Photometry and high-resolution spectroscopy of comet 21P/Giacobini-Zinner during its 2018 apparition
Y. Moulane, E. Jehin, P. Rousselot, J. Manfroid, Y. Shinnaka, F. J. Pozuelos, D. Hutsemékers, C. Opitom, B. Yang, Z. Benkhaldoun
AAstronomy & Astrophysics manuscript no. Moulane_21P c (cid:13)
ESO 2020June 11, 2020
Photometry and high-resolution spectroscopy of comet21P/Giacobini-Zinner during its 2018 apparition (cid:63)
Y. Moulane , , † , E. Jehin , P. Rousselot , J. Manfroid , Y. Shinnaka , F. J. Pozuelos , D. Hutsemékers , C. Opitom , ,B. Yang , and Z. Benkhaldoun European Southern Observatory, Alonso de Cordova 3107, Vitacura, Santiago, Chile † e-mail: [email protected] Space sciences, Technologies & Astrophysics Research (STAR) Institute, University of Liège, Liège, Belgium Oukaimeden Observatory, High Energy Physics and Astrophysics Laboratory, Cadi Ayyad University, Marrakech, Morocco Institut UTINAM UMR 6213, CNRS, Univ. Bourgogne Franche-Comté, OSU THETA, BP 1615, 25010 Besançon Cedex, France Koyama Astronomical Observatory, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UKReceived / accepted ABSTRACT
We report on photometry and high resolution spectroscopy of the chemically peculiar Jupiter-family Comet (hereafter JFC)21P / Giacobini-Zinner. Comet 21P is a well known member of the carbon-chain depleted family but displays also a depletion ofamines. We monitored continuously the comet over more than seven months with the two TRAPPIST telescopes (TN and TS), cov-ering a large heliocentric distance range from 1.60 au inbound to 2.10 au outbound with a perihelion at 1.01 au on September 10,2018. We computed and followed the evolution of the dust (represented by Af ρ ) and gas production rates of the daughter species OH,NH, CN, C , and C and their relative abundances to OH and to CN over the comet orbit. We compared them to those measured inthe previous apparitions. The activity of the comet and its water production rate reached a maximum of (3.72 ± × molec / son August 17, 2018 (r h = ρ was reached on the same date (1646 ±
13) cmin the red filter. Using a sublimation model for the nucleus, we constrained the active surface of the nucleus using the slow-rotatormodel. The abundance ratios of the various species are remarkably constant over a large range of heliocentric distances, before andafter perihelion, showing a high level of homogeneity of the ices in the surface of the nucleus. The behaviour and level of the activityof the comet is also remarkably similar over the last five orbits. About the coma dust colour, 21P shows reflectively gradients similarto JFCs. We obtained a high resolution spectrum of 21P with UVES at ESO VLT one week after perihelion. Using the CN B-X (0, 0)violet band, we measured C / C and N / N isotopic ratios of 100 ±
10 and 145 ±
10, respectively, both in very good agreement withwhat is usually found in comets. We measured an ortho-para abundance ratio of NH of 1.16 ± spin = ± Key words.
Comets: general - Comets: individual: 21P / Giacobini-Zinner - Techniques: photometry, spectroscopy
1. Introduction
Comet 21P / Giacobini-Zinner (hereafter 21P) is a JF with a shortperiod of 6.5 years. 21P was discovered in 1900 by Michel Gia-cobini and rediscovered by Ernst Zinner in 1913 . After its dis-covery, 21P was observed in most of its apparitions and manyphotometric and spectroscopic measurements were reported. InSeptember 1985, 21P was the first comet visited by the Inter-national Cometary Exporer (ICE) spacecraft to study the in-teraction between the solar wind and the cometary atmosphere(Von Rosenvinge et al. 1986; Scarf et al. 1986). 21P is alsoknown as the parent body of the Draconids meteor shower(Beech 1986; Egal et al. 2019). Many spectroscopic-photometricstudies at various wavelength ranges have been performed sinceits discovery (Schleicher et al. 1987; Cochran & Barker 1987; (cid:63) Based on observations collected at the European Southern Obser-vatory under ESO program 2101.C-5051. https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=21P;old=0;orb=0;cov=0;log=0;cad=0 Fink Uwe & Hicks 1996; Weaver et al. 1999; Lara et al. 2003;Combi et al. 2011) including production rates measurements,atomic and molecular abundances. 21P is the prototype of de-pleted comets in C and C with respect to CN and to OH (Schle-icher et al. 1987; A’Hearn et al. 1995). C and C relative abun-dances are about 5 and 10 times smaller than those measured in“typical” comets (A’Hearn et al. 1995). 21P was found to be alsodepleted in NH (Schleicher et al. 1987; Kiselev et al. 2000) andNH (Konno & Wycko ff Article number, page 1 of 14 a r X i v : . [ a s t r o - ph . E P ] J un & A proofs: manuscript no. Moulane_21P centric distances of 1.0-1.5 au (Schleicher et al. 1987). The gasand dust maximum production was observed about one monthbefore perihelion for the previous apparitions (Schleicher et al.1987; Hanner et al. 1992; Lara et al. 2003). Both its unusualcomposition and the behavior of its activity during multiple ap-paritions make 21P an object of great interest. In addition, as itis the parent body of the Draconids, a study of its dust propertiesmight be valuable. The 2018 apparition was very favorable forground-based observations since the comet was close both to theSun and the Earth at the same time and reaching high elevation.Many observed the comet again for the 2018 return using variousstate of the art instrumentation (IR and optical spectrographs onlarge telescopes) in order to better understand these peculiarities.This work is organized as follows: after the introduction andhistorical background given in section 1, we describe the ob-serving circumstances and the reduction process of TRAPPISTimages and UVES / VLT spectra in section 2. In section 3, wecompute the production rates and we discuss the gas and dustactivity pre- and post-perihelion as well as the properties of thedust. The relative molecular abundances and their evolution withrespect to the heliocentric distance are discussed in section 4 andcompared to the IR mother species abundances. In section 5, wepresent the nitrogen and carbon isotopic ratios and the NH (andNH ) ortho-para ratio derived from the UVES high resolutionspectrum. In section 6, we investigate the dynamical evolutionof comet 21P within the last 10 years. Discussion of the chem-ical composition of 21P and the possible scenarios of its deple-tion in carbon species are given in section 7. The summary andconclusions of this work are given in the last section 8.
2. Observation and data reduction
We started monitoring 21P with TRAPPIST-North (hereafterTN) at the beginning of June 2018 when the comet was at 1.55au from the Sun. The comet was then observed from the southernhemisphere with TRAPPIST-South (hereafter TS) from the be-ginning of September 2018. The pair of TRAPPIST telescopes(Jehin et al. 2011) is in such a case very useful as it allowed acontinuous monitoring of the comet before and after perihelion.We collected images with the cometary HB narrow-band filters(Farnham et al. 2000) to measure the production rates of the rad-icals OH, NH, CN, C , and C . We also acquired images withthe dust continuum filters BC, GC, and RC for blue, green andred (Farnham et al. 2000). We used the broad-band filters B, V,Rc, and Ic (Bessell 1990) to compute the Af ρ parameter whichis a proxy of the dust production rate (A’Hearn et al. 1984) andto derive the dust colours.Throughout the passage of the comet, we made a high ca-dence monitoring of 21P with images taken about twice a week.On photometric nights, we also obtained long series of obser-vations with the gas narrow-band filters, especially CN and C filters, to measure the variations of the production rates duringthe same night due to the rotation of the nucleus. We chose theexposure time of the di ff erent filters depending on the brightnessof the comet. We used exposure times between 60 s and 240s for the broad-band filters and between 600 s and 1500 s forthe narrow-band filters. Observational circumstances and num-ber of sets of each filter are summarized in Table A.1 in the ap-pendix. We started to collect data three months before perihelionto four months after perihelion. The comet reached perihelion onSeptember 10, 2018 at a heliocentric distance of 1.01 au and ageocentric distance of 0.39 au. In total the comet was observed Table 1: The scale lengths and the fluorescence e ffi ciency of dif-ferent molecules at 1 au scaled by r − h .Molecules Parent Daughter g-factors(km) (km) erg s − mol − OH(0,0) 2.4 × × × − NH(0,0) 5.0 × × × − CN( ∆ υ =
0) 1.3 × × × − C ( λ = × × × − C ( ∆ υ =
0) 2.2 × × × − Notes.
The scale lengths are equivalent to the lifetimes of molecules aswe are using a constant radial velocity of 1 km / s (A’Hearn et al. 1995).The fluorescence e ffi ciency are taken from Schleicher’s website a . a https://asteroid.lowell.edu/comet/gfactor.html on 50 di ff erent nights with both telescopes, 13 nights before per-ihelion and 37 after. We used the same procedures described inour previous papers (e.g, Opitom et al. (2015a); Moulane et al.(2018) and references therein) to reduce the data and to performthe flux calibration. To compute the production rates, we con-verted the flux of di ff erent gas species to column densities andwe adjusted their profiles with a Haser model (Haser 1957). Thissimple model, but widely used, is based on a number of assump-tions. Outgassing is assumed to be isotropic and the gas has aconstant radial velocity of 1 km / s. Parent molecules coming o ff the nucleus are decaying by photo dissociation to produce theobserved daughter molecules. The model adjustment was per-formed at a physical distance of 10 000 km from the nucleus. Ta-ble 1 shows the scale lengths and g-factors of di ff erent moleculesat 1 au scaled by r − h . More details about the Haser model and itsparameters are given in our previous works (see Moulane et al.(2018) and references therein). We would like to point out thatwe used the same parameters as those from Schleicher & Knight(2018) for the previous apparitions of 21P. We derived the Af ρ parameter, a proxy for the dust production (A’Hearn et al. 1984),from the dust profiles in the cometary dust continuum BC, GC,and RC filters and the broad-band Rc and Ic filters. It was com-puted at 10 000 km from the nucleus and corrected for the phaseangle e ff ect according to the phase function normalized at θ = ◦ derived by D. Schleicher . We obtained one spectrum of comet 21P with the Ultraviolet-Visual Echelle Spectrograph (UVES) mounted on the Unit 2telescope (UT2) at ESO’s VLT on September 18, 2018 (a weekafter perihelion, r h = ∆= +
580 covering the range 3030 to 3880 Å in the blue and 4760to 6840 Å in the red. We used a 0.44 (cid:48)(cid:48) wide slit, providing a re-solving power R ∼
80 000. We obtained one single exposure of3000 s at 8h35 UT with a mean airmass of 1.7. This exposureprovided two di ff erent spectra, both of them covering one of theabove mentioned spectral ranges.The ESO UVES pipeline was used to reduce the spectra inthe extended object mode, keeping the spatial information. Thespectra were corrected for the extinction and flux calibrated us-ing the UVES master response curve provided by ESO. One-dimensional spectra were then extracted by averaging the 2D http://asteroid.lowell.edu/comet/dustphase.html Article number, page 2 of 14oulane et al. 2020: Comet 21P / Giacobini-Zinner
27 28 29 L og [ Q ( OH )]
25 26 L og [ Q ( NH )] Schleicher 1985Schleicher 1998Schleicher 2018TN+TS 2018
25 26 L og [ Q ( C N )]
24 25 L og [ Q ( C )]
23 24-1.6 -1.4 -1.2 -1 1.2 1.4 1.6 L og [ Q ( C )] Heliocentric distance (au) 2 3-1.6 -1.4 -1.2 -1 1.2 1.4 1.6 L og [ A ( )f ρ ( R )] Heliocentric distance (au)
Ehlert et al. 2019
Fig. 1: The logarithm of the production rates (in molec / s) of each observed species and of the A(0)f ρ parameter (in cm), of comet21P during its 2018 return (this work and Schleicher & Knight (2018)) are compared with two previous apparitions in 1985 and1998 (Schleicher & Knight 2018) as a function of heliocentric distance. The dashed vertical line represents the perihelion distanceon September 10, 2018. The maximum of the gas and dust activity was reached at 1.07 au from the Sun, on August 17, 2018, 24days before perihelion.spectra with simultaneous cosmic ray rejection and then cor-rected for the Doppler shift due to the velocity of the comet withrespect to the Earth. More details about the UVES data reductionare given in the UVES manual . The dust-reflected sunlight wasfinally removed using a reference solar spectrum BASS2000 .More in depth description of the steps for UVES data reductionand the solar spectrum subtraction is given in Manfroid et al.(2009) and references therein.
3. Activity and composition
Along with our monitoring of comet 21P with the TRAPPISTtelescopes, we derived the OH, NH, CN, C , and C productionrates. They are summarized in Table A.2 and their evolution as ftp://ftp.eso.org/pub/dfs/pipelines/uves/uves-pipeline-manual-22.17.pdf http://bass2000.obspm.fr/solar_spect.php a function of the heliocentric distance are compared with twoprevious passages in Figure 1.We started to detect most of the radicals in the coma by theend of June 2018 (except NH one month later). The various pro-duction rates and the dust activity have been increasing slowlyas the comet was getting closer to the Sun (from 1.52 to 1.07au). The maximum of the activity was reached at 1.07 au fromthe Sun, on August 17, 24 days before perihelion. It then startedto decrease rapidly after perihelion. CN was detected in our datauntil the end of 2018 at 1.66 au, while OH, C , and C werenot detected anymore after the beginning of November at 1.4 auand NH early October at 1.2 au. We found that like for the pre-vious apparitions (Schleicher et al. 1987), the production ratespre-perihelion are larger by more than a factor two than post-perihelion. It is clear from Figure 1 that the asymmetric activityis seen for all species and this behaviour does not change over thevarious apparitions (Schleicher et al. 1987; Combi et al. 2011) asshown also in Figure 2 for the water production rate. The samebehavior has been reported for the parent molecules (H O, CO,
Article number, page 3 of 14 & A proofs: manuscript no. Moulane_21P CH , C H , C H , NH and CH OH) production rates derivedat infrared wavelengths during the 2018 passage (Faggi et al.2019; Roth et al. 2020). This might due to the shape of thenucleus and its spin-axis orientation. This e ff ect has been ob-served in several comets such as 9P / Tempel 1 (Schleicher 2007),81P / Wild 2 (Farnham & Schleicher 2005) and also for comet67P / Churyumov-Gerasimenko (Schleicher 2006; Opitom et al.2017). It has been shown very clearly by Rosetta mission thatthe maximum activity of 67P was well associated to the illumi-nation of the most southern regions, which were receiving themaximum of solar flux, and were subject to intense erosion (Laiet al. 2019). Recently, Marshall et al. (2019) has show for thosethree comets that the nucleus shape, the spin axis orientation,and the distribution of activity on the comet’s surface can ex-plain the water production rate light-curve as a function of theheliocentric distance.Around the maximum of the activity, the production ratesare almost the same as those measured in the previous appari-tions showing that there is no decrease of the activity level of21P over the last five orbits. Our production rates agree usuallyvery well with those derived by Schleicher & Knight (2018) whoused the same technique, while we noticed a discrepancy at largeheliocentric distance and post-perihelion in the 1985 and 1998apparitions data (Schleicher et al. 1987; Schleicher & Knight2018). This could be due to a sensitivity issue in their data asthe production rates seem to level o ff on both sides of perihe-lion while the distance increase or to a higher activity level ofthe comet after perihelion in the past. It has been also found thatthere is no significant change in the production rates of hyper-volatile molecules (CO, CH , and C H ) in comet 21P over thethree di ff erent apparitions, 1998 (Weaver et al. 1999; Mummaet al. 2000), 2005 (DiSanti et al. 2012) and 2018 (Faggi et al.2019; Roth et al. 2020). O production rate
The water production rate is the most significant indicator ofthe activity of a comet. It can be measured directly from near-infrared observations or derived from OH emission at 3090Å and radio wavelengths or from H Lyman- α emission at1216 Å (Combi et al. 1986) assuming that both OH and H arisefrom the dissociation of H O. In this work, we computed thevectorial-equivalent water production rates according to an em-pirical procedure based on a comparison of OH and water pro-duction rates derived from the mean lifetimes, velocities, andscale lengths given by Cochran & Schleicher (1993). Schle-icher et al. (1998) built an empirical relationship Q ( H O ) = . r − . h Q ( OH ) based on a r − . h dependence of the H O out-flow velocity, a photodissociation branching ratio for water toOH of 90%, and the heliocentric distance. Figure 2 shows thewater production we derived compared to previous apparitions(with di ff erent techniques) as a function of days to perihelion.We used the formula given above to convert Q(OH) to water pro-duction rates for Schleicher & Knight (2018) data. Combi et al.(2011) derived the production rates from the H Ly- α emissionobserved by the SWAN instrument on board SOHO in 1998 andin 2005. Combi & Feldman (1992) values are derived from HLy- α emission observed by the IUE mission for the 1985 appari-tion. From the Pioneer Venus Orbiter ultraviolet system (UVS)instrument, McFadden et al. (1987) derived the water productionrates from OH (3090 Å) emission. Fink Uwe & Hicks (1996)derived the water production rates from the [OI]( D) forbiddenline doublet using a correlation between the water production rates and the total photon luminosity. Faggi et al. (2019) andRoth et al. (2020) measured directly the water production ratesfrom near-infrared spectra. TRAPPIST and UVES data pointsare from this work (see section 3.2 and 5.1). The maximumin the last four apparitions was reached about one month be-fore perihelion and does not change over all apparitions, but weobserve a clear systematic di ff erence between the narrow bandand spectroscopic methods in the optical on one hand and themeasurements made from the space observations of the H Ly- α emission in the UV on the other hand. The maximum of thewater production we measured was on August 17, 24 days be-fore the perihelion, and it reached (3.72 ± × molec / s ingood agreement with Schleicher & Knight (2018) measurementof 4.20 × molec / s at the heliocentric distance 1.07 au. Us-ing the same technique for the 1985 apparition, Schleicher et al.(1987) reported Q(H O) = × molec / s when the cometwas at 1.05 au from the Sun. Using high resolution infrared spec-troscopy, Weaver et al. (1999) measured ∼ × molec / s atr h = × molec / s from the H Ly- α emis-sion observed by the SWAN / SOHO at r h = ff set between varioustechniques has been reported in previous studies and as early ascomet 1P / Halley (Schleicher et al. 1998). The origin of this dis-crepancy is not clear but it is obvious that there is a good agree-ment when the same technique is used. This indicates that thelevel of activity of 21P was the same over the past four decadesand did not decrease like comet 41P / Tuttle–Giacobini–Kresakwhich has been losing as much as 30% to 40% of its activityfrom one orbit to the next (Moulane et al. 2018).
To estimate the active area of the nucleus’ surface, we modelledthe water production using the sublimation model of Cowan &A’Hearn (1979). Due to the low thermal inertia of cometary nu-clei (Gulkis et al. 2015), the slow-rotator approach was adoptedin a number of cases as the most appropriate way to compute thecometary outgassing (see e.g., Bodewits et al. 2014; Lis et al.2019). The slow-rotator model assumes every facet of the nu-cleus is in equilibrium with the solar radiation incident upon it,with the rotational pole pointed at the Sun. As mentioned previ-ously, the size of 21P’s nucleus, necessary to convert the activearea to the active fraction of the whole surface, is not well con-strained so far, with a radius ranging from 1 to 2 km. Hence,to estimate the active fraction of the surface we assumed a ra-dius of 1.5 ± ∼ at 1.49 aupre-perihelion, reached a maximum of ∼
12 km at 1.07 au pre-perihelion, and decreased to ∼ at 1.31 au post-perihelion.Table 2 shows the minimum and maximum active areas andactive fraction for 21P using the slow-rotator model at someinteresting heliocentric distances. We obtained di ff erent valuesin comparison with previous estimations given by Combi et al.(2019). The reason is twofold; first, the already mentioned dis-crepancy in the water production rates found via di ff erent obser-vational techniques (see Section 3.2), and secondly, the modelused by the authors (fast-rotator), which is less appropriate todescribe the cometary outgassing. Article number, page 4 of 14oulane et al. 2020: Comet 21P / Giacobini-Zinner -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 Q ( H O ) [ m o l ec u l e s / s ] Time to perihelion (Day)
McFadden et al. 1987Schleicher et al. 1987Combi et al. 1992Fink et al. 1996Combi et al. 2011Combi et al. 2011Roth et al. 2020Faggi et al. 2019Schleicher et al. 2018UVES 2018TRAPPIST 2018
Fig. 2: H O production rates of comet 21P as a function of days to perihelion in 2018 compared to the previous apparitions (1985,1998 and 2005). More description about the data is given in section 3.2.Table 2: Active area (km ) and active fraction of the surface (%)for 21P using the slow-rotator model at some interesting helio-centric distances. Date UT r h Active Area Active fraction(au) (km ) (%)(a) 2018 Jun 22 -1.49 4.9 ± ± ± ± ± ± + ± ± + ± ± Notes. (a) The first measurement during our monitoring campaign, (b)the maximum activity during our monitoring campaign, (c) the lastmeasurement before perihelion passage, (d) the mean of the first mea-surements after perihelion passage with similar heliocentric distancesof 1.02 au, and (e) the last and minimum measurements during ourmonitoring campaign. Large errors in the active fractions of the surfacecame from the large uncertainties in the radius of the nucleus, which weadopted as 1.5 ± We computed the A(0)f ρ parameter at 10000 km, as defined byA’Hearn et al. (1984), using broad-band (Rc and Ic) and narrow-band dust continuum filters (RC,GC,BC) (see Table A.2). Figure3 shows its evolution as a function of time to perihelion. Ourresults are in very good agreement with those reported by Ehlertet al. (2019), as shown in the right bottom panel of Figure 1.Like for the gas, the maximum was reached on August 17 with a value of (1646.1 ± ρ values obtained with the narrow-bandfilters which are not contaminated by the gas emissions to derivethe dust colours. The normalized reflectivity gradients betweenwavelength λ and λ is defined as (A’Hearn et al. 1984; Jewitt& Meech 1986): S v (% / = A f ρ − A f ρ A f ρ + A f ρ × λ − λ (1) λ and λ are the e ff ective wavelengths of the filters:BC[4450 Å], GC[5260 Å] and RC[7128 Å].We found that the RC-GC, RC-BC and GC-BC coloursare redder than the Sun with mean values of (14.8 ± ± ± / v = / v = / ± / Article number, page 5 of 14 & A proofs: manuscript no. Moulane_21P A ( )f ρ ( c m ) Time to perihelion (Days) RCGCBCRcIc
Fig. 3: The A(0)f ρ parameter measurements, computed at10 000 km from the nucleus and corrected for the phase anglee ff ect, for the broad band (Rc and Ic) and narrow-band cometaryfilters (RC,GC,BC) as a function of days to perihelion.1993). They fall within the range observed for most JFCs (Lamy& Toth 2009; Solontoi et al. 2012; Jewitt 2015). During our longmonitoring, we did not detect any significant variation of thecolour of the dust in the coma (or any outburst). -40-20 0 20 40 60 -80 -60 -40 -20 0 20 40 60 S v ( % / A ) Time to perihelion (Day) RC-BCRC-GCGC-BC
Fig. 4: Normalized reflectivity gradients S v (% per 1000 Å) ofcomet 21P for di ff erent colour indices as a function of days toperihelion.
4. Abundances ratios
Studying the molecular abundances and their ratios with respectto the distance to the Sun gives information about the homogene-ity of a comet’s nucleus and the chemical processes involvedin the coma. Based on the relative abundance of 41 comets,A’Hearn et al. (1995) classified comets into two groups basedon their C / CN ratio. Typical comets are defined as those havinga Log[Q(C ) / Q(CN)] ≥ -0.18 while the carbon-chain depletedcomets are those below that value. This classification was con-firmed later by other photometric and spectroscopic studies oflarge data sets (Schleicher 2008; Fink 2009; Langland-Shula & Smith 2011; Cochran et al. 2012) and must reflect some di ff er-ences between the formation conditions (the pristine scenario)or a change of relative composition with time (several perihelionpassages) of these comets (the evolutionary scenario). Figure 5shows the evolution of the 21P abundance ratios of the variousradicals with respect to OH (a proxy of water) and CN, as a func-tion of heliocentric distance. It is clear that 21P abundance ratiosin the 2018 return agree with the mean values of depleted cometsgiven in A’Hearn et al. (1995). Table 3 summarizes the relativeabundances in 2018 compared to 1985 and 1998 data using thesame technique and the same Haser model parameters (Schle-icher & Knight 2018). Our 2018 ratios are the mean values for allthe data obtained (see Table A.2). Like for the activity level overthe past passages, the relative abundances did not change overthe last 5 orbits. We note that the Af ρ values derived in 1985 andin 1998 by Schleicher & Knight (2018) were computed for thenarrow band GC[5260 Å] filter while we used the BC[4450 Å]filter. After correcting their Af ρ values for the phase angle e ff ectusing the same function as for the TRAPPIST data (see section2.1), both data sets are in agreement. This indicates that there isno evidence of changes in the chemical composition in the comaof the comet at di ff erent heliocentric distances (in the range 1.0to 1.5 au) and over the five orbits, which is an argument to re-ject the evolutionary origin of the carbon chain depletion in thatcomet.Table 3: Relative molecular abundances of comet 21P over thelast passages compared to the mean values for typical comets. Log production rate ratio1985 ( a ) ( a ) ( b ) Typical comets ( c ) C / CN -0.64 -0.50 -0.52 ± ± / CN -1.42 -1.30 -1.39 ± ± / OH -2.59 -2.67 -2.62 ± ± / OH -3.23 -3.17 -3.16 ± ± / OH -4.02 -3.98 -4.03 ± ± / OH -2.66 -2.87 -2.68 ± ± ρ / CN -22.74 -22.73 -22.70 ± ± ρ / OH -25.33 -25.42 -25.32 ± ± Notes. ( a ) Schleicher & Knight (2018), ( b ) This work, ( c ) A’Hearn et al.(1995).
As seen in the bottom panel of Figure 5, there is also no ev-idence that the dust-to-gas ratio represented by A(0)f ρ / Q(CN)and A(0)f ρ / Q(OH) depends on the heliocentric distance. Wefound that this ratio in 21P is consistent with the average valueof depleted comets and higher than the mean value of the typ-ical comets as defined in A’Hearn et al. (1995) (see Table 3).Lara et al. (2003) obtained a value of Log[A(0)f ρ / Q(CN)] = -22.91 ± ff er-ent species relative to H O such as C H (2-3%), HCN(0.3-0.4%) and C H (0.5-0.8%) assuming that all species are parentmolecules. C H has been found depleted with respect to HCNby a factor five compared to other comets like Hyakutake and Article number, page 6 of 14oulane et al. 2020: Comet 21P / Giacobini-Zinner -3.5-3-2.5-2
TypicalDepleted L og Q ( C ) / Q ( OH ) -1-0.5 0 0.5 L og Q ( C ) / Q ( C N ) -4.5-4-3.5-3-2.5 L og Q ( C ) / Q ( OH ) -2-1.5-1-0.5 0 L og Q ( C ) / Q ( C N ) -3-2.5-2-1.5 L og Q ( NH ) / Q ( OH ) -0.5 0 0.5 1 L og Q ( NH ) / Q ( C N ) -26-25.5-25-1.3 -1.2 -1.1 1.1 1.2 1.31.01 L og A ( )f ρ / Q ( OH ) Heliocentric distance (au) -24-23.5-23-22.5-22-1.3 -1.2 -1.1 1.1 1.2 1.31.011.01 L og A ( )f ρ / Q ( C N ) Heliocentric distance (au)
Fig. 5: Evolution of the logarithmic production rates ratios of each species with respect to OH and to CN as a function of heliocentricdistance. The red dashed line represents the mean value of typical comets as defined in A’Hearn et al. (1995) while the blue onerepresents the mean value of the depleted group. The bottom panels shows the dust-to-gas ratio represented by A(0)f ρ -to-OH andA(0)f ρ -to-CN. The vertical dashed line shows the perihelion distance on September 10, 2018 at r h = UT Date r h (cid:52) Production rates (10 molec / s) Reference(au) (au) Q(OH) Q(H O) Q(CN) Q(HCN) Q(C ) Q(C H ) Q(C H ) Q(NH) Q(NH )2018 Jul 30 1.17 0.61 1810 ±
28 4.55 ± ± ± ±
394 - < < ± < ±
385 - 6.16 ± ( a ) - < ( a ) ± < ( a ) Roth et al. (2020)2018 Sep 07 1.01 0.39 3036 ±
357 3206 ±
112 - - - - 10.60 ± ±
586 4.30 ± < ± < ±
33 4.39 ± ± ± ±
864 - - - - 4.55 ± ±
25 - 1.68 ± ± ± ±
255 - - - - 2.92 ± Notes. ( a ) From Roth et al. (2018) measured on July 29, 2018. Upper limits are 3 σ for both Roth et al. (2020) and Faggi et al. (2019) results. Hale–Bopp, a result that has been confirmed at this apparitionby Faggi et al. (2019).We derived a Q(C ) = × molec / s which is consis-tent with the upper limit of Q(C H ) < × molec / s re-ported by Faggi et al. (2019) and < × molec / s reportedby Roth et al. (2018) at 1.18 au from the Sun. This agree-ment indicates that C could be a daughter species of C H . C also has the possibility to come from C H and HC N (Hel-bert et al. 2005; Weiler 2012; Hölscher 2015) or released fromorganic-rich grains (Combi & Fink 1997), but a detailed chem-ical model of the coma would be needed to go in more de-tails. We also found a good match between Q(CN) = × and Q(HCN) = × molec / s (Faggi et al. 2019) at 1.01 au,showing that HCN could be the main parent molecule of CN Article number, page 7 of 14 & A proofs: manuscript no. Moulane_21P in 21P. This result is known for several comets using di ff erentmethods, including comparison between HCN and CN produc-tion rates (Rauer et al. 2003; Opitom et al. 2015b), coma mor-phologies (Woodney et al. 2002), and also carbon and nitrogenisotopic ratios in both species (Manfroid et al. 2009; Bockelée-Morvan et al. 2015). We should note however that in some casesboth abundances do not agree and that other sources, for instanceextended sources, have been claimed for the CN origin (Frayet al. 2005).Some molecules such as C H , CH C H , and CH C H areproposed to be the parent molecules of C (Helbert et al. 2005;Mumma & Charnley 2011; Hölscher 2015), but these complexspecies were not observed at infrared or at radio wavelengths.NH and NH were found to be depleted in 21P in the previousapparitions (A’Hearn et al. 1995; Fink 2009). New infrared ob-servations in 2018 show very low NH in 21P, with an upperlimit ratio of Q(NH ) / Q(H O) < / Q(OH) = ) / Q(H O).
5. Optical high-resolution spectrum
The UVES spectrum o ff ered the possibility of computing inde-pendently the water production rate at the time of observation.We first measured the overall flux for the OH (0,0) band near309 nm, integrated over the whole slit. We found 1.47 × − ergs − cm − arcsec − . The fluorescence e ffi ciency computed for thisband and the heliocentric distance and velocity at the time of ob-servation was 2.62 × − s − (or 1.71 × − erg s − molecule − if scaled to 1 au; see details on the fluorescence model in Rous-selot et al. (2019)). From these values and a Monte-Carlo simu-lation of the water molecules creating OH radicals in the innercoma (model based on equations given by Combi & Delsemme(1980)) it is possible to compute the corresponding water pro-duction rate for the number of OH radicals observed in theslit (0.44 × O radial velocity, OH and H O lifetimes givenin Cochran & Schleicher (1993) and assuming that 91.8% ofwater molecules dissociate to OH (Crovisier 1989), we foundQ(H O) = × molec / s. This result is in excellent agreementwith the water production rates computed from TRAPPIST ob-servations in the same period (see Figure 2). It must, neverthe-less, be pointed out that it depends of the di ff erent parametersand can change a bit with them, especially with the water life-time. C/ C and N/ N isotopic ratios
The study of the isotopic ratios in comets has attracted consid-erable attention as it contains information about the conditionswhich prevailed at the time of formation of these objects in theearly Solar System (Jehin et al. 2009; Hyodo et al. 2013). Thecarbon C / C ratio has been determined for several cometsfrom the analysis of the C Swan band and CN B-X system inthe optical (Manfroid et al. 2009; Bockelée-Morvan et al. 2015,and references therein). Some in situ measurements have alsobeen obtained in comet 67P by the ROSINA mass spectrome-ter on-board the Rosetta spacecraft for C H , C H , CO (Rubinet al. 2017) and CO molecules (Hässig et al. 2017). All derivedvalues are compatible with the terretrial ratio of 89, except forCO that could possibly be slightly enriched in C. The nitro-gen N / N isotopic ratio was measured for the first time from high resolution spectra of the CN violet band in comets C / / N with respect to the Earthvalue (Arpigny 2003). The same ratio was found later from sub-millimeter observations of HCN in comet 17P / Holmes during itsoutburst and archival data of C / N / N ratio in ammonia via the NH radical (Rousselotet al. 2014). The values obtained are similar to the one found inHCN and CN, which was confirmed by subsequent works (Shin-naka et al. 2014; Rousselot et al. 2015; Shinnaka & Kawakita2016; Shinnaka et al. 2016; Yang et al. 2018). Recent measure-ments performed by the ROSINA mass spectrometer in comet67P provided a ratio N / N = ±
25 for NH and 130 ±
30 forN molecules (Altwegg et al. 2019).We used the C N B-X (0,0) band to estimate the C / Cand N / N isotopic ratios of 21P. We used a CN fluores-cence model to create synthetic spectra of C N, C N, and C N. More details of the model are given in Manfroid et al.(2009). Figure 6 shows the observed CN spectrum comparedto the synthetic one made under the same observational condi-tions. The ratios found for C / C and N / N are 100 ±
10 and145 ±
10, respectively. These values are consistent with those ofabout 20 comets with di ff erent dynamical origins, 91.0 ± ± C / C and N / N respectively (Manfroid et al.2009; Bockelée-Morvan et al. 2015). and NH ortho-para ratios We measured the ortho-to-para abundance ratio (OPR) of NH from the three rovibronic emissions bands (0,7,0), (0,8,0) and(0,9,0), see Figure 7, following the method described in Shin-naka et al. (2011). The derived OPRs of NH and of its parentmolecule NH , are listed for each band in Table 5 and have av-erage values of 3.38 ± ± / HDS determi-nation (NH OPR = ± T spin ) for ammonia of 27 ± OPR (see Figure 9), a possiblecosmogonic indicator linked to the formation temperature of themolecule.Table 5: Derived NH and NH OPRs in comet 21PNH band NH OPR NH OPR T spin (K)(0,7,0) 3.30 ± ± + / − (0,8,0) 3.55 ± ± + / − (0,9,0) 3.15 ± ± + / − Average 3.38 ± ± ± Article number, page 8 of 14oulane et al. 2020: Comet 21P / Giacobini-Zinner R e l a ti v e i n t e n s it y Wavelength (nm) CN ObservedCN Synthetic C N C N Fig. 6: The observed and synthetic CN spectra of the R branch of the B-X (0, 0) violet band in comet 21P.
6. Dynamical evolution
In this section we analyse the dynamical evolution of the cometwithin the last 10 yr. JFCs are highly chaotic objects, whosedynamic evolution must be studied in terms of statistics (Levi-son & Duncan 1994). With this in mind we analysed the evo-lution of the original object, i.e., comet 21P, by considering thenominal values of its orbital parameters as they are defined inJPL-HORIZONS (orbital solution JPL K182 / . We performed the integrations with thenumerical package MERCURY (Chambers 1999), using the in-tegration algorithm Bulirsch-Stoer with a time-step of 8 d andwe included the Sun, all planets and Pluto in the simulation. Inaddition, we also included non-gravitational forces. The resultsof the simulations are displayed in Figure 10.We find that the orbits of all the clones in the simulation arevery compact for a period of ∼ ff erent authors whoapplied di ff erent methods (e.g., integration algorithm used, thenumber of clones, how their clones were generated etc.) is dif-ficult to perform, and any superficial comparison might yieldwrong conclusions. Only one analysis identical to that performedhere has been carried out: for the comet 66P / du Toit by Yanget al. (2019). In that study it was found that the comet belongto the Jupiter Family for at least ∼ × yr, and the stable na-ture of its orbit was evident. This result hints that 21P is likely ayoung member of the Jupiter Family, which has crossed its per- Both sets of the orbital parameters and the covariance matrix ofthe orbit for 21P are published together in the NASA / JPL small-bodybrowser: https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=21P;old=0;orb=0;cov=1;log=0;cad=0 ihelion ∼
230 times with similar distances of q ∼
7. Discussion
As mentioned above, C and C had been found depleted as com-pared to CN in 21P already more than 50 years ago (Mianes et al.1960; Herbig 1976; Schleicher et al. 1987). In A’Hearn et al.(1995) data set, 21P was classified as the prototype of the groupdepleted in carbon-chain molecules. Figure 11 shows our C -to-CN ratio compared to 120 comets (90 comets from Schleicher(2008) and 30 comets from TRAPPIST database (Opitom 2016))as a function of the Tisserand invariant parameter with respectto Jupiter (T J ). About 30% of the comets analyzed were foundto be depleted in carbon-chain elements by varying amountsincluding di ff erent dynamical types of comets, two thirds areJFCs and one third are LPCs (A’Hearn et al. 1995; Schleicher2008; Fink 2009; Cochran et al. 2012). 21P was found to bealso depleted in NH with respect to OH (A’Hearn et al. 1995),this result was confirmed by its depletion in NH using spectro-photometric observations by Konno & Wycko ff (1989) in 1985apparition and later by Fink Uwe & Hicks (1996) in 1998 pas-sage. This depletion in both NH and NH indicates that 21Pis likely depleted in the parent molecule NH which was re-cently confirmed by (Faggi et al. 2019). 21P is not the uniquecase of a comet depleted in both carbon chain and ammoniadaughter species. A few others have been found, but with alesser degree of depletion like 43P / Wolf–Harrington and the splitcomet 73P / Schwassmann–Wachmann 3 (A’Hearn et al. 1995;Fink 2009; Cochran et al. 2012). This indicates that there mightbe a small group of similar comets that formed under similarconditions and di ff erent from other comets. But according to tax- Article number, page 9 of 14 & A proofs: manuscript no. Moulane_21P
Observed spectrumNH (OPR = 3.15)C (T rot = 4000 K) orthopara R e l a t i v e f l u x Wavelength (nm) NH (0,9,0) band on 2018 Sep. 18 Observed spectrumNH (OPR = 3.55) orthopara R e l a t i v e f l u x Wavelength (nm) NH (0,8,0) band on 2018 Sep. 18 Observed spectrumNH (OPR = 3.30) orthopara R e l a t i v e f l u x Wavelength (nm) NH (0,7,0) band on 2018 Sep. 18 Fig. 7: Comparison between the observed and modeled spectraof the NH (0,9,0), (0,8,0), and (0,7,0) bands. The modeled spec-trum of C is also plotted on the NH (0,9,0) band panel, butdue to the depleted nature of 21P, the C lines are not a ff ectingthe NH spectrum. The ortho- and para-lines of NH are labeledin these modeled spectra. The two strong emission lines at 6300Å and 6364 Å are the forbidden oxygen lines in the NH (0,8,0)band panel. We note that the intensity ratio among bands is notcorrect because we scaled intensity for each plot independently.onomy studies, no clear grouping associated with NH abundancehas been identified.Our long monitoring of the abundance ratios combined withprevious studies (Schleicher & Knight 2018; Combi et al. 2011)is ruling out the evolutionary scenario (peculiar compositiondue to repeated passages to perihelion). Indeed our observa-tions show remarkably constant abundance ratios of the di ff er-ent species, especially the depleted C and NH, before and afterperihelion, and over months. The fact that these ratios are stillthe same after five orbits, is in favor of a pristine compositionrather than compositional changes due to repeated passages ofthe comet at perihelion. Jupiter Familycomets Oort Cloud cometsortho/para statistical weight value of NH of 1.0 NH O P R Comet Number
1. 9P/Tempel 12. 21P/G-Z3. 66P/de Toit4. 73P-B/SW35. 73P-C/SW36. 81P/Wild 27. 88P/Howell8. 103P/Hartley 29. 8P/Tuttle10. 153P/H-Z 11. C/1995 O112. C/1999 S413. C/2000 WM114. C/2001 A215. C/2001 Q416. C/2002 T717. C/2002 V118. C/2002 X519. C/2002 Y120. C/2003 K4 21. C/2009 K522. C/2009 P123. C/2012 S124. C/2012 X125. C/2013 R126. C/2013 US1027. C/2014 E228. C/2014 Q2
Fig. 8: Summary of NH OPRs in comets. The orange and greencross symbols symbols are the NH OPR of 21P by VLT / UVES(this work) and by Subaru / HDS (Shinnaka et al. 2020), respec-tively. NH O P R NH T spin (K) Fig. 9: Summary of the NH T spin in 28 comets of various ori-gins. The orange and green cross symbols are the NH T spin of21P by VLT / UVES (this work) and by Subaru / HDS (Shinnakaet al. 2020), respectively.It was argued that this peculiar composition might be linkedto a higher formation temperature, closer to the sun (Schleicheret al. 1987), or in a local disk around Jupiter as it was proposedfor comet 73P (Shinnaka et al. 2011). We obtained high reso-lution, high SNR optical spectra in order to investigate the Cand the N isotopic ratios, as well as the NH2 OPR. 21P appearsto have a normal N / N ratio and a normal NH OPR, simi-lar to other comets. This is in contrast with comet 73P whichhas both peculiar N / N and OPR (see Figure 9 and Shinnakaet al. (2011)). It does not seem then that both comets are relatedand the peculiar composition of 21P still needs to be explained.These peculiarities are clearly linked to the ice composition ofthe nucleus, as the IR studies of the mother molecules are alsoshowing the same kind of depletion, with an obvious link to thedaughter species.
Article number, page 10 of 14oulane et al. 2020: Comet 21P / Giacobini-Zinner C l o s e s t e n c o un t e r s w i t h J u p i t e r ( % ) S e m i m a j o r a x i s ( a u ) E cc e n t r i c i t y I n c li n a t i o n ( d e g ) P e r i h e li o n ( a u ) Time From January 1 st , 2020 (yr) A p h e li o n ( a u ) Fig. 10: Orbital evolution of 21P and its 200 clones for 3000 yrbackward in time from January 1, 2020. From top to the bot-tom: the closest approaches with Jupiter, semi-major axis, ec-centricity, inclination, perihelion, and aphelion distance. In allpanels, the gray lines correspond to the evolution of each clone,the black line is the mean values of the clones, and the red lineis that of the nominal comet 21P. The blue-vertical line corre-sponds to the time of the closest encounter with Jupiter. The ini-tial orbital elements were taken from the JPL Small-Body DataBrowser (orbital solution JPL K182 /
8. Summary and conclusion
We performed an extensive monitoring of comet 21P on bothsides of perihelion with TRAPPIST. The gas species productionrates as well as the dust proxy, A(0)f ρ parameter, were com-puted until the detection limit. We derived the water productionrates for this apparition and we compared it, as well as the var-ious abundance ratios, to previous passages. Using a sublima-tion model for the nucleus and the water production rates, weconstrained the active area of the nucleus surface using slow-rotator approach. An accurate determination of the 21P nucleusparameters is needed to better constrain the active area fraction.Comet 21P shows an asymmetric activity with respect to peri-helion which might be due to the nucleus shape, the spin axisorientation, and the distribution of activity on the comet’s sur-face. The maximum of the gas and dust activity was about 24days before perihelion similar to the previous apparitions. Ac-cording to the molecular abundance relative to CN and OH, weconfirm that 21P is depleted in C , C and NH with respect to -1.5-1-0.5 0 0.5 1 -2 -1 0 1 2 321PJFCsOort Cloud cometsTypicalCarbon-chain depleted L og [ Q ( C ) / Q ( C N )] T jSchleicher 2008TRAPPIST data Fig. 11: The logarithm of C -to-CN ratio of 110 comets as afunction of the Tisserand invariant parameter with respect toJupiter (T J ). Filled symbol present typical comets while theopened symbol present the carbon-chain depleted comets. Ourmeasurement of comet 21P is represented by a blue diamond.The vertical dashed line at T j = H and NH ) and the daughter species from our optical ob-servations has been found. We obtained a high resolution UVESspectrum of 21P a week after perihelion and we derived C / Cand N / N isotopic ratios of 100 ±
10 and 145 ±
10 from the CNR-branch of the B-X (0, 0) violet band. The ammonia OPR wasfound equal to 1.19 ± ± ff erent dynamical types and origins and donot show any peculiarity that could be related to the low carbonchain species and ammonia abundances. Our observations arefavouring a pristine origin for this composition, rather than het-erogeneity or evolutionary scenarios of the surface composition. Acknowledgments
The research leading to these results has received funding from theARC grant for Concerted Research Actions, financed by the Wallonia-Brussels Federation. TRAPPIST-South is a project funded by the Bel-gian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) un-der grant FRFC 2.5.594.09.F. TRAPPIST-North is a project fundedby the University of Liège, and performed in collaboration with CadiAyyad University of Marrakesh. E. Jehin and D. Hutsemékers are FNRSSenior Research Associates. J. Manfroid is Honorary Research Directorof the FNRS. We thanks NASA, David Schleicher and the Lowell Ob-servatory for the loan of a set of HB comet filters. UVES observationsmade with ESO Telescopes at the La Silla Paranal Observatory underprogram DDT proposal 2101.C-5051.
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Appendix A: Observational circumstances and production rates of comet 21P with TRAPPIST telescopes.
Table A.1: Observational circumstances of comet 21P with TRAPPIST telescopes.
UT Date r h ∆ ∆ T PA Gases filters Dust filters Telescope(au) (au) (Days) ( ◦ ) OH NH CN C C BC RC GC Rc Ic TN / TS2018 Jun 09 1.61 1.07 -93.20 38.01 6 1 TN2018 Jun 19 1.52 0.94 -83.25 40.98 1 1 1 1 1 1 1 1 TN2018 Jun 22 1.49 0.90 -80.16 41.98 1 1 1 1 1 1 1 5 1 TN2018 Jun 28 1.44 0.88 -74.20 44.13 1 1 2 1 1 1 1 6 2 TN2018 Jul 09 1.34 0.78 -63.30 48.62 2 1 1 3 1 TN2018 Jul 26 1.21 0.65 -46.25 56.96 1 1 2 1 1 1 1 3 1 TN2018 Jul 30 1.18 0.62 -42.25 59.13 1 2 2 4 TN2018 Aug 17 1.07 0.48 -24.25 69.44 1 1 2 1 1 1 1 6 1 TN2018 Aug 18 1.07 0.49 -23.08 69.99 1 1 1 1 5 1 TN2018 Aug 23 1.04 0.45 -18.13 72.65 1 1 1 1 1 1 1 5 1 TN2018 Aug 29 1.03 0.42 -12.11 75.38 1 1 1 1 1 1 1 5 1 TN2018 Sep 05 1.01 0.39 -05.10 77.67 1 3 1 1 1 5 1 TN2018 Sep 09 1.01 0.39 -01.10 78.01 1 1 2 1 1 1 1 1 8 4 TN2018 Sep 15 1.01 0.39 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Notes. r h and (cid:52) are respectively the heliocentric and geocentric distances, ∆ T is the time to perihelion in days, (-) for pre-perihelion and ( + ) forpost-perihelion. PA is the Solar phase angle. Article number, page 13 of 14 & A proofs: manuscript no. Moulane_21P
Table A.2: OH, NH, CN, C , and C production rates and A( θ = ρ measurements for comet 21P with both TN and TS telescopes. UT Date r h Production rates ( × molec / s) A( θ = ρ TN / TS(au) OH NH CN C C BC RC GC Rc Ic2018 Jun 09 1.61 - - - - - - - - 236.5 ± ± ± ± ± ± ± ±
253 - 28.00 ± ± ± ± ±
365 - 32.00 ± ± ± ± ±
322 31.30 ± ± ± ± ± ± ± ± ±
278 - 45.50 ± ± ± ±
558 54.10 ± ± ± ± ± ± ± ± ±
276 - 50.80 ± ± ± ± ± ±
304 50.20 ± ± ± ± ± ± ± ± ±
286 43.50 ± ± ± ± ± ± ± ± ±
312 - 38.20 ± ± ± ± ± ± ±
328 56.60 ± ± ± ± ± ± ± ± ± ±
300 39.80 ± ± ± ± ± ± ± ± ± ±
326 38.30 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
212 28.50 ± ± ± ± ± ± ± ± ± ±
216 29.40 ± ± ± ± ± ± ± ± ± ±
249 - 28.60 ± ± ± ± ± ±
216 29.00 ± ± ± ± ± ± ± ± ± ±
254 23.80 ± ± ± ± ± ± ± ± ±
217 18.40 ± ± ± ± ± ± ± ± ± ±
182 19.50 ± ± ± ± ± ±
268 20.20 ± ± ± ± ± ± ± ±
248 10.70 ± ± ± ± ± ± ± ±
248 - 15.80 ± ± ± ± ± ± ±
247 11.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
188 9.04 ± ± ± ± ± ± ± ± ± ± ± ± ± ±
234 - 6.88 ± ± ± ± ± ±
191 - 5.62 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Notes. r h is the heliocentric distances. The A(0)f ρ values are printed at 10000 km form the nucleus and corrected from the phase angle e ffff