arXiv:1911.06271v2 [astro-ph.EP] 18 Nov 2019 h ubeSaeTlsoeoedyatrMKye al. et McKay after board day on one camera Telescope the Space a in by Hubble resolved taken the 2I/Borisov, image of disseminated coma widely inner the that noted nrdcn abnmnxd stedie fatvt in activity of in of observations. driver need is pre-discovery the the that the as without al. water, monoxide et of carbon Bolin abundance scenario introducing or high a a present al. with I et following, line McKay the by In the considered taken. not of well area is al., surface po- McKay et comet’s by total the independently of the expressed suggestion per- hyperactivity, the tential of 140 that than limit appears It more upper nucleus. of the area of active cent an finds one distance, ihBlne l’ siae pe ii f14km of et rate 1.4 McKay sublimation of with water averaged and limit an diameter 0.37 upper of nuclear estimate estimated comet’s al.’s al.’s the et on Bolin with 2019). al. et (Fitzsimmons rate production ihBlne l’ 21)wtrpouto aeestimate s rate kg production water 100 (2019) of al.’s et Bolin with of certainty yia CN/H typical coe –5 rvse ta.(09 siae nOH an estimated on 3.3 (2019) MHz of of 1667 al. time rate at et integration line production Crovisier hour OH 2–25, 15 the October of a observations from radio hand, their other the On utdi hi eemnto fapouto aeof rate re- production water a in- of of and production Sun) determination the the their 0.63 of from in AU terms sulted 11 2.38 October in was 2019 terpretation on comet 2I/Borisov the in (when oxygen atomic of line lcrncades Zdenek.Sekanina@jpl.nasa.gov. address: Electronic 2. narcn hr omncto Sknn 09)I 2019a) (Sekanina communication short recent a In obnn rvse ta.spouto aeresult rate production al.’s et Crovisier Combining ca ta.s(09 eeto fterdforbidden red the of detection (2019) al.’s et McKay eso oebr1,21;Adnu oebr1,2019 18, L November using Addendum typeset 2019; Preprint 14, November Version × × AOO AG C-UTGAN N CHUNKS AND GRAINS ICY-DUST LARGE OF HALO 10 10 ULMTO FWTRIEFO OUAINO AG,LONG-LA LARGE, OF POPULATION A FROM ICE WATER OF SUBLIMATION ae c rmtenceshsbe nraigsnetetm fdisco of o time acceleration the nongravitational since headings: measurable Subject increasing a T exert been suspec to has strongly disintegration. a enough nucleus comet’s rapid high cm the the from to to 2-3 ice contributing than subjected water halo smaller some icy-dust low initial grains and exceedingly the All was 2019 rate excessively mid-October sublimation recently. appearing by the more comet when Sun, condensation the the the for nuclear of from responsible AU th population been 5–6 that The have at suggests effect. to comparison likely sublimation This integrated is AU. the 2 wit mitigates 2I/Borisov of 2I comparing distance by perihelion investigated equal are at ice, activity water of amorphous product a grains. 27 27 e rplinLbrtr,Clfri nttt fTechno of Institute California Laboratory, Propulsion Jet oeta ffcso ulmto fwtriefo eysol oigm moving slowly very from ice water of sublimation of effects Potential oeue km molecules oeue s molecules − ± 1 7pret hsrsl svrulyidentical virtually is result This percent. 27 2 bnac ai n naalbeCN available an and ratio abundance O ae nterapoiaesaigo a of scaling approximate their on based 1. A INTRODUCTION T − × E tl mltajv 08/22/09 v. emulateapj style X 1 − 10 iha ro of error an with 2 oes niiul(IBrsv otCodcmt)—mtos da methods: — comets) Cloud Oort (2I/Borisov, individual comets: 27 s − oeue s molecules 1 ttegvnheliocentric given the at eso oebr1,21;Adnu oebr1,2019 18, November Addendum 2019; 14, November Version ERTENCESO 2I/BORISOV? OF NUCLEUS THE NEAR ∼ − 1 0A rfrhrfo h u rvnpeual yanaigof annealing by presumably driven Sun the from farther or AU 10 ± iha un- an with 4percent. 24 dnkSekanina Zdenek ABSTRACT oy 80OkGoeDie aaea A919 U.S.A. 91109, CA Pasadena, Drive, Grove Oak 4800 logy, odabd f00 n h msiiyo ..Because for assumed 0.9. one of the from emissivity differs the the regime wa- and assume sublimation 0.04 and I this of reradiation arbitrarily albedo thermal Somewhat Bond the sublimation. by ice the losses ter from the input and radiation by the Sun distance between heliocentric balance uniform given energy fairly the a a at having dictated equilibrium, mate- consisting temperature thermal refractory grains, in by contaminated are dark (i.e., rial), that ice water assume dirty I of 2I/Borisov, to sis paper earlier my of in cloud 1982). a proposed (Sekanina to grains water of sizable rates pre-existing attributed production they high 1980b); observed E1 = the C/1980 I comet by 1980 Cloud designation considered Oort old an was (Bowell; ac- for scenario (1984) is al. similar nucleus et very rel- A’Hearn small A a relatively active. a only tually of if fraction even contribute small hyperactivity thereby atively could comet’s production, water atmosphere the reported explaining its the in to per- substantially chunks to larger way and and their centimeter-sized grains on sublimating comets that and Cloud ihelion Oort Oort do the as evolution from arriving 2009). just al. amor- comets et of (Meech in annealing Cloud by ice driven water be releases to phous that believed milli- activity is beyond The a debris or characteristic this 1975). near from (Sekanina the perihelia range line with snow in a comets the Cloud commonplace (in Oort from is debris of more) tails up) of or AU type across 10 the This meter of when order times the Sun. at (on nearly- the far nucleus of still the grains was halo from comet icy-dust a released by larger pebbles occupied or and be centimeter-sized could stationary, of coma side inner projected this vector. the that orbital-velocity suggest negative a considerations in the Orbital condensation of nuclear direction the from general arcseconds extending few feature a a over shows observation, their made (2019) oeaietepasblt fapyn hshypothe- this applying of plausibility the examine To similar undergone has 2I/Borisov that propose now I h ria oino 2I/Borisov. of motion orbital the n oia otCodcmtof comet Cloud Oort nominal a h e yeatvt.Sbiainof Sublimation hyperactivity. ted togyhproi oinof motion hyperbolic strongly e egan ertenceso 2I of nucleus the near grains se ey u h aehsntbeen not has rate the but very, rgti r-icvr images pre-discovery in bright i etol agrcuk of chunks larger only left his swl sfrteprominent the for as well as , rs a endevolatilized been had cross liee-ie n larger and illimeter-sized TN GRAINS STING aanalysis ta 2 Sekanina the nucleus by McKay et al. (2019), the sublimation area Λ˙ of the putative source of detected water is also different, (cm/day) COLUMNAR SUBLIMATION RATE 2 2 equaling 5.8 km instead of 1.7 km . OF OORT CLOUD COMET ······················································· Let the sublimation rate of water ice implied by the en- −1 AND 2I/BORISOV ······································· 10 ·························· ········· ergy balance at time t, when the comet is at heliocentric ············ ······ − − ······· ···· distance r(t), be Z˙ (t), expressed in molecules cm 2 s 1. ······· ···· ········· ····· Next, I introduce a columnar sublimation rate, dΛ(t)/dt ········ ···· −2 ····· ··· or Λ(˙ t), at which the thickness of a layer or the length of 10 ······· ···· −1 ····· ··· a column of water ice contracts (in cm s , for example) ······· ···· OORT CLOUD ···· ·· due to its sublimation, by ···· ··· 2I/BORISOV COMET ····· ··· −3 ···· ·· µZ˙ (t) 10 ······ ··· Λ(˙ t)= , (1) ····· ··· δ ······ ··· ······ ··· where µ is the mass of a water molecule and δ is the bulk ······ ··· −4 ··· ·· density of water ice in the grain. Integrating (1) from an 10 ····· ··· ······ ··· early time before the sublimation began, the length of ······ ··· a column of water ice that has sublimated away by a ······ ··· ······· ···· reference time, tref , is −5 ···· ·· 10 ···· ··· tref rref · µ −1 Λ(tref)= Λ(˙ t) dt = Z˙ (r)r ˙ dr, (2) −∞ δ ∞ −300 −200 −100 0 Z Z TIME FROM PERIHELION AT 2.006 AU (days) where tref is reckoned from perihelion, tπ, and rref is the Figure 1. Comparison of preperihelion columnar rates of water heliocentric distance at time tref. In general, there are no ice sublimation from grains in the atmospheres of comet 2I/Borisov constraints on tref , but in the following I only consider the and a nominal Oort Cloud comet of equal perihelion distance of contraction of a column of water ice by its sublimation 2.006 AU. Note that because of the higher orbital velocity, 2I’s rate is lower by one order of magnitude 90 days before perihelion, along the preperihelion leg of the orbit, in which case but by five orders of magnitude 140 days before perihelion. tref tπ 0 andr ˙ 0. To− facilitate≤ the≤ integration, I introduce a new, dimen- sionless variable, 0 z 1, by substituting ≤ ≤ for 2I/Borisov and by τ = 300 days for the nominal Oort τ 0 z = exp , (3) Cloud comet in the parabolic orbit. τ0 An obvious choice for approximating a function de- fined by a sequence of (x, y) data pairs is a polynomial where τ = t tπ and τ0 > 0 is a constant. The length of a column of− water ice sublimated by time t is then y(x), whose coefficients are determined by least squares. ref The advantage of this approach is twofold: first, one can exp(τref /τ0) optimize the polynomial’s degree by searching for the Λ(tref )= τ0 (t) dz, (4) lowest possible degree that secures the requested quality F Z0 of fit; and second, the integration is straightforward. To where τref = tref tπ and follow this procedure, I write − n Λ(˙ t) τ k (t)= = Λ(˙ t) exp . (5) j(t)= ak,j z , (6) F z −τ0 F Xk=0 The columnar rates Λ(˙ t) of water ice sublimation for where j = 1 for 2I/Borisov and j = 2 for the Oort Cloud 2I/Borisov and an Oort Cloud comet of the perihelion comet. In accordance with this notation, I refer from distance of 2.006 AU, are compared in Figure 1 as a func- now on to Λ and τ0 for 2I/Borisov as Λ1 and τ0,1, for tion of time reckoned from perihelion. The lower rates the Oort Cloud comet as Λ2 and τ0.2, respectively. Ex- for 2I/Borisov stem from the higher orbital velocity in perimentation with a number of reference points (z, ) its strongly hyperbolic path, i.e., at an equal time from has shown that a cubic polynomial fits both 2I/BorisovF perihelion 2I is farther from the Sun than the Oort Cloud and the Oort Cloud comet quite adequately, if a typi- −1 comet of equal perihelion distance. cal error of approximately 0.001 cm day for j is The length of a column of water ice sublimated by the acceptable, but only over the± range of heliocentricF dis- reference time, defined by Equation (2), is obviously also tances not exceeding r =3.4 AU, equivalent to about ∗ ∗ shorter for 2I than for the nominal Oort Cloud comet. z 0.43 and t tπ = 125 days for 2I/Borisov and to 1∗ ≃ ∗1 − − To determine this quantitatively, the integration of the z2 0.45 and t∗2 tπ = 240 days for the nominal Oort expression on the right-hand side of Equation (2) or (4) Cloud≃ comet. The− failure− of any fit of this kind for all requires decisions on two issues: (i) to devise an appro- values of z smaller (and times from perihelion larger) priate method of integration; and (ii) to choose the con- than these limits has two major implications. One is the stant τ0 separately for 2I and the nominal comet in the need to devise an integration approach other than via parabolic orbit once Equation (4) is used. Equation (4) for all reference times preceding t∗ (i.e., The choice of τ0 is not at all critical, the only concern for heliocentric distances larger than r∗). And two, all being that, for the purpose of smooth integration, is reference times between t∗ and the perihelion time tπ approximately flat near perihelion, where Λ˙ reachesF its call obviously for a revision of the integration limits in maximum. This condition is satisfied by τ0 = 150 days Equation (4). Sublimation of Water from Grains in 2I/Borisov? 3
′ The remedy of the first problem is greatly facilitated by polynomials, Λj , I find (dropping the subscript ref ) the fact that at heliocentric distances exceeding 3.4 AU the incident solar radiation is spent overwhelmingly on exp(τj /τ0) Λj (t)= τ0,j j dz +Λj(t ) reradiation, so that the columnar rate of water ice subli- ∗ ∗j exp(τ /τ0) F mation follows closely a relation Z j (14) ′ ′ ˙ = τ0,j Λ (t) Λ (t )] + o[Λj (t) , j =1, 2, Λ= A exp B√r , (7) j − j ∗j − 1 13 −1 − 2 where A =6.7 10 cm day andB = 21.587 AU . where τj∗ = t∗j tπ, o[x] means a negligible contribution One bypasses Equation× (4) by integrating directly Equa- to x, and again− j = 1 for 2I/Borisov and j = 2 for the tion (2) to obtain for the length of the sublimated column nominal Oort Cloud comet. of water ice by time t∗ an expression I already remarked that cubic polynomials represent ∗ adequate approximations for both objects; the columns t ′ Λj sublimated by time t (t∗j
f r Time 2I/Borisov Oort Cloud comet = ∗ =1.562. (13) from f 1 sr q s − ∗− peri- Distance Column Column Distance Column Column helion from Sun rate Λ˙ length Λ from Sun rate Λ˙ length Λ Inserting the numerical values into Equation (12), one (days) (AU) (cm/day) (cm) (AU) (cm/day) (cm) obtains Λ2(t∗2 ) < 0.0073 cm for the nominal Oort Cloud −180 ...... 2.907 0.006 0.05 comet and from the hyperbolic-to-parabolic ratio of the −160 ...... 2.751 0.013 0.23 radial velocities Λ1(t∗1 ) < 0.0036 cm for 2I/Borisov, both −140 ...... 2.603 0.024 0.62 implying negligible sublimation losses along either trajec- −120 ...... 2.463 0.042 1.30 tory for centimeter-sized grains by the time the object −100 2.977 0.004 0.01 2.336 0.065 2.36 had reached 3.4 AU. −80 2.672 0.018 0.22 2.225 0.092 3.91 The second remedy, required by the limits of the poly- −60 2.406 0.052 0.89 2.133 0.119 5.99 nomial approximation (6) to the columnar sublimation −40 2.194 0.101 2.36 2.064 0.143 8.62 rate, is predictably a relatively minor modification of −20 2.055 0.147 4.87 2.021 0.160 11.73 Equation (4). Marking now with primes the lengths of −10 2.018 0.161 6.44 2.010 0.165 13.37 the sublimated columns computed by integrating via 0 2.006 0.166 8.10 2.006 0.166 15.03 Fj 4 Sekanina
Λ Λ (cm) COLUMN OF SUBLIMATED WATER ICE (cm) COLUMN OF SUBLIMATED WATER ICE FOR OORT CLOUD COMET FOR OORT CLOUD COMET AND 2I/BORISOV AND 2I/BORISOV VS VS TIME ······························ HELIOCENTRIC ···· 10 ············ 10 DISTANCE ············ ················· ········ ············ ·· ················ ··········· ············· ·········· ··············· ········· ·············· ··········· ·············· ········· ··············· ············ ············· ········ ················ ·············· ············ ········ ················ ··············· ············ ······· ··············· ················ ··········· ······· ·············· ················ 1 ·········· ······· 1 ············· ················ ····· ··· OORT CLOUD ······· ········ ····· ···· ······· ········· 2I/BORISOV ····· ··· COMET ······· ········ ······· ····· ·········· ············· ···· OORT CLOUD ··· ······ ······· ····· ··· 2I/BORISOV ······· ········ ····· COMET ···· ······· ········ ······ ···· ········ ········· ······ ···· ········ ········· 0.1 ···· ··· 0.1 ······ ······· ····· ··· ······· ······· ···· ··· ······ ······· ··· ······ ······· ··· ······ ······ ··· ····· ······ ··· ······ ·· ······ 0.01 · 0.01 ···
−150 −100 −50 0 3 2.8 2.6 2.4 2.2 2 TIME FROM PERIHELION AT 2.006 AU (days) HELIOCENTRIC DISTANCE (AU) Figure 2. Column of water ice sublimated away from a chunk Figure 3. Column of water ice sublimated away from a chunk as as a function of time before perihelion for 2I/Borisov and an Oort a function of heliocentric distance before perihelion for 2I/Borisov Cloud comet of equal perihelion distance. and an Oort Cloud comet of equal perihelion distance. chunks would be at 6300 km from the nucleus if they had A’Hearn et al. (1984) reported in their paper a water been released 1 year before perihelion, at 8 AU from production rate of 0.74 1029 molecules s−1 at 5.25 AU the Sun. By contrast,∼ an Oort Cloud comet∼ of equal per- and 1.55 1029 molecules× s−1 at 4.63 AU from the Sun. ihelion distance would have lost by that time a column These rates× imply the surface area of a nonrotating nu- of water ice more than 6 cm thick, so only very massive cleus of, respectively, 460 km and 190 km in diameter (!) chunks, much larger than 10 cm across would still possess and even a larger rapidly rotating nucleus. Although the some remaining ice. Thus, the substantially higher or- nuclear size of C/1980 E1 is unknown, it has been esti- bital velocity and the hyperbolic shape of the trajectory mated at not more than 10 km by A’Hearn et al. (1984), have helped 2I/Borisov lose water ice at a significantly a discrepancy of more than one order of magnitude. lower rate than does an Oort Cloud of equal perihelion A’Hearn et al. resolved this disparity by assuming that distance. the production of water near 5 AU preperihelion came from a source other than the nucleus, referring to my 3. POPULATION OF LARGE GRAINS AND THE work on a population of large grains (>0.5 mm across) in HYPERACTIVITY the coma and tail of C/1980 E1 released from the nucleus The term hyperactive comets is usually employed to probably near 11–12 AU from the Sun (Sekanina 1982), refer to a small group of short-period comets, including a product of the comet’s activity on its first journey to 21P/Giacobini-Zinner, 45P/Honda-Mrkos-Pajduˇs´akov´a, the inner Solar System. Estimates of the total mass of 46P/Wirtanen, and 103P/Hartley, whose water produc- this population of grains ranged from more than 1013 g tion is anomalously high, often exceeding the level that to 5 1015 g, corresponding to a layer of between 1 cm implies the entire surface area of the nucleus is active. and ×1 m on a 10 km nucleus. ∼ The best examined member of this group is 103P, the Grains∼ observed in the tail of an Oort Cloud comet, target of the EPOXI mission, whose hyperactivity was whose perihelion is near or beyond the snow line, are re- proposed by A’Hearn et al. (2011) to be driven primarily leased from the nucleus over a period of time, but the by gaseous CO2 that blasts off chunks of sublimating wa- tail’s narrow width and the characteristic major gap be- ter ice. Yet, Harker et al. (2018) have concluded that the tween the tail and the antisolar direction demonstrate underlying cause of the hyperactivity is still unknown. that the grain release stopped long before observation. Independently of the outcome of this dispute, I believe The time it began is unfortunately not well determined that 103P or any other short-period comet is not an ap- because of poor temporal resolution among early emis- propriate standard for investigating the hyperactivity of sions in the tail orientation. Yet, I showed on an ex- 2I/Borisov because of their very different histories. A ample of comet C/1954 O1 (Baade) that measuring the much better benchmark is C/1980 E1 (Bowell), an Oort position angle of the tail’s axis (as is commonly done) Cloud comet with perihelion at 3.36 AU, which turned instead of the position angle of its maximum extent has out to be extremely hyperactive around 5 AU preperihe- a tendency to significantly underestimate both the mini- lion, although this term was not yet in use in those days. mum grain size in the tail and the heliocentric distance at Sublimation of Water from Grains in 2I/Borisov? 5 release (Sekanina 1975). For any comet displaying such a tween 6.03 AU and 5.09 AU from the Sun), taken with tail before perihelion, the heliocentric distance at release the Zwicky Transient Facility’s (ZTF) wide-field cam- must obviously exceed markedly the perihelion distance. era mounted on the 122-cm Schmidt telescope at Palo- While Oort Cloud comets discovered 60–70 years ago had mar, thus extending the observed arc of the orbit by perihelia at distances of up to at most 5 AU, more re- 5.5 months. The authors pointed out that the comet was cently the limit has moved up by several AU, yet some of at the time of magnitude 20.5 to 21.0, much brighter than these objects still display the tails, some even before per- predicted by a water ice sublimation model, and argued ihelion.1 This is a very strong argument for the onset of that the brightness was consistent with activity driven release of grains from Oort Cloud comets at heliocentric by sublimation of carbon monoxide. The plot in their distances of at least 10 AU from the Sun, correspond- Figure 6 shows, however, that between 6 AU and 2.5 AU ing to temperatures of∼ not more than 80K for a rapidly from the Sun the scattering cross-sectional area then var- − 2 rotating comet and lower than 100 K for a nonrotating ied with heliocentric distance r as r 3 rather than the ex- comet. pected r−2 or steeper. And because activity at 2.5 AU A paper by Meech et al. (2009) addresses the problem was driven∼ by sublimation of water ice and other volatiles of the potential mechanism of large-grain release at very from the nucleus, the exponent for the CO model should low temperatures; they prefer annealing of amorphous be still closer to zero. In addition, missing in Bolin et al.’s water ice, which is stable up to at least 120–130K, over Figure 6 is evidence for a definite increase in the scatter- sublimation of carbon monoxide as the driver of activity ing cross section of dust from March to May, which would far from the Sun in Oort Cloud comets. They show, in be expected in the case of CO driven activity. fact, that in laboratory experiments the annealing pro- On the other hand, if the comet’s excessive brightness cess begins at a temperature as low as 37K, correspond- observed in the ZTF images of 2I/Borisov was due to ing to a heliocentric distance of 59 AU for a rapidly ro- a population of sizable, extremely slowly moving grains, tating (isothermal) nucleus and still farther from the Sun the product of activity at very large heliocentric distance for a nonrotating nucleus. Ice physics thus provides only driven presumably by annealing of amorphous water ice modest constraints in terms of heliocentric distance at (Meech et al. 2009), one would expect the cross-sectional the time of release of grains. area to stay constant between 2019 March and May. For Additional issues relate to the grains. Relative frac- an assumed albedo of 0.04, Bolin et al.’s results sug- tions of water ice, other ices, and refractory material gest the total cross-sectional area of the comet to equal in the grains upon arrival from the Oort Cloud are un- 200 km2 at 5–6 AU before perihelion. Assuming this known. Nor is the grains’ degree of coherence and their refers∼ to the grain halo and a typical grain diameter of fate after the evacuation of water ice: does the skeleton 2 mm, the volume is 3 1011 cm3, which makes a layer hold together or does it disintegrate? And if it holds to- ∼of more than 10 cm thick× on the nucleus smaller than gether, how does the loss of water ice affect its optical 1.4 km across, in the same range as the result for the properties, such as the albedo? On the last issue, there population of grains in C/1980 E1 (Section 3). is evidence that might indicate either the grains’ failure Because the sublimation rate of water ice from grains to survive without the ice or a major drop in their reflec- in the atmosphere of 2I/Borisov increases exponentially tivity because the tails have a tendency to disappear in with time at heliocentric distances exceeding 3 AU, comets with perihelion distances below the snow line, be- reaching an integrated columnar length of 0.1 cm∼ near ing replaced near and after perihelion with tails of lesser 2.77 AU, 1 cm near 2.39 AU, 2 cm near 2.23 AU, and age. Yet, these tails also lack grains substantially smaller 4 cm near 2.1 AU (Figure 3), grains of the respective than 1 mm and no post-perihelion emission of dust is sizes become devolatilized at the respective heliocen- typically∼ detected. tric distances and subject to potential disintegration. This could explain three additional points: (i) the pre- 4. POPULATION OF LARGE GRAINS AND CHUNKS IN sumed presence, in the Hubble Space Telescope’s image 2I/BORISOV AND ABSENCE OF NONGRAVITATIONAL ACCELERATION IN ITS ORBITAL MOTION taken on October 12, of a population of centimeter-sized and larger chunks in the inner coma (Sekanina 2019a) Bolin et al. (2019) reported Ye et al.’s (2019) detec- and, simultaneously, the absence of a tail-like extension, tion of pre-discovery r-filter images of 2I/Borisov on 2019 composed of millimeter-sized grains of the same pop- March 17–18 and May 2 and 5 (when the comet was be- ulation and pointing along the direction of the nega- tive orbital-velocity vector; (ii) the comet’s hyperactiv- 1 An excellent example of what can be learned from high-quality imaging obtained at an appropriate time is Meech et al.’s (2009) ity over a broad range of heliocentric distances around image of C/1999 J2, taken on 2000 February 24, or 42 days pre- 2.5 AU preperihelion, with a major contribution by the perihelion, at 7.11 AU. Compared to the other five images of this same centimeter-sized and larger grains because of their comet in the paper, the great advantage of this one is the large an- water sublimation; and (iii) the bumps in the comet’s gle between the radius vector (p.a. 279◦) and the negative orbital velocity vector (p.a. 20◦). For the left, sharper, and perfectly recti- light curve in the course of September and early October linear boundary of the tail I measure a position angle of 13◦, which (Bolin et al. 2019), which could be triggered by clouds implies a release time of 1600 days before perihelion at 12 AU from of microscopic-sized debris of large devolatilized grains the Sun. Assuming the tail extends to the edge of the frame, the disintegrating at temporally variable rates. smallest grains are subjected to a radiation pressure acceleration of 0.0014 the Sun’s gravitational acceleration and are about 1.6 mm Bolin et al. (2019) appear to admit the presence of across. Their temperature is about 80 K. The right, much shorter, a nongravitational acceleration in the orbital motion of and less sharp boundary of the tail extends to a position angle of 2I/Borisov by noting that “[m]oderate non-gravitational about 2–3◦, implying a terminal release time 600 days before per- ihelion and a heliocentric distance of ∼8 AU. The grains’ implied force parameters have been measured for the orbit of temperature is about 100 K. The process extended for approxi- 2I in pre-discovery data when the comet’s activity was mately 1000 days with an activating temperature range of ∼20◦. weaker (Ye et al. 2019).” However, consideration of the 6 Sekanina reported outgassing rates of 2I suggests that after nor- Bolin, B. T., Lisse, C. M., Kasliwal, M. M., et al. 2019, eprint malization to 1 AU from the Sun, the nongravitational arXiv:1910.14004 Crovisier, J., Colom, P., Biver, N., et al. 2019, CBET 4691 acceleration on this comet should at best be two orders of Fitzsimmons, A., Hainaut, O., Meech, K. J., et al. 2019, ApJ, 885, magnitude lower than the observed anomalous effect on L9 1I/‘Oumuamua. In fact, Nakano (2019) linked the pre- Harker, D. E., Woodward, C. E., Kelley, M. S. P., et al. 2018, AJ, discovery astrometry from the ZTF database for 2018 155, 199 McKay, A. J., Cochran, A. L., Dello Russo, N., et al. 2019, eprint December 13 and 2019 February 24, March 17, April 9, arXiv:1910.12785 and May 2 and 5 with more than 1600 observations from Meech, K. J., Pittichov´a, J., Bar-Nun, A., et al. 2009, Icarus, 201, August 30 through November 6 with no need to incor- 719 porate nongravitational terms into the equations of mo- Nakano, S. 2019, NK 3929 tion. His purely gravitational solution provides an ex- Sekanina, Z. 1975, Icarus, 25, 218 ′′ Sekanina, Z. 1982, AJ, 87, 161 cellent fit to the dataset with a mean residual of 0 .67 Sekanina, Z. 2019a, eprint arXiv:1910.11457 and a very satisfactory distribution of individual residu-± Sekanina, Z. 2019b, eprint arXiv:1910.08208 als (which are explicitly tabulated by Nakano), free from Ye, Q.-Z., Kelley, M. S. P., Bolin, B. T., et al. 2019, in preparation any systematic trends. 5. CONCLUSIONS ADDENDUM, dated November 18, 2019 While I by no means rule out sublimation of carbon monoxide (or other volatiles not directly tied to sub- Now that the results of the pre-discovery observations limation of water ice) from 2I/Borisov, I see no com- investigated by Ye et al. (2019, eprint arXiv:1911.05902) pelling evidence from the pre-discovery observations for have been published, two of the highlights of their work CO driving the comet’s activity before water ice sublima- stand out as the most diagnostic: (i) a ballooning of the tion began to gradually dominate, as documented by the cross-sectional area of the comet from an undetected level data acquired since discovery. I find that the observa- (with a 3σ upper limit of 140 km2) in November 2018 to tions reported thus far are consistent with a pre-existing about 330 km2 a month later at heliocentric distances population of (initially) millimeter-sized and larger icy- r near 8 AU; and (ii) the comet’s intrinsic brightness, dust grains and chunks in the coma, presumably a prod- which varies approximately as r−2 from 8 AU down all uct of the process of annealing of amorphous water ice the way to 2.4 AU, implies an essentially constant cross- (Meech et al. 2009) that proceeded in the conglomerate sectional area over this range of heliocentric distances, nucleus when the comet was, say, 10 AU or farther from until at least early October 2019, a 10-month period. the Sun. The presence of such a massive grain popula- The most straightforward interpretation of the findings tion made the comet bright in the 2019 March–May im- — which should likewise accommodate the high produc- ages, at 5–6 AU from the Sun. Devolatilization and sub- tion rate of water in October — is liberation, over a pe- sequent disintegration of the smallest, millimeter-sized riod of several weeks to a few months and at extremely grains from this population was being completed in the low velocities, of a large amount of icy-dust debris from course of September of 2019, and their microscopic-sized the nucleus into the atmosphere, where it has been lin- relics were gradually but temporally unevenly eliminated gering for the 10 months seemingly unaltered. The pro- from the comet’s proximity by solar radiation pressure. cess of annealing as a driver of this activity, proposed by By mid-October, eight weeks before perihelion, subli- Meech et al. (2009), was based on Bar-Nun et al.’s labo- mation of water continued only from the halo’s chunks ratory experiments, but independent and/or more recent >2–3 cm in diameter, the grain population’s sublimation work on annealing [e.g., S. A. Sandford & L. J. Allaman- cross section dropping from the initial 200 km2 down dola (1988, Icarus, 76, 201), B. Schmitt et al. (1989, ESA 2 2 ∼ to <6 km or <30 km , depending on whether one uses SP-302, 65), O.’ O.´ G´alvez et al. (2008, Icarus, 197, 599), McKay et al.’s (2019) or Crovisier et al.’s (2019 data. L. J. Karssemeijer et al. (2013, ApJ, 781, 16), R. Mart´ın- Before the comet reaches perihelion, water sublimation Dom´enech et al. (2014, A&A, 564, A8), A. N. Greenberg from the nucleus should begin to dominate and the hy- et al. (2017, MNRAS, 469, S517)] does in general sup- peractivity vanish, if 2I evolves as do Oort Cloud comets. port this suggestion. It is possible that the process was As of mid-November 2019, the activity of 2I/Borisov has already in progress in November 2018 or perhaps even closely replicated — except for the reduced sublimation earlier, lasting for a few months. Some of the experi- effect — that of Oort Cloud comets of similar perihelion ments indicate that especially CO2/H2O ice mixtures ex- distance, as previously suspected (Sekanina 2019b); it hibit a strong annealing effect above 90 K, equivalent to remains to be seen whether this affinity is going to be the relevant range of heliocentric distances beyond 8 AU. maintained throughout 2I’s journey about the Sun. Crystallization of amorphous ice, which also could trigger activity, should start near the subsolar point at about the This research was carried out at the Jet Propulsion same time or soon afterward. One has to keep in mind a Laboratory, California Institute of Technology, under potentially large temperature variations over the surface contract with the National Aeronautics and Space Ad- of the nucleus. ministration. The requirement of extremely low velocities implies large size of the released debris. An order-of-magnitude REFERENCES estimate for the velocities is derived from an extreme condition that after 10 months the chunks should stay A’Hearn, M. F., Schleicher, D. G., Feldman, P. D., et al. 1984, AJ, 89, 579 confined to within a fairly small distance, say, 5000 to 10 000 km, of the nucleus, even if they keep expanding; A’Hearn, M. F., Belton, M. J. S., Delamere, W. A., et al. 2011, − Science, 332, 1396 (erratum, 2012) this suggests 0.2 to 0.4 m s 1, comparable to the velocity Sublimation of Water from Grains in 2I/Borisov? 7 of escape from a small comet. If an averagepiece of debris nearer perihelion, as shown in Table 1. It is still unclear is between 0.1 cm and 1 cm across and of a bulk density whether, or at what rate, does the scattering cross sec- of 0.5 g cm−3, the estimated mass of fragments with the tion of the devolatilized debris drop with time. Potential cross-sectional area of 330 km2 is (1–10) 1011 g. On a fragmentation temporarily increases the cross section but nucleus of less than 1.4 km across (Bolin× et al. 2019) has eventually the opposite effect as microscopic debris is and equal density, this mass would be distributed in a removed by solar radiation pressure. In addition, the size layer of more than 3–30 cm thick, an estimate whose up- of the contribution from increasing activity of the nucleus per bound is in order-of-magnitude agreement with the itself at r< 3 AU is yet to be determined. On the other thickness of a layer of grains released from the nucleus hand, the total sublimation cross section in mid-October of C/1980 E1, estimated by A’Hearn et al. (1984) from seems to have been at least crudely established to range their determination of the comet’s sublimation rate of between 6 km2 and 30 km2. Interestingly, the size of water ice near 5 AU preperihelion. the largest water-ice depleted pieces of debris just about The pre-discovery observations refer to a total scatter- equals the size of the debris that, released near 8 AU ing cross section of the debris, offering no information from the Sun, was in mid-October, at the Hubble Space of the sublimation cross section, which is assumed to be Telescope’s imaging time, at the boundary of the inner the same near 8 AU, but dropping with decreasing helio- coma. Thus, the inner coma, within 6000 km or so centric distance because of progressive depletion of wa- of the nucleus, still contains sublimating∼ chunks released ter ice from smaller fragments by increasing sublimation near 8 AU from the Sun.