Draft version June 17, 2020 Typeset using LATEX twocolumn style in AASTeX62

Observations of Disintegrating Long-Period C/2019 Y4 (ATLAS) – A Sibling of C/1844 Y1 ()

Man-To Hui (許文韜)1 and Quan-Zhi Ye (葉泉志)2

1Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA 2Department of Astronomy, University of Maryland, College Park, MD 20742, USA

(Received 2020; Revised June 17, 2020; Accepted 2020)

ABSTRACT We present a study of C/2019 Y4 (ATLAS) using Sloan gri observations from mid-January to early April 2020. During this timespan, the comet brightened with a growth in the effective cross-section of (2.0 ± 0.1) × 102 m2 s−1 from the beginning to ∼70 d preperihelion in late March 2020, followed by a brightness fade and the comet gradually losing the central condensation. Meanwhile, the comet became progressively bluer, and was even bluer than the (g − r ≈ 0.2) when the brightness peaked, likely due to activation of subterranean fresh volatiles exposed to sunlight. With the tailward-bias corrected −7 astrometry we found an enormous radial nongravitational parameter, A1 = (+2.25 ± 0.13) × 10 au d−2 in the heliocentric motion of the comet. Taking all of these finds into consideration, we conclude that the comet has disintegrated since mid-March 2020. By no means was the split new to the comet, as we quantified that the comet had undergone another split event around last perihelion ∼5 kyr ago, during which its sibling C/1844 Y1 (Great Comet) was produced, with the in-plane component of the −1 separation velocity &1 m s . We constrained that the nucleus of C/2019 Y4 before disintegration was &60 m in radius, and has been protractedly ejecting dust grains of ∼10-40 µm(assuming dust bulk density 0.5 g cm−3) with ejection speed ∼30 m s−1 in early March 2020 and increased to ∼80 m s−1 towards the end of the month for grains of ∼10 µm.

Keywords: : general — comets: individual (C/1844 Y1, C/2019 Y4) — methods: data analysis

1. INTRODUCTION Comet), and therefore is a potential sibling of the latter 2 C/2019 Y4 (ATLAS) was a long-period comet that and shares a common progenitor. 5 was discovered by the Terrestrial-Impact Last While as many as ∼10 have been identi- Alert System (ATLAS) at Mauna Loa, Hawai‘i, on UT fied to be members of over than a hundred families 2019 December 28.6.1 The current orbital solution indi- (Nesvorn´yet al. 2015), so far only a small number of cates that the comet orbits around the Sun in a highly comet families have been found, the majority of which elliptical trajectory, with eccentricity e = 0.999, peri- consist of only several members except the Kreutz fam- helion distance q = 0.25 au, and inclination i = 45◦.4. ily and the 96P/Machholz complex (e.g., Boehnhardt Even before the official announcement of the discovery 2004; Marsden 2005; Sekanina & Chodas 2005). This is probably due to the fact that after disruption, small arXiv:2004.10990v2 [astro-ph.EP] 16 Jun 2020 was made by the Center (MPC), ama- teur astronomer M. Meyer noticed and reported that comets are wiped out as a consequence of their higher the orbit of C/2019 Y4 (thence momentarily designated susceptibility to rotational instability due to anisotropic as A10j7UG, when the arc was merely few days) car- loss (e.g., Jewitt 2004; Samarasinha 2007). The ries a great resemblance to that of C/1844 Y1 (Great recognition of the genetic relationship between C/1844 Y1 and C/2019 Y4 enriches the comet family samples and is therefore of good value to better understand how Corresponding author: Man-To Hui comets split and how the family members evolve. [email protected] 1 See Minor Planet Electronic Circular 2020-A112 (https:// 2 minorplanetcenter.net/mpec/K20/K20AB2.html). https://groups.io/g/comets-ml/message/28086 2 Hui & Ye 2020

In this paper, we characterised the physical properties We summarise the observations and the viewing ge- of C/2019 Y4 through Sloan gri observations (Section ometry of C/2019 Y4 from NEXT and LDT in Table 2), and investigated the genetic relationship between 1. C/1844 Y1 and C/2019 Y4 (Section3). The conclu- sions are summarised in Section4. At the time of writ- 2.1. Lightcurve & Colour ing, our new observations of C/2019 Y4 clearly showed We took measurements of comet C/2019 Y4 in the that the nucleus of the comet has split into multiple in- NEXT and LDT images using an aperture of fixed lin- dividual optocentres, and the process is still ongoing. ear radius % = 104 km projected at the distance of the Our detailed analysis of the observed disintegration will comet from the optocentre. The equivalent apparent be presented in another paper in preparation. angular size of the aperture is always large enough such that the slight trailing of the comet in the NEXT data 2. OBSERVATION from January to February 2020 would not be a concern. Figure3a shows our multiband lightcurve measurements We use the publicly available images of comet C/2019 as functions of time, in terms of time from the of Y4 taken by the Ningbo Education Xinjiang Telescope perihelion passage of C/2019 Y4 (tp = TDB 2020 May (NEXT), which is a 0.6 m telescope located at Xing- 31.0). The comet apparently brightened on its way to ming Observatory, Xinjiang, China. Regular monitor- perihelion in a continuous manner until t − tp & −70 d, ing of C/2019 Y4 started on 2020 January 19 and con- after which the downtrend in brightness was seen. tinued to the start of this project. Images were taken We also show the colour of the comet in terms of g −r with a 2k×2k CCD mostly through Sloan g, r, and i and r − i colour indices respectively in the left and right filters, yet in a few nights only r-band images were ob- panels of Figure4. Interestingly, while the r − i colour tained. As the telescope did not follow the nonsidereal index of the comet remained constant and sun-like (i.e., motion, a slight trailing of the comet can be noticed in (r − i) = +0.12 ± 0.02; Willmer 2018) given the mea- images from January to February 2020 (see Figure1), surement uncertainties, the colour across the g and r when longer individual exposures were used. The images bands seems to indicate that the comet had a blueing 00 have an unbinned pixel scale of 0. 63, with a field-of- trend from a reddish colour (g − r ≈ 0.6, in comparison 0 0 view of 22 × 22 , and a typical full-wide-half-maximum to the Sun’s (g − r) = +0.46 ± 0.04; Willmer 2018) 00 00 (FWHM) of 2 -3 . We employed AstroImageJ (Collins since January 2020, reached a dip at an epoch of ∼60 et al. 2017) to subtract bias and dark frames from d preperihelion, when the comet appeared even bluer the images, which were subsequently divided by flat than the Sun (g − r ≈ 0.2), and began to be redden- frames. Then we derived plate constants of the im- ing afterwards. Accordingly, we argue that the blueing ages with the Gaia DR2 catalog (Gaia Collaboration dip was caused by gas emission from a massive amount et al. 2018); the photometric image zeropoints were of previously buried fresh volatiles suddenly exposed to derived with the Pan-STARRS DR1 catalog (Magnier the sunlight, indicative of a disintegration event in mid- et al. 2013) using field stars with sun-like colors (de- March 2020. fined as color indices within ±0.2 mag from the so- We evaluated the intrinsic lightcurve of the comet lar value). The zeropoints were then converted to the by correcting the varying observing geometry and com- SDSS photometric system using the relation derived in puted its absolute magnitude from the apparent magni- (Tonry et al. 2012). The procedure was performed with tude from PHOTOMETRYPIPELINE (Mommert 2017). Additional Sloan g, r, and i-band images of C/2019 Y4 mλ (1, 1, 0) = mλ (rH, ∆, α)−5 log (rH∆)+2.5 log φ (α) , were obtained with the Large Monolithic Imager (LMI; (1) Massey et al. 2013) on the 4.3 m Lowell Discovery Tele- in which λ is the magnitude bandpass, rH and ∆ are scope (LDT; formerly known as the Discovery Chan- the heliocentric and topocentric distances, respectively, nel Telescope) tracking nonsidereally on 2020 January both expressed in au, and φ (α) is the phase function 15 and March 01. These images have a field-of-view of of the comet, approximated by the empirical Halley- 12.03 × 12.03, with a pixel scale of 000. 24 after a 2 × 2 on- Marcus phase function (Marcus 2007; Schleicher & Bair chip binning, and a typical FWHM of ∼100 for the field 2011). The resulting intrinsic lightcurve of C/2019 Y4 is stars. We handled and photometrically calibrated the plotted in Figure3b, from which we clearly notice that LDT images following exactly the same procedures that the lightcurve trend appears broadly the same as the one we applied to the NEXT images. Figure2 shows two of in Figure3a. Indeed the comet continuously brightened the individual r-band images of the comet from the two until .70 d preperihelion, thereafter followed by a con- nights at LDT. spicuous fading process in an intrinsic manner, which we C/1844 Y1 & C/2019 Y4 3

Figure 1. Selected r-band coadded images of comet C/2019 Y4 (ATLAS) from NEXT at Xingming Observatory, with intensity stretched in the same logarithmic scale. Dates in UT are labelled. In the lower left a scale bar of 3000 in length is shown and applicable to all of the panels. The red and white arrows respectively mark the position angles of the antisolar direction and the negative heliocentric velocity vector projected onto the sky plane. Equatorial north is up and east is left. The comet appears slightly trailed in the upper panels because the individual exposure times were longer and the telescope did not track nonsidereally.

pr = 0.1 is the assumed value for the r-band geomet- ric albedo of cometary dust (Zubko et al. 2017), as the true value remains unconstrained. The reason why we only focus on the r-band data here is that these im- ages have less contamination from gaseous emission than the g-band ones do, and they have higher sensitivity than the i-band images do. By employing Equation (2), we estimated the change in the effective cross-section within the fixed photometric aperture during the bright- ening part (−140 . t − tp . −80 d) of the lightcurve Figure 2. Comet C/2019 Y4 (ATLAS) in r-band images in 2 2 to be ∆Ce = (9.9 ± 0.5) × 10 km , corresponding to the same logarithmic scale from LDT at Lowell Observatory. an average growth rate in the effective cross-section of Dates in UT are labelled. A scale bar of 1500 in length is D E ˙ 2 2 −1 given. The red and white arrows bear the same meanings as Ce = (2.0 ± 0.1)×10 m s . Assuming that the in- in Figure1. Equatorial north is up and east is left. creased cross-section consists of dust grains with mean radius a¯ and bulk density ρd, the average net mass-loss rate within the photometric aperture is then given by think also acts as a piece of evidence that a disintegra- D E 4 D E tion event has occurred to comet C/2019 Y4. M˙ = ρ a¯ C˙ . (3) d 3 d e 2.2. Activity & Nucleus Size The product of a¯ and ρd is inversely proportional to the The change in the intrinsic brightness is mostly re- β parameter (0.03 . β . 0.1, see Section 2.3). Substi- lated to the variation in the effective scattering geomet- D E tution into Equation (3) gives us M˙ ≈ 4 ± 2 kg s−1 ric cross-section of the dust particles through d for C/2019 Y4 during the observed brightening period. πr2 0 0.4[m ,r −mr (1,1,0)] Ce = 10 , (2) An approach to constrain the nucleus size of C/2019 pr Y4 is to estimate the minimum active surface that would where Ce is the cross-section, m ,r = −26.93 is the ap- be needed to supply the mass-loss rate during the bright- parent r-band magnitude of the Sun at the mean Earth- ening process, provided that the activity was all driven 8 Sun distance r0 = 1.5 × 10 km (Willmer 2018), and by sublimation of water (H2O) ice. The corresponding 4 Hui & Ye 2020

(a) (b)

Figure 3. The apparent (a) and intrinsic (b) Sloan g, r and i-band lightcurves of comet C/2019 Y4 (ATLAS) as functions of time (in terms of time from the perihelion epoch of the comet, tp = TDB 2020 May 31.0) from NEXT (cross) and LDT (plus). Datapoints from different filters are colour coded as indicated in the legend. Equation (1) was applied to obtain panel (b) from panel (a). See Section 2.1 for details. During the observed timespan, the comet brightened intrinsically until ∼70 days prior to the perihelion, whereafter a decline in brightness was seen.

(a) (b)

Figure 4. The temporal evolution of the colour of comet C/2019 Y4 (ATLAS) in terms of colour indices (a) g − r and (b) r − i from NEXT (cross) and LDT (plus). During the observed timespan, while no statistically confident r − i variation was witnessed, we can notice a blueing trend in the g − r colour until ∼60 d preperihelion, after which the comet appeared to be reddening. C/1844 Y1 & C/2019 Y4 5

Table 1. Observing Information and Viewing Geometry of Comet C/2019 Y4 (ATLAS)

a b c d ◦ e ◦ f ◦ g ◦ h ◦ i Date (UT) Telescope Filter texp (s) rH (au) ∆ (au) α ( ) ε ( ) θ− ( ) θ−V ( ) ψ ( ) 2020 Jan 15† LDT g, r, i 180 2.685 1.998 17.5 124.9 272.4 268.7 2.1 2020 Jan 19 NEXT g, r, i 210 2.623 1.898 17.2 128.2 267.7 266.6 0.6 2020 Jan 29 NEXT g, r, i 180 2.479 1.688 16.5 134.3 253.5 260.5 -3.5 2020 Feb 02 NEXT g, r, i 150 2.418 1.609 16.4 136.1 246.1 257.3 -5.5 2020 Feb 12 NEXT r 150 2.270 1.441 17.0 137.6 225.1 247.5 -10.9 2020 Feb 20 NEXT g, r, i 150 2.147 1.328 18.9 135.3 206.1 237.0 -15.8 2020 Feb 21 NEXT g, r, i 150 2.132 1.316 19.2 134.8 203.8 235.6 -16.4 2020 Feb 22 NEXT g, r, i 150 2.116 1.304 19.6 134.3 201.5 234.1 -17.0 2020 Mar 01 LDT r 30 1.994 1.220 22.9 128.5 183.3 220.8 -22.1 2020 Mar 01 NEXT g, r, i 90 1.989 1.217 23.1 128.2 182.6 220.2 -22.3 2020 Mar 13 NEXT g, r, i 90 1.795 1.126 30.0 115.5 154.6 194.2 -30.0 2020 Mar 27 NEXT g, r, i 30 1.550 1.060 39.6 97.7 118.9 156.7 -38.0 2020 Mar 28 NEXT g, r, i 30 1.533 1.056 40.3 96.5 116.5 154.2 -38.5 2020 Mar 29 NEXT g, r, i 30 1.515 1.053 41.0 95.2 114.0 151.5 -39.0 2020 Mar 30 NEXT g, r, i 30 1.496 1.049 41.8 93.8 111.3 148.6 -39.5 2020 Mar 31 NEXT g, r, i 30 1.478 1.046 42.5 92.5 109.0 146.1 -39.9 2020 Apr 01 NEXT g, r, i 30 1.459 1.042 43.2 91.2 106.5 143.4 -40.4 2020 Apr 02 NEXT g, r, i 30 1.440 1.039 44.0 89.9 104.0 140.8 -40.9 2020 Apr 05 NEXT g, r, i 30 1.389 1.030 46.0 86.3 97.7 134.0 -42.0 2020 Apr 06 NEXT g, r, i 30 1.370 1.027 46.7 85.0 95.5 131.6 -42.4 aNEXT = 0.6 m Ningbo Education Xinjiang Telescope, LDT = 4.3 m Lowell Discovery Telescope. b Individual exposure time. c Heliocentric distance. dTopocentric distance. e Phase angle (Sun-comet-observer). fSolar elongation (Sun-observer-comet). gPosition angle of projected antisolar direction. hPosition angle of projected negative heliocentric velocity of the comet. i Observer to comet’s orbital plane angle with vertex at the comet. Negative values indicate observer below the orbital plane of the comet. † Sloan z images of the comet were obtained in addition to the g, r and i-band images on 2020 January 15. However, since there was no additional z images from other epochs, we omit this band throughout this paper. 6 Hui & Ye 2020 lower bound to the nucleus size can then be estimated nucleus at a common epoch constitute a synchrone line. from In the syndyne-synchrone approximation, the ejection v uD E velocity of dust grains is ignored. u M˙ d t We focused on the r-band images taken since 2020 Rn & . (4) πfs March from NEXT, in which the dust tail of C/2019 The equilibrium sublimation mass flux of H2O gas would Y4 was recorded the most clearly and the optocentre −6 −4 −1 −2 be 1.2 × 10 . fs . 1.2 × 10 kg s m at the appeared untrailed. In Figure5, we plot four exam- range of the heliocentric distances during the timespan ples of the syndyne-synchrone grid computation. Here (1.8 . rH . 2.7 au). Inserting numbers in, we obtain for better visualisation, only sparse syndyne-synchrone Rn & 60 m for the nucleus size of the comet. grids are presented. A much denser grid was used to An upper limit to the nucleus size of C/2019 Y4 could visually determine the β parameter and the dust release have been derived from our detection of the nongrav- epochs about which the dust tail appeared to be sym- itational acceleration (Section 3.1). However, strictly metrical. For data from some single observed epoch, we speaking, the nongravitational effect is only applicable find it difficult to judge whether the symmetry of the to the barycentre of the unresolved fragments, rather dust tail appeared more like a syndyne or synchrone. than an intact nucleus. The equivalent bulk density However, with results from multiple observed epochs, of the barycentre should be much lower than those we realised that the dust tail of the comet can be better of typical cometary nuclei (e.g., 533 ± 6 kg m−3 for approximated by syndyne lines with 0.03 . β . 0.1, 67P/Churyumov–Gerasimenko; P¨atzoldet al. 2016), to because the range of the β parameter remained roughly a degree we cannot firmly constrain. We thus posit that the same, whereas the dust release epoch would keep applying this approach by assuming a typical bulk den- changing, were the tail closer to a synchrone line. This sity for cometary nuclei is no longer valid. find is consistent with the fact that the comet has been active protractedly since the discovery. Assuming a typ- 2.3. Morphology −3 ical value of ρd = 0.5 g cm for the bulk density of C/2019 Y4 has been unambiguously cometary since cometary dust of C/2019 Y4, we find the grain radius our earliest observation in January 2020. Its central op- to be 10 . a¯ . 40 µm, fully within the known dust-size tocentre had been strongly condensed until 2020 April range of other long-period comets (Fulle 2004). 05, after which it started to become even more dif- As the syndyne-synchrone computation does not un- fuse and elongated (see Figure1). 3 The morphologi- veil the ejection speed of the observed dust grains of cal change, altogether with ongoing observations from the comet, we estimate this quantity, denoted as Vej, NEXT in which we see multiple optocentres in the coma, by means of measuring the apparent length of the sun- strongly indicates that the cometary nucleus has split ward extent to the dust coma `. The two quantities are into multiple pieces of fragments (Ye & Zhang 2020). connected by the following relationship This feature has been confirmed by Steele et al.(2020) p and Lin et al.(2020). A detailed study about the disin- 2βµ ∆ tan ` sin α tegration and followup observations will be presented in Vej = , (5) rH another paper in preparation. Physical properties of cometary dust can be revealed where µ = 3.96×10−14 au3 s−2 is the heliocentric grav- by studying the morphology of cometary dust tails(e.g., itational constant. We found ` ≈ 1000 on 2020 March 01, Fulle 2004). To better understand comet C/2019 Y4, ∼1500 on March 13, and ∼2500 on March 31. Substitut- here we adopted the classical syndyne-synchrone compu- ing, Equation (5) yields V ≈ 30 m s−1 at the beginning tation (e.g. Finson & Probstein 1968). A syndyne line is ej of March 2020, ∼50 m s−1 around halfway, and further loci of dust grains that are subject to the β parameter in increased to ∼80 m s−1 at the end of the month for dust common, which is the ratio between the solar radiation grains of β ∼ 0.1. This find is similar to what has been pressure force and the gravitational force of the Sun, and identified for other long-period comets (e.g., Moreno et is inversely proportional to the product of the dust bulk al. 2014). density and the grain radius, ρda, but are freed from the nucleus at various release epochs. Dust grains that are driven by different values of β and are released from the 3. FRAGMENTATION OF THE PARENT 3.1. Orbit Determination

3 The coadded image from 2020 April 05 is not shown, yet the We performed astrometry of comet C/2019 Y4 in the appearance of the comet is similar to that on April 06. r-band images from LDT and NEXT by exploiting As- C/1844 Y1 & C/2019 Y4 7

(a) (b)

5 5

0.5 0.015 0.003 0.0005

0.5 0.015

0.003 0.0005

70 340 6000 70 340 6000

(c) (d)

5 0.5

0.015 5 70 0.003

0.5 0.015 340 0.0005

0.003

0.0005 6000 70 340 6000

Figure 5. Examples of syndyne-synchrone grids for comet C/2019 Y4 (ATLAS) on (a) UT 2020 March 01, (b) March 13, (c) March 28 and (d) April 6. As pointed out by the legend in each panel, the syndynes are plotted as blue curves, with the values of the β parameter labelled as bold texts, and the synchrones are plotted as red dashed curves, with the grain release time from the observed epochs and expressed in days labelled as horizontally oriented unbolded texts. troMagic4 and codes developed by D. Tholen with the square linear fits to the centroids in the J2000 equa- Gaia DR2 catalogue (Gaia Collaboration et al. 2018). In torial east-west and declination directions, respectively, this step, we realised that the tailward bias of the astro- as functions of the aperture size (Figure6). The zero- metric measurements was readily conspicuous in most of aperture astrometry was then obtained, with its uncer- the observed images before early April 2020, after which tainties propagated from the centroiding errors. In addi- the comet apparently lost the central condensation vis- tion to our astrometric measurements of C/2019 Y4, we ibly and so no astrometry was measured.5 To make also included the astrometric observations of the comet sure that our orbit determination will not be skewed by from station T12 (Tholen NEO Follow-Up at the Univer- the tailward bias in the astrometry, we performed least- sity of Hawai‘i 2.24 m telescope) available from the MPC Observations Database6, which have been corrected for the tailward bias as well (D. Tholen, from whom we ob- 4 http://www.astromagic.it/eng/astromagic.html tained the corresponding measurement errors through 5 Actually we have measured a number of images from 2020 April 05 and 06 as a test. However, the measurement uncertain- private communication). The other astrometric obser- 00 ties reach &1 , and therefore we decided not to include these mea- surements or to continue measuring astrometry of C/2019 Y4. 6 https://minorplanetcenter.net/db search 8 Hui & Ye 2020

Figure 6. Example of the angular distance from the zero-aperture centroid in the J2000 equatorial east-west (left) and declination (right) directions as functions of the astrometric aperture size for comet C/2019 Y4 (ATLAS) in a NEXT r-band image from 2020 March 29. The dashed lines are the best-fit least-square linear functions to the datapoints. In each panel, the two vertical dotted lines mark the range of aperture radii used for the best fits. vations available from the MPC Observations Database tically significant. Furthermore, only in very few cases had to be discarded, because we do not think that they has A3 been determined meaningfully (Yeomans et al. are zero-aperture astrometry of the comet, and no as- 2004), suggesting that A3 plays a less significant role trometric uncertainty is available either. in comparison to A1 and A2. Therefore, we opted not 7 We employed the orbit determination code FindOrb to include A3 but only A1 and A2. Our best-fit non- developed by B. Gray, which incorporates gravitational gravitational solution to the orbit of C/2019 Y4 as well perturbation from the eight major planets, Pluto, the as the associated details are summarised in Table2, Moon, and the most massive 16 main-belt asteroids. where we can see that the radial nongravitational pa- −7 The code applies post-Newtonian corrections, and uses rameter of the comet, A1 = (+2.25 ± 0.13) × 10 au the planetary and lunar ephemerides DE431 (Folkner et d−2, is particularly enormous amongst the whole comet al. 2014). Initially we attempted to fit a purely gravi- population, but is by no means unseen amongst disin- −6 tational orbit to the astrometric observations, however, tegrated comets, e.g., A1 = (+1.21 ± 0.12) × 10 au the resulting astrometric residuals exhibits an obvious d−2 for C/2015 D1 (SOHO) by Hui et al.(2015), and −7 −2 systematic trend in observations beyond 3σ from both A1 = (+1.74 ± 0.11)×10 au d for C/2017 E4 (Love- the beginning and the end of the observed arc. The joy) by JPL Horizons. The obtained transverse non- 00 −8 mean RMS residual of the fit is 0. 266 from 104 obser- gravitational parameter, A2 = (−3.1 ± 1.0) × 10 au −2 vations in total. However, after we included the radial d , is far less significant than its radial counterpart A1 and transverse nongravitational parameters A1 and A2, by almost an order of magnitude, and yet is neverthe- first introduced by Marsden et al.(1973), in a nongrav- less typical in the context of disintegrated comets, e.g., −8 −2 itational force model in which the nongravitational ac- A2 = (−1.55 ± 0.09)×10 au d for C/1999 S4 (LIN- −8 −2 celeration of the nucleus is assumed to be proportional EAR), and A2 = (+6.2 ± 0.8)×10 au d for C/2010 to the mass flux of hemispherical H2O-ice sublimation X1 (Elenin), both computed by JPL Horizons. (Hui & Farnocchia, in preparation), the trend can be Our result is similar to the nongravitational solutions 8 completely removed and the mean RMS residual of the to the orbit of C/2019 Y4 by the MPC (A1 = +2.6 × 00 −7 −1 −8 −1 fit shrinks to 0. 126, only roughly the half of the one 10 au d and A2 = −2.9×10 au d , no uncertain- in the gravity-only solution. Adding the normal com- ties given) and by JPL Horizons (A1 = (+2.86 ± 0.17)× −7 −2 −8 −2 ponent of the nongravitational parameter A3 does not 10 au d and A2 = (−0.9 ± 1.2) × 10 au d ), de- improve the orbital fit. Nor is the obtained A3 statis- spite that most of their used astrometric observations

7 https://www.projectpluto.com/find orb.htm 8 https://minorplanetcenter.net/mpec/K20/K20H28.html C/1844 Y1 & C/2019 Y4 9 are likely uncorrected for the tailward bias, and the old Our primary goal is to investigate when the split event nongravitational force model by Marsden et al.(1973) between the comet pair most likely took place and how was adopted. We think that in this specific case, al- large the separation speed was. though the tailward bias is obviously present in their We adopted a simplistic two-body dynamical model used data from individual nights, it has been fortuitously for the split event as follows. At some epoch tfrg, the negated by the varying observing geometry (Table1), as progenitor of the comet pair experienced a split event, well as by the enormous nongravitational effect. during which two major components – C/1844 Y1 and In order to investigate the dynamical relationship be- C/2019 Y4 were produced. The gravitational interac- tween C/1844 Y1 and C/2019 Y4, we also derived a tion between the pair was neglected. So was gravita- gravity-only orbit for the latter, using a shorter observed tional perturbation from the major planets in the solar arc during which we found no statistically significant system, as this effect is generally relatively unimpor- nongravitational effect, because we prefer that the enor- tant (Sekanina & Kracht 2016). To make sure that this mity of the nongravitational effect is unlikely to be char- choice is valid to both C/1844 Y1 and C/2019 Y4, we acteristic of the complete orbit, but reflects the ongoing created 1,000 clones for either of the comets based on the disintegration in the current apparition. For this pur- obtained best-fit gravity-only orbital elements and the pose, we only wanted to include datapoints from the pe- covariance matrices. Then we utilised MERCURY6 (Cham- riod when the nongravitational force has not yet played bers 1999) to integrate the clones together with the nom- an important role. The earliest astrometric data from inal orbits backward to 7 kyr ago, well past the previous T12 were always included. We tested with both gravity- perihelia that took place ∼5 kyr ago. What we found only and nongravitational force models, and checked as- is that neither of the two comets had close approaches trometric residuals of the astrometry, the significance of to any of the major planets since their last perihelion the radial nongravitational parameter A1, and the mean passages, validating the choice of neglecting planetary RMS residuals of the fits. What we found is that, if any perturbation as an approximation. Our task is essen- astrometric observations from 2020 March 13 and there- tially equivalent to identifying how the orbits of C/1844 after are included, the nongravitational solution to the Y1 and C/2019 Y4 intersect and when the pair were orbit of C/2019 Y4 improves the fit considerably in com- both at the intersection point. parison to the gravity-only version. Thus, by discarding The major difference in the orbital elements of comets all of the astrometric observations starting from 2020 C/1844 Y1 and C/2019 Y4 lies in the epochs of their per- March 13, we obtained the final version of the gravity- ihelion moments, whereas all other elements are not dis- only solution to the orbit of the comet. The information tinct (Table2). Therefore for the simplistic dynamical is summarised in Table2 as well. model, we concentrated on the time interval of the peri- For C/1844 Y1, neither the MPC nor JPL Horizons helion epochs of the comet pair. As the orbit of C/2019 give the uncertainty information of its orbital elements. Y4 is more accurate, we used its elements, including pe- Thus, we extracted the topocentric astrometry from riapsis distance q, eccentricity e, inclination i, longitude Bond(1850). Only observations with both R.A. and of ascending node Ω, and ω at decl. measurements available from the same epochs were epoch TDB 1700 January 01.0, referenced to the solar used and fed into FindOrb. The equatorial coordinates system barycentric ecliptic J2000.0, for the sake that were precessed from epoch 1845.0 to 2000.0. Based upon the barycentric orbital elements of both comets remain the mean residual of the preliminary orbital solution, we largely constant between two consecutive periapsis re- downweighted all of the observations by an equal uncer- turns. In this reference system, the differences between tainty of 1500. Ten (out of 80 in total) observations with all of the orbital elements but the periapsis epoch are astrometric residuals & 3σ were rejected as outliers. Our even within the corresponding 1σ orbital element un- best-fit orbital solution for C/1844 Y1, which we found certainties of C/1844 Y1 (Table3). We focus on how to be in agreement with the published one by the MPC the separation velocity between the two comets and the and JPL Horizons at the 1σ level, is presented in Table split epoch should be can produce a difference in peri- 2, together with our solutions for C/2019 Y4. epochs of |∆tp| ≈ 175.5 yr in the following. Separation speeds between fragments of split comets −1 3.2. Split Dynamics are found to be in a range of 0.1 . Vsep . 10 m s (Boehnhardt 2004, and citations therein), of which only The similarity between the orbits of C/1844 Y1 and the in-plane component can alter the periapsis epoch, C/2019 Y4 obviously hints at a possible genetic rela- but not other orbital elements (Sekanina & Kracht tionship between the two comets that they are likely 2016). We investigated the influence of the separa- two components that split from a common progenitor. 10 Hui & Ye 2020 6 6 4 4 4 4 8 8 − − − − − − − − 10 10 10 10 10 10 10 10 × × × × × × × × Uncertainty 1.27 1.01 σ 126 . 0 7 ± 104 (0) 8 − − 10 10 Nongravitational × × 2020 Jan 01-Apr 02 Value 1 3.05 45.386566 6.08 0.252817210.99918998120.574731 4.23 177.411655 1.28 5.68 1.56 − JD 2458941.5 = 2020 Apr 02.0 +2.255 2020 May 31.020035 1.49 7 6 4 4 4 4 C/2019 Y4 − − − − − − 10 10 10 10 10 10 × × × × × × Uncertainty σ 112 . 0 ± 71 (33) Gravity-Only 2020 Jan 01-Mar 01 N/AN/A N/A N/A Value 1 45.382208 4.67 0.99924798120.570633 1.94 177.408982 4.36 3.73 0.252828387 9.66 JD 2458941.5 = 2020 Apr 02.0 2020 May 31.012757 1.90 4 4 2 2 2 3 − − − − − − 10 10 10 10 10 10 × × × × × × Uncertainty σ 521 . 15 70 (10) ± C/1844 Y1 N/AN/A N/A N/A Value 1 45.5615 1.02 1844 Dec 24-1845 Mar 11 0.2503550.998910120.6146 3.63 177.4665 5.78 2.80 7.26 JD 2395001.5 = 1845 Mar 11.0 1844 Dec 14.18922 1.67 2 1 p i e q ω t A A ) Best-Fit Orbital Solutions for Comet Pair C/1844 Y1 and C/2019 Y4 (Heliocentric Ecliptic J2000.0) 2 − )Ω ◦ Table 2. ‡ † ) ) ◦ 00 Quantity ) ◦ Osculation epoch (TDB) Observed arc Number of observations Mean RMS residual ( Note that, however, in the gravity-only solution for C/2019 Y4, the rejected observations are all from 2020 March 13 to April 02. See Section 3.1 for details. The corresponding uncertainties are in days. The unbracketed number is the number of observations used for the orbit determination, whereas the bracketed is the number of observations rejected as outliers. Perihelion distance (au) Eccentricity Inclination ( Longitude of ascending node ( Argument of perihelion ( Time of perihelion (TDB) Nongravitational parameters (au d † ‡ C/1844 Y1 & C/2019 Y4 11

Table 3. Orbital Elements for Comet Pair C/1844 Y1 and C/2019 Y4 (Solar System Barycentric Ecliptic J2000.0)

Quantity C/1844 Y1 C/2019 Y4 Value 1σ Uncertainty Value 1σ Uncertainty Periapsis distance (au) q 0.252465 3.58×10−4 0.252501953 9.75×10−7 Eccentricity e 0.998958 5.82×10−4 0.99912756 1.93×10−6 Inclination (◦) i 45.3351 1.01×10−2 45.339816 4.68×10−4 Longitude of ascending node (◦)Ω 120.5342 2.90×10−2 120.514602 4.37×10−4 Argument of periapsis (◦) ω 177.4367 7.30×10−2 177.450748 3.72×10−4 † −2 −4 Time of periapsis (TDB) tp 1844 Dec 14.4162 1.90×10 2020 May 31.903804 2.21×10 † The corresponding uncertainties are in days. Note—The orbital elements of the two comets are osculated from the gravity-only orbits in Table2 to a common osculation epoch of JD 2341972.5 = TDB 1700 January 1.0. 12 Hui & Ye 2020

Figure 7. The change in periapsis epoch as a function of the split epoch with respect to the time of periapsis passage of C/2019 Y4 (expressed in numbers of orbital revolutions) and the separation velocity in terms of its radial (top), transverse (middle), and normal (bottom) components, given by our simplistic two-body dynamical model. In each panel, the actual difference between the periapsis epochs of the comet pair C/1844 Y1 and C/2019 Y4 is plotted as a horizontal black dotted line. As indicated in the legend, the results with different RTN separation velocity components are distinguished by colours and line styles. Note from the bottom panel that no out-of-plane components of the separation velocity VN alone within the known range of the separation speeds (∼0.1-10 m s−1; Boehnhardt 2004, and citations therein) can bring about significant changes in the periapsis epoch. We prefer that the split event most likely occurred around the previous perihelion return, which was ∼5 kyr ago, and that the gap between the periapsis passages of the pair is due to the in-plane component of the separation velocity. C/1844 Y1 & C/2019 Y4 13 tion velocity in terms of radial, transverse, and normal sis epochs of the pair be caused by separation speeds (RTN) components upon the difference between the pe- within the known range of split comets. Another con- riapsis epochs of two fragments in the simplistic two- clusion we can draw is that the out-of-plane component body dynamical model. The RTN coordinate system of the separation velocity between the pair alone can- has its origin at the primary fragment, with the radial not bring about the observed periapsis epoch difference, axis pointing away from the solar system barycentre, the which is similar to what Sekanina & Kracht(2016) found normal axis directed along the total angular momentum for another comet pair C/1988 F1 (Levy) and C/1988 of the primary fragment, and the transverse axis con- J1 (Shoemaker-Holt). structed to form a right-handed orthogonal system. At To ensure that the planetary perturbation will not some split epoch tfrg, the state vector of the primary drastically alter the conclusion we drew based on the fragment was computed from the orbital elements. The simplistic two-body model, we also employed our code, total velocity of the secondary fragment was updated which includes planetary perturbation and has been by adding the separation velocity Vsep to the velocity utilised to analyse the split event of of the primary fragment. Thereby a new state vector P/2016 J1 (PANSTARRS) (Hui et al. 2017), to find was obtained, which was then converted into the orbital a best-fit nonlinear least-squared solution to the split elements for the secondary fragment. parameters between C/1844 Y1 and C/2019 Y4. We We searched for conditions which should be satisfied treated C/2019 Y4 as the major component, and used for the split between C/1844 Y1 and C/2019 Y4 from its nominal orbit. The major difference here from the the latest possible orbital revolution, such that the ob- application in Hui et al.(2017) is that, instead of fitting served gap between the periapsis moments of the comet a list of topocentric astrometric observations, we fitted pair can be achieved. Given the periodicity of their or- the heliocentric orbital elements of C/1844 Y1 (Table2) bits, there is an indefinite number of desired conditions with the associated covariance matrix from Section 3.1, from more than a single orbital revolution ago. The and minimised the following quantity reason why we consider only the latest possible orbital 2 T revolution for the split event is as follows. Firstly, comet χ (tfrg,VR,VT,VN) = ∆E W∆E, (6) C/2019 Y4 is being fragmenting in the current appari- where ∆E is the orbital element residual vector and W tion, indicative of the nucleus as a loosely bound ag- is the weight matrix determinable from the covariance gregate as typical cometary nuclei (e.g., Weissman et matrix of the orbital elements E = (q, e, i, Ω, ω, t ) of al. 2004, and citations therein). Secondly, given that p C/1844 Y1 (e.g., Milani & Gronchi 2010). Using differ- the number of the observed split events of long-period ent initial guesses, we soon realised that unless adopt- comets was ∼30 amongst a total number of ∼103 long- ing an exhaustive and extensive search, which will be period comets discovered in the past ∼150 yr (identified extremely time consuming, the code would converge to using the JPL Small-Body Database Search Engine), different solutions, indicative of the existence of multi- we can estimate a lower limit to the splitting rate as ple local minima. We present two of the best-fitted solu- ∼2% per century for each long-period comet, which is tions we obtained are listed in Table4. Although there comparable to the one for short-period comets (∼3% is no definite solution to the split parameters between per century per comet; Boehnhardt 2004). Assuming C/1844 Y1 and C/2019 Y4 from the N-body dynami- that all long-period comets behave alike, within one or- cal model, we think that the conclusion based on the bit (∼5 kyr) around the Sun, their progenitor (or any simplistic two-body model remains valid with inclusion of its descendants) would experience at least one split of planetary perturbation, because the best-fit solutions event. Therefore, limiting our search for the split be- all have in-plane components of the separation velocity tween comets C/1844 Y1 and C/2019 Y4 only within a 1 m s−1 and the split epochs around the previous per- timeframe not too much more than one orbital revolu- & ihelion of C/2019 Y4, at heliocentric distance r 10 tion in the past is a reasonable confinement. H . au. In Figure7, we plot the change in the periapsis epoch Although the fragmentation mechanism that led to ∆t as a function of the RTN components of the sepa- p the disruption between the pair remains unclear, we can ration velocity and the split epoch. We can learn that safely rule out the possibility of tidal disruption, because only if the split event that produced C/1844 Y1 and the perihelion distance is larger than the Roche radius of C/2019 Y4 occurred around the previous perihelion pas- the Sun for comets (a few solar radii) by at least an order sage, which was ∼5 kyr ago, and the in-plane compo- of magnitude, and there was no close approach to any nent of the separation velocity between the pair was 1 & of the major planets in the timeframe we investigated m s−1, can the observed difference between the periap- either. We postulate that possible fragmentation mech- 14 Hui & Ye 2020

Table 4. Fragmentation Solutions for Comet Pair C/1844 Y1 and C/2019 Y4

Quantity Solution I Solution II † Split epoch (TDB) tfrg B.C. 2901 Sep 2 ± 20 B.C. 2902 Mar 16 ± 6 RTN separation velocity (m s−1)

Radial component VR −3.1 ± 0.1 +1.9 ± 0.1

Transverse component VT +5.0 ± 0.3 −0.2 ± 0.3

Normal component VN 0 ± 0 +0.1 ± 1.9 Goodness of fit χ2 11.3 8.3 O-C residuals‡ Perihelion distance (au) ∆q −5.38 × 10−4 −2.13 × 10−5 Eccentricity ∆e −1.45 × 10−4 −1.47 × 10−4 Inclination (◦) ∆i −4.20 × 10−3 −6.14 × 10−3 Longitude of ascending node (◦) ∆Ω +1.90 × 10−2 +1.84 × 10−2 Argument of perihelion (◦) ∆ω −3.99 × 10−2 −1.67 × 10−2 −4 −3 Time of periapsis (d) ∆tp −2.08 × 10 −1.39 × 10 † The corresponding uncertainties are in days. ‡ The differences between the observed and computed orbital elements of C/1844 Y1. Note—Only the nominal orbit of C/2019 Y4 was used for the computation, and therefore the uncertainties of the split parameters presented in the table must have been seriously underestimated. We have fixed VN = 0 in Solution I, of which the split epoch would place the separation between C/1844 Y1 and C/2019 Y4 at a heliocentric distance of rH ≈ 4 au postperihelion. The split epoch of Solution II corresponds to the split event at rH ≈ 4 au preperihelion. Compared to the (∼5 kyr), we think that the conclusion from the simplistic two-body dynamic model that the split event occurred around the previous perihelion return and the magnitude of the in-plane component of the separation velocity −1 Vsep & 1 m s is validated.

anisms include rotational instability due to anisotropic the Sun in late March 2020 from an earlier colour mass loss, excessive internal thermal stress or gas pres- that was slightly red (g − r ≈ 0.6) in January and sure (Boehnhardt 2004, and citations therein), and over- February 2020 before the fade in brightness oc- whelming differential stress due to dynamic sublimation curred. This is likely due to that a massive amount pressure (Steckloff et al. 2015). A detailed discussion of of previously buried fresh volatiles suddenly ex- the potential physical mechanisms that caused the ob- posed to sunlight. served ongoing disintegration event of C/2019 Y4 will be presented in another paper in preparation. 3. With the tailward-bias corrected astrometric ob- 4. SUMMARY servations, we detected an enormous radial non- The key conclusions of our study on long-period comet gravitational effect in the heliocentric motion of −7 −2 C/2019 Y4 (ATLAS), the sibling of C/1844 Y1 (Great the comet, A1 = (+2.25 ± 0.13) × 10 au d . Comet) are listed as follows: The transverse nongravitational parameter, A2 = (−3.1 ± 1.0) × 10−8 au d−2, is far less significant. 1. C/2019 Y4 was observed to brighten intrinsically Altogether, we conclude that C/2019 Y4 has dis- with a growth rate in the effective scattering cross- integrated since mid-March 2020. section (2.0 ± 0.1)×102 m2 s−1 from January 2020, until ∼70 d prior to its perihelion passage, where- after the comet started to fade in brightness and 4. The split between the comet pair C/1844 Y1 and started to lose its central condensation. C/2019 Y4 occurred around the previous perihe- lion passage of the progenitor, with the magnitude 2. The colour of the comet across the g and r bands of the in-plane component of their separation ve- −1 once turned even bluer (g − r ≈ 0.2) than that of locity &1 m s . C/1844 Y1 & C/2019 Y4 15

5. We estimate that the nucleus of C/2019 Y4 was the Chinese Academy of Sciences. NEXT is funded by &60 m in radius before the observed disintegra- the Ningbo Bureau of Education and supported by the tion event. The dominant grains in the dust tail Xinjiang Astronomical Observatory. LDT is operated at in March 2020 had 0.03 . β . 0.1 (correspond- Lowell Observatory, a private, nonprofit institution ded- ing mean dust radii ∼10-40 µm, assuming a bulk icated to astrophysical research and public appreciation −3 density of ρd = 0.5 g cm ) and were ejected pro- of astronomy. Lowell operates the LDT in partnership tractedly, with ejection speed ∼30 m s−1 in early with Boston University, the University of Maryland, the of the month, and increased to ∼80 m s−1 at the University of Toledo, Northern Arizona University and end for grains of β ∼ 0.1, similar to those of other Yale University. The Large Monolithic Imager was built long-period comets. by Lowell Observatory using funds provided by the Na- tional Science Foundation (AST-1005313). The LDT observations were obtained by the University of Mary- We thank Jon Giorgini, Bill Gray, and Paul Wiegert land observing team, consisted of L. M. Feaga, Q.-Z. Ye, for helpful discussions, Xing Gao for obtaining the J. M. Bauer, T. L. Farnham, C. E. Holt, M. S. P. Kelley, NEXT images, Ana Hayslip, Casey Kyte, Ishara Nisley, J. M. Sunshine, and M. M. Knight. and LaLaina Shumar for assistance in acquiring the LDT data, David Tholen for sharing us with details of his as- Facilities: 4.3 m LDT, 0.6 m NEXT trometric measurements, and the anonymous reviewer for their insightful comments. The operation of Xing- Software: AstroImageJ(Collinsetal.2017), FindOrb, ming Observatory was made possible by the generous IDL, MERCURY6 (Chambers 1999), PHOTOMETRYPIPELINE support from the Xinjiang Astronomical Observatory of (Mommert 2017)

REFERENCES

Boehnhardt, H. 2004, Comets II, M. C. Festou, H. U. Marcus, J. N. 2007, International Comet Quarterly, 29, 39 Keller, & H. A. Weaver (eds.), University of Arizona Marsden, B. G., Sekanina, Z., & Yeomans, D. K. 1973, AJ, Press, Tucson, 745 pp., 301 78, 211 Bond, G. P. 1850, AJ, 1, 97 Marsden, B. G. 2005, ARA&A, 43, 75 Chambers, J. E. 1999, MNRAS, 304, 793 Massey, P., Dunham, E. W., Bida, T. A., et al. 2013, Collins, K. A., Kielkopf, J. F., Stassun, K. G., et al. 2017, American Astronomical Society Meeting Abstracts #221 AJ, 153, 77 221, 345.02 Farnocchia, D., Chesley, S. R., Chamberlin, A. B., & Milani, A., & Gronchi, G. F. 2010, Theory of Orbital Tholen, D. J. 2015, Icarus, 245, 94 Determination, ISBN 978-0-521-87389-5, Cambridge Finson, M. J., & Probstein, R. F. 1968, ApJ, 154, 327 University Press, Cambridge Folkner, W. M., Williams, J. G., Boggs, D. H., Park, R. S., Mommert, M. 2017, Astronomy and Computing, 18, 47 & Kuchynka, P. 2014, Interplanetary Network Progress Moreno, F., Pozuelos, F., Aceituno, F., et al. 2014, ApJ, Report, 196, 1 791, 118 Fulle, M. 2004, Comets II, M. C. Festou, H. U. Keller, and Nesvorn´y,D., Broˇz,M., & Carruba, V. 2015, Asteroids IV, H. A. Weaver (eds.), University of Arizona Press, Tucson, P. Michel, F. E. DeMeo, & W. F. Bottke (eds.), 745 pp., p. 565 University of Arizona Press, Tucson, 895 pp., 297 Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. P¨atzold,M., Andert, T., Hahn, M., et al. 2016, Nature, 2018, A&A, 616, A1 530, 63 Hui, M.-T., Ye, Q.-Z., Knight, M., et al. 2015, ApJ, 813, 73 Samarasinha, N. H. 2007, Advances in Space Research, 39, Hui, M.-T., Jewitt, D., & Du, X. 2017, AJ, 153, 141 421 Jewitt, D. C. 2004, Comets II, M. C. Festou, H. U. Keller, Schleicher, D. G., & Bair, A. N. 2011, AJ, 141, 177 and H. A. Weaver (eds.), University of Arizona Press, Sekanina, Z., & Chodas, P. W. 2005, ApJS, 161, 551 Tucson, 745 pp., 659 Sekanina, Z., & Kracht, R. 2016, ApJ, 823, 2 Lin, Z.-Y., Hsia, C.-H., & Ip, W.-H. 2020, The Steckloff, J. K., Johnson, B. C., Bowling, T., et al. 2015, Astronomer’s Telegram 13629, 1 Icarus, 258, 430 Magnier, E. A., Schlafly, E., Finkbeiner, D., et al. 2013, Steele, I. A., Smith, R. J., & Marchant, J. 2020, The ApJS, 205, 20 Astronomer’s Telegram 13622, 1 16 Hui & Ye 2020

Tonry, J. L., Stubbs, C. W., Lykke, K. R., et al. 2012, ApJ, Willmer, C. N. A. 2018, ApJS, 236, 47 750, 99 Ye, Q., & Zhang, Q. 2020, The Astronomer’s Telegram 13620, 1 Vereˇs,P., Farnocchia, D., Chesley, S. R., & Chamberlin, Yeomans, D. K., Chodas, P. W., Sitarski, G., et al. 2004, A. B. 2017, Icarus, 296, 139 Comets II, M. C. Festou, H. U. Keller, and H. A. Weaver Weissman, P. R., Asphaug, E., & Lowry, S. C. 2004, (eds.), University of Arizona Press, Tucson, 745 pp., 137 Comets II, M. C. Festou, H. U. Keller, and H. A. Weaver Zubko, E., Videen, G., Shkuratov, Y., et al. 2017, JQSRT, (eds.), University of Arizona Press, Tucson, 745 pp., 337 202, 104