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The combination of close approach, brightness and large solar elongation of comet 41P/Tuttle–Giacobini–Kresák (hereafter 41P) made it the target of observations worldwide for several months. We report results from our observations of comet 41P obtained in March 2017 using the Large Monolithic Imager on Lowell Observatory’s 4.3-m Discovery Channel Telescope (DCT) and in May 2017 using the UltraViolet–Optical Telescope (UVOT) on board the Earth-orbiting Swift Gamma Ray Burst Mission6 (Extended Data Table 1).

We used comet-specific narrowband filters7 on the DCT to capture the emission of cyanogen gas. Cyanogen coma structures have been used to infer rotational properties of otherwise unobservable comet nuclei since their discovery in comet 1P/Halley8. Volatile ices at or near the surface of a comet sublimate when exposed to sunlight during the diurnal cycle of the comet. As the gas moves outwards, it and daughter species produced by photodissociation trace spirals or arcs that can be used to infer the rotation of the comet. Cyanogen is one of the most effective gases in this respect, owing to its large fluorescence efficiency in sunlight. Its use is widespread9 and its connection to the rotation of comet nuclei has been verified by in situ missions such as EPOXI10. During our first epoch of observations (Extended Data Table 2), we identified rotating spiral arms, of which one is persistent whereas a second is visible for only part of the rotation (Fig. 1). The repetition of these features indicates a rotation period of 19.75–20.05 h during 6–9 March11.

Figure 1: Repeating cyanogen jets in the coma of comet 41P/Tuttle–Giacobini–Kresák.
figure 1

Sequence of DCT images showing the cyanogen coma of comet 41P, enhanced to reveal two rotating jets (labelled J1 and J2). The images, obtained on 7 and 8 March 2017, progress in a clockwise direction, as indicated by the curved arrows. Nearly identical morphologies are seen in the left two panels, which were obtained 20.1 h apart, and the sequence suggests that these two images are slightly more than one full rotation apart, leading to the derived 19.9-h period. The other panels, labelled in the upper left corner with the fraction of the period (phase) when the image was obtained, show a continuously changing morphology that precludes any periods that are sub-multiples of the 19.9-h derived value. Each panel spans approximately 20,000 km at the distance of the comet, is centred on the position of the nucleus (too small to be resolved), and is oriented with north up and east to the left. The direction to the Sun is indicated in the middle-top panel. Images were enhanced by dividing out the averaged azimuthal profile. Regions that are brighter than average at that distance from the nucleus are white and regions that are fainter are black. The white streaks are background stars.

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For our second epoch, we adopted a photometric technique, using variations in the brightness of the comet to measure periodicity. Although these two techniques measure different characteristics, they both identify repetitions in their respective phenomena and we assume that the associated periodicity reflects the rotation of the nucleus. We used Swift/UVOT to observe comet 41P on 7–9 May 2017 and measured all of the light within 1,600 km of the nucleus, including molecular emissions and sunlight reflected by dust grains. The light contributed by the small nucleus was negligible during this time, indicating that variations in brightness in our aperture were dominated by the material that had recently been released from the nucleus. The photometric variations are small and slowly varying (Fig. 2, Extended Data Table 2). Although the light curve is incomplete, the unobserved parts can reasonably be inferred, resulting in a single-peaked sinusoid (the hallmark of activity being modulated by changes in illumination induced by rotation) with a period of 46–60 h. The 14-h range arises because the alignment of the overlapping segment of the phased sine curve is affected by changes in the activity of the comet with its increasing distance to the Sun. We therefore conclude that during the two months of our observations, there was a substantial change in the rotation period, with an average increase of 0.40–0.67 h per day. For the discussion presented here, we adopt 53 h, the middle of our range, as our representative period.

Figure 2: Light curve of the inner coma measured by Swift/UVOT on 7–10 May 2017.
figure 2

The data acquired on 9.4–10 May are repeated as red triangles, phase-shifted to best match the data acquired on 7.5–8 May (black circles). Depending on the decrease in the activity of the comet with heliocentric distance (Methods), a range of periods of 46–60 h is found (Extended Data Fig. 2). The central period (53 h) is shown here. Error bars indicate 1σ stochastic uncertainties.

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A cyanogen morphology similar to that seen in our DCT observations was observed on 18–27 March 201712, but the structure took 24 h to repeat on 19 and 21 March, and increased continuously to nearly 27 h on 26 and 27 March (Fig. 3). During the densest coverage in late March, the morphology repeated at progressively later times on subsequent nights, revealing a daily trend that is consistent with our ensemble dataset from March to May. The consistent repetition of the morphology at the end of each lengthening period over such an extended time suggests that any non-principal axis component of rotation is small. Furthermore, we cannot conceive a scenario in which non-principal axis rotation could mimic the observed continuously changing period. Therefore, we assume that the nucleus was in a state of simple rotation.

Figure 3: Rotation periods for comet 41P measured as a function of time relative to perihelion.
figure 3

Perihelion occurred on 12 April 2017. The period increased at an average rate of at least 0.53 h per day over more than 60 days, an unprecedented rate of change. The different observations are indicated by symbols: Swift (circles; this work), DCT (squares; ref. 11 and this work) and results acquired12 using the Lowell Observatory’s 31″ telescope (diamonds). The dashed line is a guide to the eye. Error bars indicate 1σ absolute uncertainties; the error bar on the Swift observation (circle) indicates the range of possible solutions due to the uncertainty in the change of activity as a function of heliocentric distance.

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Rotation periods have been measured for scores of comets, many with extensive coverage, but 41P is only the eighth comet for which a conclusive change in period has been measured. Furthermore, the fractional change and rate of change in period for comet 41P far exceed those observed in other comets (Extended Data Table 3). Changes in rotation period depend on the size, shape, internal structure, activity and rotational state of the nucleus of the comet1,2,4,5. The radius of the nucleus of comet 41P is13 0.7–1.0 km, which is less than 70%–90% of all measured radii of Jupiter-family comets14. The water production rate of comet 41P peaked around 2 × 1029 molecules per second in 2001 and 2 × 1028 molecules per second in 200615. Our Swift observations suggest that production rates in 2017 were similar to those in 2006 (Extended Data Fig. 1). This result implies that more than 50% of the surface of the comet could be active, whereas most comets have less than 3% surface activity16. Finally, although the 20-h rotation period of comet 41P in March was long compared to most comets, the rotation period of more than 46 h that was measured in May is among the longest known13. It is this combination of slow rotation, high activity and a small nucleus that contribute to the rapid changes of the rotation state of comet 41P.

However, these characteristics are not unique to comet 41P. In 2010, comet 103P/Hartley 2 had an initial period of 16.5 h, a peak water production rate three times higher than that of 41P and a smaller effective radius10 of 0.57 km. Even with the more extreme combination of these characteristics, its primary rotation period changed by only 2 h in the three months around perihelion16 (Extended Data Table 3), more than an order of magnitude less than that of 41P. Therefore, other factors must also have a role in producing the net torque in comet 41P, which is much more efficient than that in any other known comet. The Deep Impact fly-by of comet 103P allowed a close examination of the activity of its nucleus10, and the details that were observed enable us to explore possible differences between comets 103P and 41P. The visible jets from comet 103P are primarily along the long axis, with little moment arm for producing torques; some of the water from 103P comes from icy grains in the coma, reducing the amount of gas that contributes to torques18,19; and finally, the non-principal axis rotation of 103P acts to randomize the direction of the torques, reducing their efficiency.

Using the results from the four then-available comets that exhibited changes in period, an empirical parameter X has been suggested to relate cometary activity and changes in angular momentum18. This parameter was found to be nearly constant within a range of 1–2, leading to the conclusion that net torques are nearly the same irrespective of the effective active fractions of the nucleus. From our observations of comet 41P, we compute an X parameter of more than 50, inconsistent with that conclusion. (X parameters for comets 19P/Borrelly20 and 67P/Churyumov–Gerasimenko21 also lie well outside the 1–2 range; see Extended Data Table 3.) The deviation from this range implies that the torques, when integrated over all active areas, do not necessarily cancel out and that the physical characteristics of nuclei greatly affect the net efficiency of the torques. The effects of non-uniform activity and local topography are well illustrated by the results of the Rosetta mission to comet 67P/Churyumov–Gerasimenko, which demonstrated that the rotation period first increased, then decreased as new parts of the surface of the comet became illuminated2. The active regions on the surface of comet 41P are probably oriented in such a way that its torques are highly optimized in comparison to many other comets.

We extrapolated the rotation period of the comet in time to investigate its possible past and future behaviour (Fig. 4). Our model assumes that activity levels and effective torques are constant from apparition to apparition; for example, it assumes that the orientation of the spin axis and the water production did not change substantially. It suggests that, in the near future, the rotation period could exceed 100 h. At such slow rotation rates the stabilizing gyroscope effect disappears and off-axis torques can tip the nucleus into an excited rotation state. If strong torques persist, then the rotation period of the nucleus can begin to shorten again, but with a different orientation of its rotational angular momentum vector. Such behaviour is consistent with simulations of the long-term evolution of spin states of small cometary nuclei, which indicate that most comets go through a large change in their rotation period soon after their activation5. This large change leads to a temporary excitation of the spin state of the nucleus, and for most comets the rotation period will evolve slowly thereafter. Simulations also show that, in some cases, uniformly active surfaces can cause comets to respond unpredictably to changes in their spin state. Such comets may have inherently variable spin states, experiencing large changes in their rotation period during each perihelion passage.

Figure 4: Extrapolation of the rotation period of comet 41P in time.
figure 4

We modelled past and future absolute values of the period (|P|) by extrapolating the 2017 torques to other perihelion passages (upward steps). This scenario suggests that the nucleus could evolve from rapid rotation near the fragmentation limit3 (red shading) to an excited, unstable spin state4,5 (blue shading) in only a few orbits. The 2017 observations are indicated by filled circles.

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Projecting back in time, comet 41P may have been near the critical fragmentation limit (with a period of around 5 h)3 in the recent past. It exhibited large outbursts in activity in 1973 and 200115,22, and these events may be related to the evolution of its spin state. The rapid rotation may have caused these outbursts via fragmentation or landslides23; alternatively, the outbursts may have given rise to the spin evolution by exposing new active areas that generate outgassing torques.

Methods

Photometry

Swift/UVOT observations were obtained with the V-band filter, centred at 547 nm with a full-width at half-maximum (FWHM) of 75 nm. We measured the brightness of the coma using photometry extracted from a circular aperture centred on the nucleus with a 1,600-km (10–11-arcsec) radius at the distance of the comet. The median background flux was determined from an annulus with an inner radius of 50 arcsec and an outer radius of 100 arcsec (beyond the visible extent of the coma). We followed a standard calibration procedure24 to derive the apparent magnitudes, V. These were then converted into absolute magnitudes, H, at 1 au to account for changes in the geocentric distance Δ, heliocentric distance rh and phase angle PA (using a phase function normalized to a phase angle of 90°, PA(90))25 of the comet during our observation using the relation:

The relation between the activity of the comet and its heliocentric distance, which increased from 1.099 au to 1.108 au during the Swift observations, is currently not well constrained. This implies that a range of scale factors A are possible for the activity-corrected brightness H′ of the comet:

where r0 is the heliocentric distance of the comet at the first Swift observation (1.099 au). Larger scale factors imply longer rotation periods. We considered scale factors of A = 0 (an relation; see equation (1)), A = 28 (an early empirical fit to the current brightness trend26), and an upper limit of A = 35 (derived from an empirical fit to the brightness trend during the apparitions of 1995 and 200126). As is shown in Extended Data Fig. 2, this results in a range of possible periods of repetition between 46 h and 60 h, with a central solution around 53 h (A = 17). Independent of the rh correction, periods shorter than 46 h are not possible with our light curve (under our assumptions of simple rotation and no outburst or other unusual activity).

There are too few measurements with the DCT to construct a meaningful light curve, and the night of 8 March was not photometric (owing to Cirrus clouds); consequently, our observations focus on morphology rather than absolute measurements.

Production rates

We used Swift/UVOT images to determine water production rates following a previously outlined method24. The UVW1 filter (central wavelength, 260 nm; FWHM, 70 nm) encompasses the three strong OH A–X transitions. We first created stacks containing all UVW1 images and V-band images acquired on 4–9 May 2017 using a clipped mean routine. We then removed the continuum contribution to the light measured with this filter by subtracting a weighted V-band image. There was no obvious repetitive morphology in the OH images. Fluxes in apertures with radii of 5–300 arcsec (775–46,500 km at the comet) were converted into OH column densities assuming fluorescence rates at the heliocentric velocity and distance of the comet27. Production rates were derived using a vectorial model28.

Active area

We derived the minimum active area corresponding to the measured water production rate using a sublimation model29. We assume that every surface element has constant solar elevation—as would be the case if the spin axis were pointed at the Sun (an obliquity of 90 degrees) or if the nucleus were rotating very slowly—and is therefore in local, instantaneous equilibrium with sunlight. This maximizes the sublimation averaged over the entire surface and results in a minimum total active area. We further assumed a Bond albedo of 0.02 and 100% infrared emissivity. The modelled H2O sublimation rate is 3.35 × 1017 molecules per cm2 at 1.05 au. Assuming a peak water production rate of 2 × 1028 molecules per second (Extended Data Fig. 1), we find an active area of at least 6 km2, equivalent to an active fraction of 50%–97% of a spherical nucleus with a radius of 0.7–1 km.

Modelling the change in rotation period

To extrapolate the rotation period of comet 41P to past and future apparitions we used the relation between the rate of change of the angular velocity dω/dt, the water mass loss rate Q and the radius of the nucleus R (ref. 18):

We assumed a nucleus with a radius of 0.7 km and used our measurements of the production rate and the average change of rotation period during the current apparition to determine the constant C empirically. To estimate the orbital gas mass loss, we fitted the empirical relation between the brightness of the comet and its heliocentric distance () to the SOHO measurements of water production rates during the 2006 apparition15. We assumed abundances of 10% for both CO and CO2 relative to water, and that activity beyond 3 au is negligible. When the nucleus reaches a rotation frequency of 0, the period is infinite, hence the growth off the top of Fig. 4. At this point in the model, the rotation reverses (rotational pole flip) and the period decreases from infinity. However, in reality the rotation will become excited, the illumination on the surface will change and the torques should also change.

Integrating the gas production rates from 3 au before to 3 au after perihelion results in a mass loss rate of 6 × 109 kg in volatiles per orbit, or about 1% of the mass of the nucleus for a density of 500 kg m−3.

Rotation evolution models5 assume a certain initial spin state and evolution is modelled for 10–100 orbits. Comet 41P has orbited the Sun approximately 30 times since its discovery in 1858. After considering several scenarios, hyperbolic evolution after 10–30 orbits was concluded previously, with the spin states of the comets evolving continuously throughout the simulations5. However, these models5 did not explore the full parameter space4 and we are hesitant to imply a more quantitative interpretation of them.

Data availability

All Swift/UVOT data are available from the Barbara A. Mikulski Archive for Space Telescopes (https://archive.stsci.edu) and from the Swift Archive Portal (http://www.swift.ac.uk/swift_portal/) under programme ID 1316125. The photometric measurements are provided as Source Data for Fig. 2. Other data that support the findings of this study are available from the corresponding author on reasonable request.