HALO MINOR AND PARHELIA ===================== John Pazmino NYSkies Astronomy Inc www.nyskies.org email@example.com 2001 August 1
Introduction ---------- At the Observing Group meeting of 1997 September 12 I presented a tuitional talk on solar halos with handouts. With the major solar halo displays of April of 2000 there was a new upsurge in interest. SInce then several other displays attracted wide attention among New York astronomers. While halos and associated phaenomena are not strictly astronomy in nature, home based astronomers find them fascinating.
Atmospheric ice crystals ---------------------- Halo apparitions are caused by sunlight being reflected and refracted by crystals of ice floating in the stratosphere some 10 to 15 kilometers up. The basic shape of the crystals is a regular hexagon of greater or lesser thickness. If this thickness is more than the diameter across the hexagon itself, we call the shape a prism. Lesser thickness makes the shape a plate or tablet. Overall the crystals are a millimeterish in size. With the many faces and angles on the crystal there are an amazingly large number of lightpaths thru them and, therefore, an equally amazingly large number of optical effects they cause. The diversity comes also from the orientation and wobbling of the crystals as they float in the upper air.
Restricted case of crystals ------------------------- Here we look only at crystals which are randomly faced so sunlight can enter them from any angle and at those which are hovering upright. That is, with their hexagon faces horizontal. It turns out that the different lightpaths thru the crystal produce luminous effects of quite a range of prominence. While there are many theoreticly possible effects, some are as yet unrecorded because they may have been overlooked for their dimness. The refractions causing the halo minor and parhelia produce really vivid displays and are about the most common of all.
What halos look like ------------------ In appearance on the sky the halo minor is a ring of colored light centered on the Sun having a radius of (rounded) 22 degrees. It looks gigantic when seen for the first time! This is indeed the halo 'minor' because there is a related other halo effect of 46 degree radius, called the halo major. Usually the halo is broken or corrupted, with only certain parts visible and others missing. When the entire ring is out in a clear cloudless sky the sight is truly awesome. The parhelia, also called sundogs and mock suns, are colored luminous spots just outside of the halo minor on the left and right of the Sun. Usually one or the other is the more showy. Sometimes only one of the pair, a parhelion, is out. By tradition, not thoroly adhaered to, halo phaenomena are named in Latin. Parhelion is a neuter noun. The left and right ones are, therefore, sinistrum and dextrum. Altho the cause of the halo minor and parhelia is similar, it can easily happen that the halo and sundogs are seen independently of each other. Hence, even with just these two types of solar optical effect, there is a nice variety of apparition.
Refraction and reflection ----------------------- When sunlight passes thru a prism it is refracted out of its approach path. It is also dispersed into a spectrum, being that sunlight contains many wavelengths. In general, an atmospheric effect in the sky can be quickly typed as refractive if it is spectrally tinted. If it is of a single hue, nominally white but possibly biased by intervening dust, haze, cloud, it is due entirely to reflection. Recall that reflection has no spectral dispersion. Hence, while a spectrally tinted apparition must include refraction, there may be accompanying reflection which causes no additional coloration. In the situation at hand, sunlight passes thru one of the flanks of the prism or tablet and exits thru the second flank beyond. Numbering the flanks 1 thru 6 around the crystal, the light enters thru #1 and leaves thru #3 or #5. Face #2, #4, and #6 are missed.
Optics of halos ------------- With the prism or tablet being an equiangular equilateral hexagon the adjacent faces meet at 120 degrees (interior angle). With the skipped face in between, the angle 'seen' by the sunlight is only 60 degrees, as if the figure were an equilateral triangle. As it turns out, the amount of original light that actually gets thru the prism varies with the angle of approach such that there is in fact a minimum deviation of the beam that yields the maximum thruput of light. Deviations of greater degree suffer increasingly more light loss. For ice this angle is 21.839 degrees. In the squillions of crystals struck by sunlight, those which happen to produce by their chance orientation toward the Sun the minimum deviation of the sunlight will pass the most of that sunlight thru them. These rays of brightest light are bent 21.839 degrees from the incoming path. The effect on the sky is a bright spectral spot 21.839 (say 22) degrees away from the Sun. For the randomly oriented field of crystals, there will be such spots 22 degrees away in all directions. They blend together into a continuous ring to make the halo minor. In general, an optical effect that is symmetrical around the Sun in all directions is caused by a totally randomized orientation of crystals. One with a bias relative to the Sun, like the parhelia, are caused by crystals with some preferential orientation. Hence, by casual bare-eye observation of solar halos we gain come fascinating intelligence about the atmosphere many kilometers up! One intriguing side effect of the refraction process is that the sky inside of the 22 degree halo is darker than that outside of it. This is not just a contrast effect. Rays from the Sun which would reach the observer from within 22 degrees are diverted to 22 and more degrees away. There is a real withdrawal of illumination within the halo minor. Because of the brilliance of the daytime sky, this weird feature is best seen when the Moon causes a halo minor. In the softer light at night, the sky within the halo can seem quite dark, with that on the outside appearing grayed over.
Optics of parhelia ---------------- When the crystals are short and stubby, being more like tablets, they can come to an equilibrium position with their hexagon faces horizontal and their flanks upright. There being far more crystals in this orientation -- with a depletion in the other directions -- the refraction takes places only to the left and right of the Sun. The effect is two bright spectral spots alongside the Sun and on his same altitude above the horizon. These are the parhelia. For the Sun of the horizon, so the rays hit the crystals square on, these spots are merely the two extreme lateral ends of the halo minor itself. If you see parhelia and the halo at sunrise or sunset, the parhelia will be enhanced spots right on the halo, to the left and right of the Sun. When the Sun is above the horizon, the lightray hits the crystal obliquely, changing the geometry of the path thru it. The ray 'sees' a larger prism angle and a longer internal path. The result is that the minimum angle is larger than 22 degrees and the parhelia are thrown farther away from the Sun. If there is a halo minor also, the parhelia at higher Sun altitude stand more and more outside the halo. In the extreme case, the angle and path conspire to capture the lightray and reflect it back toward the Sun! It never passes thru to the observer. This happens at Sun altitude of 60.7 degrees. This is why we can not see parhelia in midday in summer from the City. The halo minor, caused by jumbled up crystals, can be seen at all solar altitudes. Ideally the ice crystals are nice and perfect and cover most of the entire sky, producing complete richly colored effects. Normally the field of crystals occupies only a part of the sky and the crystals are corrupted by inclusions or breakage, making for a rough-edged incomplete display. As the ice field drifts thru the upper air, the display can evolve on a timescale of minutes. It is rare for a halo display to persist for many hours. Most are visible for an hour or so at most and often for only many minutes. The display can be interdicted by intervening haze or cloud. A halo complete in a clear sky may be interrupted from a lower cloud covering part of it. Or a parhelion may fade by extinction from a passing cloud. All in all, just these two simple optical phaenomena can offer a rich diversity of apparitions.
Occurrence of halos ----------------- Like with any other atmosphere behavior, it is impossible to forecast a halo display. We must be lucky to be outdoors when one erupts in our sky. Thus, the rule is simple and cruel: Monitor the sky often when outdoors! Never the less, there is for New York a tendency of halos to accompany the approach of cirrostratus or cirrus clouds. These are high elevation clouds full of ice crystals. Sadly, orthodox home astronomy pretty much dismisses the daytime sky. Discussion of solar halos is wanting in the usual litterature or is incompetent and superficial. Yet halos are one of the more glorious sights in the sky -- and about the easiest of wonders to behold! So spectacular can they be that some anthropologists and historians believe that many 'visions' noted in ancient writings may in fact be solar halo displays. For instance, it is now generally accepted that Constantine the Great, Roman emperor, saw a halo system resembling the Crucifixion surrounded by a glory. This inspired him to convert to Christianity, conquer Asia Minor, and build his capital Constantinopolis.
Documenting halo phaenomena ------------------------- As a result of this neglect of solar halos, there is no organized effort to collect observations, issue procedures and forms, publish and study reports, and all that. In Europe some of the national home astronomy centers do have sections for watching solar halos, with nice webpages, but they are not generally accepted beyond their frontiers. So we're kind of on our own. The best as at now to do is just describe the apparition, including the usual observer basic data, and publish it in the club's newsletter or website. Note the general weather conditions and cloud cover. Include sketches, photos, and images of the display.
Looking into the Sun ------------------ First off, be careful not to stare into the Sun! It's easy when sweeping the open sky to accidently hit the Sun with your glance. No enduring harm is likely in this case. Just don't try to look at the Sun on purpose, OK? Hide the Sun behind a pole, tree, roof edge so it does not hit your eye. In this sense, we on Manhattan actually see more halos than our folk in the flatter parts of the City. Why? We on Manhattan are always in the shadow of the towers and can look at the [slices of] sky without worrying about inadvertently looking into the Sun! And, please, use a rigid shield. Wind-blown leaves, flag, or banner will soon enough get you into trouble. So will a momentarily stopped el train, large truck, construction crane. Or, a small cloud drifting across the Sun.
Measurements in the sky --------------------- With the lack of standard procedures for recording halo displays, you should collect at least the measurements necessary to properly plot the features on a chart. Ask, "What dimensions do I need to reconstruct this feature on my chart?". Hence, things like the alt- azimuth of small spots and centers of patches, endpoints of arcs and lines, top and bottom vertices of circles are all welcome items to capture. Note that with the impracticality of determining for sure the north point by day, azimuths are always relative. The meridian of the Sun is the zero of azimuth. Degrees run left and right from the Sun or all the way thru the circle rightward from the Sun. Use the typical hand-arm method for estimating angular extent on the sky. A ruler held against the sky at armslength can serve in a pinch. The centimeter marks are more or less degree marks. For widely spaced points, bow the ruler outward and hold the ends with both hands. Remember that the length of a line on the sky is NOT the length between its endpoints! For sure the line will not be part of a great circle. In the stead, note the alt-azimuth of the endpoints and of several waypoints. For banking off of the Sun, first hide him behind a shield. Then note that there is almost always an aureola around him, bright and round. The center of this aureola is the place of the Sun. To distinguish between coords on the sky relative to the ground from coords around a point, for the latter use the clockface method. 12 o'clock is up to the zenith, 3 o'clock is straight to the right, and so on. This helps separate the 'lat-lon' type of measure from the 'run-bearing' measures.
Plotting halos ------------ One thing that makes plotting a display much easier is the stereographic chart. On such a chart all lines, arcs, circles do plot as true circles and arcs, with no funny ellipses or odd curves to draw. You can make blank charts by ruler and compass or copy one from a cartography book. Put fields around the edges for the basic observing information. A labelled alt-azimuth grid can be included. Keep a supply of these charts, pencils, watch, ruler handy when ever you are outdoors or near a skyview. For us on Manhattan we keep this kit in our workplace desk, particularly if we are blessed with a large window with a prospect toward the sky. Otherwise we stuff one in our pocket for the noontime walk around the block. No special artistry is needed. A heavy line or large dot for the brighter features is just fine. Thin lines and small dots mark the weaker features. Uncertain parts of the display are shown with dashed lines and small 'X's. For simple displays you can annotate the features with their measurements. Complex displays are best labelled with numbers or letters keyed to an offchart explanation.
Photographing halos ----------------- Photographing halo displays can be tricky. The display comes unexpectedly and we don't got a camera at hand! If you fix to look out for halo displays keep your camera handy when outdoors or near a skyview. The lens should be, for the 35mm film size, 50mm or less in focal length. This fits enough of the sky onto the film to give context to the image. A 70mm to 135mm lens gives detail in specific parts of the display but is too constrictive for general views. Use ordinary daylight film, what ever you normally load the camera with. Slides are preferrible but prints are OK. With modern film scanners either the negative or the slide can capture about the same detail for making computer images. So far, among the usual models sold for home snapshooters, digital cameras do badly on sky pictures. Their auto-everything function thwarts proper exposure of the sky. For manual control of the exposure you need one of the more fancy expensive models. Expose directly on the sky, not on the landscape below it. Know the meter's sensing pattern in the viewfinder. On the whole you'll shoot at 1-1/2 to 2 stops less than for the land at the same moment. The ground will look underexposed compared to a landscape picture, but the halo will stand out better with more vivid colors. Be careful not to 'blind' the camera with the Sun. To include him in the picture, use the aureola trick explained above. On the other hand, try to include some foreground objects to give scale to the picture. No special treatment of the film is needed. The halo pictures for the photofinisher are ordinary daylight pictures. In fact, the usual situation is to take halo pictures mixed in with other mundane pictures on the same roll. You do need good written notes during the picture-taking so you can label the pictures with the observing information. You can key the pictures to the parts of the handdrawn skychart, too. This is a capital way to enhance your report for your club's website.
Books about halos --------------- Despite the innate beauty and somewhat rarity of halos, there are few complete books about them. The allout favorite starting book remains Minnaert's 'Light and color in the open air' a Dover reprint. Many many astronomers grew up with this book. It covers all kinds of naked-eye optical effects in the sky besides halos. Humphrey's 'Physics of the air', either the original hardback or Dover reprint, is a technical treatise on atmospherics. While many parts are badly ediurnate, the sections on halos are still valid. Expect to exercise your calculette with this book. 'Rainbows, halos, and glories' by Greenler is a 1980ish work with many color pictures and examples of early computer simulation of halos. In the Petersen series of nature guides there is 'Field guide to the atmosphere' by Schaefer and Day. It has little text on halos but many interesting pictures of them. For pictures of halos by which to anticipate what they look like, there are no compilations within casual reach. For such an interesting phaenomenon of nature this may at first seem strange. But it is a skill to photograph the open sky. Then, too, the camera and the display too often do not show up together. The result is that most halo pictures are indistinct, too dim, filled with obscuring clouds, badly composed and framed, and so on. Yet there are gems out there if you look hard enough. Many home astronomers include solar halo pictures on their own or club's website. Usually these are of some one spectacular display they saw. Look also at the geology or meteorology department sites of major universities. They may collect good examples for their educational needs or to show off some project.
Websites for halos ---------------- Disappointingly, far too many halo-themed websites are casual about halos. They have meager details, like encyclopedia or science book articles. But by the end of the 20th century a few good ones are emerging. All these sites have images of halo effects and most have links to other sites. I left out sites with pretty pictures included in galleries of other astronomy images. University of Illinois has 'light and optics' on halos as part of its atmospheric phaenomena page. 'www2010.atmos.uiuc.edu/(Gh)/guide/mtr/opt/home.rxml'. Mind your typing; this IS a peculiar address. German Halo Observers hosts 'Atlas of halos' and the programs HaloSky and HaloET on this mixed English-German website. 'members.tripod.com/~regenbogen' Jarmo Moilinen has observations of a possible new halo feature he spotted. 'friendly.netppi.fi/~jarmom/haloguide/index.htm'. He also has a section on terrestrial meteor craters. Tomas Trzicky's website is all in Czech; just go for the pictures. 'www.volny.cz/trzicky/atmos/halo.htm' Dave Reilly's website has his Atmosim program and some tuition on halos. 'www.soundprobe.freeserve.co.uk/halo' Les Crowley & Michael Schroeder host their HALO program for modelling halos at their website. 'dspace.dial.pipex.com/lc/halo/halosim.htm' Hans Schremmer's website is all in German but is rather thoro in explaining halos. 'www.schremmer.de' Jarkko Korhonen's wensite has brief explanation of halos. 'samba.student.oulu.fi/jarkkoko/FRONT.HTM.' Last field is caps. Finnish Halo Observers Network is a section of URSA, FInnish Astronomical Society, with tuitional material and illustrations. It has daughter pages for halo pictures taken by URSA members. 'www.ursa.fi/ursa/jaostot/halot/english.html' Timo Leponiemi has 'Halot' site all in FInnish but with quite nice pictures. 'www.sci.fi/~fmbb/astro/halot.htm' Searching the Net for halo information is a bit hit or miss. There is no overall best name for the phaenomenon and you turn up all kinds of totally irrelevant sites. Keying on just 'halos' will get you sites for flowers, certain pasteries, religious symbols, certain ducks, new age junk, songs and singers, sports teams, and companies with 'halo' in their names.
QBASIC/GWBASIC program for parhelia --------------------------------- Simulations of halos is far advanced from in 1997, when I found only one lousy program. I then rolled my own parhelia simulation for my Sinclair computer. I later translated it into GWBASIC or QBASIC for the greater readership. You can try it yourself; here's the listing. The 'fnasn' thingie is a workaround for GWBASIC's and QBASIC's lack of a true arcsine function. If you really want to understand the arcane maths, do ask. For now, trust me, this program does work correctly. Do not try to rekey this code. Cut it out between the 'cut here' lines and paste it into a new file called PARHELIA.BAS. Let QBASIC or GWBASIC load and run this new file.
= = = 8< = cut here = 8< = = = 4 DEF fnasn (q) = ATN(q / SQR(1 - (q ^ 2))) 6 LET pi = 3.14159: LET n = 1.31: LET aa = pi / 3 8 FOR h = 0 TO 60 STEP 2 10 LET hh = h * pi / 180: LET nn = (n / COS(hh)) * COS(fnasn(SIN(hh) / n)) 12 LET ad = 2 * fnasn(nn * SIN(aa / 2)) 14 LET md = ad - aa: LET sd = 2 * fnasn(COS(hh) * SIN(md / 2)) 16 LET md = md * 180 / pi: LET sd = sd * 180 / pi: LET hd = sd - 21.8393 18 LPRINT : LPRINT "alt of Sun = "; h: LPRINT "azm offest = "; md 20 LPRINT "dist from Sun = "; sd: LPRINT "dist from 22deg halo = "; hd 22 NEXT h = = = 8< = cut here = 8< = = =
Computer modelling ---------------- Now, in the beginning of the thous, a burst of new and exciting programs were issued. All come from the websites noted above. The quickest and easiest for home astronomers is HaloSky for DOS. This is a planetarium that in the daytime superimposes halos around the Sun! The displays are precalcked for each solar altitude by HALO, an other program noted below. The planetarium has custom stardata, horizon skyline, and cities info. Moon phase and bright planets are displayed. In twilight, the halos and brighter stars are together in the sky! You need the prime file plus 5 support files. HaloET for DOS is a true modeller for halos. It sends lightrays from the Sun thru fields of ice crystals and plots the resulting deviations of these rays on a skychart. This requires editing the parameter files and some grounding in atmospheric optics. But it is fast and powerful and accurate. For Windows 95 there are Atmosim and HALO. These do require Win95; I found nothing for Win3.x. Atmosim is an unfinished offering but the main operations do work. There are no proper instructions, only the short text on its website. After some playing around I did get it to plot some simple halos. HALO demands close attention and expertise in atmospherics. It produces gorgeous plots and has simulations for several major historical displays. Scenes can be saved as PCX files; these are the ones used by HaloSky. Be careful! You need a 32-bit, not a 16-bit unzipper to keep the long file names embedded in the package. That's it! Keep looking up. And now you should do so by day as well as by night.