Activity Analysis on 68P/Klemola and 78P/Gehrels 2 in 2018–2020 Perihelion Passage

We performed secular monitoring broadband photometric observations on Jupiter Family Comets (JFCs) 68P/Klemola and 78P/Gehrels 2 from 2018 November to 2020 March with the Yaoan High Precision Telescope. Our main purpose is to study the dust activity, coma properties, and dynamical history of the two comets and analyze the activity evolution of 78P/Gehrels 2 in the recent past. We use aperture photometry to obtain the magnitude and the A(0)f ρ values from the R band observations. The maximum A(0)f ρ values we recorded for 68P/Klemola and 78P/Gehrels 2 are 339.7 ± 4.4 cm and 1028.1 ± 13.3 cm, respectively, showing that the activity of 68P/Klemola is of middle level while 78P/Gehrels 2 is one of the most active JFCs. The mean color of 78P/Gehrels 2 is (B − V) = 0.88 ± 0.02 and (V − R) = 0.27 ± 0.02. Dynamical history analysis suggests that 78P/Gehrels 2 could have actually resided in this region for a long time in the past 1 Myr, though it recently migrated into the inner solar system. The high activity of 78P/Gehrels 2 reported in the past three perihelion passages could be attributed to the perihelion distance decl. from 2.3 to 2.0 au before 1997 that boosted the water-ice sublimation rate and formed new active regions. The activity decl. over recent apparitions could be attributed to the reformation of the dust mantle.


Introduction
Comets are living fossils that could date back to the origin of the solar system.Among the many classifications of comets, Jupiter family comets (hereafter JFCs) refer to a class of comets whose orbits are gravitationally controlled by Jupiter, with their Tisserand parameter to Jupiter T J > 2 (Vaghi 1973).Dynamical analysis shows that the JFCs were likely to originate in the Kuiper Belt or its scattered disk at the edge of the solar system and migrate from the Centaur population with resonant "orbital gateway" (Lowry et al. 2008;Sarid et al. 2019).Thus, they are known to contain a large amount of volatile ices (Mumma & Charnley 2011;Zhao et al. 2020), the sublimation processes of which give rise to the formation of coma and tail, which is described as the cometary activity.Although space missions have visited multiple comets in the past 50 yr and their observations, especially the Rosetta mission, have revolutionized our understanding of comets, investigating the diversity within the activity of JFCs still depends on ground-based monitoring observations.Generally, the JFCs are less active than the other types of comets, especially long period comets (Solontoi et al. 2012;Garcia et al. 2020).It is commonly believed that the long residence time of JFCs in the inner solar system should be responsible for their low activity because the volatiles near their surface become exhausted during the longterm sublimation process.From the estimate of mass-loss rates, a typical JFC could only maintain activity for around 1000 revolutions in the inner solar system (Thomas 2020).In this opinion, the activity evolution of JFCs is likely to be related to their dynamical history and it declines over revolutions.This idea is supported by various studies, indicating that some of the most active JFCs migrated into the inner solar system within the past a few hundred years (Rickman et al. 1991;Meech & Svoren 2004;Ip et al. 2016).It is expected that a dormant or dead JFC is the one who stayed in the inner solar system for a long time, some inactive asteroids in JFC orbits such as (3552) Don Quixote and (5370) Taranis could be the remnant of JFCs (Meech & Svoren 2004), whereas a very active JFC is believed to enter this region recently or subject to recent massive massloss events.
68P/Klemola (hereafter 68P) is a JFC that was poorly investigated in the past.It was discovered by Arnold R. Klemola on 1965 October 28 with the 20 inch double astrograph at the Yale-Columbia Southern Station.In its 2019-2020 apparition, 68P passed its perihelion on 2019 November 9 with perihelion distance of 1.794 au.The geometry condition is favorable for observations around its perihelion in this apparition.The nucleus size of 68P has been interpreted by several sources and is 2.5 km in the catalog of Tancredi et al. (2006), 2.2 km in the Horizon system of Jet Propulsion Laboratory (JPL)5 , and 2.8 km with infrared observations conducted by Fernández et al. (2013).This suggests that 68P has a medium nucleus size among JFCs, whose sizes of nuclei range from less than 1 km to more than 5 km (Solontoi et al. 2012).The astrometric analysis adopted from Minor Planet Center (MPC)6 indicates that there has been no significant change of its orbital elements since its discovery.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.78P/Gehrels 2 (hereafter 78P) is also a JFC.It was discovered by Tom Gehrels with Palomar Observatoryʼs 122 cm Schmidt Telescope on 1973 September 29.Its orbital period is 7.22 yr and it passed its most recent perihelion on 2019 April 2 with perihelion distance of 2.014 au.Though the geometry condition forbade observations at perihelion and 200 days afterwards in this perihelion passage, the continuous high luminosity of this comet allowed long-term monitoring program from 2018 November to 2020 March.The nucleus size of 78P ranges from 1.35 to 1.7 km in multiple sources (Snodgrass et al. 2008;Fernández et al. 2013).Among them, we adopt 1.41 ± 0.12 km from the result of Lowry et al. (2003), assuming albedo of 0.04 (Richardson et al. 2007), obtained through a snapshot observation at heliocentric distance of 5.5 au when the comet had a stellar appearance.This indicates that 78P is a bit smaller than 68P.Despite having small nucleus size and long perihelion distance, 78P was reported to have ultra-high activity in the past perihelion passages.In the 2004 perihelion passage, a snapshot observation indicated the Afρ value was 846 ± 55 cm near perihelion with 7200 km aperture size (Mazzotta Epifani & Palumbo 2011).In its next return in 2011-2012, near perihelion Afρ value reached 380 and 470 cm with 10,000 km aperture size normalized to phase angle 30° ( Pozuelos et al. 2014a), which indicates that 78P is among the highest activity level in JFCs.Additionally, it is intriguing that several observations on the gas emission of 78P suggest that the gas activity is, however, not as active as the dust activity.In 1989, spectroscopic observations of 78P at 2.35 au did not identify any notable gas emissions (Fink & Hicks 1996).A 'Hearn et al. (1995), with their own observations, categorized this comet into a carbon-chain depleted class.Polarimetric observations suggest that 78P could be a member of low-P max class of comets whose maximum polarization value was about (18 ± 3)% (Roy Choudhury et al. 2014).Dynamical analysis suggests that unlike the relatively stable orbit of 68P, the orbital elements of 78P are extremely vulnerable to the perturbation of Jupiter due to frequent close approach events.According to the close approach data in the JPL Horizon system, except for the estimate close approach to Jupiter of 0.96 au in 1971 that might lead to its discovery, another close approach of 0.62 au in 1995 reduced the perihelion distance from 2.35 au in 1989 apparition to 2.00 au in 1997 apparition.It predicts that in 2029, a close approach event with nominal distance of 0.02 au will dramatically change the present orbital status.The orbital elements of 68P and 78P are listed in Table 1.
The purpose of this paper is to present the observation results of the monitoring program of comet 68P and 78P from 2018 November to 2020 March.Section 2 introduces our observations and data reduction procedures.We discuss several observational results including aperture photometric analysis, morphological structures, and dynamical history analysis in Section 3. In Section 4, we discuss the activity evolution of 78P in multiple apparitions.

Observation and Data Reduction
Both 68P and 78P were observed with the Yaoan High Precision Telescope (YAHPT; IAU code O49) with Johnson-Kron-Cousins B, V, R broadband filters.Located at the Purple Mountain Observatory Yaoan Station in Yunnan Province, southwest China, the 80 cm Ritchey-Chretien telescope is equipped with a 2048 × 2048 pixel 2 PI CCD camera.The field of view (FOV) is 11.8 arcmin 2 and the spatial resolution for each axis is 0 347 per pixel.The observations of 68P lasted 26 nights from 2019 September 26 to 2020 January 11.The observations of 78P were divided into two parts because of geometric conditions.The observations before perihelion lasted 25 nights from 2018 November 6 to 2019 February 12, while the observations after the perihelion lasted 37 nights from 2019 October 19 to 2020 March 27.All the astrometric data used in this research are queried from MPC, and the circumstances of the observations are shown in Tables 2 and 3.
With the differential tracking guidance system equipped in the YAHPT, the exposure time is not limited by the sky motion of the comet compared to the standard seeing of 1 3 on the observation site.However, for slow moving comets such as 78P, we still used the sidereal tracking mode to prevent additional errors.After the standard procedures of bias subtraction, flat-fielding and removal of cosmic rays, we determined the position of the optocenter of comet by the "centroid" algorithm used in IRAF (Tody 1986(Tody , 1993)).The comet images taken in one night were aligned according to the position of the optocenter and combined to make one "final" frame.The flux calibration was made with the help of Aladin skymap and the UCAC4 star catalog and the data reduction was processed with IRAF.

Coma Photometry and Activity
To derive the magnitude and the Afρ value of the comet, we laid a fixed aperture of 10,000 km projected on the sky at the geocentric distance of the cometʼs nucleus to conduct aperture photometric analysis on the comet.The Afρ value is a proxy for cometary activity proposed by A' Hearn et al. (1984), and it is derived with the following formula: where A is the grain albedo, f is the filling factor, ρ is the aperture used in photometry, r h and Δ represent, respectively, the heliocentric and geocentric distance of the comet nucleus, and m s and m c represent the solar magnitude and the comet magnitude measured with aperture photometry in the R filter, because the spectrum that R band covers is relatively free from significant gas emission bands in broadband photometry (Tozzi et al. 2003;Lara et al. 2004;Meech et al. 2009;Clements & Fernandez 2021).Since the visual magnitude and the Afρ values are affected by the scattering efficiencies of the dust particles in the coma, which are closely connected with the phase angle, here we adopt the Schleicher-Marcus model to normalize the Afρ value to phase angle 0°, generally called the A(0)fρ (Schleicher & Bair 2011).The phase correction requires our understanding of the phase function of the comet, which basically presents a U-shape pattern.The most accurate determination of the phase function comes from space missions.The Schleicher-Marcus model is based on various observations from 1P/Halley to other comets both from space missions and ground-based observations, and is one of the most commonly employed models in phase correction.Another frequently used method is linear phase correction, which is not adequately accurate when the phase angle is near 0°.For 68P, the phase angles ranged from 22°.4 to 33°.0 in our observations, the difference of the phase factors due to the phase angle variation is up to 20%.While for 78P, the phase angles ranged from 3°.0 to 25°.8, close to the backscattering enhancement at zero degree, the difference of the phase factor could reach 50% at some circumstances.Without this correction, a brightness bulge will be falsely produced in the secular light curve at small phase angle and it could be misinterpreted as an outburst.
The derived multiband magnitude along with the A(0)fρ values are shown in Tables 2 and 3, and the A(0)fρ curve is visualized in Figure 1.During our observations of 68P from 2019 September 26 to 2020 January 11, the highest A(0)fρ value of 339.7 ± 4.4 cm is recorded on 2019 September 28, 42 days before perihelion.However, we did not have observations between October 1 and 30, and the A(0)fρ curve of 68P exhibits significant fluctuations, making it rather challenging to confirm its changes in activity status.Numerically, the A(0)fρ values observed before perihelion are generally greater than those at similar heliocentric distance after perihelion.Additionally, the quadratic fit of the curve indicates that the vertex likely falls before perihelion, which could be associated with the seasonal effect of the comet.We add the only available Afρ data from published literature of 68P in the 1987 to Figure 1 (A' Hearn et al. 1995).After phase correction, 68P had an A(0) fρ value of around 150 cm at the heliocentric distance of 1.91 au, which aligns reasonably well with our observations.For 78P, the first half of our observations from 2018 November 6 to 2019 February 12 recorded the inbound passage.During this period, the activity of 78P increased rapidly and monotonically with decreasing heliocentric distance from 2.33 to 2.05 au.The maximum A(0)fρ value reported was 1028.1 ± 13.3 cm on 2019 February 12, 49 days before perihelion.Consolidating magnitude data from MPC, the absolute magnitude generally displays a symmetrical distribution before and after perihelion in the past few apparitions, indicating that the seasonal effect on 78P makes little change on the peak of the A(0)fρ curve.Hence, it could continue to exhibit a general symmetric pattern in 2018-2019 apparition and the activity will peak at around perihelion, which we were unable to observe.Thus, we expect that the peak A(0)fρ value would be about 10% higher than our measurement in the extrapolation of the curve fit.The other half of our observations started on 2019 October 19, 200 days after perihelion.It ended on 2020 March 27, 78P in the afterward observations were too faint to conduct any photometric analysis.The heliocentric distance ranged from 2.55 to 3.28 au during this period.Generally, the A(0)fρ values were decreasing with increasing heliocentric distance during this period and maintained a relatively low-level activity at the end of our observations.It is also noted that the increasing rate of activity of 78P inside heliocentric distance of 2.4 au inbound is much higher than the decreasing rate of activity outside heliocentric distance of 2.5 au outbound in Figure 1.The unfavorable geometric condition after perihelion makes it unclear how the change rate of the activity varied in this period.Since the two observation periods did not overlap in heliocentric distance, we collect available magnitude data within the heliocentric distance range symmetrically corresponding to our post-perihelion observations from MPC, which shows reasonably similar trends to our observations after perihelion.This suggests that the A(0)fρ curve is likely symmetric beyond 2.4 au before and after perihelion.Consequently, we can conclude that the variation rate of A(0)fρ exhibits differently for 78P before and after 2.4 au, a change that might be associated with 78P's past orbital changes in 1995, further discussion on the activity evolution over apparitions can be found in Section 4.
Serving as a good proxy to characterize the dust activity, A (0)fρ values are theoretically proportional to the dust production rate times the cross sections of the ejecta divided by dust ejection velocity, in the case of isotropic and steady emission (Fulle et al. 2010).However, an estimate of dust production rate is highly dependent on the dust environment parameters and on the assumptions about the optical properties of the dust particles (Rousselot et al. 2014;Shi et al. 2019).Therefore, in order to estimate how active 68P and 78P are in the JFCs, we plot the A(0)fρ values of 68P and 78P, and collect published data from other literatures of other JFCs with different heliocentric distances in Figure 2, where a series of observations covering large span on heliocentric distance in one regression are specifically labeled and other records containing single value or multiple measurements at similar heliocentric distance are marked as miscellaneous data (Lowry et al. 1999(Lowry et al. , 2003;;Mazzotta Epifani et al. 2008;Bertini et al. 2009;Lamy et al. 2009;Lara et al. 2011;Mazzotta Epifani & Palumbo 2011;Lin et al. 2012;Moreno et al. 2012;Solontoi et al. 2012;Pozuelos et al. 2014aPozuelos et al. , 2014b;;Shi et al. 2014;Kwon et al. 2016;Moulane et al. 2018;Borysenko et al. 2019;Garcia et al. 2020;Xu et al. 2022).We tend to use the collected Afρ values with photometric aperture at around 10,000 km and normalize them to 0°phase angle with the same Schleicher-Marcus phase correction method.For 68P, the A(0)fρ measurements before perihelion are generally higher than those on the outbound passage, and they are comparable to 64P/Swift-Gehrels and 60P/Tsuchinshan 2 with similar heliocentric distance range, suggesting that the dust activity of 68P is in the intermediate position among JFCs compared to other comets.While the maximum A(0)fρ value for 78P stands among the highest value in the JFCs, comparable to two very active comets, 81P/Wild 2 and 67P/Churyumov-Gerasimenko. Therefore, 78P can be considered as one of the most active JFCs.
With a same 10,000 km aperture is described above in obtaining Afρ values, the derived B band and V band    Snodgrass et al. 2008;Shi et al. 2023).Although narrowband observations in the past indicated that 78P did not have notable gas emission, these observations all occurred prior to the orbital change around 1995, when the perihelion distance dropped from 2.34 to 2.00 au (see Section 4).Because such orbital change could lead to a rise of surface temperatures near perihelion, triggering a potential source of gas activity, we cannot rule out the possibility of gas contamination in the colors obtained above.

Coma Morphology and Dust Environment
In Figure 3 we show a selection of the best quality observed images of 68P and 78P, the length of each side of the images is the projected distance of 50,000 km at the comet nucleus.The visual appearances of both comets indicate evident activity, exhibiting an elongated coma.The coma length of 68P was maintained at a cometocentric projected distance of 15,000 km during the observations.On the other hand, 78P had coma length of 40,000 km cometocentric projected distance at its highest activity level.While the coma radius was reduced to 12,000 km in the last few days of our observations, and the visual appearance of the coma became near circular, when 78P was away from its perihelion the activity decreased to a relatively low level.The reduction of the coma radius could be the result of decreasing activity level, and the near circular shape was related to the small phase angle indicating that the elongated direction of the coma was near our line of sight, thus the projection of the tail became obscure.
To investigate the dust environment of 68P and 78P, we first adopt Larson-Sekanina image enhancement methods to find the hidden morphological structures in our data.The Larson-Sekanina method applies radial and angular differencing on the images and it is widely used in morphological studies.We distinguish the artificial false structure by comparing with other enhancement methods, such as the azimuthal average method (Larson & Sekanina 1984;Farnham 2009;Samarasinha & Larson 2014), proving that the morphological structure presented in the enhanced images really exists.The morphological structures revealed by Larson-Sekanina method are shown in Figure 4, the length of each side of the images is the projected distance of 50,000 km at the comet nucleus.For 68P,  a small fan-like structure covering about 45°angle extending 10°-30°east by south continues to appear near the anti-solar direction, until it finally fades into the background.The major part of this structure extends to a projected cometocentric distance of around 10,000 km, and it appears to have clockwise spiral patterns in nearly all of the enhanced images, which can be confirmed by the visual appearance of the coma.It is noted that the direction of the fan-like structure in 68P deviates from the anti-solar direction, which is the direction of the acceleration of the dust particles by the solar radiation pressure.The clockwise spiral patterns provide an explanation that the ejection pattern on 68P could be subjected to a major cone ejection that points to the southeast in the sky projection, and the overall direction of the ejection velocity deviates the antisolar direction, thus producing a projectile motion-like clockwise spiral.A similar structure is also presented on 78P.Compared to those on 68P, the fan structures of 78P also have clockwise spiral patterns but they are clearly more obvious, covering a wider angle of 90°-120°, extending a longer length of projected cometocentric distance of 20,000 km.Considering that the A(0)fρ values of 78P largely overwhelm those of 68P, the strength of the morphological structures could probably be related to the activity level of the comet.In addition, both 68P and 78P have a sunward circular spot in the images near perihelion that, considering the shape of the structure, does not necessarily represent the presence of an anti-solar jet, but the increasing activity in the sunward direction could be responsible for this phenomenon.As the heliocentric distance of the comet gradually increases and the activity presented by the A (0)fρ values generally decreases, the length and the visibility of the morphological structure declines and it finally becomes unrecognizable in the last few observations.We also conduct Monte Carlo simulation for the dust coma based on the description of Moreno (2022) and the FP-like model on the Internet service Comet-toolbox7 (Vincent 2014).The model is based on two major assumptions: (1) dust particles ejected from nucleus (i.e., when they decouple with the gas) have a certain ejection velocity depending on the size of each particle and the motion of these particles is only affected by solar gravity and radiation pressure; and (2) dust grains are assumed as homogeneous carbonaceous spherical particles, their optical characteristics can be obtained with Mie theory.The two free parameters of this model are the ejection velocity and the power index α of dust size distribution, assuming that the dust particles follow the power-law distribution.These two parameters were proven to be good indicators for dust environment in previous research and they are intrinsically related to the dust production rate (Fulle 1989(Fulle , 2004)).The basic scenario of this model is that the comet's activity turned on at a certain date and since then a series of dust particles with various sizes following power-law distribution are released from the comet's position at regular intervals until the date corresponding to the observed image.All dust particles ejected before the observation time are individually computed for their orbital parameters, thus obtaining their position in the equatorial coordinate system at the observation time.A synthetic image is reconstructed based on the FOV and pixel resolution of the observed image.In each pixel, we sum the total scattering cross sections of the dust particles reside in and determine the brightness.The obtained synthetic image is compared with the observed image, adjusting free parameters to obtain the optimal combination that fits the appearance of the observed coma using criteria in Fulle et al. (2022).
In our simulation, we assume isotropic emission for both comets, which means the direction of ejection is randomly distributed on the assumed spherical surface.The lower and upper limits of the radii are 1 μm and 1 cm, refer to the setup of previous models (Moreno et al. 2004;Moreno et al. 2014).In each release, the number of dust particles is derived from a normalized dust production rate curve dependent on the heliocentric distance, converted from the A(0)fρ value obtained in the photometric results (Rousselot et al. 2014).The turn-on dates of both comets are 2019 March 1 for 68P and 2018 May 16 for 78P, respectively.They are also determined by this dust production rate curve that the dust production rate at the turnon point was negligible compared with at the observation time.The time interval of dust particle release is 0.01 day and the total number of particles ejected in the simulation is of 10 9 mag.Since the terminal velocity of the dust particles is the function of particle radius, we adopted the ejection velocity estimate in Rousselot et al. (2014) that writes: where β is the ratio of solar gravity to the solar radiation pressure and it uniquely characterizes the radius of each dust particle.Meanwhile, f is the scaling factor for the ejection velocity, which is regarded as a free parameter in our model.
Figure 5 shows the isophote contour plot for observational image of 68P on 2019 September 28 (the upper left-hand panel), 78P on 2019 February 5 (the lower left-hand panel) and the corresponding optimal synthetic images produced by dust coma model (the right-hand panel).However, due to the highly anisotropic emission of 68P mentioned above, our model assuming isotropic emission cannot produce synthetic images with similar morphology, no matter how we vary the parameters in the model.Still, we provide a set of free parameters that make the difference between the observational images and synthetic images minimal.The optimal free parameters for 68P are α = −3.5 and f = 1.5, and for 78P are α = −3.5 and f = 1.1.This result suggests that the dust size distribution is similar between 68P and 78P, and that the brightness is evenly contributed by different sizes of dust particles.68P has a higher terminal ejection velocity considering that it has higher velocity scaling factor f and smaller heliocentric distance, but numerically the difference in the terminal ejection velocity is not large enough to cover their difference in A(0)fρ value.Hence, 68P has an overall lower activity than 78P.

Dynamical History Analysis
A long-term integration of the comet could reveal its dynamical history and show how it might migrate into the inner solar system (Levison & Duncan 1994).This analysis may also provide an explanation of the cometʼs current physical properties and activity.Due to the chaotic nature of the orbit, an accurate result is impossible to obtain, but statistical analysis is still reliable with multiple clones released with slightly different initial orbital elements of the original comet (Kim et al. 2022).To determine the dynamical history of 68P and 78P, we use the Bulirsch-Stoer integrator in Mercury N-body integration package version 6.2 (Chambers 1999).We generate 100 clones following Gaussian distribution with 2σ uncertainties of the orbital elements of the comets from the Horizon system in JPL.The orbits of the clones are integrated backward for 1 Myr.The perturbing bodies are set to be the eight planets, the clones are treated as test particles, and the non-gravitational force is set to zero because the deviation of orbital elements caused by emission jets from comet nucleus is negligible in the scale of orbital evolution (Lacerda 2013;Pozuelos et al. 2014a).The output time interval is 10 yr.Once the semimajor axes of the clones goes beyond 1000 au, it will be labeled as lost and further calculation will not be continued.
The results of the backward integration are shown in Figure 6 with timescale of 5000 yr and 1 Myr.For 68P, after 5000 yr backward integration, more than 60% of the clones still remained in the JFC region and almost all of the clones showed a trend that their semimajor axes gradually decreased in the past 5000 yr.With 90% confidence, 68P entered the JFC region 1010 yr ago, and is still a somewhat young comet compared to the result of Pozuelos et al. (2014a).In the 1 Myr backward integration, almost 90% of the clones were lost.One of the remaining 12 clones stayed in the JFC region, while five stayed in the Centaur region and six stayed in the trans-Neptunian region.78P does not show much difference with 68P, except that it might have come into the JFC region more recently.After 5000 yr backward integration, only 40% of the clones remained in the JFC region.With 90% confidence, 78P only entered the JFC region 300 yr ago.Twenty-four clones of 78P survive the 1 Myr backward integration, which is twice as much as that of 68P.One of them stayed in the JFC region, while 13 stayed in the Centaur region and 10 stayed in trans-Neptunian region.This shows a similar pattern with 68P-the surviving clones of both comets 1 Myr ago nearly consisted of half Centaur and half trans-Neptunian objects.
However, a detailed survey of the evolution path of each clone tells a different story.The orbits of these clones show significant variation from their source regions to the inner solar system as the result of planetary gravitational perturbations.But one commonality of these orbits is that they often travel back and forth through regions of different dynamical class comets (Levison & Duncan 1994;Rickman et al. 2015;Ip et al. 2016).Moreover, some of the clones even reached a closer perihelion distance than the current orbit in the past 1 Myr.Since the thermodynamic conditions of the solar system remained essentially the same over the past 1 Myr, whenever a comet migrated into an orbit that close enough to the Sun, it was bound to create remarkable activity.The detailed information of the clones of 68P and 78P that once showed up in the inner solar system in the past is summarized in Table 4, where the "expected residence duration" is the product of "fraction of clones visited" and the "averaged residence duration."This value can demonstrate how long this comet could have stayed in these regions with different perihelion distance and presented activity level corresponding to the amount of solar radiation.The expected residence duration seems to rise with the increase of perihelion distance.68P may have resided in the region of perihelion distance in 1.0-1.5 au and 1.5-2.0au for more than 3000 yr, respectively, indicating that it is a very dynamically old comet.In contrast, 78Pʼs possible residence duration with closer perihelion distance is limited to the order of hundreds of years, much lower than that of 68P, making it likely to acquire higher activity when the orbital changes reduce the perihelion distance.

Activity Evolution of 78P
From the previous section, we can conclude that the activity of 78P was high in the 2018-2019 perihelion passage, which is consistent with other observations of the past two apparitions in 2004and 2011(Mazzotta Epifani & Palumbo 2011;Pozuelos et al. 2014a).According to Pozuelos et al. (2014a), the reason that 78P had a high level of activity was that it probably migrated into the JFC region 300 yr ago.Thus, it preserved a large amount of volatiles near its surface that sublimated when it came closer to the Sun, and we can interpret that it would remain highly active close to perihelion over regressions.But the Afρ value of 78P given by A' Hearn et al. (1995) at heliocentric distance of 2.36 au near perihelion was only Af log 1.80 ( ) r = and that of 68P was Af log 2.07 ( ) r = at 1.91 au.Considering that the gaseous emission of 78P was defined as depleted at that time (A'Hearn et al. 1995;Fink & Hicks 1996), this suggests that in the 1980s the maximum activity of 78P was even less than that of 68P.On the contrary, the dust production of 78P in 2011 apparition was relatively higher than 22P/Kopff, one of the most active comet in JFCs, in the 2009 perihelion passage (Moreno et al. 2012;Pozuelos et al. 2014a), indicating a significant increase in the dust production of 78P, while the variation of activity of 68P is negligible.The difference in activity in the past 30 yr implies that the active nature of 78P we observed was formed recently.There are two explanations that could be attributed to the significant increase of activity.One is that 78P experienced a large mass-loss event in the recent past, triggering the sublimation of deeper water-ice reservoir.But in this scenario the increasing dust emission from some reservoirs would form an overall more anisotropic emission pattern, while the emission of 78P was reported to be mostly isotropic (Pozuelos et al. 2014a).The other possibility is that according to the Horizon system of JPL, the perihelion distance of 78P reduced from 2.34 au in 1989 apparition to 2.00 au in 1997 apparition due to a close encounter with Jupiter in 1995 (see Table 5).Since the sublimation of water-ice on the nucleus is highly relevant to the solar radiation, closer perihelion distance will lead to higher surface temperature, boosting the production rate of volatiles.Thus, we can conclude that the reduce of perihelion distance in the recent apparition could be responsible for the current high activity of 78P, and this comet was not so active before the close encounter that resulted in the orbital change.
Reviewing the dynamical history analysis in Section 3.3, Table 4 suggests that 78P could have visited the JFC region many times in the past 1 Myr, and its former orbit has more than 60% possibility to reach 2.0-2.5 au perihelion distance.The total time spent in the past was sufficient to reduce its water-ice activity to a level lower than 68P during the longlasting sublimation at around 2.4 au.This phenomenon can be linked to the significant variation of change rate of A(0)fρ before and after 2.4 au presented in Section 3.1, suggesting that 78P might experience less erosion in the current orbital region than in the orbital region before the orbit change in 1995.In addition, in the close approach event, Jupiter can greatly vary 78Pʼs orbit but the influence on its orientation is limited, thus we can calculate the movement of the subsolar point from the variation of longitude of perihelion in the orbital elements, which is about 3°.4,suggesting that the seasonal effect on 78P should be relatively similar before and after the inward orbital migration.
Another interesting aspect is that the A(0)fρ value, representing the activity of 78P, seemed to decrease in the past three perihelion passages.The Afρ value observed on 2004 October 6 was 846 ± 55 cm with phase angle of 19°.1 and 7200 km aperture.However, this result was not dealt with a phase angle correction and the author reported that the Afρ value decreased with increasing cometocentric distance (Mazzotta Epifani & Palumbo 2011).After the corrections applied to normalize the result to 10,000 km aperture and 0°phase angle, with the Schleicher-Marcus model as we have described in Section 3.1, the A(0)fρ value would be around 1480 cm.In the next apparition, on 2011 January 4 an Afρ value of 470 cm was recorded with 10,000 km aperture, and the author adopted a linear phase angle correction to normalize the Afρ value to 30°p hase angle (Pozuelos et al. 2014a).After changing the phase angle correction method, the obtained A(0)fρ was 1140 cm.Along with our own measurement of A(0)fρ of 1028 cm on 2019 February 12, all these three observations were around perihelion, so they may represent the highest activity in each regression.The recorded maximum A(0)fρ decreased from 1480 cm in 2004 apparition at heliocentric distance of 2.016 au to 1140 cm in 2011 apparition at 2.009 au and then to 1028 cm in 2019 apparition at 2.054 au.The extrapolation of the A(0)fρ curve indicates that the 0.05 au difference of heliocentric distance will result in a roughly 10% rise in the peak activity in 2019, close to the result in 2011.But the 20% of activity drop between 2004 and 2011 certainly describes a lowering trend.
Considering that the time period of one regression is negligible in the entire history of a JFC presenting activity, which is roughly estimated to be around 1000 regressions (Thomas 2020), a roughly 20% decrease in activity in 15 yr is quite astounding with no alteration in other parameters.
Based on the thermophysical model on the nucleus of Fulle et al. (2020), we can further discuss the variation of activity of 78P in the past 30 yr.In the model we can roughly calculate several thermophysical properties near the nucleus surface including the surface temperature, heat conductivity, temperature, and pressure at the sublimation front, and the water-ice production rate both with heliocentric distance of 2.36 and 2.01 au, corresponding to the perihelion distance of the orbit before and after the orbital change.The equations can be expressed as follows (Fulle et al. 2022): In the equations, T f is the temperature at the water-ice sublimation front, T s is the surface temperature, s is the depth of sublimation front, ΔT is the averaged temperature gradient near surface, P P T T exp -Pa is the gas pressure from the sublimating water ice, where P 0 = 3.23 × 10 12 Pa and T 0 = 6134.6K refer to Gundlach et al. (2020), Q is the water production rate, r g = 1 μm and r p = 1 cm are the mean radius of grains and pebbles, align with the assumption in the dust environment estimate in Section 3.2, m g is the mass of waterice molecule, k b is the Boltzmann constant, L = 2.86 × 10 6 J kg −1 is the latent heat of water (Gundlach et al. 2020), σ is the Stefan-Boltzmann constant, λ is the heat conductivity, S e is the solar constant, r h is the heliocentric distance, A N = 0.04 is the bond albedo, and ò = 0.9 is the infrared emissivity of the nucleus.In the energy balance equation (Equation ( 8)), we adopt the method Chandler et al. (2020) to calculate the averaged surface temperature by introducing a factor χ = 4 used for a fast-rotating isothermal body whose rotation period is relatively short compared to the thermal wave propagation (Schorghofer 2008;Hsieh & Sheppard 2015).
According to our calculation, a 0.35 au decrease of perihelion distance from 2.36 to 2.01 au will result in about 11 K increase for temperature at the water-ice sublimation front from 180.8 to 191.7 K, while the water production rate will increase about 700%.If we assume that the dust-to-ice ratio of 78P did not alter largely, then the dust production rate will also gain about 700%.Since the above analysis indicates that the variation of activity shown in A(0)fρ value before and after the orbital change is about 1300% and the seasonal effect on 78P altered little in the process, the primary contributor to the increased activity of 78P after the orbital migration was the increased production of volatile due to the decrease in heliocentric distance.The additional increase in activity could be attributed to the generation of more active regions in the sunlit areas, possibly associated with eruptions resulting from increased pressure of volatile after the comet first entered the new orbit.Rosetta also observed mini-outburst with following activity on 67P (Knollenberg et al. 2016;Vincent et al. 2016;Agarwal et al. 2017;Pajola et al. 2017).Since the newly formed activity on 78P lifts the dust to eject from the nucleus, the large dust grains are more likely to fall back on the surface because it is harder to accelerate them to the escape velocity of the nucleus.According to the "rubble" mantle model and the research on 17P/Holmes, the dust mantle tends to form and thicken very quickly, within one or two orbital periods, in the inner solar system (Meech & Svoren 2004;Kwon et al. 2016).The reformation of the dust mantle is consistent with the significant activity drop of 78P in the past 20 yr because the dust mantle can inhibit further activity and brings the activity of 78P closer to a stable state, just as the insignificant activity variation between 2011 and 2019 apparition indicates.This means that in the next perihelion passage in 2026 the activity of 78P will possibly be as high as that it was in 2019.The high activity now presented on 78P will be short-lived in the foreseeable future because current simulation in the JPL Horizon system shows that the perihelion distance of 78P will unfortunately increase to about 4 au in the 0.02 au close approach with Jupiter in 2029.By that time, 78P will definitely be a faint comet again at such heliocentric distance, or it may even be a dormant comet until it is brought back to the inner solar system.

Conclusion
We performed secular monitoring broadband photometric observations on JFCs 68P and 78P from 2018 November to 2020 March.The R band A(0)fρ value was computed and normalized to zero phase angle.The maximum A(0)fρ values we recorded for 68P and 78P are 339.7 ± 4.4 cm and 1028.1 ± 13.3 cm, respectively.Comparing them with other JFCs, we can conclude that the activity of 68P is of mediate level while 78P is the one of the most active JFCs.The multiband photometry of 78P indicates that the mean color during our observation is (B − V ) = 0.88 ± 0.05 and (V − R) = 0.27 ± 0.02, indicating that the B − V is redder and V − R is bluer than the mean color of the active JFCs.The morphology in R band for the dust coma is investigated with both subtraction of azimuthal average method and the Larson-Sekanina method to distinguish the artifacts produced in the image enhancement.Both comets show fan-like structures near the anti-solar direction, and they too have counterclockwise spiral patterns, but the structure of 78P is more obvious than 68P and the covering angular range is larger, indicating their connection with the strength of dust activity.The analysis of the 1 Myr backward integration shows the dynamical history of the comets.For the most recent entrance to JFC region, 68P probably entered the JFC region 1200 yr ago while 78P entered only 300 yr ago, which means that 78P is a very young member of JFC.The activity of 78P recorded in the past apparitions suggests that 78P was not so active before the 1997 apparition when its perihelion distance decreased from 2.36 to 2.01 au.While it was highly active in the past three apparitions, its peak activity showed significant decl.over regressions.We conclude that this phenomenon results from the change of perihelion distance between 1989 and 1997 that boosted the water-ice sublimation rate and formed new active regions.The recent activity decl.could be attributed to the reformation of the dust mantle.
magnitudes are also listed in Table2.The mean colors of 78P were measured to be (B − V ) = 0.88 ± 0.05 and (V − R) = 0.27 ± 0.02.Compared to the mean color of active JFCs given in the previous research, which showed that (B − V ) = 0.75 ± 0.02 and (V − R) = 0.47 ± 0.02(Solontoi et al. 2012;Jewitt 2015), the B − V color of 78P is redder while the V − R color is relatively bluer.In the past observations of 78P, the colors were measured in two different apparitions.On 2004 October 6, 21 days before perihelion, the colors were (B − V ) = 0.74 ± 0.15 and (V − R) = 0.48 ± 0.12 (Mazzotta Epifani & Palumbo 2011).In observations three months earlier than our observations, the color was g − r = 0.55 ± 0.01, similar to the previous B − V results after conversion(Kelley et al. 2019).The apparent bluer V − R values were observed in a significant fraction of comets and were typically attributed to the gaseous emission flux covered in the bandwidth of V band

Figure 1 .
Figure 1.A(0)fρ curves for 78P (left) and 68P (right) with respect to heliocentric distance.The straight line in the middle of each panel indicates the comet's perihelion distance.

Figure 3 .
Figure 3. Selected co-added R band images of 78P and 68P.The Y-axis of the image is aligned to the North and East is aligned to the left.The FOV is approximately 50,000 km × 50,000 km for each image.The orange arrow represents the solar direction while the blue arrow represents the velocity direction of the comet.The red cross marks the center of the image.

Figure 4 .
Figure 4. Figure 3 after applying Larson-Sekanina image enhancement methods.The FOV is 50,000 km × 50,000 km for each image.The orange arrow represents the solar direction while the blue arrow represents the velocity direction of the comet.The red cross marks the center of the image.

Figure 5 .
Figure 5.Comparison between observational images (left-hand) and synthetic images (right-hand) produced by dust coma model, the upper panel shows the appearance of 68P on 2019 September 28 and the lower panel shows the appearance of 78P on 2019 February 5.The size of all the images is 50,000 km × 50,000 km, the contours in the image represent 20.6, 20.3, 20.0, 19.7, 19.4 mag arcsec 2 -for 68P and 19.9, 19.8, 19.7, 19.6 and 19.5 mag arcsec 2 -for 78P, respectively.

Figure 6 .
Figure6.These plots represent that in 1 Myr backward integration of 68P (all upper panels) and 78P (all lower panels), how many clones have survived and where the surviving clones resided with respect to time from now.The left-hand panels show a shorter case of 5000 yr backward integration and the right-hand panels show the number of surviving clones in the past 1 Myr.

Table 2 (
Continued) a Geocentric distance.b Heliocentric distance.Negative value denotes that the comet was inbound to the perihelion.c Phase angle.d Broadband filter and integration time in seconds times the number of images.

Table 3
Summary of the Observation Log of 68P/Klemola a Geocentric distance.b Heliocentric distance.Negative value denotes that the comet was inbound to the perihelion.c Phase angle.d Broadband filter and integration time in seconds times the number of images.

Table 4
Perihelion Distance Distribution of 78P and 68P Clones in the Past 5000 yr to 1 Myr

Table 5
Orbital Elements of 78P in 1989 and 1997 Apparitions