EDUCATIONAL ACTIVITY 3.
Calculating the height of formation of the Northern Lights.
by
Mr. Juan Carlos Casado. Astrophotographer tierrayestrellas.com, Barcelona.
Dr. Miquel Serra-Ricart. Astronomer Instituto de Astrofísica de Canarias, Tenerife.
Mr. Miguel Ángel Pio, Astronomer Instituto de Astrofísica de Canarias, Tenerife.
1 - Activity objectives
Through this activity we will learn how to calculate the height of formation of the
Northern Lights from digital photos.
The objectives that we want to achieved are:
- Implement a methodology for the calculation of a physical parameter (height)
from an observable (digital images) as a technique for teaching applications,
documentaries and research. Apply knowledge of trigonometry and basic atomic
physics.
- Understand and apply basic analytical techniques of images (angular scale,
height of stars, ...).
- Work cooperatively as a team, valuing individual contributions and expressing
democratic attitudes.
2 - Instrumentation
The practice or activity will take place from digital images obtained in Greenland
(Denmark) in August 2012.
3 – Phenomenon.
The Northern Lights are one of the greatest natural spectacles that can be observed from
Earth. In the activity we will see what they are, how they are produced and where it can be
observed. Also we will show two methods to calculate or estimate the height at which they
form.
3.1.- What are Northern Lights.
The Northern Lights or Aurora is a phenomenon in the form of glitter or glow in the night
sky visible in areas of high latitudes (Arctic and Antarctic), but occasionally it may appear at
lower latitudes for short periods of time.
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Figure 1 : Austral Aurora photographed from the Amundsen-Scott station located at the geographic
South Pole, the July 14, 2011 by Robert Schwarz.
In the Northern Hemisphere (most populated) is known as Aurora Borealis (term due to
the French philosopher and scientist Pierre Gassendi in 1621) or popularly "Northern Lights". In
the southern hemisphere Aurora Australis occurs, which simultaneously follows the same
patterns of activity as the Northern Lights. The Aurora Australis is visible especially in
Antarctica (Figure 1), although it can be seen from the southern areas of Australia and South
America.
Auroras are not a phenomenon unique to Earth. Other planets like Jupiter and Saturn,
with strong magnetic fields, show similar phenomena.
3.2.- What is the origin of the Northern Lights.
The Sun is continuously emitting high-energy particles, as well as all types of
electromagnetic radiation, including visible light. This flow of particles is the so-called solar
wind (hot gas or plasma), which is composed mainly of positive ions and electrons. There are
very energetic phenomena such as flares or coronal mass ejections (CME stands for Coronal
Mass Ejection in English) that increase the intensity of the solar wind. The solar wind particles
traveling at speeds from 300 km / s (slow solar wind) to 1,000 km / s (fast solar wind), so that
cross the Earth-Sun distance in about two or three days. In the vicinity of the Earth, the solar
wind is deflected into space by Earth's magnetic field or magnetosphere.
The solar wind pushes the magnetosphere and deform it, so that instead of a uniform
beam of magnetic field lines as those that show an imaginary magnet placed in a north-south
inside the Earth, what it is produced is a elongated structure with a long tail with the shape of a
comet, in the opposite direction to the sun (Figure 2).
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Figure 2 : Artistic representation of the sun emitting the solar wind and a coronal
mass ejection that moves through space. When he reaches the Earth, most of the particles
are deflected by Earth's magnetic field, which takes the form of a comet tail. A few
particles are driven into the atmosphere of our planet canalized towards the magnetic
poles along the lines of terrestrial magnetic field strength, which are displayed in the
figure as green lines.
A small part of the solar wind particles penetrate into the atmosphere following the earth's
magnetic field lines, so that they are driven along the path that they mark. Trapped particles in
the magnetosphere collide with neutral atoms and molecules in Earth's upper atmosphere,
typically atomic oxygen (O) and molecular nitrogen (N2) found in the neutral state and in its
lowest energy level, called fundamental level. The energy contribution provided by the particles
from the Sun carries those atoms and molecules to the so-called excited states and they will
return to their fundamental level emitting energy in form of light (Figure 3). That light is what
we see from the ground and we called auroras.
The Northern Lights are caused typically between 100 km and 400 km because at this
altitude the atmosphere, though thin, is still dense enough that collisions with solar particles
occur significantly.
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Figure 3 : When an electron from the solar wind collides with an
atom of oxygen (O) or a nitrogen molecule (N2) of the upper
atmosphere, it transfers energy which get the atom to an excited
state. Upon return to the ground state, the atom emit energy as
ligth as follows, with a characteristic wavelength, corresponding
to a specific color, as shown in Fig.
3.3.- Where, when and how to observe the Northern Lights.
The Northern Lights occur in some areas of the earth called auroral ovals, which are
located around the north and south magnetic poles, respectively (Figure 4).
Figure 4 : Northern auroral oval. You can
see areas of frequent occurrence of
auroras and the decrease of the width of
the oval in the oriented areas in the
terrestrial dayside (top image).
The more intense is the solar wind and more energetic the particles ejected from the Sun,
greater are the ovals. Therefore, if solar activity is moderate to low, the ovals are thin and in the
case of boreal boundaries move farther north. However, during the great storms, the northern
oval widens and moves further south.
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Figure 5 : Areas of increased occurrence of auroras in the northern ovals (left) and south (right).
The position of the geomagnetic poles slowly changing with time (about 60km per year), therefore, the
Northern Lights ovals also change slowly.
If solar activity is very intense, sometimes oval extends through the southern United
States and Europe. For a given level of solar activity, the thinnest part of the auroral oval is
always on the dayside terrestrial (earth meridian noon), while the thickest part of the oval is
located on the night side of Earth, and therefore more likely to see the aurora from local
midnight.
The zones of highest frequency at which one can observe the auroras correspond to a
circle situated in the auroral ovals (Figure 5). In the northern hemisphere this zone extends from
Alaska, northern Canada, southern Greenland, Iceland, northern Scandinavia (Norway, Sweden,
Finland) and northern Siberia. The zone of maximum occurrence of Aurora Australis is found in
Antarctica. In these ovals, the frequency of auroras per year may exceed the 240 nights during
periods of high solar activity (discrete auroras), decreasing both inwards and outwards of the
oval (diffuse aurora). By contrast the inhabitants of the southern USA, Mexico, southern
Europe, and its surrounding areas may experience the aurora (diffuse type) only once in life. It
is estimated that in Ecuador terrestrial aurora can be seen every 200 years.
In Spain, you can see very rarely times; the probability is about one per year in the north,
decreasing to 0.2 per year in the south. Coinciding with the last maximum of solar activity, the
aurora was seen in areas of the Mediterranean and the Spanish the 6 April 2000 (Figure 6). And
still is remembered the Northern Lights January 25, 1938, during the Spanish Civil War, which
was observable from Andalusia
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Figure 6 : Aurora borealis (diffuse type) visible as an intense red
lighting with structure, in the north of Figueres (Girona), on April 6, 2000.
Photo of Peter Horst.
Our star has cycles of activity. During peak periods the solar wind increases and therefore
is easier to observe auroras. The main observable in solar activity is the amount of spots that has
the sun on the surface. Sunspots are areas of the surface cooler than their surroundings so they
appear as dark images. After several years of data, it has been discovered that the amount of
spots on the surface of the sun rises every 11 years or so, so that the cycle of activity is for 11
years (known as "undecenal cycle"). The last peak occurred in late 2000 and according to the
latest data is expected a new high in early 2013.
The auroral are phenomenon low luminous, so it can be observed only at night. The weak
auroras have brightness similar to the Milky Way one, while the brightest can come to have
luminosity similar to the full moon. Due to the fact that auroras are visible only in the
circumpolar regions, they shall not be observable during the summer due to the phenomenon of
the midnight sun. Auroras can be observed from August to May, being the best months to
observe them which are close to the equinoxes (September to March) due to the better
geometric disposition of the Earth's magnetic fields, which results in the appearance of
Geomagnetic Storms that facilitate the entry of solar energetic particles at the poles.
Auroras have very different forms, structures and colours, which also change rapidly with
time. During one night, the Northern Lights may begin as a single elongated arc that is
spreading on the horizon, generally in an east-west. Around midnight, the arc may start to
increase its brightness. They begin to form waves or curls along the arc and also vertical
structures that looks like curtains of light or rays, very elongated and thin. At one point the
whole sky can be filled with bands, spirals, and rays of light that tremble and move rapidly from
horizon to horizon. The activity can last from a few minutes to hours, but usually the process
takes about 15 or 20 minutes. As dawn approaches the activity decreases and only small areas of
the sky appear bright until dawn comes.
In normal conditions of illumination, our human eye can see colours from violet, which in
the electromagnetic spectrum having a wavelength of about 390 nm to red, about 700 nm. When
the aurora is weak it apparently has no colour, because under environmental of low
illuminations conditions our eyes only has some sensitive cells called rods that can detected
something, which only distinguish light without colour. As the brightness increases, the colour
vision starts with the cones, the cells that allow us to distinguish colours, appearing greenish
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tones, the most common colour and sensitive to our vision (green 555nm). With digital cameras
you can see, besides the red tones, a wide range of colours (blue, purple, yellow, ...).
Some observers claim to have heard sound coming from the aurora, as hisses, crackles
and pops. Although auroras are located over 100 km. altitude, it seems that the magnetic field
associated with the aurora creates an electrostatic charge that makes sizzling branches of trees,
although the instrumental measurements have been inconclusive1.
4 – Methodology
4.1.- Estimation of altitude by the colours. Method 1 – Colours.
The colours we see in the aurora depend on the atomic or molecular component of the
upper atmosphere that is, by the solar wind particles (mostly electrons), excited and the energy
level that those atoms or molecules reach. As seen above, an excited atom or molecule returns to
ground state, emitting a photon with a specific energy, which is perceived as a certain colour.
Hundreds of kilometres of altitude, in addition to the normal air (composed primarily of
molecular oxygen and nitrogen), is also atomic oxygen. The main components of the
atmosphere, nitrogen and oxygen produce the full range of colours of the aurora, although
sometimes gases like hydrogen and helium can also emit colours.
-Oxygen
The energy emission from oxygen atoms, which are excited by electrons, has some
peculiarities that are worth explaining. Usually an excited atom or molecule returns to a normal
state immediately, and the emission of a photon occurs in microseconds. The oxygen atom,
however, takes time. Only after a ¾ of a second it returns to the ground state emitting a Green
photon. For the Red photon takes nearly 2 minutes! If during this time the atom collides with
another particle, it lost the energy by the collision and therefore not emits light. Collisions are
more likely if the atmosphere is more dense (low altitude). This is the reason why the oxygen
red only appears from 200km, where collisions between air molecules and atoms are rare.
Below 100 km altitude even the colour green is not possible. This occurs in the lower edges of
the Aurora: the green emission is quenched by collisions, and all that remains is a mixture of
blue / red (pink) from the emission of molecular nitrogen.
1
See the cientific article http://www.acoustics.hut.fi/projects/aurora/BNAM-ukl.pdf
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Figure 7: In the graph, which shows the emission spectrum of
atomic oxygen, are marked main emission lines, corresponding to the
green being the most common in the Northern Lights.
In summary, oxygen is responsible for the two primary colours of the aurora, the green
energy of a transition to 557.7 nm (remember that one nanometre is 10-9 m while a Armstrong
10-10 m), while the red colour is produced by a less frequent transition at 630 nm (figure 7).
-Nitrogen
Nitrogen, which a collision can extract some of its outer electrons (ionization), produces a
blue light, while if it is excited by the collision of an electron, its emittion is red (Figure 8).
Figure 8 : Visible spectrum of molecular nitrogen from the auroras, with
emission lines.
Schematically and with all the information available, we can make an estimation of the
height of formation of the aurora from its colours.
1.- Above 200 km, it shows the reddish hue of atomic oxygen (Figure 9a).
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2.- Among the 100-200 km altitude highlights the greenish, which is characteristic (the
most abundant of the auroras, Figure 9a, b, c) emission of atomic oxygen.
3.- Around 120 km are the blue-violet colours of molecular nitrogen (Figure 9c).
4.- In situations of high activity (solar storm) a pink band appears at the 90-100 km
altitude produced by molecular nitrogen and the lower edge of the aurora (Figure 9b).
Figure 9 : The colour of the aurora is indicative of the level of formation (see text for details). All images were taken
by M.C. Sosa Diaz in the expedition Shelios 2000 (more information at shelios.com/sh2000). The rights of the
images are of tierrayestrellas.com
4.2.- Calculation of the height of formation of the aurora by parallax. Method 2 Parallax
The height at which a polar aurora forms can be calculated from photographs taken by
two observers spaced several kilometres. Each observer will see the same aurora projected on a
background of stars slightly different. This angular separation can be measured, and knowing
the distance between the two observers (by its location on a map or GPS), you can calculate the
height that is the aurora. By this procedure, the Norwegian physicist Carl Störmer using 40,000
photographs obtained between 1909 and 1944 estimated the altitude limits of the aurora: 70 to
1,100 km, with an average around 100 km altitude.
Let’s call O1 and O2 the positions of each observer, which are located in similar heights
levels above the sea level. Are separated by a distance d known. We can assume this separation
d as a straight line (a few kilometres in relation to the earth's circumference). Looking at the
same aurora A, it is projected on a different background sky, creating an angle α that can be
measured (parallax) (Figure 10).
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Figure 10 : Calculation of the height of formation of the aurora by parallax or
triangulation (details in text). Figure J.C. Casado.
By similar triangles, the angle α’ formed by the vertices of the triangle O1AO2 is equals to
the angle α.
We want to find the height h of the aurora, which is perpendicular to the surface (line O1
O2). The angles β1 and β2 are known, as are the height of the aurora on the horizon (which
coincides with the height of the stars on which is projected) views, respectively, by the
observers O1 and O2. In the O1AO2 triangle, this ratio is satisfied (Theorem of the sinus):
ℎ1
𝑑
=
[1]
𝑠𝑖𝑛 𝛾
𝑠𝑖𝑛 𝛼′
Solving we have h1 [1]:
ℎ1 = 𝑑 ∙
𝑠𝑖𝑛 𝛾
[2]
𝑠𝑖𝑛 𝛼′
Now we can solve the triangle O1AP and find the height h:
𝑠𝑖𝑛 𝛽1 =
ℎ
[3]
ℎ1
Where you get the height h of the polar aurora (replacing h1 en [2] and knowing that
sin(𝛾) = sin(180º − 𝛽2 ) = sin(𝛽2 ):
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ℎ=𝑑 ∙
𝑠𝑖𝑛 𝛽1 ∙ 𝑠𝑖𝑛 𝛽2
[4]
𝑠𝑖𝑛 𝛼 ′
also the ratio, α′ = β2 − β1 , therefore we can apply the formula as follows:
1)
Calculate the height of the aurora on the horizon for any of the two
observers (e.g. O1 β1 ) and calculate the parallax α′ (from the angular scale of the
images and the separation in pixels of the projection of the dawn, on the stellar
background in each of the images).
2)
Calculate the height of the aurora with respect to the horizon for the two
observers, knowing that α′ = β2 − β1 .
For the above calculations we will use some field stars (found in digital photographs) that
match with the position of the aurora. It will be necessary to know the exact coordinates of the
observers, the height above the sea level and the exact time of observation. You will also need
to have some software for calculations of the heights β1 β2 (eg free software Stellarium available
in stellarium.org).
5 - Internet Addresses
 http://www.shelios.com Scientific expeditions for The Shelios group to observe
astronomical phenomena, including aurora borealis (Shelios 2000 and Shelios 2011),
including live broadcasts over the Internet (sky-live.tv).
 http://spaceweather.com
including auroras.
Solar activity and Earth's space environment,
 Solar Images and storm warnings (SOHO, ESA):
sohowww.estec.esa.nl/data/realtime-images.html
sohowww.estec.esa.nl/whatsnew/
 Solar Activity and forecasts
Europe: http://sidc.oma.be/index.php3
United States: http://www.swpc.noaa.gov/
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