# X-rays Trace the Volatile Content of Interstellar Objects

Samuel H. C. Cabot Yale University, 52 Hillhouse, New Haven, CT 06511, USA  Q.
Daniel Wang Astronomy Department, University of Massachusetts, Amherst, MA
01003, USA  Darryl Z. Seligman NSF Astronomy and Astrophysics Postdoctoral
Fellow  Department of Astronomy and Carl Sagan Institute, Cornell University,
122 Sciences Drive, Ithaca, NY, 14853, USA

###### Abstract

The non-detection of a coma surrounding 1I/‘Oumuamua, the first discovered
interstellar object (ISO), has prompted a variety of hypotheses to explain its
nongravitational acceleration. Given that forthcoming surveys are poised to
identify analogues of this enigmatic object, it is prudent to devise
alternative approaches to characterization. In this study, we posit X-ray
spectroscopy as a surprisingly effective probe of volatile ISO compositions.
Heavily ionized metals in the solar wind interact with outgassed neutrals and
emit high-energy photons in a process known as charge exchange, and charge
exchange induced X-rays from comets and planetary bodies have been observed
extensively in our Solar System. We develop a model to predict the X-ray flux
of an ISO based on its chemical inventory and ephemeris. We find that while
standard cometary constituents, such as H2O, CO2, CO, and dust are best probed
via optical or infrared observations, we predict strong X-ray emission
generated by charge exchange with extended comae of H2 and N2 — species which
lack strong infrared fluorescence transitions. We find that XMM-Newton would
have been sensitive to charge exchange emission from 1I/‘Oumuamua during the
object’s close approach to Earth, and that constraints on composition may have
been feasible. We argue for follow-up X-ray observations of newly discovered
ISOs with close-in perihelia. Compositional constraints on the general ISO
population could reconcile the apparently self-conflicting nature of
1I/‘Oumuamua, and provide insight into the earliest stages of planet formation
in extrasolar systems.

ISOs (52); Comets (280)

##  1 Introduction

Knowledge of the compositions of minor bodies has considerably influenced our
understanding of the early Solar System. While investigations of their
dynamical histories are limited by the Solar System’s chaotic nature (Wisdom,
1980; Laskar, 1989; Batygin & Laughlin, 2008; Laskar & Gastineau, 2009),
compositional measurements of minor bodies — especially of their interiors —
have the potential to reveal their formation environments (Öberg et al.,
2011).

Remarkably, the Solar System likely ejected tens of earth masses of volatile
rich material during the early stages of its formation and evolution (Hahn &
Malhotra, 1999; Gomes et al., 2004; Tsiganis et al., 2005; Morbidelli et al.,
2005; Levison et al., 2008; Raymond et al., 2018, 2020). Therefore, it is
reasonable to expect that extrasolar planetary systems contribute to a
galactic population of interstellar comets, and that some will encounter the
Solar System on hyperbolic trajectories (Moro-Martín et al., 2009; Engelhardt
et al., 2017; Cook et al., 2016). Naturally, it came as a surprise that
1I/‘Oumuamua, the first discovered ISO, exhibited none of the typical
properties of Solar System comets (for recent reviews, see Moro-Martín, 2022;
Jewitt & Seligman, 2022). It had no visible coma (Meech et al., 2017; Jewitt
et al., 2017; Trilling et al., 2018; Bolin et al., 2018), an extreme shape
(e.g., Knight et al., 2017; Mashchenko, 2019), a reddened reflection spectrum
(Masiero, 2017), a young dynamical age (e.g., Mamajek, 2017; Hsieh et al.,
2021) and non-zero nongravitational acceleration (Micheli et al., 2018).

The second discovered ISO, 2I/Borisov, was unambiguously a comet (Jewitt &
Luu, 2019), perhaps more inline with expectations. Its cometary activity was
readily measured and typical carbon and nitrogen bearing species were detected
(Opitom et al., 2019; Kareta et al., 2020; Lin et al., 2020; Bannister et al.,
2020; Xing et al., 2020; Aravind et al., 2021). ALMA and Hubble observations
revealed that it was enriched in CO relative to H2O (Bodewits et al., 2020;
Cordiner et al., 2020). This finding suggests that 2I/Borisov formed exterior
to the CO snowline in the protoplanetary disk (Price et al., 2021; Seligman et
al., 2022) of a very young (Lisse et al., 2022) or a very carbon-enriched
system (cf. Bodewits et al., 2020).

‘Oumuamua’s former provenance remains in question, and dynamically backtracing
either ISO to their respective host systems is difficult (Mamajek, 2017;
Bailer-Jones et al., 2018). 1I/‘Oumuamua’s peculiar properties and elusiveness
to follow-up spectroscopy have prompted a variety of theories regarding its
origin. If the measured nongravitational acceleration was driven by cometary
outgassing, this would be energetically consistent with a composition of H2
(Füglistaler & Pfenniger, 2018; Seligman & Laughlin, 2020; Levine & Laughlin,
2021), N2 (Jackson & Desch, 2021; Desch & Jackson, 2021), or CO (Seligman et
al., 2021). Confirming an H2 or N2 composition would have immediately revealed
a new mechanism of generating minor bodies: formation in the cores of
molecular clouds (Seligman & Laughlin, 2020), or ejection of ice from the
surfaces of Pluto analogues due to impact events (Desch & Jackson, 2021).
Alternatively, if the acceleration was caused by radiation pressure (Micheli
et al., 2018), then 1I/‘Oumuamua must have been extremely porous (Moro-Martín,
2019; Sekanina, 2019; Flekkøy et al., 2019; Luu et al., 2020) or thin (Bialy &
Loeb, 2018). While H2O, CO2, and CO species in cometary comae are easily
measured via infrared spectroscopy, the possible presence of difficult to
detect homonuclear H2 or N2 prompts a search for alternative methods for
characterizing interstellar comets.

This study presents such a new approach: X-ray observations of solar wind (SW)
charge exchange (CX). X-ray observations of an interstellar object should
immediately reveal the presence of an outgassed coma. CX involves the transfer
of electrons from a cool neutral medium to heavily ionized metals in the SW.
Following the unexpected detection of X-rays emanating from C/1996 B2
(Hyakutake) (Lisse et al., 1996; Cravens, 1997), CX has been observed with a
multitude of other comets (Dennerl et al., 1997; Cravens, 2000, 2002; Lisse et
al., 1999, 2004; Bodewits et al., 2007). CX conveys information about the
composition and speed of the solar wind (Beiersdorfer et al., 2001; Bodewits
et al., 2007; Gu et al., 2016). Studies have also linked CX emission to
physical and chemical properties of the minor body and its coma through the
morphology of the X-ray emission profile (Wegmann et al., 2004) and emission
line ratios (Mullen et al., 2017).

Indeed, there are encouraging prospects for discovering additional ISOs in the
coming decade. Population synthesis models of the galactic population of ISOs
have demonstrated that the Rubin Observatory Legacy Survey of Space and Time
(LSST) will detect $1-2$ 1I/‘Oumuamua analogues every year (Hoover et al.,
2022).

This paper is organized as follows. In §2, we discuss the advantages and
limitations of X-ray observations for characterizing minor bodies, and outline
a simple model of charge exchange emission. We apply our model to 1I/‘Oumuamua
and 2I/Borisov in §3, and compare our predictions to the known correlation
between X-ray and visible-band flux. Our model suggests that if 1I/‘Oumuamua
did indeed outgas a coma, that CX would have been detectable with current-
generation X-ray facilities during the period that it approached Earth. §4
establishes expectations for detecting CX with new ISOs discovered by the
Rubin Observatory. Finally, our conclusions are summarized in §5. We refer the
reader to Appendix A for a brief review of CX fundamentals, and to Appendix B
for the details of our CX model.

##  2 Motivation & Model

This section establishes use cases for X-ray observations of interstellar
objects, and sets forth an analytic model of X-ray emission from outgassed
comae. It also specifies the traits of ISOs (i.e., bulk composition and
orbital trajectory) from which we expect robust detection of X-ray emission
with present-day facilities.

###  2.1 Information Gained from X-ray Observations

As a primer, it is useful to review the prototypical case of CX from an
outgassed coma: C/1996 B2 (Hyakutake), a long-period comet which came within
0.23 au of the Sun at perihelion. Infrared observations yielded unambiguous
detections of H2O, CO, CH4, and C2H6 (Mumma et al., 1996; Dello Russo et al.,
2002), Contemporaneously, significant X-ray emission was detected out to $\sim
100,000$ km (6.7$\times 10^{-4}$ au) from its nucleus by Lisse et al. (1996).
CX was suggested as the responsible process by Cravens (1997), and reaffirmed
by Wegmann et al. (1998). Other mechanisms (e.g., thermal bremsstrahlung,
scattering, and fluorescence) may be ruled out (Krasnopolsky, 1997; Lisse et
al., 1999, 2004). Since this detection, sophisticated models of CX with
cometary comae have been developed, such as the hydrodynamical simulations by
Wegmann et al. (2004), and CX has been observed with comae of numerous other
comets (e.g. Ewing et al., 2013; Bodewits et al., 2007).

X-rays have been conventionally of limited value for compositional studies of
minor bodies. For one, CX detections arise only from significantly extended
comae. Moreover, the most immediate insights conveyed are the morphology of
the coma and the properties of the solar wind (Lisse et al., 2004).
Infrared/radio spectroscopy remains the de facto technique for detecting
molecular species which exhibit solar-pumped fluorescence transitions
(Crovisier & Encrenaz, 1983; Bockelée-Morvan et al., 2004). Such species
(reviewed by e.g. Biver & Bockelée-Morvan, 2016; Bockelée-Morvan & Biver,
2017) include H2O, CO, CO2, CH4, C2H2, C2H6, and HCN. Complementary to
infrared observations, UV spectroscopy can measure the production of some
additional species (Biver et al., 2022) such as noble gases and homonuclear
diatomic molecules. However, except for a small number of tenuous reports of
their sublimation (e.g., Ar in Hale-Bopp, Stern et al., 2000) noble gases
remained elusive in comets prior to in situ detections in 67P (Rubin et al.,
2018) by the European Space Agency’s Rosetta mission. Rosetta also confirmed
the presence O2 and N2 in comets (Rubin et al., 2015; Bieler et al., 2015).

This study explores a novel use case for X-ray observations: to reveal an
outgassed coma that is invisible in the infrared, and which may arise from the
perihelion passage of an interstellar object. While the composition of
1I/‘Oumuamua remains debated, a number of candidate species (Table 1) are
monotomic or homonuclear diatomic, and will not fluoresce in the infrared.
However, CX will occur at a neutral medium, even one that does not produce
observable thermal emission, fluorescence, or scattering. Therefore, the
outgassed coma of an interstellar object may be X-ray bright even in the
absence of infrared and optical detections. In particular, X-ray observations
offer a promising avenue for remote sensing an H2 or N2 coma. Both of these
species are thermodynamically consistent with 1I/‘Oumuamua’s nongravitational
acceleration under outgassing, and comprise the focus of this study. Per
Seligman et al. (2021), we benchmark results to a CO composition (c.f.
Trilling et al., 2018); although this molecule is more readily detected in the
infrared.

Table 1: Cryogenic chemical properties for volatiles which may be constituents of ISOs. For each species, we report the temperature of sublimation ($T_{\rm Sub}$), ideal adiabatic index ($\gamma$), enthalpy of sublimation ($\Delta H$), and sound speed ($c_{s}$) per Equation B10. We also report the total energy input to a single particle ($\mathcal{H}$) per Equation B9. Data from Shakeel et al. (2018), except for CO which is obtained from Stephenson & Malanowski (1987) and the NIST database. Species | $\textit{T}_{\rm Sub}$ | $\gamma$ | $\Delta H$ | $c_{s}$ | $\mathcal{H}$
---|---|---|---|---|---
| ($\rm{K}$) |  | (${\rm kJ\,mole^{-1}}$) | (km s-1) | (${\rm kJ}\times 10^{-23}$)
H2 | 6 | 7/5 | 1 | 0.19 | 0.18
Ne | 9 | 5/3 | 1.9 | 0.11 | 0.34
N2 | 25 | 7/5 | 7.34 | 0.14 | 1.27
CO | 58 | 7/5 | 7.6 | 0.15 | 1.37
Ar | 30 | 5/3 | 7.79 | 0.15 | 1.36
O2 | 30 | 7/5 | 9.26 | 0.10 | 1.60
Kr | 40 | 5/3 | 11.53 | 0.12 | 2.01
Xe | 55 | 5/3 | 15.79 | 0.12 | 2.75
CO2 | 82 | 8/6 | 28.84 | 0.14 | 4.94
H2O | 155 | 8/6 | 54.46 | 0.31 | 9.33

###  2.2 Scaling Relationships

In Appendix B, we develop a model that links X-ray flux to a minor body’s
physical properties. Specifically, it depends on the following key parameters:
the neutral production rate $(Q_{\rm gas})$, mean radius of the nucleus $(a)$,
perihelion distance $(r_{\rm peri})$, sublimation + kinetic energy of the
relevant volatiles $(\mathcal{H})$, geocentric distance $(\Delta_{e})$, solar
wind number density $(n_{\rm SW})$, CX interaction area of the coma
$(\mathcal{A})$, and X-ray lumonisty $(L_{\rm X})$ and flux $(F_{\rm X})$. The
pertinent relationships are as follows:

$\displaystyle Q_{\rm gas}$ $\displaystyle\propto a^{2}r_{\rm
peri}^{-2}\mathcal{H}^{-1}$ (1) $\displaystyle\mathcal{A}$
$\displaystyle\propto Q_{\rm gas}^{2}{\rm\,(to\,leading\,order)}$ (2)
$\displaystyle n_{\rm SW}$ $\displaystyle\propto r_{\rm peri}^{-2}$ (3)
$\displaystyle L_{\rm X}$ $\displaystyle\propto n_{\rm SW}\mathcal{A}$ (4)
$\displaystyle F_{\rm X}$ $\displaystyle\propto\Delta_{e}^{-2}L_{\rm X}\propto
a^{4}r_{\rm peri}^{-6}\mathcal{H}^{-2}\Delta_{e}^{-2}.$ (5)

In our model, constants of proportionality are calibrated to measurements of
C/1996 B2 (Hyakutake) (Lisse et al. (1996), Appendix B). The above scaling
relationships demonstrate that the X-ray brightness of a minor body can be
significantly enhanced by a close-in perihelion passage and a particularly
volatile composition. Figure 1 shows a schematic of such an ISO encounter,
where the scaling relationships and underlying physical processes are depicted
in the individual panels.

Figure 1: Schematic of solar wind charge exchange with the outgassed neutrals
in the coma of an ISO. Panel 1: An instantaneous view of the inner solar
system and the trajectory of an ISO, currently at perihelion ($r_{\rm peri}$).
Panel 2: The flux of solar radiation ($F_{\odot}$) heats the volatiles on the
ISO’s surface, which causes sublimation and outgassing of neutral volatiles at
a rate $Q_{\rm gas}$. Panel 3: Solar wind ions (with number density $n_{\rm
SW}$) interact with the outgassed coma through charge exchange. Electrons are
transferred from the neutral coma to the bare or H-like solar wind ions, and
the subsequent cascade emits X-rays. The coma’s interaction cross-section
($\mathcal{A}$) scales with $Q_{\rm gas}^{2}$. As a result, the X-ray
luminosity follows $L_{\rm X}\propto r_{\rm peri}^{-6}$ (Equation 5, §2.2).

###  2.3 Detection Thresholds

In this section we guage the feasibility of detecting CX with an outgassed
coma, including the requisite X-ray flux and exposure durations. Our
predictions are for the EPIC pn detector onboard XMM-Newton, which has the
advantage of a larger effective area (approximately $A=900$ cm2 at 0.5 kev)
compared to the other space-based X-ray detectors. To estimate the
detectability of a comet or ISO, one needs to account for the noise
contribution from the background, which is chiefly made of background AGNs and
the diffuse hot plasma emission from the general interstellar and
circumgalactic media of the Galaxy, the Local Bubble, and solar wind charge
exchange emission within the heliosphere (e.g., McCammon et al., 2002;
Koutroumpa, 2012). Based on archival blank-sky EPIC pn observations, we
estimate that the total background intensity is $\Sigma=1.4\times 10^{-3}$
counts s-1 arcmin-2 in the $0.5-0.7$ keV band, for example, which encloses the
typically strong Ovii and Oviii K$\alpha$ lines. The total background
intensity also includes the contribution from non-X-ray (cosmic-ray induced
instrument) events. Let $\Phi_{X}$ denote the X-ray flux at the detector due
to CX with the target (units of counts s-1 cm-2), and let $\tau$ denote the
exposure duration. Furthermore, we assume that nearly all of the signal is
contained within a solid angle $\Omega$ for simplicity. Then the signal-to-
noise (S/N) of the CX signature is

${\rm S/N}=\Phi_{X}A\sqrt{\tau}/\sqrt{\Phi_{X}A+\Sigma\Omega}\,.$ (6)

Alternatively, this equation can also be rearranged into an expression for
$\tau$ for a desired S/N threshold.

One caveat is that a continuous exposure may be ineffective for fast-moving
targets. Photon events may, however, be spatially calibrated across discrete
slews that keep the object on the focal plane array (FPA). This enables
multiple on-target pointings and reconstruction of events in the cometocentric
frame based on the attitude of the telescope. The maximum exposure duration
for any one pointing is then limited by the field of view of the telescope and
the angular velocity of the target. For reference, 1I/‘Oumuamua’s angular
velocity reached $1.4\times 10^{-4}$ deg. s-1 at closest approach to Earth.
The crossing time for XMM-Newton’s $30^{\prime}\times 30^{\prime}$ field of
view would have been up to $\sim 3.5$ ks.

Space-based X-ray observatories have minimum solar elongation angles
($\psi_{\odot}^{\rm min}$) for reasons pertaining to detector safety (e.g.,
avoiding burn-out incidents similar to ROSAT’s), thermal stability, and power
supply. For Chandra, $\psi_{\odot}^{\rm min}=46.4^{\circ}$, and for XMM-
Newton, $\psi_{\odot}^{\rm min}=70^{\circ}$. These constraints permit
observations of small bodies at $R\geq 0.72$ au and $R\geq 0.94$ au,
respectively. These lower bounds can only be attained under optimal alignment
between Earth and the object. Future missions will likely have similar safety
exclusion zones to protect equipment at the FPA.

Figure 2: Exposure time (ks) required for a 5$\sigma$ detection of CX X-ray
emission (Equation B12), as a function of outgassing rate $Q_{\rm gas}$ and
perihelion distance $r_{\rm peri}$. Geocentric distance is fixed at
$\Delta_{e}=1$ au. The background rate and effective area correspond to that
of EPIC pn on XMM-Newton. For reference, markers are plotted at locations
representative of real minor bodies: light-blue (‘H’) corresponds to $Q_{\rm
gas}=1.5\times 10^{29}$ s-1 observed at 1.0 au — similar to C/1996 B2
(Hyakutake); tan (‘B’) corresponds to $Q_{\rm gas}=10^{27}$ s-1 observed at
2.0 au — similar to 2I/Borisov; coral (‘O’) corresponds to $Q_{\rm
gas}=2.8\times 10^{28}$ s-1 observed at 0.25 au and $Q_{\rm gas}=1.8\times
10^{27}$ s-1 observed at 1.0 au — estimates corresponding to 1I/‘Oumuamua
under a CO composition. The solar elongation angles of Chandra
($\psi_{\odot}^{\rm min}=46.4^{\circ}$) and XMM-Newton ($\psi_{\odot}^{\rm
min}=70^{\circ}$) impose lower bounds ($\sin\psi_{\odot}^{\rm min}$) on
observable $r_{p}$, and their respective restricted zones are hatched in the
figure. The lower bound is attained only in the ideal orbital case and
observable heliocentric distances are typically significantly larger due to
spacecraft limitations.

Figure 2 depicts the exposure times necessary to achieve S/N $=5$ as a
function of $Q_{\rm gas}$ and $r_{\rm peri}$, specifically for the XMM-Newton
pn detector. For simplicity, the geocentric distance is assumed $\Delta_{e}=1$
au. The X-ray luminosity of CX is given by Equation B12, and the angular
extent of the emission is set by $\tilde{b}$ (Equation B7). Markers in Figure
2 are located at outgassing rates and perihelia of real minor bodies (the
outgassing rate of 1I/‘Oumuamua was not directly measured, but is estimated in
§3).

This figure immediately conveys the feasibility of detecting CX emission from
outgassed comae with currently operational facilities. For modest exposure
times of order $10$ ks, CX should be detectable when $Q>10^{27}$ s-1 over a
range of $r_{\rm peri}$. Qualitatively, this finding is consistent with
previous high-significance ROSAT detections of CX with six comets (Dennerl et
al., 1997), whose ougassing rates were between $Q_{\rm gas}=2\times
10^{27}-9\times 10^{29}$ s-1. The heliocentric distances in this sample were
between $R=0.99-1.96$ au, and geocentric distances between
$\Delta_{e}=0.12-1.61$ au (these comets are discussed further in §3.3). While
the minor bodies need not be observed at perihelion, our model indicates that
$F_{\rm X}$ scales more strongly with heliocentric distance ($R$) than with
$\Delta_{e}$ (Lisse et al., 1999) per Equations B8 & B11. As discussed in the
next section, 1I/‘Oumuamua’s proximity to the Earth and Sun would have made it
amenable to X-ray observations. On the other hand, 2I/Borisov would have been
a more difficult case because it only came within a minimum $2$ au of the Sun.

##  3 Detectability of X-rays from 2I/Borisov and 1I/‘Oumuamua

We proceed to estimate the X-ray luminosity for the only two identified ISOs
that traversed our Solar System: 1I/‘Oumuamua and 2I/Borisov. We first
estimate $L_{\rm X}$ using the analytic framework presented in the previous
section. We then make an independent estimate based on known trends between
optical and X-ray luminosities for comets.

We briefly review pertinent measurements of both ISOs. From its photometric
lightcurve structure, 1I/‘Oumuamua is estimated to have had an oblate 6:6:1
ellipsoidal geometry (Mashchenko, 2019). Its albedo ($p$) was not constrained,
so its true dimensions are uncertain. Meech et al. (2017) and Bolin et al.
(2018) measured an effective radius of $\sim 0.1$ km assuming an albedo of
0.04. The light curve fit by Mashchenko (2019) yielded dimensions $115\times
111\times 19$ m with $p=0.1$. For our order-of-magnitude calculations, we
treat 1I/‘Oumuamua as spherical with radius of $a=100$ m. However, we
emphasize that the true dimensions are albedo-dependent, and the lengths scale
as $1/\sqrt{p}$. At perihelion of $r_{\rm peri}=0.25$ au, 1I/‘Oumuamua’s
distance to Earth was $\Delta_{e}=1.23$ au with an apparent magnitude $V=21$.
The object reached an apparent magnitude of $V=19.7$ at its closest approach
to Earth with $\Delta_{e}=0.16$ au. Infrared Spitzer observations produced
non-detections when 1I/‘Oumuamua was outbound at $\sim 2$ au, providing upper
limits on the production rates of CO or CO2 (Trilling et al., 2018). However,
sporadic outgassing of CO might reconcile the nongravitational acceleration
and Spitzer non-detection (Seligman et al., 2021).

The nuclear radius of comet-like 2I/Borisov was constrained to $0.2\,{\rm
km}<a<0.5\,{\rm km}$ based on its brightness profile and nongravitational
acceleration assuming a range of plausible bulk densities (Jewitt & Luu, 2019;
Bolin et al., 2020). We adopt a nominal radius of $a=300$ m. Unlike 1I, gas
emission activity typical of comets was definitely detected from this body.
When contemporaneous measurements of H2O and CO production rates were obtained
after perihelion ($r_{\rm peri}=2$ au), CO dominated the outflow. Specifically
Bodewits et al. (2020) measured $Q({\rm CO})=7.5\times 10^{26}$ s-1 at 3.3
days after perihelion and $Q({\rm CO})=1.07\times 10^{27}$ s-1 at 22.4 days
after perihelion. Also, Cordiner et al. (2020) measured $Q({\rm CO})=4.4\times
10^{26}$ s-1 in observations conducted $7-8$ days after perihelion. While
water production exceeded $Q({\rm H_{2}O})=10^{27}$ s-1 prior to perihelion,
it dropped below $6\times 10^{26}$ s-1 for observations conducted after
perihelion (Bodewits et al., 2020). Jewitt et al. (2020) measured $V=16.6$ at
26 days after perihelion, when 2I/Borisov’s distances were $R=2.1$ au and
$\Delta_{e}=1.9$ au.

In the following, $Q_{\rm gas}$ denotes the total outgassing rate across all
neutral volatiles. In certain instances, a dominant species $X$ was
determined, in which case its outgassing rate is denoted $Q({X})$. Our
predictions for $L_{\rm X}$ neglect subtle dependencies on properties of the
solar wind and coma. In the optically thick regime, all solar wind minor ions
will undergo charge exchange. However, the X-ray lines emitted depend on the
neutral composition (Mullen et al., 2016). Also, CX cross sections depend
strongly on the solar wind velocity (Kharchenko & Dalgarno, 2001; Beiersdorfer
et al., 2001; Bodewits et al., 2007).

###  3.1 Analytic Predictions for 2I/Borisov

For 2I/Borisov, we adopt the measured production rate $Q({\rm CO})=1.07\times
10^{27}$ s-1 at $R=2.07$ au (Bodewits et al., 2020). We note that Equation B8
would predict $Q_{\rm gas}=5.9\times 10^{26}$ s-1 near perihelion, and
modifying the scaling relation to take into account a CO composition (i.e., an
$\mathcal{H}$ appropriate for CO ice) yields $Q_{\rm gas}=4.0\times 10^{27}$
s-1, which are both within an order-of-magnitude of the observed value.
Accounting for the reduced solar wind density at 2 au, we calculate $L_{\rm
X}=7.5\times 10^{11}$ erg s-1 (see Table 2). A 900 cm2 effective area
(characteristic of EPIC pn) at Earth would detect $6.3\times 10^{-5}$ counts
s-1, which would require a considerable 400 ks exposure for a $5\sigma$
detection. Indeed, most previous CX detections in comets have involved much
brighter X-ray luminosities $L_{\rm X}>10^{14}$ erg s-1 (Lisse et al., 1999,
2004).

Since there are observations of 2I/Borisov at multiple points along its
trajectory, we may perform a more detailed comparison between our model and
measurements of outgassing over time. We plot the observed time-evolution of
$Q({\rm H_{2}O})$ and $Q({\rm CO})$ in Figure 4 with our production rate model
(Equation B8). Our model, which was calibrated to observations of C/1996 B2
(Hyakutake), predicts water production rates within a factor a few of those
observed. The discrepancies may be due to composition inhomogeneities in the
nuclues and/or the sporadic nature of outgassing. On the other hand, our high
model values show that Borisov could not be made of pure CO, but is more in
line with the $\sim 10-20\%$ vs. water maximal abundances of CO found in solar
system comets (Bockelée-Morvan & Biver, 2017).

###  3.2 Analytic Predictions for 1I/‘Oumuamua

As a baseline estimate for 1I/‘Oumuamua, we assume a bulk composition of CO,
which is energetically compatible with the nongravitational acceleration and
revised Spitzer limits on the production rate given the low activity state
outbound at 2 au (Trilling et al., 2018; Seligman et al., 2021). Equation B8
with $\mathcal{H}$ corresponding to a CO composition suggests $Q_{\rm
gas}=2.8\times 10^{28}$ s-1 at perihelion (the leftmost marker in Figure 2),
and $Q_{\rm gas}=4.4\times 10^{26}$ s-1 at $2$ au, in agreement with the
Seligman et al. (2021) estimate, as expected.

With X-ray flux received at Earth depending strongly on the target’s distance
from the Sun, 1I/‘Oumuamua would have only become accessible to XMM-Newton at
its minimum observable heliocentric distance $R=0.943$ au. This geometry is
depicted in Figure 3. It would have been prudent to observe 1I/‘Oumuamua in
X-ray at this time, which roughly corresponded with 1I/‘Oumuamua’s closest
approach to Earth.

At $R=0.943$ au and $\Delta_{e}=0.276$ au, we estimate $Q_{\rm gas}=2.0\times
10^{27}$ s-1, $L_{\rm X}=1.2\times 10^{13}$ erg s-1, and a flux at Earth of
$F_{\rm X}=5.4\times 10^{-14}$ erg s-1 cm-2. Assuming an N2 (Desch & Jackson,
2021) or H2 (Seligman & Laughlin, 2020) composition yields even higher $F_{\rm
X}$, as reported in Table 2. For any of these three highly volatile
compositions, a signal would have been unambiguously detected in a $<1$ ks
X-ray follow-up exposure, producing a unique, easily obtained, positive
outgassing detection.

Figure 3: Trajectory and X-ray observability of 1I/‘Oumuamua, prior to its
discovery. Plotted lines connect the instantaneous positions of Earth and
1I/‘Oumuamua. Blue lines denote a solar elongation angle meeting X-ray
observing requirements, $\psi_{\odot}\geq\psi_{\odot}^{\rm min}$, where
$\psi_{\odot}^{\rm min}=70^{\circ}$ for XMM-Newton. The smallest heliocentric
distance allowed by this constraint is denoted $R^{*}=0.943$ au. At this time,
the distance between Earth and 1I/‘Oumuamua was $\Delta_{e}^{*}=0.276$ au.

Figure 4: Time-evolution of production rates for 2I/Borisov near perihelion
(for CO, H2O, and OH). Figure adapted from Seligman et al. (2022). References
for data are provided in their Table 2. The measurements demonstrate that CO
production was substantially greater than H2O production after perihelion —
the only time when both species were observed contemporaneously. Our
production rate model (Equation B8) is plotted as dashed lines, holding
2I/Borisov’s radius as a constant $a=0.3$ km, and adopting an appropriate
$\mathcal{H}$ for H2O and CO. We obtained 2I/Borisov’s heliocentric distance
with a rebound (Rein & Liu, 2012) simulation using the Mercurius integrator
(Rein et al., 2019). For reference, the trajectory of 2I/Borisov through the
Solar System is shown at right, with perihelion marked. The solid blue portion
corresponds to the timespan plotted in the left panel.

###  3.3 Observations of CX with Comets

Detections of CX from Solar System comets help gauge conditions under which we
may detect CX from ISOs. The detection of X-rays from C/1996 B2 (Hyakutake)
(Lisse et al., 1996) prompted Dennerl et al. (1997) to search archival ROSAT
data for other instances of CX with comet comae. Confirmed cases include:
C/1990 Kl (Levy), C/1990 Ni (Tsuchiya-Kiuchi), 45P (Honda-Mrkos-Pajduskova;
HMP), and C/1991 A2 (Arai). The faintest target was 45P, with $F_{\rm
X}=1.5\times 10^{-13}$ erg s-1 cm-2, which was detected at high confidence by
ROSAT with a 191 s exposure.

This comet sample serves as an independent diagnostic for selecting ISOs with
detectable CX emission. It is established that a correlation exists between
comet X-ray ($L_{\rm X}$) and optical ($L_{\rm opt}$) luminosities (e.g.,
Lisse et al., 1999, 2004). $L_{\rm X}$ plateaus for the brighest comets, but
follows linear trend for modest luminosities $L_{\rm X}<10^{15}$ erg s-1 where
$L_{\rm X}\sim 10^{-4}L_{\rm opt}$; however, there is dependence on the dust-
to-gas ratio [D/G] that induces $1-2$ dex of scatter. Using the trend
presented by Dennerl et al. (1997), we estimate 2I/Borisov’s X-ray luminosity
as $L_{\rm X}=6.1\times 10^{12}$ erg s-1 near perihelion, based on its
$V=16.6$. For 1I/‘Oumuamua, at close approach to Earth and $V=19.7$, we find
$L_{\rm X}=2.6\times 10^{9}$ erg s-1. (Note that this estimate likely
underestimates X-ray emission from 1I/‘Oumuamua, and serves only as a foil to
other estimates presented in this section.)

It is worth mentioning that dusty comae (e.g., C/Hale–Bopp 1995 O1 or
17P/Holmes, Lisse et al., 1997, 2013) may destroy solar wind ions without
concomitant CX X-ray production (Dennerl et al., 1997; Lisse et al., 2004).
This effect may prove an obstacle to X-ray observations of dusty ISOs.
However, the typical dust content of ISOs is unclear. Jewitt et al. (2017) and
Meech et al. (2017) placed stringent upper bounds on 1I/‘Oumuamua’s dust
production rate, at $2\times 10^{-4}$ kg s-1 and $1.7\times 10^{-3}$ kg s-1
respectively. Estimates of 2I/Borisov’s reach as high as 35 kg s-1 (Kim et
al., 2020).

Table 2: Estimated X-ray luminosity ($L_{\rm X}$) and flux ($F_{\rm X}$) of 2I/Borisov and 1I/‘Oumuamua using our model. For 1I/‘Oumuamua, quoted outgassing rates ($Q_{\rm gas}$) depend on the object’s assumed bulk composition, and heliocentric ($R$) and geocentric ($\Delta_{e}$) distances. 1I/‘Oumuamua’s pericenter was $R=r_{\rm peri}=0.25$ au; however, the solar elongation constraint for XMM-Newton was first satisfied at $R=0.943$ au. For 2I/Borisov, we quote values based on our CX emission model, but adopted the measured $Q$(CO) (Bodewits et al., 2020). For both objects we also estimate $L_{\rm X}$ from an empirically derived relationship with $L_{\rm opt}$. Object | Method |  $R$ (au) |  $Q_{\rm gas}$ (s-1) |  $L_{\rm X}$ (ergs s-1) |  $F_{\rm X}$ (ergs s-1 cm-2)
---|---|---|---|---|---
2I/Borisov | Measured $Q$(CO) and modeled CX emission. | $2$ | $1.07\times 10^{27}$ | $7.5\times 10^{11}$ | $6.2\times 10^{-17}$
2I/Borisov | Empirical relationship between $L_{\rm opt}$ and $L_{\rm X}$. | $2$ | - | $6.1\times 10^{12}$ | $6.0\times 10^{-16}$
1I/‘Oumuamua | Modeled $Q$(CO) and CX emission. | $0.943$ | $2.0\times 10^{27}$ | $1.2\times 10^{13}$ | $5.4\times 10^{-14}$
1I/‘Oumuamua | Modeled $Q$(CO) and CX emission at $r_{\rm peri}$. | $0.25$ | $2.8\times 10^{28}$ | $3.3\times 10^{16}$ | $7.7\times 10^{-12}$
1I/‘Oumuamua | Modeled $Q$(N2) and CX emission. | $0.943$ | $1.3\times 10^{28}$ | $4.7\times 10^{14}$ | $2.2\times 10^{-12}$
1I/‘Oumuamua | Modeled $Q$(H2) and CX emission. | $0.943$ | $1.5\times 10^{28}$ | $6.9\times 10^{14}$ | $3.2\times 10^{-12}$
1I/‘Oumuamua | Empirical relationship between $L_{\rm opt}$ and $L_{\rm X}$. | $0.943$ | - | $2.6\times 10^{9}$ | $3.6\times 10^{-17}$

##  4 Future ISO CX X-ray Expectations

For the prospects of detecting CX X-ray emission with a future ISO, it is
important to establish: (1) a set of criteria that provides high-odds of
detecting CX X-ray emission; and (2) an estimated fraction of ISOs discovered
that will exhibit a detectable X-ray flux. To accomplish these goals, we
conduct a Monte Carlo analysis assuming Rubin Observatory sky parameters (as
the largest and deepest continual all-sky survey of the next decade, e.g., Li
et al., 2022) which incorporates baseline predictions for the distribution of
perihelia and geocentric distances of ISO trajectories, as well as their size
distribution and possible compositions.

###  4.1 Trajectories

Our Monte Carlo analysis involves randomly drawing orbital configurations for
ISOs from previous population synthesis studies. We predict X-ray flux at the
minimum heliocentric distance that satisfies the solar elongation angle
constraint of XMM-Newton. This alignment occurs at time $t^{*}$, defined as:

$\displaystyle t^{*}\equiv\underset{t}{\operatorname{argmin}}$
$\displaystyle\|\mathbf{R}(t)\|$ (7) s.t.
$\displaystyle\cos^{-1}\left(-\frac{\left(\mathbf{R}(t)-\mathbf{R^{\prime}}(t)\right)\cdot\mathbf{R^{\prime}}(t)}{\|\mathbf{R}(t)-\mathbf{R^{\prime}}(t)\|\|\mathbf{R^{\prime}}(t)\|}\right)\geq\psi_{\odot}^{\rm
min}\,,$

where $\mathbf{R}$ and $\mathbf{R^{\prime}}$ are vectors representing the
positions of the ISO and Earth, respectively, with the Sun at the origin. The
ISO’s hyperbolic trajectory may be expressed in a Cartesian coordinate system
where $\mathbf{R}=\\{R_{1},R_{2},0\\}$:

$R_{2}=\pm\sqrt{e^{2}-1}\\\
\times\sqrt{(R_{1}+eq/(e-1))^{2}-(q/(e-1))^{2}}\,,$ (8)

with eccentricity $e>1$ and perihelion $r_{\rm peri}$ sampled from
distributions provided by Hoover et al. (2022). Their study coupled dynamical
simulations with the local stellar velocity dispersion to constrain the
population of 1I/‘Oumuamua-like ISOs that the Rubin Observatory will find.
They computed the probability density of perihelia, which indicates that
$10\%,25\%$, and $50\%$ of detected ISOs will attain $r_{\rm peri}\leq 0.35$,
$0.54$, and $0.83$ au, respectively. Under this distribution, it is clear that
2I/Borisov had an unlikely large perihelion at 2 au (and was anomalous with
respect to other orbital parameters, such as distance from the solar apex at
encounter, and eccentricity). By contrast, 1I/‘Oumuamua’s perihelion distance
of 0.25 au was unexpectedly small.

Next, we sample Earth’s position as a unit vector with azimuthal and polar
angles jointly distributed according to $p(\theta,\phi)=\sin{\phi}/4\pi$, and
scaled by 1 au. In reality, the orientation of the ISO’s trajectory with
respect to the ecliptic is determined by the inbound velocity vector and
impact parameter. Stellar kinematics are a good proxy for the galactic
distribution of ISOs; however, the typical ages of ISOs are poorly constrained
at a population level. We assume the above distribution of ($\theta$, $\phi$)
for our order-of-magnitude calculations. The distances
$R^{*}=\|\mathbf{R}(t^{*})\|$ and
$\Delta_{e}^{*}=\|\mathbf{R}(t^{*})-\mathbf{R^{\prime}}(t^{*})\|$ are solved
for numerically by fixing Earth’s position and assuming $\psi_{\odot}^{\rm
min}=70^{\circ}$. These distances are shown in Figure 3, with 1I/‘Oumuamua’s
trajectory as an example. In cases where the entirety of the ISO’s orbit lies
within the solar avoidance zone, the Monte Carlo X-ray flux is immediately set
to zero.

We neglect the hyperbolic velocity $v_{\infty}$ in our analysis since the vast
majority of ISOs accessible to the Rubin Observatory will have $v_{\infty}\leq
40$ km s-1. Larger velocities, however, would augment the solar wind ion
collision rate by a factor of $10\%$ or greater. It is prudent to conduct
X-ray observations of such ISOs during the inbound portion of their
trajectories.

###  4.2 Bulk Properties

The composition of a neutral medium does not strongly affect the X-ray power
density from CX in the optically thick regime. However, the coma’s density
profile depends on the neutral production rate, which in turn depends on the
volatility of surface material in the nucleus of an ISO. While Equation B8
estimates neutral production for bulk compositions similar to C/1996 B2
(Hyakutake)’s, it is straightforward to account for alternative materials. The
flux of molecules ejected from a unit surface area patch of the object (in
units of s-1 cm-2) is (e.g., Seligman et al., 2022),

$\mathcal{N}=\frac{(1-p)I(t)-\epsilon\sigma T_{\rm Sub}^{4}}{\Delta
H/\mathcal{N}_{A}+\gamma k_{B}\textit{T}_{\rm Sub}}.$ (9)

In the above, $p$ is the albedo, $I(t)$ is the time-dependent, solar
irradiance, and $\epsilon$ is the surface emissivity. Besides $I(t)$ and
physical constants, each parameter in the above equation is material-
dependent. In practice, grey-body emission from the minor body is negligible
and the incident radiation term dominates. Using the definition in Equation
B9, exchanging $I(t)$ for the incident solar flux, and integrating Equation 9
over the illuminated surface area ($\Sigma_{I}$) yields,

$Q_{\rm gas}=(1-p)\iint_{S}\,\bigg{(}\,\frac{L_{\odot}}{4\pi
R^{2}\mathcal{H}}\,\bigg{)}\,d\Sigma_{I}\,.$ (10)

Albedo is unconstrained but is likely of order $p\sim 0.1$ for most minor
bodies in the Solar System. The average projected surface area over all
viewing angles is $1/4$ times the total surface area for any convex object
(Meltzer, 1949), so $\Sigma_{I}\simeq\Sigma/4$, where $\Sigma$ is the total
surface area of the object. For a sphere, $\Sigma_{I}=\pi a^{2}$, where $a$ is
the radius as defined earlier in this paper. Therefore, Equation 10 has the
same functional form as Equation B8.

Hoover et al. (2022) noted that the size distribution of ISOs could enhance
the Rubin Observatory’s yield and estimated detection rates for a range of
absolute magnitudes (see their Table 2). Many minor body populations adhere to
a power-law size distribution

$n(>a)=ka^{-\beta},$ (11)

for some powerlaw index $\beta$ and normalization constant $k$. Do et al.
(2018) note that $\beta>3$ for ISOs, or else the mass would diverge at large
radii. In a collisionally evolved system $\beta=2.5$ (Dohnanyi, 1969).
However, Solar System comets have a more complex collisional history, with a
powerlaw index that depends on the size regime. For example, $\beta=1.45$ in
the $1-10$ km range, and $\beta=1.91$ in the $2-5$ km subset (Meech et al.,
2004). For main-belt asteroids, $\beta=1.0-1.4$ for sub-km diameters
(depending on location within the belt), and $\beta=1.8$ for larger objects
(Yoshida et al., 2003). The distribution for ISOs may be shallow in the case
that they are ejected from their respective systems before attaining
collisional equilibrium. Also, the bulk of ISOs may be well-described by a
single value of $\beta$, but the frequency will necessarily drop off for the
largest and smallest objects due to physical limitations. We incorporate the
uncertainty surrounding $\beta$ into our analysis by drawing it randomly from
a uniform distribution: $\beta\sim\mathcal{U}(1.0,2.0)$. As more ISOs are
detected, it will be important to reconsider their size distribution.

###  4.3 X-ray Flux

We further restrict the number of free parameters by assuming the Rubin
Observatory will detect $1.5$ ISOs per year, the average of the optimistic and
conservative rates presented by Hoover et al. (2022). The remaining free
parameters are $a$, $R$, and composition. We randomly draw a nuclear radius
$a$ by first drawing a value for $\beta$, and subsequently sampling Equation
11. We truncate the distribution at $a_{\rm min}=25$ m and $a_{\rm max}=10$
km, which prohibits ISOs larger than most Solar System comets and also
guarantees they are large enough to realistically be detected by the Rubin
Observatory (an object with $1/4$ the radius of 1I/‘Oumuamua and with the same
albedo will have $V=24$ at the same $q=0.25$ au). The new cumulative
probability distribution is:

$n(>a)=\frac{(a^{-\beta}-a_{\rm max}^{-\beta})}{(a_{\rm min}^{-\beta}-a_{\rm
max}^{-\beta})}.$ (12)

The minimum allowed heliocentric distance $R=R^{*}$ is determined per Equation
7, and the neutral production is calculated using Equation B8 for four
representative pure compositions: H2, N2, CO, and H2O. We make an important
modification, however, by drawing the heliocentric distance scaling exponent
from a random uniform distribution $x\sim\mathcal{U}({-4.33,-1.82})$ as
opposed to a fixed $x=-2$, per Combi et al. (2019). The CX flux is then
calculated using Equation B3 and an optically thick cross-section given by
Equation B6 and correction factor $\kappa$.

Figure 5 summarizes our results, and demonstrates the viability of using
X-rays as a diagnostic probe of ISOs across different compositional
assumptions. As discussed earlier, composition has a profound effect on the
extent of the outgassed coma and the expected X-ray flux. In the most
conservative scenario that ISOs are predominantly composed of water ice, then
about 3% found by the Rubin Observatory will exhibit $F_{\rm X}\gtrsim
2.7\times 10^{-15}$ erg s-1 cm-2, which can be robustly detected by a 10 ks
exposure (i.e., $\tau_{5\sigma}=10$ ks corresponds to a 5$\sigma$ detection;
about 6% are accessible with a $\tau_{5\sigma}=100$ ks exposure). Another
$90\%$ of H2O-dominated ISOs will exhibit undetectable levels of CX emission
(i.e., $\tau_{5\sigma}>$1000 ks). If CO is the dominant constituent of ISOs,
then about $10\%$ will emit X-rays detectable with a 10 ks exposure. The
detectability fraction is even higher for the most volatile compositions,
reaching $31\%$ for N2 ice and $34\%$ for H2 ice. With a longer 100 ksec
exposure, these fractions reach 19%, 47%, and 50% for CO, N2, and H2,
respectively.

These statistics suggest that the Rubin Observatory will discover new ISOs
amenable to X-ray spectroscopic characterization. If the survey finds 15
2I/Borisov analogues (i.e., CO-dominated interstellar comets) over a ten-year
campaign, then approximately $1-2$ of them will be accessible with a 10 ks
EPIC pn exposure. The Rubin Observatory will probably detect one such ISO in
its first five years of operation. The approach is similarly effective for
1I/‘Oumuamua analogues. X-ray emission should be detectable for about one
third of N2-dominated and H2-dominated ISOs. On the other hand, consistent
non-detections of CX emission will point to an alternative, refractory
composition. For objects that exhibit nongravitational acceleration, lack of
X-rays may also indicate an alternative mechanism that provides the required
force (e.g., radiation pressure).

Figure 5: Cumulative distribution function of X-ray flux ($F_{\rm X}$) for
ISOs detected by the Rubin Observatory. Equivalently, the fraction of ISOs
detected by the Rubin Observatory that will exhibit a given X-ray flux or
less. Four distributions are depicted, each corresponding to an ISO population
comprised of a different pure volatile: H2O (blue), CO (red), N2 (green), or
H2 (orange). On the top x-axis, $F_{\rm X}$ is converted into an exposure
duration ($\tau_{5\sigma}$) that would yield a 5$\sigma$ detection with XMM-
Newton EPIC pn. The vertical blue line delineates $F_{\rm X}\simeq 2.7\times
10^{-15}$ erg s-1 cm-2; a signal which would be detected at 5$\sigma$
confidence with at 10 ks exposure. For example, about 10% of CO-dominated ISOs
detected by the Rubin Observatory will exhibit this X-ray flux or greater.

##  5 Conclusions

In this paper, we propose X-ray spectroscopy as a means of detecting outgassed
comae and revealing highly volatile compositions of interstellar objects, a
new class of astrophysical phenomena. The neutral gas comae of ISOs should
undergo charge exchange with solar wind ions in the same manner as has been
widely observed with Solar System comets. We suggest a tiered list of
scientific goals that are realistically achievable by existing and concept
X-ray missions, sorted by feasibility:

  1. 1.

Photometric detection of CX (i.e., at $\geq 5\sigma$ significance) in order to
detect an outgassed coma. Modest exposure times of order 10 ks may reveal a
statistically significant X-ray flux originating from an interstellar object,
particularly when observed at heliocentric distances $R\lesssim 1$ au. The
viable parameter space is depicted in Figure 6 for pn onboard XMM-Newton.
Confidently detecting X-ray emission over a bandpass of $0.5-0.7$ keV would
immediately reveal the existence of a coma undergoing CX with solar wind ions.
X-ray observations of 1I/‘Oumuamua near its close approach to Earth would have
either confirmed the presence of a coma, or placed an upper bound on the
production rate to a point that another mechanism would be necessary to
explain the anomalous acceleration.

  2. 2.

Joint constraints on $a$ and $Q_{\rm gas}$ in order to infer an ISO’s volatile
content. Once an ISO’s ephemeris is determined, the X-ray flux is degenerate
with $a$ and $\mathcal{H}$. By assuming a range of plausible albedos, one can
constrain $a$ from an optical light curve (e.g., Mashchenko, 2019). The radius
is also constrained by the energetics of nongravitational acceleration. For
example, Seligman & Laughlin (2020) suggested various ices (H2, Ne, N2, Ar,
O2, Kr, Xe, CO2, H2O) that could be compatible with 1I/‘Oumuamua’s outbound
acceleration. For a subset of these species (N2, H2, CO, Ne, plus CH4),
Jackson & Desch (2021) showed the relationship between nongravitational
acceleration, albedo, and mean spherical radius. Across these different
species, the allowable range for $a$ lies between $20-25$ m for albedo
$p>0.6$. However, their respective sublimation energies ($\mathcal{H}$) vary
by a factor of $10$, which, according to our model, implies $\mathcal{A}$
varies by a factor of $100$. This interaction area is probed by the X-ray flux
from CX. If the nuclear radius of an ISO can be constrained within a factor of
order unity, then an anomalously high $F_{\rm X}$ would immediately reveal an
exotic, highly-volatile composition due to the inverse proportionality between
$Q_{\rm gas}$ and $\mathcal{H}$. We reiterate that a non-detection in X-ray
would favor low-volatility ices (e.g., H2O, CO2) or an alternative
acceleration mechanism.

  3. 3.

Measuring line strength ratios towards robustly determining the coma
composition. Mullen et al. (2017) demonstrated that relative CX emission line
strengths (including strong transitions from Cv, Cvi, and Ovii) depend on the
neutral target medium. Specifically, N2, H2O, O, OH, CO, and CO2 targets were
considered in their study. A high-fidelity X-ray spectrum may be achievable by
existing facilities for the brightest ISOs. However, this method is most
amenable to next-generation X-ray telescopes which feature both large
effective areas and high-spectral resolution. A detailed study of this
approach, and its feasibility with X-ray concept missions, would be
scientifically useful.

Baseline estimates of the Rubin Observatory’s yield suggest around 15 new ISOs
over a ten-year campaign. If these objects are predominantly composed of CO,
about one or two will exhibit detectable levels of X-ray flux. In the case
that most ISOs are comprised of H2 ice, CX will be observable for about five
of them. Efforts to understand this mysterious population benefit from
broadband spectroscopy — infrared, optical, and UV observations provide
complementary insights into physical and chemical properties of the nucleus
and coma. As X-ray observations of CX with comets have been an active area of
study, similar efforts directed toward ISOs will at the very least reaffirm
findings made at other wavelengths, and potentially discern the true
compositions of these minor bodies.

## Acknowledgments

We thank the referees of this manuscript for their constructive comments,
which significantly improved the presentation of the paper. We extend
particular thanks to Carey Lisse for a number of detailed and insightful
recommendations which led to a much stronger final version. We also thank Greg
Laughlin for his review of the manuscript and for constructive discussions.
D.Z.S. acknowledges financial support from the National Science Foundation
Grant No. AST-2107796, NASA Grant No. 80NSSC19K0444 and NASA Contract
NNX17AL71A from the NASA Goddard Spaceflight Center. D.Z.S. is supported by an
NSF Astronomy and Astrophysics Postdoctoral Fellowship under award
AST-2202135. This research award is partially funded by a generous gift of
Charles Simonyi to the NSF Division of Astronomical Sciences. The award is
made in recognition of significant contributions to Rubin Observatory’s Legacy
Survey of Space and Time.

##  Appendix A Review of Solar Wind Charge Exchange

Since the discovery of strong X-ray emission from a cool cometary source,
C/Hyakutake 1996B2, in 1996 by Lisse et al., solar wind charge exchange has
gained considerable traction for its ability to explain X-ray emission from
objects within the Solar System. CX models have successfully explained
observed X-rays from the volatile comae of Solar System comets (Cravens, 1997;
Wegmann et al., 1998), as well as emission originating from Earth (Wargelin et
al., 2004; Fujimoto et al., 2007), Mars (Kallio et al., 1997; Dennerl, 2002),
Venus (Dennerl et al., 2002), and Jupiter (Metzger et al., 1983; Cravens et
al., 2003).

In order to produce X-ray emission, heavy ions from the solar wind interact
with cool atomic and molecular gas surrounding the object. This process also
produces a source of X-ray emission from star-forming galaxies such as M82
(e.g., Liu et al., 2012; Zhang et al., 2014). In such a galaxy, CX occurs at
the interface between hot and cool interstellar gases, likely responsible for
the enhanced forbidden transitions of K$\alpha$ triplet emissions from He-like
ions and high-order transitions in Lyman series of H-like ions (Zhang et al.,
2014). There has also been tentative detection of charge exchange in galaxy
clusters (Gu et al., 2018).

The general CX reaction is

${\rm A^{q+}+N\xrightarrow[]{}(A^{*})^{(q-1)+}+N^{+}},$ (A1)

where the ion ${\rm A^{q+}}$ gains an electron from the neutral species ${\rm
N}$ (atomic or molecular, often H, H2 and He). The integer ${\rm q}$ denotes
the initial ionization state of the species A. The electron is in an excited
state, denoted by the superscript $*$. As it cascades to the ground state, the
electron emits X-ray and UV photons. Implicit in this equation are initial and
final state quantum numbers ($n$, $l$, and $m$) of the transferred electron.
The most probable final-state principal quantum number $n$ is given by
Equation 2.6 of Janev & Winter (1985), which is an approximation that is
generally applied while modeling this process (Smith et al., 2012).

The CX interaction cross-section ($\sigma_{\rm sq}$) for a given species
(denoted by subscript s) and charge (denoted by subscript q) was modeled by
Wegmann et al. (1998), and is given by,

$\sigma_{\rm sq}=\,\bigg{(}\,\frac{{\rm q}-1}{{\rm q}^{2}/2n^{2}-|I_{{\rm
p,s}}/27.2\,{\rm eV}|}\,\bigg{)}^{2}\,\times 0.88\times 10^{-16}\;({\rm
cm^{2}}).$ (A2)

The variables ${\rm q}$ and $I_{{\rm p,s}}$ in Equation A2 correspond to the
dimensionless integer charge of the ion and ionization potential (measured in
eV) of the target species, respectively.

For comets, the solar wind typically interacts with volatile coma particles.
Some of the most common target species outgassed by Solar System comets are
water and its constituents (O, OH, H) (Cochran et al., 2015; Biver & Bockelée-
Morvan, 2016; Bockelée-Morvan & Biver, 2017). All of these species have
similar ionization energies $\sim 13$ eV (Wegmann et al., 1998). CX cross-
sections are $\sim 10^{-15}$ to $10^{-14}$ ${\rm cm^{2}}$ for heavy solar wind
ions such as Oviii, Ovii, Cvii, Cvi, Nvii, Neix, Six, and Fexii. That is,
charge exchange occurs when these ions come within $\sim 1$ nm of the neutral
targets. The energy difference between the captured electron’s initial
(excited) state and ground state ($E_{\rm excit}$) can reach several hundred
eV. Therefore, these transitions provide significant contributions to EUV and
X-ray radiation. CX emission from cometary comae has rich observational and
theoretical backing, as reviewed by Bodewits et al. (2012) and Dennerl et al.
(2012).

Our main concern is charge exchange between the solar wind and the outgassed
species within an ISO’s coma. Assuming that a given solar wind ion undergoes
charge exchange once during its passage through the neutral medium, the X-ray
power density $P_{\rm sj}$ for transition (j) at a given position
${\mathbf{r}}$ is:

$P_{\rm sj}({\mathbf{r}})=\Phi_{\rm sq}({\mathbf{r}})\,\sigma_{\rm sq}\,b_{\rm
sqj}\,n_{\rm n}({\mathbf{r}})\,\Delta E_{\rm sqj}\,,$ (A3)

(Cravens, 1997, 2000; Cravens et al., 2009) which has units of eV cm-3 s-1.
Here $\Phi_{\rm sq}$ denotes the solar wind flux of a given ion, $\sigma_{\rm
sq}$ is the CX cross-section (Equation A2), $b_{\rm sqj}$ is the spectral
cascading probability for transition (j) which releases a photon of energy
$\Delta E_{\rm sqj}$, and $n_{\rm n}$ is the number density of neutral
species. The solar wind flux may be written as $\Phi_{\rm sq}=f_{\rm sq}n_{\rm
SW}u_{\rm SW}$, where $n_{\rm SW}$ and $u_{\rm SW}$ correspond to solar wind
proton number density and velocity, respectively. The solar wind fraction of a
given species/charge is $f_{\rm sq}$. These quantities are functions of
position in space. For example, the unshocked solar wind has a typical speed
of $\sim 400$ km s-1 and density of $\sim 0.4$ cm-3 at 5 au (Cravens et al.,
2003). The density $n_{\rm SW}$ falls off as the square of distance from the
host star (Cravens, 2000). While the solar wind flux varies over time, the
fraction of heavy ions to protons in the solar wind remains fairly consistent
at $f\approx 10^{-3}$. Intensity is obtained by integrating Equation A3 over a
given path length (i.e., performing a line integral).

##  Appendix B Charge Exchange with Outgassed Comae

Our prescription for CX emission is calibrated to observations of C/1996 B2
(Hyakutake) and early models that described its X-ray luminosity. Wegmann et
al. (1998) calculated the total X-ray emissivity by summing over all solar
wind ions in Equation A3. They adopted parameter values of $\sigma_{\rm
sq}=3\times 10^{-15}$ cm2, $f_{\rm O}=0.0005$, and $1100$ eV emitted per
oxygen ion in the solar wind based on summing the CX excited state energies of
all ions and weighting them according to their relative abundance fraction.
Further, they assumed an ‘effectivity’ of $0.4$ which replaces the $b_{\rm
sqj}$ terms. The power density is approximately

$P_{\rm X}({\mathbf{r}^{\prime}})=4\times 10^{-20}n_{\rm SW}n_{\rm
n}({\mathbf{r}^{\prime}}){\rm\,erg\,cm^{3}\,s^{-1}}\,,$ (B1)

where the density of neutrals at distance $\mathbf{r^{\prime}}$ from the
comet’s nucleus follows

$n_{\rm n}(\mathbf{r^{\prime}})=\,\bigg{(}\,\frac{Q_{\rm gas}}{4\pi
v\mathbf{|r^{\prime}|}^{2}}\,\bigg{)}\,e^{-{|\mathbf{r^{\prime}}|}/{\lambda}}\,,$
(B2)

for a total neutral production rate $Q_{\rm gas}$, outflow velocity $v$, and
photodestruction length scale $\lambda$. Wegmann et al. (1998) adopted $Q_{\rm
gas}=1.5\times 10^{29}$ s-1 and $n_{\rm SW}=7$ cm-3. By neglecting
photodestruction, which Cravens (1997) deemed negligible within $5\times
10^{5}$ km, and adopting a nominal $v=1$ km s-1, integration over a sphere of
beam radius $135,000$ km yields $L_{\rm X}\sim 6\times 10^{15}$ erg s-1,
comparable to the measured luminosity and other estimates in the literature.
As follows, we determine expectations for CX emission from the comae of other
minor bodies.

###  B.1 Luminosity from the Optically Thick Coma

CX produces a surface luminosity, $4\pi I$ (Cravens et al., 2003), given by
the equation,

$4\pi I=n_{\rm SW}\,u_{\rm SW}f\,N\,\Delta E\,.$ (B3)

Each ion contributes, on average, $N$ photons of typical energy $\Delta E$,
and the solar wind minor ion fraction is given by $f$. The total luminosity is
obtained by integrating Equation B3 over the effective surface area. Our
baseline model assumes that this area is the region where the coma is
optically thick to CX. That is, it satisfies the criterion:

$\int_{S}\,(\,\sigma_{\rm sq}n_{\rm n}({\mathbf{r}^{\prime}})\,)\,ds>1$ (B4)

for a linear projected path $S$ of the solar wind through the coma, where
${\mathbf{r}^{\prime}}$ is the distance from the cometary nucleus as in
Equation B2. As long as the coma neutral column is large enough that the solar
wind is fully depleted of all highly stripped minor ions, the individual
transition probabilities are not important. For simplicity, we also fix the
cross-section at $\sigma_{\rm sq}=3\times 10^{-15}$ cm2. This value is
consistent with expectations from the ionization potentials of H2
($I_{p,s}\approx 15.4$ eV) and N2 ($I_{p,s}\approx 15.6$ eV). Considering
these compositions and those more typical of comets, we find $2\times
10^{-15}$ cm2 $\leq\sigma_{\rm sq}\leq 13\times 10^{-15}$ cm2 for ion charges
$+5\leq q\leq+7$. We assume that the coma is approximately spherical and
follows a neutral density profile given by Equation B2. We define the impact
parameter, $b$, as the minimum distance between the path $S$ and the nucleus.
Also, let $R$ be the distance between the Sun and the nucleus, and assume that
$R\gg b$. We parameterize the path $S$ as a function of $\mathbf{r^{\prime}}$.
We define the dimensionless parameter $x\equiv|\mathbf{r^{\prime}}|/b$ and a
coefficient $K\equiv\sigma_{\rm sq}Q_{\rm gas}/4\pi w$. By substituting
Equation B2 into Equation B4 with these new parameters, the optically thick
transition occurs where

$\frac{2K}{b}\int_{1}^{\infty}\frac{1}{x\sqrt{x^{2}-1}}e^{-bx/\lambda}dx=1\,,$
(B5)

or, equivalently, where

$\frac{2K}{b}\int_{0}^{\pi/2}e^{-b\,{\rm sec}{\theta}/\lambda}d\theta=1\,.$
(B6)

Equation B6 is equivalent to a function $b=b(\sigma_{\rm sq},w,\lambda,Q_{\rm
gas})$ which may be evaluated numerically. It returns a distance within which
the coma is optically thick to CX. For physically plausible photodestruction
scales of $\lambda=10^{8}-10^{11}$ cm (Combi et al., 2004), a reasonable
approximation is that $b\propto Q_{\rm gas}$ in the regime $Q_{\rm
gas}<10^{28}$ s-1. Figure 6 shows the validity of this approximation for
different assumed $\lambda$. As $\lambda\rightarrow\infty$, the function
approaches a linear relationship.

Figure 6: Relationship between outgassing rate $Q_{\rm gas}$ and radius $b$
within which a coma is optically thick to CX. Since $b$ lacks a closed form
(Equation B6), it is solved for numerically. The function is plotted for
several assumptions of the ionization scale $\lambda$. In all cases $v=1$ km
s-1. Our main analysis assumes $\lambda=5\times 10^{10}$ cm (red line). As
$\lambda$ increases, the function approaches a linear relationship between
$Q_{\rm gas}$ and $b$ (black dashed line).

Taking C/1996 B2 (Hyakutake) as a nominal example (hence the above assumed
$\lambda$ and $Q_{\rm gas}$ values), then we find $b\approx 10,000$ km which
is in reasonable agreement with the 30,000 km penetration depth estimated by
Wegmann et al. (1998). In order to estimate total X-ray luminosity, we assume
$n_{\rm SW}=7$ cm-3 at 1 au, $u_{\rm SW}=400$ km s-1, $f=0.001$, $N=1$, and
$\Delta E=550$ eV. The above equations predict $L_{\rm X}=8.2\times 10^{14}$
erg s-1 from the optically thick region alone. This estimate is about
$5\times$ less than the total luminosity measured by ROSAT. Using a refined
hydrodynamical model, Wegmann et al. (2004) also estimated $L_{\rm X}$ for
C/1996 B2 (Hyakutake) during its close approach to Earth. Their measurements
were centered around $10^{16}$ erg s-1, which is higher than the initial
estimate from Lisse et al. (1996). The discrepancy between these literature
estimates and our own is probably due to significant emission that took place
in optically thin regions of the coma, currently unaccounted for in our model
for the optically thick zone. Therefore, it is useful to calibrate our model
and correct for this component per the following.

###  B.2 Extensions to the Analytic Model

Holding other parameters constant, $b$ scales linearly with $Q_{\rm gas}$ in
the regime $Q_{\rm gas}<10^{30}$ s-1 for $\lambda\sim 5\times 10^{10}$ cm. The
CX interaction area in this regime can be approximated by $\pi
b^{2}\approx\Gamma Q_{\rm gas}^{2}$, with $\Gamma=1.5\times 10^{-40}$ s2 cm2.
A similar conclusion was reached by Wegmann et al. (2004), who developed a
hydrodynamical model of X-ray emission morphology and applied it to
observations of comets. They derived a relationship $L_{\rm X}=CHQ_{\rm
gas}^{2}$ where $H=u_{\rm SW}n_{\rm SW}fN\Delta E$ is the heavy ion solar wind
flux. By fitting their estimates of $HQ_{\rm gas}^{2}$ to observed X-ray
luminosities of comets, they determined a constant of proportionality
$C=10^{-38}$ s2 cm2. Let $\mathcal{A}$ define an effective, optically thick
surface area that would yield a given $L_{\rm X}$. Then the relationship found
by Wegmann et al. (2004) is equivalent to $\mathcal{A}=CQ_{\rm gas}^{2}$. We
adopt a correction factor $\kappa\equiv\sqrt{C/\Gamma}\approx 8.1$ that
defines a new effective radius,

$\tilde{b}\equiv\kappa b$ (B7)

In other words, $\kappa$ is a factor that increases the radius of the CX
interaction area from $b$ to $\tilde{b}$, thereby approximately accounting for
emission from regions beyond the optically thick zone. Prior observations of
CX within cometary comae (e.g. Lisse et al., 1999, 2004) have produced
detections of significant X-ray emission extending as little as $\sim 5\times
10^{4}$ km (for 2P/Encke 2003), and as far as an apparent limit at $\sim
10^{6}$ km (for C/1996 B2 (Hyakutake), C/1991 K1 (Levy), and C/1995 O1 (Hale-
Bopp)).

We adopt $Q_{\rm gas}\propto a^{2}R^{-2}$, where $a$ is body’s radius, and $R$
is the instantaneous heliocentric distance. The $R^{-2}$ dependency is the
same as that of the incident solar radiation. While physically motivated, this
scaling simplifies true cometary activity. Following a long-baseline survey of
water outgassed by 61 comets, Combi et al. (2019) found generally steeper
scaling: $Q({\rm H_{2}O})\propto R^{x}$, with $-4.33\leq x\leq-1.82$ depending
on taxonomic class. This finding is incorporated into our expectations for
future ISO observations in §4.

Our model must also account for the fact that more volatile species will
sublimate and outgas at higher rates (potential compositions are discussed
further in §4). We use the following scaling relation,

$Q_{\rm gas}=1.5\times 10^{29}\times\Big{(}\frac{a}{2.4\,{\rm
km}}\Big{)}^{2}\Big{(}\frac{R}{1\,{\rm\,au}}\Big{)}^{-2}\Big{(}\frac{\mathcal{H}}{9.3\times
10^{-23}\,{\rm kJ}}\Big{)}^{-1}{\rm s}^{-1}\,,$ (B8)

which is calibrated to the nuclear radius of C/1996 B2 (Hyakutake) (Lisse et
al., 1999), and the production rate adopted by Wegmann et al. (1998).
Production rates for OH were measured by Schleicher (1996), and varied from
$\log_{10}Q({\rm OH})=28.89$ (at $R=0.94$ au) to $\log_{10}Q({\rm OH})=29.17$
(at $R=1.08$ au). In the above, $\mathcal{H}$ is the total energy input for
each coma particle,

$\mathcal{H}\equiv\Delta H/\mathcal{N}_{A}+\gamma k\textit{T}_{\rm Sub}\,.$
(B9)

The above expression involves enthalpy of sublimation $(\Delta H)$,
temperature of sublimation ($T_{\rm Sub}$), and adiabatic index of the
escaping vapor ($\gamma$), all of which are material dependent (Table 1). The
quantity $\mathcal{H}$ is the sum of two components: the energy required to
sublimate an ice molecule (the first term) and the energy required to heat the
molecule to the outflow velocity (the second term). In the case of water,
$\mathcal{H_{\rm H_{2}O}}=9.3\times 10^{-23}$ kJ (values for other species are
listed in Table 1). Chemical properties also determine the outgassing velocity
$v$:

$v\simeq c_{s}=\sqrt{\gamma k\textit{T}_{\rm Sub}/\mu m_{H}}\,,$ (B10)

for mean molecular weight $\mu$ and sound speed $c_{s}$. For typical values
$v=0.3-1$ km s-1, $Q<10^{30}$ s-1, photodestruction timescales $t_{\rm
photo}<10^{7}$ s, and $\lambda=wt_{\rm photo}$, the optically thick radius
does not exceed $10^{6}$ km under our model. It is limited by the exponential
decay term in Equation B2. We reiterate that only monotomic and homonuclear
diatomic species (having zero diplole moment) will be more amenable to CX
X-ray characterization than to infrared fluorescence spectroscopy.

The normalization in Equation B8 is to C/1996 B2 (Hyakutake), and the
expression should be considered an order-of-magnitude estimate of $Q_{\rm
gas}$ for other objects. Ideally, one may use independent estimates of $Q_{\rm
gas}$ obtained either from infrared spectroscopy or a more detailed
theoretical model that accounts for the target’s composition. For most Solar
System comets, $Q_{\rm gas}\simeq Q({\rm H_{2}O})+Q({\rm CO_{2}})+Q({\rm
CO})$, which is the sum of production rates of the most common volatile
components in comets (Bockelée-Morvan & Biver, 2017). Nevertheless, Equation
B8 enables baseline predictions for new minor bodies, and is especially useful
for population-level predictions when given distributions for $a$ and
perihelion $r_{\rm peri}$. Additionally, we assume that the solar wind proton
number density is given by,

$n_{\rm SW}(R)=7\,{\rm cm}^{-3}\,\Big{(}\frac{R}{1{\rm\,au}}\Big{)}^{-2},$
(B11)

which is maximized at perihelion when $R=r_{\rm peri}$. Note, flares can
enhance the solar wind ion flux, thus improving the feasibility of CX X-ray
observations at larger $R$. For example, a flare nearly doubled the soft X-ray
count rate from C/1999 S4 (LINEAR) (Lisse et al., 2001).

Combining Equations B3 & B7, we arrive at a general model for X-ray luminosity

$L_{\rm X}=\pi\tilde{b}^{2}n_{\rm SW}u_{\rm SW}fN\Delta E,$ (B12)

which is a function of $\\{\sigma_{\rm sq},\lambda,a,r_{\rm peri},\mu,\Delta
H,\gamma,T_{\rm Sub}\\}$, assuming observations take place at perihelion.
Also, a nominal $\lambda=5\times 10^{10}$ cm is adopted for our analysis. We
use this model to predict the luminosity of CX emission with ISOs in §4, and a
schematic of the entire CX process with ISOs is shown in Figure 1. It is worth
explicitly highlighting our model’s dependence on perihelion distance. We
demonstrated an approximately linear relationship between $b$ and $Q_{\rm
gas}$, where $Q_{\rm gas}\propto r_{\rm peri}^{-2}$ through its dependence on
the solar radiation flux $F_{\odot}\propto r_{\rm peri}^{-2}$. The CX surface
area follows $\mathcal{A}\propto b^{2}$, and the incident heavy ion flux
follows $n_{\rm SW}\propto r_{\rm peri}^{-2}$. Therefore, $L_{\rm X}\propto
r_{\rm peri}^{-6}$: the perihelion of an ISO strongly dictates whether its CX
X-ray emission is detectable (similar scaling relationships were explored by
Lisse et al., 1999).

## References

  * Aravind et al. (2021) Aravind, K., Ganesh, S., Venkataramani, K., et al. 2021, MNRAS, 502, 3491, doi: 10.1093/mnras/stab084
  * Bailer-Jones et al. (2018) Bailer-Jones, C. A. L., Farnocchia, D., Meech, K. J., et al. 2018, AJ, 156, 205, doi: 10.3847/1538-3881/aae3eb
  * Bannister et al. (2020) Bannister, M. T., Opitom, C., Fitzsimmons, A., et al. 2020, arXiv e-prints, arXiv:2001.11605.  https://arxiv.org/abs/2001.11605
  * Batygin & Laughlin (2008) Batygin, K., & Laughlin, G. 2008, ApJ, 683, 1207, doi: 10.1086/589232
  * Beiersdorfer et al. (2001) Beiersdorfer, P., Lisse, C. M., Olson, R. E., Brown, G. V., & Chen, H. 2001, ApJ, 549, L147, doi: 10.1086/319143
  * Bialy & Loeb (2018) Bialy, S., & Loeb, A. 2018, ApJ, 868, L1
  * Bieler et al. (2015) Bieler, A., Altwegg, K., Balsiger, H., et al. 2015, Nature, 526, 678, doi: 10.1038/nature15707
  * Biver & Bockelée-Morvan (2016) Biver, N., & Bockelée-Morvan, D. 2016, IAU Focus Meeting, 29A, 228, doi: 10.1017/S1743921316002945
  * Biver et al. (2022) Biver, N., Dello Russo, N., Opitom, C., & Rubin, M. 2022, arXiv e-prints, arXiv:2207.04800.  https://arxiv.org/abs/2207.04800
  * Bockelée-Morvan & Biver (2017) Bockelée-Morvan, D., & Biver, N. 2017, Philosophical Transactions of the Royal Society of London Series A, 375, 20160252, doi: 10.1098/rsta.2016.0252
  * Bockelée-Morvan et al. (2004) Bockelée-Morvan, D., Crovisier, J., Mumma, M. J., & Weaver, H. A. 2004, in Comets II, ed. M. C. Festou, H. U. Keller, & H. A. Weaver, 391
  * Bodewits et al. (2007) Bodewits, D., Christian, D. J., Torney, M., et al. 2007, A&A, 469, 1183, doi: 10.1051/0004-6361:20077410
  * Bodewits et al. (2012) Bodewits, D., Christian, D. J., Carter, J. A., et al. 2012, Astronomische Nachrichten, 333, 335, doi: 10.1002/asna.201211659
  * Bodewits et al. (2020) Bodewits, D., Noonan, J. W., Feldman, P. D., et al. 2020, Nature Astronomy, 4, 867, doi: 10.1038/s41550-020-1095-2
  * Bolin et al. (2018) Bolin, B. T., Weaver, H. A., Fernandez, Y. R., et al. 2018, ApJ, 852, L2, doi: 10.3847/2041-8213/aaa0c9
  * Bolin et al. (2020) Bolin, B. T., Lisse, C. M., Kasliwal, M. M., et al. 2020, AJ, 160, 26, doi: 10.3847/1538-3881/ab9305
  * Cochran et al. (2015) Cochran, A. L., Levasseur-Regourd, A.-C., Cordiner, M., et al. 2015, Space Sci. Rev., 197, 9, doi: 10.1007/s11214-015-0183-6
  * Combi et al. (2004) Combi, M. R., Harris, W. M., & Smyth, W. H. 2004, in Comets II, ed. M. C. Festou, H. U. Keller, & H. A. Weaver, 523
  * Combi et al. (2019) Combi, M. R., Mäkinen, T. T., Bertaux, J. L., Quémerais, E., & Ferron, S. 2019, Icarus, 317, 610, doi: 10.1016/j.icarus.2018.08.031
  * Cook et al. (2016) Cook, N. V., Ragozzine, D., Granvik, M., & Stephens, D. C. 2016, ApJ, 825, 51, doi: 10.3847/0004-637X/825/1/51
  * Cordiner et al. (2020) Cordiner, M. A., Milam, S. N., Biver, N., et al. 2020, Nature Astronomy, 4, 861, doi: 10.1038/s41550-020-1087-2
  * Cravens (2000) Cravens, T. 2000, Advances in Space Research, 26, 1443 , doi: https://doi.org/10.1016/S0273-1177(00)00100-9
  * Cravens (1997) Cravens, T. E. 1997, Geophysical Research Letters, 24, 105, doi: 10.1029/96GL03780
  * Cravens (2000) Cravens, T. E. 2000, ApJ, 532, L153, doi: 10.1086/312574
  * Cravens (2002) Cravens, T. E. 2002, Science, 296, 1042, doi: 10.1126/science.1070001
  * Cravens et al. (2009) Cravens, T. E., Robertson, I. P., Snowden, S., et al. 2009, in American Institute of Physics Conference Series, Vol. 1156, American Institute of Physics Conference Series, ed. R. K. Smith, S. L. Snowden, & K. D. Kuntz, 37–51, doi: 10.1063/1.3211832
  * Cravens et al. (2003) Cravens, T. E., Waite, J. H., Gombosi, T. I., et al. 2003, Journal of Geophysical Research: Space Physics, 108, doi: 10.1029/2003JA010050
  * Crovisier & Encrenaz (1983) Crovisier, J., & Encrenaz, T. 1983, A&A, 126, 170
  * Dello Russo et al. (2002) Dello Russo, N., Mumma, M. J., DiSanti, M. A., & Magee-Sauer, K. 2002, Journal of Geophysical Research (Planets), 107, 5095, doi: 10.1029/2001JE001838
  * Dennerl (2002) Dennerl, K. 2002, A&A, 394, 1119, doi: 10.1051/0004-6361:20021116
  * Dennerl et al. (2002) Dennerl, K., Burwitz, V., Englhauser, J., Lisse, C., & Wolk, S. 2002, A&A, 386, 319, doi: 10.1051/0004-6361:20020097
  * Dennerl et al. (1997) Dennerl, K., Englhauser, J., & Trümper, J. 1997, Science, 277, 1625, doi: 10.1126/science.277.5332.1625
  * Dennerl et al. (2012) Dennerl, K., Lisse, C. M., Bhardwaj, A., et al. 2012, Astronomische Nachrichten, 333, 324, doi: 10.1002/asna.201211663
  * Desch & Jackson (2021) Desch, S. J., & Jackson, A. P. 2021, Journal of Geophysical Research (Planets), 126, e06807, doi: 10.1029/2020JE006807
  * Do et al. (2018) Do, A., Tucker, M. A., & Tonry, J. 2018, ApJ, 855, L10, doi: 10.3847/2041-8213/aaae67
  * Dohnanyi (1969) Dohnanyi, J. S. 1969, J. Geophys. Res., 74, 2531, doi: 10.1029/JB074i010p02531
  * Engelhardt et al. (2017) Engelhardt, T., Jedicke, R., Vereš, P., et al. 2017, AJ, 153, 133, doi: 10.3847/1538-3881/aa5c8a
  * Ewing et al. (2013) Ewing, I., Christian, D. J., Bodewits, D., et al. 2013, ApJ, 763, 66, doi: 10.1088/0004-637X/763/1/66
  * Flekkøy et al. (2019) Flekkøy, E. G., Luu, J., & Toussaint, R. 2019, ApJ, 885, L41, doi: 10.3847/2041-8213/ab4f78
  * Füglistaler & Pfenniger (2018) Füglistaler, A., & Pfenniger, D. 2018, A&A, 613, A64
  * Fujimoto et al. (2007) Fujimoto, R., Mitsuda, K., McCammon, D., et al. 2007, Progress of Theoretical Physics Supplement, 169, 71, doi: 10.1143/PTPS.169.71
  * Gomes et al. (2004) Gomes, R. S., Morbidelli, A., & Levison, H. F. 2004, Icarus, 170, 492, doi: 10.1016/j.icarus.2004.03.011
  * Gu et al. (2016) Gu, L., Kaastra, J., & Raassen, A. J. J. 2016, A&A, 588, A52, doi: 10.1051/0004-6361/201527615
  * Gu et al. (2018) Gu, L., Mao, J., de Plaa, J., et al. 2018, A&A, 611, A26, doi: 10.1051/0004-6361/201731861
  * Hahn & Malhotra (1999) Hahn, J. M., & Malhotra, R. 1999, AJ, 117, 3041, doi: 10.1086/300891
  * Hoover et al. (2022) Hoover, D. J., Seligman, D. Z., & Payne, M. J. 2022, , 3, 71, doi: 10.3847/PSJ/ac58fe
  * Hsieh et al. (2021) Hsieh, C.-H., Laughlin, G., & Arce, H. G. 2021, ApJ, 917, 20, doi: 10.3847/1538-4357/ac0729
  * Jackson & Desch (2021) Jackson, A. P., & Desch, S. J. 2021, Journal of Geophysical Research (Planets), 126, e06706, doi: 10.1029/2020JE006706
  * Janev & Winter (1985) Janev, R. K., & Winter, H. 1985, Phys. Rep., 117, 265, doi: 10.1016/0370-1573(85)90118-8
  * Jewitt et al. (2020) Jewitt, D., Kim, Y., Mutchler, M., et al. 2020, ApJ, 896, L39, doi: 10.3847/2041-8213/ab99cb
  * Jewitt & Luu (2019) Jewitt, D., & Luu, J. 2019, ApJ, 886, L29, doi: 10.3847/2041-8213/ab530b
  * Jewitt et al. (2017) Jewitt, D., Luu, J., Rajagopal, J., et al. 2017, ApJL, 850, L36, doi: 10.3847/2041-8213/aa9b2f
  * Jewitt & Seligman (2022) Jewitt, D., & Seligman, D. Z. 2022, arXiv e-prints, arXiv:2209.08182.  https://arxiv.org/abs/2209.08182
  * Kallio et al. (1997) Kallio, E., Luhmann, J. G., & Barabash, S. 1997, Journal of Geophysical Research: Space Physics, 102, 22183, doi: 10.1029/97JA01662
  * Kareta et al. (2020) Kareta, T., Andrews, J., Noonan, J. W., et al. 2020, ApJ, 889, L38, doi: 10.3847/2041-8213/ab6a08
  * Kharchenko & Dalgarno (2001) Kharchenko, V., & Dalgarno, A. 2001, ApJ, 554, L99, doi: 10.1086/320929
  * Kim et al. (2020) Kim, Y., Jewitt, D., Mutchler, M., et al. 2020, ApJ, 895, L34, doi: 10.3847/2041-8213/ab9228
  * Knight et al. (2017) Knight, M. M., Protopapa, S., Kelley, M. S. P., et al. 2017, ApJL, 851, L31, doi: 10.3847/2041-8213/aa9d81
  * Koutroumpa (2012) Koutroumpa, D. 2012, Astronomische Nachrichten, 333, 341, doi: 10.1002/asna.201211666
  * Krasnopolsky (1997) Krasnopolsky, V. 1997, Icarus, 128, 368, doi: 10.1006/icar.1997.5722
  * Laskar (1989) Laskar, J. 1989, Nature, 338, 237, doi: 10.1038/338237a0
  * Laskar & Gastineau (2009) Laskar, J., & Gastineau, M. 2009, Nature, 459, 817, doi: 10.1038/nature08096
  * Levine & Laughlin (2021) Levine, W. G., & Laughlin, G. 2021, ApJ, 912, 3, doi: 10.3847/1538-4357/abec85
  * Levison et al. (2008) Levison, H. F., Morbidelli, A., Van Laerhoven, C., Gomes, R., & Tsiganis, K. 2008, Icarus, 196, 258, doi: 10.1016/j.icarus.2007.11.035
  * Li et al. (2022) Li, X., Ragosta, F., Clarkson, W. I., & Bianco, F. B. 2022, ApJS, 258, 2, doi: 10.3847/1538-4365/ac3bca
  * Lin et al. (2020) Lin, H. W., Lee, C.-H., Gerdes, D. W., et al. 2020, ApJ, 889, L30, doi: 10.3847/2041-8213/ab6bd9
  * Lisse et al. (1999) Lisse, C., Christian, D., Dennerl, K., et al. 1999, Icarus, 141, 316, doi: https://doi.org/10.1006/icar.1999.6176
  * Lisse et al. (2001) Lisse, C. M., Christian, D. J., Dennerl, K., et al. 2001, Science, 292, 1343, doi: 10.1126/science.292.5520.1343
  * Lisse et al. (2004) Lisse, C. M., Cravens, T. E., & Dennerl, K. 2004, X-ray and extreme ultraviolet emission from comets, ed. M. C. Festou, H. U. Keller, & H. A. Weaver, 631
  * Lisse et al. (1996) Lisse, C. M., Dennerl, K., Englhauser, J., et al. 1996, Science, 274, 205, doi: 10.1126/science.274.5285.205
  * Lisse et al. (1997) Lisse, C. M., Fernández, Y. R., A’Hearn, M. F., et al. 1997, Earth Moon and Planets, 78, 251, doi: 10.1023/A:1006261303055
  * Lisse et al. (1999) Lisse, C. M., Fernández, Y. R., Kundu, A., et al. 1999, Icarus, 140, 189, doi: 10.1006/icar.1999.6131
  * Lisse et al. (2013) Lisse, C. M., Christian, D. J., Wolk, S. J., et al. 2013, Icarus, 222, 752, doi: 10.1016/j.icarus.2012.09.025
  * Lisse et al. (2022) Lisse, C. M., Gladstone, G. R., Young, L. A., et al. 2022, , 3, 112, doi: 10.3847/PSJ/ac6097
  * Liu et al. (2012) Liu, J., Wang, Q. D., & Mao, S. 2012, MNRAS, 420, 3389, doi: 10.1111/j.1365-2966.2011.20263.x
  * Luu et al. (2020) Luu, J. X., Flekkøy, E. G., & Toussaint, R. 2020, ApJ, 900, L22
  * Mamajek (2017) Mamajek, E. 2017, Research Notes of the American Astronomical Society, 1, 21, doi: 10.3847/2515-5172/aa9bdc
  * Mashchenko (2019) Mashchenko, S. 2019, MNRAS, 489, 3003, doi: 10.1093/mnras/stz2380
  * Masiero (2017) Masiero, J. 2017, arXiv e-prints, arXiv:1710.09977.  https://arxiv.org/abs/1710.09977
  * McCammon et al. (2002) McCammon, D., Almy, R., Apodaca, E., et al. 2002, ApJ, 576, 188, doi: 10.1086/341727
  * Meech et al. (2004) Meech, K. J., Hainaut, O. R., & Marsden, B. G. 2004, Icarus, 170, 463, doi: 10.1016/j.icarus.2004.03.014
  * Meech et al. (2017) Meech, K. J., Weryk, R., Micheli, M., et al. 2017, Nature, 552, 378, doi: 10.1038/nature25020
  * Meltzer (1949) Meltzer, B. 1949, Nature, 150, 201
  * Metzger et al. (1983) Metzger, A. E., Gilman, D. A., Luthey, J. L., et al. 1983, Journal of Geophysical Research: Space Physics, 88, 7731, doi: 10.1029/JA088iA10p07731
  * Micheli et al. (2018) Micheli, M., Farnocchia, D., Meech, K. J., et al. 2018, Nature, 559, 223, doi: 10.1038/s41586-018-0254-4
  * Morbidelli et al. (2005) Morbidelli, A., Levison, H. F., Tsiganis, K., & Gomes, R. 2005, Nature, 435, 462, doi: 10.1038/nature03540
  * Moro-Martín (2019) Moro-Martín, A. 2019, ApJ, 872, L32
  * Moro-Martín (2022) Moro-Martín, A. 2022, arXiv e-prints, arXiv:2205.04277.  https://arxiv.org/abs/2205.04277
  * Moro-Martín et al. (2009) Moro-Martín, A., Turner, E. L., & Loeb, A. 2009, ApJ, 704, 733, doi: 10.1088/0004-637X/704/1/733
  * Mullen et al. (2017) Mullen, P. D., Cumbee, R. S., Lyons, D., et al. 2017, ApJ, 844, 7, doi: 10.3847/1538-4357/aa7752
  * Mullen et al. (2016) Mullen, P. D., Cumbee, R. S., Lyons, D., & Stancil, P. C. 2016, ApJS, 224, 31, doi: 10.3847/0067-0049/224/2/31
  * Mumma et al. (1996) Mumma, M. J., Disanti, M. A., dello Russo, N., et al. 1996, Science, 272, 1310, doi: 10.1126/science.272.5266.1310
  * Öberg et al. (2011) Öberg, K. I., Murray-Clay, R., & Bergin, E. A. 2011, ApJ, 743, L16, doi: 10.1088/2041-8205/743/1/L16
  * Opitom et al. (2019) Opitom, C., Fitzsimmons, A., Jehin, E., et al. 2019, A&A, 631, L8, doi: 10.1051/0004-6361/201936959
  * Price et al. (2021) Price, E. M., Cleeves, L. I., Bodewits, D., & Öberg, K. I. 2021, arXiv e-prints, arXiv:2103.12751.  https://arxiv.org/abs/2103.12751
  * Raymond et al. (2018) Raymond, S. N., Armitage, P. J., & Veras, D. 2018, ApJ, 856, L7, doi: 10.3847/2041-8213/aab4f6
  * Raymond et al. (2020) Raymond, S. N., Kaib, N. A., Armitage, P. J., & Fortney, J. J. 2020, ApJ, 904, L4, doi: 10.3847/2041-8213/abc55f
  * Rein & Liu (2012) Rein, H., & Liu, S. F. 2012, A&A, 537, A128, doi: 10.1051/0004-6361/201118085
  * Rein et al. (2019) Rein, H., Hernandez, D. M., Tamayo, D., et al. 2019, MNRAS, 485, 5490, doi: 10.1093/mnras/stz769
  * Rubin et al. (2015) Rubin, M., Altwegg, K., Balsiger, H., et al. 2015, Science, 348, 232, doi: 10.1126/science.aaa6100
  * Rubin et al. (2018) —. 2018, Science Advances, 4, eaar6297, doi: 10.1126/sciadv.aar6297
  * Schleicher (1996) Schleicher, D. 1996, IAU circular 6372
  * Sekanina (2019) Sekanina, Z. 2019, arXiv e-prints.  https://arxiv.org/abs/1901.08704
  * Seligman & Laughlin (2020) Seligman, D., & Laughlin, G. 2020, ApJ, 896, L8, doi: 10.3847/2041-8213/ab963f
  * Seligman et al. (2021) Seligman, D. Z., Levine, W. G., Cabot, S. H. C., Laughlin, G., & Meech, K. 2021, ApJ, 920, 28, doi: 10.3847/1538-4357/ac1594
  * Seligman et al. (2022) Seligman, D. Z., Rogers, L. A., Cabot, S. H. C., et al. 2022, arXiv e-prints, arXiv:2204.13211.  https://arxiv.org/abs/2204.13211
  * Shakeel et al. (2018) Shakeel, H., Wei, H., & Pomeroy, J. 2018, The Journal of Chemical Thermodynamics, 118, 127, doi: https://doi.org/10.1016/j.jct.2017.11.004
  * Smith et al. (2012) Smith, R., Foster, A., & Brickhouse, N. 2012, Astronomische Nachrichten, 333, 301, doi: 10.1002/asna.201211673
  * Stephenson & Malanowski (1987) Stephenson, R. M., & Malanowski, S. 1987, Properties of Organic Compounds (Springer Dordrecht), 1–471.  https://doi.org/10.1007/978-94-009-3173-2
  * Stern et al. (2000) Stern, S. A., Slater, D. C., Festou, M. C., et al. 2000, ApJ, 544, L169, doi: 10.1086/317312
  * Trilling et al. (2018) Trilling, D. E., Mommert, M., Hora, J. L., et al. 2018, AJ, 156, 261
  * Tsiganis et al. (2005) Tsiganis, K., Gomes, R., Morbidelli, A., & Levison, H. F. 2005, Nature, 435, 459, doi: 10.1038/nature03539
  * Wargelin et al. (2004) Wargelin, B. J., Markevitch, M., Juda, M., et al. 2004, ApJ, 607, 596, doi: 10.1086/383410
  * Wegmann et al. (2004) Wegmann, R., Dennerl, K., & Lisse, C. M. 2004, A&A, 428, 647, doi: 10.1051/0004-6361:20041008
  * Wegmann et al. (1998) Wegmann, R., Schmidt, H., Lisse, C., Dennerl, K., & Englhauser, J. 1998, Planetary and Space Science, 46, 603 , doi: https://doi.org/10.1016/S0032-0633(97)00196-7
  * Wisdom (1980) Wisdom, J. 1980, AJ, 85, 1122, doi: 10.1086/112778
  * Xing et al. (2020) Xing, Z., Bodewits, D., Noonan, J., & Bannister, M. T. 2020, ApJ, 893, L48, doi: 10.3847/2041-8213/ab86be
  * Yoshida et al. (2003) Yoshida, F., Nakamura, T., Watanabe, J.-I., et al. 2003, PASJ, 55, 701, doi: 10.1093/pasj/55.3.701
  * Zhang et al. (2014) Zhang, S., Wang, Q. D., Ji, L., et al. 2014, ApJ, 794, 61, doi: 10.1088/0004-637X/794/1/61