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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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).

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 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.

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).

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

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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 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).

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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Figure 8 : Visible spectrum of molecular nitrogen from the auroras, with emission lines.

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).

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

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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

same aurora A, it is projected on a different background sky, creating an angle α that can be measured (parallax) (Figure 10).

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

sin γ= d

sinα '[1]

Solving we have h1 [1]:

h1=d ∙sin γ

sin α '[2]

Now we can solve the triangle O1AP and find the height h:

sin β1=hh1

[3]

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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.

Where you get the height h of the polar aurora (replacing h1 en [2] and knowing that sin(γ )=sin ¿) = sin(β2):

h=d ∙sin β1 ∙ sin β2

sinα '[4]

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 Solar activity and Earth's space environment, including auroras.

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.php3United States: http://www.swpc.noaa.gov/

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