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 EDUCATIONAL ACTIVITY 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. Dr. Lorraine Hanlon. Astronomer University College Dublin, Irland. Dr. Luciano Nicastro. Astronomer Istituto Nazionale di Astrofisica, IASF Bologna. 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: 1. 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. 2. Understand and apply basic statistical techniques (error calculations). 3. Understand and apply basic analytical techniques of images (angular scale, height of stars, ...). 4. Work cooperatively as a team, valuing individual contributions and expressing democratic
attitudes. 5. Contributing to scientific knowledge of the Aurora and Solar Activity. 2. Instrumentation The practice or activity will take place from digital images obtained in Greenland (Denmark) in
August 2013. 3. Phenomenon Northern Lights 1 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. Figura 1. Aurora Borealis photographed from a Tasiusaq farm located south of Greenland (J.C. Casadostarryearth.com). 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 2 Northern Lights. The Aurora Australis is visible especially in Antarctica (Fig. 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 an elongated structure with a long tail with the shape of a comet, in the opposite
direction to the sun (Fig. 2). Northern Lights 3 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 (Fig. 3). That light is what we see from the ground and we called
auroras. Northern Lights 4 The Northern Lights are emitted typically between 100 and 400 km because at this altitude the
atmosphere, though thin, is still dense enough that collisions with solar particles occur significantly. 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 emits energy as
light with a characteristic wavelength, corresponding
to a specific color, as shown in this figure. 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 (Fig. 4). Northern Lights 5 Figure 4. Northern auroral oval. You can see the areas of frequent occurrence of auroras, and the reduction of
the width of the oval on the dayside facing areas road (bottom of the image). The colors indicate the probability
of observing an aurora and the red line is the southern (lower latitude) from where you can see the auroras (see
model Ref6 OVATION-NASA). Northern Lights 6 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. Figure 5. Evolution of the Magnetic North Pole. Auroras are formed in an oval around the Earth's magnetic
poles (see Fig. 4). 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 (Fig. 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
Northern Lights 7 the aurora (diffuse type) only once in life. It is estimated that in Ecuador terrestrial aurora can be seen
every 200 years. In southern Europe, you can see this phenomenon very rarely times; the probability is about one per
year at France, decreasing to 0.2 per year in the south of Spain or Italy. Coinciding with the last
maximum of solar activity, the aurora was seen in areas of the Mediterranean and the Spanish the 6
April 2000 (Fig. 6). And still is remembered the Northern Lights January 25, 1938, during the Spanish
Civil War, which was observable from Andalusia. 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 Pere 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 late 2013. Northern Lights 8 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 tones, the most common colour and
sensitive to our vision (green 555 nm). 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. 1 See the scientific article http://www.acoustics.hut.fi/projects/aurora/BNAM-ukl.pdf Northern Lights 9 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 it takes nearly
2 minutes! If during this time the atom collides with another particle, it loses its energy in the collision
and therefore does not emit light. Collisions are more likely if the atmosphere is more dense (low
altitude). This is the reason why the oxygen red emission only appears above 200 km, 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. 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. Northern Lights 10 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 Angstrom 10-10 m), while the
red colour is produced by a less frequent transition at 630 nm (Fig. 7). – Nitrogen Nitrogen, for which a collision can extract some of its outer electrons (ionization), produces a blue
light. However if it is only excited by the collision of an electron, its emission is red (Fig. 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 (Fig. 9a).
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 (Fig. 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 (Fig. 9b).
Northern Lights 11 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 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 where the aurora was
produced. 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) (Fig. 10). Northern Lights 12 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. Northern Lights 13 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, and we know the height of that stars, so we also know the
height of the aurora) views respectively by the observers O1 and O2. In the O1AO2 triangle, this ratio is
satisfied (Theorem of the sinus): h!
d
=
[1] sin γ sin α′
Solving we have h1 [1]: h! = d ∙
sin γ
[2] sin α′
Now, if we use triangle O1AP, we can find the height h: sin β! =
h
[3] h!
So finally, we get the height h of the polar aurora (replacing h1 by its expression in [2] and knowing
that sin(γ) = sin(180º − β2 ) = sin(β! ): h = d ∙
sin β! ∙ sin β! [4] sin α!
and also knowing that α! = β! − β! , therefore we can apply the formula as follows: 1) Calculate the height of the aurora from the horizon for the two observers (e.g. O1 β! ), from the
angular scale of the images and the separation in pixels of the projection of the aurora, on the stellar
background, for each of the images of each observer. 2) And then, calculate the height h of the aurora from the horizon for the two observers knowing
α! = β! − β! , and considering d is known, so you just have to put values in the expression [4]. 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 where they are, and the exact time of observation. You will also need to
Northern Lights 14 have some stellar software to use to calculate the heights β1 β2 (e.g. the free software Stellarium
available at stellarium.org). 5. References ref1 - Images of the Sun (photosphere) from internet. 1. From the Space (SOHO satellite): http://sohowww.nascom.nasa.gov/data/realtime/hmi_igr/1024/latest.jpg 2. From a network of ground Telescopes (GONG): http://gong2.nso.edu/dailyimages/ 3. Images of the Sun (photosphere) through a robotic Solar telescope (TAD, Teide
Observatory, IAC) from the GLORIA project: http://users.gloria-project.eu (Solar
Experiment) ref2 - Images of Great Celestial Shows: http://www.tierrayestrellas.com ref3 - Solar Influences Data Analysis Center - SIDC, Royal Observatory of Belgium: http://sidc.oma.be/index.php3 ref4 - Space Weather Prediction Center - SWPC, USA: http://www.swpc.noaa.gov/ ref5 - Aurora forecast (OVATION model): http://helios.swpc.noaa.gov/ovation/index.html Northern Lights 15