Terrestrial deuterium-to-hydrogen ratio in water in hyperactive comets
D. C. Lis, D. Bockelée-Morvan, R. Güsten, N. Biver, J. Stutzki, Yan Delorme, C. Durán, H. Wiesemeyer, Y. Okada
AAstronomy & Astrophysics manuscript no. Wirtanen-Final2 c (cid:13)
ESO 2019April 24, 2019 L etter to the E ditor Terrestrial deuterium-to-hydrogen ratio in water in hyperactivecomets
Dariusz C. Lis , , Dominique Bockelée-Morvan , Rolf Güsten , Nicolas Biver , Jürgen Stutzki , Yan Delorme ,Carlos Durán , Helmut Wiesemeyer , Yoko Okada Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Drove Drive, Pasadena, CA 91109, USA Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, LERMA, F-75005, Paris, France LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, 5 placeJules Janssen, 92195 Meudon, France Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany I. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Germanyc (cid:13)
ABSTRACT
The D / H ratio in cometary water has been shown to vary between 1 and 3 times the Earth’s oceans value, in both Oort cloud cometsand Jupiter-family comets originating from the Kuiper belt. This has been taken as evidence that comets contributed a relativelysmall fraction of the terrestrial water. We present new sensitive spectroscopic observations of water isotopologues in the Jupiter-family comet 46P / Wirtanen carried out using the GREAT spectrometer aboard the Stratospheric Observatory for Infrared Astronomy(SOFIA). The derived D / H ratio of (1 . ± . × − is the same as in the Earth’s oceans. Although the statistics are limited, weshow that interesting trends are already becoming apparent in the existing data. A clear anti-correlation is seen between the D / H ratioand the active fraction, defined as the ratio of the active surface area to the total nucleus surface. Comets with an active fraction above0.5 typically have D / H ratios in water consistent with the terrestrial value. These hyperactive comets, such as 46P / Wirtanen, requirean additional source of water vapor in their coma, explained by the presence of subliming icy grains expelled from the nucleus. Theobserved correlation may suggest that hyperactive comets belong to a population of ice-rich objects that formed just outside the snowline, or in the outermost regions of the solar nebula, from water thermally reprocessed in the inner disk that was transported outwardduring the early disk evolution. The observed anti-correlation between the active fraction and the nucleus size seems to argue againstthe first interpretation, as planetesimals near the snow line are expected to undergo rapid growth. Alternatively, isotopic properties ofwater outgassed from the nucleus and icy grains may be di ff erent due to fractionation e ff ects at sublimation. In this case, all cometsmay share the same Earth-like D / H ratio in water, with profound implications for the early solar system and the origin of Earth’soceans.
Key words.
Comets: general – Comets: individual: 46P / Wirtanen - Submillimeter: planetary systems – Astrochemistry – Kuiperbelt: general
1. Introduction
One of the key questions for modern astrophysics and planetaryscience concerns the development of the conditions of habitabil-ity in planetary systems, such as the early protosolar nebula. Wa-ter, an essential ingredient for carbon-based life as we know it(Westall 2018), is formed primarily via surface reactions in icymantles of interstellar dust grains (the gas-phase chemistry onlybecomes e ffi cient at temperatures above ∼
300 K). These grainssubsequently find their way through dense protostellar cores toprotoplanetary disks, where they are partially processed ther-mally in the warm inner disk before being locked up in smallbodies such as comets or asteroids (van Dishoeck et al. 2014).In the standard model of the protosolar nebula, the tempera-ture in the terrestrial planet forming zone was too high for wa-ter ice to survive. Consequently, the Earth accreted dry and thepresent-day water would have been delivered in a later phase,together with organics, by external sources such as comets orasteroids (O’Brien et al. 2018). An alternative explanation isin situ, early delivery of Earth’s water, either incorporated intoolivine grains or through the oxidation of an early hydrogen at- mosphere by FeO in the terrestrial magma ocean, both of whichmay have contributed to some degree (see O’Brien et al. 2018and references therein).The D / H ratio provides key constraints on the origin andthermal history of water molecules. Deuterium was produced inthe Big Bang, with an abundance of about 2 . × − with respectto hydrogen (Cooke et al. 2014). The reference protosolar D / Hratio in hydrogen is 2 . × − , which is close to the Big Bangvalue (Geiss & Gloeckler 1998). However, in the cold, dense,CO-depleted interstellar medium, deuterium atoms are preferen-tially sequestered in heavy molecules due to di ff erences in zero-point vibrational energies (Ceccarelli et al. 2014). Consequently,the D / H ratio in heavy molecules may be enhanced by orders ofmagnitude, and doubly or even triply deuterated species havebeen detected (Lis et al. 2002; Parise et al. 2004). Deuterationin water is less extreme than in other molecules, with water D / Hratios of order 0.001—0.01 typically measured in low-mass pro-tostars similar to our Sun (Ceccarelli et al. 2014). Subsequentisotopic exchanges between water molecules and molecular hy-drogen in the warm inner disk drives the ratio back toward theprotosolar value (Drouart et al. 1999).
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The highest solar system D / H ratios in water, about 7 . × − measured in LL3 matrix clays or R chondrites (Deloule et al.1998; Alexander et al. 2012; McCanta et al. 2008), are close tothe interstellar medium values. The D / H ratio in Earth’s oceanwater, the Vienna Standard Mean Ocean Water (VSMOW), issignificantly lower, (1 . ± . × − , although still en-hanced with respect to the protosolar ratio in hydrogen. How rep-resentative this value is for the bulk of Earth’s water is a subjectof discussion in the light of recent measurements of a low D / Hratio in deep mantle materials (Hallis 2015). Currently, carbona-ceous chondrites, in particular CI and CM types, appear to bestmatch the terrestrial D / H ratio (Alexander et al. 2012).Comets are the most primitive volatile-rich bodies in thesolar system. The D / H ratio has been measured in a handfulof Oort cloud comets, with typical values of about twice VS-MOW (Bockelée-Morvan et al. 2015). The
Herschel
Space Ob-servatory provided the first measurements of the D / H ratio intwo Jupiter-family comets, 103P / Hartley (Hartogh et al. 2011)and 45P / Honda-Mrkos-Pajdušáková (Lis et al. 2013), both con-sistent with VSMOW. A relatively high D / H ratio, three timesVSMOW, was subsequently measured by
Rosetta in anotherJupiter-family comet 67P / Churyumov-Gerasimenko (Altwegg etal. 2015). The VSMOW D / H value measured in the Oort cloudcomet C / / H ratio in cometary water havebeen interpreted as reflecting their formation in di ff erent regionsof the solar nebula. Models considering isotopic exchanges in anevolving accretion disk predict an increase in the D / H ratio withincreasing distance from the star (Drouart et al. 1999). The sameisotopic diversity observed in both Oort cloud and Jupiter-familycomets could then be explained by the recent evidence that theformation zones of the two families largely overlapped and ex-tended over a broad range of heliocentric distances (Brasser &Morbidelli 2013).In this Letter we present a new measurement of the D / H ra-tio in the Jupiter-family comet 46P / Wirtanen carried out usingthe Stratospheric Observatory for Infrared Astronomy (SOFIA).This comet, which was the initial target of the
Rosetta mission,has an orbital period of 5.439 yr and made a close approachto Earth (0.08 au) a few days after its perihelion passage on2018 December 12 at 22:20 UT (perihelion distance q = / Wirtanen belongs to the category of hyperac-tive comets, emitting more water molecules than can be expectedgiven the size of the nucleus, which is explained by the presenceof sublimating water-ice-rich particles within the coma. Using asample of comets with known D / H ratios in water and nucleussizes, we show that a remarkable correlation is present betweenthe D / H ratio and hyperactivity.
2. SOFIA observations of comet 46P/Wirtanen
Previous spectroscopic detections of HDO were obtained fromobservations of ro-vibrational and rotational transitions in theinfrared and submillimeter domains (Bockelée-Morvan et al.2015). Low-energy rotational transitions of water are not acces-sible from the ground or suborbital platforms. However, the at-mosphere at stratospheric altitudes is su ffi ciently transparent atthe frequencies of water isotopologues. In particular, the 547 and509 GHz 1 , − , transitions of H O and HDO, previously ob-served in several comets by
Herschel , are now accessible fromSOFIA and can be used to accurately measure the D / H isotopicratio. This requires assumptions about the O / O isotopic ra-tio, which has been shown to be relatively uniform in comets, 500 ±
50, and close to the terrestrial ratio (Bockelée-Morvan etal. 2015).The close 2018 December apparition of comet 46P / Wirtanenprovided an excellent opportunity to demonstrate the utility ofSOFIA for D / H measurements. Observations presented herewere carried out during five SOFIA flights between 2018 De-cember 14 and 20 UT. During each flight, comet Wirtanen wasobserved in a single flight leg of about 3 hours (the longest timeallowed by the flight planning). A typical observing sequenceconsisted of a 7 – 17 min on-source integration at the frequencyof the 1 , − , transition of H O, followed by a 26 – 34 minon-source integration at the frequency of the 1 , − , transitionof HDO. Monitoring the H O emission was important for aver-aging out possible variations in the water production rate duringthe period of the observations. Additional observational detailsare provided in Appendix A.1.Average spectra of the H
O and HDO transitions are shownin Figure 1. The integrated H
O line intensity is 305 ± − on the main beam brightness temperature scale (15.3 σ , average of all observations). The corresponding integratedline intensity of the HDO emission is 27 ± . − (3.1 σ ). The resulting HDO / H O line intensity ratio is 0 . ± . . ± .
009 in comet 103P / Hartley (Hartogh etal. 2011). To model the water isotopologue emission, we used acometary excitation model similar to that previously applied to
Herschel observations (Hartogh et al. 2011; Lis et al. 2013),and assumed a O / O isotopic ratio of 500 (see AppendixA.2). The resulting D / H ratio in water is (1 . ± . × − ,where the uncertainty includes statistical, calibration, modeling,and O / O isotopic ratio uncertainties, combined in quadrature.Comet 46P / Wirtanen is thus the third Jupiter-family comet witha D / H ratio consistent with the Earth’s ocean value.
3. Correlation between the D/H ratio andhyperactivity
When both the water production rate and the nucleus size areknown, it is possible to compute the active fractional area ofthe nucleus (or active fraction) by dividing the active area bythe total nucleus surface. Comets with high active fractions arereferred to as hyperactive comets. This hyperactivity requiresan additional source of water vapor, explained by the pres-ence of subliming icy grains in the coma that have been ex-pelled from the nucleus. The archetype of a hyperactive comet is103P / Hartley, studied by the Deep Impact spacecraft, for whichboth icy grains and water overproduction were observed (Pro-topapa et al. 2014; Kelley et al. 2015, 2013). Interestingly,the three Jupiter-family comets with a terrestrial D / H ratio, 46P,103P, and 45P, all belong to the category of hyperactive comets.We therefore investigated quantitatively how the D / H ratio cor-relates with the active fraction using a sample of comets fromthe literature.The active fraction was computed using a sublimation modeland water production rates derived from Lyman- α observationsby the Solar Wind Anisotropies (SWAN) instrument aboard theSolar and Heliocentric Observatory (SOHO) (Combi et al. 2019)(see Appendix A.3). Since the SWAN field of view is large, wa-ter production rates include direct production from the nucleussurface and from subliming icy grains. We computed the activefraction using both production rates at 1 au and at perihelion.In the sample of comets with D / H determinations (or signifi-cant upper limits), only eight comets have a known nucleus size,most of them from spacecraft images or radar measurements
Article number, page 2 of 9is et al.: D / H ratio in hyperactive comets
Fig. 1.
Spectra of the water isotopologues in comet 46P / Wirtanen. The1 , − , H O and HDO transitions are shown in the upper and lowerpanels, respectively. The intensity scale is the main beam brightnesstemperature. The spectral resolution is 0.24 MHz, corresponding to ap-proximately 0.14 km s − . A Gaussian fit to the H O spectrum (greenline, upper panel) gives a line center velocity v o = . ± .
04 km s − and a full width at half maximum line width ∆ v = . ± .
09 km s − .Vertical dotted lines indicate the velocity range used in computations ofthe integrated line intensities (–1.04 to 1.2 km s − ). The green line inthe lower panel shows the expected HDO line intensity assuming D / Hequal to VSMOW. The inset in the upper panel shows the evolution ofthe H
O integrated line intensity as a function of UT time. Error barsinclude statistical and calibration uncertainties, combined in quadrature,and the gray shaded area shows the corresponding uncertainty on theaverage H
O line intensity (ensemble average). (Appendix A.3): 1P / Halley, 8P / Tuttle, 45P / Honda-Mrkos-Pajdušáková, 46P / Wirtanen, 67P / Churyumov-Gerasimenko,103P / Hartley, C / / / ff ective radius has been constrainedto be < ff ective nucleusradius of comet 46P / Wirtanen is estimated to 0.63 km fromradar imaging. Figure 2 shows a striking anti-correlation between the D / Hratio and the active fraction computed at perihelion. The sametrend for a D / H ratio decreasing towards the telluric value withincreasing active fraction is observed when using the active frac-tion at 1 au from the Sun (Fig. A.1). Values for the D / H ratios aretaken from the review of Bockelée-Morvan et al. (2015), exceptfor comet C / ± × − (Appendix A.4). This long-periodcomet displayed outbursts and fragmentation events over a fewmonths before and after perihelion, when it released icy grainsand chunks, hence the large active fraction (Fig. 2, Combi et al. https: // uanews.arizona.edu / story / ua-researcher-captures-rare-radar-images-comet-46pwirtanen Fig. 2. D / H ratio in cometary water as a function of the active fractioncomputed from the water production rates measured at perihelion. Theuncertainties on the active fraction (horizontal error bars) include a 30%uncertainty on the water production rates (Combi et al. 2019) and theuncertainty on the nucleus size. The color of each symbol indicates acomet; see legend at right, where the dynamical class is also indicated:Oort cloud (OC) or short-period Jupiter-family (JF) comets. The bluehorizontal line corresponds to the VSMOW D / H value. The upper limitfor the D / H ratio in comet 45P is indicated by a downward arrow andthe lower limit for the active fraction in comet 2009P1 by a right arrow.The dash-dotted line shows the expected D / H assuming two sources ofwater: D-rich (3.5 × VSMOW) from the nucleus and D-poor (VSMOW).Comets with an active fraction equal to 0.08 are assumed to release onlyD-rich water. / H ratio reported by Bockelée-Morvan et al. (1998)of (2.9 ± × − was measured during an outburst, with alarge uncertainty mainly related to the scatter in reported wa-ter production rates. For this new evaluation, we used updated Q (H O) values (Combi et al. 2005).We investigated the processes responsible for the excess oficy grains in hyperactive comets by considering a sample of 18comets with determined nucleus sizes and water production ratesat perihelion (Appendix A.3). As shown in Fig. 3, hyperactiv-ity is not observed for comets with e ff ective nucleus radii largerthan 1.2 km (12 comets in our sample), whereas comets withsmaller nuclei, though underrepresented considering the size dis-tribution of cometary nuclei (Fernández et al. 2013), are all hy-peractive. This suggests that the large amount of subliming icyaggregates or chunks in hyperactive comets is not related to ahigher ice / refractory content. A comparison between the well-studied comets 67P and 103P shows that even though the nu-cleus gas production is much lower in 103P than in 67P, owingto a smaller nucleus size (Fig. 3), the mass loss rate in chunksis larger for 103P (Fulle et al. 2019), thereby explaining its hy-peractivity. Estimates of the refractory-to-ice mass ratio in 67P(Herique et al. 2016; Pätzold et al. 2019; Fulle et al. 2019)converge to values between δ = δ = ff et al 2019). However,it remains to be demonstrated why small nuclei eject chunks soe ffi ciently. Article number, page 3 of 9 & A proofs: manuscript no. Wirtanen-Final2
Fig. 3.
Active fraction at perihelion as a function of the nucleus size fora sample of 18 comets. The uncertainties in the active fraction (verti-cal error bars) include a 30% uncertainty on the water production rates(Combi et al. 2019) and the uncertainty on the nucleus size. The hori-zontal error bars show the uncertainties in the nucleus size. Green sym-bols refer to comets for which the D / H ratio in water has been measured.
4. Discussion
Under the hypothesis that hyperactive comets belong to a pop-ulation of ice-rich comets, their Earth-like D / H ratio would beconsistent with their formation in the protoplanetary disk justoutside the snow line where a large enhancement in the ice sur-face density is expected, thus favoring planetesimal formation(Schoonenberg & Ormel 2017). This would explain the sur-prising result from
Rosetta that ice-poor, D-rich comets, suchas comet 67P, are less rich in water than material from carbona-ceous meteorites formed closer to the Sun (Fulle et al. 2019).Alternatively, these hyperactive comets could have formed in theoutermost regions of the solar nebula. Indeed, modeling showsthat a non-monotonic dependence of the D / H ratio in the solarnebula may be expected. The ratio would decrease again in theouter regions of the disk, because water molecules that under-went isotopic exchanges at high temperatures near the youngstar would have been transported outward during the early diskevolution (Yang et al. 2013). The anti-correlation between hy-peractivity and nucleus size appears inconsistent with the firstexplanation as planetesimals near the snow line are expected toundergo rapid growth.An alternative explanation is that the isotopic properties ofwater outgassed from the nucleus surface and icy grains maybe di ff erent, owing to fractionation processes during the subli-mation of water ice. The observed anti-correlation can be re-produced with two sources of water contributing to the mea-sured water production rate and the active fraction: D-rich watermolecules released from the nucleus and an additional source ofD-poor water molecules from sublimating icy grains (see dash-dotted line in Fig. 2). Laboratory experiments on samples of pureice show small deuterium fractionation e ff ects (Lécuyer et al.2017). In experiments with water ice mixed with dust, the re-leased water vapor is depleted in deuterium, explained by pref-erential adsorption of HDO on dust grains (Moores et al. 2012).This e ff ect goes in the opposite direction to the observed trend,while conversely the VSMOW D / H value from subliming icygrains is likely representative of buried nucleus water ice. Al-ternatively, a non-steady-state regime of water ice sublimation could explain the factor 2 − / H O values measured for comet 67P at di ff erent periodsare very uniform (Altwegg et al. 2017).
5. Conclusion
Enlarging the number of accurate D / H measurements in bothJupiter-family and Oort cloud comets is required to better con-strain the observed correlation. Taking these measurements fromthe ground is challenging. Nearly simultaneous spectroscopicobservations of low-energy rotational lines of H
O and HDOin a matching field of view encompassing a large fraction of thecoma using the GREAT spectrometer aboard SOFIA can play akey role in this endeavor. In this context, the next close appari-tion of comet 67P / Churyumov-Gerasimenko in 2021 Novemberwill o ff er an excellent opportunity to re-measure the D / H ratio inthis comet using spectroscopic techniques.The understanding of the observed correlation calls for de-tailed investigations of the mechanisms leading to dust andchunk ejection, and cometary hyperactivity. Further experimen-tal and modeling work on evaporative fractionation is alsoclearly needed, and may ultimately establish that all cometsshare the same Earth-like water D / H ratio, with profound im-plications on the early solar system and the origin of the Earth’soceans.
Acknowledgements.
Based on observations made with the NASA / DLR Strato-spheric Observatory for Infrared Astronomy (SOFIA). SOFIA is jointly oper-ated by the Universities Space Research Association, Inc. (USRA), under NASAcontract NAS2-97001, and the Deutsches SOFIA Institut (DSI) under DLR con-tract 50 OK 0901 to the University of Stuttgart. GREAT is a development bythe MPI für Radioastronomie and the KOSMA / Universität zu Köln, in cooper-ation with the DLR Institut für Optische Sensorsysteme, financed by the partic-ipating institutes, by the German Aerospace Center (DLR) under grants 50 OK1102, 1103, and 1104, and within the Collaborative Research Centre 956, fundedby the Deutsche Forschungsgemeinschaft (DFG). Mixers for Channel 1 of the4GREAT (4G-1) instrument have been designed and developed by LERMA (Ob-servatoire de Paris, CNRS, Sorbonne Université, Université de Cergy-Pontoise)in the framework of the
Herschel / HIFI project, with funding from the CNES. Partof this research was carried out at the Jet Propulsion Laboratory, California In-stitute of Technology, under a contract with the National Aeronautics and SpaceAdministration. We thank the SOFIA project o ffi ce for their excellent supportand for adapting the operations and engineering support to the visibility con-straints of the comet. We thank J. Blum, M. Fulle, and A. Morbidelli for theuseful discussions. Note added in proof:
After the present manuscript was acceptedfor publication, it was brought to our attention that the corre-lation between the active fraction and the nucleus size was in-dependently found by Sosa & Fernández (2011, MNRAS 416,767).
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Appendix A: Appendix
Appendix A.1: Observations
The observations of comet 46P / Wirtanen reported here were car-ried out using the GREAT heterodyne spectrometer (Heymincket al. 2012) aboard SOFIA during five flights between 2018 De-cember 14 and 20 UT, out of Palmdale, CA, USA. The instru-ment was operated in its upGREAT HFA / / ff erent frequencies.The lowest frequency band, 4G-1, was used for the observa-tions reported here. The tuning setup and the basic instrumentcharacteristics are summarized in Table A.1. Although severalother transitions of interest were covered in the higher-frequencychannels, only OH was detected at a low signal-to-noise ratio,and the other upper limits are not constraining owing to the muchhigher system temperatures at these frequencies.The instrument was operated in double-beam chopped mode,with a chopper throw of 200 (cid:48)(cid:48) , at a rate of 2.5 Hz. The comet wastracked using an ephemeris based on the orbital solution 181-11generated using JPL Horizons . Pointing was established by thetelescope operators directly on the optical core of the comet to anaccuracy of 2 – 3 (cid:48)(cid:48) . The local oscillator frequency was updatedevery 4 minutes according to the ephemeris, introducing a max-imum velocity tracking error of about 0.002 km s − . Prior to theflight series, the optical axis of the GREAT instrument had beenaligned to the optical imagers by observations of Mars. The mainbeam coupling e ffi ciencies, also determined from observationsof Mars, and the di ff raction limited half-power beam widths arelisted in Table A.1. The observations were performed at flight al-titudes between 40,000 and 43,000 feet. Atmospheric conditionswere typical for late autumn flights out of Palmdale, CA, with aresidual water vapor column of about 15–20 µ m, which resultedin typical single-sideband system temperatures T sys of about 300K (Table A.1).The calibration at the frequencies of the HDO and H O linesis challenging. Locally, the lines are a ff ected by the proximityof their rather narrow telluric counterparts, shifted by about ± − at the time of observation. Moreover, the transmission atthe H O frequency is strongly a ff ected by the broad absorptionof the nearby telluric H O line at 557 GHz (50% transmissiononly). The spectra were corrected for atmospheric losses follow-ing the usual calibration scheme (Pickett et al. 1998) based ontwo load signals (one at ambient temperature and one at a coldtemperature) to determine the instrument gain and a blank skysignal (chopper o ff phase), to which the atmospheric model wasfit in order to correct the observed signal to outside the atmo-sphere. The resulting calibration uncertainties at the frequenciesof 509 and 547 GHz are 10% and 15%, respectively.Calibrated spectra provided by the instrument pipeline werefurther reduced and analyzed using the IRAM Gildas software .A linear baseline was first subtracted from each scan and theresulting spectra were then averaged with 1 / σ weighting by ra-diometric noise. The observing log is shown in Table A.2. Theheliocentric and geocentric distance of the comet changed onlyslightly during the period of the observations, with average val-ues of 1.058 and 0.079 au, respectively. The total on-source inte-gration time is 64 and 150 min for H O and HDO, respectively.There is some evidence for day-to-day variations in the H
Oline intensity (the intensity on December 19 UT seems lowercompared to the other days; see inset in the upper panel of Fig. https: // ssd.jpl.nasa.gov / horizons.cgi http: // / IRAMFR / GILDAS
O wereobserved on each flight and we do not expect day-to-day vari-ations in the isotopic ratio, we use the average spectra in thesubsequent analysis.
Appendix A.2: Modeling
To convert the observed line intensities into molecular produc-tion rates, we used an excitation model similar to that used inour earlier
Herschel studies (Hartogh et al. 2011; Lis et al.2013). We computed several models with di ff erent assumptionsfor the collisions with electrons. We used electron density fac-tors x ne =
0, 0.1, and 0.2 and a contact surface scaling factor X re = . / Hartley. We also computed models with constant tempera-tures of 40 and 60 K, consistent with ground-based methanol ob-servations carried out by members of our team using the IRAM30m telescope. The maximum di ff erence in the isotopic ratios re-trieved using the various models is 15%. In our analysis we usedthe average molecular production rates provided by the variousmodels with a conservative modeling uncertainty of 10%.The observed line intensities lead to average HDO and H Oproduction rates of (2 . ± . × s − and (1 . ± . × s − , respectively, where the uncertainties include the statisticaland calibration uncertainties, and a 10% modeling uncertainty,combined in quadrature. Assuming a O / O isotopic ratio of500 ±
50, we derive a H
O production rate of (7 . ± . × s − . The resulting D / H ratio in water, (1 . ± . × − , is closeto the Earth’s ocean value. The uncertainty includes a 10% un-certainty for the O / O isotopic ratio, combined in quadraturewith the statistical, calibration, and modeling uncertainties.
Appendix A.3: Computations of the active fraction
To compute the active fractional area, we used the sublimationmodel of Cowan & A’Hearn (1979) for a rotational pole pointedat the Sun, which is identical to both the non-rotating case andto the case of zero thermal inertia. This model is appropriate, ascometary nuclei have low thermal inertia (Gulkis et al. 2015).We use tabulated values for the average water sublimation rateper surface unit, Z , as a function of the heliocentric distance, r h .Calculations are carried out for a Bond albedo of 0.05 and 100%infrared emissivity. At r h = Z = . × mol s − m − . Theactive area ( AA ) is obtained by dividing the water production rateby Z , and the active fractional area is obtained by dividing AA by the nucleus surface area (4 π r N , where r N is the e ff ective nu-cleus radius). We note that the derived active areas only providea crude estimation of the ice exposed to the solar radiation, be-causethe utilized sublimation model is simplistic. For example, theactive fractions derived here di ff er by a large but constant factorfrom those computed assuming rapidly rotating nuclei (Combiet al. 2019).We consider water production rates Q (H O) derived fromLyman- α observations by the Solar Wind Anisotropies (SWAN)instrument aboard the Solar and Heliocentric Observatory Article number, page 6 of 9is et al.: D / H ratio in hyperactive comets
Table A.1.
Instrument tuning and performance.
Transition ν IF c T sys Θ η mb (GHz) (GHz) (K) ( (cid:48)(cid:48) )H O (1 , − , ) 547.676440 5.4 U 317 50.3 0.63HDO (1 , − , ) 509.292420 6.2 / ffi ciency. Table A.2.
SOFIA observations of comet 46P / Wirtanen.
Flight UT Time r h ∆ t (H O) σ (H O) t (HDO) σ (HDO)(hr) (au) (au) (min) (mK) (min) (mK)1 Dec 14, 4.89-7.47 1.056 0.079 16.5 80 29.2 432 Dec 17, 7.56-9.68 1.057 0.078 7.2 125 30.8 383 Dec 18, 9.59-12.17 1.058 0.078 13.8 112 30.3 374 Dec 19, 9.78-12.00 1.059 0.079 14.9 85 25.6 425 Dec 20, 9.83-12.33 1.060 0.081 11.6 105 34.1 31Entries in the table are flight number, UT range in hours, average heliocentric and geocentric distance of the comet (au) as given bythe ephemeris, total on-source integration time (minutes), and the resulting rms noise level in a 0.14 km s − velocity channel (mK)for H O and HDO. The comet reached perihelion on December 12 at 22:20 UT and made the closest approach to the Earth onDecember 16 at 13:06 UT. At a 0.08 au geocentric distance, the field of view on the comet was about 3000 km.(SOHO) (Combi et al. 2019). Over 90% of the observed hydro-gen atoms are produced by H O or its photodissociation prod-uct OH. We use the reported absolute water production rates at r h = / post-perihelion power laws with r h to de-rive water production rates at perihelion by averaging the pro-duction rates deduced from pre- and post-perihelion laws. Forsome short-period comets, the SWAN survey includes multipleapparitions (e.g., 1997 and 2002 for 46P). In this case, we usedthe average results for multiple apparitions (Table 4 of Combi etal. 2019). The SWAN survey does not include comet 1P / Halley,for which we assumed Q(H O) = × s − ( r h = . r − h variation for Q(H O); Feldman et al. 1997). Water pro-duction rates used to compute the active fractions are listed inTable A.3 (values at perihelion). For consistency, we did not con-sider the water production rate of 46P derived from the SOFIA2018 observations (Sect. A.1), which is about a factor of twolower than the SWAN value (Table A.3), possibly because ofthe smaller projected field of view for this close apparition. Thistrend between aperture size and water production is observed forhyperactive comets.To study how the active fraction correlates with thenucleus size, we added to our sample ten short-periodcomets with well-characterized water production ratesand nucleus sizes: 2P / Encke, 9P / Tempel 1, 10P / Tempel 2,19P / Borrelly, 21P / Giacobini-Zinner, 41P / Tuttle-Giacobini-Kresak, 55P / Tempel-Tuttle, 73P / Schwassmann-Wachmann 3,81P / Wild 2, and 96P / Machholz 1. Water production rates arefrom Combi et al. (2019), except for 9P, 10P, and 81P, forwhich we used measurements from Biver et al. (2007), Biveret al. (2012), and de Val-Borro et al. (2010). Most of thenucleus sizes are given in Combi et al. (2019). For C / / ff ective nucleus radii are 2.72, 5.9 km, and 2.1 km, respectively (A’Hearn etal. 1989, 2005; Brownlee et al. 2004). Comet properties andderived active fractions at perihelion are summarized in TableA.3.There are strong biases in this study. Comets with low waterproduction rates (below 5 × s − at 1 au) are not considered.In addition, small nuclei are largely underrepresented, consid-ering estimates of the size distribution of short-period comets(Fernández et al. 2013). Therefore, our sample does not includesmall comets with low active fractions, which may be present inthe population of short-period comets, because their surface hasbeen heavily mantled by refractory dust. However, large ( r N > / H ratio on the nucleus size, but donot find a statistically significant correlation between these twoquantities.
Appendix A.4: D/H ratio in comet C/1996 B2 (Hyakutake)
The HDO production rate in comet Hyakutake was measured tobe (1 . ± . × s − , averaging data obtained on March23.5 and 24.5 UT, 1996 with the Caltech Submillimeter Obser-vatory (CSO) (Bockelée-Morvan et al. 1998). A D / H ratio of(2 . ± . × − was derived using a water production rateof (2 . ± . × s − , corresponding to the average of re-ported measurements using observations of H O (IR), OH (UV,radio), H Lyman- α , and OI (optical). An updated analysis of the Article number, page 7 of 9 & A proofs: manuscript no. Wirtanen-Final2
Table A.3.
Comet properties and derived active fractions.
Comet q a r bN D / H c Q (H O) d Active fraction e (au) (km) s −
1P 0.59 5.50 (3.10 ± × − × (3.3 ± × −
8P 1.03 3.10 (4.09 ± × − × (8.5 ± × −
45P 0.53 0.43 ± < × − × (1.6 ± ×
46P 1.05 0.63 ± ± × − × (1.2 ± ×
67P 1.24 2.00 (5.30 ± × − × (8.3 ± × − ± × − × (7.2 ± × − C / ± ± × − × (3.4 ± × − C / ± ± × − × (6.1 ± × C / < ± × − × (3.9 ± × −
2P 0.33 2.40 ± × (2.9 ± × −
9P 1.51 2.72 0.8 × (6.3 ± × −
10P 1.42 5.90 ± × (3.2 ± × −
19P 1.36 2.40 0.5 × (4.1 ± × −
21P 1.04 1.82 ± × (2.7 ± × −
41P 1.05 0.70 1.1 × (5.5 ± × −
55P 0.98 1.84 ± × (3.1 ± × −
73P 0.94 1.10 ± × (1.4 ± ×
81P 1.60 2.10 1.0 × (1.5 ± × −
96P 0.12 3.20 ± × (1.2 ± × − Notes: (a) Perihelion distance. (b) Nucleus e ff ective radius. See references in Combi et al. (2019) and Sect. A.3. For spacecraft andradar data, the error was assumed to be insignificant. (c) D / H in water. References in the review of Bockelée-Morvan et al. (2015),except for 67P (Altwegg et al. 2015), C / Fig. A.1. D / H ratio in cometary water as a function of the active frac-tion computed based on the water production rates at 1 au from the Sun.The color of each symbol indicates a comet; see legend at right, wherethe dynamical class is also indicated: Oort cloud (OC) or short-periodJupiter-family (JF) comets. The uncertainties on the active fraction (hor-izontal bars) include a 30% uncertainty on the water production rates(Combi et al. 2019) and the uncertainty on the nucleus size.
H Lyman- α SWAN observations (Combi et al. 2005) indicatesa higher water production rate than that adopted in Bockelée-Morvan et al. (1998). Combi et al. (2005) compare SWAN re-trievals to other Q (H O) measurements and conclude that thereis a relatively good agreement, taking into account modeling in-duced di ff erences. Using the daily tabulated Q (H O) values in
Fig. A.2.
Active fraction at perihelion as a function of perihelion dis-tance for a sample of 18 comets. Green symbols refer to comets forwhich the D / H ratio in water has been measured. The uncertainties onthe active fraction (vertical bars) include a 30% uncertainty on the waterproduction rates (Combi et al. 2019) and the uncertainty on the nucleussize.
Table 2 of Combi et al. (2005) and using interpolation, we de-rive Q (H O) = . × s − during the time of the HDOobservations. Assuming a 25% uncertainty for Q (H O) (Combiet al. 2005), the revised D / H ratio in comet Hyakutake is then(1 . ± . × − .HDO was detected in comet Hyakutake during an outburst.We therefore re-evaluated the HDO / H O production rate ratio
Article number, page 8 of 9is et al.: D / H ratio in hyperactive comets using the methanol lines observed in the same spectrum as HDOand the re-evaluated CH OH average abundance relative to wa-ter outside the outburst period. Using water production ratesfrom Combi et al. (2005) and the methanol production rates de-rived from JCMT, PdBi, and CSO observations before and afterthe 19–24 March outburst period (Biver et al. 1999; Lis et al.1997), we find Q (CH OH) / Q(H O) = . ± . Q (HDO) / Q (CH OH) = . ± . Q (HDO) / Q (H O = (3 . ± × − and consequently D / H = (1 . ± . × − , in agreementwith the value derived above. Appendix A.5: D/H ratio in comet C/2014 Q2 (Lovejoy)
A D / H ratio in water of (1 . ± . × − was measured in cometC / / H = (3 . ± . × − . The inconsistencybetween the two values, which is marginal when considering theuncertainties of the two measurements, can be explained if thiscomet is a hyperactive comet. The VSMOW value measured inthe millimeter would characterize water subliming from grains,whereas the value obtained in the IR would sample mainly wa-ter released directly from the nucleus. The size of the nucleus ofthis comet is currently unknown, so the active fraction cannot becomputed.. The inconsistencybetween the two values, which is marginal when considering theuncertainties of the two measurements, can be explained if thiscomet is a hyperactive comet. The VSMOW value measured inthe millimeter would characterize water subliming from grains,whereas the value obtained in the IR would sample mainly wa-ter released directly from the nucleus. The size of the nucleus ofthis comet is currently unknown, so the active fraction cannot becomputed.