: first, it includes several factors that
we have regarded as unknown constants (e.g., the capture fraction of spores by
target planets, the relation between habitability and the presence of life,
the typical speed of interstellar objects, and the absolute value of escape
fraction of the interstellar organic compounds from source planets). Our
results are therefore naturally more qualitative than quantitative. Second,
our calculation was done on a single simulation snapshot. That is, it assumes
the spatial distribution to be static, while the actual Milky Way rotates and
evolves. As such, these results only apply if the typical timescale for
panspermia is much shorter than the dynamical timescale of a galaxy. Third,
although we have used one of the best mock Milky-Way proxies available, some
differences exist between the actual Milky Way and g15784, which may lead to
differences in panspermia probability. For example, our mock galaxy has a
larger value of bulge-to-disc light ratio than the actual Milky Way (Brook et
al., 2012), and the galactic bulge has been suggested to be well-suited for
panspermia (e.g., Chen et al., 2018; Balbi et al., 2020). Finally, higher-
resolution galaxy simulations with proper implementation of large-scale
effects may provide a more realistic estimation of panspermia probability by,
among other things, not having to account for self panspermia (e.g., Schaye et
al., 2015; Crain et al., 2015; Lee et al., 2021).

The authors thank Michael Gowanlock and Heeseung Zoe for helpful discussions.
We acknowledge Jeremy Bailin, Greg Stinson, Hugh Couchman and James Wadsley
for carrying out the MUGS simulation and allowing us access to the data. SEH
was partly supported by Basic Science Research Program through the National
Research Foundation of Korea funded by the Ministry of Education
(2018R1A6A1A06024977). SEH was also partly supported by the project 우주거대구조를
이용한 암흑우주 연구 (“Understanding Dark Universe Using Large Scale Structure of the
Universe”), funded by the Ministry of Science. ONS thanks the DIM ACAV+ for
postdoctoral funding. The authors acknowledge the Korea Institute for Advanced
Study for providing computing resources (KIAS Center for Advanced Computation
Linux Cluster System). Computational data were transferred through a high-
speed network provided by the Korea Research Environment Open NETwork
(KREONET).

## References

  * Adams & Spergel (2005) Adams, F. C., & Spergel, D. N. 2005, Astrobiology, 5, 497, doi: 10.1089/ast.2005.5.497
  * Allen et al. (2006) Allen, P. D., Driver, S. P., Graham, A. W., et al. 2006, MNRAS, 371, 2, doi: 10.1111/j.1365-2966.2006.10586.x
  * Anders & Fritze-v. Alvensleben (2003) Anders, P., & Fritze-v. Alvensleben, U. 2003, A&A, 401, 1063, doi: 10.1051/0004-6361:20030151
  * Arrhenius & Borns (1908) Arrhenius, S., & Borns, H. 1908, Worlds in the making; the evolution of the universe
  * Balbi et al. (2020) Balbi, A., Hami, M., & Kovac̆ević, A. 2020, Life, 10, doi: 10.3390/life10080132
  * Brook et al. (2012) Brook, C. B., Stinson, G. S., Gibson, B. K., et al. 2012, MNRAS, 426, 690, doi: 10.1111/j.1365-2966.2012.21738.x
  * Bruzual & Charlot (2003) Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000, doi: 10.1046/j.1365-8711.2003.06897.x
  * Burchell (2007) Burchell, M. 2007, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6694, Survival of microbial life under shock compression: implications for Panspermia, 669416
  * Burchell et al. (2001) Burchell, M. J., Shrine, N. R. G., Mann, J., et al. 2001, Advances in Space Research, 28, 707, doi: 10.1016/S0273-1177(01)00319-2
  * Burke et al. (2015) Burke, C. J., Christiansen, J. L., Mullally, F., et al. 2015, ApJ, 809, 8, doi: 10.1088/0004-637X/809/1/8
  * Carroll-Nellenback et al. (2019) Carroll-Nellenback, J., Frank, A., Wright, J., & Scharf, C. 2019, AJ, 158, 117, doi: 10.3847/1538-3881/ab31a3
  * Chen et al. (2018) Chen, H., Forbes, J. C., & Loeb, A. 2018, ApJ, 855, L1, doi: 10.3847/2041-8213/aaab46
  * Collins et al. (2005) Collins, G. S., Melosh, H. J., & Marcus, R. A. 2005, , 40, 817, doi: 10.1111/j.1945-5100.2005.tb00157.x
  * Crain et al. (2015) Crain, R. A., Schaye, J., Bower, R. G., et al. 2015, MNRAS, 450, 1937, doi: 10.1093/mnras/stv725
  * Crick & Orgel (1973) Crick, F. H. C., & Orgel, L. E. 1973, Icarus, 19, 341, doi: 10.1016/0019-1035(73)90110-3
  * Cumming et al. (2008) Cumming, A., Butler, R. P., Marcy, G. W., et al. 2008, PASP, 120, 531, doi: 10.1086/588487
  * Davenport (2016) Davenport, J. R. A. 2016, ApJ, 829, 23, doi: 10.3847/0004-637X/829/1/23
  * Đošović et al. (2019) Đošović, V., Vukotić, B., & Ćirković, M. M. 2019, A&A, 625, A98, doi: 10.1051/0004-6361/201834588
  * Dodd et al. (2017) Dodd, M. S., Papineau, D., Grenne, T., et al. 2017, Nature, 543, 60, doi: 10.1038/nature21377
  * Dong et al. (2018) Dong, C., Jin, M., Lingam, M., et al. 2018, Proceedings of the National Academy of Science, 115, 260, doi: 10.1073/pnas.1708010115
  * Ferland et al. (1998) Ferland, G. J., Korista, K. T., Verner, D. A., et al. 1998, PASP, 110, 761, doi: 10.1086/316190
  * Gibson et al. (2013) Gibson, B. K., Pilkington, K., Brook, C. B., Stinson, G. S., & Bailin, J. 2013, A&A, 554, A47, doi: 10.1051/0004-6361/201321239
  * Gillon et al. (2016) Gillon, M., Jehin, E., Lederer, S. M., et al. 2016, Nature, 533, 221, doi: 10.1038/nature17448
  * Ginsburg et al. (2018) Ginsburg, I., Lingam, M., & Loeb, A. 2018, ApJ, 868, L12, doi: 10.3847/2041-8213/aaef2d
  * Gladman et al. (2005) Gladman, B., Dones, L., Levison, H. F., & Burns, J. A. 2005, Astrobiology, 5, 483, doi: 10.1089/ast.2005.5.483
  * Gobat & Hong (2016) Gobat, R., & Hong, S. E. 2016, A&A, 592, A96, doi: 10.1051/0004-6361/201628834
  * Gonzalez et al. (2001) Gonzalez, G., Brownlee, D., & Ward, P. 2001, Icarus, 152, 185, doi: 10.1006/icar.2001.6617
  * Gowanlock et al. (2011) Gowanlock, M. G., Patton, D. R., & McConnell, S. M. 2011, Astrobiology, 11, 855, doi: 10.1089/ast.2010.0555
  * Grimaldi et al. (2021) Grimaldi, C., Lingam, M., & Balbi, A. 2021, AJ, 162, 23, doi: 10.3847/1538-3881/abfe61
  * Haldane (1954) Haldane, J. B. S. 1954, in New Biology 16, ed. M. L. Johnson, M. Abercrombie, & G. E. Fogg (Harmondsworth: Penguin), 12
  * He et al. (2019) He, M. Y., Ford, E. B., & Ragozzine, D. 2019, MNRAS, 490, 4575, doi: 10.1093/mnras/stz2869
  * Higuchi & Kokubo (2019) Higuchi, A., & Kokubo, E. 2019, MNRAS, 2747, doi: 10.1093/mnras/stz3153
  * Horneck et al. (1994) Horneck, G., Bücker, H., & Reitz, G. 1994, Advances in Space Research, 14, 41, doi: 10.1016/0273-1177(94)90448-0
  * Horneck et al. (2001) Horneck, G., Rettberg, P., Reitz, G., et al. 2001, Origins of Life and Evolution of the Biosphere, 31, 527
  * Housen & Holsapple (2011) Housen, K. R., & Holsapple, K. A. 2011, Icarus, 211, 856, doi: 10.1016/j.icarus.2010.09.017
  * Hoyle & Wickramasinghe (1978) Hoyle, F., & Wickramasinghe, C. 1978, Lifecloud. The origin of life in the universe
  * Hoyle & Wickramasinghe (1977) Hoyle, F., & Wickramasinghe, N. C. 1977, Nature, 266, 241, doi: 10.1038/266241b0
  * Hoyle et al. (1986) Hoyle, F., Wickramasinghe, N. C., & Al-Mufti, S. 1986, Earth Moon and Planets, 35, 79, doi: 10.1007/BF00054136
  * Hoyle et al. (1983) Hoyle, F., Wickramasinghe, N. C., Jansz, E. R., & Jayatissa, P. M. 1983, Ap&SS, 95, 227, doi: 10.1007/BF00661179
  * Hughes (2003) Hughes, D. W. 2003, MNRAS, 338, 999, doi: 10.1046/j.1365-8711.2003.06157.x
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Kawaguchi et al. (2013) Kawaguchi, Y., Yang, Y., Kawashiri, N., et al. 2013, Origins of Life and Evolution of the Biosphere, 43, 411, doi: 10.1007/s11084-013-9346-1
  * Kennicutt (1998) Kennicutt, Robert C., J. 1998, ApJ, 498, 541, doi: 10.1086/305588
  * Koike et al. (1992) Koike, J., Oshima, T., Koike, K. A., et al. 1992, Advances in Space Research, 12, 271, doi: 10.1016/0273-1177(92)90182-W
  * Kopparapu et al. (2013) Kopparapu, R. K., Ramirez, R., Kasting, J. F., et al. 2013, ApJ, 765, 131, doi: 10.1088/0004-637X/765/2/131
  * Krijt et al. (2017) Krijt, S., Bowling, T. J., Lyons, R. J., & Ciesla, F. J. 2017, ApJ, 839, L21, doi: 10.3847/2041-8213/aa6b9f
  * Kroupa et al. (1993) Kroupa, P., Tout, C. A., & Gilmore, G. 1993, MNRAS, 262, 545, doi: 10.1093/mnras/262.3.545
  * Kruijssen et al. (2019) Kruijssen, J. M. D., Pfeffer, J. L., Reina-Campos, M., Crain, R. A., & Bastian, N. 2019, MNRAS, 486, 3180, doi: 10.1093/mnras/sty1609
  * Lee et al. (2021) Lee, J., Shin, J., Snaith, O. N., et al. 2021, ApJ, 908, 11, doi: 10.3847/1538-4357/abd08b
  * Li & Draine (2001) Li, A., & Draine, B. T. 2001, ApJ, 554, 778, doi: 10.1086/323147
  * Licquia & Newman (2015) Licquia, T. C., & Newman, J. A. 2015, ApJ, 806, 96, doi: 10.1088/0004-637X/806/1/96
  * Lin & Loeb (2015) Lin, H. W., & Loeb, A. 2015, ApJ, 810, L3, doi: 10.1088/2041-8205/810/1/L3
  * Lineweaver et al. (2004) Lineweaver, C. H., Fenner, Y., & Gibson, B. K. 2004, Science, 303, 59, doi: 10.1126/science.1092322
  * Lingam (2016) Lingam, M. 2016, MNRAS, 455, 2792, doi: 10.1093/mnras/stv2533
  * Lingam & Loeb (2017) Lingam, M., & Loeb, A. 2017, Proceedings of the National Academy of Science, 114, 6689, doi: 10.1073/pnas.1703517114
  * Lingam & Loeb (2018) —. 2018, AJ, 156, 193, doi: 10.3847/1538-3881/aae09a
  * Lingam & Loeb (2021) Lingam, M., & Loeb, A. 2021, Life in the Cosmos: From Biosignatures to Technosignatures (Harvard University Press)
  * Mamajek (2017) Mamajek, E. 2017, Research Notes of the American Astronomical Society, 1, doi: 10.3847/2515-5172/aa9bdc
  * Mastrapa et al. (2001) Mastrapa, R. M. E., Glanzberg, H., Head, J. N., Melosh, H. J., & Nicholson, W. L. 2001, Earth and Planetary Science Letters, 189, 1, doi: 10.1016/S0012-821X(01)00342-9
  * McKinney (2010) McKinney, W. 2010, in Proceedings of the 9th Python in Science Conference, ed. S. van der Walt & J. Millman, 51 – 56
  * McMillan (2011) McMillan, P. J. 2011, MNRAS, 414, 2446, doi: 10.1111/j.1365-2966.2011.18564.x
  * Meech et al. (2017) Meech, K. J., Weryk, R., Micheli, M., et al. 2017, Nature, 552, 378, doi: 10.1038/nature25020
  * Melosh (1988) Melosh, H. J. 1988, Nature, 332, 687, doi: 10.1038/332687a0
  * Melosh (2003) —. 2003, Astrobiology, 3, 207, doi: 10.1089/153110703321632525
  * Mojzsis et al. (1996) Mojzsis, S. J., Arrhenius, G., McKeegan, K. D., et al. 1996, Nature, 384, 55, doi: 10.1038/384055a0
  * Naidu et al. (2021) Naidu, R. P., Conroy, C., Bonaca, A., et al. 2021, arXiv e-prints, arXiv:2103.03251.  https://arxiv.org/abs/2103.03251
  * Napier (2004) Napier, W. M. 2004, MNRAS, 348, 46, doi: 10.1111/j.1365-2966.2004.07287.x
  * Neukum & Ivanov (1994) Neukum, G., & Ivanov, B. A. 1994, in Hazards Due to Comets and Asteroids, ed. T. Gehrels, M. S. Matthews, & A. M. Schumann, 359
  * Nickerson et al. (2013) Nickerson, S., Stinson, G., Couchman, H. M. P., Bailin, J., & Wadsley, J. 2013, MNRAS, 429, 452, doi: 10.1093/mnras/sts348
  * Onofri et al. (2012) Onofri, S., de la Torre, R., de Vera, J.-P., et al. 2012, Astrobiology, 12, 508, doi: 10.1089/ast.2011.0736
  * Osterbrock & Ferland (2006) Osterbrock, D. E., & Ferland, G. J. 2006, Astrophysics of gaseous nebulae and active galactic nuclei
  * Pasini & Price (2015) Pasini, J. L. S., & Price, M. C. 2015, in Lunar and Planetary Science Conference, Lunar and Planetary Science Conference, 2725
  * Petigura et al. (2013) Petigura, E. A., Marcy, G. W., & Howard, A. W. 2013, ApJ, 770, 69, doi: 10.1088/0004-637X/770/1/69
  * Pilkington et al. (2012) Pilkington, K., Few, C. G., Gibson, B. K., et al. 2012, A&A, 540, A56, doi: 10.1051/0004-6361/201117466
  * Prantzos (2008) Prantzos, N. 2008, Space Sci. Rev., 135, 313, doi: 10.1007/s11214-007-9236-9
  * Price et al. (2013) Price, M. C., Solscheid, C., Burchell, M. J., et al. 2013, Icarus, 222, 263, doi: 10.1016/j.icarus.2012.10.035
  * Pritchet et al. (2008) Pritchet, C. J., Howell, D. A., & Sullivan, M. 2008, ApJ, 683, L25, doi: 10.1086/591314
  * Raskin et al. (2009) Raskin, C., Scannapieco, E., Rhoads, J., & Della Valle, M. 2009, ApJ, 707, 74, doi: 10.1088/0004-637X/707/1/74
  * Sarantopoulou et al. (2011) Sarantopoulou, E., Gomoiu, I., Kollia, Z., & Cefalas, A. C. 2011, Planet. Space Sci., 59, 63, doi: 10.1016/j.pss.2010.11.002
  * Schaye et al. (2015) Schaye, J., Crain, R. A., Bower, R. G., et al. 2015, MNRAS, 446, 521, doi: 10.1093/mnras/stu2058
  * Secker et al. (1994) Secker, J., Lepock, J., & Wesson, P. 1994, Ap&SS, 219, 1, doi: 10.1007/BF00657856
  * Secker et al. (1996) Secker, J., Wesson, P. S., & Lepock, J. R. 1996, JRASC, 90, 184.  https://arxiv.org/abs/astro-ph/9607139
  * Shen et al. (2010) Shen, S., Wadsley, J., & Stinson, G. 2010, MNRAS, 407, 1581, doi: 10.1111/j.1365-2966.2010.17047.x
  * Simon et al. (2017) Simon, J. B., Armitage, P. J., Youdin, A. N., & Li, R. 2017, ApJ, 847, L12, doi: 10.3847/2041-8213/aa8c79
  * Snaith et al. (2016) Snaith, O. N., Bailin, J., Gibson, B. K., et al. 2016, MNRAS, 456, 3119, doi: 10.1093/mnras/stv2788
  * Spergel et al. (2007) Spergel, D. N., Bean, R., Doré, O., et al. 2007, ApJS, 170, 377, doi: 10.1086/513700
  * Stapleton (1930) Stapleton, O. 1930, Last and First Men: A Story of the Near and Far Future, London: Methuen
  * Stewart et al. (2008) Stewart, K. R., Bullock, J. S., Wechsler, R. H., Maller, A. H., & Zentner, A. R. 2008, ApJ, 683, 597, doi: 10.1086/588579
  * Stinson et al. (2006) Stinson, G., Seth, A., Katz, N., et al. 2006, MNRAS, 373, 1074, doi: 10.1111/j.1365-2966.2006.11097.x
  * Stinson et al. (2010) Stinson, G. S., Bailin, J., Couchman, H., et al. 2010, MNRAS, 408, 812, doi: 10.1111/j.1365-2966.2010.17187.x
  * Stöffler et al. (2007) Stöffler, D., Horneck, G., Ott, S., et al. 2007, Icarus, 186, 585, doi: 10.1016/j.icarus.2006.11.007
  * van Zuilen et al. (2002) van Zuilen, M. A., Lepland, A., & Arrhenius, G. 2002, Nature, 418, 627, doi: 10.1038/nature00934
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: https://doi.org/10.1038/s41592-019-0686-2
  * Wadsley et al. (2004) Wadsley, J. W., Stadel, J., & Quinn, T. 2004, New A, 9, 137, doi: 10.1016/j.newast.2003.08.004
  * Wadsley et al. (2008) Wadsley, J. W., Veeravalli, G., & Couchman, H. M. P. 2008, MNRAS, 387, 427, doi: 10.1111/j.1365-2966.2008.13260.x
  * Wallis & Wickramasinghe (2004) Wallis, M. K., & Wickramasinghe, N. C. 2004, MNRAS, 348, 52, doi: 10.1111/j.1365-2966.2004.07355.x
  * Weber & Greenberg (1985) Weber, P., & Greenberg, J. M. 1985, Nature, 316, 403, doi: 10.1038/316403a0
  * Wells et al. (2003) Wells, L. E., Armstrong, J. C., & Gonzalez, G. 2003, Icarus, 162, 38, doi: 10.1016/S0019-1035(02)00077-5
  * Wesson (2010) Wesson, P. S. 2010, Space Sci. Rev., 156, 239, doi: 10.1007/s11214-010-9671-x
  * Wickramasinghe & Wickramasinghe (2003) Wickramasinghe, N. C., & Wickramasinghe, J. T. 2003, Ap&SS, 286, 453, doi: 10.1023/A:1026352911978
  * Yamagishi et al. (2018) Yamagishi, A., Kawaguchi, Y., Hashimoto, H., et al. 2018, Astrobiology, 18, 1369, doi: 10.1089/ast.2017.1751
  * Zackrisson et al. (2016) Zackrisson, E., Calissendorff, P., González, J., et al. 2016, ApJ, 833, 214, doi: 10.3847/1538-4357/833/2/214
  * Zechmeister et al. (2019) Zechmeister, M., Dreizler, S., Ribas, I., et al. 2019, A&A, 627, A49, doi: 10.1051/0004-6361/201935460

##  Appendix A Escape fractions and weights

In the case of natural panspermia, we assume that life first develops on the
surface of a planet within its star HZ, and that spores are then ejected from
it by high velocity impacts. In general, few fragments reach planetary escape
velocity and none stellar escape velocity. For interstellar panspermia to
happen, therefore, the fragments must be accelerated by unspecified processes,
which we assume only depend on the host mass star through its escape velocity
within the HZ. Fig. 14 shows the distribution of fragment velocities after
impact and the (arbitrarily-scaled) stellar escape fraction. Fig. 15 shows the
evolution of the escape fraction $w_{\rm esc}$ over time, assuming that the
frequency of impacts follows the one derived from Lunar cratering (Neukum &
Ivanov, 1994):

$N_{\rm impact}(t)\propto\exp\left(6.93\,\frac{t_{\rm E}-t}{\rm
Gyr}\right)\,,$ (A1)

where $t_{\rm E}$ the current age of the Earth. Finally, Fig. 16 shows the
distribution of escape fractions $f_{\rm esc}$ computed for star particles, as
a function of their galactocentric distance, and Fig. 17 their correlation
with habitability. There exists a strong correlation $f_{\rm esc}$ and
habitability within the DiskHalo region, whereas star particles in the
CentralDisk tend to have lower $w_{\rm esc}$ due to their higher
metallicities. Interestingly, rather sharp linear lower boundaries exist in
both $f_{\rm cradle}$-$f_{\rm esc}$ and $f_{\rm target}$-$f_{\rm esc}$
parameter spaces, where most of $f_{\rm esc}$ goes to zero at $f_{\rm
cradle}<0.082$ and $f_{\rm target}<0.095$ (Fig. 17). Finally, the Spheroids
show a radial distribution of $f_{\rm esc}$ similar to that of the main
galaxy, though at smaller scale.

Figure 14: Top: Distribution of ejecta velocities from an impactor population
with $f(m)\propto m^{-1.6}$, for a planet within the HZ of a
$0.1\mathinner{{\rm M}_{\odot}}$ (red) and $1\mathinner{{\rm M}_{\odot}}$
(blue) star, respectively. The dashed vertical line shows the approximate
escape velocity of an Earth-mass planet, here set at $10{\rm km/s}$ for
convenience. Bottom: relative fraction of escaping material $w_{\rm esc}$ as a
function of host star mass, assuming that the mass of HZ terrestrial planets
does not vary with host star mass. Only the mass range for which the HZ is
defined (Kopparapu et al., 2013) is shown.  Figure 15: Escape fractions for
star particles with a KTG93 IMF, as a function of their age. The solid blue
curve shows the instantaneous $f_{\rm esc}$ and the dashed red one the
cumulative $f_{\rm esc}$ over the lifetime of the star particle.  Figure 16:
The escape weight ($f_{\rm esc}$) as a function of galactocentric radius in
g15784 at $z=0$, drawn in a logarithmic scale. Note that the escape weight is
shown in artibrary unit. Figure 17: The escape weight ($f_{\rm esc}$) as a
function of three habitability levels ($f_{\rm hab}$, $f_{\rm cradle}$, and
$f_{\rm target}$) in g15784 at $z=0$, drawn in a logarithmic scale.

##  Appendix B Unnormalized panspermia probabilities

Fig. 18 shows the cumulative probabilities of $f_{\rm pp/stp}/f_{\rm hab}$ of
g15784 at $z=0$. In both cases, the overall shape of the probability
distribution is similar to those of $f_{\rm pp/stp}$, mainly due to the narrow
range of $f_{\rm hab}$. Specifically, $P(>f_{\rm pp}/f_{\rm hab})$ follows a
power-law relation of $P\propto(f_{\rm pp}/f_{\rm hab})^{-1/4}$ for
$10^{-3}\lesssim f_{\rm pp}/f_{\rm hab}\lesssim 10^{2}$, falling to (nearly)
zero for $f_{\rm pp}/f_{\rm hab}\gtrsim 10^{2}$. On the other hand, $P(>f_{\rm
stp}/f_{\rm hab})$ is nearly zero for $f_{\rm stp}/f_{\rm hab}\gtrsim 2$ and
plateaus at $P\simeq 0.7$ around $f_{\rm stp}/f_{\rm hab}\simeq 0.3$ and
$0.01$ for $\ell_{\rm surv}\lesssim 100\mathinner{{\rm pc}}$ and $\gtrsim
100\mathinner{{\rm pc}}$, respectively. We note that the cumulative
probability does not exceed 70% in g15784 because the remaining 30% of star
particles have zero habitabilites.

Figure 18: Cumulative probabilities of the ratios between panspermia
probabilities ($f_{\rm pp/stp}$) and natural habitability ($f_{\rm hab}$) in
g15784 at $z=0$, assuming the exp damage model with varying $\ell_{\rm surv}$.
The dashed vertical line marks $f_{\rm pp/stp}=f_{\rm hab}$. Both $f_{\rm pp}$
and $f_{\rm stp}$ are normalized so that their sum over g15784 is same as the
sum of $f_{\rm hab}$.

Table 1 shows probabilities of $\hat{f}_{\rm pp/stp}>f_{\rm hab}$ for various
values $\mathcal{R}$. The probability of star particles with $\hat{f}_{\rm
pp}>f_{\rm hab}$ is much lower than the naïve expectation that
$P(\mathcal{R})\simeq\mathcal{R}/(\mathcal{R}+1)$. For example, when
$\mathcal{R}=1$, i.e., the total panspermia probability and total habitability
is the same, only 3% of star particles have $\hat{f}_{\rm pp}>f_{\rm hab}$,
rather than half as would be expected. In fact, $P(\hat{f}_{\rm pp}>f_{\rm
hab})>1/2$ occurs only at very high values of $\mathcal{R}\gtrsim 10^{3.5}$.
This ensures that only a tiny fraction of star particles dominate the
panspermia process of the entire galaxy. On the other hand, $P(\hat{f}_{\rm
stp}>f_{\rm hab})$ matches better the naïve expectation for values of
$\mathcal{R}\gtrsim 1$.

Table 1: Probability of star particles with _unnormalized_ panspermia probabilities greater than natural habitability in g15784 at $z=0$, for various values of $\mathcal{R}$). $\mathcal{R}$ |  $P(\hat{f}_{\rm pp}>f_{\rm hab})$ |  $P(\hat{f}_{\rm stp}>f_{\rm hab})$
---|---|---
$10^{-2}$ | $\lesssim 0.1\%$ | 0
$10^{-1}$ | 1% | 0
$10^{0}$ | 3% | 40%
$10^{1}$ | 6% | 70%
$10^{2}$ | 10% | 70%
$10^{3}$ | 20% | 70%
$10^{4}$ | 70% | 70%