# Thermosphere

Figure 1. Structure of the Earth's atmosphere
Figure 2. Average temperature and molar mass of air as a function of altitude. The decrease in molar mass with increasing altitude reflects the changing composition of the air.

The thermosphere (from the Greek θερμός thermós “warm, hot” and σφαίρα sphaira “sphere”) is the altitude area of ​​the earth's atmosphere in which its temperature rises again (above the ozone layer) with altitude. The clearly pronounced temperature minimum at the lower limit of the thermosphere is called the mesopause and lies at an altitude of 80–100 km. The area of ​​the steepest rise in temperature is around 120 km. The strongly fluctuating (neutral particle) temperature of the exosphere is reached at an altitude of around 500–600 km .

The thermosphere largely overlaps with the ionosphere . It is true that the degree of ionization is only almost 1 in the exosphere, but the maximum of the electron density lies roughly in the middle of the thermosphere. This is about radiation absorption and energy balance. For the electrical properties see the article ionosphere, for the consequences of particle radiation see polar light .

Even at the mesopause, the pressure and density are about five orders of magnitude smaller than on the ground. This is where meteors begin their trail and spacecraft their re-entry from space . Within the thermosphere, the density drops by a further seven orders of magnitude . In the upper thermosphere there are already low satellite orbits .

## Pressure and density

Figure 3. Pressure and density of the earth's atmosphere. The horizontal scales are logarithmic (tick marks at powers of ten of the pressure or density).

As in the lower part of the atmosphere, the air pressure decreases with increasing altitude. However, due to the influence of the temperature increasing with altitude and the changing composition, the decrease occurs more slowly. In the upper part of the thermosphere, the pressure roughly follows an exponential function that results from the barometric altitude formula.

Although the atmosphere is extremely thin here, the air resistance is noticeable over a longer period of time. The International Space Station (ISS), which orbits the earth at an altitude of about 350 km, would lose so much altitude within a few years without regular increase in its orbit by rocket engines that it fell to earth.

The density of the atmospheric gas decreases almost exponentially with altitude (Fig. 3).

The total mass  M of the atmosphere within a vertical column of one square meter cross-sectional area A above the earth's surface is:

${\ displaystyle {\ frac {M} {A}} = \ rho _ {\ mathrm {A}} \ cdot H \ approx 10 ^ {4} \, \ mathrm {\ frac {kg} {m ^ {2} }}}$

With

• the atmospheric density ρ A = 1.29 kg / m 3 on the ground at a height of z = 0 m
• the mean scale height H ≃ 8 km of the lower atmosphere.

80% of this mass is already within the troposphere, while the thermosphere makes up only about 0.002% of the total mass. Therefore no measurable influence of the thermosphere on the lower atmospheric layers is expected.

## Chemical composition

Gas molecules are dissociated and ionized by the solar X-ray , ultraviolet and corpuscular radiation , which is why gases in the thermosphere predominantly occur as plasma consisting of ions , electrons and neutral particles. The radiation intensity increases with altitude and the rate of recombination decreases , which is why the degree of ionization increases and the mean particle mass ( indicated as molar mass in Fig. 2 ) decreases. Another reason for the decrease in molar mass is that light particles have a higher speed at the same temperature and are therefore less influenced by gravity . In this way, light atoms and ions accumulate in the upper part of the thermosphere.

## Constituents of the neutral gas

Turbulence is responsible for the fact that the neutral gas in the area below the turbo pause at an altitude of about 110 km is a gas mixture with constant molar mass (Fig. 2).

Above the turbo pause, the gas begins to separate . As a result of dynamic processes, the different constituents constantly try to reach their equilibrium state through diffusion . Their barometric height formulas have scale heights that are inversely proportional to their molar masses. Therefore, above about 200 km altitude, the lighter constituents such as atomic oxygen  (O), helium  (He) and hydrogen  (H) gradually dominate . There, the mean scale height is almost 10 times greater than in the lower atmospheric layers (Fig. 2). The composition of the air varies with the geographical location, the time of day and the season, but also with solar activity and geomagnetic fluctuations .

## history

In the time before space exploration , the only information about the altitude range above 70 km was indirect; they came from ionospheric research and the earth's magnetic field :

With the launch of the Russian Sputnik satellite , it was possible for the first time to systematically determine the deceleration of the orbit time from the Doppler effect measurements of the satellite signal and to derive the air density in the high atmosphere as well as its temporal and spatial variations. Mainly involved in these first measurements were Luigi Giuseppe Jacchia and Jack W. Slowey (USA), Desmond King-Hele (England) and Wolfgang Priester as well as Hans-Karl Paetzold (Germany). Today, a large number of satellites directly measure the most diverse components of the atmospheric gas in this altitude range.

## Energy budget

The thermospheric temperature can be determined from observations of the gas density, but also directly with the help of satellite measurements. The temperature profile obeys the law pretty well ( Bates profile ): ${\ displaystyle T}$

(1) ${\ displaystyle T = T _ {\ infty} - (T _ {\ infty} -T _ {\ mathrm {o}}) \ cdot {\ frac {1} {e ^ {s (z-z _ {\ mathrm {o}) })}}}}$

With

• the globally averaged exospheric temperature above about 400 km altitude${\ displaystyle T _ {\ infty}}$
• the reference temperature = 355 K${\ displaystyle T _ {\ mathrm {o}}}$
• the reference altitude = 120 km${\ displaystyle z _ {\ mathrm {o}}}$
• an empirical parameter that decreases with .${\ displaystyle s}$${\ displaystyle T _ {\ infty}}$

From this equation, the heat supply can be determined above q o ≃ 0.8 to 1.6 m W / m 2 height. This heat is given off to the lower layers of the atmosphere through thermal conduction . ${\ displaystyle z _ {\ mathrm {o}}}$

The exosphere temperature , which is constant above altitude, serves as a measure of solar ultraviolet and X-ray radiation (XUV). Now the solar radio emission at 10.7 cm is a good indicator of solar activity. Therefore, an empirical lets numerical value equation derived which with valid links and for geomagnetic quiet conditions: ${\ displaystyle T _ {\ infty}}$ ${\ displaystyle F}$${\ displaystyle F}$${\ displaystyle T _ {\ infty}}$

(2) ${\ displaystyle T _ {\ infty} \ approx 500 + 3 {,} 4 \ cdot F_ {0}}$

With

• ${\ displaystyle T _ {\ infty}}$in  K
• the Covington Index in , d. H. a value for  , averaged over a month.${\ displaystyle F _ {\ mathrm {o}}}$${\ displaystyle 10 ^ {- 2} \, \ mathrm {\ frac {W} {m ^ {2} \ cdot Hz}}}$${\ displaystyle F}$

Typically, the Covington Index varies between about 70 and 250 over the course of the 11-year sunspot cycle and never falls below 50. This means that even in geomagnetically calm conditions it fluctuates between about 740 and 1350 K. ${\ displaystyle T _ {\ infty}}$

The residual temperature of 500 K in the second equation is derived About half of power supply from the magneto sphere and the other half of atmospheric waves from the troposphere , in the lower Thermosphere dissipated be.

## Energy sources

### Solar XUV radiation

The high temperatures in the thermosphere are caused by solar X-rays and extreme ultraviolet radiation (XUV) with wavelengths less than 170 nm, which are almost completely absorbed here. Part of the neutral gas is ionized and is responsible for the formation of the ionospheric layers. The visible solar radiation from 380 to 780 nm remains almost constant with a range of variation of less than 0.1% ( solar constant ).

In contrast, the solar XUV radiation is extremely variable over time. B. Solar X-rays associated with solar flares increase dramatically in a matter of minutes. Fluctuations with periods of 27 days or 11 years are among the prominent variations in solar XUV radiation, but irregular fluctuations over all periods of time are the rule.

In magnetospheric calm conditions, the XUV radiation provides about half of the energy supply in the thermosphere (approx. 500 K). This happens during the day, with a maximum near the equator .

### Solar wind

A second energy source is the supply of energy from the magnetosphere , which in turn owes its energy to the interaction with the solar wind .

The mechanism of this energy transport is not yet known in detail. One possibility would be a hydromagnetic process: particles of the solar wind penetrate the polar regions of the magnetosphere, where the geomagnetic field lines are essentially directed vertically. This creates an electric field that is directed from morning to evening. Electric discharge currents can flow into the ionospheric dynamo layer along the last closed field lines of the earth's magnetic field with their base points in the polar light zones . There they reach the evening side as electrical Pedersen and Hall currents in two narrow current bands (DP1) and from there back to the magnetosphere ( magnetospheric electrical convection field ). Due to ohmic losses of the Pedersen currents, the thermosphere is heated up, especially in the polar light zones.

If the magnetospheric conditions are disturbed, high-energy, electrically charged particles from the magnetosphere also penetrate the aurora zones, which drastically increase the electrical conductivity there and thus increase the electrical currents. This phenomenon can be observed on the ground as polar lights .

In the case of low magnetospheric activity, this energy input is about a quarter of the total energy budget in equation 2, i.e. about 250 K. During strong magnetospheric activity, this proportion increases considerably and, under extreme conditions, can far exceed the influence of XUV radiation.

### Atmospheric waves

There are two types of large-scale atmospheric waves in the lower atmosphere:

• internal waves with finite vertical wavelengths , which can transport wave energy upwards and whose amplitudes grow exponentially with height
• external waves with infinitely large vertical wavelengths whose wave energy decreases exponentially outside their source area and which cannot transport wave energy.

Many atmospheric tidal waves as well as the atmospheric gravity waves that are excited in the lower atmosphere belong to the internal waves. Since their amplitudes grow exponentially, these waves are destroyed by turbulence at altitudes around 100 km at the latest , and their wave energy is converted into heat. This is the approximately 250 K portion in Equation 2.

The all-day tidal wave (1, −2), which is best adapted to the heat source in the troposphere in terms of its meridional structure , is an external wave and only plays a marginal role in the lower atmosphere. In the thermosphere, however, this wave develops into the dominant tidal wave. It drives the electric Sq-Strom at altitudes between about 100 and 200 km.

Thermal warming, essentially by tidal waves, occurs preferentially on the diurnal hemisphere at low and medium latitudes. Their variability depends on the meteorological conditions and rarely exceeds 50%.

## dynamics

Above about 150 km all atmospheric waves degenerate into external waves and a vertical wave structure is hardly visible any more. Their meridional structure is that of the spherical functions  P n m with

• a meridional wave number  m (m = 0: zonally averaged waves; m = 1: all-day waves; m = 2: half-day waves, etc.)
• the zonal wavenumber n.

As a first approximation, the thermosphere behaves like a damped oscillator system with a low-pass filter effect. H. Small-scale waves (with large wave numbers n and m) are suppressed compared to large-scale waves.

In the case of low magnetospheric activity, the observed temporally and spatially varying exosphere temperature can be described by a sum of spherical functions:

${\ displaystyle T (\ varphi, \ lambda, t) = T _ {\ infty} \ left \ {1+ \ Delta {T_ {2}} ^ {0} {P_ {2}} ^ {0} (\ varphi ) + \ Delta {T_ {1}} ^ {0} {P_ {1}} ^ {0} (\ phi) \ cos [\ omega _ {\ mathrm {a}} (t-t _ {\ mathrm {a }})] + \ Delta {T_ {1}} ^ {1} {P_ {1}} ^ {1} (\ varphi) \ cos (\ tau - \ tau _ {\ mathrm {d}}) + \ dots \ right \}}$
Figure 4.Schematic meridional-height cross-section of the circulation systems
of (a) symmetrical wind component of the zonal mean (P 2 0 ),
of (b) antisymmetrical wind component (P 1 0 ) and
of (d) symmetrical all-day wind component (P 1 1 ) at 3 am and 3 pm local time.
(c) shows the horizontal wind vectors of the all-day wave in the northern hemisphere.

It is

${\ displaystyle T _ {\ infty}}$ is the global mean temperature of the exosphere (of the order of 1000 K).

The second term (with ) is generated by the different solar heating in low and high latitudes. A thermal wind system is created, with winds towards the poles in the upper circulation branch and opposite winds in the lower branch (Fig. 4a). It ensures a heat balance between low and high latitudes. The coefficient ΔT 2 0 ≈ 0.004 is small, as the Joule warming in the aurora zones partially compensates for the solar XUV-related excess heat in low latitudes. ${\ displaystyle {P_ {2}} ^ {0} = {\ tfrac {1} {2}} (3 \ sin ^ {2} \ varphi -1)}$

The third term (with ) is responsible for the transport of the excess heat from the summer hemisphere to the winter hemisphere (Fig. 4b). Its relative amplitude is approximately ΔT 1 0 ≃ 0.13. ${\ displaystyle {P_ {1}} ^ {0} = \ sin \ varphi}$

Finally, the fourth term (with ) the dominant tidal wave (1, −2)) describes the transport of the excess heat from the day side to the night side (Fig. 4d). Its relative amplitude is approximately ΔT 1 1 ≃ 0.15. ${\ displaystyle P_ {1} ^ {1} = \ cos \ phi}$

Further terms (e.g. half-year or half-day waves) must be added to the above equation, but are of less importance (see above low-pass effect).

Corresponding sums can be derived for air pressure , air density, gas constituents, etc.

## Thermosphere and ionospheric storms

The magnetospheric disturbances , which can be observed on the ground as geomagnetic disturbances, vary much more than the solar XUV radiation . They are difficult to predict and fluctuate from minutes to several days. The reaction of the thermosphere to a strong magnetospheric storm is called a thermosphere storm.

Since the energy is supplied at higher latitudes (mainly in the aurora zones), the sign of the second term P 2 0 in equation 3 changes : Heat is now transported from the polar regions to the lower latitudes. In addition to this term, other higher-order terms are involved, but they quickly fade away. The sum of these terms determines the "running time" of the disturbances from high to low latitudes, i.e. the reaction time of the thermosphere.

At the same time, an ionospheric storm can develop. The change in the density ratio of nitrogen molecules (N 2 ) to oxygen atoms (O) is important for the development of such an ionospheric disturbance : an increase in the N 2 density increases the loss processes of the ionospheric plasma and is therefore a decrease in the electron density in the ionospheric plasma F-layer responsible ( negative ionospheric storm).

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