Kordylewski cloud

Kordylewski clouds, sometimes called lunar libration clouds,^[1] are concentrations of dust that exist at the L₄ and L₅ Lagrangian points of the Earth–Moon system. They were first reported by Polish astronomer Kazimierz Kordylewski in 1961, who observed the clouds from the Tatra Mountains in former Czechoslovakia. The clouds are likely composed of trapped dust particles from the interplanetary dust cloud. Dust particles remain for decades, forming large, rapidly-evolving bands within the clouds. Eventually, perturbations from the Sun lead to their escape.

Polarimetric photograph of the L₅ cloud on 12 August 2023. Darker shades of gray correspond to higher dust density.

Following Kordylewski's discovery, inconsistent observations by other astronomers led to their existence being controversial. Attempts to observe the sparse clouds were complicated by their exceedingly dim nature, making them difficult to discriminate against gegenschein and atmospheric airglow even in very dark skies. Observations from the ground, air, and space reported both positive and negative detections, and a 1991–92 encounter from the Hiten spacecraft failed to find the clouds. In 2018, they were tentatively confirmed to exist by a team of Hungarian astronomers through polarimetry. Due to their elusiveness they are sometimes nicknamed ghost moons.^[2]

History

Following French astronomer Frédéric Petit's spurious report of a second moon of Earth in 1846, other astronomers began searching for potential undiscovered moons.^{[3]: 145–146} From 1953 to 1956, a team of astronomers led by Clyde Tombaugh planned to search for small natural satellites near the Moon's Lagrange points—dynamically stable regions of space—but were prevented by poor weather.^[4]: 12 In 1951, Polish astronomer Kazimierz Kordylewski began his own search for Trojan satellites at the lunar L₄ and L₅ Lagrange points. This search was also unsuccessful, but in 1956 Josef Witkowski suggested to Kordylewski to instead search for faint, diffuse dust clouds.^[5]: 1240

The clouds were first observed with the naked eye by Kordylewski in October 1956, at the Skalnaté pleso Observatory in the Tatra Mountains of former Czechoslovakia. Even with very dark skies, the faint clouds were observed with difficulty. They appeared as slight brightenings near the lunar L₄ and L₅ points at least 2° in diameter and 1–2 magnitudes fainter than the brightest gegenschein.^{[6]: 63 [5]: 1240} On 6 March and 6 April 1961, Kordylewski successfully photographed two distinct clouds at the lunar L₅ point from Kasprowy Wierch's summit observatory. The photographs were taken using a Jupiter 3 f/1.5 50 mm Leica camera, with an exposure time of 11 minutes on March and 12 minutes in April. The photographs were photometrically analyzed, with Kordylewski publishing his results on Acta Astronomica in 1961^[7] and an International Astronomical Union circular announcing the clouds' discovery on 23 May of that year.^[8]

Debate on existence

Further attempts to detect the Kordylewski clouds were often conflicting and controversial.^[1] Ground-based observations of the clouds are complicated by their exceedingly dim nature, making observations sensitive to weather, gegenschein, and airglow.^[9]: 5 Following Kordylewski's announcement on 1961, other professional and amateur astronomers attempted to observe the clouds, initially without success.^[10]: 1 On 4 January 1964, astronomer J. W. Simpson and his colleagues R. G. Miller and G. Gardner observed the L₅ Kordylewski cloud. Thence until 1967, the team took about 100 photographs of the cloud.^{[11][10]: 1} In 1966, NASA organized an airborn observations campaign, reporting detections of "circular or elliptical nebulous patches" at both Lagrange points on four flights.^[12] Other astronomers reported negative detections through optical or radar observations.^[13] From 1962 to 1963, a United States Geological Survey attempt to photograph the clouds from Chacaltaya, Bolivia gave inconclusive results.^[14] A photographic search for the L₅ cloud was conducted from March 1966 to March 1967 by astronomer Robert Roosen at the McDonald Observatory failed to find any clouds.^[15]: 429 Astronomers C. Wolff, L. Dundelman, and L. C. Haughney attempted to aerially photograph the clouds, flying well away from land over the Pacific Ocean to minimize light pollution. The team did not detect any clouds.^[14]

Later observation attempts from space were conducted; space-based observations have the advantage of avoiding atmospheric airglow.^[14] In 1975, researcher J. R. Roach analyzed photographic data collected from 1969 to 1970 by the sixth Orbiting Solar Observatory telescope (OSO-6). The imagery was taken in green visible light,^[a] revealing clouds near both Lagrange points that appeared to librate around each point.^[16] A team of researchers led by R. H. Munro analyzed data taken by the coronograph aboard the Skylab space station, aiming to detect potential forward scattered sunlight by the clouds. No clouds could be distinguished against the solar coronal background.^[1]: 1313 In 1991–1992, the Japanese Hiten spacecraft made single looping passes around the lunar L₄ and L₅ points, failing to detect the dust clouds with its dust counting instrument.^[18]

With mixed observational results, several astronomers expressed skepticism of the Kordylewski clouds' existence.^[9]: 3 In 1969, Roosen and Wolff published an article arguing against the existence of dust clouds within the Earth–Moon system, asserting on theoretical grounds that any such clouds would be unstable and destroyed by perturbations from the Sun or from the Moon's orbital eccentricity. Instead, they suggested that reported positive detections may be due to passing interplanetary dust clouds.^[13] In 1970, astronomer Naosuke Sekiguchi computed the behavior of dust, stating that dust tends to disperse from the lunar lagrange points and suggested that positive detections may have been transient dispersing clouds. A similar analysis conducted by GP. Horedt, meanwhile, was inconclusive regarding dust behavior near the lagrange points.^[19]: 323 Other astronomers suggested the possibility that the Kordylewski clouds quickly vary in structure over time as an explanation to conflicting ground observations.^[20][9]: 3 Additionally, successful reported observations of a cloud at the L₅ point are around three times more common than those for the L₄ point.^[10]: 2

Current status

The Kordylewski clouds were tentatively confirmed in 2018 by a team of astronomers led by Judit Slíz-Balogh.^[21] The team first developed computer models to simulate the dynamical behavior of dust particles at the L₅ point, including predictions of what the simulated cloud would appear like in polarimetric observations from Earth.^[22]: 5551 Polarimetric observations of the area around the L₅ point where then conducted over several months in 2017 at a private observatory in Badacsonytördemic, Hungary. As a control, the same region of sky was photographed when thin cirrus clouds and contrails passed overhead or when the L₅ point was not in view. Using a CCD camera with three linearly polarizing filters attached to its lens, the team successfully photographed L₅ features with polarization characteristics consistent with light scattered by dust clouds.^{[23]: 763–764} When compared against the control photographs, the polarization characteristics differed from those expected of clouds, contrails, or zodiacal dust.^[23]: 768 Slíz-Balogh's team then compared their photographs of the clouds to their earlier computer models, finding that the photographed cloud structures matched predictions. The team published their confirmation of the clouds' existence in the Monthly Notices of the Royal Astronomical Society in 2018.^{[23]: 767 [24]}

A followup observation campaign was led by Slíz-Balogh on 31 October 2021 and 3 July 2022, targeting both the L₄ and L₅ points.^[25]: 5238 Using the same methods and location as the 2017 observations, the L₄ and L₅ clouds were successfully photographed.^[25]: 5240

Properties

Structure and variability

Diagram showing the Lagrangian points of the Earth–Moon system. Kordylewski clouds exist in the regions of L₄ and L₅.

The Kordylewski clouds are large and heterogeneous structures,^{[22]: 5559 [25]: 5237} with ground-based observations suggesting an apparent diameter of several degrees.^{[20]: 1528 [b]} The clouds have an elongated, relatively dense "core" about 25,000 km in size and aligned parallel to the Moon's orbital plane.^{[22]: 5556 [c]} A diffuse series of dusty bands or blobs extend from the center perpendicular to the ecliptic plane, giving the clouds a striped appearance in polarized light.^{[22]: 5556 [25]: 5237} Simulations of the clouds suggest an asymmetry, with the L₅ cloud's core being denser than that of the L₄ cloud.^[10]: 6

Observations and modelling indicate that the Kordylewski clouds' structures change over time,^[9]: 3 and their structures and densities are influenced by the rate at which dust is trapped at the Lagrange points.^[23]: 766 The structure of the clouds vary over timescales as short as a few days,^[22]: 5556 and they may be transient, ephemeral features.^[23]: 766 Modelling by Slíz-Balogh and collaborators indicate that the structure of the clouds is also controlled by different populations of trapped dust. Dust populations are trapped at different times and with different velocities, with populations older than 20–25 days forming bands. The evolution of these populations lead to bands appearing, disappearing, or changing in density.^[22]: 5556 Modelling by Nathan R. Boone and Robert A. Battinger in 2021 demonstrated that the density of the clouds may also vary with respect to solar perturbations as it causes structures within the clouds to expand and collapse.^{[27]: 2327–2328}

Dynamics and source

Simulated trajectories of different-sized dust particles in the L₄ cloud in a corotating reference frame. β is a parameter describing acceleration from solar radiation pressure; it is inversely proportional to size.

The Kordylewski clouds are located near the lunar L₄ and L₅ points,^[10]: 1 which are 60° ahead and behind the Moon along its orbit, respectively.^[28] The clouds are not centered exactly on the L₄ and L₅ points; ground observations have noted the clouds displaced by 6–10° or more away from those points.^{[29]: 32 [30]: 214}

In the restricted three-body problem, the five Lagrange points represent points of equilibrium.^[31]: 1 Although points L₁–L₃ are unstable, the L₄ and L₅ points are stable so long as the mass ratio of the primary and secondary is large enough: particles at these two points can become trapped.^{[31]: 6–7} The mass ratio between the Earth and the Moon is great enough to ensure theoretical stability of the lunar L₄ and L₅ points.^[10]: 5550 However, gravitational tides from the Sun and solar radiation pressure—relevant for dust particles—disrupt the stability of the lunar L₄ and L₅ points.^[32]: 3 Nevertheless, numerical simulations suggest that dust particles near these points are able to be temporarily captured into the Kordylewski clouds, potentially remaining for decades in small "islands of stability".^{[32]: 26 [22]: 5550}

The Kordylewski clouds are likely supplied by dust from interplanetary space.^[32]: 26 The interplanetary dust cloud near Earth is quite homogeneous; despite this, models result in the L₅ cloud trapping up to 9% more dust than the L₄ cloud. This modelled asymmetry is similar to asymmetries in other trojan populations, such as between the two Jupiter trojan asteroid camps, but its exact cause is still unknown.^{[10]: 5–6} Captured dust populations are initially evenly distributed within the clouds, forming bands after 20–25 days. Mean-motion resonances with the Moon may contribute to the formation of the bands.^[33]: 3573 After becoming destabilized, dust particles then escape from the Earth–Moon system back into interplanetary space.^[10]: 6

Exploration

Scale model of the Hiten spacecraft

In October 1991, the Hiten spacecraft executed a looping halo trajectory around the lunar L₄ point; it then executed a similar looping trajectory around the lunar L₅ point in January 1992. Hiten was en route to the Moon as a part of its extended mission, but the excursions to the lunar L₄ and L₅ points were planned to search for the Kordylewski clouds using its Munich Dust Counter (MDC) instrument.^{[34]: 70–71} No increase in dust impact rates were detected, though this could be due to the MDC's insensitivity to low-velocity dust impacts or from Hiten missing the clouds entirely.^{[9]: 6 [18]}

Proposed missions

Exploration of the Kordylewski clouds was suggested as early as 1963 by Arvydas Kliore, proposing either a flyby or rendezvous mission.^[9]: 5 At the International Electric Propulsion Conference in 1988, Keith Ryden and collaborators proposed a rendezvous mission to the Kordylewski clouds using ion propulsion. Such a spacecraft would weigh a total of 300 kg (660 lb), of which 60 kg (130 lb) would be xenon propellant. The probe would be parked in low-Earth orbit, before continuously raising its orbit in a spiral trajectory and rendezvousing with the L₅ cloud.^[35] In 1997, N. S. Moeed and J. C. Zarnecki proposed reactivating the Giotto spacecraft, an ESA probe originally designed to flyby and study Halley's comet, for an extended mission intercepting the L₄ cloud. Though some of its instruments were damaged by dust impacts whilst travelling through Halley's coma, the proposal sought to use its Dust Impact Detector System to study the L₄ cloud.^[20]: 1529 Giotto was set for its second encounter with Earth on 1 July 1999.^[36] The proposal called for a correction burn six months before encounter to deflect the spacecraft towards the L₄ cloud. Approaching at a velocity of about 3.4 km/s, Giotto would traverse the cloud in just under three hours.^[20]: 1530 Giotto was not reactivated for its second Earth encounter.^[37]

In 2021, a team of researchers led by Peng Wang proposed a coordinated space- and ground-based observation campaign for the Kordylewski clouds. After injection into a highly eccentric orbit, the spacecraft would conduct multiple flybys of both Kordylewski clouds, sampling them with a dust counter. Ground-based observations could be used to guide the spacecraft toward the clouds' locations. A lunar flyby is then executed, setting the spacecraft to the L₄ point. After rendezvousing with the L₄ point, it enters a halo orbit, further exploring the cloud's structure and dynamics.^[9]: 7

Due to their dynamical stability, the L₄ and L₅ points have attracted attention for their potential to support space infrastructure for both civilian and military applications. However, the same mechanisms that trap dust in the Kordylewski clouds can also trap artificial space debris, potentially leading to a hazardous space environment within the clouds in the future.^{[27]: 2319–2320} In contrast, the risk of collision from natural debris in the Kordylewski clouds appears to be low. Modelling from researchers Nathan R. Boone and Robert A. Battinger in 2021 concluded that the likelihood of a Kordylewski cloud particle substantially threatening a spacecraft is 9.702×10⁻⁹%.^[27]: 2330

See also

• Sodium tail of the Moon
• Zodiacal light
• Trojan moons of Saturn
  • Telesto and Calypso, trojans of Tethys
  • Helene and Polydeuces, trojans of Dione

Notes

1. Data was taken at a wavelength of 5000 angstroms (500 nm),^[16]: 173 corresponding to "green" light at 498–530 nm.^[17]
2. Compare the apparent diameter of the Moon of 0.53°.^[26]
3. A size of 25,000 km for the dense core is given only for the L₅ cloud.^[10]: 5