The Volatile Carbon-to-oxygen Ratio as a Tracer for the Formation Locations of Interstellar Comets

A fundamental complication regarding measuring and comparing C/O ratios for different stars is that the stellar variations in this ratio are relatively small. Therefore, accurately comparing stellar C/O ratios requires a high level of both precision and accuracy. In stars with similar surface temperature and gravity to the Sun, commonly referred to as solar twins or solar-type stars, the C/O ratio can be measured with a high precision. The calibration to the Sun implies that the systematic errors of the abundance ratios for solar twins are almost the same for each star and mostly cancel.

Bedell et al. (2018) performed a differential study of the chemical composition of solar twins and showed that the C/O ratio in the sample did not vary significantly. However, they reported a slight dependence of this ratio on the stellar metallicity, which is a measure of heavy-element enrichment resulting from galactic chemical evolution. Nissen (2015) presented an analogous analysis for a sample of 21 solar twins and reported similar results. The reported C/O ratios for the solar twins measured by both studies are shown in Figure 2 (with data drawn from Figure 11 of Nissen 2015 and Figure 7 of Bedell et al. 2018). While the lowest-metallicity stars have lower C/O ratios, the mean C/O ratio of all of these stars is 0.50, and the standard deviation is σ = 0.04. All of these measurements are calibrated to measured solar abundances, which can be measured with very low uncertainties using a three-dimensional local thermodynamic equilibrium (LTE) analysis of molecular lines (Amarsi et al. 2021).

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Extrapolating the C/O ratio for stars with different masses and temperatures than the Sun is less straightforward. Brewer et al. (2016) and Delgado Mena et al. (2021) performed almost-differential studies of stars that are similar but not identical to the Sun. These authors reported high precision for samples of 1617 (Brewer et al. 2016) and 1111 F, G, and K stars (Delgado Mena et al. 2021), but systematic errors in the measurements are present. Figure 5 in Delgado Mena et al. (2021) shows that the C/O ratio does vary with age, similar to what was found by Nissen (2015) and Bedell et al. (2018).

The largest source of systematic uncertainty in stellar C/O measurements is that the inferred abundance ratios are derived from spectral lines that do not form under LTE and require advanced radiative transfer calculations. Ultimately, these discrepancies vary primarily with T_eff, $\mathrm{log}(g)$, and [Fe/H] (Amarsi et al. 2019). Encouragingly, the differences are small for stars where ∣T_eff − T_⊙∣ ≤ 100 K, so the solar twin measurements outlined in the previous subsection that do not incorporate non-LTE effects are still reliable.

An example of how these systematic errors work is shown in Figure 7 of Bedell et al. (2018), which compares their data on solar twins to the more general sample of Brewer et al. (2016). Bedell et al. (2018) demonstrated that the true C/O ratio varies slightly from star to star with an effect that is several times larger than their measurement errors; the standard deviation of the sample is ∼0.04, while the estimated measurement uncertainties are ∼0.02. These results are also very similar to those of the advanced non-LTE study by Amarsi et al. (2019), even though this sample included stars with a much wider range of stellar parameters.

The analysis presented by Amarsi et al. (2021) indicated that the limiting factor in measuring the solar C/O ratio is the atomic and molecular data, rather than the model solar atmosphere. Therefore, errors on the absolute abundances of carbon and oxygen do not cancel but should be combined in quadrature to calculate the uncertainty on the solar C/O ratio. The quoted accuracy is ∼0.05 dex, where $\mathrm{log}({N}_{{\rm{O}}}/{N}_{{\rm{C}}})\,=0.23\pm 0.05$ dex, or C/O = 0.59 ± 0.06. This uncertainty only applies to the absolute abundance scale. Therefore, for any homogeneous population of stars (like solar twins), the uncertainty in the scatter of the distribution is much less than 0.05 dex.

For stars that are very unlike the Sun, such as cool M-type stars, the spectra are veiled by millions of molecular lines. These introduce a different set of systematic errors that have still not been quantified and solved. Veyette et al. (2016) indicated that while the C/O ratio influences M dwarf spectra, it is unclear if synthetic spectra are good enough to fit this to a precision better than the star-to-star scatter. In case measurements of the C/O ratio in M dwarfs are acquired and calibrated on FGK stars, the 0.05 dex accuracy of the solar C/O ratio will limit those results as well. Increasing the accuracy of the atomic and molecular constants via improved laboratory measurements and theoretical calculations is the only way to reduce this dominant source of uncertainty.

The population of interstellar comets originates from an unknown and undifferentiated assortment of stellar populations. Therefore, in this study, we assume that the bulk composition and mean and scatter of the elemental ratios of these stars are similar to the solar twins. Our justification for this is that there is no process that would differentially change the abundance ratios of interstellar comet-producing stars as a function of stellar mass. It is important to note that the location of the true mean has 0.05 dex uncertainty. Therefore, the predictions presented in Section 6 would scale based on the true mean when it is further constrained.

In this subsection, we review the currently measured compositional properties of solar system comets and calculate the inferred C/O ratios using a variety of combinations of species. As a starting place, we refer to the sample of 87 comets with measured production rates of carbon-bearing molecules C₂, C₃, CN, and OH over a period of 17 yr (A'Hearn et al. 1995). These comets do not have measured production rates of CO and CO₂. In Figure 3, we show the C/O ratio of these comets calculated using only the production rates of C₂, C₃, and CN relative to H₂O (inferred from OH). The conversion from OH to H₂O is calculated using the branching ratio of H₂O photodissociation and the heliocentric distance (Cochran & Schleicher 1993; McKay et al. 2019). These objects span a range of cometary families, and every estimated C/O ratio is <0.1, less than that expected between the H₂O and CO₂ snow lines (Figure 1). The C/O ratio tends to increase with decreasing heliocentric distance due to the increase in C₂/CN ratios, which is also reflected when plotted as a function of perihelia (see Figure 3, panel A and Figure 15 of A'Hearn et al. 1995 and Fink 2009). This is likely related to the fact that, in addition to being released via photodissociation of more complex molecules, these species are also released from thermal degradation of carbonaceous dust grains such as the CHON grains discovered during the Halley flyby (Lawler & Brownlee 1992), a process that is more efficient closer to the Sun.

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Toward constraining the C/O ratio in the volatiles of known comets, we compiled an extensive list of comets with H₂O, CO, and/or CO₂ production rates measured at some point in their trajectory. In Table 1, we show the measured production rate ratios and associated uncertainties of CO₂ and CO relative to H₂O in this substantially smaller sample of solar system comets. We calculate the observed C/O ratio in the coma using the equation

$$\begin{eqnarray}\begin{array}{rcl}{\rm{C}}/{\rm{O}} & = & \left[\left(\displaystyle \frac{Q(\mathrm{CO})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)+\left(\displaystyle \frac{Q({\mathrm{CO}}_{2})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)+2\left(\displaystyle \frac{Q({{\rm{C}}}_{2})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)\right.\\ & & +\,3\left(\displaystyle \frac{Q({{\rm{C}}}_{3})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)+\left(\displaystyle \frac{{\rm{Q}}(\mathrm{CN})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)\\ & & \left.+\left(\displaystyle \frac{Q({\mathrm{CH}}_{3}\mathrm{OH})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)\right]\Space{0ex}{0.25ex}{0ex}/\left[1+\left(\displaystyle \frac{Q(\mathrm{CO})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)\right.\\ & & \left.+2\left(\displaystyle \frac{Q({\mathrm{CO}}_{2})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)+\left(\displaystyle \frac{Q({\mathrm{CH}}_{3}\mathrm{OH})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)\right],\end{array}\end{eqnarray} \tag{ 1 }$$

where the 1 in the denominator represents the normalized H₂O production rates, specifically Q(H₂O)/Q(H₂O), and Q(X) is the production rate of a species in units of molecules per second. Note that OH is not included explicitly in Equation (1) because it is used to infer the H₂O production rate as described previously in this section. Although O₂ was detected in 67P with a mean abundance of 3.80 ± 0.85 relative to H₂O (Bieler et al. 2015), we neglect its relative contribution to the C/O ratio in Equation (1) because this is not easily detectable remotely. We calculated the C/O ratio using only the production rates of measured species in Equation (1).

In Figure 4, we show the C/O ratio in the sample of comets presented in Table 1. We also include the sample of comets in Figure 3, whose C/O is generally much lower because of the lack of measured CO₂ and CO production rates. We also include a sample of extrasolar planetesimals from polluted white dwarfs, which reflect the bulk composition of a recently accreted planetesimal. These data include 16 polluted white dwarfs from Xu et al. (2013), Farihi et al. (2013), Xu et al. (2014), Wilson et al. (2015), and Wilson et al. (2016) (see Table 3 in Wilson et al. 2016). The polluted white dwarf events all have inferred C/O < 0.5, and all but two have C/O < 0.1.

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It is important to note that the C/O derived from volatile production rates based on coma observations neglects grains that would otherwise contribute to the bulk C/O (Combi et al. 2020; Hoang et al. 2020, 2019). For example, Rubin et al. (2019) pointed out the substantial refractory inventory of carbon in the dust grains and organics of 67P/Churyumov-Gerasimenko. The oxygen inventory of dust grains also rivals that of ices (Table 4 in Rubin et al. 2019), but both depend on the dust-to-ice weight ratio, which was assumed to be around 1–3. Here we only focus on the volatile C/O, which is representative the C/O of gas and ices in the formation location of the protoplanetary disk.

There are a small subset of objects that have C/O ≥ 0.5. The most notable objects are 2I/Borisov, R2, and 'Oumuamua. We show four postperihelion measurements of Borisov's C/O ratio and a nominal C/O value for 'Oumuamua, under the assumption that its nongravitational acceleration was driven by outgassing of CO (Seligman et al. 2021b). The Centaur 29P also has a high C/O > 0.5, but its large heliocentric distance, ≳6 au, implies that there is likely more H₂O present in the comet that is inactive. Objects R2 and 2I are atypical with respect to the bulk composition of every other cometary object that has had its production rates measured. It is worth noting that the comets C/2009 P1 Garradd, C/2010 G2 Hill, and C/2006 W3 Christensen (labeled in Figure 4) also have high C/O ratios, which may also imply a distant formation location. However, these C/O ratios are still lower than those of R2 and 2I.

In Figure 5, we show the estimated C/O ratios for comets that have measured production rates for H₂O, CO, CO₂, C₂, C₃, and CN. Consistently, with only one exception, the inferred C/O is larger by about an order of magnitude when calculated from CO₂ and CO production rates compared to when calculated from C₂, C₃, and CN. This implies that observations of interstellar comet production rates should prioritize H₂O, CO₂, and CO in order to estimate the volatile C/O ratio as a tracer for formation location. However, measurements of any carbon- or oxygen-bearing species would improve the estimates of the C/O ratio. The comets in Figure 5 are 1P/Halley 1682 Q1, 8P/Tuttle 1858 A1, 19P/Borrelly 1904 Y2, 103P/Hartley 2 1986 E2, 67P/Churyumov-Gerasimenko 1969 R1, 22P/Kopff 1906 Q1, 81P/Wild 2 1978 A2, 88P/Howell 1981 Q1, 9P/Tempel 1 1867 G1, 116P/Wild 4 1990 B1, C/Bradfield 1979 Y1, C/Austin 1989 X1, and C/Levy 1990 K1.

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In Table 2, we provide a review of all of the production rates for the various species that were measured for 2I/Borisov. In Figure 6, we show all of these production rates as function of date and heliocentric distance. While CN, C₂, C₃, NH₂, and HCN were detected in the coma, the activity was dominated by H₂O and CO. Observations sensitive to CO were only obtained after perihelion, so it is feasible that there was significant production of CO prior to perihelion.

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Table 2. Various Production Rates for Molecules Observed for 2I/Borisov

Date	r H [au]	$Q(\mathrm{CN})$	Q(C2)	Q(C3)	Q(OH)	Q(NH2)	Q(H2 O)	Q(CO)	$Q(\mathrm{HCN})$	Reference
9/20/19	2.67	3.7 ± 0.4	<4							Fitzsimmons et al. (2019)
9/20/19	2.67	<5	<8							Kareta et al. (2020)
9/27/19	2.56						<8.2			Xing et al. (2020)
10/1/19	2.50	1.1 ± 2.0	<2.5							Kareta et al. (2020)
10/1/19	2.51	1.8 ± 0.1	<0.9	<0.3						Opitom et al. (2019)
10/2/19	2.50	1.9 ± 0.1	<0.6	<0.2	<20					Opitom et al. (2019)
10/9/19	2.41	1.59 ± 0.09	<0.44							Kareta et al. (2020)
10/10/19	2.39	1.69 ± 0.04	<0.162							Kareta et al. (2020)
10/11/19	2.38						6.3 ± 1.5			McKay et al. (2020)
10/13/19	2.36	2.1 ± 0.1	<0.6	<0.3	<20					Opitom et al. (2019)
10/18/19	2.31	1.9 ± 0.6								Opitom et al. (2019)
10/20/19	2.29	1.6 ± 0.5								Opitom et al. (2019)
10/26/19	2.23	1.9 ± 0.3								Kareta et al. (2020)
10/31/19	2.18	2.0 ± 0.2								Lin et al. (2020)
11/1/19	2.17						7.0 ± 1.5			Xing et al. (2020)
11/4/19	2.15	2.4 ± 0.2	5.5 ± 0.4	0.03 ± 0.01						Lin et al. (2020)
11/10/19	2.12	1.9 ± 0.5								Bannister et al. (2020)
11/14/19	2.09	1.8 ± 0.2	1.1			4.20				Bannister et al. (2020)
11/17/19	2.08	1.9 ± 0.5								Bannister et al. (2020)
10/28/19–11/18/19	2.21–2.06								<6.3	Bergman et al. (2022)
11/25/19	2.04	1.6 ± 0.5								Bannister et al. (2020)
11/26/19	2.04	1.8 ± 0.2								Bannister et al. (2020)
11/26/19	2.04	1.5 ± 0.5	1.1			4.80				Bannister et al. (2020)
11/30/19	2.01	3.36 ± 0.25	1.82 ± 0.6	0.197 ± 0.052						Aravind et al. (2021)
12/1/19	2.01						10.7 ± 1.2			Xing et al. (2020)
12/3/19	2.01							3.3 ± 0.8		Yang et al. (2021)
12/11/19	2.01							7.5 ± 2.3		Bodewits et al. (2020)
12/15-16/19	2.02							4.4 ± 0.7	0.7 ± 0.11	Cordiner et al. (2020)
12/19-22/19	2.03						4.9 ± 0.9	6.4 ± 1.4		Bodewits et al. (2020)
12/21/19	2.03						4.9 ± 0.9			Xing et al. (2020)
12/22/19	2.03	6.68 ± 0.27	2.3 ± 0.82	0.714 ± 0.074						Aravind et al. (2021)
12/30/19	2.07							10.7 ± 6.4		Bodewits et al. (2020)
1/13/20	2.16						<5.6	8.7 ± 3.1		Bodewits et al. (2020)
1/14/20	2.17						<6.2			Xing et al. (2020)
2/17/20	2.54						<2.3			Xing et al. (2020)

Note. Productions rates are in units of 10²⁴ molecules s^–1, except for H₂O and CO, which are 10²⁶. Errors are included where possible.

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The compositions of R2 and 2I are indicative of formation exterior to the CO snow line. In Figure 7, we show comparisons of the bulk composition of typical carbon-enriched and carbon-depleted solar system comets, R2, and 2I. The differences between these four compositions are striking, especially when viewed in a pie chart. The orders-of-magnitude higher abundance of CO ice than H₂O in R2 is difficult to explain with typical cometary formation scenarios (Mousis et al. 2022).

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In any case, it is feasible that planetary systems typically produce two distinct populations of comets: CO-enriched objects exterior to the CO snow line and CO-depleted objects interior to the CO snow line. The existence of a single interstellar comet with a high measured C/O ratio may imply that comets that form exterior to the CO snow line are more readily ejected, while CO-depleted objects are more likely to remain gravitationally bound to the star. The validity of this hypothesis will be revealed when more interstellar comets are detected and the fraction of the population that are CO-enriched is better constrained.

It is worth noting that cometary production rates and ratios of different species change as a function of age and position in their trajectory. Given this, we advocate for multiple observations of the relevant production rates at various heliocentric distances for future interstellar comets. We discuss this further in Sections 5, 5.4, and 7.

The host system of an interstellar comet cannot be determined from its trajectory. As we show in this subsection, however, the composition of an interstellar comet provides some constraints on the host system. We calculate the total reservoir of disk material interior and exterior to the CO ice line as a function of stellar mass in order to provide some constraints on the host system. From these calculations, we provide constraints on the types of stars that can produce CO-enriched comets like Borisov.

We constructed a grid of circumstellar disk models and calculated the fraction of total material predicted to be CO-enriched. We set the inner and outer disk boundaries for each disk at 10 times the stellar radius and $100\,\mathrm{au}{(M/{M}_{\odot })}^{1/3}$, respectively. In addition, we set the CO ice line at $30\,\mathrm{au}{(M/{M}_{\odot })}^{l/2}$, where l ∼ 3.5 is the exponent in the mass–luminosity relationship L ∝ M^l . The surface mass density is approximated with a power law Σ = Σ_o r^−α . Although the classic minimum-mass solar nebula construction adopted α = 1.5 (Weidenschilling 1977; Hayashi 1981), we allow for α to vary.

From these values, we compute the fraction of material in the circumstellar disk that is CO-enriched and CO-depleted. We assume that the CO-enriched fraction is the percentage of mass that is located exterior to the CO ice line. Figure 8 shows the mass fraction of each disk that is CO-enriched. More massive stars push d_CO to farther radii and have a lower fraction of CO-enriched material. In addition, larger α leads to a steeper decline in the disk surface density and also decreases the fraction of material exterior to the CO ice line.

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As a point of reference, a solar-mass star would have 70%, 46%, and 15% of its disk mass exterior to the CO ice line for α = 1.0, 1.5, and 2.0, respectively. A 0.08 M_⊙ M dwarf and a 1.5 M_⊙ A dwarf would have approximately 91% and 28% of their disk masses exterior to their CO ice lines for α = 1.5.

While this calculation provides an estimate of the fraction of CO-enriched material as a function of stellar and disk properties, the ejection efficiencies of CO-enriched comets will depend on the cometary formation efficiency and the ejection mechanisms and rates. The propensity for stars of various masses to eject CO-enriched comets will depend on the typical outcomes of planet formation as a function of stellar mass. One possibility is that planets with a large Safronov number (the ratio of the escape velocity to the orbital velocity) form at large semimajor axes for M dwarf stars, although this idea has been theoretically disfavored (Laughlin et al. 2004). If the CO-enriched composition of Borisov is representative of typical compositions of interstellar comets, then it seems unlikely that stars larger than the Sun contribute substantially to the overall population.

In this subsection, we perform numerical simulations tracking the aspect ratio, size, and density of a kilometer-scale interstellar comet like 2I/Borisov during the past 10 Gyr of evolution. We back-trace the trajectory from initial assumptions about the composition, bulk density, and size when the object enters the solar system, and we calculate the geometric changes from continuous desorption from cosmic rays and intermittent FUV photons. ¹³ The nominal solar system entrance is defined as the heliocentric distance when the change in radius becomes asymptotic.

We adopt three initial compositions for a comet composed entirely of (i) H₂O, (ii) CO₂, and (iii) CO ice with a roughly spherical nucleus with a 1 km diameter and aspect ratio of 1:1:0.98. The bulk density of the comet is assumed to be the same as that of the ice, although it is important to note that solar system comets are porous, with typical bulk densities of <0.5 g cm⁻³. However, the relative mass loss of different volatiles does not sensitively depend on the assumed bulk density.

At each time step of length Δτ in the simulation, we calculate the addition of an ellipsoidal shell of material desorbed from the surface. The time when the comet enters the solar system is t₀, and positive/negative Δτ corresponds to time intervals moving forward/backward in time for the remainder of these calculations. The surface integrated production rate, ${ \mathcal N }$, of sublimated molecules for a given species, X per unit time, is given by the equation

$$\begin{eqnarray}&&{ \mathcal N }(t,X)=+\displaystyle \frac{{\rm{\Sigma }}(t){{\rm{\Phi }}}_{\mathrm{CR}}}{{\rm{\Delta }}H(X)/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}(X)},\end{eqnarray} \tag{ 2 }$$

where ΔH(X) is the molar enthalpy of sublimation of the volatile species X, T_Sub(X) is its sublimation temperature, Σ is the ellipsoidal surface area at time t, and γ is the adiabatic index of the escaping vapor. This calculation assumes that 100% of the energy received is deposited into desorption of ice via sublimation and neglects the contribution to radiative cooling of the grain via blackbody emission (which is negligible at ISM temperatures).

The change in the comet's mass, δ m, during each time step of length Δτ is given by multiplying Equation (2) by the mass of the species and the time-step length, $\delta {\rm{m}}=-\mu {{\rm{m}}}_{{\rm{u}}}{ \mathcal N }{\rm{\Delta }}\tau$, for a species with mass μ m_u, where m_u is the atomic mass constant. The negative sign ensures that mass is added/removed from the body as the integration moves backward/forward in time. The resulting change in volume, δ V, is given by δ V = δ m/ρ, where ρ is the bulk density of the volatile species that is sublimated. In order to explicitly demand mass conservation, we solve for roots of the cubic equation, ζ(δ h), where δ h is the change in length of each principal axis, denoted a, b, and c,

$$\begin{eqnarray}&&\zeta (\delta h)=\delta V-\displaystyle \frac{4}{3}\pi \left((a+\delta h)(b+\delta h)(c+\delta h)-{abc}\right).\end{eqnarray} \tag{ 3 }$$

The signs of δ V and δ h depend on whether the integration is backward (δ V > 0, δ h > 0) or forward (δ V < 0, δ h < 0) in time. We verified that the results were not sensitive to the initial aspect ratios. We show the thermodynamic properties for the relevant species in Table 3.

The relative mass loss of CO and CO₂ with respect to H₂O is shown in Figure 9. The top axis indicates the present-day maximum vertical excursion in the galactic orbit corresponding to the age on the lower x-axis. This approximates the vertical velocity dispersion, and therefore age, due to dynamical heating and primordial dispersion. 'Oumuamua and Borisov had ages close to τ_1I ∼ 35 Myr and τ_2I ∼ 710 Myr, given that the maximum vertical excursion ${z}_{\mathrm{ISO}}\sim \sqrt{\tau }$ (Hsieh et al. 2021). The H₂O/CO₂/CO comet grew to diameters of ∼1.004/1.010/1.021, ∼1.400/1.963/3.078, and ∼4.958/10.629/21.781 km after 10⁷, 10⁹, and 10¹⁰ yr of (backward) evolution. The evolution is not constant after >10⁸ yr, when the larger surface areas of the CO₂ and CO comets relative to the H₂O comet significantly enhance the intercepted energy flux, so these ratios should be interpreted as upper limits.

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In this subsection, assuming a spherical geometry throughout the evolution, we derive a simplified analytic form for the evolution in the ISM as a function of age. At any time step in the integration, the rate of change of the comet's volume due to the ongoing ablation is given by

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{{dV}(t,X)}{{dt}}=-3{\left(\,\displaystyle \frac{4\pi }{3}\,\right)}^{1/3}\left(\displaystyle \frac{\mu {m}_{{\rm{u}}}}{\rho }\right)\\ \,\times \,\left(\displaystyle \frac{{{\rm{\Phi }}}_{\mathrm{CR}}}{{\rm{\Delta }}H(X)/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}(X)}\right)V{\left(t\right)}^{2/3},\end{array}\end{eqnarray} \tag{ 4 }$$

where V(t) is the volume of the comet at time t in the integration. The assumption of spherical symmetry allows for the substitution for surface area Σ = 3V/R = 3(4π/3)^1/3 V^2/3, where R is the radius of the comet. Equation (4) can be integrated via the expression

$$\begin{eqnarray}\begin{array}{rcl}{\displaystyle \int }_{{V}_{0}}^{{V}_{i}}{V}^{-2/3}\,{dV} & = & -{\displaystyle \int }_{{t}_{0}}^{{t}_{0}-{\tau }_{\mathrm{ISO}}}3{\left(\displaystyle \frac{4\pi }{3}\right)}^{1/3}\left(\displaystyle \frac{\mu {{\rm{m}}}_{{\rm{u}}}}{\rho }\right)\\ & & \times \,\left(\displaystyle \frac{{{\rm{\Phi }}}_{\mathrm{CR}}}{{\rm{\Delta }}H/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}}\right)\,{dt},\end{array}\end{eqnarray} \tag{ 5 }$$

where V₀ represents the volume when it enters the solar system, while V_i is the volume at the time of ejection. Here τ_ISO is the duration of the journey in the ISM or ISO age and is positive. Equation (5) can be integrated to give the linear function for the radius,

$$\begin{eqnarray}&&{R}_{i}={R}_{0}+\left(\displaystyle \frac{\mu {m}_{{\rm{u}}}}{\rho }\right)\left(\,\displaystyle \frac{{{\rm{\Phi }}}_{\mathrm{CR}}}{{\rm{\Delta }}H/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}}\,\right){\tau }_{\mathrm{ISO}}\,,\end{eqnarray} \tag{ 6 }$$

where R₀ and R_i are the radius when it enters the solar system and upon ejection, respectively.

We verified that Equation (6) produced good agreement with the numerical calculations shown in Figure 9 in the previous subsection. Equation (6) can be generalized for any mixture of volatiles as long as the bulk density of the comet remains constant. After this processing transpires, the outer rind of a comet with a mixture of ices will be devoid of the molecules with the lowest ΔH and T_Sub. The interior of the comet will still retain the composition upon ejection.

In this subsection, we extend the previous calculation to account for processing in the solar system. Since the interior composition remains intact in the ISM, postperihelion observations will be representative of the primordial compositions if the solar system processing removes the ISM-processed surface.

To quantify this effect, we derive an analytic function for the radius evolution in the solar system, analogous to Equation (6) for the ISM. A schematic diagram of these two processes is shown in Figure 10. For the encounter in the solar system, the rate of change of the comet's volume is

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{{dV}(t,X)}{{dt}}=-3{\left(\displaystyle \frac{4\pi }{3}\right)}^{1/3}\left(\displaystyle \frac{1}{({\rm{\Delta }}H/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}})}\right)\\ \,\times \,\left(\displaystyle \frac{\mu {m}_{{\rm{u}}}}{\rho }\right)\left(\displaystyle \frac{{L}_{\odot }}{4\pi {r}_{H}^{2}}\right)\xi (1-p)V{\left(t\right)}^{2/3},\end{array}\end{eqnarray} \tag{ 7 }$$

where L_⊙ is the solar luminosity, ξ is the ratio of the projected surface area to the total surface area, p is the Bond albedo, r_H is the heliocentric distance at a given point in the trajectory, and ξ = 1/4 averaged over all projection angles (Meltzer 1949). This value is an upper limit because we do not include radiative cooling, which would decrease the magnitude of the mass lost in the solar system. ¹⁴

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From the conservation of angular momentum, we have ${r}_{H}^{2}\dot{\theta }={{bv}}_{\infty }$, where θ is the angle from the perihelia in the plane of the hyperbolic trajectory, v_∞ is the hyperbolic excess velocity, and b is the impact parameter. Combining $\dot{\theta }\,={{bv}}_{\infty }/{r}_{H}^{2}$ with Equation (7) to change the integration variables from t to θ leads the r_H ² factors to conveniently cancel and yields

$$\begin{eqnarray}&&\begin{array}{l}{\displaystyle \int }_{{V}_{0}}^{{V}_{f}}{V}^{-2/3}\,{dV}=-{\displaystyle \int }_{{\theta }_{\min }}^{{\theta }_{\max }}3{\left(\displaystyle \frac{4\pi }{3}\right)}^{1/3}\left(\displaystyle \frac{\mu {{\rm{m}}}_{{\rm{u}}}}{\rho }\right)\left(\displaystyle \frac{1}{{{bv}}_{\infty }}\right)\\ \,\times \,\left(\displaystyle \frac{1}{({\rm{\Delta }}H(X)/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}(X))}\right)\\ \,\times \,\left(\displaystyle \frac{{L}_{\odot }}{4\pi }\right)\left(\xi (1-p)\right)d\theta ,\end{array}\end{eqnarray} \tag{ 8 }$$

where V_f is the final volume after the solar system encounter. The angle between the asymptotes for a hyperbolic orbit is given by ¹⁵

$$\begin{eqnarray}&&{\theta }_{\max }-{\theta }_{\min }=2{\cos }^{-1}(-1/e),\end{eqnarray} \tag{ 9 }$$

where the eccentricity of the trajectory is in turn related to b and v_∞,

$$\begin{eqnarray}&&{e}^{2}=1+\displaystyle \frac{{b}^{2}{v}_{\infty }^{4}}{{G}^{2}{M}_{\odot }^{2}}.\end{eqnarray} \tag{ 10 }$$

Equation (8) integrates to

$$\begin{eqnarray}&&\begin{array}{l}{R}_{f}={R}_{0}-2\left(\displaystyle \frac{\mu {m}_{{\rm{u}}}}{\rho }\right)\left(\,\displaystyle \frac{1}{{\rm{\Delta }}H/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}}\,\right)\\ \,\times \,\left(\displaystyle \frac{{L}_{\odot }}{4\pi }\right)\left(\xi (1-p)\right)\left(\displaystyle \frac{1}{{{bv}}_{\infty }}\right)\left({\cos }^{-1}\left(-\displaystyle \frac{1}{e}\right)\right),\end{array}\end{eqnarray} \tag{ 11 }$$

where R_f is the final radius of the object after the encounter with the solar system.

In the previous two subsections, we calculated the change in radius of an interstellar comet due to (i) nonthermal cosmic ray–induced desorption in the ISM (Equation (6)) and (ii) stellar irradiation during the encounter with the solar system (Equation (11)). In this subsection, we evaluate the relative importance of these two processes as a function of the age and trajectory of an interstellar comet. We define the change in radius in the ISM and solar system as ΔR_ISM = R_i − R₀ and ΔR_SS = R₀ − R_f . The relative change in radius is given by the dimensionless quantity,

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{\Delta }}{R}_{\mathrm{SS}}}{{\rm{\Delta }}{R}_{\mathrm{ISM}}}=\displaystyle \frac{{\cos }^{-1}\left(-1/e\right)}{2\pi }\left(\displaystyle \frac{{L}_{\odot }\,\xi (1-p)}{{{\rm{\Phi }}}_{\mathrm{CR}}\,b\,{v}_{\infty }{\tau }_{\mathrm{ISO}}}\right).\end{eqnarray} \tag{ 12 }$$

Compositional measurements will be representative of the primordial material for objects where ΔR_SS/ΔR_ISM ≥ 1. Equation (12) can be written as the following scaled relationship:

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{{\rm{\Delta }}{R}_{\mathrm{SS}}}{{\rm{\Delta }}{R}_{\mathrm{ISM}}} & = & 0.59\left(\displaystyle \frac{1-p}{0.9}\right)\left(\displaystyle \frac{0.85\mathrm{au}}{b}\right)\left(\displaystyle \frac{26\mathrm{km}\,{{\rm{s}}}^{-1}}{{v}_{\infty }}\right)\\ & & \times \,\left(\displaystyle \frac{{\cos }^{-1}(-1/e)}{{\cos }^{-1}(-1/1.2)}\right)\left(\displaystyle \frac{3.5\times {10}^{8}\mathrm{yr}}{{\tau }_{\mathrm{ISO}}}\right),\end{array}\end{eqnarray} \tag{ 13 }$$

where the values of b, v_∞, e, and τ_ISO of 'Oumuamua have been used.

We show the relative change in radius in the solar system and ISM for a range of b and v_∞ in Figure 11 for Borisov- and 'Oumuamua-aged objects. 'Oumuamua experienced comparable erosion in the solar system and ISM with ΔR_SS/ΔR_ISM =0.59, while Borisov had ΔR_SS/ΔR_ISM < 10⁻². Previously,Kim et al. (2020) estimated that Borisov only lost ∼0.4 m of surface material in the solar system and similarly concluded that compositional observations were not representative of the primordial material. Hoover et al. (2022) presented the orbital distribution of interstellar objects detected by LSST, assuming that all of the objects had an absolute magnitude similar to that of 'Oumuamua. We show the cumulative distribution functions for b and v_∞ in Figure 12, from Figures 12 and 15 of Hoover et al. (2022). The LSST will detect objects out to b ∼ 3 au with 20 km s⁻¹ < v_∞ < 60 km s⁻¹. These limits are reflected in Figure 11. Roughly 80% of the detected objects will have v_∞ < 40 km s⁻¹ and b < 2 au. Objects the age of 'Oumuamua will have ΔR_SS/ΔR_ISM ∼ 1 only for b ≤ 0.5 au. No objects the age of Borisov will have ΔR_SS/ΔR_ISM ≥ 1. From incorporating the results of the marginal cumulative distribution functions, we calculate that <5% of objects with ages similar to 'Oumuamua will have ΔR_SS/ΔR_ISM > 1. Spectroscopic measurements during a tidal disruption event, activity-driven disintegration event, or space-based impactor collision could reveal the primordial composition.

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In this subsection, we outline a method to approximate the primordial C/O ratio from the observed production rates. As we showed in the previous subsection, the majority of interstellar comets will not exhibit activity representative of their primordial composition (unless they break apart under the action of tides, activity, rotation, and/or collisions). Moreover, processing in the ISM should preferentially remove CO and CO₂ with respect to H₂O (Figure 9). Therefore, the C/O ratio inferred from H₂O, CO₂, and CO production rates after processing are lower limits on the primordial C/O ratio.

The volatile C/O ratio of an interstellar comet that has production rates for CO₂, CO, and H₂O measured during its apparition is given by

$$\begin{eqnarray}&&\begin{array}{l}{\left({\rm{C}}/{\rm{O}}\right)}_{\mathrm{Obs}}=\left[{\left(\displaystyle \frac{Q(\mathrm{CO})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}+{\left(\displaystyle \frac{Q({\mathrm{CO}}_{2})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}\right]\\ /\left[1+{\left(\displaystyle \frac{Q(\mathrm{CO})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}+2{\left(\displaystyle \frac{Q({\mathrm{CO}}_{2})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}\right],\end{array}\end{eqnarray} \tag{ 14 }$$

where the subscript "Obs" indicates the quantity when observed in the solar system. This is analogous to the observed C/O ratio in Equation (1).

The goal of this subsection is to derive an approximate upper limit on the primordial C/O ratio from the observed ratio. In order to estimate this limit, we assume that the time-averaged desorption of molecules in the ISM affects all species equally (i.e., each species has a similar cross section to galactic cosmic rays). The ratio of production rates in the ISM likely varies at any given snapshot during this journey. However, we assume that the total time-averaged ratio of molecules desorbed is mediated by the thermodynamic properties of each species. As long as the comet is old enough such that this time averaging is a reasonable approximation, then the ratio of molecules desorbed is independent of the comet's age. In this idealized scenario, the composition of the processed comet surface reaches a steady state (depleted in the more volatile species) wherein the relative ablation rates of the various species are balanced by the addition of fresh unprocessed primordial material at the base of the active volume as the processed surface extends deeper into the body due to the ongoing erosion.

The steady-state composition of the processed surface is set by the thermodynamic properties of the species and the initial primordial composition of the comet. Assuming that the observed C/O ratio of the coma during its apparition in the solar system represents the composition of the ISM-processed surface of the nucleus,

$$\begin{eqnarray}&&{\left(\displaystyle \frac{Q(X)}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}=\displaystyle \frac{1}{{{\rm{\Phi }}}_{X}}{\left(\displaystyle \frac{Q(X)}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Prim}},\end{eqnarray} \tag{ 15 }$$

where the ratio Φ_X is defined as

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{X}=\left(\displaystyle \frac{{\rm{\Delta }}H({{\rm{H}}}_{2}{\rm{O}})/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}({{\rm{H}}}_{2}{\rm{O}})}{{\rm{\Delta }}H(X)/{N}_{A}+\gamma {{kT}}_{\mathrm{Sub}}(X)}\,\right).\end{eqnarray} \tag{ 16 }$$

In the case where the production rates of CO₂, CO, and H₂O are measured, the primordial C/O ratio can be estimated as

$$\begin{eqnarray}&&\begin{array}{l}{\left({\rm{C}}/{\rm{O}}\right)}_{\mathrm{Prim}}\\ \ \ =\left[{{\rm{\Phi }}}_{\mathrm{CO}}{\left(\displaystyle \frac{Q(\mathrm{CO})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}+{{\rm{\Phi }}}_{{\mathrm{CO}}_{2}}{\left(\displaystyle \frac{Q({\mathrm{CO}}_{2})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}\right]\\ /\left[1+{{\rm{\Phi }}}_{\mathrm{CO}}{\left(\displaystyle \frac{Q(\mathrm{CO})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}+2\,{{\rm{\Phi }}}_{{\mathrm{CO}}_{2}}{\left(\displaystyle \frac{Q({\mathrm{CO}}_{2})}{Q({{\rm{H}}}_{2}{\rm{O}})}\right)}_{\mathrm{Obs}}\right].\end{array}\end{eqnarray} \tag{ 17 }$$

The values of ${{\rm{\Phi }}}_{{\mathrm{CO}}_{2}}=1.89$ and Φ_CO = 6.41 are calculated using Equation (16) and the values in Table 3. Since ${{\rm{\Phi }}}_{{\mathrm{CO}}_{2}},{{\rm{\Phi }}}_{\mathrm{CO}}\gt 1$, the measured C/O ratios of interstellar comets based on CO₂, CO, and H₂O production rates measured in the solar system are lower limits on the interstellar comets' primordial C/O ratios.

In Figure 13, we show the ratio of the primordial to observed C/O ratios given by Equations (14) and (17) for a range of production rates of CO and CO₂ relative to H₂O. This transformation can be applied to the production rates of interstellar comets to estimate their primordial C/O values and can be extended to include measured production rates for any species. For Borisov, the production rates of CO and H₂O measured between 2019 December 19 and 22 imply a C/O ratio of ∼0.56, which would correspond to a primordial C/O ratio of ∼0.89.

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Admittedly, the assumptions involved in transforming from the observed to primordial C/O ratio (Figure 13) are highly idealized. The processing in the ISM of an interstellar comet is likely a much more complicated process than the one described here. Therefore, we only apply the transformation derived here to estimate limits on the primordial composition in Section 6. The purpose of this calculation is not to calculate a definitive primordial C/O ratio from the observed one. Interior compositional measurements obtained during an interception mission would provide a more accurate calibration of the transformation from observed to primordial compositional ratios.

Borisov was enriched in CO compared to most solar system comets, despite the fact that it had ΔR_SS/ΔR_ISM <<1. Moreover, if the nongravitational acceleration of 'Oumuamua was caused by the sublimation of CO (Seligman et al. 2021b), then the C/O ratio would have been close to unity. Therefore, it may be that the preferential erosion of CO in an interstellar comet is a minor effect.

It is possible that the exposure to the galactic radiation environment produces a comet-like object with an insulating crust of volatile-depleted "regolith" of low thermal conductivity (Cooper et al. 2003). This regolith could shield subsurface layers, leaving them intact. This was initially pointed out as a possible explanation for 'Oumuamua's lack of coma by Jewitt et al. (2017) and elaborated upon with detailed thermal modeling by Fitzsimmons et al. (2018). Seligman & Laughlin (2018) demonstrated that less than 10 cm of regolith coating was sufficient to protect subsurface volatiles from sublimating, even when exposed to the solar radiation (Figure 1 in that paper). This layer is smaller than the layer removed from Borisov during its solar system passage estimated by Kim et al. (2020). Such mantled regolith crusts could help to preserve the interior of an interstellar comet through interstellar space.

In this section, we describe observations of an interstellar comet that would reveal its formation location and the facilities capable of obtaining them. We identify the primary science goal as constraining the elemental C/O ratio in the gaseous coma of the interstellar comet and describe several other secondary objectives. The following quantities and ratios would be useful to measure for this goal.

• 1.  
  Elemental ratios (C/O, N/O, S/O) (direct from UV, inferred from VIS/NIR/submillimeter molecule abundances)
• 2.  
  Molecular abundances (NUV/VIS/NIR/submillimeter)

  • (a)  
    Molecules: H₂O, CO, CO₂ (N/UV, VIS, NIR, submillimeter)
  • (b)  
    Radicals: OH, CN, C₂, C₃ (NUV, VIS, NIR)

Production ratios of "parent" volatiles like H₂O, CO₂, or CO at regular intervals during the apparition will provide a direct measurement of the C/O ratio. Large field-of-view observations of the broader atomic comae in the ultraviolet with fortuitous viewing geometry would provide atomic carbon and oxygen abundances. Regular observations of daughter molecules (produced via the breakdown of "parent" molecules) such as OH, CN, and C₂ would offer an additional constraint on the bulk carbon-compound abundance. Measured daughter molecules would also enable comparisons with solar system comets that do not have measured CO₂, CO, and H₂O production rates.

In this subsection, we identify observational facilities capable of achieving the identified science goals. For many of the goals, there are only a handful of ground- or space-based facilities capable of achieving them. A nonexhaustive comparison of the objectives, required wavelength coverage, and relevant facilities are listed in Table 4.

In general, measuring the C/O ratio directly requires a census of all relevant ions, atoms, molecules, and radicals in the coma. However, a decent understanding can be achieved through monitoring the production rates of H₂O, CO, and CO₂ (Figure 3). Measuring the production rates of these species directly will require Hubble or the James Webb Space Telescope (JWST) and a ground-based millimeter-wave facility such as the Atacama Large Millimeter/submillimeter Array (ALMA). The CO is observable from the ground at millimeter wavelengths and in the near-infrared (NIR), while H₂O and CO₂ require space-based infrared observations in most cases. With the Spitzer satellite past its lifetime, JWST is the most capable space-based facility sensitive to these infrared emissions. If the comet is sufficiently bright, H₂O and CO can be measured with Keck-NIRSPEC or IRTF-iShell. The Stratospheric Observatory For Infrared Astronomy (Temi et al. 2018) could pursue similar objectives and measurements as JWST but with lessened sensitivity.

The detection of CO in 2I/Borisov is an excellent example of a limiting detection for an interstellar comet (Bodewits et al. 2020). When Borisov was detected at ∼2 au from both the Sun and the Earth, its V-band magnitude was ∼17. The CO detection required 17,901 integration s (5 orbits of exposures) with the Hubble Space Telescope (HST) COS instrument at that magnitude. While the relationship between the V-band magnitude and CO production rates is not well understood, future UV spectral observations should be planned assuming similar requirements. Although space-based UV or IR observations are the most reliable way to characterize these parent molecules, they also require the objects to be brighter than for proxy measurements.

Proxies for H₂O, like OH, OI, or atomic hydrogen, can be obtained for dim comets under fortuitous conditions. For comets of lower apparent brightness, near-ultraviolet (NUV), visible, and NIR observations will remain viable for a significant fraction of the observable trajectory. The OH radical can be converted to the H₂O production rate (see Section 4 and references therein) and is observable from the ground in the NUV. However, these observations require telescopes with instrumentation sensitivity at wavelengths comparable to the atmospheric cutoff. Moreover, the extinction of 3100 Å light is extremely sensitive to airmass, so the comet's sky position is as important as its brightness and H₂O production rate. To circumvent this, the H₂O production rate of Borisov was measured in the 0-0 band of OH emission with the Ultraviolet-Optical Telescope (UVOT) on the Swift Observatory (Xing et al. 2020). However, Swift is currently addressing a broken reaction wheel and is not available for observations. The OI emission also approximates the H₂O production rate (McKay et al. 2020). This requires the oxygen emission to be sufficiently blue- or redshifted from atmospheric emission by the geocentric motion of the comet. This is only feasible for a subset of comets with suitable trajectories.

The carbon budget of an interstellar comet can be approximated by measuring the production rates of carbon-bearing radicals CN, C₂, and C₃ between ∼3800 and ∼5600 Å. This is obtainable with visible-wavelength spectroscopy or specialized filters like the Hale–Bopp filter set (Farnham et al. 2000; which also encompasses an OH 0-0 transition). These specialized filter sets can be used to characterize faint comets not observable with visible spectroscopy. However, few specialized filter sets are available outside of the Lowell Observatory and NOIRLab telescope networks. The adoption of the Hale–Bopp or a similar filter set at more sites—especially very high altitude sites like Maunakea—would greatly increase our ability to characterize faint interstellar comets.

Characterizing daughter products will also permit classification of interstellar comets according to the solar system comet taxonomies (such as "typical" versus "depleted"; A'Hearn et al. 1995). Some comets exhibit apparently typical carbon budgets (Raymond et al. 2022) without easily detected emissions from these species (Schleicher 2008). The prevalence of this effect in interstellar comets will also contextualize them within the populations native to the solar system.

Generally, observations of carbon and oxygen atoms directly would require space-based ultraviolet observations, though exceptions do exist. The HST's COS (Green et al. 2012) and STIS (Woodgate et al. 1998) instruments are the only currently available space-based ultraviolet-capable spectrographs sensitive to these emissions with guest observer capability.

The LSST will detect interstellar comets at or close to its limiting magnitude (Hoover et al. 2022). For these cases, some or all of the techniques outlined in the previous subsection cannot be applied. In this subsection, we highlight feasible alternative observational techniques when spectroscopic observations cannot be obtained.

The secular light curve, or brightness variations as a function of heliocentric distance, of a faint interstellar comet discovered by a survey such as the LSST should still be straightforward to obtain. A reliable measure of its brightness will be automatically obtained every few days by the discovery survey. Larger telescopes will only be necessary when the comet is below the detection limits of the discovery survey. Outbound observations of comets have precedent, provide additional information about the evolution of activity, and contextualize the measurements obtained when the comets were brightest (such as Hale–Bopp; see Szabó et al. 2012).

The secular light curve of a interstellar comet will provide useful information regarding its composition. The light curve of inactive objects is driven only by the heliocentric distance and the phase angle. The brightness variations of active objects are dominated by dust lofted from the surface and fluorescence of gas molecules and radicals. These effects cause a steeper slope with respect to heliocentric distance as the active volatile ratios change (Biver et al. 1997). Brightness variations as an interstellar comet crosses various ice lines will provide some compositional constraints. For example, the extent to which the light curve is smooth or punctuated by large outbursts and periods of low activity at large heliocentric distances informs (i) which volatiles drive the activity and (ii) the compositional structure within the nucleus (Kareta et al. 2021). For comets that are bright and active enough to appear extended in imaging observations, the morphology of cometary comae can also provide constraints on the overall activity state and the volatiles driving the activity (Kim et al. 2020).

In this subsection, we outline an observational strategy for a future interstellar comet with the primary goal of measuring the C/O ratio. The fraction of comets ejected from exterior to the CO snow line will be further constrained with every interstellar comet characterized in this manner. The LSST should detect ≥10 interstellar comets over 10 yr (Hoover et al. 2022), ∼50% of which have b < b_2I (Figure 12), allowing for measurements of their C/O ratio. This will provide a statistical sample of ≥seven objects to constrain the fraction ejected that formed exterior to the CO snow line and yield insights into the efficiency of various scattering mechanisms.

The observations of Borisov serve as an example to build from for future interstellar comets. Multiple observations of H₂O, CO₂, and CO, as well as the typical cometary radicals OH, CN, and C₂, were obtained and revealed the object's unique characteristics. Ideally, these observations will be repeated with future comets. Additionally, observations at heliocentric distances beyond 3 au pre- and postperihelion would inform the level to which ISM processing altered the surface composition. This would be vital information for estimating the primordial C/O ratio based on the measured one. Borisov was discovered ∼3 months prior to perihelion, limiting the time for preperihelion characterization of the molecular production rates. The drastic change in Borisov's H₂O production rate postperihelion was explained by the removal of a CO-depleted and H₂O-enriched surface (Bodewits et al. 2020). Preperihelion CO production rate measurements of a future interstellar comet would quantify the efficiency of this effect. Optimal observations of future interstellar comets would provide pre- and postperihelion characterization of the molecular abundances on either side of the H₂O ice sublimation line at ∼3 au for the extent to which discovery and observing geometry allows. This corresponds to a minimum of 4 epochs with detections or upper limits on H₂O, CO₂, and CO, as well as the more typical cometary radicals OH, CN, and C₂.

The apparent magnitude of an interstellar comet is agnostic to the extended brightness of the coma. However, the activity level controls the brightness in exposures where the bandpass is sensitive to the fluorescence of the sublimating gas or reflected sunlight from lofted dust. The apparition of 2I/Borisov was notably poor, partly because the comet only reached a geocentric distance of ∼2 au with a poor solar elongation angle. An LPC or JFC with the same absolute magnitude as Borisov would have been too poor of a target to propose observations for. However, due to its extrasolar origin, it was well characterized due to a global campaign. Therefore, limitations on the detectable activity level with certain telescopes for solar system comets should not be applied to interstellar comets.

The observatories capable of performing this suite of observations are presented in Table 4. The instrumentation and observatories are capable of measuring the C/O ratio of an interstellar comet independently. However, this system is susceptible to single-point failures. For example, in the event that the HST is unavailable during an interstellar comet apparition due to operational limitations, the H, C, O, and S atomic abundances cannot be measured directly with a single observation. If an interstellar comet is at a high decl. in the northern hemisphere during the monsoon season in Arizona and Swift UVOT is unavailable, it can only be characterizable by the IRTF and Keck observatories. This limits our ability to perform independent measurements of atomic, molecular, and radical abundances to ensure accuracy. Therefore, accurately measuring the C/O ratios of interstellar comets is directly linked to the stability of space-based observing platforms.