HALO MINOR AND PARHELIA 
 ===================== 
 John Pazmino
 NYSkies Astronomy Inc
 www.nyskies.org
 nyskies@nyskies.org
 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.