Cometary Science with the James Webb Space Telescope

At JWST wavelengths (0.6 μm $\lt \;\lambda \lt 28.5$ μm), comet spectra are generally dominated by sunlight scattered by and thermal emission from coma dust. It is a challenge for observers to accurately predict the surface brightness of a given target due to each comet's inherent variability and coma physical properties (dust and gas ejection speeds, grain parameters, presence of ice, etc.). For comets in the inner solar system, the observed energy from dust thermal emission and that from light scattered by dust are approximately equal in the 2–4 μm range, thus a single Planck function or stellar template are poor approximations. Whether the goal is to observe the continuum from dust, absorption features, emissivity features, or gas emission, having a simple model to estimate continuum brightness is beneficial to observers interested in this wavelength regime.

Light scattered by comet dust can be estimated using the ${Af}\rho$ parameter of A'Hearn et al. (1984). ${Af}\rho$ is the product of the albedo, A, the dust filling factor, f, and the radius of the circular aperture in consideration, ρ. Under certain assumptions and conditions, it is proportional to the dust production rate (Fink & Rubin 2012). It carries the units of ρ and is typically expressed in centimeters:

$$\begin{eqnarray}&&A(\theta )f\rho =\displaystyle \frac{4{{\rm{\Delta }}}^{2}{r}_{{\rm{h}}}^{2}}{\rho }\displaystyle \frac{{F}_{\lambda ,{\rm{c}}}}{{F}_{\lambda ,\odot }}{\rm{}}\;{\rm{(cm),}}\end{eqnarray} \tag{ 1 }$$

where Δ is the observer-comet distance (cm), r_h is the heliocentric distance of the comet (AU), ${F}_{\lambda ,{\rm{c}}}$ is the observed flux density of the comet within a circular aperture (W m⁻² μm⁻¹), ρ is the radius of the aperture projected to the distance of the comet (cm), and ${F}_{\lambda ,\odot }$ is the flux density of sunlight (W m⁻² μm⁻¹AU⁻²). We have written the albedo as $A(\theta )$ to emphasize that the observed albedo is a function of phase angle (Sun–comet–observer angle, θ). For observations corrected to a phase angle of 0°, we will simply write ${Af}\rho$. The albedo of A'Hearn et al. (1984) is a factor of 4 larger than the geometric albedo, A_p, of Hanner et al. (1981): $A(\theta )=4{A}_{p}(\theta ).$ Throughout the paper, we use the combined Halley–Marcus phase function from D. Schleicher to scale $A(\theta )f\rho$ to ${Af}\rho$ (Schleicher et al. 1998; Marcus 2007; Schleicher & Bair 2011).

For quantifying the thermal emission, Kelley et al. (2013) introduced the parameter $\epsilon f\rho$, which is the thermal emission equivalent to ${Af}\rho$:

$$\begin{eqnarray}&&\epsilon f\rho =\displaystyle \frac{{{\rm{\Delta }}}^{2}}{\pi \rho }\displaystyle \frac{{F}_{\lambda ,{\rm{c}}}}{{B}_{\lambda }(T)}{\rm{}}\;{\rm{(cm),}}\end{eqnarray} \tag{ 2 }$$

where is the apparent emissivity, ${F}_{\lambda ,{\rm{c}}}$ is now the observed thermal emission from dust (W m⁻² μm⁻¹) and ${B}_{\lambda }(T)$ is the Planck function evaluated at temperature T (W m⁻² μm⁻¹ and K, respectively). Similar to ${Af}\rho$, this quantity carries units of length, determined by the units of ρ. Kelley et al. (2013) recommend using the effective (color) temperature of the continuum, with a default temperature of $T=306\ {r}_{{\rm{h}}}^{-1/2}\;{\rm{K}},$ 10% warmer than an isothermal blackbody sphere in local thermodynamic equilibrium with insolation (${T}_{\mathrm{BB}}=278\ {r}_{{\rm{h}}}^{-1/2}\;{\rm{K}}$).

For exposure time calculations, we propose using a combination of the two empirical quantities above:

$$\begin{eqnarray}&&{F}_{\lambda ,{\rm{c}}}={Af}\rho \ \displaystyle \frac{{\rm{\Phi }}(\theta )\rho {F}_{\lambda ,\odot }}{4{{\rm{\Delta }}}^{2}{r}_{{\rm{h}}}^{2}}+\epsilon f\rho \ \displaystyle \frac{\pi \rho {B}_{\lambda }(T)}{{{\rm{\Delta }}}^{2}},({\rm{W}}\;{{\rm{m}}}^{-2}\;\mu {{\rm{m}}}^{-1})\end{eqnarray} \tag{ 3 }$$

where ${\rm{\Phi }}(\theta )$ is the phase function of the dust evaluated at the phase angle θ. The filling factors for ${Af}\rho$ and $\epsilon f\rho$ are not necessarily the same, as different populations of dust could dominate the measured scattered and thermal emission. In Table 1, we present seven observations of five comets with contemporaneous ${Af}\rho$ and $\epsilon f\rho$ estimates. The ratios $\epsilon f\rho /{Af}\rho =\epsilon {f}_{\mathrm{em}}/{{Af}}_{\mathrm{sca}}$ span the range 2.3–4.2. When $\epsilon f\rho$ is not known, we suggest scaling ${Af}\rho$ by the ratio $\epsilon {f}_{\mathrm{em}}/{{Af}}_{\mathrm{sca}}=3.5,$ based on the observed range in our small sample, and the assumptions (1)  ≈ 0.85–0.95, (2) $A\approx 0.25,$ and (3) the emission and scattering filling factors are similar, ${f}_{\mathrm{em}}\approx {f}_{\mathrm{sca}}$. Because the $\epsilon f\rho$ parameter depends on effective temperature, the ratio $\epsilon {f}_{\mathrm{em}}/{{Af}}_{\mathrm{sca}}$ may also be correlated with $T/{T}_{\mathrm{BB}},$ although this is not evident in the limited data set in Table 1. A caveat to our approach arises if $T/{T}_{\mathrm{BB}}$ and $\epsilon f\rho$ rely on data measured over a limited wavelength range. Any derived values may not be valid for other wavelengths, or even heliocentric distances. Specifically, shortward of ∼7.5 μm, silicates have limited absorptivity, so the 3–7 μm continuum is dominated by a warmer continuum from more absorbing carbonaceous grains.

Table 1.  Observed ${Af}\rho$ and $\epsilon f\rho$ Values and Their Ratio

Comet	${Af}\rho$	${\lambda }_{A}$	$\epsilon f\rho$	${\lambda }_{\epsilon }$	$T/{T}_{\mathrm{BB}}$	$\epsilon {f}_{\mathrm{em}}/{{Af}}_{\mathrm{sca}}$	Referencea
	(cm)	(μm)	(cm)	(μm)
1P/Halley	1205	1.25	3450	10.1	1.13	2.9	1985-08-25.6, T86, T88
1P/Halley	5710	1.25	15400	10.1	1.13	2.7	1985-12-13.3, T86, T88
73P-C/S-W 3	243	0.7	1000	13	1.07	<4.1b	S06, S11
73P-C/S-W 3c	1400	1.0	4150	4.0	1.12	3.0	S11 and this work
103P/Hartley 2	233	0.445	970	13	1.08	4.2	S10, M11
C/1986 P1 (Wilson)d	4230	1.25	9660	10.1	1.11	2.3	1987-06-1.2, H89
C/2012 K1 (PanSTARRS)	5731	0.64	14900	19.7	1.02	2.6	W15

Notes.

^aH89—Hanner & Newburn (1989), M11—Meech et al. (2011), S06—Sitko et al. (2006), S10—Sitko et al. (2010), S11—Sitko et al. (2011), T86—Tokunaga et al. (1986), T88—Tokunaga et al. (1988), W15—Woodward et al. (2015). ^bThe observations of 73P-C with the Broadband Array Spectrograph System (BASS) indicate the comet's IR brightness was increasing on hour timescales, and the ${Af}\rho$ and $\epsilon f\rho$ values given are based on observations separated by about 40 minutes. Therefore, $\epsilon f/{Af}$ is potentially an upper limit. ^cValues in this row are based on the fit to the near-IR spectrum presented in Figure 1. The continuum temperature scale factor was fixed at $T/{T}_{\mathrm{BB}}=1.12.$ ^dOld provisional designation: 1986l.

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In Figure 1, we plot a near-IR spectrum of comet 73P-C/Schwassmann–Wachmann 3 (Sitko et al. 2011), and our proposed model with the parameters $T/{T}_{\mathrm{BB}}=1.12$, ${Af}\rho$ = 1400 cm, and $\epsilon f/{Af}=3.0.$ The agreement is acceptable for first-order integration time estimations. Further refinements, e.g., wavelength-dependent ${Af}\rho$ to account for coma color, or wavelength-dependent $\epsilon f\rho$ to account for grain composition and size distribution, are not necessary.

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In addition to the dust continuum, gas emission bands are commonly observed. Here, we summarize our method to estimate total band flux. Using fluorescence g-factors (photons s⁻¹ molecule⁻¹ at 1 AU) from Crovisier & Encrenaz (1983), we generate total band fluxes in a 04 radius aperture, for either the NIRSpec integral field unit or microshutter assembly, assuming an optically thin coma (Table 3),

$$\begin{eqnarray}&&F=\displaystyle \frac{Q\rho {hcg}}{8\lambda v{{\rm{\Delta }}}^{2}{r}_{{\rm{h}}}^{2}}({\rm{W}}\;{{\rm{m}}}^{-2}),\end{eqnarray} \tag{ 4 }$$

where Q is the production rate of the molecule (molecules s⁻¹), ρ is is the radius of the aperture projected to the distance of the comet, h is the Planck constant, c is the speed of light, λ is the band central wavelength, $v=800\;{r}_{{\rm{h}}}^{-1/2}$ m s⁻¹ is the expansion speed of the gas, Δ is the observer-comet distance, and r_h is the heliocentric distance of the comet (AU). All parameters have MKS units, unless otherwise noted.

Table 2.  NIRSpec Case Study: Adopted Volatile Parameters

Species	Band	${\lambda }_{{\rm{c}}}$	Area	$\mathrm{log}\left\langle Z(1.5\;\mathrm{AU})\right\rangle$	$\mathrm{log}\left\langle Z(10\;\mathrm{AU})\right\rangle$
		(μm)	(km2)	(molec. s−1 cm−2)	(molec. s−1 cm−2)
H2O	${\nu }_{3}$	2.7	6.0	17.15	8.30
CO2	${\nu }_{2}$	4.3	0.26	17.51	14.84
CO	$\nu (1-0)$	4.7	0.080	18.03	16.36

Note.  ${\lambda }_{{\rm{C}}}$ is the approximate band center (Crovisier & Encrenaz 1983), Area is the effective active area, and $\left\langle Z\right\rangle$ is the mean sublimation rate per unit area, given at two heliocentric distances.

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Table 3.  NIRSpec Case Study: Production Rates, Total Band Fluxes, and Integration Times

					H2O			CO2			CO
rh	Δ	${E}_{\odot }$	ρ	${Af}\rho$	$\mathrm{log}Q$	$\mathrm{log}F$	t10	$\mathrm{log}Q$	$\mathrm{log}F$	t10	$\mathrm{log}Q$	$\mathrm{log}F$	t10
(AU)	(AU)	(°)	(km)	(cm)	(s−1)	(W m−2)	(s)	(s−1)	(W m−2)	(s)	(s−1)	(W m−2)	(s)
9.90	9.20	133	2668	20	19.18	−26.64	...	24.29	−20.74	...	25.27	−20.86	...
8.04	8.04	87	2330	31	21.32	−24.31	...	24.90	−19.93	12000	25.45	−20.48	...
7.05	6.55	116	1901	40	22.54	−22.91	...	25.16	−19.50	2110	25.57	−20.19	59300
5.00	4.90	90	1421	80	25.26	−19.84	28200	25.69	−18.62	127	25.87	−19.54	4100
4.01	3.63	106	1052	124	26.23	−18.60	306	25.95	−18.08	32.7	26.06	−19.08	841
1.92	1.68	87	488	540	27.62	−16.39	0.731	26.69	−16.53	0.942	26.70	−17.62	52.4
1.47	1.08	90	313	925	27.94	−15.71	0.148	26.93	−15.92	0.288	26.94	−17.02	36.8
2.39	2.16	91	627	350	27.33	−16.94	2.79	26.48	−16.99	2.56	26.51	−18.06	81.2
3.03	2.65	102	769	218	26.93	−17.59	14.9	26.25	−17.46	7.61	26.31	−18.51	186
5.19	5.10	89	1480	74	25.00	−20.14	98400	25.64	−18.71	163	25.84	−19.61	5430
6.05	5.41	126	1569	55	23.86	−21.41	...	25.42	−19.05	449	25.70	−19.88	15400
8.09	8.03	90	2329	31	21.26	−24.37	...	24.88	−19.95	13200	25.45	−20.49	...
9.04	8.50	120	2464	24	20.12	−25.61	...	24.56	−20.38	84600	25.35	−20.69	...

Note. As an approximation, an Earth-based observer viewing comet C/2013 A1 (Siding Spring) was used to generate observer-comet distances, Δ, and solar elongations, ${E}_{\odot }$. ρ is the radius of a 04 synthetic aperture projected at the distance of the comet, ${Af}\rho$ is the parameter of A'Hearn et al. (1984), Q is the production rate, F is the total band flux, t₁₀ is the integration time to achieve a signal-to-noise ratio of 10.

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Although we assume an optically thin coma, optical depth effects must be carefully considered when interpreting real spectra. For comet 9P/Tempel 1, Feaga et al. (2007) showed that optical depth effects are significant inside of ∼10 km for a water production rate of $5\times {10}^{27}$ molecules s⁻¹ and a CO₂ production rate of $5\times {10}^{26}$ molecules s⁻¹ at 1.5 AU from the Sun. For integration time estimation purposes, we neglect line opacity effects, which should only affect total band fluxes at the 10% level or less (e.g., Feaga et al. 2014).

A JWST exposure time calculator could provide a two-component model that would be adaptable to a variety of solar system sources. Continuum spectra of comet comae, comet nuclei, and asteroids can all be approximated by (1) ${F}_{\lambda ,\mathrm{refl}},$ based on a solar-type spectrum, potentially reddened, representing the reflected or scattered light, and (2) ${F}_{\lambda ,\mathrm{therm}},$ a blackbody spectrum of arbitrary temperature, representing the thermal emission:

$$\begin{eqnarray}&&{F}_{\lambda ,\mathrm{refl}}={C}_{\mathrm{refl}}\displaystyle \frac{{F}_{\lambda ,\odot }(\lambda )}{{F}_{\lambda ,\odot }({\lambda }_{\mathrm{refl},0})}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{F}_{\lambda ,\mathrm{therm}}={C}_{\mathrm{therm}}\displaystyle \frac{{B}_{\lambda }(T,\lambda )}{{B}_{\lambda }(T,{\lambda }_{\mathrm{therm},0})}\end{eqnarray} \tag{ 6 }$$

where ${C}_{\mathrm{refl}}({\lambda }_{\mathrm{refl},0})$ and ${C}_{\mathrm{therm}}({\lambda }_{\mathrm{therm},0})$ are the reflected (or scattered) and thermal emission normalization factors; ${F}_{\lambda ,\odot }$ is the solar flux density (see, e.g., ASTM International 2006); and B_λ is the Planck function. The template spectra are normalized to 1.0 at reference wavelengths ${\lambda }_{\mathrm{refl},0}$ and ${\lambda }_{\mathrm{therm},0}.$ Because ${Af}\rho$ and $\epsilon f\rho$ can change with wavelength, their values and the normalization wavelengths should be carefully chosen for the observation in consideration. For example, one might choose ${\lambda }_{\mathrm{refl},0}=1.0$ μm and ${\lambda }_{\mathrm{therm},0}=4.0$ μm for the spectrum in Figure 1. The normalization factors for a comet coma model would be based on the ${Af}\rho$ and $\epsilon f\rho$ components in Equation (3):

$$\begin{eqnarray}&&{C}_{\mathrm{refl}}={Af}\rho \displaystyle \frac{{\rm{\Phi }}(\theta )\rho }{4{{\rm{\Delta }}}^{2}{r}_{{\rm{h}}}^{2}}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{C}_{\mathrm{therm}}=\epsilon f\rho \displaystyle \frac{\pi \rho }{{{\rm{\Delta }}}^{2}}.\end{eqnarray} \tag{ 8 }$$

Thus, comet-specific parameters would not need to be incorporated into an observing tool, but arbitrary scale factors would be a necessity. Observers will need to estimate ${Af}\rho$ and $\epsilon f\rho$ based on the literature, their own experience, or recent observations.

Three gas species, H₂O, CO₂, and CO, are primarily responsible for driving cometary activity. These molecules have very different levels of volatility (e.g., Langer et al. 2000; Meech & Svoren̆ 2004; Huebner et al. 2006), suggesting that each species should dominate the comet's activity at different parts of the orbit, delineated by the abundance of each ice and the amount of solar energy available for sublimating those ices. CO may be released at heliocentric distances out to tens of AU, while CO₂ sublimation dramatically increases around 6–8 AU and H₂O sublimation near 2–3 AU. However, the limited observations available for these species indicate that cometary behavior is more complex than would otherwise be suggested by a simple energy balance model. The relative abundances not only differ from comet to comet, but also in unexpected ways with respect to heliocentric distance and sometimes before and after perihelion in a single comet (Bockelée-Morvan et al. 2004; Mumma & Charnley 2011; A'Hearn et al. 2012; Ootsubo et al. 2012; Bodewits et al. 2014; Feaga et al. 2014). These variations are due presumably to inherent compositional differences between objects reflecting their origins in the early solar system, heterogeneities in individual nuclei, and evolutionary processing from insolation.

Comprehensive data sets, i.e., those covering the production of all three molecules (H₂O, CO₂, and CO) over a wide range of times or heliocentric distances, typically depend on observations from multiple instruments and techniques. How systematic uncertainties (instrumental, observational, or theoretical) affect the relative abundances is therefore of concern. In addition, CO₂ cannot be observed from the ground, thus little is known regarding its abundance in comets or its role in comet activity outside of recent snapshot surveys (Crovisier et al. 2000; Ootsubo et al. 2012; Reach et al. 2013) and missions to comets (A'Hearn et al. 2005; Feaga et al. 2007; A'Hearn et al. 2011; Hässig et al. 2015). The wavelength coverage and sensitivities of NIRSpec, NIRCam, and NIRISS will allow JWST to simultaneously or contemporaneously measure all three of the primary species over a range of heliocentric distances. Such measurements enable studies of activity and composition at various distances and points around a comet's orbit, providing a uniform data set that cannot be achieved by other means. The high spatial resolution imaging available with NIRCam and NIRISS will also allow the investigation of heterogeneities in these species, revealed in the spatial distribution of the gases around the nucleus and their variations with time.

Here, we demonstrate the capabilities of time-domain spectroscopy with NIRSpec. Our goal is to observe H₂O, CO₂, and CO in a single comet over a wide range of heliocentric distances. We take the orbit of C/2013 A1 (Siding Spring) as a baseline (perihelion distance $q=1.4$ AU) to provide a rough idea for potential observing windows and comet brightnesses during an Oort cloud comet's journey from 10 AU pre-perihelion to 10 AU post-perihelion. We assume a coma mixing ratio of 100/10/10 for H₂O/CO₂/CO at ${r}_{{\rm{h}}}=1.5\;{\rm{AU}},$ approximately equal to the average observation listed in A'Hearn et al. (2012). Using the sublimation model of Cowan & A'Hearn (1979), this ratio corresponds to equivalent active areas of 6 km² for H₂O, 0.26 km² for CO₂, and 0.080 km² for CO. Other model quantities are summarized in Table 2. For the sublimation model, we assume a rapidly rotating nucleus with a visual albedo of 0.05, an infrared emissivity of 1.0, and the pole direction perpendicular to the orbit. Gas production rates are the product of the sublimation rate and the active area.

Water molecules have the shortest photodissociation length scale of the molecules in our study, but our apertures are no larger than 13% of this scale, so for simplicity, we neglect photodissociation. The continuum arising from dust, a source of noise, is modeled using Equation (3) with the following parameters: ${Af}\rho =2000\;{\rm{cm}}$ at 1 AU, scaling with ${r}_{{\rm{h}}}^{-2}$, $\epsilon {f}_{\mathrm{em}}/{{Af}}_{\mathrm{sca}}=3.5.$

Production rates and ${Af}\rho$ values derived from the gas and dust models are listed at approximately 1 AU steps in Table 3. We have selected epochs that would be within JWST's solar elongation constraints (85°–135°). The water production rate ($9\times {10}^{27}$ molecules s⁻¹) and ${Af}\rho$ (925 cm) at 1.5 AU are within a factor of two of actual measurements of the comet near perihelion (Schleicher et al. 2014; Bodewits et al. 2015). Comet Siding Spring's ${Af}\rho$ at 4 AU (pre-perihelion) observed by Li et al. (2014) is higher than our model by an order of magnitude (120 cm versus 2000 cm). Dynamically new comets tend to have shallow light curves upon approach to perihelion (Oort & Schmidt 1951; Whipple 1978), and we do not incorporate this aspect into our model.

Using the prototype NIRSpec exposure time calculator, we compute the integration time required to achieve a peak S/N of 10 for each band (Table 3) and plot it in Figure 2. For our low-resolution spectroscopy observations, we assumed each band may be approximated by a single line with a FWHM of 0.2 μm. Both H₂O and CO are detected in a few thousand seconds at production rates of $Q\gtrsim 5\times {10}^{25}$ molecules s⁻¹ out to ∼4.5 AU; CO₂ is detected in a few thousand seconds at $Q\gtrsim 1\times {10}^{25}$ molecules s⁻¹ out to ∼7 AU. Thus, JWST will easily be the best telescope for spectroscopic studies of comet activity at moderate and large heliocentric distance.

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Comet nuclei are aggregates of the planetesimals present in the outer solar system during the epoch of planet formation (Weissman et al. 2004; Belton et al. 2007). There is an open question concerning the homogeneity of accreted planetesimals for particular comets, i.e., are individual comets aggregates of a heterogeneous population of planetesimals formed over a range of times and distances (e.g., Weidenschilling 1997)? Are comets collisional fragments (e.g., Stern & Weissman 2001; Morbidelli & Rickman 2015) and less likely to be heterogeneous despite their origins? High spatial resolution images and spectral data cubes from flyby spacecraft have suggested comet volatiles are not uniformly distributed about nuclei (e.g., Feaga et al. 2007; A'Hearn et al. 2011), but the evidence for regions heterogeneous in dust properties relies on poorer resolution telescopic data, usually through multiple observations of a rotating comet (e.g., Ryan & Campins 1991; Wooden et al. 2004). A close approach (here, ${\rm{\Delta }}\lt 1$ AU) between a comet and JWST would allow us to observe coma features on $\lesssim 200$ km spatial scales, potentially revealing distinct active regions before they spatially mix in the coma. Such a study can test the heterogeneity of comet nuclei by observing and comparing multiple spatially resolved coma jet features.

JWST's MIRI will be able to simultaneously observe both coma dust and water gas. At $\lambda \gt 5$ μm, mid-IR spectroscopy reflects a coma's dust composition, grain sizes, and porosities through solid-state emission features and a thermal emission pseudo-continuum. We use the terms grain and aggregate interchangeably. They represent an entire particle of dust, which may be composed of smaller sub-units (the latter is implied for aggregate). Typical dust features include a broad plateau from 8 to 12 μm, primarily arising from anhydrous amorphous silicates (non-stochiometric olivine and pyroxene), and narrow emission peaks ($\lambda /{\rm{\Delta }}\lambda$ ∼ 10–20) from crystalline silicates, dominated by Mg-rich olivine (Wooden 2002; Hanner et al. 2004). MIRI also covers the ${\nu }_{2}$ water gas emission band at 6 μm, observed and studied in several comets with the Infrared Space Observatory and Spitzer Space Telescope (Crovisier et al. 1997; Woodward et al. 2007; Bockelée-Morvan et al. 2009). In addition, the NIRSpec instrument holds the potential to simultaneously detect emission from water gas and hydrocarbons, the latter via the aromatic C–H stretch at ∼3.3 μm and the aliphatic C–H stretch at ∼3.4 μm (see Li 2009).

We consider comet 46P/Wirtanen as an example exercise demonstrating the technical feasibility of an observing program designed to test coma heterogeneity. This comet has a close approach to JWST in 2018 December. In 2018 November, the comet is within the solar elongation constraints (85° and 135°) and quite bright, with integrated flux densities of the order of 1 Jy at 13 μm (05 radius aperture). However, rather than consider an observing window so soon after JWST's launch (2018 October), we instead consider the post-closest approach window starting 2019 March 13 (${r}_{{\rm{h}}}=1.56\;{\rm{AU}}$, ${\rm{\Delta }}=0.69$ AU) with non-sidereal rates of $\lesssim 53$'' hr⁻¹, well under the JWST limit of 108'' hr⁻¹.

Spatial–spectral maps of a comet's dust coma can be performed with either the Low-Resolution Spectrometer (LRS; $\lambda /{\rm{\Delta }}\lambda \sim 100$) or Medium-Resolution Spectrometer (MRS; $\lambda /{\rm{\Delta }}\lambda \sim 3000$) modes of MIRI. Typically, comet dust studies would use the LRS, because the spectral resolving power of the MRS is much greater than necessary to resolve solid-state emission features. However, we will design an observation for the MRS integral field units (IFUs), which can efficiently map a $3^{\prime\prime} \times 4^{\prime\prime}$ field of view and have a spectral resolving power appropriate for measuring individual lines in the ${\nu }_{2}$ water band.

For our model, we adopt an effective nucleus radius of 0.6 km (Lamy et al. 1998), a maximum ${Af}\rho$ of 380 cm (Farnham & Schleicher 1998), and a maximum water production rate Q(H₂O) = $1.6\times {10}^{28}$ molecules s⁻¹ at perihelion $q=1.05\;{\rm{AU}}$ (Bertaux et al. 1999). We also assume that the dust production rate scales with water production as ${r}_{{\rm{h}}}^{-4.9}$ (Bertaux et al. 1999).

The IFUs can obtain complete spectra from 5 to 28.5 μm in three exposures over a $3\buildrel{\prime\prime}\over{.} 0\times 3\buildrel{\prime\prime}\over{.} 9$ field of view, corresponding to 1500 km × 1900 km at the comet, with a spatial resolution of about 100 km per resolution element. For comparison, the current best spatial resolution of this comet obtained with mid-IR spectroscopy is 1300 km with Spitzer/IRS.

Comet Wirtanen's peak surface brightnesses estimated for the MRS IFUs are listed in Table 4. The surface brightness is an average within a 04 radius aperture (corresponding to approximately 10 resolution elements at 6 μm and a few resolution elements at 23 μm). Using the estimated MRS line sensitivities (in units of W m⁻² pixel⁻¹) and dividing by the unresolved line width for each module yields continuum sensitivity thresholds in units of flux density. These values are scaled by ${t}^{-1/2}$ to an integration time of 100 s and listed in Table 4. We expect high S/Ns in the central aperture, easily enabling mapping of the inner coma.

Table 4.  Comet 46P/Wirtanen Surface Brightness and MIRI MRS IFU Sensitivities

λ	FOV	Iλ	σ	S/N
(μm)	('')	(${10}^{-5}$ W m−2 μm−1 sr−1)	(${10}^{-5}$ W m−2 μm−1 sr−1)
6.4	$0.18\times 0.19$	1.1	0.11	10
9.2	$0.28\times 0.19$	2.9	0.05	60
14.5	$0.39\times 0.24$	3.2	0.01	320
22.5	$0.64\times 0.27$	1.6	0.02	80

Note. Computed for 2019 March 13 (${r}_{{\rm{h}}}=1.56\;{\rm{AU}}$, ${\rm{\Delta }}=0.69$ AU) in a 04 radius aperture and 100 s of integration time per module. λ is the central wavelength of the estimate, FOV is the field of view of the instrument's native resolution element, σ is the estimated 1σ continuum sensitivity, I is the modeled continuum surface brightness, and S/N is the signal-to-noise ratio per resolution element.

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For the H₂O band at 6 μm, we assume an effective g-factor of $2.4\times {10}^{-5}$ photons s⁻¹ molecule⁻¹ at 1 AU for the brightest lines, based on modeled Spitzer spectra of C/2003 K4 (LINEAR), 71P/Clark, and C/2004 B1 (LINEAR; Woodward et al. 2007; Bockelée-Morvan et al. 2009). These lines will be affected by optical depth effects, but introducing opacity is not necessary for our first-order feasibility exercise. Following Equation (4), we predict a total line flux $\sim 2\times {10}^{-18}$ W m⁻² in a 04 radius aperture, or about $2\times {10}^{-19}$ W m⁻² pixel⁻¹. The lines will be easily detected above the continuum ($\sim {10}^{-20}$ W m⁻² pixel⁻¹) with the MRS IFUs. The morphology of the water gas would be used to locate active areas on the nucleus and to identify dust that may originate from those areas. Additional context with CO₂ and CO may be obtained with immediate follow-up observations with the near-IR spectrometer. Comparisons of a particular active area's dust composition to that of the ambient coma or of other regions can be used to test the heterogeneity of the nucleus.

As preserved leftovers from the formation of the solar system, comets serve as one of the best probes for studying primitive water ice in the form it may have existed in the early outer solar system. Thus, observations of water ice in comets may allow us to test the accretion processes that led to the formation of comet nuclei and therefore of planets (e.g., Greenberg & Li 1999). Contrasting coma ice properties to observations of ice on comet surfaces will allow us to study coma–nucleus interactions and nucleus surface evolution.

Water ice has absorption bands in the near-IR at 1.5, 2.0, and 3.0 μm. The relative strength and shape of these features provides information on aggregate porosities, presence of dust within the ice, total abundance, and the size of the scattering units (following Section 3.2, we use the term grain and aggregate interchangeably). Laboratory measurements show that infrared water-ice absorption bands change position and shape as a function of phase (crystalline or amorphous) and temperature: e.g., crystalline water ice differs from its amorphous counterpart by the presence of a sharp and narrow feature at 1.65 μm apparent at $T\lesssim 200$ K (Grundy & Schmitt 1998). The best approach to investigate water-ice physical properties is through near-IR (1–5 μm) spectroscopy.

Water ice has been observed in comae using ground- and space-based telescopes and flyby spacecraft (e.g., Davies et al. 1997; Kawakita et al. 2004; Yang et al. 2009; Protopapa et al. 2014). The small sample of comae detections presently available has revealed a range of water-ice characteristics: μm and sub-μm water-ice particles have been identified, as well as one case of crystalline water ice (e.g., Yang et al. 2009; Yang & Sarid 2010; Protopapa et al. 2014; Yang et al. 2014). However, the limited number of detections prevents development of a classification scheme or taxonomy based on water-ice properties. The sample population is too small to apply statistical analyses with confidence, thereby limiting our understanding of the origins of this diversity. It may relate to the different mechanisms responsible for delivering water ice from the interior into the coma (sublimation of more volatile ices, e.g., CO₂, CO, or through large outbursts in activity). Alternatively, it may be the outcome of a preserved comet-to-comet heterogeneity. Establishing these connections is crucial if water-ice properties are to be used as observationally imposed boundary conditions on comet nucleus formation models.

On nucleus surfaces, however, water ice has only been observed with flyby and orbiting spacecraft. The observations of ice on the surfaces of comets 9P/Tempel 1 and 103P/Hartley 2 point toward sub-units with sizes of the order of 10–100 μm (Sunshine et al. 2006, 2012). This is much larger than the coma ice summarized above and the ice excavated from the interior of Tempel 1 (Sunshine et al. 2007). Thus, Sunshine et al. (2006) hypothesize that this ice is more likely due to re-condensation of water gas, rather than recently uncovered interior ice. Observations of bare nuclei can help test when this re-condensation occurs: does it require constant replenishment from an active source, or is it deposited by low activity levels as a comet recedes from the Sun? Complicating matters, Capaccioni et al. (2015) report the detection of a broad absorption band at 2.9–3.6 μm in Rosetta observations of the surface of comet 67P/Churyumov–Gerasimenko. The absorption band has a peak depth of 20% located at 3.2–3.3 μm. They suggest this feature is due to the presence of aromatic and aliphatic C–H bonds, carboxylic groups, and/or alcoholic groups. The absorption feature has not been reported on the surfaces of 9P/Tempel 1 or 103P/Hartley 2 (Sunshine et al. 2006; A'Hearn et al. 2011). Whether absorption features are due to water ice or organic molecules, the study of comet surfaces at 3–4 μm is best addressed through space-based missions or observatories.

NIRSpec is ideal for the study of water ice in comets. The prism mode covers 0.7–5 μm at a spectral resolving power of $R\sim 100,$ ideal not only to detect the broad absorption features of surface and coma ice but also to determine its chemical phase (amorphous or crystalline). The instrument's higher spectral resolving powers ($R\sim 1000$) may be sensitive to trapped CO₂ or other volatiles. Below, we summarize observations of a distant comet nucleus and coma with this instrument to illustrate future science opportunities.

3.3.1. Surface Ice

3.3.2. Water Ice in Comet Comae

JWST's capabilities will transform our understanding of faint and/or weakly active comets by enabling observations that were heretofore at the limit of experimental techniques. Such comets comprise several categories:

• 1.  
  Main belt comets (MBCs). Activity recurring from orbit to orbit has been identified in a handful of MBCs (e.g., Hsieh & Jewitt 2006; Hsieh et al. 2011, 2015), but the mechanism for this activity is unknown. To date, there have been no successful searches for signatures of volatiles on MBCs.
• 2.  
  Nearly inactive and dormant comets. A large number of suspected dead comets (inactive objects in comet-like orbits) have been identified in the asteroid population (e.g., Jewitt 2005; Jenniskens 2008), and occasionally asteroids show cometary activity. For example, Spitzer/IRAC observations of "asteroid" (3552) Don Quixote exhibited signs of CO₂ outgassing (Mommert et al. 2014). In addition, there are known comets with extremely weak or only sporadic activity, e.g., 209P/LINEAR 41 (Schleicher 2014) or 107P/Wilson–Harrington (Fernández et al. 2007). High-sensitivity observations of volatiles can help confirm or better characterize their cometary natures.
• 3.  
  Very small comets. The population of small near-Sun comets is generally thought to be $\lt 50\;{\rm{m}}$ in radius (Knight et al. 2010), too small or weakly active to be observed beyond the solar coronagraphs on SOHO or STEREO. Little is known about these small bodies, including what drives their activity: normal cometary activity via sublimation of ices or the sublimation of dust and refractory grains due to the extreme temperatures experienced near perihelion (equilibrium temperatures exceeding 1000 K; Mann et al. 2004).
• 4.  
  Distant comets. Many comets show continuous activity outside the so-called water-ice line. Their activities may be driven by the more volatile ices CO₂ or CO (Meech & Svoren̆ 2004; Meech et al. 2013; Stevenson et al. 2015), or by the exothermic annealing of water ice from amorphous to crystalline states (Meech et al. 2009; Jewitt 2009). Owing to their large distances, studies of activity are generally limited to observations of dust comae and tails.

A common theme in the above cases is faint activity. NIRCam imaging would be capable of searching for signs of very weak activity (coma and/or tail, both dust and gas) and of efficiently characterizing nucleus properties such as size, elongation, albedo, and beaming parameter. NIRSpec might be able to spectroscopically detect the driving volatiles at production rates lower than previously achievable. The comet–asteroid transition is currently poorly understood, and such results, whether of severely processed Sun-grazing/Sun-skirting comets, dormant comets, distant comets, or activated asteroids, would yield insight into the ongoing evolutionary processes of our solar system.

To demonstrate JWST's capabilities for characterizing activity in faint comets, we consider observations of main belt comet P/2010 R2 (La Sagra) in late 2021 August (${r}_{{\rm{h}}}=2.7\;{\rm{AU}},\;$ ${\rm{\Delta }}=1.9$ AU). This observing window is post-perihelion, during a period when comet La Sagra has been observed to be active with ${Af}\rho$ near 50 cm (Hsieh et al. 2012). Estimates of the dust production rate by Moreno et al. (2011) and Hsieh et al. (2012) span from 0.1 to 4 kg s⁻¹. Assuming a dust-to-gas mass production ratio of 1:1 and assuming water sublimation is driving the activity, this corresponds to a water production rate with an order of magnitude of 10²⁵ molecules s⁻¹.

For this exercise, we use NIRSpec to detect the ${\nu }_{3}$ water band at 2.7 μm, one of the strongest water bands in comets (Crovisier & Encrenaz 1983) and one that cannot be observed from the ground (Bockelée-Morvan et al. 2004). In a small aperture of radius 02, the estimated continuum flux density at 2.7 μm is $1.7\times {10}^{-18}$ W m⁻² μm⁻¹, and the water band flux is $2.3\times {10}^{-20}$ W m⁻². With the NIRSpec prototype exposure time calculator and the $R\sim 100$ prism, we model the water band as a single 0.2 μm wide line. In a 1 hr exposure, the peak of the line is detected above the continuum with an S/N of 4. Thus, we can expect JWST to provide one of the best tests for the drivers of MBC activity.