Sideline

Double-sided suns in Orange (France), August 22, 2013

Two side suns and an upper contact arch in Tofino

Auxiliary suns or Parhelia (singular Parhelion , from Greek παρά pará , German 'besides' and ήλιος hélios - 'sun') belong to the halo phenomena . They can be seen as light spots at a distance of about 22 ° on the left or right, sometimes on both sides, next to the sun . The observer has the impression that there is a second, weaker one next to the sun. In English they are referred to as sun dogs accompanying the sun or as mock suns ( mock for imitation, forgery).

Parasols are one of the most common halos. They are visible in the European sky about 60 to 80 days a year.

A similar light phenomenon can also be observed on the moon . However, due to the lower light intensity, one sees the side moon less often.

Although sub-suns often have colorations reminiscent of rainbows , they should not be confused with them. Sub-suns appear near the sun, rainbows appear on the opposite side of the sky from the sun. The causes of the optical phenomena are water droplets in the case of rainbows and ice crystals in the case of the sundecks.

Emergence

Ice crystals

Platelet-shaped ice crystal

Parasols are caused by the refraction of light in ice crystals. Even in summer, temperatures in high layers of the atmosphere are well below freezing point, so that clouds “droplets” can exist there in frozen form as ice crystals. As particularly high clouds, cirrus clouds always consist exclusively of ice crystals.

Atmospheric ice crystals can form in a multitude of different shapes depending on the temperature and humidity : hexagonal plates, columns, hollow columns, pyramids, dendrites ("snow stars"), etc. Hexagonal ( "hexagonal" ) ice crystal plates are responsible for the sun .

Low standing sun

Beam path in a hexagonal prism

First consider a light beam running in the plane of the platelet, which enters a platelet at an angle through one of the side surfaces and exits again through the next but one side surface. It is broken when passing through both side surfaces. The angles of refraction on the two mutually inclined sides (these include, if extended, the angle ε = 60 °) can be calculated in the same way as when passing through two sides of a prism . Depending on the entrance angle, the total deflection angle of the light beam measured with respect to the original beam direction assumes different values. The smallest possible value is assumed if the entry and exit angles are and are the same ${\ displaystyle \ delta}$ ${\ displaystyle \ delta _ {\ text {min}}}$

{\ displaystyle \ delta _ {\ text {min}} = 2 \ left (\ arcsin \ left (n \ cdot \ sin \ left ({\ frac {\ varepsilon} {2}} \ right) \ right) - { \ frac {\ varepsilon} {2}} \ right) \ approx 22 ^ {\ circ}}

With

${\ displaystyle n \ approx 1 {,} 31}$ , mean refractive index of ice,
${\ displaystyle \ varepsilon = 60 ^ {\ circ}}$ ,	Prism angle at the refracting edge (to be supplemented here).

For larger as well as smaller entry angles, the deflection angle is always larger than this minimum . Since the platelets are randomly oriented, the platelets of a cloud have different entry and thus different deflection angles. However, all deflection angles are greater than or equal to 22 °, and since the deflection angles in the vicinity of their minimum depend only slightly on the entrance angle, a particularly large amount of light is deflected in a direction of around 22 ° - even if all entrance angles occur equally frequently. ${\ displaystyle \ delta _ {\ text {min}}}$

A beam of light that would originally have missed the observer's eye can still arrive there after being deflected in the crystal. Those platelets that can direct the light into the observer's eye by deflecting it through the angle are precisely those that, as seen by the observer, are at the angular distance from the sun. Coming from this direction, the deflected light rays hit the eye and are perceived as brightening in the sky. ${\ displaystyle \ delta}$ ${\ displaystyle \ delta}$

Two-sided suns as lightening of a 22 ° ring.

If the platelet planes in the cloud are randomly oriented (the observation is still limited to platelets whose planes are parallel to the incidence of light), the deflection is just as likely to be to the left as to the right, up or down. An observer thus sees light arriving at him from all points at a distance around the sun. The result is a glowing ring surrounding the sun at a distance . Since most of the deflected light is visible at a distance = 22 ° from the sun, a 22 ° ring is created . This ring is relatively sharply delimited on the inner edge, as there are no rays with a deflection below 22 °. The ring only gradually decreases in brightness towards the outside. This area consists of the increasingly less frequent rays of light that have been deflected at larger angles. ${\ displaystyle \ delta}$ ${\ displaystyle \ delta}$ ${\ displaystyle \ delta}$ ${\ displaystyle \ delta _ {\ text {min}}}$

Right side sun without ring, with a clearly recognizable "tail" on the side facing away from the sun.

In a turbulence-free atmosphere, the platelets are preferably aligned in a horizontal position. If horizontally oriented platelets occur in addition to randomly oriented platelets, the light is preferably deflected horizontally to the left and right and two points of the 22 ° ring on the left and right at the level of the sun appear particularly bright. These are adjacent suns, those in this Case there are only lighter areas of the 22 ° ring.

If there are only horizontally lying platelets, no ring is created and only the isolated suns appear. For the same reasons as in the case of the ring, the sunsides have a relatively sharp edge on the sun side, while they often end in a tail on the side away from the sun.

High sun

If the sun is higher, the suns are not on the 22 ° ring (if available), but outside. The 22 ° ring also has an upper contact arc in this picture .

So far, only the situation has been considered in which the light rays enter the side surface parallel to the plane of the platelets, which is only possible for horizontally oriented platelets when the sun is low. If the sun is higher - but not higher than about 60 ° - the light beam can still emerge on the next but one side surface of a horizontal plate, but this results in slightly different angular relationships. (The beam, which is no longer parallel to the two top surfaces, can be reflected on the inside of one of these surfaces, but this does not change the refraction conditions.) Depending on the height of the sun, the minimum deflection angle and thus the observed angular distance of the light spot from the sun increases. The side sun is also getting wider and weaker.

At the same time as the sub-suns, a ring can also appear here, but this is not caused by the horizontal platelets. It comes from those platelets that are inclined in such a way that the downward sloping rays of the sun are straight parallel to the plane of the platelets. The conditions described in the previous section are thus again present here and the ring still has a radius of 22 °. The suns that are now generated by other platelets than the ring are in this case not on the ring, but a bit outside. At a sun height of 10 ° they are about half a degree outside, at 30 ° sun height three degrees and at 50 ° sun height almost eleven degrees.

Colours

Appearance

Red rays of light are refracted in an ice crystal by a smaller angle of deflection than blue rays, which is why the side of a sub-sun near the sun appears red.

Right side sun in rainbow-like colors. Red is on the inside of the 22 ° ring and the side sun.

Sub-suns can have colors that are reminiscent of a rainbow. However, there are fewer and mostly paler colors than with the rainbow.

The edge of a secondary sun on the sunny side is colored reddish, followed by yellow. In contrast to the rainbow, however, there are no pronounced green and blue tones. The secondary sun usually ends in a whitish, at best slightly bluish-colored tail.

root cause

The colors are caused by the fact that the refractive index of the ice is dependent on the wavelength and thus the color (" dispersion "). The refractive index varies from n = 1.307 at a wavelength of 650 nm (red) to n = 1.317 at 400 nm (blue). The minimum deflection angle and thus the distance from the sun in the area of greatest brightness is about 0.8 ° larger for blue light than for red light. ${\ displaystyle \ delta _ {\ text {min}}}$

The sub-sun formed from the red part of the sunlight therefore appears to the observer at the closest distance from the sun. The secondary suns formed from the other colors join one after the other on the side facing away from the sun. However, since each of the colored sub-suns has a more or less pronounced tail running in the direction away from the sun, each additional color of the sum of the tails of the sub-suns closer to the sun is superimposed. The red sub-sun as the innermost one remains non-superimposed, the yellow sub-sun superimposes on the tail of the red, the green superimposes on the red and yellow tails, and so on. The blue sub-sun finally superimposes the sum of the tails of all the other colors, so that the sum of all colors there is white and only a slightly bluish tint remains.

Comparison with the rainbow

Right leg of a rainbow for comparison. Red is on the outside of the bow.

The color splitting occurs in the same way as that on the rainbow . Even with rainbows there is - although there are water drops instead of ice crystals and a different beam path - a minimum deflection angle that varies depending on the color, around which a particularly large amount of light of the respective color is deflected. Even with the rainbow, individual arcs of the respective colors are staggered next to each other and overlap to form a multicolored band. Because of the different beam path, the tails of the individual colors are less pronounced, so that the more compact rainbows overlap less and the colors appear clearer and more demarcated than with the sub-suns.

Since the minimum deflection angle for the rainbow is around 138 ° (instead of 22 ° as with the sundeck), the rainbow forms a circle with a radius of 42 ° around the sun's counterpoint , so that the sun is outside the rainbow ring and the side of the rainbow close to the sun is its Outside is. In the case of the rainbow, the 22 ° ring and the sub-suns, the red color is on the side close to the sun, but with the rainbow this is the outside of the ring, with the 22 ° ring and the sub-suns it is the inside of the ring. ${\ displaystyle \ delta _ {\ text {min}}}$

polarization

Degree of polarization

Sunlight is originally unpolarized, but can be polarized to a greater or lesser extent by refraction or reflection . 22 ° rings and sub-suns are created by refraction and are therefore radially polarized. However, the degree of polarization generated by refraction decreases with the angle of refraction and is only around 4% for 22 ° rings and sub-suns with their small deflection angle of 22 °, so - in contrast to other types of halo - it is not directly observable. If the sun is higher than 45 °, the degree of polarization increases due to the larger angle of refraction, but does not exceed 20%.

Birefringence

Another effect related to polarization can easily be observed. Ice is birefringent , so it has slightly different refractive indices for light with different polarization directions. The sun's rays are therefore split up not only according to their color, but also according to their polarization direction when they pass through an ice sheet. The radially polarized part of the sunlight is less strongly deflected in the ice crystal than the tangentially polarized part. The sub-sun consisting of radially polarized light therefore appears 0.11 ° closer to the sun than that consisting of tangentially polarized light. The angle difference is small (it corresponds to only about a quarter of the moon's diameter), but can easily be determined by turning a polarization filter if, for example, there are prominent cloud structures as a reference point nearby.

120 ° suns

Parasols

120 ° sub-sun with part of the horizontal circle. Both are created by the reflection of the sun's rays on vertical surfaces of ice crystals.

Much less often than the 22 ° suns - namely only on one or two days a year - there are suns that are also at the height of the sun, but at a distance of 120 ° from it ("paranthelia"). They appear to the observer as whitish, colorless spots. Here, too, ice crystal flakes are the cause, but the deflection of the light beam is effected by reflection instead of refraction. The reflection takes place on the vertical side surfaces of horizontally lying ice platelets. A light beam entering through the top surface of a plate is reflected twice internally on side surfaces and thus deflected by 120 °. He leaves the tile through the floor area at the same angle corresponding to the height of the sun with which he entered the tile. If it hits the observer's eye, the observer perceives a spot of light at the same height as the sun, but because the light is deflected in a different direction. Since the reflection does not depend on the wavelength, no color splitting takes place.

Horizontal circle

If there is only a single reflection on a perpendicular crystal surface, the deflection angle is dependent on the random alignment of the perpendicular surface with respect to the light rays, while the angle of inclination of the light rays is again retained during the reflection. The result is a colorless ring that is parallel to the horizon at sun height, a horizontal circle . The ice crystal platelets, the sides of which produce a 120 ° sub-sun after double reflection, also provide vertical sides for simple reflection, so that 120 ° sub-suns can often be observed together with a horizontal circle. Horizontal circles can, however, also arise from single reflections on vertical surfaces of other crystal forms, where double reflections are not possible as with the platelets. The horizontal circle then appears without the sundeck.

observation

Often suns only appear as inconspicuous bright spots. On the left of the picture is the sun, on the right a weak sundeck.

Secondary suns require ice crystal platelets in the atmosphere. Cirrus always consist of ice crystals, even if not necessarily of platelets. If there are cirrus peaks at a distance of 22 ° to the left or right of the sun, the occurrence of secondary suns is to be expected if these cirrus peaks contain platelets.

In addition to the typical feather ( Cirrus fibratus ) and sheep clouds ( Cirrocumulus ), cirrus clouds can also appear as a transparent, diffuse and poorly structured cloud cover ( Cirrostratus ). The presence of ice clouds is then not always obvious, but side suns are possible. Contrails can also contain ice crystal platelets and cause sunshine. The ice crystals can also be located in the vicinity of the observer - for example, ice crystals can float in the air as " flickering snow " or " polar snow " at sufficiently low temperatures .

In many cases, the suns appear only as a slightly noticeable brightening or as a slight, mostly reddish discoloration. They will then only be noticed by observers who are on the lookout for them. For most observers, the angular distance between the tips of the thumb and little finger of the spread hand on the outstretched arm is about 20 degrees , so that possible locations of the suns can easily be determined.

gallery

Two sided suns in the Arctic
Double sided sunsets in Fargo , North Dakota
Unusually bright left side sun
Side suns near Echzell , Hesse
Side suns on the Hoherodskopf , Hesse
Siphoning sun over the Winnipeg Rowing Club in Winnipeg , Manitoba , Canada

Artistic symbol

The image of the side sun was often used as an artistic symbol in the literature of Goethe's time; Best known was that of Franz Schubert penultimate song cycle Winterreise , Op. 89, set to music poems by Wilhelm Müller The Sundogs ( "Three suns I saw steh'n the sky ...").

Vädersolstavlan (side sun painting )

literature

M. Vollmer: Play of light in the air - atmospheric optics for beginners. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2
The suns . In: Illustrirte Zeitung . No. 19 . J. J. Weber, Leipzig November 4, 1843, p. 298-299 ( books.google.de ).

Web links

Commons : Nebensonne - album with pictures, videos and audio files

Wiktionary: Nebensonne - explanations of meanings, word origins, synonyms, translations

Video from Russia with 22 ° and 120 ° suns

SDO Destroys a Sundog Science @ NASA February 18, 2010, on YouTube (The originally horizontally aligned ice flakes are swirled around by the sound waves, the sundeck dissolves.)

Parasols and how they arise. Article explaining how it came about using Snell's law of refraction and total reflection .

Remarks

↑ The hexagon can be thought of as being supplemented to form an equilateral triangular prism by piecing equilateral triangles on three of the hexagon sides. The two hexagonal sides that refract the light beam under consideration belong to the sides that remain free.
↑ Also differently inclined platelets produce rings, but because the incidence of light is not in the plane of the platelets, larger rings result, as described in the previous paragraph, which lie in the lightened area of the 22 ° ring, overlap each other there and do not appear separately .
↑ The diagram shows the beam path for a left sub-sun, in this case it is the right edge of the sub-sun, which is closer to the sun and is therefore colored red. In the diagram, the blue ray is to the right of the red ray; an observer, in whose eye the red ray of this crystal falls, does not see this blue ray (which passes the eye), but the blue ray from another crystal lying further to the left.
↑ ^a ^b Radially polarized means: For the observer, the direction of polarization is parallel to the connecting line between the observed ice crystal and the sun. Tangential means: The direction of polarization is perpendicular to this connecting line.
↑ In this case all rays are deflected by the same angle. Unlike the 22 ° sub-sun, it is not a continuum of deflection angles with the luminous maximum at the minimum deflection angle.

Individual evidence

↑ Parasols (EE02 / 03) . meteoros.de; Retrieved February 25, 2016
↑ M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 153
↑ M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 169
↑ M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 157
↑ ^a ^b ^c ^d ^e M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 162
↑ M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 164
↑ H. Häckel: color atlas weather phenomena. Ulmer, Stuttgart 1999, ISBN 3-8001-3511-6 , p. 88
↑ ^a ^b M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 160
↑ GP Skills: Polarized light in Nature. Cambridge University Press, Cambridge 1985, ISBN 0-521-25862-6 , p. 62
↑ ^a ^b GP skills: Polarized light in Nature. Cambridge University Press, Cambridge 1985, ISBN 0-521-25862-6 , p. 63
↑ GP Skills: Polarized light in Nature. Cambridge University Press, Cambridge 1985, ISBN 0-521-25862-6 , p. 64
↑ 120 ° suns (EE18 / 19) . meteoros.de; accessed on March 1, 2016
↑ ^a ^b M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , pp. 175f

[Prisma-3] The hexagon can be thought of as being supplemented to form an equilateral triangular prism by piecing equilateral triangles on three of the hexagon sides. The two hexagonal sides that refract the light beam under consideration belong to the sides that remain free.

[Ring-8] Also differently inclined platelets produce rings, but because the incidence of light is not in the plane of the platelets, larger rings result, as described in the previous paragraph, which lie in the lightened area of the 22 ° ring, overlap each other there and do not appear separately .

[rot-10] The diagram shows the beam path for a left sub-sun, in this case it is the right edge of the sub-sun, which is closer to the sun and is therefore colored red. In the diagram, the blue ray is to the right of the red ray; an observer, in whose eye the red ray of this crystal falls, does not see this blue ray (which passes the eye), but the blue ray from another crystal lying further to the left.

[radial-12] Radially polarized means: For the observer, the direction of polarization is parallel to the connecting line between the observed ice crystal and the sun. Tangential means: The direction of polarization is perpendicular to this connecting line.

[120Grad-18] In this case all rays are deflected by the same angle. Unlike the 22 ° sub-sun, it is not a continuum of deflection angles with the luminous maximum at the minimum deflection angle.

[Meteoros_01-1] Parasols (EE02 / 03) . meteoros.de; Retrieved February 25, 2016

[Vollmer_153-2] M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 153

[Vollmer_169-4] M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 169

[Vollmer_157-5] M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 157

[Vollmer_162-6] M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 162

[Vollmer_164-7] M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 164

[Häckel_88-9] H. Häckel: color atlas weather phenomena. Ulmer, Stuttgart 1999, ISBN 3-8001-3511-6 , p. 88

[Vollmer_160-11] M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , p. 160

[Können_62-13] GP Skills: Polarized light in Nature. Cambridge University Press, Cambridge 1985, ISBN 0-521-25862-6 , p. 62

[Können_63-14] GP skills: Polarized light in Nature. Cambridge University Press, Cambridge 1985, ISBN 0-521-25862-6 , p. 63

[Können_64-15] GP Skills: Polarized light in Nature. Cambridge University Press, Cambridge 1985, ISBN 0-521-25862-6 , p. 64

[Meteoros_02-16] 120 ° suns (EE18 / 19) . meteoros.de; accessed on March 1, 2016

[Vollmer_175f-17] M. Vollmer: plays of light in the air. Elsevier, Munich 2013, ISBN 978-3-8274-3092-2 , pp. 175f