For us, as astronomers, it is really important to understand the phenomenon in the earth's atmosphere for which the radiation of stellar objects can change. Down below, I am going to talk about the basic reasons for which we get a changed view of stellar radiation. Those causes are refraction, scintillation, and extinction. For example, because of the refraction of light, the real position of the stellar object and the measured position of the stellar object is not in the same place. Nonhomogeneity and turbulence in the earth's atmosphere distort the image of the stellar object and at the same time absorption and scattering of light can make the stellar objects look less brightness than its normal brightness.

Refraction

Eartth's atmosphere is nonhomogenous where density decreases with the height and it decreases exponentially. It can be described by the formula-

here  is the density at height h and  is when h=0. H is the scale of height, it is the height when the density decreased e times.

Refraction in the earth's atmosphere

If we look at the picture up we can see that stars original position is at P but we see it in the position P'. This happens because of the effect of refraction. The more nearby the star towards the horizon, the more radiation is refracted. Because as we know when light fall in the boundary of two layers with different density will refract. So, when these rays go through a series of refraction in the layers with different density, due to refraction we will observe the stellar object upper than it usually is. But a star in the zenith is not affected by this effect as it falls with a right angle on the layers.

Here is the formula which describes refraction, universally known as Snell's law.


Here, and are index of refraction and is the incident angle and angle of refraction.

Because of atmospheric refraction some every day's phenomenon happens. For example, dawn and dusk-length of the day are longer although the sun is below the horizon.

Transportation of radiation through a medium doesn't depend only on the properties of that medium as well as on the wavelength of the radiation. We know that the velocity of propagation depends on various parameters. For example, time and wavelength. So, the index of refraction should as well as they are closely related. n = n(x, y, z, t,  ) For example, as the refraction index depends on the wavelength so in the boundary of two medium dispersion happens with white light and that is the strong refraction of light with lower wavelength.

Scintillation

The scintillation of stars is a rapid change in its brightness. It happens because of the chaotic nature of our atmosphere, as it is nonhomogenous and nonstatic. As the light wave passes through these layers of the atmosphere, scintillation happens. For every nonhomogeneity acts like an optical lens. Plane wavefront deforms because of continuous change of index of refraction which can cause fluctuation in temperature and density. For all these reasons, fluctuation in the amplitude can happen which can cause a rapid change in the brightness. For a point source it creates a flashing effect but for the source like planets, this effect doesn't happen.

Extinction

We know that as the electromagnetic wave passes through any medium it can be absorbed or scattered. This effect can bring about weakening or the extinction of the electromagnetic radiation. In the case of absorption, it is interesting as the absorbed EM waves can increase the temperature of the gas molecule of the atmosphere. Atoms can absorb a photon if the energy of the photon is same as the energy in between two discrete energy level of the atom.


Scattering happens when EM waves interact with the particles of the atmosphere and change its direction of propagation and change its wavelength as well. The difference between absorption and scattering is that for scattering the amount of EM radiation is not decreased only decreased in a particular direction. Scattering in molecules and atoms are known as Rayleigh scattering. The intensity of the scattered radiation is inversely proportional to the fourth power of wavelength.

 For example, lower wavelengths of the sun go through more scattering in the earth's atmosphere and that's why the sky looks blue. But for a star near the horizontal goes through a series of dense layers of atmosphere and they look reddish.  Extiction law Without giving a lot of mathematical derivation, the formula for describing the change in intensity of radiation because of extinction and scattering can be described as below--  z is the angle between the star and zenith,  is the intensity in the earth's surface,  is opacity and  is the intensity in the upper boundary of earth's atmosphere. public domain I mentioned above that the absorption of light depends as well on the wavelength. Nearly 80 percent of visible ray can pass through the earth's atmosphere. Earth's atmosphere is completely non-transparent to for some part of wavelength. Most of the shorter wavelength is absorbed, for example, UV, X-ray, gamma ray. For, these reasons telescopes to detect this kind of light lies beneath the earth's atmosphere. These photons are absorbed mostly by ozone, ammonia, nitrogen and oxygen molecules. Infrared light is absorbed in by water steam and carbon dioxide as well. But as it happens in the lower atmospheric level, Em waves of this kind can be observed from balloons and from telescopes on mountains. Radio waves longer than 20 meters is reflected by the ionosphere. So, we can see that through some shorter windows of earth atmosphere, some Em waves can be observable. So, here I tried to give a general idea on the earth's atmosphere and its effect on the radiation from the stellar objects. Sorry for the photos which belong to me. I am trying to save some money to buy a graphic's tablet. So, I hope I will be able to increase the quality of my photos after that. Hope everyone a nice time until my next post.

Reference

1. Carroll and Ostlie, An Introduction to Modern Astrophysics

2. Olga Atanackovic, General Atrophysics

3. Mirjana Vukicevic, Theoretical Astrophysics

4. Erika Bohm Vitense, Introduction to stellar astrophysics

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