In the Solar System, the dust forms a huge disc-shaped cloud around the Sun in the plane of the planets’ orbits. Sunlight is scattering on these dust particles resulting in the zodiacal light. Earlier, the polarization characteritics of the zodiacal light have been studied only with point-source or very-narrow-field (1–2°) imaging polarimetry. Here we report on our Hungarian and Namibian imaging polarimetric measurements studying the zodiacal light. We present the first polarization portrait of the zodiacal light in form of wide-field (40° horizontal × 27° vertical) patterns of the degree p and the angle (or direction) γ of linear polarization. We found that p changes slightly along the ecliptic meridian so that near the ecliptic pole it is slightly larger than at other parts of the meridian. Near the ecliptic pole, the polarization direction is perpendicular (positive polarization), while near the anti-Sun (gegenschein) it is parallel (negative polarization) to the ecliptic meridian being the scattering plane. Moving along the ecliptic meridian from the anti-Sun toward the ecliptic pole, γ suffers a 90° turn (from negative to positive). Moving upward from the horizon along the solar meridian of the night sky, p of the zodiacal light decreases from ∼20% (immediately above the horizon) to ∼1–2% at 40° above ground. The polarization direction of zodiacal light is perpendicular to the solar meridian (scattering plane) of the night sky. Our imaging polarimetric results corroborate the findings of earlier point-source and very-narrow-field polarization measurements of the zodiacal light.

ABSTRACT The Kordylewski dust clouds (KDCs) near the L4 and L5 Lagrange points of the Earth and Moon have been discovered in 1961. Their long-term stability is disrupted by the Sun’s gravitation. Although computer modellings showed that both KDCs can exist for several years and some astronomers observed them with the naked eye or by photometry, other researchers could not detect them. Using imaging polarimetry, the polarization characteristics of both KDCs were first observed in 2017 and 2022 in Hungary. In 2023, these polarimetric observations were performed under the much better astroclimate of the Khomas Highland in Namibia when the L5 KDC was detected again polarimetrically. In 2024, we continued our Namibian KDC observations. Our measurements were performed with the same imaging polarimetric portable telescope that was used in 2023 in Namibia. The polarization patterns were evaluated with our algonet software. We report here on the first polarimetric observation of the short-term dynamics of the L4 KDC. We present the 3-day change of the degree and angle of polarization of the L4 KDC being an inhomogeneous sunlight-scattering particle aggregation. We conclude that the KDCs have a complex and rapid dynamics, which we plan to explore further in our next Namibian polarimetric campaigns.

ABSTRACT The Kordylewski dust clouds (KDCs) around the L5 and L4 Lagrange points of the Earth–Moon system have been first observed by imaging polarimetry in 2017 and 2022 in a Hungarian astronomical observatory. Due to the non-ideal (almost always hazy, aerosol-polluted) astroclimate of Hungary and the extremely low intensity of dust-scattered sunlight, the polarimetric hunt after both KDCs lasted 2–7 yr. Waiting for cloud- and aerosol-free atmosphere and appropriate astronomical conditions (e.g. moonless sky with above-horizon KDC) in our Hungarian observatory takes a long time. Thus, our goal was to build a portable imaging polarimetric, wide field-of-view telescope and use it in the very good astroclimate of the Isabis Astro Lodge in the Khomas Highland of Namibia. Our long term aim is to study the dynamics of KDCs with this instrument in Namibian 1-month astropolarimetric campaigns in the next decade. In this work, we describe our portable imaging polarimetric telescope and present our first KDC observation achieved with it in Namibia during our 4-week astropolarimetric campaign between 2023 July 18 and August 15. We conclude that our portable polarimetric telescope functions well. Using it in Namibia, we corroborated the existence of the L5 KDC, the polarization characteristics (polarization degree and angle) of which refer to an inhomogeneous dust cloud composed of several particle agglomerations that scatter and linearly polarize the illuminating sunlight.

Mature inflorescences of sunflowers (Helianthus annuus) orient constantly on average to the geographical east. According to one of the explanations of this phenomenon, the eastward orientation of sunflower inflorescences increases the number of attracted insect pollinators. We tested this hypothesis in three field experiments performed in flowering sunflower plantations. In experiments 1 and 2 we measured the number of insects trapped by the vertical walls of sticky sunflower models facing north, east, south, and west. In experiment 3 we counted the pollinators' landings on real sunflower inflorescences facing naturally east or turned artificially toward north, south, and west. We found that the all-day number of pollinators (predominantly bees) attracted to model and real sunflowers in H. annuus plantations is independent of the azimuth direction of sunflower heads, and after 10 h in the morning, the average number of pollinators counted every 20 min is practically constant in the rest of the day.

ABSTRACT In 1961, Kordylewski found two bright patches near the L5 Lagrange point of the Earth–Moon system. This referred to an accumulation of dust particles, later called as Kordylewski dust cloud (KDC). In spite of the photographic observation of the L5 KDC by Kordylewski and its visual (naked-eyed) or photometric confirmation by others, some astronomers assumed that the KDC cannot exist, because the gravitational perturbation of the Sun may disrupt the stabilizing effect of the triangular Lagrange points L4 and L5 of the Earth and Moon. In 2017, the L5 KDC was observed in two consecutive nights by ground-based imaging polarimetry. So far the L5 KDC has been detected 16 times and the L4 KDC only 5 times. Contrary to the visually, photometrically, and polarimetrically documented existence of the L5 KDC, a polarimetric proof does not exist for the L4 KDC. On 2022 July 3, we were able to detect the polarization signals of the L4 KDC, furthermore on 2021 October 31 we detected polarimetrically again the L5 KDC. In this work, we present the first polarimetric evidence of the existence of the L4 KDC, and corroborate polarimetrically the existence of the L5 KDC for the third time.

Aquatic insects detect water by the horizontal polarization of water-reflected light and thus are attracted to such light. Recently, in the Hungarian Lake Balaton we observed dark water patches forming between every autumn and spring because of the inflow of black suspended/dissolved organic matter into the bright lake water. Earlier, the polarization characteristics of such water surfaces were mapped by imaging polarimeters from the ground. In order to measure the reflection-polarization patterns of these dark lake patches from the higher viewpoint of flying polarotactic aquatic insects, we designed a drone-based imaging polarimeter. We found that the dark lake patches reflected light with very high (60% ≤ d ≤ 80%) degrees of horizontal polarization at the Brewster’s angle, while the bright lake water was only weakly (d < 20%) horizontally polarizing. There was a large contrast in both the radiance and degree of polarization between dark lake patches and bright lake water, while there was no such contrast in the angle of polarization. The ecological implication of these findings could be that these dark lake patches attract water-seeking polarotactic insects, which may oviposit more frequently in them than in the brighter lake water. However, it might not matter if they lay their eggs in these dark patches rather than the bright lake water, because this may simply increase the abundance of breeding flying insects in areas where dark patches are common.

Since the discovery in 1772 of the triangular Lagrange points L4 and L5 in the gravitational field of two bodies moving under the sole influence of mutual gravitational forces, astronomers found a large number of minor celestial bodies around these points of the Sun-Jupiter, Sun-Earth, Sun-Mars and Sun-Neptune systems. The L4 and L5 points of the Earth and Moon may be empty due to the gravitational perturbation of the Sun. However, in 1961 Kordylewski found two bright patches near the L5 point, which may refer to an accumulation of interplanetary particles. Since that time this formation is called the Kordylewski dust cloud (KDC). Until now only a very few computer simulations studied the formation and characteristics of the KDC. To fill this gap, we investigated a three-dimensional four-body problem consisting of the Sun, Earth, Moon and one test particle, 1860000 times separately. We mapped the size and shape of the conglomeratum of particles not escaped from the system sooner than an integration time of 3650 days around L5. Polarimetric observations of a possible KDC around L5 are presented in the second part of this paper.

Telescopes mounted with polarizers can study the neutral points of the Earths atmosphere, the solar corona, the surface of planets/moons of the Solar System, distant stars, galaxies and nebulae. These examples demonstrate well that polarimetry is a useful technique to gather astronomical information from spatially extended phenomena. There are two enigmatic celestial objects that can also effectively be studied with imaging polarimetry, namely the Kordylewski dust clouds (KDCs) positioned around the L4 and L5 triangular Lagrangian libration points of the Earth-Moon system. Although in 1961 the Polish astronomer, Kazimierz Kordylewski had observed two bright patches near the L5 point with photography, many astronomers assume that these dust clouds do not exist, because the gravitational perturbation of the Sun, solar wind and other planets may disrupt the stabilizing effect of the L4 and L5 Lagrange points of the Earth and Moon. Using ground-born imaging polarimetry, we present here new observational evidence for the existence of the KDC around the L5 point of the Earth-Moon system. Excluding artefacts induced by the telescope, cirrus clouds or condensation trails of airplanes, the only explanation remains the polarized scattering of sunlight on the particles collected around the L5 point. By our polarimetric detection of the KDC we think it is appropriate to reconsider the pioneering photometric observation of Kordylewski. Our polarimetric evidence is supported by the results of simulation of dust cloud formation in the L5 point of the Earth-Moon system presented in the first part of this paper.

The polarization pattern of the sky in various sky conditions is nowadays well known thanks to the spread of full-sky imaging polar meters. The degree of polarization is maximal along a great circle of the sky being 90 degree from the Sun, and minimal at the Sun and anti-Sun [1]. The degree of polarization also depends on the atmospheric conditions. In cloudy [2] and foggy [3] skies, as well as under canopies [4] the degree of polarisation are much smaller compared to clear skies. However the direction of polarization pattern is very robust, the typical 8-shaped pattern as well as the axis of symmetry is well recognizable. When The Sun is well below the horizon and the moonlights the atmosphere, then the axis of symmetry is the celestial great circle containing the Moon [5]. Barta et al. [6] inspected the transition of characteristics of sky polarization between sunlit and moonlit skies during twilight. Verkhovskaya [7] reported the first time that the arthropods (Arthropoda) are able to distinguish between the polarized light and not polarized one. Insects are able to utilize the sky polarization from the Sun and the Moon for their orientation. This question is dealt with by many researchers and mainly experiments with aquatic insects. It has been well known for almost for half a century that the polarized light of the sky plays an important role in the orientation of certain insects. Researchers, however, has been as yet concentrated primarily on insects flying in daytime or at dusk and entomologists have paid less attention to species active at night. Horváth & Varjú [8] discovered that some insects are able to use the polarization pattern of the sky in daytime and at dusk. According to Dragonflies & mayflies [9] and Ephemera danica, are also deceived by dry asphalt surfaces as these reflect strong horizontally polarized light. Bernáth et al. [10] found oil barrels and sparkling black plastic foils luring dragonflies and insects as if they were traps. Robertson et al. [11] found that the solar panels also operate as ecological traps.

There are as many as 18 theories for the possible functions of the stripes of zebras, one of which is to cool the animal. We performed field experiments and thermographic measurements to investigate whether thermoregulation might work for zebra-striped bodies. A zebra body was modelled by water-filled metal barrels covered with horse, cattle and zebra hides and with various black, white, grey and striped patterns. The barrels were installed in the open air for four months while their core temperature was measured continuously. Using thermography, the temperature distributions of the barrel surfaces were compared to those of living zebras. The sunlit zebra-striped barrels reproduced well the surface temperature characteristics of sunlit zebras. We found that there were no significant core temperature differences between the striped and grey barrels, even on many hot days, independent of the air temperature and wind speed. The average core temperature of the barrels increased as follows: white cattle, grey cattle, real zebra, artificial zebra, grey horse, black cattle. Consequently, we demonstrate that zebra-striped coats do not keep the body cooler than grey coats challenging the hypothesis of a thermoregulatory role of zebra stripes.

Since the discovery in 1772 of the triangular Lagrange points L4 and L5 in the gravitational field of two bodies moving under the sole influence of mutual gravitational forces, astronomers have found a large number of minor celestial bodies around these points of the Sun-Jupiter, Sun-Earth, Sun-Mars and Sun-Neptune systems. The L4 and L5 points of the Earth and Moon might be empty due to the gravitational perturbation of the Sun. However, in 1961, the Polish astronomer, Kazimierz the Polish astronomer, Kazimierz Kordylewski found two bright patches near the L5 point, which might refer to an accumulation of interplanetary particles. Since then, this formation has been called the Kordylewski dust cloud (KDC). Until now, only a very few computer simulations have studied the formation and characteristics of the KDC. To fill this gap, we have investigated a three-dimensional four-body problem consisting of the Sun, Earth, Moon and one test particle, 1 860 000 times separately. We mapped the size and shape of the conglomerate of particles that have not escaped from the system sooner than an integration time of 3650 d around L5. Polarimetric observations of a possible KDC around L5 will be presented in a following second part to this paper.

Inspired by the pioneer work of the nineteenth century photographer, William Nicholson Jennings, we studied quantitatively how realistic painted lightnings are. In order to answer this question, we examined 100 paintings and 400 photographs of lightnings. We used our software package to process and evaluate the morphology of lightnings. Three morphological parameters of the main lightning branch were analysed: (i) number of branches N-b, (ii) relative length r, and (iii) number of local maxima (peaks) N-p of the turning angle distribution. We concluded: (i) Painted lightnings differ from real ones in N-b and N-p. (ii) The r-values of painted and real lightnings vary in the same range. (iii) 67 and 22% of the studied painted and real lightnings were non-bifurcating (N-b =1, meaning only the main branch), the maximum of N-b of painted and real lightnings is 11 and 51, respectively, and painted bifurcating lightnings possess mostly 2-4 branches, while real lightnings have mostly 2-10 branches. To understand these findings, we performed two psychophysical experiments with 10 test persons, whose task was to guess Nb on photographs of real lightnings which were flashed for short time periods Delta t = (1.5, 0.75 and 1 s (characteristic to lightnings) on a monitor. We obtained that (i) test persons can estimate the number of lightning branches quite correctly if N-b <= 11. (ii) If N-b > 11, its value is strongly underestimated with exponentially increasing difference between the real and estimated numbers. (iii) The estimation is independent of the flashing period Delta t of lightning photos/pictures. (iv) The estimation is more accurate, if skeletonized lightning pictures are flashed, rather than real lightning photos. These findings explain why artists usually illustrate lightnings with branches not larger than 11.

When the sun is near the horizon, a circular band with approximately vertically polarized skylight is formed at 90° from the sun, and this skylight is only weakly reflected from the region of the water surface around the Brewster's angle (53° from the nadir). Thus, at low solar heights under a clear sky, an extended dark patch is visible on the water surface when one looks toward the north or south quarter perpendicular to the solar vertical. In this work, we study the radiance distribution of this so-called Brewster's dark patch (BDP) in still water as functions of the solar height and sky conditions. We calculate the pattern of reflectivity R of a water surface for a clear sky and obtain from this idealized situation the shape of the BDP. From three full-sky polarimetric pictures taken about a clear, a partly cloudy, and an overcast sky, we determine the R pattern and compose from that synthetic color pictures showing how the radiance distribution of skylight reflected at the water surface and the BDPs would look under these sky conditions. We also present photographs taken without a linearly polarizing filter about the BDP. Finally, we show a 19th century painting on which a river is seen with a dark region of the water surface, which can be interpreted as an artistic illustration of the BDP.

Horseflies (Tabanidae) are polarotactic, being attracted to linearly polarized light when searching for water or host animals. Although it is well known that horseflies prefer sunlit dark and strongly polarizing hosts, the reason for this preference is unknown. According to our hypothesis, horseflies use their polarization sensitivity to look for targets with higher degrees of polarization in their optical environment, which as a result facilitates detection of sunlit dark host animals. In this work, we tested this hypothesis. Using imaging polarimetry, we measured the reflection–polarization patterns of a dark host model and a living black cow under various illumination conditions and with different vegetation backgrounds. We focused on the intensity and degree of polarization of light originating from dark patches of vegetation and the dark model/cow. We compared the chances of successful host selection based on either intensity or degree of polarization of the target and the combination of these two parameters. We show that the use of polarization information considerably increases the effectiveness of visual detection of dark host animals even in front of sunny–shady–patchy vegetation. Differentiation between a weakly polarizing, shady (dark) vegetation region and a sunlit, highly polarizing dark host animal increases the efficiency of host search by horseflies.

According to Thorkild Ramskou's theory proposed in 1967, under overcast and foggy skies, Viking seafarers might have used skylight polarization analysed with special crystals called sunstones to determine the position of the invisible Sun. After finding the occluded Sun with sunstones, its elevation angle had to be measured and its shadow had to be projected onto the horizontal surface of a sun compass. According to Ramskou's theory, these sunstones might have been birefringent calcite or dichroic cordierite or tourmaline crystals working as polarizers. It has frequently been claimed that this method might have been suitable for navigation even in cloudy weather. This hypothesis has been accepted and frequently cited for decades without any experimental support. In this work, we determined the accuracy of this hypothetical sky-polarimetric Viking navigation for 1080 different sky situations characterized by solar elevation θ and cloudiness ρ, the sky polarization patterns of which were measured by full-sky imaging polarimetry. We used the earlier measured uncertainty functions of the navigation steps 1, 2 and 3 for calcite, cordierite and tourmaline sunstone crystals, respectively, and the newly measured uncertainty function of step 4 presented here. As a result, we revealed the meteorological conditions under which Vikings could have used this hypothetical navigation method. We determined the solar elevations at which the navigation uncertainties are minimal at summer solstice and spring equinox for all three sunstone types. On average, calcite sunstone ensures a more accurate sky-polarimetric navigation than tourmaline and cordierite. However, in some special cases (generally at 35° ≤ θ ≤ 40°, 1 okta ≤ ρ ≤ 6 oktas for summer solstice, and at 20° ≤ θ ≤ 25°, 0 okta ≤ ρ ≤ 4 oktas for spring equinox), the use of tourmaline and cordierite results in smaller navigation uncertainties than that of calcite. Generally, under clear or less cloudy skies, the sky-polarimetric navigation is more accurate, but at low solar elevations its accuracy remains relatively large even at high cloudiness. For a given ρ, the absolute value of averaged peak North uncertainties dramatically decreases with increasing θ until the sign (±) change of these uncertainties. For a given θ, this absolute value can either decrease or increase with increasing ρ. The most advantageous sky situations for this navigation method are at summer solstice when the solar elevation and cloudiness are 35° ≤ θ ≤ 40° and 2 oktas ≤ ρ ≤ 3 oktas.

The study investigated the efficiency of the light-trap catch of Turnip Moth (Agrotis segetum Den. et Schiff.) in connection with the polarization of the night sky. The hourly catch data of drawing during three years were assigned to the data of the 41 environmental variables. First we made cluster analysis with the data pairs. Based on this, further calculations were made between the most important influencing factors and the catch data. The results were depicted together with the confidence intervals. We can conclude that the catch at night is determined mainly by the Humidity, Sun-Sky-Pol, Moon-Sky-Pol, Moon-Pol and Clock variables, slightly influenced by Wind and H-index variables. The high relative humidity of the air has a decisive influence on the catch, because the insect can see only the distorted sky polarization pattern, and according to our assumption its orientation is hampered. The Sun stays in the first and last collection hours above the horizon at most. At this time the Sun’s sky polarization is higher than the Moon’s one. The catch is also influenced mainly in these hours. In the majority of the night, the sky polarization originated from the Moon is much higher. In these hours the Moon's modifying effect is decisive. The Moon modifies the catch when he does not stay above the horizon. The azimuth angle of the moon is also a determining factor for the effectiveness of the catch. The Moon phase angle is high when azimuth is smaller than 91.7. Meanwhile, the polarization of the sky and the polarized moonlight are high. This situation increases the effectiveness of the catch. The effect of polarized moonlight on the catch is less significant than the sky polarization.

If a human looks at the clear blue sky from which light with high enough degree of polarization d originates, an 8-shaped bowtie-like figure, the yellow Haidinger's brush can be perceived, the long axis of which points towards the sun. A band of high d arcs across the sky at 90° from the sun. A person can pick two points on that band, observe the yellow brushes and triangulate the position of the sun based on the orientation of the two observed brushes. This method has been suggested to have been used on the open sea by Viking navigators to determine the position of the invisible sun occluded by cloud or fog. Furthermore, Haidinger's brushes can also be used to locate the sun when it is below the horizon or occluded by objects on the horizon. To determine the position of the sun using the celestial polarization pattern, the d of the portion of the sky used must be greater than the viewer's degree of polarization threshold d * for perception of Haidinger's brushes. We studied under which sky conditions the prerequisite d > d * is satisfied. Using full-sky imaging polarimetry, we measured the d -pattern of skylight in the blue (450 nm) spectral range for 1296 different meteorological conditions with different solar elevation angles θ and per cent cloud cover ρ . From the measured d -patterns of a given sky we determined the proportion P of the sky for which d > d *. We obtained that P is the largest at low solar elevations θ ≈ 0° and under totally or nearly clear skies with cloud coverage ρ = 0%, when the sun's position is already easily determined. If the sun is below the horizon (−5° ≤ θ < 0°) during twilight, P = 76.17 ± 4.18% for d min ∗ = 23 % under clear sky conditions. Consequently, the sky-polarimetric Viking navigation based on Haidinger's brushes is most useful after sunset and prior to sunrise, when the sun is not visible and large sky regions are bright, clear and polarized enough for perception of Haidinger's brushes.

According to an old but still unproven theory, Viking navigators analysed the skylight polarization with dichroic cordierite or tourmaline, or birefringent calcite sunstones in cloudy/foggy weather. Combining these sunstones with their sun-dial, they could determine the position of the occluded sun, from which the geographical northern direction could be guessed. In psychophysical laboratory experiments, we studied the accuracy of the first step of this sky-polarimetric Viking navigation. We measured the adjustment error e of rotatable cordierite, tourmaline and calcite crystals when the task was to determine the direction of polarization of white light as a function of the degree of linear polarization p. From the obtained error functions e(p), the thresholds p* above which the first step can still function (i.e. when the intensity change seen through the rotating analyser can be sensed) were derived. Cordierite is about twice as reliable as tourmaline. Calcite sunstones have smaller adjustment errors if the navigator looks for that orientation of the crystal where the intensity difference between the two spots seen in the crystal is maximal, rather than minimal. For higher p (greater than pcrit) of incident light, the adjustment errors of calcite are larger than those of the dichroic cordierite (pcrit=20%) and tourmaline (pcrit=45%), while for lower p (less than pcrit) calcite usually has lower adjustment errors than dichroic sunstones. We showed that real calcite crystals are not as ideal sunstones as it was believed earlier, because they usually contain scratches, impurities and crystal defects which increase considerably their adjustment errors. Thus, cordierite and tourmaline can also be at least as good sunstones as calcite. Using the psychophysical e(p) functions and the patterns of the degree of skylight polarization measured by full-sky imaging polarimetry, we computed how accurately the northern direction can be determined with the use of the Viking sun-dial under 10 different sky conditions at 61° latitude, which was one of the main Viking sailing routes. According to our expermiments, under clear skies, using calcite or cordierite or tourmaline sunstones, Viking sailors could navigate with net orientation errors |Σmax|≤3∘. Under overcast conditions, their net navigation error depends on the sunstone type: |Σmax(calcite)|≤6∘, |Σmax(cordierite)|≤10∘ and |Σmax(tourmaline)|≤17∘.

The theory of sky-polarimetric Viking navigation has been widely accepted for decades without any information about the accuracy of this method. Previously, we have measured the accuracy of the first and second steps of this navigation method in psychophysical laboratory and planetarium experiments. Now, we have tested the accuracy of the third step in a planetarium experiment, assuming that the first and second steps are errorless. Using the fists of their outstretched arms, 10 test persons had to estimate the elevation angles (measured in numbers of fists and fingers) of black dots (representing the position of the occluded Sun) projected onto the planetarium dome. The test persons performed 2400 elevation estimations, 48% of which were more accurate than ±1°. We selected three test persons with the (i) largest and (ii) smallest elevation errors and (iii) highest standard deviation of the elevation error. From the errors of these three persons, we calculated their error function, from which the North errors (the angles with which they deviated from the geographical North) were determined for summer solstice and spring equinox, two specific dates of the Viking sailing period. The range of possible North errors Δ ω N was the lowest and highest at low and high solar elevations, respectively. At high elevations, the maximal Δ ω N was 35.6° and 73.7° at summer solstice and 23.8° and 43.9° at spring equinox for the best and worst test person (navigator), respectively. Thus, the best navigator was twice as good as the worst one. At solstice and equinox, high elevations occur the most frequently during the day, thus high North errors could occur more frequently than expected before. According to our findings, the ideal periods for sky-polarimetric Viking navigation are immediately after sunrise and before sunset, because the North errors are the lowest at low solar elevations.