HALO MINOR AND PARHELIA
---------------------
John Pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies@nyskies.org
2001 August 1 initial
2023 March 28 current
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 8 t o
10 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 constricting for general views.
Use ordinary daylight film, what ever you normally load the camera
with. Slides are preferred but prints are OK. You may have to get the
prints of halos redone if they are too muddy or flat.
Expose directly on the sky, not on the landscape below it. If
feasible, keep the Sun out of the field for the meter reading,. Else
the picture may be too under exposed. 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 under
exposed 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 photo-finisher 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 hand-drawn skychart, too. This is a
capital way to enhance your report for your club's website.
for photographing with a digital camera or picture-taking cell
phone, all of the the above advice is pertinent, skipping hat
relating to film.
By the 2020s actual digital cameras deliver images of quite the
same resolution, 'lines per m film. Cell phones still have low
resolution but yield acceptable quality halo pictures.
A digital picture can be reviewed on the spot for quick do-overs,
and there is usually no worry about running out of remaining frames.
On the smart phone you can text a display alert to other observers and
email your initial pictures to them.
Digital pictures can be loaded into an image editing software for
full-frame treatment of exposure, framing, brightness, contrast. An In
the margin of the picture, like oo foreground landscape, insert some
text your name, observing town, full date, hour, perhaps general
sky/weather conditions. image editor makes it easy to mosaic several
images taken to to span a large display. On a copy of the original
picture, your may label important features of the display.
References for halos
------------------
Despite the innate beauty and somewhat rarity of halos, there are
few complete books about them. The all-out 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.
Searching the Web for halo information is a hit or miss Labor.
There apparently are no overall webs for halo phaenomena. You may
turn up all kinds of irrelevant sites for music, solar energy,
flowers, pastries, religious symbols, ducks, new-age junk, songs and
singers, sports teams, and companies with 'halo' in their names.
QBASICC 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 and then into
QBASIC for the greater readership.
You can try it yourself; here's the listing. The 'fnasn' thingie
is a workaround for QBASIC's lack of a true arcsine function.
The arcane maths come from the books mentioned above... 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 load
and run this new file.
= = = = = 8< = cut here = 8< = = = =
DEF fnasn (q) = ATN(q / SQR(1 - (q ^ 2)))
LET pi = 3.14159: LET n = 1.31: LET aa = pi / 3
PRINT "Sun alt", "azm from sun", "dist from Sun", "dist from halo"
FOR h = 0 TO 60 STEP 2
LET hh = h * pi / 180
LET nn = (n / COS(hh)) * COS(fnasn(SIN(hh)) / n)
LET ad = 2 * fnasn(nn * SIN(aa / 2))
LET md = ad - aa: LET sd = 2 * fnasn(COS(hh) * SIN(md / 2))
LET md = md * 180 / pi: LET sd = sd * 180 / pi: LET hd = sd - 21.8393
PRINT h, md, sd, hd
NEXT h
= = = 8< = cut here = 8< = = =
Computer modelling
----------------
Now, in the beginning of the 2-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 there are Atmosim, HaloSim, and HALO. 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.
HaloSim calls for close study. For starts it has a large set of
prepared simulations to play with. the sky can be sized from a few
tens of degrees to a full hemisphere.
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.
That's it! Keep looking up. And now you should do so by day as
well as by night.
Conclusion
--------
Home astronomers often learn about solar halos by seeing one good
display and then asking among associates about it. Right up to today,
2020s, thee are frustratingly few and scanty resources to fill the
astronomer's satisfaction. Websites come and go, they may be too
skimpy in theory or description. There seems to be central clearing
house for halo phaenomena, like for occultations, eclipses, variable
stars, comets fireballs, even UFOs.Earther resources don't discuss
halos as a feature to watch for and report.
I find this peculiar. An atmospheric apparition so easy to observe
-- by day! -- could, if duly documented in a standard method, should
provide useful information about conditions in the stratosphere.It
could lead to better models of the air for aviation, climate
monitoring, tracking insolatio...
And they are drop-dead beautiful!