parhelic circle

{{Short description|Type of halo, an optical phenomenon}}

Image:Halo and sun dog - NOAA.jpg.
Photo: John Bortniak, NOAA, January 1979.]]

Image:HALO-S south pole.jpg (circle) with two sundogs (bright spots), a Parry arc, and an upper tangent arc.
Photo: Cindy McFee, NOAA, December 1980.{{cite web|url=http://www.photolib.noaa.gov/historic/nws/wea00195.htm |title=A magnificent halo |publisher=NOAA |date=1980-12-21 |accessdate=2007-04-14 |archiveurl=https://web.archive.org/web/20061213123117/http://www.photolib.noaa.gov/historic/nws/wea00195.htm |archivedate=2006-12-13 |url-status=dead }}]]

Image:Sun_halo_and_parhelic_circle.jpg, Slovenia, on May 19th, 2023. ]]

Image:A nearly complete parhelic circle.jpg and the eastern moon dog. Photo is taken by the all-sky camera of the Piszkéstető Mountain Station, Konkoly Observatory (Hungary), February 2023.]]

A parhelic circle is a type of halo, an optical phenomenon appearing as a horizontal white line on the same altitude as the Sun, or occasionally the Moon. If complete, it stretches all around the sky, but more commonly it only appears in sections.{{cite web

| url = http://www.atoptics.co.uk/halo/parcirc.htm

| title = Parhelic Circle | publisher = Atmospheric Optics

| accessdate = 2007-04-15 | author = Koby Harati

}} If the halo occurs due to light from the Moon rather than the Sun, it is known as a paraselenic circle.{{cite web

| url = https://www.atoptics.co.uk/fza40.htm

| title = Paraselenae & Paraselenic circle | publisher = Atmospheric Optics

| accessdate = 2021-10-07 | author = Les Cowley

}}

Even fractions of parhelic circles are less common than sun dogs and 22° halos. While parhelic circles are generally white in colour because they are produced by reflection, they can however show a bluish or greenish tone near the 120° parhelia and be reddish or deep violet along the fringes.{{cite web

| url = http://www.paraselene.de?uk:113554

| title = Parhelic Circle | publisher = www.paraselene.de

| accessdate = 2009-02-01 | author =

}} (including an excellent HaloSim simulation of a parhelic circle.)

Parhelic circles form as beams of sunlight are reflected by vertical or almost vertical hexagonal ice crystals. The reflection can be either external (e.g. without the light passing through the crystal) which contributes to the parhelic circle near the Sun, or internal (one or more reflections inside the crystal) which creates much of the circle away from the Sun. Because an increasing number of reflections makes refraction asymmetric some colour separation occurs away from the Sun.{{cite web

| url = http://www.atoptics.co.uk/halo/pcpaths.htm

| title = Parhelic Circle Formation | publisher = Atmospheric Optics

| accessdate = 2007-04-15 | author = Les Cowley

}} Sun dogs are always aligned to the parhelic circle (but not always to the 22° halo).{{Citation needed|date=August 2010}}

The intensity distribution of the parhelic circle is largely dominated by 1-3-2 and 1-3-8-2 rays (cf. the nomenclature by W. Tape, i.e. 1 denotes the top hexagonal face, 2 the bottom face, and 3-8 enumerate the side faces in counter-clockwise fashion. A ray is notated by the sequence in which it encounters the prism faces). The former ray-path is responsible for the blue spot halo which occurs at an azimuth.{{cite journal

| last1 = Sillanpää | first1 = M.

| last2 = Moilanen | first2 = J.

| last3 = Riikonen | first3 = M.

| last4 = Pekkola | first4 = M.

| title = Blue spot on the parhelic circle

| journal = Applied Optics

| volume = 40

| pages = 5275–5279

| date = 2001 | issue = 30

| doi=10.1364/ao.40.005275

| pmid = 18364808

|bibcode = 2001ApOpt..40.5275S }}

$\backslash theta\_\{\backslash mathfrak\{1\}\backslash mathfrak\{3\}\backslash mathfrak\{2\}\}=2\backslash arcsin\backslash left(n\backslash cos\backslash left(\backslash arcsin\backslash left(1/n\backslash right)\backslash right)/\backslash cos\backslash left(e\backslash right)\backslash right)$,

with $n$ being the material's index of refraction (not the Bravais index of refraction for inclined rays). However, many more features give a structure to the intensity pattern of the parhelic circle.{{cite journal

| last1 = Selmke | first1 = M.

| title = Artificial Halos

| journal = American Journal of Physics

| volume = 83

| issue = 9

| pages = 751–760

| url = http://scitation.aip.org/content/aapt/journal/ajp/83/9/10.1119/1.4923458

| doi = 10.1119/1.4923458

| date = 2015

|bibcode = 2015AmJPh..83..751S | url-access = subscription

}}{{cite journal

| last1 = Borchardt | first1 = S.

| last2 = Selmke | first2 = M.

| title = Intensity distribution of the parhelic circle and embedded parhelia at zero solar elevation: theory and experiments

| journal = Applied Optics

| volume = 54

| issue = 22

| pages = 6608–6615

| url = https://www.osapublishing.org/ao/abstract.cfm?uri=ao-54-22-6608

| doi = 10.1364/AO.54.006608

| date = 2015

| pmid = 26368071

|bibcode = 2015ApOpt..54.6608B | s2cid = 39382489

| url-access = subscription

}} Among the features of the parhelic circle are the Liljequist parhelia, the 90° parhelia (likely unobservable), the second order 90° parhelia (unobservable), the 22° parhelia and more.

Artificial parhelic circles can be realized by experimental means using, for instance, spinning crystals.