Hopes are being widely expressed that C2023 A3 could become a nakedeye object about the time of its perihelion passage in late 2024. However based on its past and current performance the comet is expected to disintegrate before reaching perihelion. Independent lines of evidence point to its forthcoming inevitable collapse. The first issue which was recently called attention to by I. Ferrin is this Oort cloud comets failure to brighten at a heliocentric distance exceeding 2 AU about 160 days preperihelion accompanied by a sharp drop in the production of dust Afrho. Apparent over a longer period of time but largely ignored has been the barycentric original semimajor axis inching toward negative numbers and the mean residual increasing after the lightcurve anomaly suggesting a fragmented nucleus whose motion is being affected a nongravitational acceleration and an unusually narrow teardrop dust tail with its peculiar orientation implying copious emission of large grains far from the Sun but no microscopic material recently. This evidence suggests that the comet has entered an advanced phase of fragmentation in which increasing numbers of dry fractured refractory solids stay assembled in dark porous blobs of exotic shape becoming undetectable as they gradually disperse in space.
['Astrophysics - Earth and Planetary Astrophysics']
Inevitable Endgame of Comet TsuchinshanATLAS C2023 A3
{'INEVITABLE ENDGAME OF COMET TSUCHINSHAN-ATLAS (C/2023 A3)': 'Zdenek Sekanina La Canada Flintridge, California 91011, U.S.A.; ZdenSek@gmail.com  \nVersion July 9, 2024', 'ABSTRACT': "Hopes are being widely expressed that C/2023 A3 could become a naked-eye object about the time of its perihelion passage in late 2024. However, based on its past and current performance, the comet is expected to disintegrate before reaching perihelion. Independent lines of evidence point to its forthcoming inevitable collapse. The first issue, which was recently called attention to by I. Ferrin, is this Oort cloud comet's failure to brighten at a heliocentric distance exceeding 2 AU, about 160 days preperihelion, accompanied by a sharp drop in the production of dust ( Af ρ ). Apparent over a longer period of time, but largely ignored, has been the barycentric original semimajor axis inching toward negative numbers and the mean residual increasing after the light-curve anomaly, suggesting a fragmented nucleus whose motion is being affected by a nongravitational acceleration; and an unusually narrow, teardrop dust tail with its peculiar orientation, implying copious emission of large grains far from the Sun but no microscopic dust recently. This evidence suggests that the comet has entered an advanced phase of fragmentation, in which increasing numbers of dry, fractured refractory solids stay assembled in dark, porous blobs of exotic shape, becoming undetectable as they gradually disperse in space. Subject headings: individual comets: C/2023 A3; methods: data analysis", '1. INTRODUCTION': "Initially discovered at the Purple Mountain Observatory's XuYi Station, China, on 9 January 2023, then lost and discovered a second time at the Asteroid TerrestrialImpact Last Alert System (ATLAS) search project's station at Sutherland, South Africa, 44 days later (Green 2023), comet C/2023 A3 has been monitored for nearly 17 months at the time of this writing and it still has more than two months to go before reaching perihelion. Since its minimum distance from the Sun is to be merely 0.39 AU, the comet has been widely predicted to become a very bright, possibly naked-eye object around perihelion, especially in early October, in part because of effects of forward scattering of sunlight by microscopic dust at phase angles near 180 · .  \nIn the past, such predictions for other comets with similar parameters (discovered long before perihelion as a fairly bright object, approaching the Sun to a small fraction of the Sun-Earth distance) failed miserably on a number of occasions, but proved correct in some cases. Performance prognostication for individual objects is a high-risk branch of cometary science, which is very slowly being mastered in the process of our gradually learning to understand the whims of comets. Yet, it appears that at least some comets do signal early messages that correlate with their subsequent behavior. Timely recognition and proper interpretation of these messages should pave the way for a more successful future in this unusual field of scientific endeavor.  \nComet C/2023 A3 appears to be a member of the class of undersized Oort cloud objects in orbits with small perihelion distances, many of which turned out to be unable to cope with the physical conditions they were subjected to in the inner Solar System and disintegrated as a result of progressing fragmentation. In the following I address the traits of comet C/2023 A3 that appear to be of the same or similar nature.", '2. THE LIGHT CURVE, DUST CONTENT, AND PRODUCTION OF WATER': "With all pre-discovery images the comet's light-curve database covers about 27 months. The dependence of the total brightness, normalized to a unit geocentric distance, /Ifractur ∆ , on the heliocentric distance, r , has often been expressed by a power law, /Ifractur ∆ = /Ifractur 0 r -n , whose parameters are the absolute magnitude H 0 = -2 . 5 log /Ifractur 0 and exponent n , which determines the slope d log /Ifractur ∆ /d log r . 1 For example, S. Yoshida 2 has used H 0 = 4 . 5 and n = 4 to fit all magnitude observations made between 2 March 2023 and 24 January 2024. Similarly, A. Kammerer 3 has found H 0 = 4 . 7 and n = 3 . 96 from 384 data reported by 64 observers until the end of April 2024.  \nBecause of time constraints, I have not investigated the entire light curve of the comet. From the standpoint of predicting the comet's evolution in the near future, it is the recent activity that is most critical. To assess it, I deemed it sufficient to inspect a representative light curve based on the data reported by a single observer, but on the condition of their maximum possible homogeneity to mitigate a contamination as much as possible.  \nFrom the Comet Observation Database 4 (COBS) website I eventually selected a set of 48 unfiltered CCD totalmagnitude observations made by A. Pearce with a 35-cm f/5 Schmidt Cassegrain between 21 January and 13 June 2024. Although the contribution from the outer coma may be unaccounted for, this is not a major problem, as the emphasis is on rather abrupt brightness variations that begin at the nuclear condensation. 5  \n- 2 See http://www.aerith.net/comet/catalog/search.cgi .\n- 3 See https://fg-kometen.vdsastro.de .\n- 4 See https://cobs.si .  \nFigure 1. Light curve of comet Tsuchinshan-ATLAS between 250 and 106 days before perihelion (21 January through 13 June 2024), as portrayed by a set of 48 CCD total-magnitude observations made by A. Pearce with his 35-cm f/5 Schmidt-Cassegrain. The ordinate is the total observed CCD magnitude of the comet normalized to a unit geocentric distance, H ∆ . Surprisingly, the comet was brightening at an accelerating rate before 165 days preperihelion (15 April 2024), but began to fade afterwards.  \n<!-- image -->  \nTo obtain an insight into the comet's activity variations over the past five months covered by Pearce's observations, I plotted the magnitudes, normalized to 1 AU from the Earth, H ∆ , as a function of time. This plot, displayed in Figure 1, has immediately raised the red flag because it shows a dramatic change at 165 days before perihelion, on 15 April 2024, when the intrinsic brightness reached a peak: the comet was brightening at a rate that appears to have been increasing with time before this date, but began to fade afterwards. This finding supports recent concerns expressed by I. Ferrin 6 (e.g., his message #32307).  \nTo further investigate the comet's activity, I examined the same dataset on a plot that displays the normalized magnitude H ∆ as a function of heliocentric distance r (on a logarithmic scale). This plot, presenred in Figure 2, suggests that the early segment of the light curve, before the brightness peaked, may have consisted of two parts. Up to 190 days before perihelion (21 March 2024), when the comet was 3.3 AU from the Sun, its light curve was described by the absolute magnitude H 0 = 5 . 6 ± 0 . 4 and the slope parameter n = 3 . 5 ± 0 . 3. Hence, the absolute brightness was only about 1 mag fainter than given by both Yoshida and Kammerer, as mentioned above, while the slope was slightly lower than the results of the two authors indicated. This suggests that up to 190 days before perihelion the comet showed only a moderate rate of progressive fading compared to earlier times.  \nThe latter part of the period of brightening in Figures 1 and 2, starting about 190 days before perihelion and 3.3 AU from the Sun, shows a rapid reactivation of the comet. One cannot call it an outburst because the rate of reactivation was not steep enough. However, compared to the previous part of the light curve, n doubled to n = 7 . 2 ± 0 . 3 and H 0 shot up by about 5 magnitudes to H 0 = 0 . 8 ± 0 . 4. The episode could perhaps be described as a surge of activity. It is proposed that, if not  \nFigure 2. Intrinsic brightness of comet Tsuchinshan-ATLAS as a function of heliocentric distance. The set of magnitude data from Figure 1 now shows three likely stages of evolution, as the comet's heliocentric distance was decreasing from 4 AU to 2 AU. At > 3.3 AU the light curve followed a law that did not differ too much from the law that applied far from the Sun. Between 3.3 AU and 3 AU the comet underwent a surge of activity, caused apparently by prolific fragmentation of the nucleus, which resulted in doubling the value of the slope parameter n and a jump in the absolute brightness by 5 magnitudes. By the time the comet reached 3 AU the out-of-control fragmentation of the nucleus ceased on the global scale, with further fracturing proceeding locally. This trend is seen to have continued for more than two months and is expected to continue until the ultimate collapse of the comet still before it reaches perihelion.  \n<!-- image -->  \nearlier, it was about 21 March that the nucleus began to fragment profusely. Emission from a rapidly expanding surface area of short-lived activity could explain the stepped-up brightening, which continued over a period of 25 days (from 21 March to 15 April 2024) at heliocentric distances from 3.3 to 3.0 AU, ending up with the peak at 165 days before perihelion. Once the source of extra emission got exhausted, the remaining mass began to underperform, resulting in the light curve's downturn. Occasional flare-ups caused by further episodes of local fragmentation are likely to be the cause of large scatter among the data after 15 April. This scenario has now continued for more than two months and is expected to continue until the ultimate disintegration of the nucleus. The downward trend is described by somewhat uncertain parameters: H 0 = 11 . 8 ± 0 . 4 and n = -1 . 8 ± 0 . 4.  \nThe evidence from the light curve is strongly supported by the data on a dust-content parameter Af ρ , introduced by A'Hearn et al. (1984) as a proxy to estimate the dust production rate. A website by Cazadores de Cometas 7 (Comet Hunters), which contains, among other information, an Af ρ database by mostly Spanish observers (including the Canary Islands), offers more than 150 data points for comet Tsuchinshan-ATLAS, starting in late February 2023. One of the plots shows that, reduced to a coma 10 000 km in radius, Af ρ gradually increased from a minimum of ∼ 500 cm in early March to ∼ 1800 cm in mid-August 2023. Between December 2023 and February 2024 Af ρ stayed nearly constant at 4000 cm, but in March it started increasing sharply, reaching a peak of ∼ 9000 cm by mid-April, followed by a steep drop.  \nFigure 3. Variations in the dust production parameter Af ρ of comet Tsuchinshan-ATLAS between 15 May and 17 June 2024 (135 to 102 days before perihelion). The large scatter is not necessarily caused in its entirety by errors of observation, but could in part be a product of sudden dust release during episodes of fragmentation, as depicted for the two major features between 120 and 112 days before perihelion. The Af ρ data points near the bottom appear to decrease systematically with time at a crude average rate of ∼ 14 cm per day.  \n<!-- image -->  \nThe curve of Af ρ fairly closely parallels the light curve. Particularly interesting are the variations between midMay and mid-June (from 135 to 102 days before perihelion), which are reproduced in Figure 3. The considerable scatter, similar to the scatter in the light curve, is believed to be in part triggered by short-term release of dust during minor episodes of nuclear fragmentation. The rest of the scatter could be errors of observation. The baseline data in Figure 3 are shown to follow an approximately linear systematic decrease with time at a rate of about 14 cm day -1 , with an extrapolated value of more than 800 cm at perihelion.  \nIt has been known for a fairly long time that some faint comets in orbits with small perihelion distance perish shortly before perihelion (Bortle 1991), although Jewitt & Luu (2019) did recently report a comet that disintegrated at 1.9 AU from the Sun. My investigation of the problem led to a conclusion that the objects that perish are always intrinsically faint Oort cloud comets depleted in dust (Sekanina 2019). To be able to predict the chance of survival from early observations, I introduced a synoptic index for perihelion survival , /Ifractur surv , given by a formula  \n/Ifractur surv = H 0 -5 . 7 -35 6 log q -5 3 log( Afρ ) 0 , (1)  \nwhere H 0 is the absolute magnitude, q is the perihelion distance in AU, and ( Af ρ ) 0 (in cm) is strictly to be taken at 1 AU from the Sun and at a zero phase angle. A comet is predicted to survive perihelion when /Ifractur surv < 0 and vice versa.  \nIn the following section I will demonstrate that comet Tsuchinshan-ATLAS unquestionably has arrived from the Oort cloud, so that application of the synoptic index is relevant. Even though the quantities that determine the index are rather uncertain at present, it nonetheless is of inrerest to compute a preliminary value of /Ifractur surv . To  \ndo so, I first of all adopt H 0 = 11 . 8 from the review of the light curve in Figure 2. Next, from its dependence on time proposed in Figure 3 I compute Af ρ at time t 0 when the comet reaches 1 AU from the Sun preperihelion, t 0 -t π = -38 days. The result is ( Af ρ ) 0 = 1360 cm. With the perihelion distance of 0.391 AU, the synoptic index amounts to  \n/Ifractur surv = +3 . 3 (2)  \nand the comet is predicted to have no chance of surviving perihelion.  \nOf course, one may question whether the linear extrapolation of Af ρ is appropriate and the employed values of H 0 and ( Af ρ ) 0 compatible. As a check, I fit the relevant data from Figure 3 by a power law of heliocentric distance r , similar to the light curve:  \nAfρ ( r ) = ( Afρ ) 0 r -z (3)  \nand obtain by least squares ( Af ρ ) 0 = 1170 ± 40 cm and z = -0 . 90 ± 0 . 15. The synoptic index now equals  \n/Ifractur surv = +3 . 4 , (4)  \nvery close to the result (2).  \nIn summary, from the standpoint of the perihelion survival of comet Tsuchinshan-ATLAS, both its systematic fading documented by the light curve between mid-April and mid-June 2024 and the continuing drop of Af ρ are extremely worrisome. The synoptic index predicts that the comet will perish before perihelion, as an instrumental correction of H 0 could not possibly exceed 1-2 mags.  \nIndependent of this conclusion, I should note that from the spectra taken on 31 May 2024 when the comet was 2.33 AU from the Sun, Ahuja et al. (2024) obtained two major results. One, the production rate ratio Q (C 2 )/ Q (CN) < 0.32, suggesting a carbon depleted comet; and two, Q (H 2 O)=(1 . 50 ± 0 . 37) × 10 28 s -1 , an unexpectedly high rate of water production. At 2.33 AU from the Sun, a spatially averaged sublimation rate of water ice is 1 × 10 17 cm -2 s -1 , suggesting that the total sublimating surface was 15 km 2 ! As only a small fraction of a comet's surface is known to be active, a monolithic nucleus would have been close to 10 km across - an absurd result. An unresolved cloud of sublimating bouldersized fragments offers a more plausible solution.  \nConsider ν fragments of an equal volume. Let the effective diameter of the parent nucleus before a fraction χ of its volume fragmented be D par and the effective diameter of each fragment D frg . Then  \nχD 3 par = νD 3 frg . (5)  \nLet the sublimating fraction of the surface of the parent nucleus be f par /lessmuch 1. Since the previously hidden icerich surface is, because of fragmentation, being exposed to sunlight for the first time, one can assume that for an overwhelming majority of fragments their entire surface facing the Sun is sublimating, so that f frg = 1 2 . The active surface area before fragmentation is  \nS par = πf par D 2 par , (6)  \nbut after fragmentation it is  \nS frg = 1 2 πνD 2 frg = 1 2 πν 1 3 χ 2 3 D 2 par , (7)  \nwhere I inserted for D frg from Equation (5). Here S frg is  \nTable 1  \nSets of Orbital Elements for C/2023 A3 Computed by S. Nakano (Epoch of Osculation 2024/10/17)  \nNote.  \nknown from the observation. The ratio of S frg /S par is  \nS frg S par = ν 1 3 χ 2 3 2 f par . (8)  \nFrom Equation (7) the number of fragments needed to satisfy the observed large active surface S frg equals  \nν = ( 2 S frg π ) 3 D -6 par χ -2 , (9)  \nand the effective diameter of a fragment is  \nD frg = πD 3 par χ 2 S frg . (10)  \nThe counterintuitive inverse correlation between ν and χ is explained by the fragment size varying as χ .  \nIt is enlightening to see the results after inserting some plausible numbers. The sublimation constraints dictate that S frg = 15 km 2 . From the orbital considerations in the next section one should rather prefer that D par be below 1 km. Then, for example, fracturing 75 percent of the volume of a nucleus 0.5 km in diameter will produce ∼ 100000 fragments, each 10 meters across. In reality, the fragments have of course some size distribution. The active-surface ratio S frg /S par becomes 190, if f par = 0 . 1, so that S par is less than 0.1 km 2 .", '3. THE ORBIT': "In nearly 17 months that have elapsed since its second discovery, the comet was observed for astrometry more than 4000 times. In addition, almost 30 pre-discovery images were subsequently located, obtained between 9 April and 22 December 2022 at three observatories: Panoramic Survey Telescope and Rapid Response System (Pan-STARRS 2), Haleakala Observatory (code F52); Dark Energy Camera Project (DECam), Cerro Tololo Inter-American Observatory (code W84); and Zwicky Transient Facility (ZTF), Palomar Observatory (code I41). As a result, at the time of this writing the observed arc of the orbit equals close to 27 months. One would expect that the orbital elements, including the semimajor axis, should by now be determined with very high accuracy. As described in some detail in the following, inspection of the published computation results suggests that this indeed is the case, even though there is a hitch.  \nI start with the work by S. Nakano, who has been improving the orbital elements of this comet on a number of occasions. The selected data from his results, relevant to the issues of interest here, are summarized in Table 1. Presented in the individual columns are the reference; the reciprocal barycentric original semi-major axis, (1 /a b ) orig in AU -1 (the most important column); the mean residual; the number of astrometric observations used; the orbital arc covered by these observations (in days); the date of the last observation; and the difference between the reciprocal heliocentric osculating semi-major axis (whose value depends on the choice of the epoch of osculation) and the quantity in column 2, u b = (1 /a ) osc -(1 /a b ) orig . Since Nakano has always been using the standard epoch of osculation, u b should essentially be constant.  \nThe tabulation of u b is intended to support the proposed explanation of a discrepancy with the results obtained at the Minor Planet Center (MPC), which are with two additional independent results listed in Table 2, whose format is similar to that of Table 1. Comparison of the orbital solutions that include recent observations shows an excellent agreement between the values of (1 /a b ) orig by JPL and by Williams, their difference amounting to less than 1 unit of 10 -6 AU -1 , within the errors of observation. Next comes Nakano's most recent solution, which gives a value that is more negative by 11-12 units of 10 -6 AU -1 . This is not surprising, as Kr'olikowska & Dones' (2023), who examined differences among the various methods of orbit determination, have found that Nakano's values of (1 /a b ) orig have systematically been lower by about 10 units. Whatever the source of this discrepancy, once it is accounted for, Nakano's result agrees with the other two to 1-2 units as well.  \nThe huge problem appears to be with the MPC orbits, whose values of (1 /a b ) orig exhibit major deviations. The discrepancy is so large that its source must be a major oversight. I note that the first MPC value of (1 /a b ) orig , in particular, is very close to Nakano's value of u b . The possible confusion between these two quantities could explain the problem. On the other hand, this just may happen to be a coincidence, because the respective epochs of osculation are more than six months apart and u b may have changed substantially. While the source of the discrepancy remains unclear, I accept that the barycentric original orbit of the comet based on the observations available at present is essentially a parabola.  \nTable 2 Additional Sets of Orbital Elements for C/2023 A3", 'Notes.': "- a See https://minorplanetcenter.net/db search .\n- b See https://ssd.jpl.nasa.gov . Automatically updated every few days; this entry dated 23 June 2024.  \nThe orbit determination of comet Tsuchinshan-ATLAS involves more subtle issues related to the question of the object's survival. For example, no nongravitational orbital solution has as yet been published, apparently because the gravitational solutions have been entirely satisfactory. And this may have been so, at least in part, because the comet has so far been relatively far from the Earth and the amplitude of potential systematic residuals small. This will of course change in the future and so will other things.  \nOne point of concern that I see from Nakano's results is a recent trend to more negative values of (1 /a b ) orig . The change is about 30 units or more than 7 σ of the error in the 5059 run and more than 20 σ of the error in the 5247 run. If this trend should continue, it could represent an independent confirmation of progressive fragmentation of the nucleus. This trend would necessitate to eventually incorporate the nongravitational terms.  \nI call attention to this effect for two reasons. One is that the trend toward more negative values appears in the first orbital solutions that incorporate the observations made following the light-curve anomaly in midApril. The other reason is that the mean residual from these solutions has increased relative to the previous solutions by 0 '' .1 or about 30 percent. That is a lot and it indicates that for some reason the nuclear condensation has been measured with lesser accuracy. I will return to this issue and its implications in the following section.  \nThe observers in the south have at most until the end of July to monitor the comet before it disappears in the solar glare; it will then still be more than 1 AU from the Sun. It should be seen no more afterwards.", '4. THE TAIL': "The tail completes the list of peculiarities that are being displayed by this unusual object. Plasma tails are seldom detected farther than 2 AU from the Sun, so it is not surprising that the tail of comet Tsuchinshan-ATLAS is definitely composed of dust. Except on special occasions that I address later, preperihelion dust tails are - because of dynamical constraints - rather narrow, but seldom as narrow and teardrop-shaped as displayed by this object. They typically exhibit two characteristics: have a tendency, however slight, to broaden with increasing distance from the comet's head and extend to a maximum distance along an axis that makes a small angle with the prolonged radius vector.  \nThe tail of comet Tsuchinshan-ATLAS defies either of the two rules. Fortunately, this controversial behavior provides interesting information about the comet's history and activity. Tails of this appearance and outlines, especially the tendency of getting narrower farther from the head, have in the past been observed primarily among comets arriving from the Oort cloud in orbits with large perihelion distances. The tails of these comets deviated considerably from the radius vector and their investigation had a rather bizarre history (e.g., Osterbrock 1958, Brandt 1961, Roemer 1962, Belton 1965, Sekanina 1973, Meech et al. 2009).  \nTo describe the physical significance of the odd-shaped tail of comet Tsuchinshan-ATLAS, I have selected one of many available images (which all look alike) from the recent past and I am going to explain the meaning of the displayed features below.  \nThe selected picture, in Figure 4, has been cropped from a false-color computer-processed rendition of the image taken by R. Naves, of the Observatorio Montcabre, with a 30-cm f/9 reflector on 4 June 2024. It is a long, nearly two-hour exposure, which is important in that it shows the true extent, in excess of 8 ' , of the very delicate tail. The price paid is the apparent saturation of the central coma, whose projected radius of 13 '' is equivalent to 17 000 km.  \nFigure 4 consists of two parts: the upper panel displays the image, while the lower panel offers a guide to its interpretation. Detailed information provided by Naves on the details of his observation, including the orientation and scale, has been most helpful for an accurate description of the properties of the tail. Besides its getting more narrow with increasing distance from the head, a rather stunning trait is its large angular separation of 16 · from the projected radius vector, the maximum dynamically allowed being 22 · .5 but plausible only 19 · . More than 100 days preperihelion in an orbit that comes to less than 0.4 AU from the Sun, this is by no means common.  \nThe key to understanding the length, shape, and orientation of a dust tail is a computation of the motions of ejected particles relative to the nucleus as a function of their bulk properties and time of ejection. The properties (size, shape, bulk density, morphology, and composition) determine the magnitude of the radiation pressure acceleration that a particle is subjected to after ejection. The most widely varying parameter is the particle size and the acceleration varies inversely as the size.  \n<!-- image -->  \nFigure 4. Dust tail of comet Tsuchinshan-ATLAS. Upper panel: Cropped version of the computer processed image of the comet taken by R. Naves with a 30-cm f/9 reflector of the Observatorio Montcabre, Spain, on 2024 June 4.91744 UT, the exposure time of 103 minutes. North is up, east to the left. The image is 12 ' .6 on the diagonal. The tail extends more than 8 ' in a position angle of 98 · . Note that the tail gets more narrow as the distance from the head increases, having the appearance of a teardrop. Lower panel: Four synchrones that mimick the axial directions of dust grains ejected from the nucleus (the large open circle) at different times. The heavy line, fitting the direction of the observed tail, shows the ejecta about 400 days old at the time of observation, which left the nucleus at some 6.6 AU ( ∼ 500 days before perihelion); the other three synchrones (the thinner lines) show the predicted locations of the tail that would be occupied by dust ejected at 10.6 AU ( ∼ 1000 days before perihelion); at 2.8 AU (155 days before perihelion); and at 2.6 AU (135 days before perihelion), respectively. Each synchrone contains particles of different sizes, the greater ones nearer the nucleus, the smaller ones at larger distances from it. The locations of particles of specific sizes are marked by a dot, the magnitude of the radiation pressure acceleration β (in units of the solar gravitational acceleration) being indicated. With β essentially varying as an inverse effective diameter of a particle, the plot suggests that the observed tail consisted of submillimeter-sized and larger particles that could not be lifted from the nucleus by sublimating water ice at heliocentric distances greater than 6 AU. On the other hand, the image shows quite clearly that the comet did not eject microscopic dust (submicron- and micron-sized particles) in any nontrivial amounts in the weeks and months preceding the time of observation, as the ordinary tail is completely missing. This anomaly has important implications for the process of fragmentation that this comet has been subjected to. (Image courtesy of R. Naves, Observatorio Montcabre, Spain.)  \n<!-- image -->  \nTo describe the main features of the dust-emission history of comet Tsuchinshan-ATLAS from Figure 4, one needs to compute a number of synchrones, loci of particles of different sizes ejected at equal times. It turns out that the production of dust has been characterized by two anomalies, one of which is strong emission of submillimeter-sized and larger particles at heliocentric distances around 6.6 AU, some 500 days before perihelion. As the synchrones are crowded, one cannot determine the effective ejection time from the tail orientation accurately, but Figure 4 shows no apparent contribution from heliocentric distances beyond ∼ 10 AU or more than 1000 days before perihelion. Indeed, the dust ejected with a zero velocity lined up on 4 June 2024 in a position angle of 98 · .2 when released 500 days before perihelion (6.56 AU), in 99 · .5 when 400 days (5.61 AU), in 97 · .3 when 600 days (7.46 AU), and in 95 · .4 when 1000 days (10.63 AU). The position angle is probably measured to slightly better than ± 1 · in the image in Figure 4 and the error in ejection times, a little better than ± 100 days, is greater in the direction of early emissions. 8  \nAs 500 days before perihelion corresponds to mid-May 2023 ( ± a few months, because of the uncertainty of position angle measurements), it appears that the time of major activity (derived from the orientation of the tail) coincided crudely with the time of discovery of the comet in South Africa (583 days before perihelion). Interestingly, according to Yoshida (see footnote 2) the comet's light curve was much steeper before 2 March 2023 ( ∝ r -14 ) than after this date ( ∝ r -4 ).  \nThe second anomaly is the absence of a tail consisting of freshly ejected microscopic (submicron- and micronsized) particles, whose axis is expected in position angles close to the radius vector. On 4 June 2024 the radius vector was in position angle 113 · .9, and Figure 4 shows that a 20 days old tail (ejected at 2.56 AU from the Sun) should be pointing in a position angle of 111 · and a 40 days old tail (ejected at 2.84 AU) in 109 · . Microscopic dust composed of silicate material would make the tail at least 5 ' and 18 ' long, respectively. If the emissions also contained organic or other absorbing material, the tail would be about four times longer. In any case, it should be long enough to clearly extend beyond the coma boundaries.  \nThat obviously has not been happening, even though the Af ρ levels (addressed in Section 2) have not at all been low. Thus, the cross-sectional area of solid material in the comet's head is fairly large, but it does not translate into equivalent amounts of microscopic dust that would be blown away by radiation pressure into the tail. Instead, the fragmentation process appears to essentially cease when the sizes of fragments reach a certain lower limit. From the absence of an ordinary dust tail one cannot say whether the limit is the size of pebbles or boulders or much bigger objects. The relative speeds of these large fragments are low, which may explain why the central coma of not more than 17000 km in radius appears to be saturated in Naves' image. In any case, the absence of a tail containing freshly ejected microscopic dust ejecta is unusual in a comet that is not depleted in dust. I will return to this issue in the next section to address the implications.  \nIn order to verify the conclusions based on the single image in Figure 4, I have next applied the same method to a set of 31 CCD tail-orientation observations made, along with his magnitude observations (Section 2), by A. Pearce between 13 February and 13 June 2024 (see footnote 4). Their comparison with the theoretical loci (synchrones) of dust ejected at 400, 500, and 600 days before perihelion is in Figure 5. The data between about 230 and 190 days before perihelion provide striking evidence in support of the results derived from Figure 4. Figure 5 also shows the crowding of the synchrones in June (June 4.9 UT = 114.8 days before perihelion) and illustrates the exceptional Sun-comet-Earth geometry that I referred to above.  \nThe issue is as follows: dust ejected with a zero velocity and subjected to a radiation pressure acceleration from the Sun is always located between the radius vector and the reverse orbital-velocity vector (i.e., the direction behind the comet). The angle ψ between the two vectors increases as the comet proceeds along its path about the Sun; it is near 0 · long before perihelion, 90 · at perihelion, and approaches 180 · long after perihelion. For a parabolic orbit, an excellent approximation to the orbit of comet Tsuchinshan-ATLAS, the angle equals  \ncos ψ = -1 2 √ r q sin u = ± √ 1 -q r , (11)  \nwhere r and u are, respectively, the heliocentric distance and true anomaly at the position in the orbit, and q is the perihelion distance. The plus sign applies before perihelion, the minus sign afterwards.  \nMy statement near the beginning of this section that the preperihelion dust tails of comets are narrow was based on Equation (11), as ψ provides an upper limit to the tail width. For example, in a case relevant to comet Tsuchinshan-ATLAS in April 2024, for q = 0 . 4 AU and r = 3 AU, one has ψ = 21 · .4. In reality, of course, the tails must be much more narrow than ψ .  \nThe same applies to the tail width in projection onto the plane of the sky, unless it is distorted because of the position of the Earth relative to the comet and the Sun. This happens when the Earth lies in the comet's orbit plane inside the sector bounded by the two vectors. The radius vector and the vector opposite the orbit-velocity vector then project 180 · apart from one another. When ψ is small, the comet is seen near the Sun in the sky. But when the Earth lies inside the extended sector, between the comet and the Sun, the two vectors also project 180 · apart, with the comet near opposition with the Sun. And when the Earth is not in but near the comet's orbit plane, the projected sector gets only slightly less wide than 180 · , greatly enhancing the breadth of any feature inside the sector. This is what I meant by the exception.  \nAs it turned out, comet Tsuchinshan-ATLAS offered the terrestrial observer exactly this opportunity. While the true width of the sector grew very gradually, from ∼ 19 · on 10 February to ∼ 21 · at the time of the Earth's transit across the orbit plane on 11 April, the projected width, which already equaled 90 · on 10 February, increased to 98 · on 1 March, to 124 · on 21 March, to 144 · on 31 March, and of course to 180 · at the transit time. Subsequently, the projected width dropped to 102 · by 20 April, to 48 · by 30 April, and to 27 · by 20 May,  \nFigure 5. Tail orientation of comet Tsuchinshan-ATLAS from CCD observations by A. Pearce, who used his 35-cm f/5 Schmidt-Cassegrain. The observed position angles (solid circles; equinox J2000) are compared with the theoretical synchrones for dust ejected 500 days before perihelion (thick curve), as well as 100 days earlier and later (nearly parallel thin lines). The position angles of the radius vector are plotted as a dotted curve. Marked with a diamond is the time of the Earth's transit across the comet's orbital plane, 2024 April 11.3 UT or 169.44 days preperihelion, when the tail pointed at the Sun, in a position angle of 69 · .7, and technically became an antitail. The time extends from February 4.0 UT = 236.7 days before perihelion to June 22.0 UT = 97.7 days before perihelion, a total of 139 days.  \n<!-- image -->  \nwhen ψ = 23 · . As the projection conditions continued to worsen, by 9 June the projected width of the sector diminished to 22 · , below its true width, ψ = 25 · .  \nBecause of the strong variations in the projected width of the sector between the radius vector and the reverse orbital-velocity vector, Pearce's tail orientation data, accurate to ± 2 · or so, contribute unequally to the needs of the applied method. It turns out that the degree of angular resolution of dust-emission times (i.e., the degree of crowding of synchrones), measured by the width of the occupied position-angle sector per unit range of relevant dust-emission times, must be neither too narrow nor too wide to be most useful. Between 13 February  \nand 22 March, when Pearce made eight tail-orientation observations, the angular resolution was between about 2 · and 4 · per month of dust-emission activity. Then, even though he observed the comet nine times between 24 March and 8 April, he did not report the tail a single time. As Figure 5 shows, the tail was rotating fast in this period of time (187 through 172 days before perihelion) and the angular resolution reached 7 · per month of activity. This temporary 'disappearance' of the tail indicates that the emission of dust was continuing over a long period of time and was projecting as a wide fan, whose surface brightness was obviously low enough to escape detection. If instead the dust were emitted in a  \nbrief, powerful outburst, the event would have been detected regardless of the angular resolution.  \nOn the other hand, following the Earth's crossing the comet's orbit plane on 11 April, the angular resolution of dust-emission times remained very low, comparable to 0 · .33 per month of activity when the image in Figure 4 was taken. The most useful tail observations have obviously been those from February and March (230 through 190 days before perihelion), which show that the primary emission time was 500-550 days before perihelion, extending over an estimated period of at least several months. No observation by Pearce offers any evidence on a tail made up of freshly ejected microscopic dust, confirming the conclusion based on the image of 4 June.  \nThe absence of micron-sized and smaller dust grains in the old emission is unquestionable, but only a very approximate lower limit on the size of the dust present in the tail could be esimated from the image in Figure 4. It was desirable to verify the veracity of this result. To do just that, I examined the angular tail lengths measured by Pearce in the CCD images that he obtained with his 35-cm f/5 Schmidt-Cassegrain.  \nThe results are presented in Figure 6. The observations are compared with the expected angular lengths of a tail consisting of particles ejected 500 days before perihelion (mid-May 2023; 6.6 AU from the Sun) and subjected to radiation pressure accelerations not exceeding 0.01 the solar gravitational acceleration. At an assumed bulk density of 0.5 g cm -3 such particles are about 0.2 mm or more across.  \nIt is well-known that tail lengths measured in CCD images depend on the exposure time, observing conditions (such as a degree of light pollution, air quality, etc.), and other circumstances. Furthermore, the surface brightness of tails has a tendency to decline with their age and it is rather common to see the reported length to get gradually shorter as the surface brightness drops below the detection threshhold. Given all these uncertainties, I deem the fit in Figure 6 rather satisfactory, confirming the conclusion from Figure 4 that the tail consisted of submillimeter-sized and larger dust particles.", '5. FRAGMENTATION': "In the preceding sections I have assembled extensive circumstantial evidence to support a notion that the comet's nucleus is currently, and has already been for some time, in the process of progressive fragmentation, which will continue until the point of complete deactivation and disintegration. Given the perihelion distance of 0.39 AU, I expect that the object will disappear and cease to exist as an active comet before perihelion.  \nComet Tsuchinshan-ATLAS has been at the risk of perishing before perihelion by virtue of its arrival from the Oort cloud. The comets of this class have a tendency to disintegrate if they are intrinsically faint and depleted in dust by the time they are near 1 AU from the Sun. The first condition may be diagnostic of a small, subkilometer-sized nucleus. While the dimensions of the nucleus of comet Tsuchinshan-ATLAS are unknown, the object was neither intrinsically faint nor dust-poor prior to mid-April. However, both the observed light curve and measurements of Af ρ obtained more recently have suggested that from mid-April on the comet has been fading and the rate of its dust production dropping.  \nFigure 6. Angular tail length of comet Tsuchinshan-ATLAS from CCD observations by A. Pearce, who used his 35-cm f/5 SchmidtCassegrain. Unlike for the tail orientation, the observations of tail length are affected by observing conditions and therefore less reliable. Yet, a fair degree of agreement is seen between the observations and a predicted length of a tail consisting of dust particles ejected from the nucleus 500 days before perihelion and subjected to radiation pressure accelerations of up to 0.01 the solar gravitational acceleration. Such particles are a fraction of 1 mm across and larger.  \n<!-- image -->  \nIn the following I first summarize the evidence presented in the preceding sections in the context of the proposed progressive fragmentation scenario. After that, I briefly address the expected developments in the near future, before the comet disappears in the Sun's glare. Obviously, the results of a search for the comet after perihelion will ultimately settle the issue of its whereabouts.  \nThe process of fragmentation is proposed to have begun at the latest around 21 March 2024, 190 days before perihelion and 3.3 AU from the Sun, when the rate of brightening was abruptly increased from r -3 . 5 to r -7 . 2 . For an Oort cloud comet such a change is unusual, because typically the rate of brightening declines with decreasing heliocentric distance.  \nThe likely cause of the surge or steep brightening (not an outburst!) was a rapid increase in the cross-sectional area of the sublimating surface of the nucleus, splitting in quick succession into a large number of sizable active fragments. On a short time scale of hours or days the outgassing fragments were breaking up time and again  \ninto smaller subfragments as the sublimating area continued to grow. The cloud of these objects began to slowly expand, running at the same time out of ice. Its shortage became eventually kind of a firewall that brought the runaway activity to a stop only 25 days (on 15 April 2024; 165 days before perihelion and 3 AU from the Sun) after it had started. As a result, the light curve reached a peak because the cross-sectional area of fragments around the nucleus grew no more and their outgassing was coming to a halt. The value of Af ρ started to drop more rapidly than the brightness, as increasing numbers of fragments passed the boundary of the zone of 10 000 km in radius, where this parameter is measured. The activity of the comet, whose nucleus was now reduced in size and much of its ice-rich surface was gone, began to fade, until the depleted ice was replaced with fresh supplies from the interior. In late April, May, and June, this process appears to have worked haphazardly, on a local scale. As a result, the comet's brightness was subjected to shortterm fluctuations, which made the comet look as if its activity stalled. The light curve showed that the comet was struggling, unable to 'pick up steam.'  \nThe observed appearance of the comet as a whole supports the fragmentation scenario in that starting in late June the false-color, computer-processed images showed the coma to be noticeably elongated tailward. The elongation did not change appreciably from day to day, suggesting that the flow of material was steady and/or that the material moved very slowly, as one would expect of fairly sizable relic objects left over from the original fragments after all ice sublimated away. A stunning piece of evidence that the fragments did not, on a large scale, disintegrate into microscopic dust is the absence of an ordinary dust tail adjoining the radius vector. Significantly, as of early July, no companion nuclei were detected.  \nFigure 7. Distribution of residuals in right ascension and declination left by Nakano's recent set of orbital elements of comet Tsuchinshan-ATLAS (NK 5247) from 860 astrometric observations made between 1 May and 7 June 2024. Note the sub-arcsecond systematic trends in both right ascension and declination. Nakano rejected all observations whose residuals equaled or exceeded ± 2 '' .  \n<!-- image -->  \nMAY 2024  \nNakano's sequence of the sets of orbital elements provides evidence in support of the fragmentation scenario. The reciprocal original semimajor axis from his orbital runs that incorporated the astrometric observations made after the light-curve anomaly is ∼ 30 units of 10 -6 AU -1 more negative than from the runs that did not include those observations. The difference must at least in part be due to an increased sublimationdriven nongravitational acceleration on the nucleus that grew smaller because of fragmentation. The Oort cloud comets moving in orbits with small perihelion distances have been shown by Marsden et al. (1978) to possess a greater hyperbolic excess than those in orbits with larger perihelion distances. These authors presented a formula for the dependence of (1 /a b ) orig on the perihelion distance, which predicts -0.000014 AU -1 for comet Tsuchinshan-ATLAS, close to the current value.  \nAnother relevant issue is that of a mean residual, which climbed from ± 0 '' .32-0 '' .33 to ± 0 '' .42 following inclusion of the post-anomaly data. This ∼ 30 percent increase in the error means that either the nuclear condensation became more difficult to measure accurately (because of its substantially larger dimensions, for example) or the fit provided by the purely gravitational orbits was less than entirely satisfactory. Which of the two reasons is correct could be decided by carefully inspecting the distribution of residuals: in the former case it should be broader than before but still essentially random, while one should see systematic trends in the latter case.  \nBecause of time constraints, I have inspected the problem rather superficially. I have focused on the residuals from Nakano's recent set of orbital elements (NK 5247) left by 860 astrometric observations (a small fraction of more than 4000 data points used) made between 1 May and 7 June 2024. The results of my inspection are apparent from Figure 7 and Table 3, which consistently show sub-arcsecond deviations from a random distribution.  \nTable 3 Daily Average Residuals from Orbit of Comet Tsuchinshan-ATLAS (Nakano NK 5247) in May-June 2024  \nThe distribution of residuals in right ascension in the upper half of the figure displays a wide letter V: most residuals in early May are positive trending down toward negative numbers, in late May and June back up toward positive ones. Four of the first six tabulated daily averages are positive and only one is negative. In the period of 15-20 May all averages are negative, while five of the last six averages are positive. In declination, the systematic trend in the figure is immediately obvious, as a great majority of the residuals is positive. The table shows that only six out of the 38 daily averages are negative. Whether or not these effects are products of a nongravitational acceleration remains to be seen.  \nThe only measurement of the water production rate that I am aware of at this time implies a sublimation area of 15 km 2 , a rather bewildering piece of information. By itself it allows two very different interpretations, neither one of which looks reasonable to me: an enormous nucleus or a nucleus in a highly advanced stage of fragmentation.  \nIn the short-period of time, over which the comet can still be observed from some locations, not much additional information can be gathered over what is currently known. It is hoped that the existing databases will further be expanded: the light curve, the curve of Af ρ , the orbital arc, and more data on the water production rate. Of special interest is evidence of the continuing absence of a tail made up of recent micron- and submicron-sized ejecta in images of the longest possible exposure.  \nI expect that the light and Af ρ curves will continue to drop in an uneven fashion, even though the absolute magnitude of 11.8 from the data in Figure 2 may be too pessimistic. Whether the comet will undergo another surge of brightness of the kind experienced in late March and early April depends on the size of the nucleus; a chance is that there will be none. Essentially the same uncertainty applies to Af ρ , whose variations with time appear to be governed by the same processes.  \nIn the field of orbit determination, I predict that the mean residual from gravitational orbital solutions will continue to grow and the reciprocal original semimajor axis will continue to get more hyperbolic. Sooner or later it will be necessary to introduce the nongravitational terms. Such orbital solutions should be attempted earlier rather than later and tested by how much the mean residual has been improved.  \nNew data for the water production rate will be extremely useful not only for getting a more integrated picture of the comet's physical evolution, but also for verifying the rate from the end of May.  \nOne dataset that unfortunately will not become available is a close-up view of the comet's nuclear region. One can only envision an image looking like superimposed multiple exposures of the nuclear region of comet C/2019 Y4, taken with the Hubble Space Telescope's camera (Ye et al. 2021) - a field with an enormous cloud of barely glimmering fragments, some brighter, some fainter. In the final phase of fragmentation, increasing numbers of devolatilized, fractured refractory solids stay assembled in dark, highly porous, and exotically shaped blobs that eventually become undetectable as they gradually disperse in space. One can only speculate that some (the largest?) of these blobs could possibly look like 1I/'Oumuamua.", '6. CONCLUSIONS': "The purpose of this paper is not to disappoint comet observers who have been looking forward to a new nakedeye object this coming October, but to present scientific arguments that do not appear to substantiate such hopes. Even though the prognostication of preperihelion disintegration of comets is admittedly a very risky undertaking, I believe that the time has come to go ahead with it.  \nComet Tsuchinshan-ATLAS exhibits traits that are diagnostic of extensive fragmentation of the nucleus, even though no distinct companion has been observed as of early July. Some of the features resemble the performance of past members of the Oort cloud that disintegrated before reaching perihelion at a heliocentric distance substantially smaller than 1 AU. It is primarily the peculiar light curve, as pointed out by Ferrin, as well as the parallel changes in Af ρ , especially a surge in late March through early April, a sharp peak in mid-April, when the comet was at 3 AU from the Sun, and the subsequent fading with superimposed fluctuations, which are likely to testify to additional events of local fragmentation. Also worrisome is the apparent tailward elongation of the coma seen in June. The extremely high water production rate needs confirmation.  \nIndependent support is provided by two effects in the comet's orbital motion: (i) a hyperbolic shift of 30 units of 10 -6 AU -1 in the reciprocal original semimajor axis after inclusion of astrometric observations made following the light-curve anomaly and (ii) parallel increase in the mean residual from ± 0 '' .32-0 '' .33 to ± 0 '' .42. The culprit appears to be a sublimation-driven nongravitational acceleration on the nucleus whose dimensions have been rapidly diminishing because of its continuing fragmentation. Even though detected systematic trends have as yet been in a sub-arcsecond range, they soon may grow and require the incorporation of the nongravitational terms in orbit determination efforts.  \nMost unusual is the continuing absence of an ordinary dust tail, which means that large amounts of dry, fractured solid material do not disintegrate into microscopic dust, but stay assembled in dark and highly porous bizarre bodies that I refer to above as blobs . Once they disperse in space, they are nearly impossible to detect, yet they may be omnipresent though perhaps short lived.  \nAdded after final editing: As observations continue and the data in the paper get increasingly incomplete, some of the numerical results may be affected. Apologies.", 'REFERENCES': "A'Hearn, M. F., Schleicher, D. G., Millis,R. 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